fixed dependencies
This commit is contained in:
nuknal
132
vendor/gonum.org/v1/gonum/AUTHORS
generated
vendored
Normal file
132
vendor/gonum.org/v1/gonum/AUTHORS
generated
vendored
Normal file
@@ -0,0 +1,132 @@
|
||||
# This is the official list of Gonum authors for copyright purposes.
|
||||
# This file is distinct from the CONTRIBUTORS files.
|
||||
# See the latter for an explanation.
|
||||
|
||||
# Names should be added to this file as
|
||||
# Name or Organization <email address>
|
||||
# The email address is not required for organizations.
|
||||
|
||||
# Please keep the list sorted.
|
||||
|
||||
Alexander Egurnov <alexander.egurnov@gmail.com>
|
||||
Andrei Blinnikov <goofinator@mail.ru>
|
||||
antichris <chris@u-d13.com>
|
||||
Bailey Lissington <lissington4@gmail.com>
|
||||
Bill Gray <wgray@gogray.com>
|
||||
Bill Noon <noon.bill@gmail.com>
|
||||
Brendan Tracey <tracey.brendan@gmail.com>
|
||||
Brent Pedersen <bpederse@gmail.com>
|
||||
Bulat Khasanov <afti@yandex.ru>
|
||||
Chad Kunde <kunde21@gmail.com>
|
||||
Chan Kwan Yin <sofe2038@gmail.com>
|
||||
Chih-Wei Chang <bert.cwchang@gmail.com>
|
||||
Chong-Yeol Nah <nahchongyeol@gmail.com>
|
||||
Chris Tessum <ctessum@gmail.com>
|
||||
Christophe Meessen <christophe.meessen@gmail.com>
|
||||
Christopher Waldon <christopher.waldon.dev@gmail.com>
|
||||
Clayton Northey <clayton.northey@gmail.com>
|
||||
Dan Kortschak <dan.kortschak@adelaide.edu.au> <dan@kortschak.io>
|
||||
Daniel Fireman <danielfireman@gmail.com>
|
||||
Dario Heinisch <dario.heinisch@gmail.com>
|
||||
David Kleiven <davidkleiven446@gmail.com>
|
||||
David Samborski <bloggingarrow@gmail.com>
|
||||
Davor Kapsa <davor.kapsa@gmail.com>
|
||||
DeepMind Technologies
|
||||
Delaney Gillilan <delaneygillilan@gmail.com>
|
||||
Dezmond Goff <goff.dezmond@gmail.com>
|
||||
Dong-hee Na <donghee.na92@gmail.com>
|
||||
Dustin Spicuzza <dustin@virtualroadside.com>
|
||||
Egon Elbre <egonelbre@gmail.com>
|
||||
Ekaterina Efimova <katerina.efimova@gmail.com>
|
||||
Eng Zer Jun <engzerjun@gmail.com>
|
||||
Ethan Burns <burns.ethan@gmail.com>
|
||||
Ethan Reesor <ethan.reesor@gmail.com>
|
||||
Evert Lammerts <evert.lammerts@gmail.com>
|
||||
Evgeny Savinov <notime.sea@gmail.com>
|
||||
Fabian Wickborn <fabian@wickborn.net>
|
||||
Facundo Gaich <facugaich@gmail.com>
|
||||
Fazlul Shahriar <fshahriar@gmail.com>
|
||||
Francesc Campoy <campoy@golang.org>
|
||||
Google Inc
|
||||
Gustaf Johansson <gustaf@pinon.se>
|
||||
Hossein Zolfi <hossein.zolfi@gmail.com>
|
||||
Iakov Davydov <iakov.davydov@unil.ch>
|
||||
Igor Mikushkin <igor.mikushkin@gmail.com>
|
||||
Iskander Sharipov <quasilyte@gmail.com>
|
||||
Jalem Raj Rohit <jrajrohit33@gmail.com>
|
||||
James Bell <james@stellentus.com>
|
||||
James Bowman <james.edward.bowman@gmail.com>
|
||||
James Holmes <32bitkid@gmail.com>
|
||||
Janne Snabb <snabb@epipe.com>
|
||||
Jeremy Atkinson <jchatkinson@gmail.com>
|
||||
Jes Cok <xigua67damn@gmail.com>
|
||||
Jinesi Yelizati <i63888888@163.com>
|
||||
Jonas Kahler <jonas@derkahler.de>
|
||||
Jonas Schulze <jonas.schulze@ovgu.de>
|
||||
Jonathan Bluett-Duncan <jbluettduncan@gmail.com>
|
||||
Jonathan J Lawlor <jonathan.lawlor@gmail.com>
|
||||
Jonathan Reiter <jonreiter@gmail.com>
|
||||
Jonathan Schroeder <jd.schroeder@gmail.com>
|
||||
Joost van Amersfoort <git@joo.st>
|
||||
Jordan Stoker <jordan_stoker@hotmail.com>
|
||||
Joseph Watson <jtwatson@linux-consulting.us>
|
||||
Josh Wilson <josh.craig.wilson@gmail.com>
|
||||
Julien Roland <juroland@gmail.com>
|
||||
Kai Trukenmüller <ktye78@gmail.com>
|
||||
Kent English <kent.english@gmail.com>
|
||||
Kevin C. Zimmerman <kevinczimmerman@gmail.com>
|
||||
Kirill Motkov <motkov.kirill@gmail.com>
|
||||
Konstantin Shaposhnikov <k.shaposhnikov@gmail.com>
|
||||
Leonid Kneller <recondite.matter@gmail.com>
|
||||
Lyron Winderbaum <lyron.winderbaum@student.adelaide.edu.au> <armadilloa16@gmail.com> <lyron.winderbaum@uwa.edu.au>
|
||||
Marco Leogrande <dark.knight.ita@gmail.com>
|
||||
Mark Canning <argusdusty@gmail.com>
|
||||
Mark Skilbeck <markskilbeck@gmail.com>
|
||||
Martin Diz <github@martindiz.com.ar>
|
||||
Matthew Connelly <matthew.b.connelly@gmail.com>
|
||||
Matthieu Di Mercurio <matthieu.dimercurio@gmail.com>
|
||||
Max Halford <maxhalford25@gmail.com>
|
||||
Maxim Sergeev <gudvinr@gmail.com>
|
||||
Microsoft Corporation
|
||||
MinJae Kwon <k239507@gmail.com>
|
||||
Nathan Edwards <etaoinshrdluwho@gmail.com>
|
||||
Nick Potts <nick@the-potts.com>
|
||||
Nils Wogatzky <odog@netcologne.de>
|
||||
Olivier Wulveryck <olivier.wulveryck@gmail.com>
|
||||
Or Rikon <rikonor@gmail.com>
|
||||
Patricio Whittingslow <graded.sp@gmail.com>
|
||||
Patrick DeVivo <patrick@tickgit.com>
|
||||
Pontus Melke <pontusmelke@gmail.com>
|
||||
Renee French
|
||||
Rishi Desai <desai.rishi1@gmail.com>
|
||||
Robin Eklind <r.eklind.87@gmail.com>
|
||||
Roger Welin <roger.welin@icloud.com>
|
||||
Rondall Jones <rejones7@gmail.com>
|
||||
Sam Zaydel <szaydel@gmail.com>
|
||||
Samuel Kelemen <Samuel@Kelemen.us>
|
||||
Saran Ahluwalia <ahlusar.ahluwalia@gmail.com>
|
||||
Scott Holden <scott@sshconnection.com>
|
||||
Scott Kiesel <kiesel.scott@gmail.com>
|
||||
Sebastien Binet <seb.binet@gmail.com>
|
||||
Shawn Smith <shawnpsmith@gmail.com>
|
||||
Sintela Ltd
|
||||
source{d} <hello@sourced.tech>
|
||||
Spencer Lyon <spencerlyon2@gmail.com>
|
||||
Steve McCoy <mccoyst@gmail.com>
|
||||
Taesu Pyo <pyotaesu@gmail.com>
|
||||
Takeshi Yoneda <cz.rk.t0415y.g@gmail.com>
|
||||
Tamir Hyman <hyman.tamir@gmail.com>
|
||||
The University of Adelaide
|
||||
The University of Minnesota
|
||||
The University of Washington
|
||||
Thomas Berg <tomfuture@gmail.com>
|
||||
Tobin Harding <me@tobin.cc>
|
||||
Valentin Deleplace <deleplace2015@gmail.com>
|
||||
Vincent Thiery <vjmthiery@gmail.com>
|
||||
Vladimír Chalupecký <vladimir.chalupecky@gmail.com>
|
||||
Will Tekulve <tekulve.will@gmail.com>
|
||||
Yasuhiro Matsumoto <mattn.jp@gmail.com>
|
||||
Yevgeniy Vahlis <evahlis@gmail.com>
|
||||
Yucheng Zhu <zyctc000@gmail.com>
|
||||
Yunomi <ynmtywn@gmail.com>
|
||||
Zoe Juozapaitis
|
||||
135
vendor/gonum.org/v1/gonum/CONTRIBUTORS
generated
vendored
Normal file
135
vendor/gonum.org/v1/gonum/CONTRIBUTORS
generated
vendored
Normal file
@@ -0,0 +1,135 @@
|
||||
# This is the official list of people who can contribute
|
||||
# (and typically have contributed) code to the Gonum
|
||||
# project.
|
||||
#
|
||||
# The AUTHORS file lists the copyright holders; this file
|
||||
# lists people. For example, Google employees would be listed here
|
||||
# but not in AUTHORS, because Google would hold the copyright.
|
||||
#
|
||||
# When adding J Random Contributor's name to this file,
|
||||
# either J's name or J's organization's name should be
|
||||
# added to the AUTHORS file.
|
||||
#
|
||||
# Names should be added to this file like so:
|
||||
# Name <email address>
|
||||
#
|
||||
# Please keep the list sorted.
|
||||
|
||||
Alexander Egurnov <alexander.egurnov@gmail.com>
|
||||
Andrei Blinnikov <goofinator@mail.ru>
|
||||
Andrew Brampton <brampton@gmail.com>
|
||||
antichris <chris@u-d13.com>
|
||||
Bailey Lissington <lissington4@gmail.com>
|
||||
Bill Gray <wgray@gogray.com>
|
||||
Bill Noon <noon.bill@gmail.com>
|
||||
Brendan Tracey <tracey.brendan@gmail.com>
|
||||
Brent Pedersen <bpederse@gmail.com>
|
||||
Bulat Khasanov <afti@yandex.ru>
|
||||
Chad Kunde <kunde21@gmail.com>
|
||||
Chan Kwan Yin <sofe2038@gmail.com>
|
||||
Chih-Wei Chang <bert.cwchang@gmail.com>
|
||||
Chong-Yeol Nah <nahchongyeol@gmail.com>
|
||||
Chris Tessum <ctessum@gmail.com>
|
||||
Christophe Meessen <christophe.meessen@gmail.com>
|
||||
Christopher Waldon <christopher.waldon.dev@gmail.com>
|
||||
Clayton Northey <clayton.northey@gmail.com>
|
||||
Dan Kortschak <dan.kortschak@adelaide.edu.au> <dan@kortschak.io>
|
||||
Dan Lorenc <lorenc.d@gmail.com>
|
||||
Daniel Fireman <danielfireman@gmail.com>
|
||||
Dario Heinisch <dario.heinisch@gmail.com>
|
||||
David Kleiven <davidkleiven446@gmail.com>
|
||||
David Samborski <bloggingarrow@gmail.com>
|
||||
Davor Kapsa <davor.kapsa@gmail.com>
|
||||
Delaney Gillilan <delaneygillilan@gmail.com>
|
||||
Dezmond Goff <goff.dezmond@gmail.com>
|
||||
Dong-hee Na <donghee.na92@gmail.com>
|
||||
Dustin Spicuzza <dustin@virtualroadside.com>
|
||||
Egon Elbre <egonelbre@gmail.com>
|
||||
Ekaterina Efimova <katerina.efimova@gmail.com>
|
||||
Eng Zer Jun <engzerjun@gmail.com>
|
||||
Ethan Burns <burns.ethan@gmail.com>
|
||||
Ethan Reesor <ethan.reesor@gmail.com>
|
||||
Evert Lammerts <evert.lammerts@gmail.com>
|
||||
Evgeny Savinov <notime.sea@gmail.com>
|
||||
Fabian Wickborn <fabian@wickborn.net>
|
||||
Facundo Gaich <facugaich@gmail.com>
|
||||
Fazlul Shahriar <fshahriar@gmail.com>
|
||||
Francesc Campoy <campoy@golang.org>
|
||||
Gustaf Johansson <gustaf@pinon.se>
|
||||
Hossein Zolfi <hossein.zolfi@gmail.com>
|
||||
Iakov Davydov <iakov.davydov@unil.ch>
|
||||
Igor Mikushkin <igor.mikushkin@gmail.com>
|
||||
Iskander Sharipov <quasilyte@gmail.com>
|
||||
Jalem Raj Rohit <jrajrohit33@gmail.com>
|
||||
James Bell <james@stellentus.com>
|
||||
James Bowman <james.edward.bowman@gmail.com>
|
||||
James Holmes <32bitkid@gmail.com>
|
||||
Janne Snabb <snabb@epipe.com>
|
||||
Jeremy Atkinson <jchatkinson@gmail.com>
|
||||
Jes Cok <xigua67damn@gmail.com>
|
||||
Jinesi Yelizati <i63888888@163.com>
|
||||
Jon Richards <noj.richards@gmail.com>
|
||||
Jonas Kahler <jonas@derkahler.de>
|
||||
Jonas Schulze <jonas.schulze@ovgu.de>
|
||||
Jonathan Bluett-Duncan <jbluettduncan@gmail.com>
|
||||
Jonathan J Lawlor <jonathan.lawlor@gmail.com>
|
||||
Jonathan Reiter <jonreiter@gmail.com>
|
||||
Jonathan Schroeder <jd.schroeder@gmail.com>
|
||||
Joost van Amersfoort <git@joo.st>
|
||||
Jordan Stoker <jordan_stoker@hotmail.com>
|
||||
Joseph Watson <jtwatson@linux-consulting.us>
|
||||
Josh Wilson <josh.craig.wilson@gmail.com>
|
||||
Julien Roland <juroland@gmail.com>
|
||||
Kai Trukenmüller <ktye78@gmail.com>
|
||||
Kent English <kent.english@gmail.com>
|
||||
Kevin C. Zimmerman <kevinczimmerman@gmail.com>
|
||||
Kirill Motkov <motkov.kirill@gmail.com>
|
||||
Konstantin Shaposhnikov <k.shaposhnikov@gmail.com>
|
||||
Leonid Kneller <recondite.matter@gmail.com>
|
||||
Lyron Winderbaum <lyron.winderbaum@student.adelaide.edu.au> <armadilloa16@gmail.com> <lyron.winderbaum@uwa.edu.au>
|
||||
Marco Leogrande <dark.knight.ita@gmail.com>
|
||||
Mark Canning <argusdusty@gmail.com>
|
||||
Mark Skilbeck <markskilbeck@gmail.com>
|
||||
Martin Diz <github@martindiz.com.ar>
|
||||
Matthew Connelly <matthew.b.connelly@gmail.com>
|
||||
Matthieu Di Mercurio <matthieu.dimercurio@gmail.com>
|
||||
Max Halford <maxhalford25@gmail.com>
|
||||
Maxim Sergeev <gudvinr@gmail.com>
|
||||
MinJae Kwon <k239507@gmail.com>
|
||||
Nathan Edwards <etaoinshrdluwho@gmail.com>
|
||||
Nick Potts <nick@the-potts.com>
|
||||
Nils Wogatzky <odog@netcologne.de>
|
||||
Olivier Wulveryck <olivier.wulveryck@gmail.com>
|
||||
Or Rikon <rikonor@gmail.com>
|
||||
Patricio Whittingslow <graded.sp@gmail.com>
|
||||
Patrick DeVivo <patrick@tickgit.com>
|
||||
Pontus Melke <pontusmelke@gmail.com>
|
||||
Renee French
|
||||
Rishi Desai <desai.rishi1@gmail.com>
|
||||
Robin Eklind <r.eklind.87@gmail.com>
|
||||
Roger Welin <roger.welin@icloud.com>
|
||||
Roman Werpachowski <roman.werpachowski@gmail.com>
|
||||
Rondall Jones <rejones7@gmail.com>
|
||||
Sam Zaydel <szaydel@gmail.com>
|
||||
Samuel Kelemen <Samuel@Kelemen.us>
|
||||
Saran Ahluwalia <ahlusar.ahluwalia@gmail.com>
|
||||
Scott Holden <scott@sshconnection.com>
|
||||
Scott Kiesel <kiesel.scott@gmail.com>
|
||||
Sebastien Binet <seb.binet@gmail.com>
|
||||
Shawn Smith <shawnpsmith@gmail.com>
|
||||
Spencer Lyon <spencerlyon2@gmail.com>
|
||||
Steve McCoy <mccoyst@gmail.com>
|
||||
Taesu Pyo <pyotaesu@gmail.com>
|
||||
Takeshi Yoneda <cz.rk.t0415y.g@gmail.com>
|
||||
Tamir Hyman <hyman.tamir@gmail.com>
|
||||
Thomas Berg <tomfuture@gmail.com>
|
||||
Tobin Harding <me@tobin.cc>
|
||||
Valentin Deleplace <deleplace2015@gmail.com>
|
||||
Vincent Thiery <vjmthiery@gmail.com>
|
||||
Vladimír Chalupecký <vladimir.chalupecky@gmail.com>
|
||||
Will Tekulve <tekulve.will@gmail.com>
|
||||
Yasuhiro Matsumoto <mattn.jp@gmail.com>
|
||||
Yevgeniy Vahlis <evahlis@gmail.com>
|
||||
Yucheng Zhu <zyctc000@gmail.com>
|
||||
Yunomi <ynmtywn@gmail.com>
|
||||
Zoe Juozapaitis
|
||||
23
vendor/gonum.org/v1/gonum/LICENSE
generated
vendored
Normal file
23
vendor/gonum.org/v1/gonum/LICENSE
generated
vendored
Normal file
@@ -0,0 +1,23 @@
|
||||
Copyright ©2013 The Gonum Authors. All rights reserved.
|
||||
|
||||
Redistribution and use in source and binary forms, with or without
|
||||
modification, are permitted provided that the following conditions are met:
|
||||
* Redistributions of source code must retain the above copyright
|
||||
notice, this list of conditions and the following disclaimer.
|
||||
* Redistributions in binary form must reproduce the above copyright
|
||||
notice, this list of conditions and the following disclaimer in the
|
||||
documentation and/or other materials provided with the distribution.
|
||||
* Neither the name of the Gonum project nor the names of its authors and
|
||||
contributors may be used to endorse or promote products derived from this
|
||||
software without specific prior written permission.
|
||||
|
||||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
|
||||
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
|
||||
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
|
||||
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
|
||||
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
|
||||
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
|
||||
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
||||
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
|
||||
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
51
vendor/gonum.org/v1/gonum/blas/README.md
generated
vendored
Normal file
51
vendor/gonum.org/v1/gonum/blas/README.md
generated
vendored
Normal file
@@ -0,0 +1,51 @@
|
||||
# Gonum BLAS
|
||||
|
||||
[](https://pkg.go.dev/gonum.org/v1/gonum/blas)
|
||||
[](https://godocs.io/gonum.org/v1/gonum/blas)
|
||||
|
||||
A collection of packages to provide BLAS functionality for the [Go programming
|
||||
language](http://golang.org)
|
||||
|
||||
## Installation
|
||||
```sh
|
||||
go get gonum.org/v1/gonum/blas/...
|
||||
```
|
||||
|
||||
## Packages
|
||||
|
||||
### blas
|
||||
|
||||
Defines [BLAS API](http://www.netlib.org/blas/blast-forum/cinterface.pdf) split in several
|
||||
interfaces.
|
||||
|
||||
### blas/gonum
|
||||
|
||||
Go implementation of the BLAS API (incomplete, implements the `float32` and `float64` API).
|
||||
|
||||
### blas/blas64 and blas/blas32
|
||||
|
||||
Wrappers for an implementation of the double (i.e., `float64`) and single (`float32`)
|
||||
precision real parts of the BLAS API.
|
||||
|
||||
```Go
|
||||
package main
|
||||
|
||||
import (
|
||||
"fmt"
|
||||
|
||||
"gonum.org/v1/gonum/blas/blas64"
|
||||
)
|
||||
|
||||
func main() {
|
||||
v := blas64.Vector{Inc: 1, Data: []float64{1, 1, 1}}
|
||||
v.N = len(v.Data)
|
||||
fmt.Println("v has length:", blas64.Nrm2(v))
|
||||
}
|
||||
```
|
||||
|
||||
### blas/cblas128 and blas/cblas64
|
||||
|
||||
Wrappers for an implementation of the double (i.e., `complex128`) and single (`complex64`)
|
||||
precision complex parts of the blas API.
|
||||
|
||||
Currently blas/cblas64 and blas/cblas128 require gonum.org/v1/netlib/blas.
|
||||
283
vendor/gonum.org/v1/gonum/blas/blas.go
generated
vendored
Normal file
283
vendor/gonum.org/v1/gonum/blas/blas.go
generated
vendored
Normal file
@@ -0,0 +1,283 @@
|
||||
// Copyright ©2013 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:generate ./conversions.bash
|
||||
|
||||
package blas
|
||||
|
||||
// Flag constants indicate Givens transformation H matrix state.
|
||||
type Flag int
|
||||
|
||||
const (
|
||||
Identity Flag = -2 // H is the identity matrix; no rotation is needed.
|
||||
Rescaling Flag = -1 // H specifies rescaling.
|
||||
OffDiagonal Flag = 0 // Off-diagonal elements of H are non-unit.
|
||||
Diagonal Flag = 1 // Diagonal elements of H are non-unit.
|
||||
)
|
||||
|
||||
// SrotmParams contains Givens transformation parameters returned
|
||||
// by the Float32 Srotm method.
|
||||
type SrotmParams struct {
|
||||
Flag
|
||||
H [4]float32 // Column-major 2 by 2 matrix.
|
||||
}
|
||||
|
||||
// DrotmParams contains Givens transformation parameters returned
|
||||
// by the Float64 Drotm method.
|
||||
type DrotmParams struct {
|
||||
Flag
|
||||
H [4]float64 // Column-major 2 by 2 matrix.
|
||||
}
|
||||
|
||||
// Transpose specifies the transposition operation of a matrix.
|
||||
type Transpose byte
|
||||
|
||||
const (
|
||||
NoTrans Transpose = 'N'
|
||||
Trans Transpose = 'T'
|
||||
ConjTrans Transpose = 'C'
|
||||
)
|
||||
|
||||
// Uplo specifies whether a matrix is upper or lower triangular.
|
||||
type Uplo byte
|
||||
|
||||
const (
|
||||
Upper Uplo = 'U'
|
||||
Lower Uplo = 'L'
|
||||
All Uplo = 'A'
|
||||
)
|
||||
|
||||
// Diag specifies whether a matrix is unit triangular.
|
||||
type Diag byte
|
||||
|
||||
const (
|
||||
NonUnit Diag = 'N'
|
||||
Unit Diag = 'U'
|
||||
)
|
||||
|
||||
// Side specifies from which side a multiplication operation is performed.
|
||||
type Side byte
|
||||
|
||||
const (
|
||||
Left Side = 'L'
|
||||
Right Side = 'R'
|
||||
)
|
||||
|
||||
// Float32 implements the single precision real BLAS routines.
|
||||
type Float32 interface {
|
||||
Float32Level1
|
||||
Float32Level2
|
||||
Float32Level3
|
||||
}
|
||||
|
||||
// Float32Level1 implements the single precision real BLAS Level 1 routines.
|
||||
type Float32Level1 interface {
|
||||
Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32
|
||||
Dsdot(n int, x []float32, incX int, y []float32, incY int) float64
|
||||
Sdot(n int, x []float32, incX int, y []float32, incY int) float32
|
||||
Snrm2(n int, x []float32, incX int) float32
|
||||
Sasum(n int, x []float32, incX int) float32
|
||||
Isamax(n int, x []float32, incX int) int
|
||||
Sswap(n int, x []float32, incX int, y []float32, incY int)
|
||||
Scopy(n int, x []float32, incX int, y []float32, incY int)
|
||||
Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int)
|
||||
Srotg(a, b float32) (c, s, r, z float32)
|
||||
Srotmg(d1, d2, b1, b2 float32) (p SrotmParams, rd1, rd2, rb1 float32)
|
||||
Srot(n int, x []float32, incX int, y []float32, incY int, c, s float32)
|
||||
Srotm(n int, x []float32, incX int, y []float32, incY int, p SrotmParams)
|
||||
Sscal(n int, alpha float32, x []float32, incX int)
|
||||
}
|
||||
|
||||
// Float32Level2 implements the single precision real BLAS Level 2 routines.
|
||||
type Float32Level2 interface {
|
||||
Sgemv(tA Transpose, m, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
|
||||
Sgbmv(tA Transpose, m, n, kL, kU int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
|
||||
Strmv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
|
||||
Stbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
|
||||
Stpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
|
||||
Strsv(ul Uplo, tA Transpose, d Diag, n int, a []float32, lda int, x []float32, incX int)
|
||||
Stbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float32, lda int, x []float32, incX int)
|
||||
Stpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float32, x []float32, incX int)
|
||||
Ssymv(ul Uplo, n int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
|
||||
Ssbmv(ul Uplo, n, k int, alpha float32, a []float32, lda int, x []float32, incX int, beta float32, y []float32, incY int)
|
||||
Sspmv(ul Uplo, n int, alpha float32, ap []float32, x []float32, incX int, beta float32, y []float32, incY int)
|
||||
Sger(m, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
|
||||
Ssyr(ul Uplo, n int, alpha float32, x []float32, incX int, a []float32, lda int)
|
||||
Sspr(ul Uplo, n int, alpha float32, x []float32, incX int, ap []float32)
|
||||
Ssyr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32, lda int)
|
||||
Sspr2(ul Uplo, n int, alpha float32, x []float32, incX int, y []float32, incY int, a []float32)
|
||||
}
|
||||
|
||||
// Float32Level3 implements the single precision real BLAS Level 3 routines.
|
||||
type Float32Level3 interface {
|
||||
Sgemm(tA, tB Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
|
||||
Ssymm(s Side, ul Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
|
||||
Ssyrk(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int)
|
||||
Ssyr2k(ul Uplo, t Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int)
|
||||
Strmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
|
||||
Strsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int)
|
||||
}
|
||||
|
||||
// Float64 implements the single precision real BLAS routines.
|
||||
type Float64 interface {
|
||||
Float64Level1
|
||||
Float64Level2
|
||||
Float64Level3
|
||||
}
|
||||
|
||||
// Float64Level1 implements the double precision real BLAS Level 1 routines.
|
||||
type Float64Level1 interface {
|
||||
Ddot(n int, x []float64, incX int, y []float64, incY int) float64
|
||||
Dnrm2(n int, x []float64, incX int) float64
|
||||
Dasum(n int, x []float64, incX int) float64
|
||||
Idamax(n int, x []float64, incX int) int
|
||||
Dswap(n int, x []float64, incX int, y []float64, incY int)
|
||||
Dcopy(n int, x []float64, incX int, y []float64, incY int)
|
||||
Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int)
|
||||
Drotg(a, b float64) (c, s, r, z float64)
|
||||
Drotmg(d1, d2, b1, b2 float64) (p DrotmParams, rd1, rd2, rb1 float64)
|
||||
Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64)
|
||||
Drotm(n int, x []float64, incX int, y []float64, incY int, p DrotmParams)
|
||||
Dscal(n int, alpha float64, x []float64, incX int)
|
||||
}
|
||||
|
||||
// Float64Level2 implements the double precision real BLAS Level 2 routines.
|
||||
type Float64Level2 interface {
|
||||
Dgemv(tA Transpose, m, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
|
||||
Dgbmv(tA Transpose, m, n, kL, kU int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
|
||||
Dtrmv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
|
||||
Dtbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
|
||||
Dtpmv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
|
||||
Dtrsv(ul Uplo, tA Transpose, d Diag, n int, a []float64, lda int, x []float64, incX int)
|
||||
Dtbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []float64, lda int, x []float64, incX int)
|
||||
Dtpsv(ul Uplo, tA Transpose, d Diag, n int, ap []float64, x []float64, incX int)
|
||||
Dsymv(ul Uplo, n int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
|
||||
Dsbmv(ul Uplo, n, k int, alpha float64, a []float64, lda int, x []float64, incX int, beta float64, y []float64, incY int)
|
||||
Dspmv(ul Uplo, n int, alpha float64, ap []float64, x []float64, incX int, beta float64, y []float64, incY int)
|
||||
Dger(m, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
|
||||
Dsyr(ul Uplo, n int, alpha float64, x []float64, incX int, a []float64, lda int)
|
||||
Dspr(ul Uplo, n int, alpha float64, x []float64, incX int, ap []float64)
|
||||
Dsyr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64, lda int)
|
||||
Dspr2(ul Uplo, n int, alpha float64, x []float64, incX int, y []float64, incY int, a []float64)
|
||||
}
|
||||
|
||||
// Float64Level3 implements the double precision real BLAS Level 3 routines.
|
||||
type Float64Level3 interface {
|
||||
Dgemm(tA, tB Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
|
||||
Dsymm(s Side, ul Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
|
||||
Dsyrk(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int)
|
||||
Dsyr2k(ul Uplo, t Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int)
|
||||
Dtrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
|
||||
Dtrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int)
|
||||
}
|
||||
|
||||
// Complex64 implements the single precision complex BLAS routines.
|
||||
type Complex64 interface {
|
||||
Complex64Level1
|
||||
Complex64Level2
|
||||
Complex64Level3
|
||||
}
|
||||
|
||||
// Complex64Level1 implements the single precision complex BLAS Level 1 routines.
|
||||
type Complex64Level1 interface {
|
||||
Cdotu(n int, x []complex64, incX int, y []complex64, incY int) (dotu complex64)
|
||||
Cdotc(n int, x []complex64, incX int, y []complex64, incY int) (dotc complex64)
|
||||
Scnrm2(n int, x []complex64, incX int) float32
|
||||
Scasum(n int, x []complex64, incX int) float32
|
||||
Icamax(n int, x []complex64, incX int) int
|
||||
Cswap(n int, x []complex64, incX int, y []complex64, incY int)
|
||||
Ccopy(n int, x []complex64, incX int, y []complex64, incY int)
|
||||
Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int)
|
||||
Cscal(n int, alpha complex64, x []complex64, incX int)
|
||||
Csscal(n int, alpha float32, x []complex64, incX int)
|
||||
}
|
||||
|
||||
// Complex64Level2 implements the single precision complex BLAS routines Level 2 routines.
|
||||
type Complex64Level2 interface {
|
||||
Cgemv(tA Transpose, m, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
|
||||
Cgbmv(tA Transpose, m, n, kL, kU int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
|
||||
Ctrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
|
||||
Ctbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
|
||||
Ctpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
|
||||
Ctrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex64, lda int, x []complex64, incX int)
|
||||
Ctbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex64, lda int, x []complex64, incX int)
|
||||
Ctpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex64, x []complex64, incX int)
|
||||
Chemv(ul Uplo, n int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
|
||||
Chbmv(ul Uplo, n, k int, alpha complex64, a []complex64, lda int, x []complex64, incX int, beta complex64, y []complex64, incY int)
|
||||
Chpmv(ul Uplo, n int, alpha complex64, ap []complex64, x []complex64, incX int, beta complex64, y []complex64, incY int)
|
||||
Cgeru(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
|
||||
Cgerc(m, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
|
||||
Cher(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64, lda int)
|
||||
Chpr(ul Uplo, n int, alpha float32, x []complex64, incX int, a []complex64)
|
||||
Cher2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, a []complex64, lda int)
|
||||
Chpr2(ul Uplo, n int, alpha complex64, x []complex64, incX int, y []complex64, incY int, ap []complex64)
|
||||
}
|
||||
|
||||
// Complex64Level3 implements the single precision complex BLAS Level 3 routines.
|
||||
type Complex64Level3 interface {
|
||||
Cgemm(tA, tB Transpose, m, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
|
||||
Csymm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
|
||||
Csyrk(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, beta complex64, c []complex64, ldc int)
|
||||
Csyr2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
|
||||
Ctrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
|
||||
Ctrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int)
|
||||
Chemm(s Side, ul Uplo, m, n int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta complex64, c []complex64, ldc int)
|
||||
Cherk(ul Uplo, t Transpose, n, k int, alpha float32, a []complex64, lda int, beta float32, c []complex64, ldc int)
|
||||
Cher2k(ul Uplo, t Transpose, n, k int, alpha complex64, a []complex64, lda int, b []complex64, ldb int, beta float32, c []complex64, ldc int)
|
||||
}
|
||||
|
||||
// Complex128 implements the double precision complex BLAS routines.
|
||||
type Complex128 interface {
|
||||
Complex128Level1
|
||||
Complex128Level2
|
||||
Complex128Level3
|
||||
}
|
||||
|
||||
// Complex128Level1 implements the double precision complex BLAS Level 1 routines.
|
||||
type Complex128Level1 interface {
|
||||
Zdotu(n int, x []complex128, incX int, y []complex128, incY int) (dotu complex128)
|
||||
Zdotc(n int, x []complex128, incX int, y []complex128, incY int) (dotc complex128)
|
||||
Dznrm2(n int, x []complex128, incX int) float64
|
||||
Dzasum(n int, x []complex128, incX int) float64
|
||||
Izamax(n int, x []complex128, incX int) int
|
||||
Zswap(n int, x []complex128, incX int, y []complex128, incY int)
|
||||
Zcopy(n int, x []complex128, incX int, y []complex128, incY int)
|
||||
Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int)
|
||||
Zscal(n int, alpha complex128, x []complex128, incX int)
|
||||
Zdscal(n int, alpha float64, x []complex128, incX int)
|
||||
}
|
||||
|
||||
// Complex128Level2 implements the double precision complex BLAS Level 2 routines.
|
||||
type Complex128Level2 interface {
|
||||
Zgemv(tA Transpose, m, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
|
||||
Zgbmv(tA Transpose, m, n int, kL int, kU int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
|
||||
Ztrmv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
|
||||
Ztbmv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
|
||||
Ztpmv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
|
||||
Ztrsv(ul Uplo, tA Transpose, d Diag, n int, a []complex128, lda int, x []complex128, incX int)
|
||||
Ztbsv(ul Uplo, tA Transpose, d Diag, n, k int, a []complex128, lda int, x []complex128, incX int)
|
||||
Ztpsv(ul Uplo, tA Transpose, d Diag, n int, ap []complex128, x []complex128, incX int)
|
||||
Zhemv(ul Uplo, n int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
|
||||
Zhbmv(ul Uplo, n, k int, alpha complex128, a []complex128, lda int, x []complex128, incX int, beta complex128, y []complex128, incY int)
|
||||
Zhpmv(ul Uplo, n int, alpha complex128, ap []complex128, x []complex128, incX int, beta complex128, y []complex128, incY int)
|
||||
Zgeru(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
|
||||
Zgerc(m, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
|
||||
Zher(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128, lda int)
|
||||
Zhpr(ul Uplo, n int, alpha float64, x []complex128, incX int, a []complex128)
|
||||
Zher2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, a []complex128, lda int)
|
||||
Zhpr2(ul Uplo, n int, alpha complex128, x []complex128, incX int, y []complex128, incY int, ap []complex128)
|
||||
}
|
||||
|
||||
// Complex128Level3 implements the double precision complex BLAS Level 3 routines.
|
||||
type Complex128Level3 interface {
|
||||
Zgemm(tA, tB Transpose, m, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
|
||||
Zsymm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
|
||||
Zsyrk(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, beta complex128, c []complex128, ldc int)
|
||||
Zsyr2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
|
||||
Ztrmm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
|
||||
Ztrsm(s Side, ul Uplo, tA Transpose, d Diag, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int)
|
||||
Zhemm(s Side, ul Uplo, m, n int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta complex128, c []complex128, ldc int)
|
||||
Zherk(ul Uplo, t Transpose, n, k int, alpha float64, a []complex128, lda int, beta float64, c []complex128, ldc int)
|
||||
Zher2k(ul Uplo, t Transpose, n, k int, alpha complex128, a []complex128, lda int, b []complex128, ldb int, beta float64, c []complex128, ldc int)
|
||||
}
|
||||
533
vendor/gonum.org/v1/gonum/blas/blas64/blas64.go
generated
vendored
Normal file
533
vendor/gonum.org/v1/gonum/blas/blas64/blas64.go
generated
vendored
Normal file
@@ -0,0 +1,533 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package blas64
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/blas/gonum"
|
||||
)
|
||||
|
||||
var blas64 blas.Float64 = gonum.Implementation{}
|
||||
|
||||
// Use sets the BLAS float64 implementation to be used by subsequent BLAS calls.
|
||||
// The default implementation is
|
||||
// gonum.org/v1/gonum/blas/gonum.Implementation.
|
||||
func Use(b blas.Float64) {
|
||||
blas64 = b
|
||||
}
|
||||
|
||||
// Implementation returns the current BLAS float64 implementation.
|
||||
//
|
||||
// Implementation allows direct calls to the current BLAS float64 implementation
|
||||
// giving finer control of parameters.
|
||||
func Implementation() blas.Float64 {
|
||||
return blas64
|
||||
}
|
||||
|
||||
// Vector represents a vector with an associated element increment.
|
||||
type Vector struct {
|
||||
N int
|
||||
Data []float64
|
||||
Inc int
|
||||
}
|
||||
|
||||
// General represents a matrix using the conventional storage scheme.
|
||||
type General struct {
|
||||
Rows, Cols int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// Band represents a band matrix using the band storage scheme.
|
||||
type Band struct {
|
||||
Rows, Cols int
|
||||
KL, KU int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// Triangular represents a triangular matrix using the conventional storage scheme.
|
||||
type Triangular struct {
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
N int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// TriangularBand represents a triangular matrix using the band storage scheme.
|
||||
type TriangularBand struct {
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
N, K int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// TriangularPacked represents a triangular matrix using the packed storage scheme.
|
||||
type TriangularPacked struct {
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
N int
|
||||
Data []float64
|
||||
}
|
||||
|
||||
// Symmetric represents a symmetric matrix using the conventional storage scheme.
|
||||
type Symmetric struct {
|
||||
Uplo blas.Uplo
|
||||
N int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// SymmetricBand represents a symmetric matrix using the band storage scheme.
|
||||
type SymmetricBand struct {
|
||||
Uplo blas.Uplo
|
||||
N, K int
|
||||
Data []float64
|
||||
Stride int
|
||||
}
|
||||
|
||||
// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
|
||||
type SymmetricPacked struct {
|
||||
Uplo blas.Uplo
|
||||
N int
|
||||
Data []float64
|
||||
}
|
||||
|
||||
// Level 1
|
||||
|
||||
const (
|
||||
negInc = "blas64: negative vector increment"
|
||||
badLength = "blas64: vector length mismatch"
|
||||
)
|
||||
|
||||
// Dot computes the dot product of the two vectors:
|
||||
//
|
||||
// \sum_i x[i]*y[i].
|
||||
//
|
||||
// Dot will panic if the lengths of x and y do not match.
|
||||
func Dot(x, y Vector) float64 {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
return blas64.Ddot(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Nrm2 computes the Euclidean norm of the vector x:
|
||||
//
|
||||
// sqrt(\sum_i x[i]*x[i]).
|
||||
//
|
||||
// Nrm2 will panic if the vector increment is negative.
|
||||
func Nrm2(x Vector) float64 {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return blas64.Dnrm2(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Asum computes the sum of the absolute values of the elements of x:
|
||||
//
|
||||
// \sum_i |x[i]|.
|
||||
//
|
||||
// Asum will panic if the vector increment is negative.
|
||||
func Asum(x Vector) float64 {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return blas64.Dasum(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Iamax returns the index of an element of x with the largest absolute value.
|
||||
// If there are multiple such indices the earliest is returned.
|
||||
// Iamax returns -1 if n == 0.
|
||||
//
|
||||
// Iamax will panic if the vector increment is negative.
|
||||
func Iamax(x Vector) int {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return blas64.Idamax(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Swap exchanges the elements of the two vectors:
|
||||
//
|
||||
// x[i], y[i] = y[i], x[i] for all i.
|
||||
//
|
||||
// Swap will panic if the lengths of x and y do not match.
|
||||
func Swap(x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
blas64.Dswap(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Copy copies the elements of x into the elements of y:
|
||||
//
|
||||
// y[i] = x[i] for all i.
|
||||
//
|
||||
// Copy will panic if the lengths of x and y do not match.
|
||||
func Copy(x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
blas64.Dcopy(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Axpy adds x scaled by alpha to y:
|
||||
//
|
||||
// y[i] += alpha*x[i] for all i.
|
||||
//
|
||||
// Axpy will panic if the lengths of x and y do not match.
|
||||
func Axpy(alpha float64, x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
blas64.Daxpy(x.N, alpha, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Rotg computes the parameters of a Givens plane rotation so that
|
||||
//
|
||||
// ⎡ c s⎤ ⎡a⎤ ⎡r⎤
|
||||
// ⎣-s c⎦ * ⎣b⎦ = ⎣0⎦
|
||||
//
|
||||
// where a and b are the Cartesian coordinates of a given point.
|
||||
// c, s, and r are defined as
|
||||
//
|
||||
// r = ±Sqrt(a^2 + b^2),
|
||||
// c = a/r, the cosine of the rotation angle,
|
||||
// s = a/r, the sine of the rotation angle,
|
||||
//
|
||||
// and z is defined such that
|
||||
//
|
||||
// if |a| > |b|, z = s,
|
||||
// otherwise if c != 0, z = 1/c,
|
||||
// otherwise z = 1.
|
||||
func Rotg(a, b float64) (c, s, r, z float64) {
|
||||
return blas64.Drotg(a, b)
|
||||
}
|
||||
|
||||
// Rotmg computes the modified Givens rotation. See
|
||||
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
|
||||
// for more details.
|
||||
func Rotmg(d1, d2, b1, b2 float64) (p blas.DrotmParams, rd1, rd2, rb1 float64) {
|
||||
return blas64.Drotmg(d1, d2, b1, b2)
|
||||
}
|
||||
|
||||
// Rot applies a plane transformation to n points represented by the vectors x
|
||||
// and y:
|
||||
//
|
||||
// x[i] = c*x[i] + s*y[i],
|
||||
// y[i] = -s*x[i] + c*y[i], for all i.
|
||||
func Rot(x, y Vector, c, s float64) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
blas64.Drot(x.N, x.Data, x.Inc, y.Data, y.Inc, c, s)
|
||||
}
|
||||
|
||||
// Rotm applies the modified Givens rotation to n points represented by the
|
||||
// vectors x and y.
|
||||
func Rotm(x, y Vector, p blas.DrotmParams) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
blas64.Drotm(x.N, x.Data, x.Inc, y.Data, y.Inc, p)
|
||||
}
|
||||
|
||||
// Scal scales the vector x by alpha:
|
||||
//
|
||||
// x[i] *= alpha for all i.
|
||||
//
|
||||
// Scal will panic if the vector increment is negative.
|
||||
func Scal(alpha float64, x Vector) {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
blas64.Dscal(x.N, alpha, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Level 2
|
||||
|
||||
// Gemv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y if t == blas.NoTrans,
|
||||
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
func Gemv(t blas.Transpose, alpha float64, a General, x Vector, beta float64, y Vector) {
|
||||
blas64.Dgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Gbmv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y if t == blas.NoTrans,
|
||||
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an m×n band matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
func Gbmv(t blas.Transpose, alpha float64, a Band, x Vector, beta float64, y Vector) {
|
||||
blas64.Dgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Trmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix, and x is a vector.
|
||||
func Trmv(t blas.Transpose, a Triangular, x Vector) {
|
||||
blas64.Dtrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tbmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular band matrix, and x is a vector.
|
||||
func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
|
||||
blas64.Dtbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tpmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix in packed format, and x is a vector.
|
||||
func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
|
||||
blas64.Dtpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Trsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix, and x and b are vectors.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in-place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Trsv(t blas.Transpose, a Triangular, x Vector) {
|
||||
blas64.Dtrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tbsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular band matrix, and x and b are vectors.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
|
||||
blas64.Dtbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tpsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix in packed format, and x and b are
|
||||
// vectors.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
|
||||
blas64.Dtpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Symv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n symmetric matrix, x and y are vectors, and alpha and
|
||||
// beta are scalars.
|
||||
func Symv(alpha float64, a Symmetric, x Vector, beta float64, y Vector) {
|
||||
blas64.Dsymv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Sbmv performs
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n symmetric band matrix, x and y are vectors, and alpha
|
||||
// and beta are scalars.
|
||||
func Sbmv(alpha float64, a SymmetricBand, x Vector, beta float64, y Vector) {
|
||||
blas64.Dsbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Spmv performs
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
|
||||
// and alpha and beta are scalars.
|
||||
func Spmv(alpha float64, a SymmetricPacked, x Vector, beta float64, y Vector) {
|
||||
blas64.Dspmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Ger performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * yᵀ,
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Ger(alpha float64, x, y Vector, a General) {
|
||||
blas64.Dger(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Syr performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * xᵀ,
|
||||
//
|
||||
// where A is an n×n symmetric matrix, x is a vector, and alpha is a scalar.
|
||||
func Syr(alpha float64, x Vector, a Symmetric) {
|
||||
blas64.Dsyr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Spr performs the rank-1 update
|
||||
//
|
||||
// A += alpha * x * xᵀ,
|
||||
//
|
||||
// where A is an n×n symmetric matrix in packed format, x is a vector, and
|
||||
// alpha is a scalar.
|
||||
func Spr(alpha float64, x Vector, a SymmetricPacked) {
|
||||
blas64.Dspr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
|
||||
}
|
||||
|
||||
// Syr2 performs a rank-2 update
|
||||
//
|
||||
// A += alpha * x * yᵀ + alpha * y * xᵀ,
|
||||
//
|
||||
// where A is a symmetric n×n matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Syr2(alpha float64, x, y Vector, a Symmetric) {
|
||||
blas64.Dsyr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Spr2 performs a rank-2 update
|
||||
//
|
||||
// A += alpha * x * yᵀ + alpha * y * xᵀ,
|
||||
//
|
||||
// where A is an n×n symmetric matrix in packed format, x and y are vectors,
|
||||
// and alpha is a scalar.
|
||||
func Spr2(alpha float64, x, y Vector, a SymmetricPacked) {
|
||||
blas64.Dspr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
|
||||
}
|
||||
|
||||
// Level 3
|
||||
|
||||
// Gemm computes
|
||||
//
|
||||
// C = alpha * A * B + beta * C,
|
||||
//
|
||||
// where A, B, and C are dense matrices, and alpha and beta are scalars.
|
||||
// tA and tB specify whether A or B are transposed.
|
||||
func Gemm(tA, tB blas.Transpose, alpha float64, a, b General, beta float64, c General) {
|
||||
var m, n, k int
|
||||
if tA == blas.NoTrans {
|
||||
m, k = a.Rows, a.Cols
|
||||
} else {
|
||||
m, k = a.Cols, a.Rows
|
||||
}
|
||||
if tB == blas.NoTrans {
|
||||
n = b.Cols
|
||||
} else {
|
||||
n = b.Rows
|
||||
}
|
||||
blas64.Dgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Symm performs
|
||||
//
|
||||
// C = alpha * A * B + beta * C if s == blas.Left,
|
||||
// C = alpha * B * A + beta * C if s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
|
||||
// alpha is a scalar.
|
||||
func Symm(s blas.Side, alpha float64, a Symmetric, b General, beta float64, c General) {
|
||||
var m, n int
|
||||
if s == blas.Left {
|
||||
m, n = a.N, b.Cols
|
||||
} else {
|
||||
m, n = b.Rows, a.N
|
||||
}
|
||||
blas64.Dsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Syrk performs a symmetric rank-k update
|
||||
//
|
||||
// C = alpha * A * Aᵀ + beta * C if t == blas.NoTrans,
|
||||
// C = alpha * Aᵀ * A + beta * C if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans and
|
||||
// a k×n matrix otherwise, and alpha and beta are scalars.
|
||||
func Syrk(t blas.Transpose, alpha float64, a General, beta float64, c Symmetric) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
blas64.Dsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Syr2k performs a symmetric rank-2k update
|
||||
//
|
||||
// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if t == blas.NoTrans,
|
||||
// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if t == blas.Trans or blas.ConjTrans,
|
||||
//
|
||||
// where C is an n×n symmetric matrix, A and B are n×k matrices if t == NoTrans
|
||||
// and k×n matrices otherwise, and alpha and beta are scalars.
|
||||
func Syr2k(t blas.Transpose, alpha float64, a, b General, beta float64, c Symmetric) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
blas64.Dsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Trmm performs
|
||||
//
|
||||
// B = alpha * A * B if tA == blas.NoTrans and s == blas.Left,
|
||||
// B = alpha * Aᵀ * B if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
|
||||
// B = alpha * B * A if tA == blas.NoTrans and s == blas.Right,
|
||||
// B = alpha * B * Aᵀ if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
|
||||
// a scalar.
|
||||
func Trmm(s blas.Side, tA blas.Transpose, alpha float64, a Triangular, b General) {
|
||||
blas64.Dtrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||||
}
|
||||
|
||||
// Trsm solves
|
||||
//
|
||||
// A * X = alpha * B if tA == blas.NoTrans and s == blas.Left,
|
||||
// Aᵀ * X = alpha * B if tA == blas.Trans or blas.ConjTrans, and s == blas.Left,
|
||||
// X * A = alpha * B if tA == blas.NoTrans and s == blas.Right,
|
||||
// X * Aᵀ = alpha * B if tA == blas.Trans or blas.ConjTrans, and s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
|
||||
// alpha is a scalar.
|
||||
//
|
||||
// At entry to the function, X contains the values of B, and the result is
|
||||
// stored in-place into X.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
func Trsm(s blas.Side, tA blas.Transpose, alpha float64, a Triangular, b General) {
|
||||
blas64.Dtrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||||
}
|
||||
277
vendor/gonum.org/v1/gonum/blas/blas64/conv.go
generated
vendored
Normal file
277
vendor/gonum.org/v1/gonum/blas/blas64/conv.go
generated
vendored
Normal file
@@ -0,0 +1,277 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package blas64
|
||||
|
||||
import "gonum.org/v1/gonum/blas"
|
||||
|
||||
// GeneralCols represents a matrix using the conventional column-major storage scheme.
|
||||
type GeneralCols General
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions as a and have adequate backing
|
||||
// data storage.
|
||||
func (t GeneralCols) From(a General) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
|
||||
panic("blas64: short data slice")
|
||||
}
|
||||
for i := 0; i < a.Rows; i++ {
|
||||
for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
|
||||
t.Data[i+j*t.Stride] = v
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions as a and have adequate backing
|
||||
// data storage.
|
||||
func (t General) From(a GeneralCols) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
|
||||
panic("blas64: short data slice")
|
||||
}
|
||||
for j := 0; j < a.Cols; j++ {
|
||||
for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
|
||||
t.Data[i*t.Stride+j] = v
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TriangularCols represents a matrix using the conventional column-major storage scheme.
|
||||
type TriangularCols Triangular
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, uplo and diag as a and have
|
||||
// adequate backing data storage.
|
||||
func (t TriangularCols) From(a Triangular) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("blas64: mismatched BLAS diag")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.All:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, uplo and diag as a and have
|
||||
// adequate backing data storage.
|
||||
func (t Triangular) From(a TriangularCols) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("blas64: mismatched BLAS diag")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.All:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// BandCols represents a matrix using the band column-major storage scheme.
|
||||
type BandCols Band
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and bandwidth as a and have
|
||||
// adequate backing data storage.
|
||||
func (t BandCols) From(a Band) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.KL != a.KL || t.KU != a.KU {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.KL+a.KU+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.KL+t.KU+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
for i := 0; i < a.Rows; i++ {
|
||||
for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
|
||||
t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and bandwidth as a and have
|
||||
// adequate backing data storage.
|
||||
func (t Band) From(a BandCols) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.KL != a.KL || t.KU != a.KU {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.KL+a.KU+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.KL+t.KU+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
for j := 0; j < a.Cols; j++ {
|
||||
for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
|
||||
t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TriangularBandCols represents a triangular matrix using the band column-major storage scheme.
|
||||
type TriangularBandCols TriangularBand
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t TriangularBandCols) From(a TriangularBand) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("blas64: mismatched BLAS diag")
|
||||
}
|
||||
dst := BandCols{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := Band{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t TriangularBand) From(a TriangularBandCols) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("blas64: mismatched BLAS diag")
|
||||
}
|
||||
dst := Band{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := BandCols{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a < b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func max(a, b int) int {
|
||||
if a > b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
153
vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric.go
generated
vendored
Normal file
153
vendor/gonum.org/v1/gonum/blas/blas64/conv_symmetric.go
generated
vendored
Normal file
@@ -0,0 +1,153 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package blas64
|
||||
|
||||
import "gonum.org/v1/gonum/blas"
|
||||
|
||||
// SymmetricCols represents a matrix using the conventional column-major storage scheme.
|
||||
type SymmetricCols Symmetric
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t SymmetricCols) From(a Symmetric) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t Symmetric) From(a SymmetricCols) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.
|
||||
type SymmetricBandCols SymmetricBand
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t SymmetricBandCols) From(a SymmetricBand) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
dst := BandCols{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := Band{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t SymmetricBand) From(a SymmetricBandCols) {
|
||||
if t.N != a.N {
|
||||
panic("blas64: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("blas64: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("blas64: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("blas64: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("blas64: mismatched BLAS uplo")
|
||||
}
|
||||
dst := Band{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := BandCols{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("blas64: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
6
vendor/gonum.org/v1/gonum/blas/blas64/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/blas/blas64/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package blas64 provides a simple interface to the float64 BLAS API.
|
||||
package blas64 // import "gonum.org/v1/gonum/blas/blas64"
|
||||
600
vendor/gonum.org/v1/gonum/blas/cblas128/cblas128.go
generated
vendored
Normal file
600
vendor/gonum.org/v1/gonum/blas/cblas128/cblas128.go
generated
vendored
Normal file
@@ -0,0 +1,600 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package cblas128
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/blas/gonum"
|
||||
)
|
||||
|
||||
var cblas128 blas.Complex128 = gonum.Implementation{}
|
||||
|
||||
// Use sets the BLAS complex128 implementation to be used by subsequent BLAS calls.
|
||||
// The default implementation is
|
||||
// gonum.org/v1/gonum/blas/gonum.Implementation.
|
||||
func Use(b blas.Complex128) {
|
||||
cblas128 = b
|
||||
}
|
||||
|
||||
// Implementation returns the current BLAS complex128 implementation.
|
||||
//
|
||||
// Implementation allows direct calls to the current the BLAS complex128 implementation
|
||||
// giving finer control of parameters.
|
||||
func Implementation() blas.Complex128 {
|
||||
return cblas128
|
||||
}
|
||||
|
||||
// Vector represents a vector with an associated element increment.
|
||||
type Vector struct {
|
||||
N int
|
||||
Inc int
|
||||
Data []complex128
|
||||
}
|
||||
|
||||
// General represents a matrix using the conventional storage scheme.
|
||||
type General struct {
|
||||
Rows, Cols int
|
||||
Stride int
|
||||
Data []complex128
|
||||
}
|
||||
|
||||
// Band represents a band matrix using the band storage scheme.
|
||||
type Band struct {
|
||||
Rows, Cols int
|
||||
KL, KU int
|
||||
Stride int
|
||||
Data []complex128
|
||||
}
|
||||
|
||||
// Triangular represents a triangular matrix using the conventional storage scheme.
|
||||
type Triangular struct {
|
||||
N int
|
||||
Stride int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
}
|
||||
|
||||
// TriangularBand represents a triangular matrix using the band storage scheme.
|
||||
type TriangularBand struct {
|
||||
N, K int
|
||||
Stride int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
}
|
||||
|
||||
// TriangularPacked represents a triangular matrix using the packed storage scheme.
|
||||
type TriangularPacked struct {
|
||||
N int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
Diag blas.Diag
|
||||
}
|
||||
|
||||
// Symmetric represents a symmetric matrix using the conventional storage scheme.
|
||||
type Symmetric struct {
|
||||
N int
|
||||
Stride int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
}
|
||||
|
||||
// SymmetricBand represents a symmetric matrix using the band storage scheme.
|
||||
type SymmetricBand struct {
|
||||
N, K int
|
||||
Stride int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
}
|
||||
|
||||
// SymmetricPacked represents a symmetric matrix using the packed storage scheme.
|
||||
type SymmetricPacked struct {
|
||||
N int
|
||||
Data []complex128
|
||||
Uplo blas.Uplo
|
||||
}
|
||||
|
||||
// Hermitian represents an Hermitian matrix using the conventional storage scheme.
|
||||
type Hermitian Symmetric
|
||||
|
||||
// HermitianBand represents an Hermitian matrix using the band storage scheme.
|
||||
type HermitianBand SymmetricBand
|
||||
|
||||
// HermitianPacked represents an Hermitian matrix using the packed storage scheme.
|
||||
type HermitianPacked SymmetricPacked
|
||||
|
||||
// Level 1
|
||||
|
||||
const (
|
||||
negInc = "cblas128: negative vector increment"
|
||||
badLength = "cblas128: vector length mismatch"
|
||||
)
|
||||
|
||||
// Dotu computes the dot product of the two vectors without
|
||||
// complex conjugation:
|
||||
//
|
||||
// xᵀ * y.
|
||||
//
|
||||
// Dotu will panic if the lengths of x and y do not match.
|
||||
func Dotu(x, y Vector) complex128 {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
return cblas128.Zdotu(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Dotc computes the dot product of the two vectors with
|
||||
// complex conjugation:
|
||||
//
|
||||
// xᴴ * y.
|
||||
//
|
||||
// Dotc will panic if the lengths of x and y do not match.
|
||||
func Dotc(x, y Vector) complex128 {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
return cblas128.Zdotc(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Nrm2 computes the Euclidean norm of the vector x:
|
||||
//
|
||||
// sqrt(\sum_i x[i] * x[i]).
|
||||
//
|
||||
// Nrm2 will panic if the vector increment is negative.
|
||||
func Nrm2(x Vector) float64 {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return cblas128.Dznrm2(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Asum computes the sum of magnitudes of the real and imaginary parts of
|
||||
// elements of the vector x:
|
||||
//
|
||||
// \sum_i (|Re x[i]| + |Im x[i]|).
|
||||
//
|
||||
// Asum will panic if the vector increment is negative.
|
||||
func Asum(x Vector) float64 {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return cblas128.Dzasum(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Iamax returns the index of an element of x with the largest sum of
|
||||
// magnitudes of the real and imaginary parts (|Re x[i]|+|Im x[i]|).
|
||||
// If there are multiple such indices, the earliest is returned.
|
||||
//
|
||||
// Iamax returns -1 if n == 0.
|
||||
//
|
||||
// Iamax will panic if the vector increment is negative.
|
||||
func Iamax(x Vector) int {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
return cblas128.Izamax(x.N, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Swap exchanges the elements of two vectors:
|
||||
//
|
||||
// x[i], y[i] = y[i], x[i] for all i.
|
||||
//
|
||||
// Swap will panic if the lengths of x and y do not match.
|
||||
func Swap(x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
cblas128.Zswap(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Copy copies the elements of x into the elements of y:
|
||||
//
|
||||
// y[i] = x[i] for all i.
|
||||
//
|
||||
// Copy will panic if the lengths of x and y do not match.
|
||||
func Copy(x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
cblas128.Zcopy(x.N, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Axpy computes
|
||||
//
|
||||
// y = alpha * x + y,
|
||||
//
|
||||
// where x and y are vectors, and alpha is a scalar.
|
||||
// Axpy will panic if the lengths of x and y do not match.
|
||||
func Axpy(alpha complex128, x, y Vector) {
|
||||
if x.N != y.N {
|
||||
panic(badLength)
|
||||
}
|
||||
cblas128.Zaxpy(x.N, alpha, x.Data, x.Inc, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Scal computes
|
||||
//
|
||||
// x = alpha * x,
|
||||
//
|
||||
// where x is a vector, and alpha is a scalar.
|
||||
//
|
||||
// Scal will panic if the vector increment is negative.
|
||||
func Scal(alpha complex128, x Vector) {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
cblas128.Zscal(x.N, alpha, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Dscal computes
|
||||
//
|
||||
// x = alpha * x,
|
||||
//
|
||||
// where x is a vector, and alpha is a real scalar.
|
||||
//
|
||||
// Dscal will panic if the vector increment is negative.
|
||||
func Dscal(alpha float64, x Vector) {
|
||||
if x.Inc < 0 {
|
||||
panic(negInc)
|
||||
}
|
||||
cblas128.Zdscal(x.N, alpha, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Level 2
|
||||
|
||||
// Gemv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y if t == blas.NoTrans,
|
||||
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
|
||||
// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are
|
||||
// scalars.
|
||||
func Gemv(t blas.Transpose, alpha complex128, a General, x Vector, beta complex128, y Vector) {
|
||||
cblas128.Zgemv(t, a.Rows, a.Cols, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Gbmv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y if t == blas.NoTrans,
|
||||
// y = alpha * Aᵀ * x + beta * y if t == blas.Trans,
|
||||
// y = alpha * Aᴴ * x + beta * y if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an m×n band matrix, x and y are vectors, and alpha and beta are
|
||||
// scalars.
|
||||
func Gbmv(t blas.Transpose, alpha complex128, a Band, x Vector, beta complex128, y Vector) {
|
||||
cblas128.Zgbmv(t, a.Rows, a.Cols, a.KL, a.KU, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Trmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans,
|
||||
// x = Aᴴ * x if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix, and x is a vector.
|
||||
func Trmv(t blas.Transpose, a Triangular, x Vector) {
|
||||
cblas128.Ztrmv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tbmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans,
|
||||
// x = Aᴴ * x if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular band matrix, and x is a vector.
|
||||
func Tbmv(t blas.Transpose, a TriangularBand, x Vector) {
|
||||
cblas128.Ztbmv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tpmv computes
|
||||
//
|
||||
// x = A * x if t == blas.NoTrans,
|
||||
// x = Aᵀ * x if t == blas.Trans,
|
||||
// x = Aᴴ * x if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix in packed format, and x is a vector.
|
||||
func Tpmv(t blas.Transpose, a TriangularPacked, x Vector) {
|
||||
cblas128.Ztpmv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Trsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans,
|
||||
// Aᴴ * x = b if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix and x is a vector.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in-place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Trsv(t blas.Transpose, a Triangular, x Vector) {
|
||||
cblas128.Ztrsv(a.Uplo, t, a.Diag, a.N, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tbsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans,
|
||||
// Aᴴ * x = b if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular band matrix, and x is a vector.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in-place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Tbsv(t blas.Transpose, a TriangularBand, x Vector) {
|
||||
cblas128.Ztbsv(a.Uplo, t, a.Diag, a.N, a.K, a.Data, a.Stride, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Tpsv solves
|
||||
//
|
||||
// A * x = b if t == blas.NoTrans,
|
||||
// Aᵀ * x = b if t == blas.Trans,
|
||||
// Aᴴ * x = b if t == blas.ConjTrans,
|
||||
//
|
||||
// where A is an n×n triangular matrix in packed format and x is a vector.
|
||||
//
|
||||
// At entry to the function, x contains the values of b, and the result is
|
||||
// stored in-place into x.
|
||||
//
|
||||
// No test for singularity or near-singularity is included in this
|
||||
// routine. Such tests must be performed before calling this routine.
|
||||
func Tpsv(t blas.Transpose, a TriangularPacked, x Vector) {
|
||||
cblas128.Ztpsv(a.Uplo, t, a.Diag, a.N, a.Data, x.Data, x.Inc)
|
||||
}
|
||||
|
||||
// Hemv computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n Hermitian matrix, x and y are vectors, and alpha and
|
||||
// beta are scalars.
|
||||
func Hemv(alpha complex128, a Hermitian, x Vector, beta complex128, y Vector) {
|
||||
cblas128.Zhemv(a.Uplo, a.N, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Hbmv performs
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n Hermitian band matrix, x and y are vectors, and alpha
|
||||
// and beta are scalars.
|
||||
func Hbmv(alpha complex128, a HermitianBand, x Vector, beta complex128, y Vector) {
|
||||
cblas128.Zhbmv(a.Uplo, a.N, a.K, alpha, a.Data, a.Stride, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Hpmv performs
|
||||
//
|
||||
// y = alpha * A * x + beta * y,
|
||||
//
|
||||
// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
|
||||
// and alpha and beta are scalars.
|
||||
func Hpmv(alpha complex128, a HermitianPacked, x Vector, beta complex128, y Vector) {
|
||||
cblas128.Zhpmv(a.Uplo, a.N, alpha, a.Data, x.Data, x.Inc, beta, y.Data, y.Inc)
|
||||
}
|
||||
|
||||
// Geru performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * yᵀ,
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Geru(alpha complex128, x, y Vector, a General) {
|
||||
cblas128.Zgeru(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Gerc performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * yᴴ,
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Gerc(alpha complex128, x, y Vector, a General) {
|
||||
cblas128.Zgerc(a.Rows, a.Cols, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Her performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * yᵀ,
|
||||
//
|
||||
// where A is an m×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Her(alpha float64, x Vector, a Hermitian) {
|
||||
cblas128.Zher(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Hpr performs a rank-1 update
|
||||
//
|
||||
// A += alpha * x * xᴴ,
|
||||
//
|
||||
// where A is an n×n Hermitian matrix in packed format, x is a vector, and
|
||||
// alpha is a scalar.
|
||||
func Hpr(alpha float64, x Vector, a HermitianPacked) {
|
||||
cblas128.Zhpr(a.Uplo, a.N, alpha, x.Data, x.Inc, a.Data)
|
||||
}
|
||||
|
||||
// Her2 performs a rank-2 update
|
||||
//
|
||||
// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
|
||||
//
|
||||
// where A is an n×n Hermitian matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Her2(alpha complex128, x, y Vector, a Hermitian) {
|
||||
cblas128.Zher2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data, a.Stride)
|
||||
}
|
||||
|
||||
// Hpr2 performs a rank-2 update
|
||||
//
|
||||
// A += alpha * x * yᴴ + conj(alpha) * y * xᴴ,
|
||||
//
|
||||
// where A is an n×n Hermitian matrix in packed format, x and y are vectors,
|
||||
// and alpha is a scalar.
|
||||
func Hpr2(alpha complex128, x, y Vector, a HermitianPacked) {
|
||||
cblas128.Zhpr2(a.Uplo, a.N, alpha, x.Data, x.Inc, y.Data, y.Inc, a.Data)
|
||||
}
|
||||
|
||||
// Level 3
|
||||
|
||||
// Gemm computes
|
||||
//
|
||||
// C = alpha * A * B + beta * C,
|
||||
//
|
||||
// where A, B, and C are dense matrices, and alpha and beta are scalars.
|
||||
// tA and tB specify whether A or B are transposed or conjugated.
|
||||
func Gemm(tA, tB blas.Transpose, alpha complex128, a, b General, beta complex128, c General) {
|
||||
var m, n, k int
|
||||
if tA == blas.NoTrans {
|
||||
m, k = a.Rows, a.Cols
|
||||
} else {
|
||||
m, k = a.Cols, a.Rows
|
||||
}
|
||||
if tB == blas.NoTrans {
|
||||
n = b.Cols
|
||||
} else {
|
||||
n = b.Rows
|
||||
}
|
||||
cblas128.Zgemm(tA, tB, m, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Symm performs
|
||||
//
|
||||
// C = alpha * A * B + beta * C if s == blas.Left,
|
||||
// C = alpha * B * A + beta * C if s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and
|
||||
// alpha and beta are scalars.
|
||||
func Symm(s blas.Side, alpha complex128, a Symmetric, b General, beta complex128, c General) {
|
||||
var m, n int
|
||||
if s == blas.Left {
|
||||
m, n = a.N, b.Cols
|
||||
} else {
|
||||
m, n = b.Rows, a.N
|
||||
}
|
||||
cblas128.Zsymm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Syrk performs a symmetric rank-k update
|
||||
//
|
||||
// C = alpha * A * Aᵀ + beta * C if t == blas.NoTrans,
|
||||
// C = alpha * Aᵀ * A + beta * C if t == blas.Trans,
|
||||
//
|
||||
// where C is an n×n symmetric matrix, A is an n×k matrix if t == blas.NoTrans
|
||||
// and a k×n matrix otherwise, and alpha and beta are scalars.
|
||||
func Syrk(t blas.Transpose, alpha complex128, a General, beta complex128, c Symmetric) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
cblas128.Zsyrk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Syr2k performs a symmetric rank-2k update
|
||||
//
|
||||
// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if t == blas.NoTrans,
|
||||
// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if t == blas.Trans,
|
||||
//
|
||||
// where C is an n×n symmetric matrix, A and B are n×k matrices if
|
||||
// t == blas.NoTrans and k×n otherwise, and alpha and beta are scalars.
|
||||
func Syr2k(t blas.Transpose, alpha complex128, a, b General, beta complex128, c Symmetric) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
cblas128.Zsyr2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Trmm performs
|
||||
//
|
||||
// B = alpha * A * B if tA == blas.NoTrans and s == blas.Left,
|
||||
// B = alpha * Aᵀ * B if tA == blas.Trans and s == blas.Left,
|
||||
// B = alpha * Aᴴ * B if tA == blas.ConjTrans and s == blas.Left,
|
||||
// B = alpha * B * A if tA == blas.NoTrans and s == blas.Right,
|
||||
// B = alpha * B * Aᵀ if tA == blas.Trans and s == blas.Right,
|
||||
// B = alpha * B * Aᴴ if tA == blas.ConjTrans and s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is
|
||||
// a scalar.
|
||||
func Trmm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
|
||||
cblas128.Ztrmm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||||
}
|
||||
|
||||
// Trsm solves
|
||||
//
|
||||
// A * X = alpha * B if tA == blas.NoTrans and s == blas.Left,
|
||||
// Aᵀ * X = alpha * B if tA == blas.Trans and s == blas.Left,
|
||||
// Aᴴ * X = alpha * B if tA == blas.ConjTrans and s == blas.Left,
|
||||
// X * A = alpha * B if tA == blas.NoTrans and s == blas.Right,
|
||||
// X * Aᵀ = alpha * B if tA == blas.Trans and s == blas.Right,
|
||||
// X * Aᴴ = alpha * B if tA == blas.ConjTrans and s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and
|
||||
// alpha is a scalar.
|
||||
//
|
||||
// At entry to the function, b contains the values of B, and the result is
|
||||
// stored in-place into b.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
func Trsm(s blas.Side, tA blas.Transpose, alpha complex128, a Triangular, b General) {
|
||||
cblas128.Ztrsm(s, a.Uplo, tA, a.Diag, b.Rows, b.Cols, alpha, a.Data, a.Stride, b.Data, b.Stride)
|
||||
}
|
||||
|
||||
// Hemm performs
|
||||
//
|
||||
// C = alpha * A * B + beta * C if s == blas.Left,
|
||||
// C = alpha * B * A + beta * C if s == blas.Right,
|
||||
//
|
||||
// where A is an n×n or m×m Hermitian matrix, B and C are m×n matrices, and
|
||||
// alpha and beta are scalars.
|
||||
func Hemm(s blas.Side, alpha complex128, a Hermitian, b General, beta complex128, c General) {
|
||||
var m, n int
|
||||
if s == blas.Left {
|
||||
m, n = a.N, b.Cols
|
||||
} else {
|
||||
m, n = b.Rows, a.N
|
||||
}
|
||||
cblas128.Zhemm(s, a.Uplo, m, n, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Herk performs the Hermitian rank-k update
|
||||
//
|
||||
// C = alpha * A * Aᴴ + beta*C if t == blas.NoTrans,
|
||||
// C = alpha * Aᴴ * A + beta*C if t == blas.ConjTrans,
|
||||
//
|
||||
// where C is an n×n Hermitian matrix, A is an n×k matrix if t == blas.NoTrans
|
||||
// and a k×n matrix otherwise, and alpha and beta are scalars.
|
||||
func Herk(t blas.Transpose, alpha float64, a General, beta float64, c Hermitian) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
cblas128.Zherk(c.Uplo, t, n, k, alpha, a.Data, a.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
|
||||
// Her2k performs the Hermitian rank-2k update
|
||||
//
|
||||
// C = alpha * A * Bᴴ + conj(alpha) * B * Aᴴ + beta * C if t == blas.NoTrans,
|
||||
// C = alpha * Aᴴ * B + conj(alpha) * Bᴴ * A + beta * C if t == blas.ConjTrans,
|
||||
//
|
||||
// where C is an n×n Hermitian matrix, A and B are n×k matrices if t == NoTrans
|
||||
// and k×n matrices otherwise, and alpha and beta are scalars.
|
||||
func Her2k(t blas.Transpose, alpha complex128, a, b General, beta float64, c Hermitian) {
|
||||
var n, k int
|
||||
if t == blas.NoTrans {
|
||||
n, k = a.Rows, a.Cols
|
||||
} else {
|
||||
n, k = a.Cols, a.Rows
|
||||
}
|
||||
cblas128.Zher2k(c.Uplo, t, n, k, alpha, a.Data, a.Stride, b.Data, b.Stride, beta, c.Data, c.Stride)
|
||||
}
|
||||
279
vendor/gonum.org/v1/gonum/blas/cblas128/conv.go
generated
vendored
Normal file
279
vendor/gonum.org/v1/gonum/blas/cblas128/conv.go
generated
vendored
Normal file
@@ -0,0 +1,279 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package cblas128
|
||||
|
||||
import "gonum.org/v1/gonum/blas"
|
||||
|
||||
// GeneralCols represents a matrix using the conventional column-major storage scheme.
|
||||
type GeneralCols General
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions as a and have adequate backing
|
||||
// data storage.
|
||||
func (t GeneralCols) From(a General) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if len(t.Data) < (t.Cols-1)*t.Stride+t.Rows {
|
||||
panic("cblas128: short data slice")
|
||||
}
|
||||
for i := 0; i < a.Rows; i++ {
|
||||
for j, v := range a.Data[i*a.Stride : i*a.Stride+a.Cols] {
|
||||
t.Data[i+j*t.Stride] = v
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions as a and have adequate backing
|
||||
// data storage.
|
||||
func (t General) From(a GeneralCols) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if len(t.Data) < (t.Rows-1)*t.Stride+t.Cols {
|
||||
panic("cblas128: short data slice")
|
||||
}
|
||||
for j := 0; j < a.Cols; j++ {
|
||||
for i, v := range a.Data[j*a.Stride : j*a.Stride+a.Rows] {
|
||||
t.Data[i*t.Stride+j] = v
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TriangularCols represents a matrix using the conventional column-major storage scheme.
|
||||
type TriangularCols Triangular
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, uplo and diag as a and have
|
||||
// adequate backing data storage.
|
||||
func (t TriangularCols) From(a Triangular) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("cblas128: mismatched BLAS diag")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.All:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, uplo and diag as a and have
|
||||
// adequate backing data storage.
|
||||
func (t Triangular) From(a TriangularCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("cblas128: mismatched BLAS diag")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.All:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// BandCols represents a matrix using the band column-major storage scheme.
|
||||
type BandCols Band
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and bandwidth as a and have
|
||||
// adequate backing data storage.
|
||||
func (t BandCols) From(a Band) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.KL != a.KL || t.KU != a.KU {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.KL+a.KU+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.KL+t.KU+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
for i := 0; i < a.Rows; i++ {
|
||||
for j := max(0, i-a.KL); j < min(i+a.KU+1, a.Cols); j++ {
|
||||
t.Data[i+t.KU-j+j*t.Stride] = a.Data[j+a.KL-i+i*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and bandwidth as a and have
|
||||
// adequate backing data storage.
|
||||
func (t Band) From(a BandCols) {
|
||||
if t.Rows != a.Rows || t.Cols != a.Cols {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.KL != a.KL || t.KU != a.KU {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.KL+a.KU+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.KL+t.KU+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
for j := 0; j < a.Cols; j++ {
|
||||
for i := max(0, j-a.KU); i < min(j+a.KL+1, a.Rows); i++ {
|
||||
t.Data[j+a.KL-i+i*a.Stride] = a.Data[i+t.KU-j+j*t.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// TriangularBandCols represents a triangular matrix using the band column-major storage scheme.
|
||||
type TriangularBandCols TriangularBand
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t TriangularBandCols) From(a TriangularBand) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("cblas128: mismatched BLAS diag")
|
||||
}
|
||||
dst := BandCols{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := Band{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t TriangularBand) From(a TriangularBandCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
if t.Diag != a.Diag {
|
||||
panic("cblas128: mismatched BLAS diag")
|
||||
}
|
||||
dst := Band{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := BandCols{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a < b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func max(a, b int) int {
|
||||
if a > b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
155
vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian.go
generated
vendored
Normal file
155
vendor/gonum.org/v1/gonum/blas/cblas128/conv_hermitian.go
generated
vendored
Normal file
@@ -0,0 +1,155 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package cblas128
|
||||
|
||||
import "gonum.org/v1/gonum/blas"
|
||||
|
||||
// HermitianCols represents a matrix using the conventional column-major storage scheme.
|
||||
type HermitianCols Hermitian
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t HermitianCols) From(a Hermitian) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t Hermitian) From(a HermitianCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// HermitianBandCols represents an Hermitian matrix using the band column-major storage scheme.
|
||||
type HermitianBandCols HermitianBand
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t HermitianBandCols) From(a HermitianBand) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
dst := BandCols{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := Band{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t HermitianBand) From(a HermitianBandCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
dst := Band{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := BandCols{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
155
vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric.go
generated
vendored
Normal file
155
vendor/gonum.org/v1/gonum/blas/cblas128/conv_symmetric.go
generated
vendored
Normal file
@@ -0,0 +1,155 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package cblas128
|
||||
|
||||
import "gonum.org/v1/gonum/blas"
|
||||
|
||||
// SymmetricCols represents a matrix using the conventional column-major storage scheme.
|
||||
type SymmetricCols Symmetric
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t SymmetricCols) From(a Symmetric) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i+j*t.Stride] = a.Data[i*a.Stride+j]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions and uplo as a and have adequate
|
||||
// backing data storage.
|
||||
func (t Symmetric) From(a SymmetricCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := i; j < a.N; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
case blas.Lower:
|
||||
for i := 0; i < a.N; i++ {
|
||||
for j := 0; j <= i; j++ {
|
||||
t.Data[i*t.Stride+j] = a.Data[i+j*a.Stride]
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// SymmetricBandCols represents a symmetric matrix using the band column-major storage scheme.
|
||||
type SymmetricBandCols SymmetricBand
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t SymmetricBandCols) From(a SymmetricBand) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
dst := BandCols{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := Band{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
|
||||
// From fills the receiver with elements from a. The receiver
|
||||
// must have the same dimensions, bandwidth and uplo as a and
|
||||
// have adequate backing data storage.
|
||||
func (t SymmetricBand) From(a SymmetricBandCols) {
|
||||
if t.N != a.N {
|
||||
panic("cblas128: mismatched dimension")
|
||||
}
|
||||
if t.K != a.K {
|
||||
panic("cblas128: mismatched bandwidth")
|
||||
}
|
||||
if a.Stride < a.K+1 {
|
||||
panic("cblas128: short stride for source")
|
||||
}
|
||||
if t.Stride < t.K+1 {
|
||||
panic("cblas128: short stride for destination")
|
||||
}
|
||||
if t.Uplo != a.Uplo {
|
||||
panic("cblas128: mismatched BLAS uplo")
|
||||
}
|
||||
dst := Band{
|
||||
Rows: t.N, Cols: t.N,
|
||||
Stride: t.Stride,
|
||||
Data: t.Data,
|
||||
}
|
||||
src := BandCols{
|
||||
Rows: a.N, Cols: a.N,
|
||||
Stride: a.Stride,
|
||||
Data: a.Data,
|
||||
}
|
||||
switch a.Uplo {
|
||||
default:
|
||||
panic("cblas128: bad BLAS uplo")
|
||||
case blas.Upper:
|
||||
dst.KU = t.K
|
||||
src.KU = a.K
|
||||
case blas.Lower:
|
||||
dst.KL = t.K
|
||||
src.KL = a.K
|
||||
}
|
||||
dst.From(src)
|
||||
}
|
||||
6
vendor/gonum.org/v1/gonum/blas/cblas128/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/blas/cblas128/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package cblas128 provides a simple interface to the complex128 BLAS API.
|
||||
package cblas128 // import "gonum.org/v1/gonum/blas/cblas128"
|
||||
159
vendor/gonum.org/v1/gonum/blas/conversions.bash
generated
vendored
Normal file
159
vendor/gonum.org/v1/gonum/blas/conversions.bash
generated
vendored
Normal file
@@ -0,0 +1,159 @@
|
||||
#!/usr/bin/env bash
|
||||
|
||||
# Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
# Use of this source code is governed by a BSD-style
|
||||
# license that can be found in the LICENSE file.
|
||||
|
||||
# Generate code for blas32.
|
||||
echo Generating blas32/conv.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv.go
|
||||
cat blas64/conv.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| sed -e 's/blas64/blas32/' \
|
||||
\
|
||||
>> blas32/conv.go
|
||||
|
||||
echo Generating blas32/conv_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_test.go
|
||||
cat blas64/conv_test.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| sed -e 's/blas64/blas32/' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
\
|
||||
>> blas32/conv_test.go
|
||||
|
||||
echo Generating blas32/conv_symmetric.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_symmetric.go
|
||||
cat blas64/conv_symmetric.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| sed -e 's/blas64/blas32/' \
|
||||
\
|
||||
>> blas32/conv_symmetric.go
|
||||
|
||||
echo Generating blas32/conv_symmetric_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > blas32/conv_symmetric_test.go
|
||||
cat blas64/conv_symmetric_test.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| sed -e 's/blas64/blas32/' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
\
|
||||
>> blas32/conv_symmetric_test.go
|
||||
|
||||
|
||||
# Generate code for cblas128.
|
||||
echo Generating cblas128/conv.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv.go
|
||||
cat blas64/conv.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
\
|
||||
>> cblas128/conv.go
|
||||
|
||||
echo Generating cblas128/conv_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_test.go
|
||||
cat blas64/conv_test.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
-e 's_"math"_math "math/cmplx"_' \
|
||||
\
|
||||
>> cblas128/conv_test.go
|
||||
|
||||
echo Generating cblas128/conv_symmetric.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_symmetric.go
|
||||
cat blas64/conv_symmetric.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
\
|
||||
>> cblas128/conv_symmetric.go
|
||||
|
||||
echo Generating cblas128/conv_symmetric_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_symmetric_test.go
|
||||
cat blas64/conv_symmetric_test.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
-e 's_"math"_math "math/cmplx"_' \
|
||||
\
|
||||
>> cblas128/conv_symmetric_test.go
|
||||
|
||||
echo Generating cblas128/conv_hermitian.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_hermitian.go
|
||||
cat blas64/conv_symmetric.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
-e 's/Symmetric/Hermitian/g' \
|
||||
-e 's/a symmetric/an Hermitian/g' \
|
||||
-e 's/symmetric/hermitian/g' \
|
||||
-e 's/Sym/Herm/g' \
|
||||
\
|
||||
>> cblas128/conv_hermitian.go
|
||||
|
||||
echo Generating cblas128/conv_hermitian_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas128/conv_hermitian_test.go
|
||||
cat blas64/conv_symmetric_test.go \
|
||||
| gofmt -r 'float64 -> complex128' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas128/' \
|
||||
-e 's/Symmetric/Hermitian/g' \
|
||||
-e 's/a symmetric/an Hermitian/g' \
|
||||
-e 's/symmetric/hermitian/g' \
|
||||
-e 's/Sym/Herm/g' \
|
||||
-e 's_"math"_math "math/cmplx"_' \
|
||||
\
|
||||
>> cblas128/conv_hermitian_test.go
|
||||
|
||||
|
||||
# Generate code for cblas64.
|
||||
echo Generating cblas64/conv.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv.go
|
||||
cat blas64/conv.go \
|
||||
| gofmt -r 'float64 -> complex64' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas64/' \
|
||||
\
|
||||
>> cblas64/conv.go
|
||||
|
||||
echo Generating cblas64/conv_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_test.go
|
||||
cat blas64/conv_test.go \
|
||||
| gofmt -r 'float64 -> complex64' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas64/' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
\
|
||||
>> cblas64/conv_test.go
|
||||
|
||||
echo Generating cblas64/conv_hermitian.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_hermitian.go
|
||||
cat blas64/conv_symmetric.go \
|
||||
| gofmt -r 'float64 -> complex64' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas64/' \
|
||||
-e 's/Symmetric/Hermitian/g' \
|
||||
-e 's/a symmetric/an Hermitian/g' \
|
||||
-e 's/symmetric/hermitian/g' \
|
||||
-e 's/Sym/Herm/g' \
|
||||
\
|
||||
>> cblas64/conv_hermitian.go
|
||||
|
||||
echo Generating cblas64/conv_hermitian_test.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas”; DO NOT EDIT.\n' > cblas64/conv_hermitian_test.go
|
||||
cat blas64/conv_symmetric_test.go \
|
||||
| gofmt -r 'float64 -> complex64' \
|
||||
\
|
||||
| sed -e 's/blas64/cblas64/' \
|
||||
-e 's/Symmetric/Hermitian/g' \
|
||||
-e 's/a symmetric/an Hermitian/g' \
|
||||
-e 's/symmetric/hermitian/g' \
|
||||
-e 's/Sym/Herm/g' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
\
|
||||
>> cblas64/conv_hermitian_test.go
|
||||
108
vendor/gonum.org/v1/gonum/blas/doc.go
generated
vendored
Normal file
108
vendor/gonum.org/v1/gonum/blas/doc.go
generated
vendored
Normal file
@@ -0,0 +1,108 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
/*
|
||||
Package blas provides interfaces for the BLAS linear algebra standard.
|
||||
|
||||
All methods must perform appropriate parameter checking and panic if
|
||||
provided parameters that do not conform to the requirements specified
|
||||
by the BLAS standard.
|
||||
|
||||
Quick Reference Guide to the BLAS from http://www.netlib.org/lapack/lug/node145.html
|
||||
|
||||
This version is modified to remove the "order" option. All matrix operations are
|
||||
on row-order matrices.
|
||||
|
||||
Level 1 BLAS
|
||||
|
||||
dim scalar vector vector scalars 5-element prefixes
|
||||
struct
|
||||
|
||||
_rotg ( a, b ) S, D
|
||||
_rotmg( d1, d2, a, b ) S, D
|
||||
_rot ( n, x, incX, y, incY, c, s ) S, D
|
||||
_rotm ( n, x, incX, y, incY, param ) S, D
|
||||
_swap ( n, x, incX, y, incY ) S, D, C, Z
|
||||
_scal ( n, alpha, x, incX ) S, D, C, Z, Cs, Zd
|
||||
_copy ( n, x, incX, y, incY ) S, D, C, Z
|
||||
_axpy ( n, alpha, x, incX, y, incY ) S, D, C, Z
|
||||
_dot ( n, x, incX, y, incY ) S, D, Ds
|
||||
_dotu ( n, x, incX, y, incY ) C, Z
|
||||
_dotc ( n, x, incX, y, incY ) C, Z
|
||||
__dot ( n, alpha, x, incX, y, incY ) Sds
|
||||
_nrm2 ( n, x, incX ) S, D, Sc, Dz
|
||||
_asum ( n, x, incX ) S, D, Sc, Dz
|
||||
I_amax( n, x, incX ) s, d, c, z
|
||||
|
||||
Level 2 BLAS
|
||||
|
||||
options dim b-width scalar matrix vector scalar vector prefixes
|
||||
|
||||
_gemv ( trans, m, n, alpha, a, lda, x, incX, beta, y, incY ) S, D, C, Z
|
||||
_gbmv ( trans, m, n, kL, kU, alpha, a, lda, x, incX, beta, y, incY ) S, D, C, Z
|
||||
_hemv ( uplo, n, alpha, a, lda, x, incX, beta, y, incY ) C, Z
|
||||
_hbmv ( uplo, n, k, alpha, a, lda, x, incX, beta, y, incY ) C, Z
|
||||
_hpmv ( uplo, n, alpha, ap, x, incX, beta, y, incY ) C, Z
|
||||
_symv ( uplo, n, alpha, a, lda, x, incX, beta, y, incY ) S, D
|
||||
_sbmv ( uplo, n, k, alpha, a, lda, x, incX, beta, y, incY ) S, D
|
||||
_spmv ( uplo, n, alpha, ap, x, incX, beta, y, incY ) S, D
|
||||
_trmv ( uplo, trans, diag, n, a, lda, x, incX ) S, D, C, Z
|
||||
_tbmv ( uplo, trans, diag, n, k, a, lda, x, incX ) S, D, C, Z
|
||||
_tpmv ( uplo, trans, diag, n, ap, x, incX ) S, D, C, Z
|
||||
_trsv ( uplo, trans, diag, n, a, lda, x, incX ) S, D, C, Z
|
||||
_tbsv ( uplo, trans, diag, n, k, a, lda, x, incX ) S, D, C, Z
|
||||
_tpsv ( uplo, trans, diag, n, ap, x, incX ) S, D, C, Z
|
||||
|
||||
options dim scalar vector vector matrix prefixes
|
||||
|
||||
_ger ( m, n, alpha, x, incX, y, incY, a, lda ) S, D
|
||||
_geru ( m, n, alpha, x, incX, y, incY, a, lda ) C, Z
|
||||
_gerc ( m, n, alpha, x, incX, y, incY, a, lda ) C, Z
|
||||
_her ( uplo, n, alpha, x, incX, a, lda ) C, Z
|
||||
_hpr ( uplo, n, alpha, x, incX, ap ) C, Z
|
||||
_her2 ( uplo, n, alpha, x, incX, y, incY, a, lda ) C, Z
|
||||
_hpr2 ( uplo, n, alpha, x, incX, y, incY, ap ) C, Z
|
||||
_syr ( uplo, n, alpha, x, incX, a, lda ) S, D
|
||||
_spr ( uplo, n, alpha, x, incX, ap ) S, D
|
||||
_syr2 ( uplo, n, alpha, x, incX, y, incY, a, lda ) S, D
|
||||
_spr2 ( uplo, n, alpha, x, incX, y, incY, ap ) S, D
|
||||
|
||||
Level 3 BLAS
|
||||
|
||||
options dim scalar matrix matrix scalar matrix prefixes
|
||||
|
||||
_gemm ( transA, transB, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc ) S, D, C, Z
|
||||
_symm ( side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc ) S, D, C, Z
|
||||
_hemm ( side, uplo, m, n, alpha, a, lda, b, ldb, beta, c, ldc ) C, Z
|
||||
_syrk ( uplo, trans, n, k, alpha, a, lda, beta, c, ldc ) S, D, C, Z
|
||||
_herk ( uplo, trans, n, k, alpha, a, lda, beta, c, ldc ) C, Z
|
||||
_syr2k( uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc ) S, D, C, Z
|
||||
_her2k( uplo, trans, n, k, alpha, a, lda, b, ldb, beta, c, ldc ) C, Z
|
||||
_trmm ( side, uplo, transA, diag, m, n, alpha, a, lda, b, ldb ) S, D, C, Z
|
||||
_trsm ( side, uplo, transA, diag, m, n, alpha, a, lda, b, ldb ) S, D, C, Z
|
||||
|
||||
Meaning of prefixes
|
||||
|
||||
S - float32 C - complex64
|
||||
D - float64 Z - complex128
|
||||
|
||||
Matrix types
|
||||
|
||||
GE - GEneral GB - General Band
|
||||
SY - SYmmetric SB - Symmetric Band SP - Symmetric Packed
|
||||
HE - HErmitian HB - Hermitian Band HP - Hermitian Packed
|
||||
TR - TRiangular TB - Triangular Band TP - Triangular Packed
|
||||
|
||||
Options
|
||||
|
||||
trans = NoTrans, Trans, ConjTrans
|
||||
uplo = Upper, Lower
|
||||
diag = Nonunit, Unit
|
||||
side = Left, Right (A or op(A) on the left, or A or op(A) on the right)
|
||||
|
||||
For real matrices, Trans and ConjTrans have the same meaning.
|
||||
For Hermitian matrices, trans = Trans is not allowed.
|
||||
For complex symmetric matrices, trans = ConjTrans is not allowed.
|
||||
*/
|
||||
package blas // import "gonum.org/v1/gonum/blas"
|
||||
297
vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go
generated
vendored
Normal file
297
vendor/gonum.org/v1/gonum/blas/gonum/dgemm.go
generated
vendored
Normal file
@@ -0,0 +1,297 @@
|
||||
// Copyright ©2014 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"runtime"
|
||||
"sync"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
// Dgemm performs one of the matrix-matrix operations
|
||||
//
|
||||
// C = alpha * A * B + beta * C
|
||||
// C = alpha * Aᵀ * B + beta * C
|
||||
// C = alpha * A * Bᵀ + beta * C
|
||||
// C = alpha * Aᵀ * Bᵀ + beta * C
|
||||
//
|
||||
// where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is
|
||||
// an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or
|
||||
// B are transposed.
|
||||
func (Implementation) Dgemm(tA, tB blas.Transpose, m, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
|
||||
switch tA {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
switch tB {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
aTrans := tA == blas.Trans || tA == blas.ConjTrans
|
||||
if aTrans {
|
||||
if lda < max(1, m) {
|
||||
panic(badLdA)
|
||||
}
|
||||
} else {
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
}
|
||||
bTrans := tB == blas.Trans || tB == blas.ConjTrans
|
||||
if bTrans {
|
||||
if ldb < max(1, k) {
|
||||
panic(badLdB)
|
||||
}
|
||||
} else {
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if aTrans {
|
||||
if len(a) < (k-1)*lda+m {
|
||||
panic(shortA)
|
||||
}
|
||||
} else {
|
||||
if len(a) < (m-1)*lda+k {
|
||||
panic(shortA)
|
||||
}
|
||||
}
|
||||
if bTrans {
|
||||
if len(b) < (n-1)*ldb+k {
|
||||
panic(shortB)
|
||||
}
|
||||
} else {
|
||||
if len(b) < (k-1)*ldb+n {
|
||||
panic(shortB)
|
||||
}
|
||||
}
|
||||
if len(c) < (m-1)*ldc+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if (alpha == 0 || k == 0) && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
// scale c
|
||||
if beta != 1 {
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
} else {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
dgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
}
|
||||
|
||||
func dgemmParallel(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
// dgemmParallel computes a parallel matrix multiplication by partitioning
|
||||
// a and b into sub-blocks, and updating c with the multiplication of the sub-block
|
||||
// In all cases,
|
||||
// A = [ A_11 A_12 ... A_1j
|
||||
// A_21 A_22 ... A_2j
|
||||
// ...
|
||||
// A_i1 A_i2 ... A_ij]
|
||||
//
|
||||
// and same for B. All of the submatrix sizes are blockSize×blockSize except
|
||||
// at the edges.
|
||||
//
|
||||
// In all cases, there is one dimension for each matrix along which
|
||||
// C must be updated sequentially.
|
||||
// Cij = \sum_k Aik Bki, (A * B)
|
||||
// Cij = \sum_k Aki Bkj, (Aᵀ * B)
|
||||
// Cij = \sum_k Aik Bjk, (A * Bᵀ)
|
||||
// Cij = \sum_k Aki Bjk, (Aᵀ * Bᵀ)
|
||||
//
|
||||
// This code computes one {i, j} block sequentially along the k dimension,
|
||||
// and computes all of the {i, j} blocks concurrently. This
|
||||
// partitioning allows Cij to be updated in-place without race-conditions.
|
||||
// Instead of launching a goroutine for each possible concurrent computation,
|
||||
// a number of worker goroutines are created and channels are used to pass
|
||||
// available and completed cases.
|
||||
//
|
||||
// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
|
||||
// multiplies, though this code does not copy matrices to attempt to eliminate
|
||||
// cache misses.
|
||||
|
||||
maxKLen := k
|
||||
parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
|
||||
if parBlocks < minParBlock {
|
||||
// The matrix multiplication is small in the dimensions where it can be
|
||||
// computed concurrently. Just do it in serial.
|
||||
dgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
}
|
||||
|
||||
// workerLimit acts a number of maximum concurrent workers,
|
||||
// with the limit set to the number of procs available.
|
||||
workerLimit := make(chan struct{}, runtime.GOMAXPROCS(0))
|
||||
|
||||
// wg is used to wait for all
|
||||
var wg sync.WaitGroup
|
||||
wg.Add(parBlocks)
|
||||
defer wg.Wait()
|
||||
|
||||
for i := 0; i < m; i += blockSize {
|
||||
for j := 0; j < n; j += blockSize {
|
||||
workerLimit <- struct{}{}
|
||||
go func(i, j int) {
|
||||
defer func() {
|
||||
wg.Done()
|
||||
<-workerLimit
|
||||
}()
|
||||
|
||||
leni := blockSize
|
||||
if i+leni > m {
|
||||
leni = m - i
|
||||
}
|
||||
lenj := blockSize
|
||||
if j+lenj > n {
|
||||
lenj = n - j
|
||||
}
|
||||
|
||||
cSub := sliceView64(c, ldc, i, j, leni, lenj)
|
||||
|
||||
// Compute A_ik B_kj for all k
|
||||
for k := 0; k < maxKLen; k += blockSize {
|
||||
lenk := blockSize
|
||||
if k+lenk > maxKLen {
|
||||
lenk = maxKLen - k
|
||||
}
|
||||
var aSub, bSub []float64
|
||||
if aTrans {
|
||||
aSub = sliceView64(a, lda, k, i, lenk, leni)
|
||||
} else {
|
||||
aSub = sliceView64(a, lda, i, k, leni, lenk)
|
||||
}
|
||||
if bTrans {
|
||||
bSub = sliceView64(b, ldb, j, k, lenj, lenk)
|
||||
} else {
|
||||
bSub = sliceView64(b, ldb, k, j, lenk, lenj)
|
||||
}
|
||||
dgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
|
||||
}
|
||||
}(i, j)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// dgemmSerial is serial matrix multiply
|
||||
func dgemmSerial(aTrans, bTrans bool, m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
switch {
|
||||
case !aTrans && !bTrans:
|
||||
dgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && !bTrans:
|
||||
dgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case !aTrans && bTrans:
|
||||
dgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && bTrans:
|
||||
dgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
default:
|
||||
panic("unreachable")
|
||||
}
|
||||
}
|
||||
|
||||
// dgemmSerial where neither a nor b are transposed
|
||||
func dgemmSerialNotNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for l, v := range a[i*lda : i*lda+k] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
f64.AxpyUnitary(tmp, b[l*ldb:l*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// dgemmSerial where neither a is transposed and b is not
|
||||
func dgemmSerialTransNot(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
btmp := b[l*ldb : l*ldb+n]
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f64.AxpyUnitary(tmp, btmp, ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// dgemmSerial where neither a is not transposed and b is
|
||||
func dgemmSerialNotTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] += alpha * f64.DotUnitary(atmp, b[j*ldb:j*ldb+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// dgemmSerial where both are transposed
|
||||
func dgemmSerialTransTrans(m, n, k int, a []float64, lda int, b []float64, ldb int, c []float64, ldc int, alpha float64) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f64.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func sliceView64(a []float64, lda, i, j, r, c int) []float64 {
|
||||
return a[i*lda+j : (i+r-1)*lda+j+c]
|
||||
}
|
||||
99
vendor/gonum.org/v1/gonum/blas/gonum/doc.go
generated
vendored
Normal file
99
vendor/gonum.org/v1/gonum/blas/gonum/doc.go
generated
vendored
Normal file
@@ -0,0 +1,99 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Ensure changes made to blas/native are reflected in blas/cgo where relevant.
|
||||
|
||||
/*
|
||||
Package gonum is a Go implementation of the BLAS API. This implementation
|
||||
panics when the input arguments are invalid as per the standard, for example
|
||||
if a vector increment is zero. Note that the treatment of NaN values
|
||||
is not specified, and differs among the BLAS implementations.
|
||||
gonum.org/v1/gonum/blas/blas64 provides helpful wrapper functions to the BLAS
|
||||
interface. The rest of this text describes the layout of the data for the input types.
|
||||
|
||||
Note that in the function documentation, x[i] refers to the i^th element
|
||||
of the vector, which will be different from the i^th element of the slice if
|
||||
incX != 1.
|
||||
|
||||
See http://www.netlib.org/lapack/explore-html/d4/de1/_l_i_c_e_n_s_e_source.html
|
||||
for more license information.
|
||||
|
||||
Vector arguments are effectively strided slices. They have two input arguments,
|
||||
a number of elements, n, and an increment, incX. The increment specifies the
|
||||
distance between elements of the vector. The actual Go slice may be longer
|
||||
than necessary.
|
||||
The increment may be positive or negative, except in functions with only
|
||||
a single vector argument where the increment may only be positive. If the increment
|
||||
is negative, s[0] is the last element in the slice. Note that this is not the same
|
||||
as counting backward from the end of the slice, as len(s) may be longer than
|
||||
necessary. So, for example, if n = 5 and incX = 3, the elements of s are
|
||||
|
||||
[0 * * 1 * * 2 * * 3 * * 4 * * * ...]
|
||||
|
||||
where ∗ elements are never accessed. If incX = -3, the same elements are
|
||||
accessed, just in reverse order (4, 3, 2, 1, 0).
|
||||
|
||||
Dense matrices are specified by a number of rows, a number of columns, and a stride.
|
||||
The stride specifies the number of entries in the slice between the first element
|
||||
of successive rows. The stride must be at least as large as the number of columns
|
||||
but may be longer.
|
||||
|
||||
[a00 ... a0n a0* ... a1stride-1 a21 ... amn am* ... amstride-1]
|
||||
|
||||
Thus, dense[i*ld + j] refers to the {i, j}th element of the matrix.
|
||||
|
||||
Symmetric and triangular matrices (non-packed) are stored identically to Dense,
|
||||
except that only elements in one triangle of the matrix are accessed.
|
||||
|
||||
Packed symmetric and packed triangular matrices are laid out with the entries
|
||||
condensed such that all of the unreferenced elements are removed. So, the upper triangular
|
||||
matrix
|
||||
|
||||
[
|
||||
1 2 3
|
||||
0 4 5
|
||||
0 0 6
|
||||
]
|
||||
|
||||
and the lower-triangular matrix
|
||||
|
||||
[
|
||||
1 0 0
|
||||
2 3 0
|
||||
4 5 6
|
||||
]
|
||||
|
||||
will both be compacted as [1 2 3 4 5 6]. The (i, j) element of the original
|
||||
dense matrix can be found at element i*n - (i-1)*i/2 + j for upper triangular,
|
||||
and at element i * (i+1) /2 + j for lower triangular.
|
||||
|
||||
Banded matrices are laid out in a compact format, constructed by removing the
|
||||
zeros in the rows and aligning the diagonals. For example, the matrix
|
||||
|
||||
[
|
||||
1 2 3 0 0 0
|
||||
4 5 6 7 0 0
|
||||
0 8 9 10 11 0
|
||||
0 0 12 13 14 15
|
||||
0 0 0 16 17 18
|
||||
0 0 0 0 19 20
|
||||
]
|
||||
|
||||
implicitly becomes (∗ entries are never accessed)
|
||||
|
||||
[
|
||||
* 1 2 3
|
||||
4 5 6 7
|
||||
8 9 10 11
|
||||
12 13 14 15
|
||||
16 17 18 *
|
||||
19 20 * *
|
||||
]
|
||||
|
||||
which is given to the BLAS routine as [∗ 1 2 3 4 ...].
|
||||
|
||||
See http://www.crest.iu.edu/research/mtl/reference/html/banded.html
|
||||
for more information
|
||||
*/
|
||||
package gonum // import "gonum.org/v1/gonum/blas/gonum"
|
||||
35
vendor/gonum.org/v1/gonum/blas/gonum/errors.go
generated
vendored
Normal file
35
vendor/gonum.org/v1/gonum/blas/gonum/errors.go
generated
vendored
Normal file
@@ -0,0 +1,35 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
// Panic strings used during parameter checks.
|
||||
// This list is duplicated in netlib/blas/netlib. Keep in sync.
|
||||
const (
|
||||
zeroIncX = "blas: zero x index increment"
|
||||
zeroIncY = "blas: zero y index increment"
|
||||
|
||||
mLT0 = "blas: m < 0"
|
||||
nLT0 = "blas: n < 0"
|
||||
kLT0 = "blas: k < 0"
|
||||
kLLT0 = "blas: kL < 0"
|
||||
kULT0 = "blas: kU < 0"
|
||||
|
||||
badUplo = "blas: illegal triangle"
|
||||
badTranspose = "blas: illegal transpose"
|
||||
badDiag = "blas: illegal diagonal"
|
||||
badSide = "blas: illegal side"
|
||||
badFlag = "blas: illegal rotm flag"
|
||||
|
||||
badLdA = "blas: bad leading dimension of A"
|
||||
badLdB = "blas: bad leading dimension of B"
|
||||
badLdC = "blas: bad leading dimension of C"
|
||||
|
||||
shortX = "blas: insufficient length of x"
|
||||
shortY = "blas: insufficient length of y"
|
||||
shortAP = "blas: insufficient length of ap"
|
||||
shortA = "blas: insufficient length of a"
|
||||
shortB = "blas: insufficient length of b"
|
||||
shortC = "blas: insufficient length of c"
|
||||
)
|
||||
52
vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
generated
vendored
Normal file
52
vendor/gonum.org/v1/gonum/blas/gonum/gonum.go
generated
vendored
Normal file
@@ -0,0 +1,52 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:generate ./single_precision.bash
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/internal/math32"
|
||||
)
|
||||
|
||||
type Implementation struct{}
|
||||
|
||||
// [SD]gemm behavior constants. These are kept here to keep them out of the
|
||||
// way during single precision code generation.
|
||||
const (
|
||||
blockSize = 64 // b x b matrix
|
||||
minParBlock = 4 // minimum number of blocks needed to go parallel
|
||||
)
|
||||
|
||||
func max(a, b int) int {
|
||||
if a > b {
|
||||
return a
|
||||
}
|
||||
return b
|
||||
}
|
||||
|
||||
func min(a, b int) int {
|
||||
if a > b {
|
||||
return b
|
||||
}
|
||||
return a
|
||||
}
|
||||
|
||||
// blocks returns the number of divisions of the dimension length with the given
|
||||
// block size.
|
||||
func blocks(dim, bsize int) int {
|
||||
return (dim + bsize - 1) / bsize
|
||||
}
|
||||
|
||||
// dcabs1 returns |real(z)|+|imag(z)|.
|
||||
func dcabs1(z complex128) float64 {
|
||||
return math.Abs(real(z)) + math.Abs(imag(z))
|
||||
}
|
||||
|
||||
// scabs1 returns |real(z)|+|imag(z)|.
|
||||
func scabs1(z complex64) float32 {
|
||||
return math32.Abs(real(z)) + math32.Abs(imag(z))
|
||||
}
|
||||
454
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
generated
vendored
Normal file
454
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx128.go
generated
vendored
Normal file
@@ -0,0 +1,454 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/c128"
|
||||
)
|
||||
|
||||
var _ blas.Complex128Level1 = Implementation{}
|
||||
|
||||
// Dzasum returns the sum of the absolute values of the elements of x
|
||||
//
|
||||
// \sum_i |Re(x[i])| + |Im(x[i])|
|
||||
//
|
||||
// Dzasum returns 0 if incX is negative.
|
||||
func (Implementation) Dzasum(n int, x []complex128, incX int) float64 {
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
var sum float64
|
||||
if incX == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
for _, v := range x[:n] {
|
||||
sum += dcabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
v := x[i*incX]
|
||||
sum += dcabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Dznrm2 computes the Euclidean norm of the complex vector x,
|
||||
//
|
||||
// ‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).
|
||||
//
|
||||
// This function returns 0 if incX is negative.
|
||||
func (Implementation) Dznrm2(n int, x []complex128, incX int) float64 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
var (
|
||||
scale float64
|
||||
ssq float64 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
for _, v := range x[:n] {
|
||||
re, im := math.Abs(real(v)), math.Abs(imag(v))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
re, im := math.Abs(real(x[ix])), math.Abs(imag(x[ix]))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
|
||||
// Izamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|.
|
||||
// Izamax returns -1 if n is 0 or incX is negative.
|
||||
func (Implementation) Izamax(n int, x []complex128, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
idx := 0
|
||||
max := dcabs1(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[1:n] {
|
||||
absV := dcabs1(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i + 1
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
absV := dcabs1(x[ix])
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Zaxpy adds alpha times x to y:
|
||||
//
|
||||
// y[i] += alpha * x[i] for all i
|
||||
func (Implementation) Zaxpy(n int, alpha complex128, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
c128.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (1 - n) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (1 - n) * incY
|
||||
}
|
||||
c128.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zcopy copies the vector x to vector y.
|
||||
func (Implementation) Zcopy(n int, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Zdotc computes the dot product
|
||||
//
|
||||
// xᴴ · y
|
||||
//
|
||||
// of two complex vectors x and y.
|
||||
func (Implementation) Zdotc(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotcUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotcInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zdotu computes the dot product
|
||||
//
|
||||
// xᵀ · y
|
||||
//
|
||||
// of two complex vectors x and y.
|
||||
func (Implementation) Zdotu(n int, x []complex128, incX int, y []complex128, incY int) complex128 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotuUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c128.DotuInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Zdscal scales the vector x by a real scalar alpha.
|
||||
// Zdscal has no effect if incX < 0.
|
||||
func (Implementation) Zdscal(n int, alpha float64, x []complex128, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
v := x[ix]
|
||||
x[ix] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
}
|
||||
|
||||
// Zscal scales the vector x by a complex scalar alpha.
|
||||
// Zscal has no effect if incX < 0.
|
||||
func (Implementation) Zscal(n int, alpha complex128, x []complex128, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
c128.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
c128.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Zswap exchanges the elements of two complex vectors x and y.
|
||||
func (Implementation) Zswap(n int, x []complex128, incX int, y []complex128, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
476
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx64.go
generated
vendored
Normal file
476
vendor/gonum.org/v1/gonum/blas/gonum/level1cmplx64.go
generated
vendored
Normal file
@@ -0,0 +1,476 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
math "gonum.org/v1/gonum/internal/math32"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/c64"
|
||||
)
|
||||
|
||||
var _ blas.Complex64Level1 = Implementation{}
|
||||
|
||||
// Scasum returns the sum of the absolute values of the elements of x
|
||||
//
|
||||
// \sum_i |Re(x[i])| + |Im(x[i])|
|
||||
//
|
||||
// Scasum returns 0 if incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scasum(n int, x []complex64, incX int) float32 {
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
var sum float32
|
||||
if incX == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
for _, v := range x[:n] {
|
||||
sum += scabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
v := x[i*incX]
|
||||
sum += scabs1(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Scnrm2 computes the Euclidean norm of the complex vector x,
|
||||
//
|
||||
// ‖x‖_2 = sqrt(\sum_i x[i] * conj(x[i])).
|
||||
//
|
||||
// This function returns 0 if incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scnrm2(n int, x []complex64, incX int) float32 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
var (
|
||||
scale float32
|
||||
ssq float32 = 1
|
||||
)
|
||||
if incX == 1 {
|
||||
for _, v := range x[:n] {
|
||||
re, im := math.Abs(real(v)), math.Abs(imag(v))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
re, im := math.Abs(real(x[ix])), math.Abs(imag(x[ix]))
|
||||
if re != 0 {
|
||||
if re > scale {
|
||||
ssq = 1 + ssq*(scale/re)*(scale/re)
|
||||
scale = re
|
||||
} else {
|
||||
ssq += (re / scale) * (re / scale)
|
||||
}
|
||||
}
|
||||
if im != 0 {
|
||||
if im > scale {
|
||||
ssq = 1 + ssq*(scale/im)*(scale/im)
|
||||
scale = im
|
||||
} else {
|
||||
ssq += (im / scale) * (im / scale)
|
||||
}
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(ssq)
|
||||
}
|
||||
|
||||
// Icamax returns the index of the first element of x having largest |Re(·)|+|Im(·)|.
|
||||
// Icamax returns -1 if n is 0 or incX is negative.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Icamax(n int, x []complex64, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
// Return invalid index.
|
||||
return -1
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
idx := 0
|
||||
max := scabs1(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[1:n] {
|
||||
absV := scabs1(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i + 1
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
absV := scabs1(x[ix])
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Caxpy adds alpha times x to y:
|
||||
//
|
||||
// y[i] += alpha * x[i] for all i
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Caxpy(n int, alpha complex64, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
c64.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (1 - n) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (1 - n) * incY
|
||||
}
|
||||
c64.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Ccopy copies the vector x to vector y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ccopy(n int, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Cdotc computes the dot product
|
||||
//
|
||||
// xᴴ · y
|
||||
//
|
||||
// of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cdotc(n int, x []complex64, incX int, y []complex64, incY int) complex64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotcUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotcInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Cdotu computes the dot product
|
||||
//
|
||||
// xᵀ · y
|
||||
//
|
||||
// of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cdotu(n int, x []complex64, incX int, y []complex64, incY int) complex64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotuUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || (n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return c64.DotuInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Csscal scales the vector x by a real scalar alpha.
|
||||
// Csscal has no effect if incX < 0.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Csscal(n int, alpha float32, x []complex64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
v := x[ix]
|
||||
x[ix] = complex(alpha*real(v), alpha*imag(v))
|
||||
}
|
||||
}
|
||||
|
||||
// Cscal scales the vector x by a complex scalar alpha.
|
||||
// Cscal has no effect if incX < 0.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cscal(n int, alpha complex64, x []complex64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
c64.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
c64.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Cswap exchanges the elements of two complex vectors x and y.
|
||||
//
|
||||
// Complex64 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Cswap(n int, x []complex64, incX int, y []complex64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && (n-1)*incX >= len(x)) || (incX < 0 && (1-n)*incX >= len(x)) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && (n-1)*incY >= len(y)) || (incY < 0 && (1-n)*incY >= len(y)) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
653
vendor/gonum.org/v1/gonum/blas/gonum/level1float32.go
generated
vendored
Normal file
653
vendor/gonum.org/v1/gonum/blas/gonum/level1float32.go
generated
vendored
Normal file
@@ -0,0 +1,653 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
math "gonum.org/v1/gonum/internal/math32"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
var _ blas.Float32Level1 = Implementation{}
|
||||
|
||||
// Snrm2 computes the Euclidean norm of a vector,
|
||||
//
|
||||
// sqrt(\sum_i x[i] * x[i]).
|
||||
//
|
||||
// This function returns 0 if incX is negative.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Snrm2(n int, x []float32, incX int) float32 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return math.Abs(x[0])
|
||||
}
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 {
|
||||
return f32.L2NormUnitary(x[:n])
|
||||
}
|
||||
return f32.L2NormInc(x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Sasum computes the sum of the absolute values of the elements of x.
|
||||
//
|
||||
// \sum_i |x[i]|
|
||||
//
|
||||
// Sasum returns 0 if incX is negative.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sasum(n int, x []float32, incX int) float32 {
|
||||
var sum float32
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
sum += math.Abs(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
sum += math.Abs(x[i*incX])
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Isamax returns the index of an element of x with the largest absolute value.
|
||||
// If there are multiple such indices the earliest is returned.
|
||||
// Isamax returns -1 if n == 0.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Isamax(n int, x []float32, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return -1
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return 0
|
||||
}
|
||||
if n == 0 {
|
||||
return -1 // Netlib returns invalid index when n == 0.
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
idx := 0
|
||||
max := math.Abs(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[:n] {
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
v := x[ix]
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Sswap exchanges the elements of two vectors.
|
||||
//
|
||||
// x[i], y[i] = y[i], x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sswap(n int, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Scopy copies the elements of x into the elements of y.
|
||||
//
|
||||
// y[i] = x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Scopy(n int, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Saxpy adds alpha times x to y
|
||||
//
|
||||
// y[i] += alpha * x[i] for all i
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Saxpy(n int, alpha float32, x []float32, incX int, y []float32, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
f32.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
f32.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Srotg computes a plane rotation
|
||||
//
|
||||
// ⎡ c s ⎤ ⎡ a ⎤ = ⎡ r ⎤
|
||||
// ⎣ -s c ⎦ ⎣ b ⎦ ⎣ 0 ⎦
|
||||
//
|
||||
// satisfying c^2 + s^2 = 1.
|
||||
//
|
||||
// The computation uses the formulas
|
||||
//
|
||||
// sigma = sgn(a) if |a| > |b|
|
||||
// = sgn(b) if |b| >= |a|
|
||||
// r = sigma*sqrt(a^2 + b^2)
|
||||
// c = 1; s = 0 if r = 0
|
||||
// c = a/r; s = b/r if r != 0
|
||||
// c >= 0 if |a| > |b|
|
||||
//
|
||||
// The subroutine also computes
|
||||
//
|
||||
// z = s if |a| > |b|,
|
||||
// = 1/c if |b| >= |a| and c != 0
|
||||
// = 1 if c = 0
|
||||
//
|
||||
// This allows c and s to be reconstructed from z as follows:
|
||||
//
|
||||
// If z = 1, set c = 0, s = 1.
|
||||
// If |z| < 1, set c = sqrt(1 - z^2) and s = z.
|
||||
// If |z| > 1, set c = 1/z and s = sqrt(1 - c^2).
|
||||
//
|
||||
// NOTE: There is a discrepancy between the reference implementation and the
|
||||
// BLAS technical manual regarding the sign for r when a or b are zero. Drotg
|
||||
// agrees with the definition in the manual and other common BLAS
|
||||
// implementations.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotg(a, b float32) (c, s, r, z float32) {
|
||||
// Implementation based on Supplemental Material to:
|
||||
// Edward Anderson. 2017. Algorithm 978: Safe Scaling in the Level 1 BLAS.
|
||||
// ACM Trans. Math. Softw. 44, 1, Article 12 (July 2017), 28 pages.
|
||||
// DOI: https://doi.org/10.1145/3061665
|
||||
const (
|
||||
safmin = 0x1p-126
|
||||
safmax = 1 / safmin
|
||||
)
|
||||
anorm := math.Abs(a)
|
||||
bnorm := math.Abs(b)
|
||||
switch {
|
||||
case bnorm == 0:
|
||||
c = 1
|
||||
s = 0
|
||||
r = a
|
||||
z = 0
|
||||
case anorm == 0:
|
||||
c = 0
|
||||
s = 1
|
||||
r = b
|
||||
z = 1
|
||||
default:
|
||||
maxab := math.Max(anorm, bnorm)
|
||||
scl := math.Min(math.Max(safmin, maxab), safmax)
|
||||
var sigma float32
|
||||
if anorm > bnorm {
|
||||
sigma = math.Copysign(1, a)
|
||||
} else {
|
||||
sigma = math.Copysign(1, b)
|
||||
}
|
||||
ascl := a / scl
|
||||
bscl := b / scl
|
||||
r = sigma * (scl * math.Sqrt(ascl*ascl+bscl*bscl))
|
||||
c = a / r
|
||||
s = b / r
|
||||
switch {
|
||||
case anorm > bnorm:
|
||||
z = s
|
||||
case c != 0:
|
||||
z = 1 / c
|
||||
default:
|
||||
z = 1
|
||||
}
|
||||
}
|
||||
return c, s, r, z
|
||||
}
|
||||
|
||||
// Srotmg computes the modified Givens rotation. See
|
||||
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
|
||||
// for more details.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotmg(d1, d2, x1, y1 float32) (p blas.SrotmParams, rd1, rd2, rx1 float32) {
|
||||
// The implementation of Drotmg used here is taken from Hopkins 1997
|
||||
// Appendix A: https://doi.org/10.1145/289251.289253
|
||||
// with the exception of the gam constants below.
|
||||
|
||||
const (
|
||||
gam = 4096.0
|
||||
gamsq = gam * gam
|
||||
rgamsq = 1.0 / gamsq
|
||||
)
|
||||
|
||||
if d1 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
if d2 == 0 || y1 == 0 {
|
||||
p.Flag = blas.Identity
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
var h11, h12, h21, h22 float32
|
||||
if (d1 == 0 || x1 == 0) && d2 > 0 {
|
||||
p.Flag = blas.Diagonal
|
||||
h12 = 1
|
||||
h21 = -1
|
||||
x1 = y1
|
||||
d1, d2 = d2, d1
|
||||
} else {
|
||||
p2 := d2 * y1
|
||||
p1 := d1 * x1
|
||||
q2 := p2 * y1
|
||||
q1 := p1 * x1
|
||||
if math.Abs(q1) > math.Abs(q2) {
|
||||
p.Flag = blas.OffDiagonal
|
||||
h11 = 1
|
||||
h22 = 1
|
||||
h21 = -y1 / x1
|
||||
h12 = p2 / p1
|
||||
u := 1 - float32(h12*h21)
|
||||
if u <= 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
d1 /= u
|
||||
d2 /= u
|
||||
x1 *= u
|
||||
} else {
|
||||
if q2 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
p.Flag = blas.Diagonal
|
||||
h21 = -1
|
||||
h12 = 1
|
||||
h11 = p1 / p2
|
||||
h22 = x1 / y1
|
||||
u := 1 + float32(h11*h22)
|
||||
d1, d2 = d2/u, d1/u
|
||||
x1 = y1 * u
|
||||
}
|
||||
}
|
||||
|
||||
for d1 <= rgamsq && d1 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 * gam) * gam
|
||||
x1 /= gam
|
||||
h11 /= gam
|
||||
h12 /= gam
|
||||
}
|
||||
for d1 > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 / gam) / gam
|
||||
x1 *= gam
|
||||
h11 *= gam
|
||||
h12 *= gam
|
||||
}
|
||||
|
||||
for math.Abs(d2) <= rgamsq && d2 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 * gam) * gam
|
||||
h21 /= gam
|
||||
h22 /= gam
|
||||
}
|
||||
for math.Abs(d2) > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 / gam) / gam
|
||||
h21 *= gam
|
||||
h22 *= gam
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Diagonal:
|
||||
p.H = [4]float32{0: h11, 3: h22}
|
||||
case blas.OffDiagonal:
|
||||
p.H = [4]float32{1: h21, 2: h12}
|
||||
case blas.Rescaling:
|
||||
p.H = [4]float32{h11, h21, h12, h22}
|
||||
default:
|
||||
panic(badFlag)
|
||||
}
|
||||
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
// Srot applies a plane transformation.
|
||||
//
|
||||
// x[i] = c * x[i] + s * y[i]
|
||||
// y[i] = c * y[i] - s * x[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srot(n int, x []float32, incX int, y []float32, incY int, c float32, s float32) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = c*vx+s*vy, c*vy-s*vx
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Srotm applies the modified Givens rotation to the 2×n matrix.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Srotm(n int, x []float32, incX int, y []float32, incY int, p blas.SrotmParams) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
|
||||
if p.Flag == blas.Identity {
|
||||
return
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Rescaling:
|
||||
h11 := p.H[0]
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = float32(vx*h11)+float32(vy*h12), float32(vx*h21)+float32(vy*h22)
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = float32(vx*h11)+float32(vy*h12), float32(vx*h21)+float32(vy*h22)
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.OffDiagonal:
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx+float32(vy*h12), float32(vx*h21)+vy
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx+float32(vy*h12), float32(vx*h21)+vy
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.Diagonal:
|
||||
h11 := p.H[0]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = float32(vx*h11)+vy, -vx+float32(vy*h22)
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = float32(vx*h11)+vy, -vx+float32(vy*h22)
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Sscal scales x by alpha.
|
||||
//
|
||||
// x[i] *= alpha
|
||||
//
|
||||
// Sscal has no effect if incX < 0.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sscal(n int, alpha float32, x []float32, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
f32.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
f32.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_dsdot.go
generated
vendored
Normal file
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_dsdot.go
generated
vendored
Normal file
@@ -0,0 +1,54 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Dsdot computes the dot product of the two vectors
|
||||
//
|
||||
// \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Dsdot(n int, x []float32, incX int, y []float32, incY int) float64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DdotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdot.go
generated
vendored
Normal file
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdot.go
generated
vendored
Normal file
@@ -0,0 +1,54 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sdot computes the dot product of the two vectors
|
||||
//
|
||||
// \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sdot(n int, x []float32, incX int, y []float32, incY int) float32 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f32.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdsdot.go
generated
vendored
Normal file
54
vendor/gonum.org/v1/gonum/blas/gonum/level1float32_sdsdot.go
generated
vendored
Normal file
@@ -0,0 +1,54 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sdsdot computes the dot product of the two vectors plus a constant
|
||||
//
|
||||
// alpha + \sum_i x[i]*y[i]
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sdsdot(n int, alpha float32, x []float32, incX int, y []float32, incY int) float32 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return alpha + float32(f32.DdotUnitary(x[:n], y[:n]))
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return alpha + float32(f32.DdotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy)))
|
||||
}
|
||||
629
vendor/gonum.org/v1/gonum/blas/gonum/level1float64.go
generated
vendored
Normal file
629
vendor/gonum.org/v1/gonum/blas/gonum/level1float64.go
generated
vendored
Normal file
@@ -0,0 +1,629 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
var _ blas.Float64Level1 = Implementation{}
|
||||
|
||||
// Dnrm2 computes the Euclidean norm of a vector,
|
||||
//
|
||||
// sqrt(\sum_i x[i] * x[i]).
|
||||
//
|
||||
// This function returns 0 if incX is negative.
|
||||
func (Implementation) Dnrm2(n int, x []float64, incX int) float64 {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return math.Abs(x[0])
|
||||
}
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 {
|
||||
return f64.L2NormUnitary(x[:n])
|
||||
}
|
||||
return f64.L2NormInc(x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
|
||||
// Dasum computes the sum of the absolute values of the elements of x.
|
||||
//
|
||||
// \sum_i |x[i]|
|
||||
//
|
||||
// Dasum returns 0 if incX is negative.
|
||||
func (Implementation) Dasum(n int, x []float64, incX int) float64 {
|
||||
var sum float64
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return 0
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for _, v := range x {
|
||||
sum += math.Abs(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
sum += math.Abs(x[i*incX])
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// Idamax returns the index of an element of x with the largest absolute value.
|
||||
// If there are multiple such indices the earliest is returned.
|
||||
// Idamax returns -1 if n == 0.
|
||||
func (Implementation) Idamax(n int, x []float64, incX int) int {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return -1
|
||||
}
|
||||
if len(x) <= (n-1)*incX {
|
||||
panic(shortX)
|
||||
}
|
||||
if n < 2 {
|
||||
if n == 1 {
|
||||
return 0
|
||||
}
|
||||
if n == 0 {
|
||||
return -1 // Netlib returns invalid index when n == 0.
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
idx := 0
|
||||
max := math.Abs(x[0])
|
||||
if incX == 1 {
|
||||
for i, v := range x[:n] {
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
}
|
||||
return idx
|
||||
}
|
||||
ix := incX
|
||||
for i := 1; i < n; i++ {
|
||||
v := x[ix]
|
||||
absV := math.Abs(v)
|
||||
if absV > max {
|
||||
max = absV
|
||||
idx = i
|
||||
}
|
||||
ix += incX
|
||||
}
|
||||
return idx
|
||||
}
|
||||
|
||||
// Dswap exchanges the elements of two vectors.
|
||||
//
|
||||
// x[i], y[i] = y[i], x[i] for all i
|
||||
func (Implementation) Dswap(n int, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, v := range x {
|
||||
x[i], y[i] = y[i], v
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
x[ix], y[iy] = y[iy], x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Dcopy copies the elements of x into the elements of y.
|
||||
//
|
||||
// y[i] = x[i] for all i
|
||||
func (Implementation) Dcopy(n int, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
copy(y[:n], x[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
y[iy] = x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Daxpy adds alpha times x to y
|
||||
//
|
||||
// y[i] += alpha * x[i] for all i
|
||||
func (Implementation) Daxpy(n int, alpha float64, x []float64, incX int, y []float64, incY int) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if alpha == 0 {
|
||||
return
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
f64.AxpyUnitary(alpha, x[:n], y[:n])
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
f64.AxpyInc(alpha, x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
|
||||
// Drotg computes a plane rotation
|
||||
//
|
||||
// ⎡ c s ⎤ ⎡ a ⎤ = ⎡ r ⎤
|
||||
// ⎣ -s c ⎦ ⎣ b ⎦ ⎣ 0 ⎦
|
||||
//
|
||||
// satisfying c^2 + s^2 = 1.
|
||||
//
|
||||
// The computation uses the formulas
|
||||
//
|
||||
// sigma = sgn(a) if |a| > |b|
|
||||
// = sgn(b) if |b| >= |a|
|
||||
// r = sigma*sqrt(a^2 + b^2)
|
||||
// c = 1; s = 0 if r = 0
|
||||
// c = a/r; s = b/r if r != 0
|
||||
// c >= 0 if |a| > |b|
|
||||
//
|
||||
// The subroutine also computes
|
||||
//
|
||||
// z = s if |a| > |b|,
|
||||
// = 1/c if |b| >= |a| and c != 0
|
||||
// = 1 if c = 0
|
||||
//
|
||||
// This allows c and s to be reconstructed from z as follows:
|
||||
//
|
||||
// If z = 1, set c = 0, s = 1.
|
||||
// If |z| < 1, set c = sqrt(1 - z^2) and s = z.
|
||||
// If |z| > 1, set c = 1/z and s = sqrt(1 - c^2).
|
||||
//
|
||||
// NOTE: There is a discrepancy between the reference implementation and the
|
||||
// BLAS technical manual regarding the sign for r when a or b are zero. Drotg
|
||||
// agrees with the definition in the manual and other common BLAS
|
||||
// implementations.
|
||||
func (Implementation) Drotg(a, b float64) (c, s, r, z float64) {
|
||||
// Implementation based on Supplemental Material to:
|
||||
// Edward Anderson. 2017. Algorithm 978: Safe Scaling in the Level 1 BLAS.
|
||||
// ACM Trans. Math. Softw. 44, 1, Article 12 (July 2017), 28 pages.
|
||||
// DOI: https://doi.org/10.1145/3061665
|
||||
const (
|
||||
safmin = 0x1p-1022
|
||||
safmax = 1 / safmin
|
||||
)
|
||||
anorm := math.Abs(a)
|
||||
bnorm := math.Abs(b)
|
||||
switch {
|
||||
case bnorm == 0:
|
||||
c = 1
|
||||
s = 0
|
||||
r = a
|
||||
z = 0
|
||||
case anorm == 0:
|
||||
c = 0
|
||||
s = 1
|
||||
r = b
|
||||
z = 1
|
||||
default:
|
||||
maxab := math.Max(anorm, bnorm)
|
||||
scl := math.Min(math.Max(safmin, maxab), safmax)
|
||||
var sigma float64
|
||||
if anorm > bnorm {
|
||||
sigma = math.Copysign(1, a)
|
||||
} else {
|
||||
sigma = math.Copysign(1, b)
|
||||
}
|
||||
ascl := a / scl
|
||||
bscl := b / scl
|
||||
r = sigma * (scl * math.Sqrt(ascl*ascl+bscl*bscl))
|
||||
c = a / r
|
||||
s = b / r
|
||||
switch {
|
||||
case anorm > bnorm:
|
||||
z = s
|
||||
case c != 0:
|
||||
z = 1 / c
|
||||
default:
|
||||
z = 1
|
||||
}
|
||||
}
|
||||
return c, s, r, z
|
||||
}
|
||||
|
||||
// Drotmg computes the modified Givens rotation. See
|
||||
// http://www.netlib.org/lapack/explore-html/df/deb/drotmg_8f.html
|
||||
// for more details.
|
||||
func (Implementation) Drotmg(d1, d2, x1, y1 float64) (p blas.DrotmParams, rd1, rd2, rx1 float64) {
|
||||
// The implementation of Drotmg used here is taken from Hopkins 1997
|
||||
// Appendix A: https://doi.org/10.1145/289251.289253
|
||||
// with the exception of the gam constants below.
|
||||
|
||||
const (
|
||||
gam = 4096.0
|
||||
gamsq = gam * gam
|
||||
rgamsq = 1.0 / gamsq
|
||||
)
|
||||
|
||||
if d1 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
if d2 == 0 || y1 == 0 {
|
||||
p.Flag = blas.Identity
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
var h11, h12, h21, h22 float64
|
||||
if (d1 == 0 || x1 == 0) && d2 > 0 {
|
||||
p.Flag = blas.Diagonal
|
||||
h12 = 1
|
||||
h21 = -1
|
||||
x1 = y1
|
||||
d1, d2 = d2, d1
|
||||
} else {
|
||||
p2 := d2 * y1
|
||||
p1 := d1 * x1
|
||||
q2 := p2 * y1
|
||||
q1 := p1 * x1
|
||||
if math.Abs(q1) > math.Abs(q2) {
|
||||
p.Flag = blas.OffDiagonal
|
||||
h11 = 1
|
||||
h22 = 1
|
||||
h21 = -y1 / x1
|
||||
h12 = p2 / p1
|
||||
u := 1 - float64(h12*h21)
|
||||
if u <= 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
d1 /= u
|
||||
d2 /= u
|
||||
x1 *= u
|
||||
} else {
|
||||
if q2 < 0 {
|
||||
p.Flag = blas.Rescaling // Error state.
|
||||
return p, 0, 0, 0
|
||||
}
|
||||
|
||||
p.Flag = blas.Diagonal
|
||||
h21 = -1
|
||||
h12 = 1
|
||||
h11 = p1 / p2
|
||||
h22 = x1 / y1
|
||||
u := 1 + float64(h11*h22)
|
||||
d1, d2 = d2/u, d1/u
|
||||
x1 = y1 * u
|
||||
}
|
||||
}
|
||||
|
||||
for d1 <= rgamsq && d1 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 * gam) * gam
|
||||
x1 /= gam
|
||||
h11 /= gam
|
||||
h12 /= gam
|
||||
}
|
||||
for d1 > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d1 = (d1 / gam) / gam
|
||||
x1 *= gam
|
||||
h11 *= gam
|
||||
h12 *= gam
|
||||
}
|
||||
|
||||
for math.Abs(d2) <= rgamsq && d2 != 0 {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 * gam) * gam
|
||||
h21 /= gam
|
||||
h22 /= gam
|
||||
}
|
||||
for math.Abs(d2) > gamsq {
|
||||
p.Flag = blas.Rescaling
|
||||
d2 = (d2 / gam) / gam
|
||||
h21 *= gam
|
||||
h22 *= gam
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Diagonal:
|
||||
p.H = [4]float64{0: h11, 3: h22}
|
||||
case blas.OffDiagonal:
|
||||
p.H = [4]float64{1: h21, 2: h12}
|
||||
case blas.Rescaling:
|
||||
p.H = [4]float64{h11, h21, h12, h22}
|
||||
default:
|
||||
panic(badFlag)
|
||||
}
|
||||
|
||||
return p, d1, d2, x1
|
||||
}
|
||||
|
||||
// Drot applies a plane transformation.
|
||||
//
|
||||
// x[i] = c * x[i] + s * y[i]
|
||||
// y[i] = c * y[i] - s * x[i]
|
||||
func (Implementation) Drot(n int, x []float64, incX int, y []float64, incY int, c float64, s float64) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = c*vx+s*vy, c*vy-s*vx
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = c*vx+s*vy, c*vy-s*vx
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// Drotm applies the modified Givens rotation to the 2×n matrix.
|
||||
func (Implementation) Drotm(n int, x []float64, incX int, y []float64, incY int, p blas.DrotmParams) {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (incX > 0 && len(x) <= (n-1)*incX) || (incX < 0 && len(x) <= (1-n)*incX) {
|
||||
panic(shortX)
|
||||
}
|
||||
if (incY > 0 && len(y) <= (n-1)*incY) || (incY < 0 && len(y) <= (1-n)*incY) {
|
||||
panic(shortY)
|
||||
}
|
||||
|
||||
if p.Flag == blas.Identity {
|
||||
return
|
||||
}
|
||||
|
||||
switch p.Flag {
|
||||
case blas.Rescaling:
|
||||
h11 := p.H[0]
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = float64(vx*h11)+float64(vy*h12), float64(vx*h21)+float64(vy*h22)
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = float64(vx*h11)+float64(vy*h12), float64(vx*h21)+float64(vy*h22)
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.OffDiagonal:
|
||||
h12 := p.H[2]
|
||||
h21 := p.H[1]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = vx+float64(vy*h12), float64(vx*h21)+vy
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = vx+float64(vy*h12), float64(vx*h21)+vy
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
case blas.Diagonal:
|
||||
h11 := p.H[0]
|
||||
h22 := p.H[3]
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:n]
|
||||
for i, vx := range x {
|
||||
vy := y[i]
|
||||
x[i], y[i] = float64(vx*h11)+vy, -vx+float64(vy*h22)
|
||||
}
|
||||
return
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
vx := x[ix]
|
||||
vy := y[iy]
|
||||
x[ix], y[iy] = float64(vx*h11)+vy, -vx+float64(vy*h22)
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dscal scales x by alpha.
|
||||
//
|
||||
// x[i] *= alpha
|
||||
//
|
||||
// Dscal has no effect if incX < 0.
|
||||
func (Implementation) Dscal(n int, alpha float64, x []float64, incX int) {
|
||||
if incX < 1 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
return
|
||||
}
|
||||
if n < 1 {
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if (n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if alpha == 0 {
|
||||
if incX == 1 {
|
||||
x = x[:n]
|
||||
for i := range x {
|
||||
x[i] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
for ix := 0; ix < n*incX; ix += incX {
|
||||
x[ix] = 0
|
||||
}
|
||||
return
|
||||
}
|
||||
if incX == 1 {
|
||||
f64.ScalUnitary(alpha, x[:n])
|
||||
return
|
||||
}
|
||||
f64.ScalInc(alpha, x, uintptr(n), uintptr(incX))
|
||||
}
|
||||
50
vendor/gonum.org/v1/gonum/blas/gonum/level1float64_ddot.go
generated
vendored
Normal file
50
vendor/gonum.org/v1/gonum/blas/gonum/level1float64_ddot.go
generated
vendored
Normal file
@@ -0,0 +1,50 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
// Ddot computes the dot product of the two vectors
|
||||
//
|
||||
// \sum_i x[i]*y[i]
|
||||
func (Implementation) Ddot(n int, x []float64, incX int, y []float64, incY int) float64 {
|
||||
if incX == 0 {
|
||||
panic(zeroIncX)
|
||||
}
|
||||
if incY == 0 {
|
||||
panic(zeroIncY)
|
||||
}
|
||||
if n <= 0 {
|
||||
if n == 0 {
|
||||
return 0
|
||||
}
|
||||
panic(nLT0)
|
||||
}
|
||||
if incX == 1 && incY == 1 {
|
||||
if len(x) < n {
|
||||
panic(shortX)
|
||||
}
|
||||
if len(y) < n {
|
||||
panic(shortY)
|
||||
}
|
||||
return f64.DotUnitary(x[:n], y[:n])
|
||||
}
|
||||
var ix, iy int
|
||||
if incX < 0 {
|
||||
ix = (-n + 1) * incX
|
||||
}
|
||||
if incY < 0 {
|
||||
iy = (-n + 1) * incY
|
||||
}
|
||||
if ix >= len(x) || ix+(n-1)*incX >= len(x) {
|
||||
panic(shortX)
|
||||
}
|
||||
if iy >= len(y) || iy+(n-1)*incY >= len(y) {
|
||||
panic(shortY)
|
||||
}
|
||||
return f64.DotInc(x, y, uintptr(n), uintptr(incX), uintptr(incY), uintptr(ix), uintptr(iy))
|
||||
}
|
||||
2940
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
generated
vendored
Normal file
2940
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx128.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
2976
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx64.go
generated
vendored
Normal file
2976
vendor/gonum.org/v1/gonum/blas/gonum/level2cmplx64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
2400
vendor/gonum.org/v1/gonum/blas/gonum/level2float32.go
generated
vendored
Normal file
2400
vendor/gonum.org/v1/gonum/blas/gonum/level2float32.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
2366
vendor/gonum.org/v1/gonum/blas/gonum/level2float64.go
generated
vendored
Normal file
2366
vendor/gonum.org/v1/gonum/blas/gonum/level2float64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
1751
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx128.go
generated
vendored
Normal file
1751
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx128.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
1771
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx64.go
generated
vendored
Normal file
1771
vendor/gonum.org/v1/gonum/blas/gonum/level3cmplx64.go
generated
vendored
Normal file
File diff suppressed because it is too large
Load Diff
925
vendor/gonum.org/v1/gonum/blas/gonum/level3float32.go
generated
vendored
Normal file
925
vendor/gonum.org/v1/gonum/blas/gonum/level3float32.go
generated
vendored
Normal file
@@ -0,0 +1,925 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2014 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
var _ blas.Float32Level3 = Implementation{}
|
||||
|
||||
// Strsm solves one of the matrix equations
|
||||
//
|
||||
// A * X = alpha * B if tA == blas.NoTrans and side == blas.Left
|
||||
// Aᵀ * X = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// X * A = alpha * B if tA == blas.NoTrans and side == blas.Right
|
||||
// X * Aᵀ = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and alpha is a
|
||||
// scalar.
|
||||
//
|
||||
// At entry to the function, X contains the values of B, and the result is
|
||||
// stored in-place into X.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Strsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if d != blas.NonUnit && d != blas.Unit {
|
||||
panic(badDiag)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
if va != 0 {
|
||||
k := ka + i + 1
|
||||
f32.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed
|
||||
if ul == blas.Upper {
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
if va != 0 {
|
||||
i := ia + k + 1
|
||||
f32.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is to the right of X.
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, vb := range btmp {
|
||||
if vb == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(-btmp[k], a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f32.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
if btmp[k] == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(-btmp[k], a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha*btmp[j] - f32.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssymm performs one of the matrix-matrix operations
|
||||
//
|
||||
// C = alpha * A * B + beta * C if side == blas.Left
|
||||
// C = alpha * B * A + beta * C if side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
|
||||
// is a scalar.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssymm(s blas.Side, ul blas.Uplo, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
if s != blas.Right && s != blas.Left {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(m-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta != 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
isUpper := ul == blas.Upper
|
||||
if s == blas.Left {
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := alpha * a[i*lda+i]
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j, v := range btmp {
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += atmp * v
|
||||
}
|
||||
|
||||
for k := 0; k < i; k++ {
|
||||
var atmp float32
|
||||
if isUpper {
|
||||
atmp = a[k*lda+i]
|
||||
} else {
|
||||
atmp = a[i*lda+k]
|
||||
}
|
||||
atmp *= alpha
|
||||
f32.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
for k := i + 1; k < m; k++ {
|
||||
var atmp float32
|
||||
if isUpper {
|
||||
atmp = a[i*lda+k]
|
||||
} else {
|
||||
atmp = a[k*lda+i]
|
||||
}
|
||||
atmp *= alpha
|
||||
f32.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if isUpper {
|
||||
for i := 0; i < m; i++ {
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float32
|
||||
atmp := a[j*lda+j+1 : j*lda+n]
|
||||
btmp := b[i*ldb+j+1 : i*ldb+n]
|
||||
ctmp := c[i*ldc+j+1 : i*ldc+n]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float32
|
||||
atmp := a[j*lda : j*lda+j]
|
||||
btmp := b[i*ldb : i*ldb+j]
|
||||
ctmp := c[i*ldc : i*ldc+j]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssyrk performs one of the symmetric rank-k operations
|
||||
//
|
||||
// C = alpha * A * Aᵀ + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * Aᵀ * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
//
|
||||
// where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and
|
||||
// beta are scalars.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, beta float32, c []float32, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = alpha * f32.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
} else {
|
||||
for jc, vc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = vc*beta + alpha*f32.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = alpha * f32.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
} else {
|
||||
for j, vc := range ctmp {
|
||||
ctmp[j] = vc*beta + alpha*f32.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
} else if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, a[l*lda+i:l*lda+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, a[l*lda:l*lda+i+1], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Ssyr2k performs one of the symmetric rank 2k operations
|
||||
//
|
||||
// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
//
|
||||
// where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and
|
||||
// alpha and beta are scalars.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Ssyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, col) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(row-1)+col {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] = alpha * (tmp1 + tmp2)
|
||||
}
|
||||
} else {
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] *= beta
|
||||
ctmp[jc] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta == 0 {
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] = alpha * (tmp1 + tmp2)
|
||||
}
|
||||
} else {
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float32
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
switch beta {
|
||||
case 0:
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
case 1:
|
||||
default:
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb+i : l*ldb+n]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda+i : l*lda+n] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
switch beta {
|
||||
case 0:
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
case 1:
|
||||
default:
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb : l*ldb+i+1]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda : l*lda+i+1] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Strmm performs one of the matrix-matrix operations
|
||||
//
|
||||
// B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
|
||||
// B = alpha * Aᵀ * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
|
||||
// B = alpha * B * Aᵀ if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is a scalar.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Strmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float32, a []float32, lda int, b []float32, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if d != blas.NonUnit && d != blas.Unit {
|
||||
panic(badDiag)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
k := ka + i + 1
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f32.ScalUnitary(tmp, btmp)
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
i := ia + k + 1
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f32.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f32.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is on the right
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(tmp, a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := 0; k < n; k++ {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f32.AxpyUnitary(tmp, a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j, vb := range btmp {
|
||||
tmp := vb
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f32.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := btmp[j]
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f32.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
913
vendor/gonum.org/v1/gonum/blas/gonum/level3float64.go
generated
vendored
Normal file
913
vendor/gonum.org/v1/gonum/blas/gonum/level3float64.go
generated
vendored
Normal file
@@ -0,0 +1,913 @@
|
||||
// Copyright ©2014 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
var _ blas.Float64Level3 = Implementation{}
|
||||
|
||||
// Dtrsm solves one of the matrix equations
|
||||
//
|
||||
// A * X = alpha * B if tA == blas.NoTrans and side == blas.Left
|
||||
// Aᵀ * X = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// X * A = alpha * B if tA == blas.NoTrans and side == blas.Right
|
||||
// X * Aᵀ = alpha * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, X and B are m×n matrices, and alpha is a
|
||||
// scalar.
|
||||
//
|
||||
// At entry to the function, X contains the values of B, and the result is
|
||||
// stored in-place into X.
|
||||
//
|
||||
// No check is made that A is invertible.
|
||||
func (Implementation) Dtrsm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if d != blas.NonUnit && d != blas.Unit {
|
||||
panic(badDiag)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
if va != 0 {
|
||||
k := ka + i + 1
|
||||
f64.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(-va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
if nonUnit {
|
||||
tmp := 1 / a[i*lda+i]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed
|
||||
if ul == blas.Upper {
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
if va != 0 {
|
||||
i := ia + k + 1
|
||||
f64.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
if nonUnit {
|
||||
tmp := 1 / a[k*lda+k]
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(-va, btmpk, b[i*ldb:i*ldb+n])
|
||||
}
|
||||
}
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is to the right of X.
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k, vb := range btmp {
|
||||
if vb == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(-btmp[k], a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if alpha != 1 {
|
||||
f64.ScalUnitary(alpha, btmp)
|
||||
}
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
if btmp[k] == 0 {
|
||||
continue
|
||||
}
|
||||
if nonUnit {
|
||||
btmp[k] /= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(-btmp[k], a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha*btmp[j] - f64.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
if nonUnit {
|
||||
tmp /= a[j*lda+j]
|
||||
}
|
||||
btmp[j] = tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsymm performs one of the matrix-matrix operations
|
||||
//
|
||||
// C = alpha * A * B + beta * C if side == blas.Left
|
||||
// C = alpha * B * A + beta * C if side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m symmetric matrix, B and C are m×n matrices, and alpha
|
||||
// is a scalar.
|
||||
func (Implementation) Dsymm(s blas.Side, ul blas.Uplo, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
|
||||
if s != blas.Right && s != blas.Left {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(m-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if alpha == 0 && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta != 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
isUpper := ul == blas.Upper
|
||||
if s == blas.Left {
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := alpha * a[i*lda+i]
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j, v := range btmp {
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += atmp * v
|
||||
}
|
||||
|
||||
for k := 0; k < i; k++ {
|
||||
var atmp float64
|
||||
if isUpper {
|
||||
atmp = a[k*lda+i]
|
||||
} else {
|
||||
atmp = a[i*lda+k]
|
||||
}
|
||||
atmp *= alpha
|
||||
f64.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
for k := i + 1; k < m; k++ {
|
||||
var atmp float64
|
||||
if isUpper {
|
||||
atmp = a[i*lda+k]
|
||||
} else {
|
||||
atmp = a[k*lda+i]
|
||||
}
|
||||
atmp *= alpha
|
||||
f64.AxpyUnitary(atmp, b[k*ldb:k*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if isUpper {
|
||||
for i := 0; i < m; i++ {
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float64
|
||||
atmp := a[j*lda+j+1 : j*lda+n]
|
||||
btmp := b[i*ldb+j+1 : i*ldb+n]
|
||||
ctmp := c[i*ldc+j+1 : i*ldc+n]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
for j := 0; j < n; j++ {
|
||||
tmp := alpha * b[i*ldb+j]
|
||||
var tmp2 float64
|
||||
atmp := a[j*lda : j*lda+j]
|
||||
btmp := b[i*ldb : i*ldb+j]
|
||||
ctmp := c[i*ldc : i*ldc+j]
|
||||
for k, v := range atmp {
|
||||
ctmp[k] += tmp * v
|
||||
tmp2 += btmp[k] * v
|
||||
}
|
||||
c[i*ldc+j] *= beta
|
||||
c[i*ldc+j] += tmp*a[j*lda+j] + alpha*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsyrk performs one of the symmetric rank-k operations
|
||||
//
|
||||
// C = alpha * A * Aᵀ + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * Aᵀ * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
//
|
||||
// where A is an n×k or k×n matrix, C is an n×n symmetric matrix, and alpha and
|
||||
// beta are scalars.
|
||||
func (Implementation) Dsyrk(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, beta float64, c []float64, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = alpha * f64.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
} else {
|
||||
for jc, vc := range ctmp {
|
||||
j := jc + i
|
||||
ctmp[jc] = vc*beta + alpha*f64.DotUnitary(atmp, a[j*lda:j*lda+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = alpha * f64.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
} else {
|
||||
for j, vc := range ctmp {
|
||||
ctmp[j] = vc*beta + alpha*f64.DotUnitary(a[j*lda:j*lda+k], atmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
} else if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f64.AxpyUnitary(tmp, a[l*lda+i:l*lda+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta != 1 {
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp := alpha * a[l*lda+i]
|
||||
if tmp != 0 {
|
||||
f64.AxpyUnitary(tmp, a[l*lda:l*lda+i+1], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dsyr2k performs one of the symmetric rank 2k operations
|
||||
//
|
||||
// C = alpha * A * Bᵀ + alpha * B * Aᵀ + beta * C if tA == blas.NoTrans
|
||||
// C = alpha * Aᵀ * B + alpha * Bᵀ * A + beta * C if tA == blas.Trans or tA == blas.ConjTrans
|
||||
//
|
||||
// where A and B are n×k or k×n matrices, C is an n×n symmetric matrix, and
|
||||
// alpha and beta are scalars.
|
||||
func (Implementation) Dsyr2k(ul blas.Uplo, tA blas.Transpose, n, k int, alpha float64, a []float64, lda int, b []float64, ldb int, beta float64, c []float64, ldc int) {
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.Trans && tA != blas.NoTrans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
row, col := k, n
|
||||
if tA == blas.NoTrans {
|
||||
row, col = n, k
|
||||
}
|
||||
if lda < max(1, col) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, col) {
|
||||
panic(badLdB)
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(row-1)+col {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(row-1)+col {
|
||||
panic(shortB)
|
||||
}
|
||||
if len(c) < ldc*(n-1)+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
if beta == 0 {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
if beta == 0 {
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] = alpha * (tmp1 + tmp2)
|
||||
}
|
||||
} else {
|
||||
for jc := range ctmp {
|
||||
j := i + jc
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[jc] *= beta
|
||||
ctmp[jc] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
btmp := b[i*ldb : i*ldb+k]
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
if beta == 0 {
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] = alpha * (tmp1 + tmp2)
|
||||
}
|
||||
} else {
|
||||
for j := 0; j <= i; j++ {
|
||||
var tmp1, tmp2 float64
|
||||
binner := b[j*ldb : j*ldb+k]
|
||||
for l, v := range a[j*lda : j*lda+k] {
|
||||
tmp1 += v * btmp[l]
|
||||
tmp2 += atmp[l] * binner[l]
|
||||
}
|
||||
ctmp[j] *= beta
|
||||
ctmp[j] += alpha * (tmp1 + tmp2)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc+i : i*ldc+n]
|
||||
switch beta {
|
||||
case 0:
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
case 1:
|
||||
default:
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb+i : l*ldb+n]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda+i : l*lda+n] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < n; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+i+1]
|
||||
switch beta {
|
||||
case 0:
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
case 1:
|
||||
default:
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
for l := 0; l < k; l++ {
|
||||
tmp1 := alpha * b[l*ldb+i]
|
||||
tmp2 := alpha * a[l*lda+i]
|
||||
btmp := b[l*ldb : l*ldb+i+1]
|
||||
if tmp1 != 0 || tmp2 != 0 {
|
||||
for j, v := range a[l*lda : l*lda+i+1] {
|
||||
ctmp[j] += v*tmp1 + btmp[j]*tmp2
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Dtrmm performs one of the matrix-matrix operations
|
||||
//
|
||||
// B = alpha * A * B if tA == blas.NoTrans and side == blas.Left
|
||||
// B = alpha * Aᵀ * B if tA == blas.Trans or blas.ConjTrans, and side == blas.Left
|
||||
// B = alpha * B * A if tA == blas.NoTrans and side == blas.Right
|
||||
// B = alpha * B * Aᵀ if tA == blas.Trans or blas.ConjTrans, and side == blas.Right
|
||||
//
|
||||
// where A is an n×n or m×m triangular matrix, B is an m×n matrix, and alpha is a scalar.
|
||||
func (Implementation) Dtrmm(s blas.Side, ul blas.Uplo, tA blas.Transpose, d blas.Diag, m, n int, alpha float64, a []float64, lda int, b []float64, ldb int) {
|
||||
if s != blas.Left && s != blas.Right {
|
||||
panic(badSide)
|
||||
}
|
||||
if ul != blas.Lower && ul != blas.Upper {
|
||||
panic(badUplo)
|
||||
}
|
||||
if tA != blas.NoTrans && tA != blas.Trans && tA != blas.ConjTrans {
|
||||
panic(badTranspose)
|
||||
}
|
||||
if d != blas.NonUnit && d != blas.Unit {
|
||||
panic(badDiag)
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
k := n
|
||||
if s == blas.Left {
|
||||
k = m
|
||||
}
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if len(a) < lda*(k-1)+k {
|
||||
panic(shortA)
|
||||
}
|
||||
if len(b) < ldb*(m-1)+n {
|
||||
panic(shortB)
|
||||
}
|
||||
|
||||
if alpha == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := range btmp {
|
||||
btmp[j] = 0
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
nonUnit := d == blas.NonUnit
|
||||
if s == blas.Left {
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
for ka, va := range a[i*lda+i+1 : i*lda+m] {
|
||||
k := ka + i + 1
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := m - 1; i >= 0; i-- {
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[i*lda+i]
|
||||
}
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
f64.ScalUnitary(tmp, btmp)
|
||||
for k, va := range a[i*lda : i*lda+i] {
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, b[k*ldb:k*ldb+n], btmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for k := m - 1; k >= 0; k-- {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for ia, va := range a[k*lda+k+1 : k*lda+m] {
|
||||
i := ia + k + 1
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for k := 0; k < m; k++ {
|
||||
btmpk := b[k*ldb : k*ldb+n]
|
||||
for i, va := range a[k*lda : k*lda+k] {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
if va != 0 {
|
||||
f64.AxpyUnitary(alpha*va, btmpk, btmp)
|
||||
}
|
||||
}
|
||||
tmp := alpha
|
||||
if nonUnit {
|
||||
tmp *= a[k*lda+k]
|
||||
}
|
||||
if tmp != 1 {
|
||||
f64.ScalUnitary(tmp, btmpk)
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is on the right
|
||||
if tA == blas.NoTrans {
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := n - 1; k >= 0; k-- {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(tmp, a[k*lda+k+1:k*lda+n], btmp[k+1:n])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for k := 0; k < n; k++ {
|
||||
tmp := alpha * btmp[k]
|
||||
if tmp == 0 {
|
||||
continue
|
||||
}
|
||||
btmp[k] = tmp
|
||||
if nonUnit {
|
||||
btmp[k] *= a[k*lda+k]
|
||||
}
|
||||
f64.AxpyUnitary(tmp, a[k*lda:k*lda+k], btmp[:k])
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
// Cases where a is transposed.
|
||||
if ul == blas.Upper {
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j, vb := range btmp {
|
||||
tmp := vb
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f64.DotUnitary(a[j*lda+j+1:j*lda+n], btmp[j+1:n])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
return
|
||||
}
|
||||
for i := 0; i < m; i++ {
|
||||
btmp := b[i*ldb : i*ldb+n]
|
||||
for j := n - 1; j >= 0; j-- {
|
||||
tmp := btmp[j]
|
||||
if nonUnit {
|
||||
tmp *= a[j*lda+j]
|
||||
}
|
||||
tmp += f64.DotUnitary(a[j*lda:j*lda+j], btmp[:j])
|
||||
btmp[j] = alpha * tmp
|
||||
}
|
||||
}
|
||||
}
|
||||
301
vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
generated
vendored
Normal file
301
vendor/gonum.org/v1/gonum/blas/gonum/sgemm.go
generated
vendored
Normal file
@@ -0,0 +1,301 @@
|
||||
// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.
|
||||
|
||||
// Copyright ©2014 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package gonum
|
||||
|
||||
import (
|
||||
"runtime"
|
||||
"sync"
|
||||
|
||||
"gonum.org/v1/gonum/blas"
|
||||
"gonum.org/v1/gonum/internal/asm/f32"
|
||||
)
|
||||
|
||||
// Sgemm performs one of the matrix-matrix operations
|
||||
//
|
||||
// C = alpha * A * B + beta * C
|
||||
// C = alpha * Aᵀ * B + beta * C
|
||||
// C = alpha * A * Bᵀ + beta * C
|
||||
// C = alpha * Aᵀ * Bᵀ + beta * C
|
||||
//
|
||||
// where A is an m×k or k×m dense matrix, B is an n×k or k×n dense matrix, C is
|
||||
// an m×n matrix, and alpha and beta are scalars. tA and tB specify whether A or
|
||||
// B are transposed.
|
||||
//
|
||||
// Float32 implementations are autogenerated and not directly tested.
|
||||
func (Implementation) Sgemm(tA, tB blas.Transpose, m, n, k int, alpha float32, a []float32, lda int, b []float32, ldb int, beta float32, c []float32, ldc int) {
|
||||
switch tA {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
switch tB {
|
||||
default:
|
||||
panic(badTranspose)
|
||||
case blas.NoTrans, blas.Trans, blas.ConjTrans:
|
||||
}
|
||||
if m < 0 {
|
||||
panic(mLT0)
|
||||
}
|
||||
if n < 0 {
|
||||
panic(nLT0)
|
||||
}
|
||||
if k < 0 {
|
||||
panic(kLT0)
|
||||
}
|
||||
aTrans := tA == blas.Trans || tA == blas.ConjTrans
|
||||
if aTrans {
|
||||
if lda < max(1, m) {
|
||||
panic(badLdA)
|
||||
}
|
||||
} else {
|
||||
if lda < max(1, k) {
|
||||
panic(badLdA)
|
||||
}
|
||||
}
|
||||
bTrans := tB == blas.Trans || tB == blas.ConjTrans
|
||||
if bTrans {
|
||||
if ldb < max(1, k) {
|
||||
panic(badLdB)
|
||||
}
|
||||
} else {
|
||||
if ldb < max(1, n) {
|
||||
panic(badLdB)
|
||||
}
|
||||
}
|
||||
if ldc < max(1, n) {
|
||||
panic(badLdC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if m == 0 || n == 0 {
|
||||
return
|
||||
}
|
||||
|
||||
// For zero matrix size the following slice length checks are trivially satisfied.
|
||||
if aTrans {
|
||||
if len(a) < (k-1)*lda+m {
|
||||
panic(shortA)
|
||||
}
|
||||
} else {
|
||||
if len(a) < (m-1)*lda+k {
|
||||
panic(shortA)
|
||||
}
|
||||
}
|
||||
if bTrans {
|
||||
if len(b) < (n-1)*ldb+k {
|
||||
panic(shortB)
|
||||
}
|
||||
} else {
|
||||
if len(b) < (k-1)*ldb+n {
|
||||
panic(shortB)
|
||||
}
|
||||
}
|
||||
if len(c) < (m-1)*ldc+n {
|
||||
panic(shortC)
|
||||
}
|
||||
|
||||
// Quick return if possible.
|
||||
if (alpha == 0 || k == 0) && beta == 1 {
|
||||
return
|
||||
}
|
||||
|
||||
// scale c
|
||||
if beta != 1 {
|
||||
if beta == 0 {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] = 0
|
||||
}
|
||||
}
|
||||
} else {
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := range ctmp {
|
||||
ctmp[j] *= beta
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
sgemmParallel(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
}
|
||||
|
||||
func sgemmParallel(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// dgemmParallel computes a parallel matrix multiplication by partitioning
|
||||
// a and b into sub-blocks, and updating c with the multiplication of the sub-block
|
||||
// In all cases,
|
||||
// A = [ A_11 A_12 ... A_1j
|
||||
// A_21 A_22 ... A_2j
|
||||
// ...
|
||||
// A_i1 A_i2 ... A_ij]
|
||||
//
|
||||
// and same for B. All of the submatrix sizes are blockSize×blockSize except
|
||||
// at the edges.
|
||||
//
|
||||
// In all cases, there is one dimension for each matrix along which
|
||||
// C must be updated sequentially.
|
||||
// Cij = \sum_k Aik Bki, (A * B)
|
||||
// Cij = \sum_k Aki Bkj, (Aᵀ * B)
|
||||
// Cij = \sum_k Aik Bjk, (A * Bᵀ)
|
||||
// Cij = \sum_k Aki Bjk, (Aᵀ * Bᵀ)
|
||||
//
|
||||
// This code computes one {i, j} block sequentially along the k dimension,
|
||||
// and computes all of the {i, j} blocks concurrently. This
|
||||
// partitioning allows Cij to be updated in-place without race-conditions.
|
||||
// Instead of launching a goroutine for each possible concurrent computation,
|
||||
// a number of worker goroutines are created and channels are used to pass
|
||||
// available and completed cases.
|
||||
//
|
||||
// http://alexkr.com/docs/matrixmult.pdf is a good reference on matrix-matrix
|
||||
// multiplies, though this code does not copy matrices to attempt to eliminate
|
||||
// cache misses.
|
||||
|
||||
maxKLen := k
|
||||
parBlocks := blocks(m, blockSize) * blocks(n, blockSize)
|
||||
if parBlocks < minParBlock {
|
||||
// The matrix multiplication is small in the dimensions where it can be
|
||||
// computed concurrently. Just do it in serial.
|
||||
sgemmSerial(aTrans, bTrans, m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
}
|
||||
|
||||
// workerLimit acts a number of maximum concurrent workers,
|
||||
// with the limit set to the number of procs available.
|
||||
workerLimit := make(chan struct{}, runtime.GOMAXPROCS(0))
|
||||
|
||||
// wg is used to wait for all
|
||||
var wg sync.WaitGroup
|
||||
wg.Add(parBlocks)
|
||||
defer wg.Wait()
|
||||
|
||||
for i := 0; i < m; i += blockSize {
|
||||
for j := 0; j < n; j += blockSize {
|
||||
workerLimit <- struct{}{}
|
||||
go func(i, j int) {
|
||||
defer func() {
|
||||
wg.Done()
|
||||
<-workerLimit
|
||||
}()
|
||||
|
||||
leni := blockSize
|
||||
if i+leni > m {
|
||||
leni = m - i
|
||||
}
|
||||
lenj := blockSize
|
||||
if j+lenj > n {
|
||||
lenj = n - j
|
||||
}
|
||||
|
||||
cSub := sliceView32(c, ldc, i, j, leni, lenj)
|
||||
|
||||
// Compute A_ik B_kj for all k
|
||||
for k := 0; k < maxKLen; k += blockSize {
|
||||
lenk := blockSize
|
||||
if k+lenk > maxKLen {
|
||||
lenk = maxKLen - k
|
||||
}
|
||||
var aSub, bSub []float32
|
||||
if aTrans {
|
||||
aSub = sliceView32(a, lda, k, i, lenk, leni)
|
||||
} else {
|
||||
aSub = sliceView32(a, lda, i, k, leni, lenk)
|
||||
}
|
||||
if bTrans {
|
||||
bSub = sliceView32(b, ldb, j, k, lenj, lenk)
|
||||
} else {
|
||||
bSub = sliceView32(b, ldb, k, j, lenk, lenj)
|
||||
}
|
||||
sgemmSerial(aTrans, bTrans, leni, lenj, lenk, aSub, lda, bSub, ldb, cSub, ldc, alpha)
|
||||
}
|
||||
}(i, j)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial is serial matrix multiply
|
||||
func sgemmSerial(aTrans, bTrans bool, m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
switch {
|
||||
case !aTrans && !bTrans:
|
||||
sgemmSerialNotNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && !bTrans:
|
||||
sgemmSerialTransNot(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case !aTrans && bTrans:
|
||||
sgemmSerialNotTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
case aTrans && bTrans:
|
||||
sgemmSerialTransTrans(m, n, k, a, lda, b, ldb, c, ldc, alpha)
|
||||
return
|
||||
default:
|
||||
panic("unreachable")
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a nor b are transposed
|
||||
func sgemmSerialNotNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for l, v := range a[i*lda : i*lda+k] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
f32.AxpyUnitary(tmp, b[l*ldb:l*ldb+n], ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a is transposed and b is not
|
||||
func sgemmSerialTransNot(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
btmp := b[l*ldb : l*ldb+n]
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f32.AxpyUnitary(tmp, btmp, ctmp)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where neither a is not transposed and b is
|
||||
func sgemmSerialNotTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for i := 0; i < m; i++ {
|
||||
atmp := a[i*lda : i*lda+k]
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
for j := 0; j < n; j++ {
|
||||
ctmp[j] += alpha * f32.DotUnitary(atmp, b[j*ldb:j*ldb+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// sgemmSerial where both are transposed
|
||||
func sgemmSerialTransTrans(m, n, k int, a []float32, lda int, b []float32, ldb int, c []float32, ldc int, alpha float32) {
|
||||
// This style is used instead of the literal [i*stride +j]) is used because
|
||||
// approximately 5 times faster as of go 1.3.
|
||||
for l := 0; l < k; l++ {
|
||||
for i, v := range a[l*lda : l*lda+m] {
|
||||
tmp := alpha * v
|
||||
if tmp != 0 {
|
||||
ctmp := c[i*ldc : i*ldc+n]
|
||||
f32.AxpyInc(tmp, b[l:], ctmp, uintptr(n), uintptr(ldb), 1, 0, 0)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func sliceView32(a []float32, lda, i, j, r, c int) []float32 {
|
||||
return a[i*lda+j : (i+r-1)*lda+j+c]
|
||||
}
|
||||
224
vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
generated
vendored
Normal file
224
vendor/gonum.org/v1/gonum/blas/gonum/single_precision.bash
generated
vendored
Normal file
@@ -0,0 +1,224 @@
|
||||
#!/usr/bin/env bash
|
||||
|
||||
# Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
# Use of this source code is governed by a BSD-style
|
||||
# license that can be found in the LICENSE file.
|
||||
|
||||
WARNINGF32='//\
|
||||
// Float32 implementations are autogenerated and not directly tested.\
|
||||
'
|
||||
WARNINGC64='//\
|
||||
// Complex64 implementations are autogenerated and not directly tested.\
|
||||
'
|
||||
|
||||
# Level1 routines.
|
||||
|
||||
echo Generating level1float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32.go
|
||||
cat level1float64.go \
|
||||
| gofmt -r 'blas.Float64Level1 -> blas.Float32Level1' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'blas.DrotmParams -> blas.SrotmParams' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.L2NormInc -> f32.L2NormInc' \
|
||||
| gofmt -r 'f64.L2NormUnitary -> f32.L2NormUnitary' \
|
||||
| gofmt -r 'f64.ScalInc -> f32.ScalInc' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e "s_^\(func (Implementation) \)Id\(.*\)\$_$WARNINGF32\1Is\2_" \
|
||||
-e 's_^// Id_// Is_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
-e 's_safmin = 0x1p-1022_safmin = 0x1p-126_' \
|
||||
>> level1float32.go
|
||||
|
||||
echo Generating level1cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1cmplx64.go
|
||||
cat level1cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level1 -> blas.Complex64Level1' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
\
|
||||
| gofmt -r 'c128.AxpyInc -> c64.AxpyInc' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotcInc -> c64.DotcInc' \
|
||||
| gofmt -r 'c128.DotcUnitary -> c64.DotcUnitary' \
|
||||
| gofmt -r 'c128.DotuInc -> c64.DotuInc' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
| gofmt -r 'c128.ScalInc -> c64.ScalInc' \
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
| gofmt -r 'dcabs1 -> scabs1' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Zdot\(.*\)\$_$WARNINGC64\1Cdot\2_" \
|
||||
-e 's_^// Zdot_// Cdot_' \
|
||||
-e "s_^\(func (Implementation) \)Zdscal\(.*\)\$_$WARNINGC64\1Csscal\2_" \
|
||||
-e 's_^// Zdscal_// Csscal_' \
|
||||
-e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e "s_^\(func (Implementation) \)Iz\(.*\)\$_$WARNINGC64\1Ic\2_" \
|
||||
-e 's_^// Iz_// Ic_' \
|
||||
-e "s_^\(func (Implementation) \)Dz\(.*\)\$_$WARNINGC64\1Sc\2_" \
|
||||
-e 's_^// Dz_// Sc_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math"_math "gonum.org/v1/gonum/internal/math32"_' \
|
||||
>> level1cmplx64.go
|
||||
|
||||
echo Generating level1float32_sdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_sdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc -> f32.DotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_sdot.go
|
||||
|
||||
echo Generating level1float32_dsdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_dsdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r '[]float64 -> []float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc -> f32.DdotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DdotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1Ds\2_" \
|
||||
-e 's_^// D_// Ds_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_dsdot.go
|
||||
|
||||
echo Generating level1float32_sdsdot.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level1float32_sdsdot.go
|
||||
cat level1float64_ddot.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.DotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)) -> alpha + float32(f32.DdotInc(x, y, f(n), f(incX), f(incY), f(ix), f(iy)))' \
|
||||
| gofmt -r 'f64.DotUnitary(a, b) -> alpha + float32(f32.DdotUnitary(a, b))' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1Sds\2_" \
|
||||
-e 's_^// D\(.*\)$_// Sds\1 plus a constant_' \
|
||||
-e 's_\\sum_alpha + \\sum_' \
|
||||
-e 's/n int/n int, alpha float32/' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level1float32_sdsdot.go
|
||||
|
||||
|
||||
# Level2 routines.
|
||||
|
||||
echo Generating level2float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level2float32.go
|
||||
cat level2float64.go \
|
||||
| gofmt -r 'blas.Float64Level2 -> blas.Float32Level2' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyIncTo -> f32.AxpyIncTo' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
|
||||
| gofmt -r 'f64.DotInc -> f32.DotInc' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.ScalInc -> f32.ScalInc' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
| gofmt -r 'f64.Ger -> f32.Ger' \
|
||||
| gofmt -r 'f64.GemvN -> f32.GemvN' \
|
||||
| gofmt -r 'f64.GemvT -> f32.GemvT' \
|
||||
| gofmt -r 'Implementation{}.Dscal -> Implementation{}.Sscal' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level2float32.go
|
||||
|
||||
echo Generating level2cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level2cmplx64.go
|
||||
cat level2cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level2 -> blas.Complex64Level2' \
|
||||
\
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'c128.AxpyInc -> c64.AxpyInc' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotuInc -> c64.DotuInc' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
| gofmt -r 'c128.ScalInc -> c64.ScalInc' \
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math/cmplx"_cmplx "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
>> level2cmplx64.go
|
||||
|
||||
# Level3 routines.
|
||||
|
||||
echo Generating level3float32.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level3float32.go
|
||||
cat level3float64.go \
|
||||
| gofmt -r 'blas.Float64Level3 -> blas.Float32Level3' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyUnitaryTo -> f32.AxpyUnitaryTo' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
| gofmt -r 'f64.ScalUnitary -> f32.ScalUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> level3float32.go
|
||||
|
||||
echo Generating sgemm.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > sgemm.go
|
||||
cat dgemm.go \
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'sliceView64 -> sliceView32' \
|
||||
\
|
||||
| gofmt -r 'dgemmParallel -> sgemmParallel' \
|
||||
| gofmt -r 'computeNumBlocks64 -> computeNumBlocks32' \
|
||||
| gofmt -r 'dgemmSerial -> sgemmSerial' \
|
||||
| gofmt -r 'dgemmSerialNotNot -> sgemmSerialNotNot' \
|
||||
| gofmt -r 'dgemmSerialTransNot -> sgemmSerialTransNot' \
|
||||
| gofmt -r 'dgemmSerialNotTrans -> sgemmSerialNotTrans' \
|
||||
| gofmt -r 'dgemmSerialTransTrans -> sgemmSerialTransTrans' \
|
||||
\
|
||||
| gofmt -r 'f64.AxpyInc -> f32.AxpyInc' \
|
||||
| gofmt -r 'f64.AxpyUnitary -> f32.AxpyUnitary' \
|
||||
| gofmt -r 'f64.DotUnitary -> f32.DotUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)D\(.*\)\$_$WARNINGF32\1S\2_" \
|
||||
-e 's_^// D_// S_' \
|
||||
-e 's_^// d_// s_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/f64"_"gonum.org/v1/gonum/internal/asm/f32"_' \
|
||||
>> sgemm.go
|
||||
|
||||
echo Generating level3cmplx64.go
|
||||
echo -e '// Code generated by "go generate gonum.org/v1/gonum/blas/gonum”; DO NOT EDIT.\n' > level3cmplx64.go
|
||||
cat level3cmplx128.go \
|
||||
| gofmt -r 'blas.Complex128Level3 -> blas.Complex64Level3' \
|
||||
\
|
||||
| gofmt -r 'float64 -> float32' \
|
||||
| gofmt -r 'complex128 -> complex64' \
|
||||
\
|
||||
| gofmt -r 'c128.ScalUnitary -> c64.ScalUnitary' \
|
||||
| gofmt -r 'c128.DscalUnitary -> c64.SscalUnitary' \
|
||||
| gofmt -r 'c128.DotcUnitary -> c64.DotcUnitary' \
|
||||
| gofmt -r 'c128.AxpyUnitary -> c64.AxpyUnitary' \
|
||||
| gofmt -r 'c128.DotuUnitary -> c64.DotuUnitary' \
|
||||
\
|
||||
| sed -e "s_^\(func (Implementation) \)Z\(.*\)\$_$WARNINGC64\1C\2_" \
|
||||
-e 's_^// Z_// C_' \
|
||||
-e 's_"gonum.org/v1/gonum/internal/asm/c128"_"gonum.org/v1/gonum/internal/asm/c64"_' \
|
||||
-e 's_"math/cmplx"_cmplx "gonum.org/v1/gonum/internal/cmplx64"_' \
|
||||
>> level3cmplx64.go
|
||||
7
vendor/gonum.org/v1/gonum/floats/README.md
generated
vendored
Normal file
7
vendor/gonum.org/v1/gonum/floats/README.md
generated
vendored
Normal file
@@ -0,0 +1,7 @@
|
||||
# Gonum floats
|
||||
|
||||
[](https://pkg.go.dev/gonum.org/v1/gonum/floats)
|
||||
[](https://godocs.io/gonum.org/v1/gonum/floats)
|
||||
|
||||
Package floats provides a set of helper routines for dealing with slices of float64.
|
||||
The functions avoid allocations to allow for use within tight loops without garbage collection overhead.
|
||||
11
vendor/gonum.org/v1/gonum/floats/doc.go
generated
vendored
Normal file
11
vendor/gonum.org/v1/gonum/floats/doc.go
generated
vendored
Normal file
@@ -0,0 +1,11 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package floats provides a set of helper routines for dealing with slices
|
||||
// of float64. The functions avoid allocations to allow for use within tight
|
||||
// loops without garbage collection overhead.
|
||||
//
|
||||
// The convention used is that when a slice is being modified in place, it has
|
||||
// the name dst.
|
||||
package floats // import "gonum.org/v1/gonum/floats"
|
||||
807
vendor/gonum.org/v1/gonum/floats/floats.go
generated
vendored
Normal file
807
vendor/gonum.org/v1/gonum/floats/floats.go
generated
vendored
Normal file
@@ -0,0 +1,807 @@
|
||||
// Copyright ©2013 The Gonum Authors. All rights reserved.
|
||||
// Use of this code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package floats
|
||||
|
||||
import (
|
||||
"errors"
|
||||
"math"
|
||||
"sort"
|
||||
|
||||
"gonum.org/v1/gonum/floats/scalar"
|
||||
"gonum.org/v1/gonum/internal/asm/f64"
|
||||
)
|
||||
|
||||
const (
|
||||
zeroLength = "floats: zero length slice"
|
||||
shortSpan = "floats: slice length less than 2"
|
||||
badLength = "floats: slice lengths do not match"
|
||||
badDstLength = "floats: destination slice length does not match input"
|
||||
)
|
||||
|
||||
// Add adds, element-wise, the elements of s and dst, and stores the result in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func Add(dst, s []float64) {
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, 1, s, dst)
|
||||
}
|
||||
|
||||
// AddTo adds, element-wise, the elements of s and t and
|
||||
// stores the result in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func AddTo(dst, s, t []float64) []float64 {
|
||||
if len(s) != len(t) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, 1, s, t)
|
||||
return dst
|
||||
}
|
||||
|
||||
// AddConst adds the scalar c to all of the values in dst.
|
||||
func AddConst(c float64, dst []float64) {
|
||||
f64.AddConst(c, dst)
|
||||
}
|
||||
|
||||
// AddScaled performs dst = dst + alpha * s.
|
||||
// It panics if the slice argument lengths do not match.
|
||||
func AddScaled(dst []float64, alpha float64, s []float64) {
|
||||
if len(dst) != len(s) {
|
||||
panic(badLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, alpha, s, dst)
|
||||
}
|
||||
|
||||
// AddScaledTo performs dst = y + alpha * s, where alpha is a scalar,
|
||||
// and dst, y and s are all slices.
|
||||
// It panics if the slice argument lengths do not match.
|
||||
//
|
||||
// At the return of the function, dst[i] = y[i] + alpha * s[i]
|
||||
func AddScaledTo(dst, y []float64, alpha float64, s []float64) []float64 {
|
||||
if len(s) != len(y) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(dst) != len(y) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, alpha, s, y)
|
||||
return dst
|
||||
}
|
||||
|
||||
// argsort is a helper that implements sort.Interface, as used by
|
||||
// Argsort and ArgsortStable.
|
||||
type argsort struct {
|
||||
s []float64
|
||||
inds []int
|
||||
}
|
||||
|
||||
func (a argsort) Len() int {
|
||||
return len(a.s)
|
||||
}
|
||||
|
||||
func (a argsort) Less(i, j int) bool {
|
||||
return a.s[i] < a.s[j]
|
||||
}
|
||||
|
||||
func (a argsort) Swap(i, j int) {
|
||||
a.s[i], a.s[j] = a.s[j], a.s[i]
|
||||
a.inds[i], a.inds[j] = a.inds[j], a.inds[i]
|
||||
}
|
||||
|
||||
// Argsort sorts the elements of dst while tracking their original order.
|
||||
// At the conclusion of Argsort, dst will contain the original elements of dst
|
||||
// but sorted in increasing order, and inds will contain the original position
|
||||
// of the elements in the slice such that dst[i] = origDst[inds[i]].
|
||||
// It panics if the argument lengths do not match.
|
||||
func Argsort(dst []float64, inds []int) {
|
||||
if len(dst) != len(inds) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
for i := range dst {
|
||||
inds[i] = i
|
||||
}
|
||||
|
||||
a := argsort{s: dst, inds: inds}
|
||||
sort.Sort(a)
|
||||
}
|
||||
|
||||
// ArgsortStable sorts the elements of dst while tracking their original order and
|
||||
// keeping the original order of equal elements. At the conclusion of ArgsortStable,
|
||||
// dst will contain the original elements of dst but sorted in increasing order,
|
||||
// and inds will contain the original position of the elements in the slice such
|
||||
// that dst[i] = origDst[inds[i]].
|
||||
// It panics if the argument lengths do not match.
|
||||
func ArgsortStable(dst []float64, inds []int) {
|
||||
if len(dst) != len(inds) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
for i := range dst {
|
||||
inds[i] = i
|
||||
}
|
||||
|
||||
a := argsort{s: dst, inds: inds}
|
||||
sort.Stable(a)
|
||||
}
|
||||
|
||||
// Count applies the function f to every element of s and returns the number
|
||||
// of times the function returned true.
|
||||
func Count(f func(float64) bool, s []float64) int {
|
||||
var n int
|
||||
for _, val := range s {
|
||||
if f(val) {
|
||||
n++
|
||||
}
|
||||
}
|
||||
return n
|
||||
}
|
||||
|
||||
// CumProd finds the cumulative product of the first i elements in
|
||||
// s and puts them in place into the ith element of the
|
||||
// destination dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
//
|
||||
// At the return of the function, dst[i] = s[i] * s[i-1] * s[i-2] * ...
|
||||
func CumProd(dst, s []float64) []float64 {
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
if len(dst) == 0 {
|
||||
return dst
|
||||
}
|
||||
return f64.CumProd(dst, s)
|
||||
}
|
||||
|
||||
// CumSum finds the cumulative sum of the first i elements in
|
||||
// s and puts them in place into the ith element of the
|
||||
// destination dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
//
|
||||
// At the return of the function, dst[i] = s[i] + s[i-1] + s[i-2] + ...
|
||||
func CumSum(dst, s []float64) []float64 {
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
if len(dst) == 0 {
|
||||
return dst
|
||||
}
|
||||
return f64.CumSum(dst, s)
|
||||
}
|
||||
|
||||
// Distance computes the L-norm of s - t. See Norm for special cases.
|
||||
// It panics if the slice argument lengths do not match.
|
||||
func Distance(s, t []float64, L float64) float64 {
|
||||
if len(s) != len(t) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(s) == 0 {
|
||||
return 0
|
||||
}
|
||||
if L == 2 {
|
||||
return f64.L2DistanceUnitary(s, t)
|
||||
}
|
||||
var norm float64
|
||||
if L == 1 {
|
||||
for i, v := range s {
|
||||
norm += math.Abs(t[i] - v)
|
||||
}
|
||||
return norm
|
||||
}
|
||||
if math.IsInf(L, 1) {
|
||||
for i, v := range s {
|
||||
absDiff := math.Abs(t[i] - v)
|
||||
if absDiff > norm {
|
||||
norm = absDiff
|
||||
}
|
||||
}
|
||||
return norm
|
||||
}
|
||||
for i, v := range s {
|
||||
norm += math.Pow(math.Abs(t[i]-v), L)
|
||||
}
|
||||
return math.Pow(norm, 1/L)
|
||||
}
|
||||
|
||||
// Div performs element-wise division dst / s
|
||||
// and stores the value in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func Div(dst, s []float64) {
|
||||
if len(dst) != len(s) {
|
||||
panic(badLength)
|
||||
}
|
||||
f64.Div(dst, s)
|
||||
}
|
||||
|
||||
// DivTo performs element-wise division s / t
|
||||
// and stores the value in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func DivTo(dst, s, t []float64) []float64 {
|
||||
if len(s) != len(t) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
return f64.DivTo(dst, s, t)
|
||||
}
|
||||
|
||||
// Dot computes the dot product of s1 and s2, i.e.
|
||||
// sum_{i = 1}^N s1[i]*s2[i].
|
||||
// It panics if the argument lengths do not match.
|
||||
func Dot(s1, s2 []float64) float64 {
|
||||
if len(s1) != len(s2) {
|
||||
panic(badLength)
|
||||
}
|
||||
return f64.DotUnitary(s1, s2)
|
||||
}
|
||||
|
||||
// Equal returns true when the slices have equal lengths and
|
||||
// all elements are numerically identical.
|
||||
func Equal(s1, s2 []float64) bool {
|
||||
if len(s1) != len(s2) {
|
||||
return false
|
||||
}
|
||||
for i, val := range s1 {
|
||||
if s2[i] != val {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// EqualApprox returns true when the slices have equal lengths and
|
||||
// all element pairs have an absolute tolerance less than tol or a
|
||||
// relative tolerance less than tol.
|
||||
func EqualApprox(s1, s2 []float64, tol float64) bool {
|
||||
if len(s1) != len(s2) {
|
||||
return false
|
||||
}
|
||||
for i, a := range s1 {
|
||||
if !scalar.EqualWithinAbsOrRel(a, s2[i], tol, tol) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// EqualFunc returns true when the slices have the same lengths
|
||||
// and the function returns true for all element pairs.
|
||||
func EqualFunc(s1, s2 []float64, f func(float64, float64) bool) bool {
|
||||
if len(s1) != len(s2) {
|
||||
return false
|
||||
}
|
||||
for i, val := range s1 {
|
||||
if !f(val, s2[i]) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// EqualLengths returns true when all of the slices have equal length,
|
||||
// and false otherwise. It also returns true when there are no input slices.
|
||||
func EqualLengths(slices ...[]float64) bool {
|
||||
// This length check is needed: http://play.golang.org/p/sdty6YiLhM
|
||||
if len(slices) == 0 {
|
||||
return true
|
||||
}
|
||||
l := len(slices[0])
|
||||
for i := 1; i < len(slices); i++ {
|
||||
if len(slices[i]) != l {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// Find applies f to every element of s and returns the indices of the first
|
||||
// k elements for which the f returns true, or all such elements
|
||||
// if k < 0.
|
||||
// Find will reslice inds to have 0 length, and will append
|
||||
// found indices to inds.
|
||||
// If k > 0 and there are fewer than k elements in s satisfying f,
|
||||
// all of the found elements will be returned along with an error.
|
||||
// At the return of the function, the input inds will be in an undetermined state.
|
||||
func Find(inds []int, f func(float64) bool, s []float64, k int) ([]int, error) {
|
||||
// inds is also returned to allow for calling with nil.
|
||||
|
||||
// Reslice inds to have zero length.
|
||||
inds = inds[:0]
|
||||
|
||||
// If zero elements requested, can just return.
|
||||
if k == 0 {
|
||||
return inds, nil
|
||||
}
|
||||
|
||||
// If k < 0, return all of the found indices.
|
||||
if k < 0 {
|
||||
for i, val := range s {
|
||||
if f(val) {
|
||||
inds = append(inds, i)
|
||||
}
|
||||
}
|
||||
return inds, nil
|
||||
}
|
||||
|
||||
// Otherwise, find the first k elements.
|
||||
nFound := 0
|
||||
for i, val := range s {
|
||||
if f(val) {
|
||||
inds = append(inds, i)
|
||||
nFound++
|
||||
if nFound == k {
|
||||
return inds, nil
|
||||
}
|
||||
}
|
||||
}
|
||||
// Finished iterating over the loop, which means k elements were not found.
|
||||
return inds, errors.New("floats: insufficient elements found")
|
||||
}
|
||||
|
||||
// HasNaN returns true when the slice s has any values that are NaN and false
|
||||
// otherwise.
|
||||
func HasNaN(s []float64) bool {
|
||||
for _, v := range s {
|
||||
if math.IsNaN(v) {
|
||||
return true
|
||||
}
|
||||
}
|
||||
return false
|
||||
}
|
||||
|
||||
// LogSpan returns a set of n equally spaced points in log space between,
|
||||
// l and u where N is equal to len(dst). The first element of the
|
||||
// resulting dst will be l and the final element of dst will be u.
|
||||
// It panics if the length of dst is less than 2.
|
||||
// Note that this call will return NaNs if either l or u are negative, and
|
||||
// will return all zeros if l or u is zero.
|
||||
// Also returns the mutated slice dst, so that it can be used in range, like:
|
||||
//
|
||||
// for i, x := range LogSpan(dst, l, u) { ... }
|
||||
func LogSpan(dst []float64, l, u float64) []float64 {
|
||||
Span(dst, math.Log(l), math.Log(u))
|
||||
for i := range dst {
|
||||
dst[i] = math.Exp(dst[i])
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// LogSumExp returns the log of the sum of the exponentials of the values in s.
|
||||
// Panics if s is an empty slice.
|
||||
func LogSumExp(s []float64) float64 {
|
||||
// Want to do this in a numerically stable way which avoids
|
||||
// overflow and underflow
|
||||
// First, find the maximum value in the slice.
|
||||
maxval := Max(s)
|
||||
if math.IsInf(maxval, 0) {
|
||||
// If it's infinity either way, the logsumexp will be infinity as well
|
||||
// returning now avoids NaNs
|
||||
return maxval
|
||||
}
|
||||
var lse float64
|
||||
// Compute the sumexp part
|
||||
for _, val := range s {
|
||||
lse += math.Exp(val - maxval)
|
||||
}
|
||||
// Take the log and add back on the constant taken out
|
||||
return math.Log(lse) + maxval
|
||||
}
|
||||
|
||||
// Max returns the maximum value in the input slice. If the slice is empty, Max will panic.
|
||||
func Max(s []float64) float64 {
|
||||
return s[MaxIdx(s)]
|
||||
}
|
||||
|
||||
// MaxIdx returns the index of the maximum value in the input slice. If several
|
||||
// entries have the maximum value, the first such index is returned.
|
||||
// It panics if s is zero length.
|
||||
func MaxIdx(s []float64) int {
|
||||
if len(s) == 0 {
|
||||
panic(zeroLength)
|
||||
}
|
||||
max := math.NaN()
|
||||
var ind int
|
||||
for i, v := range s {
|
||||
if math.IsNaN(v) {
|
||||
continue
|
||||
}
|
||||
if v > max || math.IsNaN(max) {
|
||||
max = v
|
||||
ind = i
|
||||
}
|
||||
}
|
||||
return ind
|
||||
}
|
||||
|
||||
// Min returns the minimum value in the input slice.
|
||||
// It panics if s is zero length.
|
||||
func Min(s []float64) float64 {
|
||||
return s[MinIdx(s)]
|
||||
}
|
||||
|
||||
// MinIdx returns the index of the minimum value in the input slice. If several
|
||||
// entries have the minimum value, the first such index is returned.
|
||||
// It panics if s is zero length.
|
||||
func MinIdx(s []float64) int {
|
||||
if len(s) == 0 {
|
||||
panic(zeroLength)
|
||||
}
|
||||
min := math.NaN()
|
||||
var ind int
|
||||
for i, v := range s {
|
||||
if math.IsNaN(v) {
|
||||
continue
|
||||
}
|
||||
if v < min || math.IsNaN(min) {
|
||||
min = v
|
||||
ind = i
|
||||
}
|
||||
}
|
||||
return ind
|
||||
}
|
||||
|
||||
// Mul performs element-wise multiplication between dst
|
||||
// and s and stores the value in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func Mul(dst, s []float64) {
|
||||
if len(dst) != len(s) {
|
||||
panic(badLength)
|
||||
}
|
||||
for i, val := range s {
|
||||
dst[i] *= val
|
||||
}
|
||||
}
|
||||
|
||||
// MulTo performs element-wise multiplication between s
|
||||
// and t and stores the value in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func MulTo(dst, s, t []float64) []float64 {
|
||||
if len(s) != len(t) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
for i, val := range t {
|
||||
dst[i] = val * s[i]
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// NearestIdx returns the index of the element in s
|
||||
// whose value is nearest to v. If several such
|
||||
// elements exist, the lowest index is returned.
|
||||
// It panics if s is zero length.
|
||||
func NearestIdx(s []float64, v float64) int {
|
||||
if len(s) == 0 {
|
||||
panic(zeroLength)
|
||||
}
|
||||
switch {
|
||||
case math.IsNaN(v):
|
||||
return 0
|
||||
case math.IsInf(v, 1):
|
||||
return MaxIdx(s)
|
||||
case math.IsInf(v, -1):
|
||||
return MinIdx(s)
|
||||
}
|
||||
var ind int
|
||||
dist := math.NaN()
|
||||
for i, val := range s {
|
||||
newDist := math.Abs(v - val)
|
||||
// A NaN distance will not be closer.
|
||||
if math.IsNaN(newDist) {
|
||||
continue
|
||||
}
|
||||
if newDist < dist || math.IsNaN(dist) {
|
||||
dist = newDist
|
||||
ind = i
|
||||
}
|
||||
}
|
||||
return ind
|
||||
}
|
||||
|
||||
// NearestIdxForSpan return the index of a hypothetical vector created
|
||||
// by Span with length n and bounds l and u whose value is closest
|
||||
// to v. That is, NearestIdxForSpan(n, l, u, v) is equivalent to
|
||||
// Nearest(Span(make([]float64, n),l,u),v) without an allocation.
|
||||
// It panics if n is less than two.
|
||||
func NearestIdxForSpan(n int, l, u float64, v float64) int {
|
||||
if n < 2 {
|
||||
panic(shortSpan)
|
||||
}
|
||||
if math.IsNaN(v) {
|
||||
return 0
|
||||
}
|
||||
|
||||
// Special cases for Inf and NaN.
|
||||
switch {
|
||||
case math.IsNaN(l) && !math.IsNaN(u):
|
||||
return n - 1
|
||||
case math.IsNaN(u):
|
||||
return 0
|
||||
case math.IsInf(l, 0) && math.IsInf(u, 0):
|
||||
if l == u {
|
||||
return 0
|
||||
}
|
||||
if n%2 == 1 {
|
||||
if !math.IsInf(v, 0) {
|
||||
return n / 2
|
||||
}
|
||||
if math.Copysign(1, v) == math.Copysign(1, l) {
|
||||
return 0
|
||||
}
|
||||
return n/2 + 1
|
||||
}
|
||||
if math.Copysign(1, v) == math.Copysign(1, l) {
|
||||
return 0
|
||||
}
|
||||
return n / 2
|
||||
case math.IsInf(l, 0):
|
||||
if v == l {
|
||||
return 0
|
||||
}
|
||||
return n - 1
|
||||
case math.IsInf(u, 0):
|
||||
if v == u {
|
||||
return n - 1
|
||||
}
|
||||
return 0
|
||||
case math.IsInf(v, -1):
|
||||
if l <= u {
|
||||
return 0
|
||||
}
|
||||
return n - 1
|
||||
case math.IsInf(v, 1):
|
||||
if u <= l {
|
||||
return 0
|
||||
}
|
||||
return n - 1
|
||||
}
|
||||
|
||||
// Special cases for v outside (l, u) and (u, l).
|
||||
switch {
|
||||
case l < u:
|
||||
if v <= l {
|
||||
return 0
|
||||
}
|
||||
if v >= u {
|
||||
return n - 1
|
||||
}
|
||||
case l > u:
|
||||
if v >= l {
|
||||
return 0
|
||||
}
|
||||
if v <= u {
|
||||
return n - 1
|
||||
}
|
||||
default:
|
||||
return 0
|
||||
}
|
||||
|
||||
// Can't guarantee anything about exactly halfway between
|
||||
// because of floating point weirdness.
|
||||
return int((float64(n)-1)/(u-l)*(v-l) + 0.5)
|
||||
}
|
||||
|
||||
// Norm returns the L norm of the slice S, defined as
|
||||
// (sum_{i=1}^N s[i]^L)^{1/L}
|
||||
// Special cases:
|
||||
// L = math.Inf(1) gives the maximum absolute value.
|
||||
// Does not correctly compute the zero norm (use Count).
|
||||
func Norm(s []float64, L float64) float64 {
|
||||
// Should this complain if L is not positive?
|
||||
// Should this be done in log space for better numerical stability?
|
||||
// would be more cost
|
||||
// maybe only if L is high?
|
||||
if len(s) == 0 {
|
||||
return 0
|
||||
}
|
||||
if L == 2 {
|
||||
return f64.L2NormUnitary(s)
|
||||
}
|
||||
var norm float64
|
||||
if L == 1 {
|
||||
for _, val := range s {
|
||||
norm += math.Abs(val)
|
||||
}
|
||||
return norm
|
||||
}
|
||||
if math.IsInf(L, 1) {
|
||||
for _, val := range s {
|
||||
norm = math.Max(norm, math.Abs(val))
|
||||
}
|
||||
return norm
|
||||
}
|
||||
for _, val := range s {
|
||||
norm += math.Pow(math.Abs(val), L)
|
||||
}
|
||||
return math.Pow(norm, 1/L)
|
||||
}
|
||||
|
||||
// Prod returns the product of the elements of the slice.
|
||||
// Returns 1 if len(s) = 0.
|
||||
func Prod(s []float64) float64 {
|
||||
prod := 1.0
|
||||
for _, val := range s {
|
||||
prod *= val
|
||||
}
|
||||
return prod
|
||||
}
|
||||
|
||||
// Reverse reverses the order of elements in the slice.
|
||||
func Reverse(s []float64) {
|
||||
for i, j := 0, len(s)-1; i < j; i, j = i+1, j-1 {
|
||||
s[i], s[j] = s[j], s[i]
|
||||
}
|
||||
}
|
||||
|
||||
// Same returns true when the input slices have the same length and all
|
||||
// elements have the same value with NaN treated as the same.
|
||||
func Same(s, t []float64) bool {
|
||||
if len(s) != len(t) {
|
||||
return false
|
||||
}
|
||||
for i, v := range s {
|
||||
w := t[i]
|
||||
if v != w && !(math.IsNaN(v) && math.IsNaN(w)) {
|
||||
return false
|
||||
}
|
||||
}
|
||||
return true
|
||||
}
|
||||
|
||||
// Scale multiplies every element in dst by the scalar c.
|
||||
func Scale(c float64, dst []float64) {
|
||||
if len(dst) > 0 {
|
||||
f64.ScalUnitary(c, dst)
|
||||
}
|
||||
}
|
||||
|
||||
// ScaleTo multiplies the elements in s by c and stores the result in dst.
|
||||
// It panics if the slice argument lengths do not match.
|
||||
func ScaleTo(dst []float64, c float64, s []float64) []float64 {
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
if len(dst) > 0 {
|
||||
f64.ScalUnitaryTo(dst, c, s)
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// Span returns a set of N equally spaced points between l and u, where N
|
||||
// is equal to the length of the destination. The first element of the destination
|
||||
// is l, the final element of the destination is u.
|
||||
// It panics if the length of dst is less than 2.
|
||||
//
|
||||
// Span also returns the mutated slice dst, so that it can be used in range expressions,
|
||||
// like:
|
||||
//
|
||||
// for i, x := range Span(dst, l, u) { ... }
|
||||
func Span(dst []float64, l, u float64) []float64 {
|
||||
n := len(dst)
|
||||
if n < 2 {
|
||||
panic(shortSpan)
|
||||
}
|
||||
|
||||
// Special cases for Inf and NaN.
|
||||
switch {
|
||||
case math.IsNaN(l):
|
||||
for i := range dst[:len(dst)-1] {
|
||||
dst[i] = math.NaN()
|
||||
}
|
||||
dst[len(dst)-1] = u
|
||||
return dst
|
||||
case math.IsNaN(u):
|
||||
for i := range dst[1:] {
|
||||
dst[i+1] = math.NaN()
|
||||
}
|
||||
dst[0] = l
|
||||
return dst
|
||||
case math.IsInf(l, 0) && math.IsInf(u, 0):
|
||||
for i := range dst[:len(dst)/2] {
|
||||
dst[i] = l
|
||||
dst[len(dst)-i-1] = u
|
||||
}
|
||||
if len(dst)%2 == 1 {
|
||||
if l != u {
|
||||
dst[len(dst)/2] = 0
|
||||
} else {
|
||||
dst[len(dst)/2] = l
|
||||
}
|
||||
}
|
||||
return dst
|
||||
case math.IsInf(l, 0):
|
||||
for i := range dst[:len(dst)-1] {
|
||||
dst[i] = l
|
||||
}
|
||||
dst[len(dst)-1] = u
|
||||
return dst
|
||||
case math.IsInf(u, 0):
|
||||
for i := range dst[1:] {
|
||||
dst[i+1] = u
|
||||
}
|
||||
dst[0] = l
|
||||
return dst
|
||||
}
|
||||
|
||||
step := (u - l) / float64(n-1)
|
||||
for i := range dst {
|
||||
dst[i] = l + step*float64(i)
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// Sub subtracts, element-wise, the elements of s from dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func Sub(dst, s []float64) {
|
||||
if len(dst) != len(s) {
|
||||
panic(badLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, -1, s, dst)
|
||||
}
|
||||
|
||||
// SubTo subtracts, element-wise, the elements of t from s and
|
||||
// stores the result in dst.
|
||||
// It panics if the argument lengths do not match.
|
||||
func SubTo(dst, s, t []float64) []float64 {
|
||||
if len(s) != len(t) {
|
||||
panic(badLength)
|
||||
}
|
||||
if len(dst) != len(s) {
|
||||
panic(badDstLength)
|
||||
}
|
||||
f64.AxpyUnitaryTo(dst, -1, t, s)
|
||||
return dst
|
||||
}
|
||||
|
||||
// Sum returns the sum of the elements of the slice.
|
||||
func Sum(s []float64) float64 {
|
||||
return f64.Sum(s)
|
||||
}
|
||||
|
||||
// Within returns the first index i where s[i] <= v < s[i+1]. Within panics if:
|
||||
// - len(s) < 2
|
||||
// - s is not sorted
|
||||
func Within(s []float64, v float64) int {
|
||||
if len(s) < 2 {
|
||||
panic(shortSpan)
|
||||
}
|
||||
if !sort.Float64sAreSorted(s) {
|
||||
panic("floats: input slice not sorted")
|
||||
}
|
||||
if v < s[0] || v >= s[len(s)-1] || math.IsNaN(v) {
|
||||
return -1
|
||||
}
|
||||
for i, f := range s[1:] {
|
||||
if v < f {
|
||||
return i
|
||||
}
|
||||
}
|
||||
return -1
|
||||
}
|
||||
|
||||
// SumCompensated returns the sum of the elements of the slice calculated with greater
|
||||
// accuracy than Sum at the expense of additional computation.
|
||||
func SumCompensated(s []float64) float64 {
|
||||
// SumCompensated uses an improved version of Kahan's compensated
|
||||
// summation algorithm proposed by Neumaier.
|
||||
// See https://en.wikipedia.org/wiki/Kahan_summation_algorithm for details.
|
||||
var sum, c float64
|
||||
for _, x := range s {
|
||||
// This type conversion is here to prevent a sufficiently smart compiler
|
||||
// from optimising away these operations.
|
||||
t := float64(sum + x)
|
||||
if math.Abs(sum) >= math.Abs(x) {
|
||||
c += (sum - t) + x
|
||||
} else {
|
||||
c += (x - t) + sum
|
||||
}
|
||||
sum = t
|
||||
}
|
||||
return sum + c
|
||||
}
|
||||
6
vendor/gonum.org/v1/gonum/floats/scalar/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/floats/scalar/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package scalar provides a set of helper routines for dealing with float64 values.
|
||||
package scalar // import "gonum.org/v1/gonum/floats/scalar"
|
||||
171
vendor/gonum.org/v1/gonum/floats/scalar/scalar.go
generated
vendored
Normal file
171
vendor/gonum.org/v1/gonum/floats/scalar/scalar.go
generated
vendored
Normal file
@@ -0,0 +1,171 @@
|
||||
// Copyright ©2013 The Gonum Authors. All rights reserved.
|
||||
// Use of this code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package scalar
|
||||
|
||||
import (
|
||||
"math"
|
||||
"strconv"
|
||||
)
|
||||
|
||||
// EqualWithinAbs returns true when a and b have an absolute difference
|
||||
// not greater than tol.
|
||||
func EqualWithinAbs(a, b, tol float64) bool {
|
||||
return a == b || math.Abs(a-b) <= tol
|
||||
}
|
||||
|
||||
// minNormalFloat64 is the smallest normal number. For 64 bit IEEE-754
|
||||
// floats this is 2^{-1022}.
|
||||
const minNormalFloat64 = 0x1p-1022
|
||||
|
||||
// EqualWithinRel returns true when the difference between a and b
|
||||
// is not greater than tol times the greater absolute value of a and b,
|
||||
//
|
||||
// abs(a-b) <= tol * max(abs(a), abs(b)).
|
||||
func EqualWithinRel(a, b, tol float64) bool {
|
||||
if a == b {
|
||||
return true
|
||||
}
|
||||
delta := math.Abs(a - b)
|
||||
if delta <= minNormalFloat64 {
|
||||
return delta <= tol*minNormalFloat64
|
||||
}
|
||||
// We depend on the division in this relationship to identify
|
||||
// infinities (we rely on the NaN to fail the test) otherwise
|
||||
// we compare Infs of the same sign and evaluate Infs as equal
|
||||
// independent of sign.
|
||||
return delta/math.Max(math.Abs(a), math.Abs(b)) <= tol
|
||||
}
|
||||
|
||||
// EqualWithinAbsOrRel returns true when a and b are equal to within
|
||||
// the absolute or relative tolerances. See EqualWithinAbs and
|
||||
// EqualWithinRel for details.
|
||||
func EqualWithinAbsOrRel(a, b, absTol, relTol float64) bool {
|
||||
return EqualWithinAbs(a, b, absTol) || EqualWithinRel(a, b, relTol)
|
||||
}
|
||||
|
||||
// EqualWithinULP returns true when a and b are equal to within
|
||||
// the specified number of floating point units in the last place.
|
||||
func EqualWithinULP(a, b float64, ulp uint) bool {
|
||||
if a == b {
|
||||
return true
|
||||
}
|
||||
if math.IsNaN(a) || math.IsNaN(b) {
|
||||
return false
|
||||
}
|
||||
if math.Signbit(a) != math.Signbit(b) {
|
||||
return math.Float64bits(math.Abs(a))+math.Float64bits(math.Abs(b)) <= uint64(ulp)
|
||||
}
|
||||
return ulpDiff(math.Float64bits(a), math.Float64bits(b)) <= uint64(ulp)
|
||||
}
|
||||
|
||||
func ulpDiff(a, b uint64) uint64 {
|
||||
if a > b {
|
||||
return a - b
|
||||
}
|
||||
return b - a
|
||||
}
|
||||
|
||||
const (
|
||||
nanBits = 0x7ff8000000000000
|
||||
nanMask = 0xfff8000000000000
|
||||
)
|
||||
|
||||
// NaNWith returns an IEEE 754 "quiet not-a-number" value with the
|
||||
// payload specified in the low 51 bits of payload.
|
||||
// The NaN returned by math.NaN has a bit pattern equal to NaNWith(1).
|
||||
func NaNWith(payload uint64) float64 {
|
||||
return math.Float64frombits(nanBits | (payload &^ nanMask))
|
||||
}
|
||||
|
||||
// NaNPayload returns the lowest 51 bits payload of an IEEE 754 "quiet
|
||||
// not-a-number". For values of f other than quiet-NaN, NaNPayload
|
||||
// returns zero and false.
|
||||
func NaNPayload(f float64) (payload uint64, ok bool) {
|
||||
b := math.Float64bits(f)
|
||||
if b&nanBits != nanBits {
|
||||
return 0, false
|
||||
}
|
||||
return b &^ nanMask, true
|
||||
}
|
||||
|
||||
// ParseWithNA converts the string s to a float64 in value.
|
||||
// If s equals missing, weight is returned as 0, otherwise 1.
|
||||
func ParseWithNA(s, missing string) (value, weight float64, err error) {
|
||||
if s == missing {
|
||||
return 0, 0, nil
|
||||
}
|
||||
value, err = strconv.ParseFloat(s, 64)
|
||||
if err == nil {
|
||||
weight = 1
|
||||
}
|
||||
return value, weight, err
|
||||
}
|
||||
|
||||
// Round returns the half away from zero rounded value of x with prec precision.
|
||||
//
|
||||
// Special cases are:
|
||||
//
|
||||
// Round(±0) = +0
|
||||
// Round(±Inf) = ±Inf
|
||||
// Round(NaN) = NaN
|
||||
func Round(x float64, prec int) float64 {
|
||||
if x == 0 {
|
||||
// Make sure zero is returned
|
||||
// without the negative bit set.
|
||||
return 0
|
||||
}
|
||||
// Fast path for positive precision on integers.
|
||||
if prec >= 0 && x == math.Trunc(x) {
|
||||
return x
|
||||
}
|
||||
pow := math.Pow10(prec)
|
||||
intermed := x * pow
|
||||
if math.IsInf(intermed, 0) {
|
||||
return x
|
||||
}
|
||||
x = math.Round(intermed)
|
||||
|
||||
if x == 0 {
|
||||
return 0
|
||||
}
|
||||
|
||||
return x / pow
|
||||
}
|
||||
|
||||
// RoundEven returns the half even rounded value of x with prec precision.
|
||||
//
|
||||
// Special cases are:
|
||||
//
|
||||
// RoundEven(±0) = +0
|
||||
// RoundEven(±Inf) = ±Inf
|
||||
// RoundEven(NaN) = NaN
|
||||
func RoundEven(x float64, prec int) float64 {
|
||||
if x == 0 {
|
||||
// Make sure zero is returned
|
||||
// without the negative bit set.
|
||||
return 0
|
||||
}
|
||||
// Fast path for positive precision on integers.
|
||||
if prec >= 0 && x == math.Trunc(x) {
|
||||
return x
|
||||
}
|
||||
pow := math.Pow10(prec)
|
||||
intermed := x * pow
|
||||
if math.IsInf(intermed, 0) {
|
||||
return x
|
||||
}
|
||||
x = math.RoundToEven(intermed)
|
||||
|
||||
if x == 0 {
|
||||
return 0
|
||||
}
|
||||
|
||||
return x / pow
|
||||
}
|
||||
|
||||
// Same returns true when the inputs have the same value, allowing NaN equality.
|
||||
func Same(a, b float64) bool {
|
||||
return a == b || (math.IsNaN(a) && math.IsNaN(b))
|
||||
}
|
||||
134
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyinc_amd64.s
generated
vendored
Normal file
134
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,134 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVDDUP X2, X3
|
||||
#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
|
||||
// MOVDDUP X4, X5
|
||||
#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
|
||||
// MOVDDUP X6, X7
|
||||
#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
|
||||
// MOVDDUP X8, X9
|
||||
#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
|
||||
|
||||
// ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
// ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
// ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
// ADDSUBPD X8, X9
|
||||
#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+16(FP), SI // SI = &x
|
||||
MOVQ y_base+40(FP), DI // DI = &y
|
||||
MOVQ n+64(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JE axpyi_end
|
||||
MOVQ ix+88(FP), R8 // R8 = ix // Load the first index
|
||||
SHLQ $4, R8 // R8 *= sizeof(complex128)
|
||||
MOVQ iy+96(FP), R9 // R9 = iy
|
||||
SHLQ $4, R9 // R9 *= sizeof(complex128)
|
||||
LEAQ (SI)(R8*1), SI // SI = &(x[ix])
|
||||
LEAQ (DI)(R9*1), DI // DI = &(y[iy])
|
||||
MOVQ DI, DX // DX = DI // Separate Read/Write pointers
|
||||
MOVQ incX+72(FP), R8 // R8 = incX
|
||||
SHLQ $4, R8 // R8 *= sizeof(complex128)
|
||||
MOVQ incY+80(FP), R9 // R9 = iy
|
||||
SHLQ $4, R9 // R9 *= sizeof(complex128)
|
||||
MOVUPS alpha+0(FP), X0 // X0 = { imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x1, X1, X1 // X1 = { real(a), imag(a) }
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ axpyi_tail // if BX == 0 { goto axpyi_tail }
|
||||
|
||||
axpyi_loop: // do {
|
||||
MOVUPS (SI), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS (SI)(R8*1), X4
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
MOVUPS (SI), X6
|
||||
MOVUPS (SI)(R8*1), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X1, X2
|
||||
MULPD X0, X3
|
||||
MULPD X11, X4
|
||||
MULPD X10, X5
|
||||
MULPD X1, X6
|
||||
MULPD X0, X7
|
||||
MULPD X11, X8
|
||||
MULPD X10, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DX), X3
|
||||
ADDPD (DX)(R9*1), X5
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
ADDPD (DX), X7
|
||||
ADDPD (DX)(R9*1), X9
|
||||
MOVUPS X3, (DI) // dst[i] = X_(i+1)
|
||||
MOVUPS X5, (DI)(R9*1)
|
||||
LEAQ (DI)(R9*2), DI
|
||||
MOVUPS X7, (DI)
|
||||
MOVUPS X9, (DI)(R9*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R9*2), DI // DI = &(DI[incY*2])
|
||||
DECQ BX
|
||||
JNZ axpyi_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail: // do {
|
||||
MOVUPS (SI), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD X1, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X0, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DI), X3
|
||||
MOVUPS X3, (DI) // y[i] = X_i
|
||||
ADDQ R8, SI // SI = &(SI[incX])
|
||||
ADDQ R9, DI // DI = &(DI[incY])
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
141
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyincto_amd64.s
generated
vendored
Normal file
141
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyincto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,141 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVDDUP X2, X3
|
||||
#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
|
||||
// MOVDDUP X4, X5
|
||||
#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
|
||||
// MOVDDUP X6, X7
|
||||
#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
|
||||
// MOVDDUP X8, X9
|
||||
#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
|
||||
|
||||
// ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
// ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
// ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
// ADDSUBPD X8, X9
|
||||
#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyIncTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+56(FP), SI // SI = &x
|
||||
MOVQ y_base+80(FP), DX // DX = &y
|
||||
MOVQ n+104(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JE axpyi_end
|
||||
MOVQ ix+128(FP), R8 // R8 = ix // Load the first index
|
||||
SHLQ $4, R8 // R8 *= sizeof(complex128)
|
||||
MOVQ iy+136(FP), R9 // R9 = iy
|
||||
SHLQ $4, R9 // R9 *= sizeof(complex128)
|
||||
MOVQ idst+32(FP), R10 // R10 = idst
|
||||
SHLQ $4, R10 // R10 *= sizeof(complex128)
|
||||
LEAQ (SI)(R8*1), SI // SI = &(x[ix])
|
||||
LEAQ (DX)(R9*1), DX // DX = &(y[iy])
|
||||
LEAQ (DI)(R10*1), DI // DI = &(dst[idst])
|
||||
MOVQ incX+112(FP), R8 // R8 = incX
|
||||
SHLQ $4, R8 // R8 *= sizeof(complex128)
|
||||
MOVQ incY+120(FP), R9 // R9 = incY
|
||||
SHLQ $4, R9 // R9 *= sizeof(complex128)
|
||||
MOVQ incDst+24(FP), R10 // R10 = incDst
|
||||
SHLQ $4, R10 // R10 *= sizeof(complex128)
|
||||
MOVUPS alpha+40(FP), X0 // X0 = { imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x1, X1, X1 // X1 = { real(a), imag(a) }
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ axpyi_tail // if BX == 0 { goto axpyi_tail }
|
||||
|
||||
axpyi_loop: // do {
|
||||
MOVUPS (SI), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS (SI)(R8*1), X4
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
|
||||
MOVUPS (SI), X6
|
||||
MOVUPS (SI)(R8*1), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X1, X2
|
||||
MULPD X0, X3
|
||||
MULPD X11, X4
|
||||
MULPD X10, X5
|
||||
MULPD X1, X6
|
||||
MULPD X0, X7
|
||||
MULPD X11, X8
|
||||
MULPD X10, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DX), X3
|
||||
ADDPD (DX)(R9*1), X5
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
ADDPD (DX), X7
|
||||
ADDPD (DX)(R9*1), X9
|
||||
MOVUPS X3, (DI) // dst[i] = X_(i+1)
|
||||
MOVUPS X5, (DI)(R10*1)
|
||||
LEAQ (DI)(R10*2), DI
|
||||
MOVUPS X7, (DI)
|
||||
MOVUPS X9, (DI)(R10*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R10*2), DI // DI = &(DI[incDst*2])
|
||||
DECQ BX
|
||||
JNZ axpyi_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail: // do {
|
||||
MOVUPS (SI), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD X1, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X0, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DX), X3
|
||||
MOVUPS X3, (DI) // y[i] X_(i+1)
|
||||
ADDQ R8, SI // SI += incX
|
||||
ADDQ R9, DX // DX += incY
|
||||
ADDQ R10, DI // DI += incDst
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
122
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitary_amd64.s
generated
vendored
Normal file
122
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,122 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVDDUP X2, X3
|
||||
#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
|
||||
// MOVDDUP X4, X5
|
||||
#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
|
||||
// MOVDDUP X6, X7
|
||||
#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
|
||||
// MOVDDUP X8, X9
|
||||
#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
|
||||
|
||||
// ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
// ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
// ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
// ADDSUBPD X8, X9
|
||||
#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyUnitary(alpha complex128, x, y []complex128)
|
||||
TEXT ·AxpyUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+16(FP), SI // SI = &x
|
||||
MOVQ y_base+40(FP), DI // DI = &y
|
||||
MOVQ x_len+24(FP), CX // CX = min( len(x), len(y) )
|
||||
CMPQ y_len+48(FP), CX
|
||||
CMOVQLE y_len+48(FP), CX
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
PXOR X0, X0 // Clear work registers and cache-align loop
|
||||
PXOR X1, X1
|
||||
MOVUPS alpha+0(FP), X0 // X0 = { imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x1, X1, X1 // X1 = { real(a), imag(a) }
|
||||
XORQ AX, AX // i = 0
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ caxy_tail // if BX == 0 { goto caxy_tail }
|
||||
|
||||
caxy_loop: // do {
|
||||
MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS 16(SI)(AX*8), X4
|
||||
MOVUPS 32(SI)(AX*8), X6
|
||||
MOVUPS 48(SI)(AX*8), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X1, X2
|
||||
MULPD X0, X3
|
||||
MULPD X11, X4
|
||||
MULPD X10, X5
|
||||
MULPD X1, X6
|
||||
MULPD X0, X7
|
||||
MULPD X11, X8
|
||||
MULPD X10, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DI)(AX*8), X3
|
||||
ADDPD 16(DI)(AX*8), X5
|
||||
ADDPD 32(DI)(AX*8), X7
|
||||
ADDPD 48(DI)(AX*8), X9
|
||||
MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
|
||||
MOVUPS X5, 16(DI)(AX*8)
|
||||
MOVUPS X7, 32(DI)(AX*8)
|
||||
MOVUPS X9, 48(DI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
DECQ BX
|
||||
JNZ caxy_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
|
||||
caxy_tail: // do {
|
||||
MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD X1, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X0, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DI)(AX*8), X3
|
||||
MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
|
||||
ADDQ $2, AX // i += 2
|
||||
LOOP caxy_tail // } while --CX > 0
|
||||
|
||||
caxy_end:
|
||||
RET
|
||||
123
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitaryto_amd64.s
generated
vendored
Normal file
123
vendor/gonum.org/v1/gonum/internal/asm/c128/axpyunitaryto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,123 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVDDUP X2, X3
|
||||
#define MOVDDUP_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xDA
|
||||
// MOVDDUP X4, X5
|
||||
#define MOVDDUP_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xEC
|
||||
// MOVDDUP X6, X7
|
||||
#define MOVDDUP_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0x12; BYTE $0xFE
|
||||
// MOVDDUP X8, X9
|
||||
#define MOVDDUP_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC8
|
||||
|
||||
// ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X2_X3 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
// ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X4_X5 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
// ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X6_X7 BYTE $0x66; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
// ADDSUBPD X8, X9
|
||||
#define ADDSUBPD_X8_X9 BYTE $0x66; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyUnitaryTo(dst []complex128, alpha complex64, x, y []complex128)
|
||||
TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+40(FP), SI // SI = &x
|
||||
MOVQ y_base+64(FP), DX // DX = &y
|
||||
MOVQ x_len+48(FP), CX // CX = min( len(x), len(y), len(dst) )
|
||||
CMPQ y_len+72(FP), CX
|
||||
CMOVQLE y_len+72(FP), CX
|
||||
CMPQ dst_len+8(FP), CX
|
||||
CMOVQLE dst_len+8(FP), CX
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
MOVUPS alpha+24(FP), X0 // X0 = { imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x1, X1, X1 // X1 = { real(a), imag(a) }
|
||||
XORQ AX, AX // i = 0
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ caxy_tail // if BX == 0 { goto caxy_tail }
|
||||
|
||||
caxy_loop: // do {
|
||||
MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS 16(SI)(AX*8), X4
|
||||
MOVUPS 32(SI)(AX*8), X6
|
||||
MOVUPS 48(SI)(AX*8), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3 // Load and duplicate imag elements (xi, xi)
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // duplicate real elements (xr, xr)
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X1, X2
|
||||
MULPD X0, X3
|
||||
MULPD X11, X4
|
||||
MULPD X10, X5
|
||||
MULPD X1, X6
|
||||
MULPD X0, X7
|
||||
MULPD X11, X8
|
||||
MULPD X10, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DX)(AX*8), X3
|
||||
ADDPD 16(DX)(AX*8), X5
|
||||
ADDPD 32(DX)(AX*8), X7
|
||||
ADDPD 48(DX)(AX*8), X9
|
||||
MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
|
||||
MOVUPS X5, 16(DI)(AX*8)
|
||||
MOVUPS X7, 32(DI)(AX*8)
|
||||
MOVUPS X9, 48(DI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
DECQ BX
|
||||
JNZ caxy_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
|
||||
caxy_tail: // Same calculation, but read in values to avoid trampling memory
|
||||
MOVUPS (SI)(AX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD X1, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X0, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
// X_(i+1) = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
ADDPD (DX)(AX*8), X3
|
||||
MOVUPS X3, (DI)(AX*8) // y[i] = X_(i+1)
|
||||
ADDQ $2, AX // i += 2
|
||||
LOOP caxy_tail // } while --CX > 0
|
||||
|
||||
caxy_end:
|
||||
RET
|
||||
6
vendor/gonum.org/v1/gonum/internal/asm/c128/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/internal/asm/c128/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package c128 provides complex128 vector primitives.
|
||||
package c128 // import "gonum.org/v1/gonum/internal/asm/c128"
|
||||
153
vendor/gonum.org/v1/gonum/internal/asm/c128/dotcinc_amd64.s
generated
vendored
Normal file
153
vendor/gonum.org/v1/gonum/internal/asm/c128/dotcinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,153 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVDDUP_XPTR__X3 LONG $0x1E120FF2 // MOVDDUP (SI), X3
|
||||
#define MOVDDUP_XPTR_INCX__X5 LONG $0x120F42F2; WORD $0x062C // MOVDDUP (SI)(R8*1), X5
|
||||
#define MOVDDUP_XPTR_INCX_2__X7 LONG $0x120F42F2; WORD $0x463C // MOVDDUP (SI)(R8*2), X7
|
||||
#define MOVDDUP_XPTR_INCx3X__X9 LONG $0x120F46F2; WORD $0x0E0C // MOVDDUP (SI)(R9*1), X9
|
||||
|
||||
#define MOVDDUP_8_XPTR__X2 LONG $0x56120FF2; BYTE $0x08 // MOVDDUP 8(SI), X2
|
||||
#define MOVDDUP_8_XPTR_INCX__X4 LONG $0x120F42F2; WORD $0x0664; BYTE $0x08 // MOVDDUP 8(SI)(R8*1), X4
|
||||
#define MOVDDUP_8_XPTR_INCX_2__X6 LONG $0x120F42F2; WORD $0x4674; BYTE $0x08 // MOVDDUP 8(SI)(R8*2), X6
|
||||
#define MOVDDUP_8_XPTR_INCx3X__X8 LONG $0x120F46F2; WORD $0x0E44; BYTE $0x08 // MOVDDUP 8(SI)(R9*1), X8
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define INC_X R8
|
||||
#define INCx3_X R9
|
||||
#define INC_Y R10
|
||||
#define INCx3_Y R11
|
||||
#define NEG1 X15
|
||||
#define P_NEG1 X14
|
||||
|
||||
// func DotcInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128)
|
||||
TEXT ·DotcInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dot_end
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
MOVQ ix+72(FP), INC_X // INC_X = ix * sizeof(complex128)
|
||||
SHLQ $4, INC_X
|
||||
MOVQ iy+80(FP), INC_Y // INC_Y = iy * sizeof(complex128)
|
||||
SHLQ $4, INC_Y
|
||||
LEAQ (X_PTR)(INC_X*1), X_PTR // X_PTR = &(X_PTR[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*1), Y_PTR // Y_PTR = &(Y_PTR[iy])
|
||||
MOVQ incX+56(FP), INC_X // INC_X = incX
|
||||
SHLQ $4, INC_X // INC_X *= sizeof(complex128)
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y = incY
|
||||
SHLQ $4, INC_Y // INC_Y *= sizeof(complex128)
|
||||
MOVSD $(-1.0), NEG1
|
||||
SHUFPD $0, NEG1, NEG1 // { -1, -1 }
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = n % 4
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ dot_tail // if n <= 4 { goto dot_tail }
|
||||
MOVAPS NEG1, P_NEG1 // Copy NEG1 to P_NEG1 for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = 3 * incX * sizeof(complex128)
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = 3 * incY * sizeof(complex128)
|
||||
|
||||
dot_loop: // do {
|
||||
MOVDDUP_XPTR__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_XPTR_INCX__X5
|
||||
MOVDDUP_XPTR_INCX_2__X7
|
||||
MOVDDUP_XPTR_INCx3X__X9
|
||||
|
||||
MOVDDUP_8_XPTR__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MOVDDUP_8_XPTR_INCX__X4
|
||||
MOVDDUP_8_XPTR_INCX_2__X6
|
||||
MOVDDUP_8_XPTR_INCx3X__X8
|
||||
|
||||
// X_i = { -imag(x[i]), -imag(x[i]) }
|
||||
MULPD NEG1, X2
|
||||
MULPD P_NEG1, X4
|
||||
MULPD NEG1, X6
|
||||
MULPD P_NEG1, X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVUPS (Y_PTR), X10
|
||||
MOVUPS (Y_PTR)(INC_Y*1), X11
|
||||
MOVUPS (Y_PTR)(INC_Y*2), X12
|
||||
MOVUPS (Y_PTR)(INCx3_Y*1), X13
|
||||
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X10, X3
|
||||
MULPD X11, X5
|
||||
MULPD X12, X7
|
||||
MULPD X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPD $0x1, X10, X10
|
||||
SHUFPD $0x1, X11, X11
|
||||
SHUFPD $0x1, X12, X12
|
||||
SHUFPD $0x1, X13, X13
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X10, X2
|
||||
MULPD X11, X4
|
||||
MULPD X12, X6
|
||||
MULPD X13, X8
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// psum += result[i]
|
||||
ADDPD X3, SUM
|
||||
ADDPD X5, P_SUM
|
||||
ADDPD X7, SUM
|
||||
ADDPD X9, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[incY*4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
ADDPD P_SUM, SUM // sum += psum
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
MOVDDUP_XPTR__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_8_XPTR__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD NEG1, X2 // X_i = { -imag(x[i]) , -imag(x[i]) }
|
||||
MOVUPS (Y_PTR), X10 // X_j = { imag(y[i]) , real(y[i]) }
|
||||
MULPD X10, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
SHUFPD $0x1, X10, X10 // X_j = { real(y[i]) , imag(y[i]) }
|
||||
MULPD X10, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDPD X3, SUM // sum += result[i]
|
||||
ADDQ INC_X, X_PTR // X_PTR += incX
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += incY
|
||||
DECQ TAIL
|
||||
JNZ dot_tail // } while --TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVUPS SUM, sum+88(FP)
|
||||
RET
|
||||
143
vendor/gonum.org/v1/gonum/internal/asm/c128/dotcunitary_amd64.s
generated
vendored
Normal file
143
vendor/gonum.org/v1/gonum/internal/asm/c128/dotcunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,143 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVDDUP_XPTR_IDX_8__X3 LONG $0x1C120FF2; BYTE $0xC6 // MOVDDUP (SI)(AX*8), X3
|
||||
#define MOVDDUP_16_XPTR_IDX_8__X5 LONG $0x6C120FF2; WORD $0x10C6 // MOVDDUP 16(SI)(AX*8), X5
|
||||
#define MOVDDUP_32_XPTR_IDX_8__X7 LONG $0x7C120FF2; WORD $0x20C6 // MOVDDUP 32(SI)(AX*8), X7
|
||||
#define MOVDDUP_48_XPTR_IDX_8__X9 LONG $0x120F44F2; WORD $0xC64C; BYTE $0x30 // MOVDDUP 48(SI)(AX*8), X9
|
||||
|
||||
#define MOVDDUP_XPTR_IIDX_8__X2 LONG $0x14120FF2; BYTE $0xD6 // MOVDDUP (SI)(DX*8), X2
|
||||
#define MOVDDUP_16_XPTR_IIDX_8__X4 LONG $0x64120FF2; WORD $0x10D6 // MOVDDUP 16(SI)(DX*8), X4
|
||||
#define MOVDDUP_32_XPTR_IIDX_8__X6 LONG $0x74120FF2; WORD $0x20D6 // MOVDDUP 32(SI)(DX*8), X6
|
||||
#define MOVDDUP_48_XPTR_IIDX_8__X8 LONG $0x120F44F2; WORD $0xD644; BYTE $0x30 // MOVDDUP 48(SI)(DX*8), X8
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define IDX AX
|
||||
#define I_IDX DX
|
||||
#define NEG1 X15
|
||||
#define P_NEG1 X14
|
||||
|
||||
// func DotcUnitary(x, y []complex128) (sum complex128)
|
||||
TEXT ·DotcUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
PXOR SUM, SUM // sum = 0
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dot_end
|
||||
XORPS P_SUM, P_SUM // psum = 0
|
||||
MOVSD $(-1.0), NEG1
|
||||
SHUFPD $0, NEG1, NEG1 // { -1, -1 }
|
||||
XORQ IDX, IDX // i := 0
|
||||
MOVQ $1, I_IDX // j := 1
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = floor( TAIL / 4 )
|
||||
SHRQ $2, LEN // LEN = TAIL % 4
|
||||
JZ dot_tail // if LEN == 0 { goto dot_tail }
|
||||
|
||||
MOVAPS NEG1, P_NEG1 // Copy NEG1 to P_NEG1 for pipelining
|
||||
|
||||
dot_loop: // do {
|
||||
MOVDDUP_XPTR_IDX_8__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_16_XPTR_IDX_8__X5
|
||||
MOVDDUP_32_XPTR_IDX_8__X7
|
||||
MOVDDUP_48_XPTR_IDX_8__X9
|
||||
|
||||
MOVDDUP_XPTR_IIDX_8__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MOVDDUP_16_XPTR_IIDX_8__X4
|
||||
MOVDDUP_32_XPTR_IIDX_8__X6
|
||||
MOVDDUP_48_XPTR_IIDX_8__X8
|
||||
|
||||
// X_i = { -imag(x[i]), -imag(x[i]) }
|
||||
MULPD NEG1, X2
|
||||
MULPD P_NEG1, X4
|
||||
MULPD NEG1, X6
|
||||
MULPD P_NEG1, X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10
|
||||
MOVUPS 16(Y_PTR)(IDX*8), X11
|
||||
MOVUPS 32(Y_PTR)(IDX*8), X12
|
||||
MOVUPS 48(Y_PTR)(IDX*8), X13
|
||||
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X10, X3
|
||||
MULPD X11, X5
|
||||
MULPD X12, X7
|
||||
MULPD X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPD $0x1, X10, X10
|
||||
SHUFPD $0x1, X11, X11
|
||||
SHUFPD $0x1, X12, X12
|
||||
SHUFPD $0x1, X13, X13
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X10, X2
|
||||
MULPD X11, X4
|
||||
MULPD X12, X6
|
||||
MULPD X13, X8
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// psum += result[i]
|
||||
ADDPD X3, SUM
|
||||
ADDPD X5, P_SUM
|
||||
ADDPD X7, SUM
|
||||
ADDPD X9, P_SUM
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
ADDQ $8, I_IDX // I_IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
ADDPD P_SUM, SUM // sum += psum
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
MOVDDUP_XPTR_IDX_8__X3 // X_(i+1) = { real(x[i]) , real(x[i]) }
|
||||
MOVDDUP_XPTR_IIDX_8__X2 // X_i = { imag(x[i]) , imag(x[i]) }
|
||||
MULPD NEG1, X2 // X_i = { -imag(x[i]) , -imag(x[i]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]) , real(y[i]) }
|
||||
MULPD X10, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
SHUFPD $0x1, X10, X10 // X_j = { real(y[i]) , imag(y[i]) }
|
||||
MULPD X10, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDPD X3, SUM // SUM += result[i]
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
ADDQ $2, I_IDX // I_IDX += 2
|
||||
DECQ TAIL
|
||||
JNZ dot_tail // } while --TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVUPS SUM, sum+48(FP)
|
||||
RET
|
||||
141
vendor/gonum.org/v1/gonum/internal/asm/c128/dotuinc_amd64.s
generated
vendored
Normal file
141
vendor/gonum.org/v1/gonum/internal/asm/c128/dotuinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,141 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVDDUP_XPTR__X3 LONG $0x1E120FF2 // MOVDDUP (SI), X3
|
||||
#define MOVDDUP_XPTR_INCX__X5 LONG $0x120F42F2; WORD $0x062C // MOVDDUP (SI)(R8*1), X5
|
||||
#define MOVDDUP_XPTR_INCX_2__X7 LONG $0x120F42F2; WORD $0x463C // MOVDDUP (SI)(R8*2), X7
|
||||
#define MOVDDUP_XPTR_INCx3X__X9 LONG $0x120F46F2; WORD $0x0E0C // MOVDDUP (SI)(R9*1), X9
|
||||
|
||||
#define MOVDDUP_8_XPTR__X2 LONG $0x56120FF2; BYTE $0x08 // MOVDDUP 8(SI), X2
|
||||
#define MOVDDUP_8_XPTR_INCX__X4 LONG $0x120F42F2; WORD $0x0664; BYTE $0x08 // MOVDDUP 8(SI)(R8*1), X4
|
||||
#define MOVDDUP_8_XPTR_INCX_2__X6 LONG $0x120F42F2; WORD $0x4674; BYTE $0x08 // MOVDDUP 8(SI)(R8*2), X6
|
||||
#define MOVDDUP_8_XPTR_INCx3X__X8 LONG $0x120F46F2; WORD $0x0E44; BYTE $0x08 // MOVDDUP 8(SI)(R9*1), X8
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define INC_X R8
|
||||
#define INCx3_X R9
|
||||
#define INC_Y R10
|
||||
#define INCx3_Y R11
|
||||
|
||||
// func DotuInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128)
|
||||
TEXT ·DotuInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
PXOR SUM, SUM // sum = 0
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dot_end
|
||||
MOVQ ix+72(FP), INC_X // INC_X = ix * sizeof(complex128)
|
||||
SHLQ $4, INC_X
|
||||
MOVQ iy+80(FP), INC_Y // INC_Y = iy * sizeof(complex128)
|
||||
SHLQ $4, INC_Y
|
||||
LEAQ (X_PTR)(INC_X*1), X_PTR // X_PTR = &(X_PTR[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*1), Y_PTR // Y_PTR = &(Y_PTR[iy])
|
||||
MOVQ incX+56(FP), INC_X // INC_X = incX
|
||||
SHLQ $4, INC_X // INC_X *= sizeof(complex128)
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y = incY
|
||||
SHLQ $4, INC_Y // INC_Y *= sizeof(complex128)
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // LEN = LEN % 4
|
||||
SHRQ $2, LEN // LEN = floor( LEN / 4 )
|
||||
JZ dot_tail // if LEN <= 4 { goto dot_tail }
|
||||
PXOR P_SUM, P_SUM // psum = 0
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = 3 * incX * sizeof(complex128)
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = 3 * incY * sizeof(complex128)
|
||||
|
||||
dot_loop: // do {
|
||||
MOVDDUP_XPTR__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_XPTR_INCX__X5
|
||||
MOVDDUP_XPTR_INCX_2__X7
|
||||
MOVDDUP_XPTR_INCx3X__X9
|
||||
|
||||
MOVDDUP_8_XPTR__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MOVDDUP_8_XPTR_INCX__X4
|
||||
MOVDDUP_8_XPTR_INCX_2__X6
|
||||
MOVDDUP_8_XPTR_INCx3X__X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVUPS (Y_PTR), X10
|
||||
MOVUPS (Y_PTR)(INC_Y*1), X11
|
||||
MOVUPS (Y_PTR)(INC_Y*2), X12
|
||||
MOVUPS (Y_PTR)(INCx3_Y*1), X13
|
||||
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X10, X3
|
||||
MULPD X11, X5
|
||||
MULPD X12, X7
|
||||
MULPD X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPD $0x1, X10, X10
|
||||
SHUFPD $0x1, X11, X11
|
||||
SHUFPD $0x1, X12, X12
|
||||
SHUFPD $0x1, X13, X13
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X10, X2
|
||||
MULPD X11, X4
|
||||
MULPD X12, X6
|
||||
MULPD X13, X8
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// psum += result[i]
|
||||
ADDPD X3, SUM
|
||||
ADDPD X5, P_SUM
|
||||
ADDPD X7, SUM
|
||||
ADDPD X9, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[incY*4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --BX > 0
|
||||
ADDPD P_SUM, SUM // sum += psum
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
MOVDDUP_XPTR__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_8_XPTR__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MOVUPS (Y_PTR), X10 // X_j = { imag(y[i]) , real(y[i]) }
|
||||
MULPD X10, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
SHUFPD $0x1, X10, X10 // X_j = { real(y[i]) , imag(y[i]) }
|
||||
MULPD X10, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDPD X3, SUM // sum += result[i]
|
||||
ADDQ INC_X, X_PTR // X_PTR += incX
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += incY
|
||||
DECQ TAIL // --TAIL
|
||||
JNZ dot_tail // } while TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVUPS SUM, sum+88(FP)
|
||||
RET
|
||||
130
vendor/gonum.org/v1/gonum/internal/asm/c128/dotuunitary_amd64.s
generated
vendored
Normal file
130
vendor/gonum.org/v1/gonum/internal/asm/c128/dotuunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,130 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVDDUP_XPTR_IDX_8__X3 LONG $0x1C120FF2; BYTE $0xC6 // MOVDDUP (SI)(AX*8), X3
|
||||
#define MOVDDUP_16_XPTR_IDX_8__X5 LONG $0x6C120FF2; WORD $0x10C6 // MOVDDUP 16(SI)(AX*8), X5
|
||||
#define MOVDDUP_32_XPTR_IDX_8__X7 LONG $0x7C120FF2; WORD $0x20C6 // MOVDDUP 32(SI)(AX*8), X7
|
||||
#define MOVDDUP_48_XPTR_IDX_8__X9 LONG $0x120F44F2; WORD $0xC64C; BYTE $0x30 // MOVDDUP 48(SI)(AX*8), X9
|
||||
|
||||
#define MOVDDUP_XPTR_IIDX_8__X2 LONG $0x14120FF2; BYTE $0xD6 // MOVDDUP (SI)(DX*8), X2
|
||||
#define MOVDDUP_16_XPTR_IIDX_8__X4 LONG $0x64120FF2; WORD $0x10D6 // MOVDDUP 16(SI)(DX*8), X4
|
||||
#define MOVDDUP_32_XPTR_IIDX_8__X6 LONG $0x74120FF2; WORD $0x20D6 // MOVDDUP 32(SI)(DX*8), X6
|
||||
#define MOVDDUP_48_XPTR_IIDX_8__X8 LONG $0x120F44F2; WORD $0xD644; BYTE $0x30 // MOVDDUP 48(SI)(DX*8), X8
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define IDX AX
|
||||
#define I_IDX DX
|
||||
|
||||
// func DotuUnitary(x, y []complex128) (sum complex128)
|
||||
TEXT ·DotuUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dot_end
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
XORQ IDX, IDX // IDX = 0
|
||||
MOVQ $1, DX // j = 1
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = floor( LEN / 4 )
|
||||
SHRQ $2, LEN // LEN = LEN % 4
|
||||
JZ dot_tail // if LEN == 0 { goto dot_tail }
|
||||
|
||||
dot_loop: // do {
|
||||
MOVDDUP_XPTR_IDX_8__X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_16_XPTR_IDX_8__X5
|
||||
MOVDDUP_32_XPTR_IDX_8__X7
|
||||
MOVDDUP_48_XPTR_IDX_8__X9
|
||||
|
||||
MOVDDUP_XPTR_IIDX_8__X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MOVDDUP_16_XPTR_IIDX_8__X4
|
||||
MOVDDUP_32_XPTR_IIDX_8__X6
|
||||
MOVDDUP_48_XPTR_IIDX_8__X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10
|
||||
MOVUPS 16(Y_PTR)(IDX*8), X11
|
||||
MOVUPS 32(Y_PTR)(IDX*8), X12
|
||||
MOVUPS 48(Y_PTR)(IDX*8), X13
|
||||
|
||||
// X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPD X10, X3
|
||||
MULPD X11, X5
|
||||
MULPD X12, X7
|
||||
MULPD X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPD $0x1, X10, X10
|
||||
SHUFPD $0x1, X11, X11
|
||||
SHUFPD $0x1, X12, X12
|
||||
SHUFPD $0x1, X13, X13
|
||||
|
||||
// X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPD X10, X2
|
||||
MULPD X11, X4
|
||||
MULPD X12, X6
|
||||
MULPD X13, X8
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
// psum += result[i]
|
||||
ADDPD X3, SUM
|
||||
ADDPD X5, P_SUM
|
||||
ADDPD X7, SUM
|
||||
ADDPD X9, P_SUM
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
ADDQ $8, I_IDX // I_IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
ADDPD P_SUM, SUM // SUM += P_SUM
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
MOVDDUP_XPTR_IDX_8__X3 // X_(i+1) = { real(x[i] , real(x[i]) }
|
||||
MOVDDUP_XPTR_IIDX_8__X2 // X_i = { imag(x[i]) , imag(x[i]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]) , real(y[i]) }
|
||||
MULPD X10, X3 // X_(i+1) = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
SHUFPD $0x1, X10, X10 // X_j = { real(y[i]) , imag(y[i]) }
|
||||
MULPD X10, X2 // X_i = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDPD X3, SUM // psum += result[i]
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
ADDQ $2, I_IDX // I_IDX += 2
|
||||
DECQ TAIL // --TAIL
|
||||
JNZ dot_tail // } while TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVUPS SUM, sum+48(FP)
|
||||
RET
|
||||
69
vendor/gonum.org/v1/gonum/internal/asm/c128/dscalinc_amd64.s
generated
vendored
Normal file
69
vendor/gonum.org/v1/gonum/internal/asm/c128/dscalinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,69 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define SRC SI
|
||||
#define DST SI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC R9
|
||||
#define INC3 R10
|
||||
#define ALPHA X0
|
||||
#define ALPHA_2 X1
|
||||
|
||||
#define MOVDDUP_ALPHA LONG $0x44120FF2; WORD $0x0824 // MOVDDUP 8(SP), X0
|
||||
|
||||
// func DscalInc(alpha float64, x []complex128, n, inc uintptr)
|
||||
TEXT ·DscalInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SRC // SRC = &x
|
||||
MOVQ n+32(FP), LEN // LEN = n
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dscal_end
|
||||
|
||||
MOVDDUP_ALPHA // ALPHA = alpha
|
||||
MOVQ inc+40(FP), INC // INC = inc
|
||||
SHLQ $4, INC // INC = INC * sizeof(complex128)
|
||||
LEAQ (INC)(INC*2), INC3 // INC3 = 3 * INC
|
||||
MOVUPS ALPHA, ALPHA_2 // Copy ALPHA and ALPHA_2 for pipelining
|
||||
MOVQ LEN, TAIL // TAIL = LEN
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ dscal_tail // if LEN == 0 { goto dscal_tail }
|
||||
|
||||
dscal_loop: // do {
|
||||
MOVUPS (SRC), X2 // X_i = x[i]
|
||||
MOVUPS (SRC)(INC*1), X3
|
||||
MOVUPS (SRC)(INC*2), X4
|
||||
MOVUPS (SRC)(INC3*1), X5
|
||||
|
||||
MULPD ALPHA, X2 // X_i *= ALPHA
|
||||
MULPD ALPHA_2, X3
|
||||
MULPD ALPHA, X4
|
||||
MULPD ALPHA_2, X5
|
||||
|
||||
MOVUPS X2, (DST) // x[i] = X_i
|
||||
MOVUPS X3, (DST)(INC*1)
|
||||
MOVUPS X4, (DST)(INC*2)
|
||||
MOVUPS X5, (DST)(INC3*1)
|
||||
|
||||
LEAQ (SRC)(INC*4), SRC // SRC += INC*4
|
||||
DECQ LEN
|
||||
JNZ dscal_loop // } while --LEN > 0
|
||||
|
||||
dscal_tail:
|
||||
ANDQ $3, TAIL // TAIL = TAIL % 4
|
||||
JE dscal_end // if TAIL == 0 { return }
|
||||
|
||||
dscal_tail_loop: // do {
|
||||
MOVUPS (SRC), X2 // X_i = x[i]
|
||||
MULPD ALPHA, X2 // X_i *= ALPHA
|
||||
MOVUPS X2, (DST) // x[i] = X_i
|
||||
ADDQ INC, SRC // SRC += INC
|
||||
DECQ TAIL
|
||||
JNZ dscal_tail_loop // } while --TAIL > 0
|
||||
|
||||
dscal_end:
|
||||
RET
|
||||
66
vendor/gonum.org/v1/gonum/internal/asm/c128/dscalunitary_amd64.s
generated
vendored
Normal file
66
vendor/gonum.org/v1/gonum/internal/asm/c128/dscalunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,66 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define SRC SI
|
||||
#define DST SI
|
||||
#define LEN CX
|
||||
#define IDX AX
|
||||
#define TAIL BX
|
||||
#define ALPHA X0
|
||||
#define ALPHA_2 X1
|
||||
|
||||
#define MOVDDUP_ALPHA LONG $0x44120FF2; WORD $0x0824 // MOVDDUP 8(SP), X0
|
||||
|
||||
// func DscalUnitary(alpha float64, x []complex128)
|
||||
TEXT ·DscalUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SRC // SRC = &x
|
||||
MOVQ x_len+16(FP), LEN // LEN = len(x)
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dscal_end
|
||||
|
||||
MOVDDUP_ALPHA // ALPHA = alpha
|
||||
XORQ IDX, IDX // IDX = 0
|
||||
MOVUPS ALPHA, ALPHA_2 // Copy ALPHA to ALPHA_2 for pipelining
|
||||
MOVQ LEN, TAIL // TAIL = LEN
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ dscal_tail // if LEN == 0 { goto dscal_tail }
|
||||
|
||||
dscal_loop: // do {
|
||||
MOVUPS (SRC)(IDX*8), X2 // X_i = x[i]
|
||||
MOVUPS 16(SRC)(IDX*8), X3
|
||||
MOVUPS 32(SRC)(IDX*8), X4
|
||||
MOVUPS 48(SRC)(IDX*8), X5
|
||||
|
||||
MULPD ALPHA, X2 // X_i *= ALPHA
|
||||
MULPD ALPHA_2, X3
|
||||
MULPD ALPHA, X4
|
||||
MULPD ALPHA_2, X5
|
||||
|
||||
MOVUPS X2, (DST)(IDX*8) // x[i] = X_i
|
||||
MOVUPS X3, 16(DST)(IDX*8)
|
||||
MOVUPS X4, 32(DST)(IDX*8)
|
||||
MOVUPS X5, 48(DST)(IDX*8)
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dscal_loop // } while --LEN > 0
|
||||
|
||||
dscal_tail:
|
||||
ANDQ $3, TAIL // TAIL = TAIL % 4
|
||||
JZ dscal_end // if TAIL == 0 { return }
|
||||
|
||||
dscal_tail_loop: // do {
|
||||
MOVUPS (SRC)(IDX*8), X2 // X_i = x[i]
|
||||
MULPD ALPHA, X2 // X_i *= ALPHA
|
||||
MOVUPS X2, (DST)(IDX*8) // x[i] = X_i
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
DECQ TAIL
|
||||
JNZ dscal_tail_loop // } while --TAIL > 0
|
||||
|
||||
dscal_end:
|
||||
RET
|
||||
33
vendor/gonum.org/v1/gonum/internal/asm/c128/scal.go
generated
vendored
Normal file
33
vendor/gonum.org/v1/gonum/internal/asm/c128/scal.go
generated
vendored
Normal file
@@ -0,0 +1,33 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package c128
|
||||
|
||||
// ScalUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha * v
|
||||
// }
|
||||
func ScalUnitaryTo(dst []complex128, alpha complex128, x []complex128) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// ScalIncTo is
|
||||
//
|
||||
// var idst, ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha * x[ix]
|
||||
// ix += incX
|
||||
// idst += incDst
|
||||
// }
|
||||
func ScalIncTo(dst []complex128, incDst uintptr, alpha complex128, x []complex128, n, incX uintptr) {
|
||||
var idst, ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha * x[ix]
|
||||
ix += incX
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
116
vendor/gonum.org/v1/gonum/internal/asm/c128/scalUnitary_amd64.s
generated
vendored
Normal file
116
vendor/gonum.org/v1/gonum/internal/asm/c128/scalUnitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,116 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define SRC SI
|
||||
#define DST SI
|
||||
#define LEN CX
|
||||
#define IDX AX
|
||||
#define TAIL BX
|
||||
#define ALPHA X0
|
||||
#define ALPHA_C X1
|
||||
#define ALPHA2 X10
|
||||
#define ALPHA_C2 X11
|
||||
|
||||
#define MOVDDUP_X2_X3 LONG $0xDA120FF2 // MOVDDUP X2, X3
|
||||
#define MOVDDUP_X4_X5 LONG $0xEC120FF2 // MOVDDUP X4, X5
|
||||
#define MOVDDUP_X6_X7 LONG $0xFE120FF2 // MOVDDUP X6, X7
|
||||
#define MOVDDUP_X8_X9 LONG $0x120F45F2; BYTE $0xC8 // MOVDDUP X8, X9
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
// func ScalUnitary(alpha complex128, x []complex128)
|
||||
TEXT ·ScalUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+16(FP), SRC // SRC = &x
|
||||
MOVQ x_len+24(FP), LEN // LEN = len(x)
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE scal_end
|
||||
|
||||
MOVUPS alpha+0(FP), ALPHA // ALPHA = { imag(alpha), real(alpha) }
|
||||
MOVAPS ALPHA, ALPHA_C
|
||||
SHUFPD $0x1, ALPHA_C, ALPHA_C // ALPHA_C = { real(alpha), imag(alpha) }
|
||||
|
||||
XORQ IDX, IDX // IDX = 0
|
||||
MOVAPS ALPHA, ALPHA2 // Copy ALPHA and ALPHA_C for pipelining
|
||||
MOVAPS ALPHA_C, ALPHA_C2
|
||||
MOVQ LEN, TAIL
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ scal_tail // if BX == 0 { goto scal_tail }
|
||||
|
||||
scal_loop: // do {
|
||||
MOVUPS (SRC)(IDX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS 16(SRC)(IDX*8), X4
|
||||
MOVUPS 32(SRC)(IDX*8), X6
|
||||
MOVUPS 48(SRC)(IDX*8), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i]) }
|
||||
MULPD ALPHA_C, X2
|
||||
MULPD ALPHA, X3
|
||||
MULPD ALPHA_C2, X4
|
||||
MULPD ALPHA2, X5
|
||||
MULPD ALPHA_C, X6
|
||||
MULPD ALPHA, X7
|
||||
MULPD ALPHA_C2, X8
|
||||
MULPD ALPHA2, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
|
||||
// real(result[i]): real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
MOVUPS X3, (DST)(IDX*8) // x[i] = X_(i+1)
|
||||
MOVUPS X5, 16(DST)(IDX*8)
|
||||
MOVUPS X7, 32(DST)(IDX*8)
|
||||
MOVUPS X9, 48(DST)(IDX*8)
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
DECQ LEN
|
||||
JNZ scal_loop // } while --LEN > 0
|
||||
|
||||
scal_tail:
|
||||
ANDQ $3, TAIL // TAIL = TAIL % 4
|
||||
JZ scal_end // if TAIL == 0 { return }
|
||||
|
||||
scal_tail_loop: // do {
|
||||
MOVUPS (SRC)(IDX*8), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD ALPHA_C, X2 // X_i = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i]) }
|
||||
MULPD ALPHA, X3 // X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
|
||||
// real(result[i]): real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
MOVUPS X3, (DST)(IDX*8) // x[i] = X_(i+1)
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
DECQ TAIL
|
||||
JNZ scal_tail_loop // } while --LEN > 0
|
||||
|
||||
scal_end:
|
||||
RET
|
||||
121
vendor/gonum.org/v1/gonum/internal/asm/c128/scalinc_amd64.s
generated
vendored
Normal file
121
vendor/gonum.org/v1/gonum/internal/asm/c128/scalinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,121 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define SRC SI
|
||||
#define DST SI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC R9
|
||||
#define INC3 R10
|
||||
#define ALPHA X0
|
||||
#define ALPHA_C X1
|
||||
#define ALPHA2 X10
|
||||
#define ALPHA_C2 X11
|
||||
|
||||
#define MOVDDUP_X2_X3 LONG $0xDA120FF2 // MOVDDUP X2, X3
|
||||
#define MOVDDUP_X4_X5 LONG $0xEC120FF2 // MOVDDUP X4, X5
|
||||
#define MOVDDUP_X6_X7 LONG $0xFE120FF2 // MOVDDUP X6, X7
|
||||
#define MOVDDUP_X8_X9 LONG $0x120F45F2; BYTE $0xC8 // MOVDDUP X8, X9
|
||||
|
||||
#define ADDSUBPD_X2_X3 LONG $0xDAD00F66 // ADDSUBPD X2, X3
|
||||
#define ADDSUBPD_X4_X5 LONG $0xECD00F66 // ADDSUBPD X4, X5
|
||||
#define ADDSUBPD_X6_X7 LONG $0xFED00F66 // ADDSUBPD X6, X7
|
||||
#define ADDSUBPD_X8_X9 LONG $0xD00F4566; BYTE $0xC8 // ADDSUBPD X8, X9
|
||||
|
||||
// func ScalInc(alpha complex128, x []complex128, n, inc uintptr)
|
||||
TEXT ·ScalInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+16(FP), SRC // SRC = &x
|
||||
MOVQ n+40(FP), LEN // LEN = len(x)
|
||||
CMPQ LEN, $0
|
||||
JE scal_end // if LEN == 0 { return }
|
||||
|
||||
MOVQ inc+48(FP), INC // INC = inc
|
||||
SHLQ $4, INC // INC = INC * sizeof(complex128)
|
||||
LEAQ (INC)(INC*2), INC3 // INC3 = 3 * INC
|
||||
|
||||
MOVUPS alpha+0(FP), ALPHA // ALPHA = { imag(alpha), real(alpha) }
|
||||
MOVAPS ALPHA, ALPHA_C
|
||||
SHUFPD $0x1, ALPHA_C, ALPHA_C // ALPHA_C = { real(alpha), imag(alpha) }
|
||||
|
||||
MOVAPS ALPHA, ALPHA2 // Copy ALPHA and ALPHA_C for pipelining
|
||||
MOVAPS ALPHA_C, ALPHA_C2
|
||||
MOVQ LEN, TAIL
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ scal_tail // if BX == 0 { goto scal_tail }
|
||||
|
||||
scal_loop: // do {
|
||||
MOVUPS (SRC), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVUPS (SRC)(INC*1), X4
|
||||
MOVUPS (SRC)(INC*2), X6
|
||||
MOVUPS (SRC)(INC3*1), X8
|
||||
|
||||
// X_(i+1) = { real(x[i], real(x[i]) }
|
||||
MOVDDUP_X2_X3
|
||||
MOVDDUP_X4_X5
|
||||
MOVDDUP_X6_X7
|
||||
MOVDDUP_X8_X9
|
||||
|
||||
// X_i = { imag(x[i]), imag(x[i]) }
|
||||
SHUFPD $0x3, X2, X2
|
||||
SHUFPD $0x3, X4, X4
|
||||
SHUFPD $0x3, X6, X6
|
||||
SHUFPD $0x3, X8, X8
|
||||
|
||||
// X_i = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i]) }
|
||||
// X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i]) }
|
||||
MULPD ALPHA_C, X2
|
||||
MULPD ALPHA, X3
|
||||
MULPD ALPHA_C2, X4
|
||||
MULPD ALPHA2, X5
|
||||
MULPD ALPHA_C, X6
|
||||
MULPD ALPHA, X7
|
||||
MULPD ALPHA_C2, X8
|
||||
MULPD ALPHA2, X9
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
|
||||
// real(result[i]): real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
ADDSUBPD_X4_X5
|
||||
ADDSUBPD_X6_X7
|
||||
ADDSUBPD_X8_X9
|
||||
|
||||
MOVUPS X3, (DST) // x[i] = X_(i+1)
|
||||
MOVUPS X5, (DST)(INC*1)
|
||||
MOVUPS X7, (DST)(INC*2)
|
||||
MOVUPS X9, (DST)(INC3*1)
|
||||
|
||||
LEAQ (SRC)(INC*4), SRC // SRC = &(SRC[inc*4])
|
||||
DECQ LEN
|
||||
JNZ scal_loop // } while --BX > 0
|
||||
|
||||
scal_tail:
|
||||
ANDQ $3, TAIL // TAIL = TAIL % 4
|
||||
JE scal_end // if TAIL == 0 { return }
|
||||
|
||||
scal_tail_loop: // do {
|
||||
MOVUPS (SRC), X2 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVDDUP_X2_X3 // X_(i+1) = { real(x[i], real(x[i]) }
|
||||
SHUFPD $0x3, X2, X2 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
MULPD ALPHA_C, X2 // X_i = { real(ALPHA) * imag(x[i]), imag(ALPHA) * imag(x[i]) }
|
||||
MULPD ALPHA, X3 // X_(i+1) = { imag(ALPHA) * real(x[i]), real(ALPHA) * real(x[i]) }
|
||||
|
||||
// X_(i+1) = {
|
||||
// imag(result[i]): imag(ALPHA)*real(x[i]) + real(ALPHA)*imag(x[i]),
|
||||
// real(result[i]): real(ALPHA)*real(x[i]) - imag(ALPHA)*imag(x[i])
|
||||
// }
|
||||
ADDSUBPD_X2_X3
|
||||
|
||||
MOVUPS X3, (DST) // x[i] = X_i
|
||||
ADDQ INC, SRC // SRC = &(SRC[incX])
|
||||
DECQ TAIL
|
||||
JNZ scal_tail_loop // } while --TAIL > 0
|
||||
|
||||
scal_end:
|
||||
RET
|
||||
180
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs.go
generated
vendored
Normal file
180
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs.go
generated
vendored
Normal file
@@ -0,0 +1,180 @@
|
||||
// Copyright ©2020 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package c128
|
||||
|
||||
import (
|
||||
"math"
|
||||
"math/cmplx"
|
||||
)
|
||||
|
||||
// Add is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] += v
|
||||
// }
|
||||
func Add(dst, s []complex128) {
|
||||
for i, v := range s {
|
||||
dst[i] += v
|
||||
}
|
||||
}
|
||||
|
||||
// AddConst is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] += alpha
|
||||
// }
|
||||
func AddConst(alpha complex128, x []complex128) {
|
||||
for i := range x {
|
||||
x[i] += alpha
|
||||
}
|
||||
}
|
||||
|
||||
// CumSum is
|
||||
//
|
||||
// if len(s) == 0 {
|
||||
// return dst
|
||||
// }
|
||||
// dst[0] = s[0]
|
||||
// for i, v := range s[1:] {
|
||||
// dst[i+1] = dst[i] + v
|
||||
// }
|
||||
// return dst
|
||||
func CumSum(dst, s []complex128) []complex128 {
|
||||
if len(s) == 0 {
|
||||
return dst
|
||||
}
|
||||
dst[0] = s[0]
|
||||
for i, v := range s[1:] {
|
||||
dst[i+1] = dst[i] + v
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// CumProd is
|
||||
//
|
||||
// if len(s) == 0 {
|
||||
// return dst
|
||||
// }
|
||||
// dst[0] = s[0]
|
||||
// for i, v := range s[1:] {
|
||||
// dst[i+1] = dst[i] * v
|
||||
// }
|
||||
// return dst
|
||||
func CumProd(dst, s []complex128) []complex128 {
|
||||
if len(s) == 0 {
|
||||
return dst
|
||||
}
|
||||
dst[0] = s[0]
|
||||
for i, v := range s[1:] {
|
||||
dst[i+1] = dst[i] * v
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// Div is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] /= v
|
||||
// }
|
||||
func Div(dst, s []complex128) {
|
||||
for i, v := range s {
|
||||
dst[i] /= v
|
||||
}
|
||||
}
|
||||
|
||||
// DivTo is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] = v / t[i]
|
||||
// }
|
||||
// return dst
|
||||
func DivTo(dst, s, t []complex128) []complex128 {
|
||||
for i, v := range s {
|
||||
dst[i] = v / t[i]
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// DotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += cmplx.Conj(v) * y[i]
|
||||
// }
|
||||
// return sum
|
||||
func DotUnitary(x, y []complex128) (sum complex128) {
|
||||
for i, v := range x {
|
||||
sum += cmplx.Conj(v) * y[i]
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// L2DistanceUnitary returns the L2-norm of x-y.
|
||||
func L2DistanceUnitary(x, y []complex128) (norm float64) {
|
||||
var scale float64
|
||||
sumSquares := 1.0
|
||||
for i, v := range x {
|
||||
v -= y[i]
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := cmplx.Abs(v)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// L2NormUnitary returns the L2-norm of x.
|
||||
func L2NormUnitary(x []complex128) (norm float64) {
|
||||
var scale float64
|
||||
sumSquares := 1.0
|
||||
for _, v := range x {
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := cmplx.Abs(v)
|
||||
if math.IsNaN(absxi) {
|
||||
return math.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math.IsInf(scale, 1) {
|
||||
return math.Inf(1)
|
||||
}
|
||||
return scale * math.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// Sum is
|
||||
//
|
||||
// var sum complex128
|
||||
// for i := range x {
|
||||
// sum += x[i]
|
||||
// }
|
||||
func Sum(x []complex128) complex128 {
|
||||
var sum complex128
|
||||
for _, v := range x {
|
||||
sum += v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
109
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_amd64.go
generated
vendored
Normal file
109
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_amd64.go
generated
vendored
Normal file
@@ -0,0 +1,109 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !noasm && !gccgo && !safe
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
package c128
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha complex128, x, y []complex128)
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []complex128, alpha complex128, x, y []complex128)
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// DscalUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// x[i] = complex(real(v)*alpha, imag(v)*alpha)
|
||||
// }
|
||||
func DscalUnitary(alpha float64, x []complex128)
|
||||
|
||||
// DscalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
|
||||
// ix += inc
|
||||
// }
|
||||
func DscalInc(alpha float64, x []complex128, n, inc uintptr)
|
||||
|
||||
// ScalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] *= alpha
|
||||
// ix += incX
|
||||
// }
|
||||
func ScalInc(alpha complex128, x []complex128, n, inc uintptr)
|
||||
|
||||
// ScalUnitary is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] *= alpha
|
||||
// }
|
||||
func ScalUnitary(alpha complex128, x []complex128)
|
||||
|
||||
// DotcUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * cmplx.Conj(v)
|
||||
// }
|
||||
// return sum
|
||||
func DotcUnitary(x, y []complex128) (sum complex128)
|
||||
|
||||
// DotcInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * cmplx.Conj(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotcInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128)
|
||||
|
||||
// DotuUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotuUnitary(x, y []complex128) (sum complex128)
|
||||
|
||||
// DotuInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotuInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128)
|
||||
176
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_noasm.go
generated
vendored
Normal file
176
vendor/gonum.org/v1/gonum/internal/asm/c128/stubs_noasm.go
generated
vendored
Normal file
@@ -0,0 +1,176 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !amd64 || noasm || gccgo || safe
|
||||
// +build !amd64 noasm gccgo safe
|
||||
|
||||
package c128
|
||||
|
||||
import "math/cmplx"
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha complex128, x, y []complex128) {
|
||||
for i, v := range x {
|
||||
y[i] += alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []complex128, alpha complex128, x, y []complex128) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha*v + y[i]
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
y[iy] += alpha * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []complex128, incDst, idst uintptr, alpha complex128, x, y []complex128, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha*x[ix] + y[iy]
|
||||
ix += incX
|
||||
iy += incY
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
|
||||
// DscalUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// x[i] = complex(real(v)*alpha, imag(v)*alpha)
|
||||
// }
|
||||
func DscalUnitary(alpha float64, x []complex128) {
|
||||
for i, v := range x {
|
||||
x[i] = complex(real(v)*alpha, imag(v)*alpha)
|
||||
}
|
||||
}
|
||||
|
||||
// DscalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
|
||||
// ix += inc
|
||||
// }
|
||||
func DscalInc(alpha float64, x []complex128, n, inc uintptr) {
|
||||
var ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
|
||||
ix += inc
|
||||
}
|
||||
}
|
||||
|
||||
// ScalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] *= alpha
|
||||
// ix += incX
|
||||
// }
|
||||
func ScalInc(alpha complex128, x []complex128, n, inc uintptr) {
|
||||
var ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
x[ix] *= alpha
|
||||
ix += inc
|
||||
}
|
||||
}
|
||||
|
||||
// ScalUnitary is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] *= alpha
|
||||
// }
|
||||
func ScalUnitary(alpha complex128, x []complex128) {
|
||||
for i := range x {
|
||||
x[i] *= alpha
|
||||
}
|
||||
}
|
||||
|
||||
// DotcUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * cmplx.Conj(v)
|
||||
// }
|
||||
// return sum
|
||||
func DotcUnitary(x, y []complex128) (sum complex128) {
|
||||
for i, v := range x {
|
||||
sum += y[i] * cmplx.Conj(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotcInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * cmplx.Conj(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotcInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += y[iy] * cmplx.Conj(x[ix])
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotuUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotuUnitary(x, y []complex128) (sum complex128) {
|
||||
for i, v := range x {
|
||||
sum += y[i] * v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotuInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotuInc(x, y []complex128, n, incX, incY, ix, iy uintptr) (sum complex128) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += y[iy] * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return sum
|
||||
}
|
||||
151
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyinc_amd64.s
generated
vendored
Normal file
151
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,151 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
|
||||
// MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
|
||||
// ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
|
||||
// MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
|
||||
// MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
|
||||
// ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
|
||||
// MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
|
||||
// MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
|
||||
// ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
|
||||
// MOVSHDUP X9, X8
|
||||
#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
|
||||
// MOVSLDUP X9, X9
|
||||
#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
|
||||
// ADDSUBPS X8, X9
|
||||
#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SI // SI = &x
|
||||
MOVQ y_base+32(FP), DI // DI = &y
|
||||
MOVQ n+56(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JE axpyi_end
|
||||
MOVQ ix+80(FP), R8 // R8 = ix
|
||||
MOVQ iy+88(FP), R9 // R9 = iy
|
||||
LEAQ (SI)(R8*8), SI // SI = &(x[ix])
|
||||
LEAQ (DI)(R9*8), DI // DI = &(y[iy])
|
||||
MOVQ DI, DX // DX = DI // Read/Write pointers
|
||||
MOVQ incX+64(FP), R8 // R8 = incX
|
||||
SHLQ $3, R8 // R8 *= sizeof(complex64)
|
||||
MOVQ incY+72(FP), R9 // R9 = incY
|
||||
SHLQ $3, R9 // R9 *= sizeof(complex64)
|
||||
MOVSD alpha+0(FP), X0 // X0 = { 0, 0, imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPS $0x11, X1, X1 // X1 = { 0, 0, real(a), imag(a) }
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ axpyi_tail // if BX == 0 { goto axpyi_tail }
|
||||
|
||||
axpyi_loop: // do {
|
||||
MOVSD (SI), X3 // X_i = { imag(x[i+1]), real(x[i+1]) }
|
||||
MOVSD (SI)(R8*1), X5
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
MOVSD (SI), X7
|
||||
MOVSD (SI)(R8*1), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
MULPS X11, X4
|
||||
MULPS X10, X5
|
||||
MULPS X1, X6
|
||||
MULPS X0, X7
|
||||
MULPS X11, X8
|
||||
MULPS X10, X9
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
MOVSD (DX), X2
|
||||
MOVSD (DX)(R9*1), X4
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
MOVSD (DX), X6
|
||||
MOVSD (DX)(R9*1), X8
|
||||
ADDPS X2, X3
|
||||
ADDPS X4, X5
|
||||
ADDPS X6, X7
|
||||
ADDPS X8, X9
|
||||
|
||||
MOVSD X3, (DI) // y[i] = X_i
|
||||
MOVSD X5, (DI)(R9*1)
|
||||
LEAQ (DI)(R9*2), DI // DI = &(DI[incDst])
|
||||
MOVSD X7, (DI)
|
||||
MOVSD X9, (DI)(R9*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R9*2), DI // DI = &(DI[incDst])
|
||||
DECQ BX
|
||||
JNZ axpyi_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail: // do {
|
||||
MOVSD (SI), X3 // X_i = { imag(x[i+1]), real(x[i+1]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { real(x[i]), real(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { imag(x[i]), imag(x[i]) }
|
||||
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3 // (ai*x1r+ar*x1i, ar*x1r-ai*x1i)
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
MOVSD (DI), X4
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI) // y[i] = X_i
|
||||
ADDQ R8, SI // SI += incX
|
||||
ADDQ R9, DI // DI += incY
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
156
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyincto_amd64.s
generated
vendored
Normal file
156
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyincto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,156 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
|
||||
// MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
|
||||
// ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
|
||||
// MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
|
||||
// MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
|
||||
// ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
|
||||
// MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
|
||||
// MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
|
||||
// ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
|
||||
// MOVSHDUP X9, X8
|
||||
#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
|
||||
// MOVSLDUP X9, X9
|
||||
#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
|
||||
// ADDSUBPS X8, X9
|
||||
#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyIncTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+48(FP), SI // SI = &x
|
||||
MOVQ y_base+72(FP), DX // DX = &y
|
||||
MOVQ n+96(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JE axpyi_end
|
||||
MOVQ ix+120(FP), R8 // Load the first index
|
||||
MOVQ iy+128(FP), R9
|
||||
MOVQ idst+32(FP), R10
|
||||
LEAQ (SI)(R8*8), SI // SI = &(x[ix])
|
||||
LEAQ (DX)(R9*8), DX // DX = &(y[iy])
|
||||
LEAQ (DI)(R10*8), DI // DI = &(dst[idst])
|
||||
MOVQ incX+104(FP), R8 // Incrementors*8 for easy iteration (ADDQ)
|
||||
SHLQ $3, R8
|
||||
MOVQ incY+112(FP), R9
|
||||
SHLQ $3, R9
|
||||
MOVQ incDst+24(FP), R10
|
||||
SHLQ $3, R10
|
||||
MOVSD alpha+40(FP), X0 // X0 = { 0, 0, imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPS $0x11, X1, X1 // X1 = { 0, 0, real(a), imag(a) }
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelining
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, CX // CX = n % 4
|
||||
SHRQ $2, BX // BX = floor( n / 4 )
|
||||
JZ axpyi_tail // if BX == 0 { goto axpyi_tail }
|
||||
|
||||
axpyi_loop: // do {
|
||||
MOVSD (SI), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSD (SI)(R8*1), X5
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
MOVSD (SI), X7
|
||||
MOVSD (SI)(R8*1), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
MULPS X11, X4
|
||||
MULPS X10, X5
|
||||
MULPS X1, X6
|
||||
MULPS X0, X7
|
||||
MULPS X11, X8
|
||||
MULPS X10, X9
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
MOVSD (DX), X2
|
||||
MOVSD (DX)(R9*1), X4
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
MOVSD (DX), X6
|
||||
MOVSD (DX)(R9*1), X8
|
||||
ADDPS X2, X3
|
||||
ADDPS X4, X5
|
||||
ADDPS X6, X7
|
||||
ADDPS X8, X9
|
||||
|
||||
MOVSD X3, (DI) // y[i] = X_i
|
||||
MOVSD X5, (DI)(R10*1)
|
||||
LEAQ (DI)(R10*2), DI // DI = &(DI[incDst])
|
||||
MOVSD X7, (DI)
|
||||
MOVSD X9, (DI)(R10*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R10*2), DI // DI = &(DI[incDst])
|
||||
DECQ BX
|
||||
JNZ axpyi_loop // } while --BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail:
|
||||
MOVSD (SI), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]) }
|
||||
MOVSD (DX), X4
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI) // y[i] = X_i
|
||||
ADDQ R8, SI // SI += incX
|
||||
ADDQ R9, DX // DX += incY
|
||||
ADDQ R10, DI // DI += incDst
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
160
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitary_amd64.s
generated
vendored
Normal file
160
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,160 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
|
||||
// MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
|
||||
// ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
|
||||
// MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
|
||||
// MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
|
||||
// ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
|
||||
// MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
|
||||
// MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
|
||||
// ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
|
||||
// MOVSHDUP X9, X8
|
||||
#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
|
||||
// MOVSLDUP X9, X9
|
||||
#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
|
||||
// ADDSUBPS X8, X9
|
||||
#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyUnitary(alpha complex64, x, y []complex64)
|
||||
TEXT ·AxpyUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SI // SI = &x
|
||||
MOVQ y_base+32(FP), DI // DI = &y
|
||||
MOVQ x_len+16(FP), CX // CX = min( len(x), len(y) )
|
||||
CMPQ y_len+40(FP), CX
|
||||
CMOVQLE y_len+40(FP), CX
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
PXOR X0, X0 // Clear work registers and cache-align loop
|
||||
PXOR X1, X1
|
||||
MOVSD alpha+0(FP), X0 // X0 = { 0, 0, imag(a), real(a) }
|
||||
SHUFPD $0, X0, X0 // X0 = { imag(a), real(a), imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPS $0x11, X1, X1 // X1 = { real(a), imag(a), real(a), imag(a) }
|
||||
XORQ AX, AX // i = 0
|
||||
MOVQ DI, BX // Align on 16-byte boundary for ADDPS
|
||||
ANDQ $15, BX // BX = &y & 15
|
||||
JZ caxy_no_trim // if BX == 0 { goto caxy_no_trim }
|
||||
|
||||
// Trim first value in unaligned buffer
|
||||
XORPS X2, X2 // Clear work registers and cache-align loop
|
||||
XORPS X3, X3
|
||||
XORPS X4, X4
|
||||
MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X2 = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X3 = { real(x[i]), real(x[i]) }
|
||||
MULPS X1, X2 // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X0, X3 // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]), real(a)*real(x[i]) - imag(a)*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
MOVSD (DI)(AX*8), X4 // X3 += y[i]
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI)(AX*8) // y[i] = X3
|
||||
INCQ AX // i++
|
||||
DECQ CX // --CX
|
||||
JZ caxy_end // if CX == 0 { return }
|
||||
|
||||
caxy_no_trim:
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelineing
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, CX // CX = n % 8
|
||||
SHRQ $3, BX // BX = floor( n / 8 )
|
||||
JZ caxy_tail // if BX == 0 { goto caxy_tail }
|
||||
|
||||
caxy_loop: // do {
|
||||
// X_i = { imag(x[i]), real(x[i]), imag(x[i+1]), real(x[i+1]) }
|
||||
MOVUPS (SI)(AX*8), X3
|
||||
MOVUPS 16(SI)(AX*8), X5
|
||||
MOVUPS 32(SI)(AX*8), X7
|
||||
MOVUPS 48(SI)(AX*8), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]),
|
||||
// imag(a) * real(x[i+1]), real(a) * real(x[i+1]) }
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]),
|
||||
// real(a) * imag(x[i+1]), imag(a) * imag(x[i+1]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
MULPS X11, X4
|
||||
MULPS X10, X5
|
||||
MULPS X1, X6
|
||||
MULPS X0, X7
|
||||
MULPS X11, X8
|
||||
MULPS X10, X9
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// imag(result[i+1]): imag(a)*real(x[i+1]) + real(a)*imag(x[i+1]),
|
||||
// real(result[i+1]): real(a)*real(x[i+1]) - imag(a)*imag(x[i+1]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]),
|
||||
// imag(result[i+1]) + imag(y[i+1]), real(result[i+1]) + real(y[i+1]) }
|
||||
ADDPS (DI)(AX*8), X3
|
||||
ADDPS 16(DI)(AX*8), X5
|
||||
ADDPS 32(DI)(AX*8), X7
|
||||
ADDPS 48(DI)(AX*8), X9
|
||||
MOVUPS X3, (DI)(AX*8) // y[i:i+1] = X_i
|
||||
MOVUPS X5, 16(DI)(AX*8)
|
||||
MOVUPS X7, 32(DI)(AX*8)
|
||||
MOVUPS X9, 48(DI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
DECQ BX // --BX
|
||||
JNZ caxy_loop // } while BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
|
||||
caxy_tail: // do {
|
||||
MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X2 = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X3 = { real(x[i]), real(x[i]) }
|
||||
MULPS X1, X2 // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X0, X3 // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(a)*real(x[i]) - imag(a)*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
MOVSD (DI)(AX*8), X4 // X3 += y[i]
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI)(AX*8) // y[i] = X3
|
||||
INCQ AX // ++i
|
||||
LOOP caxy_tail // } while --CX > 0
|
||||
|
||||
caxy_end:
|
||||
RET
|
||||
157
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitaryto_amd64.s
generated
vendored
Normal file
157
vendor/gonum.org/v1/gonum/internal/asm/c64/axpyunitaryto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,157 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X3_X2 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xD3
|
||||
// MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X3_X3 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xDB
|
||||
// ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X2_X3 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xDA
|
||||
|
||||
// MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X5_X4 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xE5
|
||||
// MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X5_X5 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xED
|
||||
// ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X4_X5 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xEC
|
||||
|
||||
// MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X7_X6 BYTE $0xF3; BYTE $0x0F; BYTE $0x16; BYTE $0xF7
|
||||
// MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X7_X7 BYTE $0xF3; BYTE $0x0F; BYTE $0x12; BYTE $0xFF
|
||||
// ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X6_X7 BYTE $0xF2; BYTE $0x0F; BYTE $0xD0; BYTE $0xFE
|
||||
|
||||
// MOVSHDUP X9, X8
|
||||
#define MOVSHDUP_X9_X8 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x16; BYTE $0xC1
|
||||
// MOVSLDUP X9, X9
|
||||
#define MOVSLDUP_X9_X9 BYTE $0xF3; BYTE $0x45; BYTE $0x0F; BYTE $0x12; BYTE $0xC9
|
||||
// ADDSUBPS X8, X9
|
||||
#define ADDSUBPS_X8_X9 BYTE $0xF2; BYTE $0x45; BYTE $0x0F; BYTE $0xD0; BYTE $0xC8
|
||||
|
||||
// func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64)
|
||||
TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+32(FP), SI // SI = &x
|
||||
MOVQ y_base+56(FP), DX // DX = &y
|
||||
MOVQ x_len+40(FP), CX
|
||||
CMPQ y_len+64(FP), CX // CX = min( len(x), len(y), len(dst) )
|
||||
CMOVQLE y_len+64(FP), CX
|
||||
CMPQ dst_len+8(FP), CX
|
||||
CMOVQLE dst_len+8(FP), CX
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
MOVSD alpha+24(FP), X0 // X0 = { 0, 0, imag(a), real(a) }
|
||||
SHUFPD $0, X0, X0 // X0 = { imag(a), real(a), imag(a), real(a) }
|
||||
MOVAPS X0, X1
|
||||
SHUFPS $0x11, X1, X1 // X1 = { real(a), imag(a), real(a), imag(a) }
|
||||
XORQ AX, AX // i = 0
|
||||
MOVQ DX, BX // Align on 16-byte boundary for ADDPS
|
||||
ANDQ $15, BX // BX = &y & 15
|
||||
JZ caxy_no_trim // if BX == 0 { goto caxy_no_trim }
|
||||
|
||||
MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X2 = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X3 = { real(x[i]), real(x[i]) }
|
||||
MULPS X1, X2 // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X0, X3 // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]), real(a)*real(x[i]) - imag(a)*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
MOVSD (DX)(AX*8), X4 // X3 += y[i]
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI)(AX*8) // dst[i] = X3
|
||||
INCQ AX // i++
|
||||
DECQ CX // --CX
|
||||
JZ caxy_tail // if BX == 0 { goto caxy_tail }
|
||||
|
||||
caxy_no_trim:
|
||||
MOVAPS X0, X10 // Copy X0 and X1 for pipelineing
|
||||
MOVAPS X1, X11
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, CX // CX = n % 8
|
||||
SHRQ $3, BX // BX = floor( n / 8 )
|
||||
JZ caxy_tail // if BX == 0 { goto caxy_tail }
|
||||
|
||||
caxy_loop:
|
||||
// X_i = { imag(x[i]), real(x[i]), imag(x[i+1]), real(x[i+1]) }
|
||||
MOVUPS (SI)(AX*8), X3
|
||||
MOVUPS 16(SI)(AX*8), X5
|
||||
MOVUPS 32(SI)(AX*8), X7
|
||||
MOVUPS 48(SI)(AX*8), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_i = { imag(a) * real(x[i]), real(a) * real(x[i]),
|
||||
// imag(a) * real(x[i+1]), real(a) * real(x[i+1]) }
|
||||
// X_(i-1) = { real(a) * imag(x[i]), imag(a) * imag(x[i]),
|
||||
// real(a) * imag(x[i+1]), imag(a) * imag(x[i+1]) }
|
||||
MULPS X1, X2
|
||||
MULPS X0, X3
|
||||
MULPS X11, X4
|
||||
MULPS X10, X5
|
||||
MULPS X1, X6
|
||||
MULPS X0, X7
|
||||
MULPS X11, X8
|
||||
MULPS X10, X9
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(result[i]): real(a)*real(x[i]) - imag(a)*imag(x[i]),
|
||||
// imag(result[i+1]): imag(a)*real(x[i+1]) + real(a)*imag(x[i+1]),
|
||||
// real(result[i+1]): real(a)*real(x[i+1]) - imag(a)*imag(x[i+1]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// X_i = { imag(result[i]) + imag(y[i]), real(result[i]) + real(y[i]),
|
||||
// imag(result[i+1]) + imag(y[i+1]), real(result[i+1]) + real(y[i+1]) }
|
||||
ADDPS (DX)(AX*8), X3
|
||||
ADDPS 16(DX)(AX*8), X5
|
||||
ADDPS 32(DX)(AX*8), X7
|
||||
ADDPS 48(DX)(AX*8), X9
|
||||
MOVUPS X3, (DI)(AX*8) // y[i:i+1] = X_i
|
||||
MOVUPS X5, 16(DI)(AX*8)
|
||||
MOVUPS X7, 32(DI)(AX*8)
|
||||
MOVUPS X9, 48(DI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
DECQ BX // --BX
|
||||
JNZ caxy_loop // } while BX > 0
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE caxy_end
|
||||
|
||||
caxy_tail: // do {
|
||||
MOVSD (SI)(AX*8), X3 // X3 = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X2 = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X3 = { real(x[i]), real(x[i]) }
|
||||
MULPS X1, X2 // X2 = { real(a) * imag(x[i]), imag(a) * imag(x[i]) }
|
||||
MULPS X0, X3 // X3 = { imag(a) * real(x[i]), real(a) * real(x[i]) }
|
||||
|
||||
// X3 = { imag(a)*real(x[i]) + real(a)*imag(x[i]),
|
||||
// real(a)*real(x[i]) - imag(a)*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
MOVSD (DX)(AX*8), X4 // X3 += y[i]
|
||||
ADDPS X4, X3
|
||||
MOVSD X3, (DI)(AX*8) // y[i] = X3
|
||||
INCQ AX // ++i
|
||||
LOOP caxy_tail // } while --CX > 0
|
||||
|
||||
caxy_end:
|
||||
RET
|
||||
7
vendor/gonum.org/v1/gonum/internal/asm/c64/conj.go
generated
vendored
Normal file
7
vendor/gonum.org/v1/gonum/internal/asm/c64/conj.go
generated
vendored
Normal file
@@ -0,0 +1,7 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package c64
|
||||
|
||||
func conj(c complex64) complex64 { return complex(real(c), -imag(c)) }
|
||||
6
vendor/gonum.org/v1/gonum/internal/asm/c64/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/internal/asm/c64/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package c64 provides complex64 vector primitives.
|
||||
package c64 // import "gonum.org/v1/gonum/internal/asm/c64"
|
||||
160
vendor/gonum.org/v1/gonum/internal/asm/c64/dotcinc_amd64.s
generated
vendored
Normal file
160
vendor/gonum.org/v1/gonum/internal/asm/c64/dotcinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,160 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVSHDUP_X3_X2 LONG $0xD3160FF3 // MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X5_X4 LONG $0xE5160FF3 // MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X7_X6 LONG $0xF7160FF3 // MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X9_X8 LONG $0x160F45F3; BYTE $0xC1 // MOVSHDUP X9, X8
|
||||
|
||||
#define MOVSLDUP_X3_X3 LONG $0xDB120FF3 // MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X5_X5 LONG $0xED120FF3 // MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X7_X7 LONG $0xFF120FF3 // MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X9_X9 LONG $0x120F45F3; BYTE $0xC9 // MOVSLDUP X9, X9
|
||||
|
||||
#define ADDSUBPS_X2_X3 LONG $0xDAD00FF2 // ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X4_X5 LONG $0xECD00FF2 // ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X6_X7 LONG $0xFED00FF2 // ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X8_X9 LONG $0xD00F45F2; BYTE $0xC8 // ADDSUBPS X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define INC_X R8
|
||||
#define INCx3_X R9
|
||||
#define INC_Y R10
|
||||
#define INCx3_Y R11
|
||||
#define NEG1 X15
|
||||
#define P_NEG1 X14
|
||||
|
||||
// func DotcInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64)
|
||||
TEXT ·DotcInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dotc_end
|
||||
MOVQ ix+72(FP), INC_X
|
||||
MOVQ iy+80(FP), INC_Y
|
||||
LEAQ (X_PTR)(INC_X*8), X_PTR // X_PTR = &(X_PTR[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*8), Y_PTR // Y_PTR = &(Y_PTR[iy])
|
||||
MOVQ incX+56(FP), INC_X // INC_X = incX * sizeof(complex64)
|
||||
SHLQ $3, INC_X
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y = incY * sizeof(complex64)
|
||||
SHLQ $3, INC_Y
|
||||
MOVSS $(-1.0), NEG1
|
||||
SHUFPS $0, NEG1, NEG1 // { -1, -1, -1, -1 }
|
||||
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = LEN % 4
|
||||
SHRQ $2, LEN // LEN = floor( LEN / 4 )
|
||||
JZ dotc_tail // if LEN == 0 { goto dotc_tail }
|
||||
|
||||
MOVUPS NEG1, P_NEG1 // Copy NEG1 for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
|
||||
dotc_loop: // do {
|
||||
MOVSD (X_PTR), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSD (X_PTR)(INC_X*1), X5
|
||||
MOVSD (X_PTR)(INC_X*2), X7
|
||||
MOVSD (X_PTR)(INCx3_X*1), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_(i-1) = { -imag(x[i]), -imag(x[i]) }
|
||||
MULPS NEG1, X2
|
||||
MULPS P_NEG1, X4
|
||||
MULPS NEG1, X6
|
||||
MULPS P_NEG1, X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVSD (Y_PTR), X10
|
||||
MOVSD (Y_PTR)(INC_Y*1), X11
|
||||
MOVSD (Y_PTR)(INC_Y*2), X12
|
||||
MOVSD (Y_PTR)(INCx3_Y*1), X13
|
||||
|
||||
// X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
MULPS X10, X3
|
||||
MULPS X11, X5
|
||||
MULPS X12, X7
|
||||
MULPS X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPS $0xB1, X10, X10
|
||||
SHUFPS $0xB1, X11, X11
|
||||
SHUFPS $0xB1, X12, X12
|
||||
SHUFPS $0xB1, X13, X13
|
||||
|
||||
// X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
MULPS X10, X2
|
||||
MULPS X11, X4
|
||||
MULPS X12, X6
|
||||
MULPS X13, X8
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i]) * real(x[i]) + real(y[i]) * imag(x[i]),
|
||||
// real(result[i]): real(y[i]) * real(x[i]) - imag(y[i]) * imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// SUM += X_i
|
||||
ADDPS X3, SUM
|
||||
ADDPS X5, P_SUM
|
||||
ADDPS X7, SUM
|
||||
ADDPS X9, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[INC_X*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[INC_Y*4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dotc_loop // } while --LEN > 0
|
||||
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM + SUM }
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dotc_end
|
||||
|
||||
dotc_tail: // do {
|
||||
MOVSD (X_PTR), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MULPS NEG1, X2 // X_(i-1) = { -imag(x[i]), imag(x[i]) }
|
||||
MOVUPS (Y_PTR), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
ADDQ INC_X, X_PTR // X_PTR += INC_X
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += INC_Y
|
||||
DECQ TAIL
|
||||
JNZ dotc_tail // } while --TAIL > 0
|
||||
|
||||
dotc_end:
|
||||
MOVSD SUM, sum+88(FP) // return SUM
|
||||
RET
|
||||
208
vendor/gonum.org/v1/gonum/internal/asm/c64/dotcunitary_amd64.s
generated
vendored
Normal file
208
vendor/gonum.org/v1/gonum/internal/asm/c64/dotcunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,208 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVSLDUP_XPTR_IDX_8__X3 LONG $0x1C120FF3; BYTE $0xC6 // MOVSLDUP (SI)(AX*8), X3
|
||||
#define MOVSLDUP_16_XPTR_IDX_8__X5 LONG $0x6C120FF3; WORD $0x10C6 // MOVSLDUP 16(SI)(AX*8), X5
|
||||
#define MOVSLDUP_32_XPTR_IDX_8__X7 LONG $0x7C120FF3; WORD $0x20C6 // MOVSLDUP 32(SI)(AX*8), X7
|
||||
#define MOVSLDUP_48_XPTR_IDX_8__X9 LONG $0x120F44F3; WORD $0xC64C; BYTE $0x30 // MOVSLDUP 48(SI)(AX*8), X9
|
||||
|
||||
#define MOVSHDUP_XPTR_IDX_8__X2 LONG $0x14160FF3; BYTE $0xC6 // MOVSHDUP (SI)(AX*8), X2
|
||||
#define MOVSHDUP_16_XPTR_IDX_8__X4 LONG $0x64160FF3; WORD $0x10C6 // MOVSHDUP 16(SI)(AX*8), X4
|
||||
#define MOVSHDUP_32_XPTR_IDX_8__X6 LONG $0x74160FF3; WORD $0x20C6 // MOVSHDUP 32(SI)(AX*8), X6
|
||||
#define MOVSHDUP_48_XPTR_IDX_8__X8 LONG $0x160F44F3; WORD $0xC644; BYTE $0x30 // MOVSHDUP 48(SI)(AX*8), X8
|
||||
|
||||
#define MOVSHDUP_X3_X2 LONG $0xD3160FF3 // MOVSHDUP X3, X2
|
||||
#define MOVSLDUP_X3_X3 LONG $0xDB120FF3 // MOVSLDUP X3, X3
|
||||
|
||||
#define ADDSUBPS_X2_X3 LONG $0xDAD00FF2 // ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X4_X5 LONG $0xECD00FF2 // ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X6_X7 LONG $0xFED00FF2 // ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X8_X9 LONG $0xD00F45F2; BYTE $0xC8 // ADDSUBPS X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define IDX AX
|
||||
#define I_IDX DX
|
||||
#define NEG1 X15
|
||||
#define P_NEG1 X14
|
||||
|
||||
// func DotcUnitary(x, y []complex64) (sum complex64)
|
||||
TEXT ·DotcUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dotc_end
|
||||
XORQ IDX, IDX // i = 0
|
||||
MOVSS $(-1.0), NEG1
|
||||
SHUFPS $0, NEG1, NEG1 // { -1, -1, -1, -1 }
|
||||
|
||||
MOVQ X_PTR, DX
|
||||
ANDQ $15, DX // DX = &x & 15
|
||||
JZ dotc_aligned // if DX == 0 { goto dotc_aligned }
|
||||
|
||||
MOVSD (X_PTR)(IDX*8), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSD (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS NEG1, X2 // X_(i-1) = { -imag(x[i]), imag(x[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
MOVAPS X3, SUM // SUM = X_i
|
||||
INCQ IDX // IDX++
|
||||
DECQ LEN // LEN--
|
||||
JZ dotc_ret // if LEN == 0 { goto dotc_ret }
|
||||
|
||||
dotc_aligned:
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $7, TAIL // TAIL = LEN % 8
|
||||
SHRQ $3, LEN // LEN = floor( LEN / 8 )
|
||||
JZ dotc_tail // if LEN == 0 { return }
|
||||
MOVUPS NEG1, P_NEG1 // Copy NEG1 for pipelining
|
||||
|
||||
dotc_loop: // do {
|
||||
MOVSLDUP_XPTR_IDX_8__X3 // X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSLDUP_16_XPTR_IDX_8__X5
|
||||
MOVSLDUP_32_XPTR_IDX_8__X7
|
||||
MOVSLDUP_48_XPTR_IDX_8__X9
|
||||
|
||||
MOVSHDUP_XPTR_IDX_8__X2 // X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i+1]), imag(x[i+1]) }
|
||||
MOVSHDUP_16_XPTR_IDX_8__X4
|
||||
MOVSHDUP_32_XPTR_IDX_8__X6
|
||||
MOVSHDUP_48_XPTR_IDX_8__X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]), imag(y[i+1]), real(y[i+1]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10
|
||||
MOVUPS 16(Y_PTR)(IDX*8), X11
|
||||
MOVUPS 32(Y_PTR)(IDX*8), X12
|
||||
MOVUPS 48(Y_PTR)(IDX*8), X13
|
||||
|
||||
// X_(i-1) = { -imag(x[i]), -imag(x[i]), -imag(x[i]+1), -imag(x[i]+1) }
|
||||
MULPS NEG1, X2
|
||||
MULPS P_NEG1, X4
|
||||
MULPS NEG1, X6
|
||||
MULPS P_NEG1, X8
|
||||
|
||||
// X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]),
|
||||
// imag(y[i+1]) * real(x[i+1]), real(y[i+1]) * real(x[i+1]) }
|
||||
MULPS X10, X3
|
||||
MULPS X11, X5
|
||||
MULPS X12, X7
|
||||
MULPS X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]), real(y[i+1]), imag(y[i+1]) }
|
||||
SHUFPS $0xB1, X10, X10
|
||||
SHUFPS $0xB1, X11, X11
|
||||
SHUFPS $0xB1, X12, X12
|
||||
SHUFPS $0xB1, X13, X13
|
||||
|
||||
// X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]),
|
||||
// real(y[i+1]) * imag(x[i+1]), imag(y[i+1]) * imag(x[i+1]) }
|
||||
MULPS X10, X2
|
||||
MULPS X11, X4
|
||||
MULPS X12, X6
|
||||
MULPS X13, X8
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i]) * real(x[i]) + real(y[i]) * imag(x[i]),
|
||||
// real(result[i]): real(y[i]) * real(x[i]) - imag(y[i]) * imag(x[i]),
|
||||
// imag(result[i+1]): imag(y[i+1]) * real(x[i+1]) + real(y[i+1]) * imag(x[i+1]),
|
||||
// real(result[i+1]): real(y[i+1]) * real(x[i+1]) - imag(y[i+1]) * imag(x[i+1]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// SUM += X_i
|
||||
ADDPS X3, SUM
|
||||
ADDPS X5, P_SUM
|
||||
ADDPS X7, SUM
|
||||
ADDPS X9, P_SUM
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dotc_loop // } while --LEN > 0
|
||||
|
||||
ADDPS SUM, P_SUM // P_SUM = { P_SUM[1] + SUM[1], P_SUM[0] + SUM[0] }
|
||||
XORPS SUM, SUM // SUM = 0
|
||||
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dotc_end
|
||||
|
||||
dotc_tail:
|
||||
MOVQ TAIL, LEN
|
||||
SHRQ $1, LEN // LEN = floor( LEN / 2 )
|
||||
JZ dotc_tail_one // if LEN == 0 { goto dotc_tail_one }
|
||||
|
||||
dotc_tail_two: // do {
|
||||
MOVSLDUP_XPTR_IDX_8__X3 // X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSHDUP_XPTR_IDX_8__X2 // X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS NEG1, X2 // X_(i-1) = { -imag(x[i]), imag(x[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0xB1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
DECQ LEN
|
||||
JNZ dotc_tail_two // } while --LEN > 0
|
||||
|
||||
ADDPS SUM, P_SUM // P_SUM = { P_SUM[1] + SUM[1], P_SUM[0] + SUM[0] }
|
||||
XORPS SUM, SUM // SUM = 0
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ dotc_end
|
||||
|
||||
dotc_tail_one:
|
||||
MOVSD (X_PTR)(IDX*8), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSD (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS NEG1, X2 // X_(i-1) = { -imag(x[i]), imag(x[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
|
||||
dotc_end:
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM[0] + SUM[0] }
|
||||
MOVHLPS P_SUM, P_SUM // P_SUM = { P_SUM[1], P_SUM[1] }
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM[1] + SUM[0] }
|
||||
|
||||
dotc_ret:
|
||||
MOVSD SUM, sum+48(FP) // return SUM
|
||||
RET
|
||||
148
vendor/gonum.org/v1/gonum/internal/asm/c64/dotuinc_amd64.s
generated
vendored
Normal file
148
vendor/gonum.org/v1/gonum/internal/asm/c64/dotuinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,148 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVSHDUP_X3_X2 LONG $0xD3160FF3 // MOVSHDUP X3, X2
|
||||
#define MOVSHDUP_X5_X4 LONG $0xE5160FF3 // MOVSHDUP X5, X4
|
||||
#define MOVSHDUP_X7_X6 LONG $0xF7160FF3 // MOVSHDUP X7, X6
|
||||
#define MOVSHDUP_X9_X8 LONG $0x160F45F3; BYTE $0xC1 // MOVSHDUP X9, X8
|
||||
|
||||
#define MOVSLDUP_X3_X3 LONG $0xDB120FF3 // MOVSLDUP X3, X3
|
||||
#define MOVSLDUP_X5_X5 LONG $0xED120FF3 // MOVSLDUP X5, X5
|
||||
#define MOVSLDUP_X7_X7 LONG $0xFF120FF3 // MOVSLDUP X7, X7
|
||||
#define MOVSLDUP_X9_X9 LONG $0x120F45F3; BYTE $0xC9 // MOVSLDUP X9, X9
|
||||
|
||||
#define ADDSUBPS_X2_X3 LONG $0xDAD00FF2 // ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X4_X5 LONG $0xECD00FF2 // ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X6_X7 LONG $0xFED00FF2 // ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X8_X9 LONG $0xD00F45F2; BYTE $0xC8 // ADDSUBPS X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define INC_X R8
|
||||
#define INCx3_X R9
|
||||
#define INC_Y R10
|
||||
#define INCx3_Y R11
|
||||
|
||||
// func DotuInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64)
|
||||
TEXT ·DotuInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dotu_end
|
||||
MOVQ ix+72(FP), INC_X
|
||||
MOVQ iy+80(FP), INC_Y
|
||||
LEAQ (X_PTR)(INC_X*8), X_PTR // X_PTR = &(X_PTR[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*8), Y_PTR // Y_PTR = &(Y_PTR[iy])
|
||||
MOVQ incX+56(FP), INC_X // INC_X = incX * sizeof(complex64)
|
||||
SHLQ $3, INC_X
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y = incY * sizeof(complex64)
|
||||
SHLQ $3, INC_Y
|
||||
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = LEN % 4
|
||||
SHRQ $2, LEN // LEN = floor( LEN / 4 )
|
||||
JZ dotu_tail // if TAIL == 0 { goto dotu_tail }
|
||||
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
|
||||
dotu_loop: // do {
|
||||
MOVSD (X_PTR), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSD (X_PTR)(INC_X*1), X5
|
||||
MOVSD (X_PTR)(INC_X*2), X7
|
||||
MOVSD (X_PTR)(INCx3_X*1), X9
|
||||
|
||||
// X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSHDUP_X3_X2
|
||||
MOVSHDUP_X5_X4
|
||||
MOVSHDUP_X7_X6
|
||||
MOVSHDUP_X9_X8
|
||||
|
||||
// X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSLDUP_X3_X3
|
||||
MOVSLDUP_X5_X5
|
||||
MOVSLDUP_X7_X7
|
||||
MOVSLDUP_X9_X9
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]) }
|
||||
MOVSD (Y_PTR), X10
|
||||
MOVSD (Y_PTR)(INC_Y*1), X11
|
||||
MOVSD (Y_PTR)(INC_Y*2), X12
|
||||
MOVSD (Y_PTR)(INCx3_Y*1), X13
|
||||
|
||||
// X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
MULPS X10, X3
|
||||
MULPS X11, X5
|
||||
MULPS X12, X7
|
||||
MULPS X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]) }
|
||||
SHUFPS $0xB1, X10, X10
|
||||
SHUFPS $0xB1, X11, X11
|
||||
SHUFPS $0xB1, X12, X12
|
||||
SHUFPS $0xB1, X13, X13
|
||||
|
||||
// X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
MULPS X10, X2
|
||||
MULPS X11, X4
|
||||
MULPS X12, X6
|
||||
MULPS X13, X8
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i]) * real(x[i]) + real(y[i]) * imag(x[i]),
|
||||
// real(result[i]): real(y[i]) * real(x[i]) - imag(y[i]) * imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// SUM += X_i
|
||||
ADDPS X3, SUM
|
||||
ADDPS X5, P_SUM
|
||||
ADDPS X7, SUM
|
||||
ADDPS X9, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[INC_X*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[INC_Y*4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dotu_loop // } while --LEN > 0
|
||||
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM + SUM }
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dotu_end
|
||||
|
||||
dotu_tail: // do {
|
||||
MOVSD (X_PTR), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MOVUPS (Y_PTR), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
ADDQ INC_X, X_PTR // X_PTR += INC_X
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += INC_Y
|
||||
DECQ TAIL
|
||||
JNZ dotu_tail // } while --TAIL > 0
|
||||
|
||||
dotu_end:
|
||||
MOVSD SUM, sum+88(FP) // return SUM
|
||||
RET
|
||||
197
vendor/gonum.org/v1/gonum/internal/asm/c64/dotuunitary_amd64.s
generated
vendored
Normal file
197
vendor/gonum.org/v1/gonum/internal/asm/c64/dotuunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,197 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define MOVSLDUP_XPTR_IDX_8__X3 LONG $0x1C120FF3; BYTE $0xC6 // MOVSLDUP (SI)(AX*8), X3
|
||||
#define MOVSLDUP_16_XPTR_IDX_8__X5 LONG $0x6C120FF3; WORD $0x10C6 // MOVSLDUP 16(SI)(AX*8), X5
|
||||
#define MOVSLDUP_32_XPTR_IDX_8__X7 LONG $0x7C120FF3; WORD $0x20C6 // MOVSLDUP 32(SI)(AX*8), X7
|
||||
#define MOVSLDUP_48_XPTR_IDX_8__X9 LONG $0x120F44F3; WORD $0xC64C; BYTE $0x30 // MOVSLDUP 48(SI)(AX*8), X9
|
||||
|
||||
#define MOVSHDUP_XPTR_IDX_8__X2 LONG $0x14160FF3; BYTE $0xC6 // MOVSHDUP (SI)(AX*8), X2
|
||||
#define MOVSHDUP_16_XPTR_IDX_8__X4 LONG $0x64160FF3; WORD $0x10C6 // MOVSHDUP 16(SI)(AX*8), X4
|
||||
#define MOVSHDUP_32_XPTR_IDX_8__X6 LONG $0x74160FF3; WORD $0x20C6 // MOVSHDUP 32(SI)(AX*8), X6
|
||||
#define MOVSHDUP_48_XPTR_IDX_8__X8 LONG $0x160F44F3; WORD $0xC644; BYTE $0x30 // MOVSHDUP 48(SI)(AX*8), X8
|
||||
|
||||
#define MOVSHDUP_X3_X2 LONG $0xD3160FF3 // MOVSHDUP X3, X2
|
||||
#define MOVSLDUP_X3_X3 LONG $0xDB120FF3 // MOVSLDUP X3, X3
|
||||
|
||||
#define ADDSUBPS_X2_X3 LONG $0xDAD00FF2 // ADDSUBPS X2, X3
|
||||
#define ADDSUBPS_X4_X5 LONG $0xECD00FF2 // ADDSUBPS X4, X5
|
||||
#define ADDSUBPS_X6_X7 LONG $0xFED00FF2 // ADDSUBPS X6, X7
|
||||
#define ADDSUBPS_X8_X9 LONG $0xD00F45F2; BYTE $0xC8 // ADDSUBPS X8, X9
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
#define IDX AX
|
||||
#define I_IDX DX
|
||||
#define NEG1 X15
|
||||
#define P_NEG1 X14
|
||||
|
||||
// func DotuUnitary(x, y []complex64) (sum complex64)
|
||||
TEXT ·DotuUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE dotu_end
|
||||
XORQ IDX, IDX // IDX = 0
|
||||
|
||||
MOVQ X_PTR, DX
|
||||
ANDQ $15, DX // DX = &x & 15
|
||||
JZ dotu_aligned // if DX == 0 { goto dotu_aligned }
|
||||
|
||||
MOVSD (X_PTR)(IDX*8), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSD (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
MOVAPS X3, SUM // SUM = X_i
|
||||
INCQ IDX // IDX++
|
||||
DECQ LEN // LEN--
|
||||
JZ dotu_end // if LEN == 0 { goto dotu_end }
|
||||
|
||||
dotu_aligned:
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $7, TAIL // TAIL = LEN % 8
|
||||
SHRQ $3, LEN // LEN = floor( LEN / 8 )
|
||||
JZ dotu_tail // if LEN == 0 { goto dotu_tail }
|
||||
PXOR P_SUM, P_SUM
|
||||
|
||||
dotu_loop: // do {
|
||||
MOVSLDUP_XPTR_IDX_8__X3 // X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSLDUP_16_XPTR_IDX_8__X5
|
||||
MOVSLDUP_32_XPTR_IDX_8__X7
|
||||
MOVSLDUP_48_XPTR_IDX_8__X9
|
||||
|
||||
MOVSHDUP_XPTR_IDX_8__X2 // X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
|
||||
MOVSHDUP_16_XPTR_IDX_8__X4
|
||||
MOVSHDUP_32_XPTR_IDX_8__X6
|
||||
MOVSHDUP_48_XPTR_IDX_8__X8
|
||||
|
||||
// X_j = { imag(y[i]), real(y[i]), imag(y[i+1]), real(y[i+1]) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10
|
||||
MOVUPS 16(Y_PTR)(IDX*8), X11
|
||||
MOVUPS 32(Y_PTR)(IDX*8), X12
|
||||
MOVUPS 48(Y_PTR)(IDX*8), X13
|
||||
|
||||
// X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]),
|
||||
// imag(y[i+1]) * real(x[i+1]), real(y[i+1]) * real(x[i+1]) }
|
||||
MULPS X10, X3
|
||||
MULPS X11, X5
|
||||
MULPS X12, X7
|
||||
MULPS X13, X9
|
||||
|
||||
// X_j = { real(y[i]), imag(y[i]), real(y[i+1]), imag(y[i+1]) }
|
||||
SHUFPS $0xB1, X10, X10
|
||||
SHUFPS $0xB1, X11, X11
|
||||
SHUFPS $0xB1, X12, X12
|
||||
SHUFPS $0xB1, X13, X13
|
||||
|
||||
// X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]),
|
||||
// real(y[i+1]) * imag(x[i+1]), imag(y[i+1]) * imag(x[i+1]) }
|
||||
MULPS X10, X2
|
||||
MULPS X11, X4
|
||||
MULPS X12, X6
|
||||
MULPS X13, X8
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i]) * real(x[i]) + real(y[i]) * imag(x[i]),
|
||||
// real(result[i]): real(y[i]) * real(x[i]) - imag(y[i]) * imag(x[i]),
|
||||
// imag(result[i+1]): imag(y[i+1]) * real(x[i+1]) + real(y[i+1]) * imag(x[i+1]),
|
||||
// real(result[i+1]): real(y[i+1]) * real(x[i+1]) - imag(y[i+1]) * imag(x[i+1]),
|
||||
// }
|
||||
ADDSUBPS_X2_X3
|
||||
ADDSUBPS_X4_X5
|
||||
ADDSUBPS_X6_X7
|
||||
ADDSUBPS_X8_X9
|
||||
|
||||
// SUM += X_i
|
||||
ADDPS X3, SUM
|
||||
ADDPS X5, P_SUM
|
||||
ADDPS X7, SUM
|
||||
ADDPS X9, P_SUM
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dotu_loop // } while --LEN > 0
|
||||
|
||||
ADDPS SUM, P_SUM // P_SUM = { P_SUM[1] + SUM[1], P_SUM[0] + SUM[0] }
|
||||
XORPS SUM, SUM // SUM = 0
|
||||
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dotu_end
|
||||
|
||||
dotu_tail:
|
||||
MOVQ TAIL, LEN
|
||||
SHRQ $1, LEN // LEN = floor( LEN / 2 )
|
||||
JZ dotu_tail_one // if LEN == 0 { goto dotc_tail_one }
|
||||
|
||||
dotu_tail_two: // do {
|
||||
MOVSLDUP_XPTR_IDX_8__X3 // X_i = { real(x[i]), real(x[i]), real(x[i+1]), real(x[i+1]) }
|
||||
MOVSHDUP_XPTR_IDX_8__X2 // X_(i-1) = { imag(x[i]), imag(x[i]), imag(x[i]+1), imag(x[i]+1) }
|
||||
MOVUPS (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0xB1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
DECQ LEN
|
||||
JNZ dotu_tail_two // } while --LEN > 0
|
||||
|
||||
ADDPS SUM, P_SUM // P_SUM = { P_SUM[1] + SUM[1], P_SUM[0] + SUM[0] }
|
||||
XORPS SUM, SUM // SUM = 0
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ dotu_end
|
||||
|
||||
dotu_tail_one:
|
||||
MOVSD (X_PTR)(IDX*8), X3 // X_i = { imag(x[i]), real(x[i]) }
|
||||
MOVSHDUP_X3_X2 // X_(i-1) = { imag(x[i]), imag(x[i]) }
|
||||
MOVSLDUP_X3_X3 // X_i = { real(x[i]), real(x[i]) }
|
||||
MOVSD (Y_PTR)(IDX*8), X10 // X_j = { imag(y[i]), real(y[i]) }
|
||||
MULPS X10, X3 // X_i = { imag(y[i]) * real(x[i]), real(y[i]) * real(x[i]) }
|
||||
SHUFPS $0x1, X10, X10 // X_j = { real(y[i]), imag(y[i]) }
|
||||
MULPS X10, X2 // X_(i-1) = { real(y[i]) * imag(x[i]), imag(y[i]) * imag(x[i]) }
|
||||
|
||||
// X_i = {
|
||||
// imag(result[i]): imag(y[i])*real(x[i]) + real(y[i])*imag(x[i]),
|
||||
// real(result[i]): real(y[i])*real(x[i]) - imag(y[i])*imag(x[i]) }
|
||||
ADDSUBPS_X2_X3
|
||||
|
||||
ADDPS X3, SUM // SUM += X_i
|
||||
|
||||
dotu_end:
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM[0] + SUM[0] }
|
||||
MOVHLPS P_SUM, P_SUM // P_SUM = { P_SUM[1], P_SUM[1] }
|
||||
ADDPS P_SUM, SUM // SUM = { P_SUM[1] + SUM[0] }
|
||||
|
||||
dotu_ret:
|
||||
MOVSD SUM, sum+48(FP) // return SUM
|
||||
RET
|
||||
85
vendor/gonum.org/v1/gonum/internal/asm/c64/scal.go
generated
vendored
Normal file
85
vendor/gonum.org/v1/gonum/internal/asm/c64/scal.go
generated
vendored
Normal file
@@ -0,0 +1,85 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package c64
|
||||
|
||||
// ScalUnitary is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] *= alpha
|
||||
// }
|
||||
func ScalUnitary(alpha complex64, x []complex64) {
|
||||
for i := range x {
|
||||
x[i] *= alpha
|
||||
}
|
||||
}
|
||||
|
||||
// ScalUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha * v
|
||||
// }
|
||||
func ScalUnitaryTo(dst []complex64, alpha complex64, x []complex64) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// ScalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] *= alpha
|
||||
// ix += incX
|
||||
// }
|
||||
func ScalInc(alpha complex64, x []complex64, n, incX uintptr) {
|
||||
var ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
x[ix] *= alpha
|
||||
ix += incX
|
||||
}
|
||||
}
|
||||
|
||||
// ScalIncTo is
|
||||
//
|
||||
// var idst, ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha * x[ix]
|
||||
// ix += incX
|
||||
// idst += incDst
|
||||
// }
|
||||
func ScalIncTo(dst []complex64, incDst uintptr, alpha complex64, x []complex64, n, incX uintptr) {
|
||||
var idst, ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha * x[ix]
|
||||
ix += incX
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
|
||||
// SscalUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// x[i] = complex(real(v)*alpha, imag(v)*alpha)
|
||||
// }
|
||||
func SscalUnitary(alpha float32, x []complex64) {
|
||||
for i, v := range x {
|
||||
x[i] = complex(real(v)*alpha, imag(v)*alpha)
|
||||
}
|
||||
}
|
||||
|
||||
// SscalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
|
||||
// ix += inc
|
||||
// }
|
||||
func SscalInc(alpha float32, x []complex64, n, inc uintptr) {
|
||||
var ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
x[ix] = complex(real(x[ix])*alpha, imag(x[ix])*alpha)
|
||||
ix += inc
|
||||
}
|
||||
}
|
||||
180
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs.go
generated
vendored
Normal file
180
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs.go
generated
vendored
Normal file
@@ -0,0 +1,180 @@
|
||||
// Copyright ©2020 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package c64
|
||||
|
||||
import (
|
||||
"gonum.org/v1/gonum/internal/cmplx64"
|
||||
"gonum.org/v1/gonum/internal/math32"
|
||||
)
|
||||
|
||||
// Add is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] += v
|
||||
// }
|
||||
func Add(dst, s []complex64) {
|
||||
for i, v := range s {
|
||||
dst[i] += v
|
||||
}
|
||||
}
|
||||
|
||||
// AddConst is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] += alpha
|
||||
// }
|
||||
func AddConst(alpha complex64, x []complex64) {
|
||||
for i := range x {
|
||||
x[i] += alpha
|
||||
}
|
||||
}
|
||||
|
||||
// CumSum is
|
||||
//
|
||||
// if len(s) == 0 {
|
||||
// return dst
|
||||
// }
|
||||
// dst[0] = s[0]
|
||||
// for i, v := range s[1:] {
|
||||
// dst[i+1] = dst[i] + v
|
||||
// }
|
||||
// return dst
|
||||
func CumSum(dst, s []complex64) []complex64 {
|
||||
if len(s) == 0 {
|
||||
return dst
|
||||
}
|
||||
dst[0] = s[0]
|
||||
for i, v := range s[1:] {
|
||||
dst[i+1] = dst[i] + v
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// CumProd is
|
||||
//
|
||||
// if len(s) == 0 {
|
||||
// return dst
|
||||
// }
|
||||
// dst[0] = s[0]
|
||||
// for i, v := range s[1:] {
|
||||
// dst[i+1] = dst[i] * v
|
||||
// }
|
||||
// return dst
|
||||
func CumProd(dst, s []complex64) []complex64 {
|
||||
if len(s) == 0 {
|
||||
return dst
|
||||
}
|
||||
dst[0] = s[0]
|
||||
for i, v := range s[1:] {
|
||||
dst[i+1] = dst[i] * v
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// Div is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] /= v
|
||||
// }
|
||||
func Div(dst, s []complex64) {
|
||||
for i, v := range s {
|
||||
dst[i] /= v
|
||||
}
|
||||
}
|
||||
|
||||
// DivTo is
|
||||
//
|
||||
// for i, v := range s {
|
||||
// dst[i] = v / t[i]
|
||||
// }
|
||||
// return dst
|
||||
func DivTo(dst, s, t []complex64) []complex64 {
|
||||
for i, v := range s {
|
||||
dst[i] = v / t[i]
|
||||
}
|
||||
return dst
|
||||
}
|
||||
|
||||
// DotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += conj(v) * y[i]
|
||||
// }
|
||||
// return sum
|
||||
func DotUnitary(x, y []complex64) (sum complex64) {
|
||||
for i, v := range x {
|
||||
sum += cmplx64.Conj(v) * y[i]
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// L2DistanceUnitary returns the L2-norm of x-y.
|
||||
func L2DistanceUnitary(x, y []complex64) (norm float32) {
|
||||
var scale float32
|
||||
sumSquares := float32(1.0)
|
||||
for i, v := range x {
|
||||
v -= y[i]
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := cmplx64.Abs(v)
|
||||
if math32.IsNaN(absxi) {
|
||||
return math32.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math32.IsInf(scale, 1) {
|
||||
return math32.Inf(1)
|
||||
}
|
||||
return scale * math32.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// L2NormUnitary returns the L2-norm of x.
|
||||
func L2NormUnitary(x []complex64) (norm float32) {
|
||||
var scale float32
|
||||
sumSquares := float32(1.0)
|
||||
for _, v := range x {
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := cmplx64.Abs(v)
|
||||
if math32.IsNaN(absxi) {
|
||||
return math32.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math32.IsInf(scale, 1) {
|
||||
return math32.Inf(1)
|
||||
}
|
||||
return scale * math32.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// Sum is
|
||||
//
|
||||
// var sum complex64
|
||||
// for i := range x {
|
||||
// sum += x[i]
|
||||
// }
|
||||
func Sum(x []complex64) complex64 {
|
||||
var sum complex64
|
||||
for _, v := range x {
|
||||
sum += v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
77
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_amd64.go
generated
vendored
Normal file
77
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_amd64.go
generated
vendored
Normal file
@@ -0,0 +1,77 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !noasm && !gccgo && !safe
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
package c64
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha complex64, x, y []complex64)
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64)
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// DotcUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * conj(v)
|
||||
// }
|
||||
// return sum
|
||||
func DotcUnitary(x, y []complex64) (sum complex64)
|
||||
|
||||
// DotcInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * conj(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotcInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64)
|
||||
|
||||
// DotuUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotuUnitary(x, y []complex64) (sum complex64)
|
||||
|
||||
// DotuInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotuInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64)
|
||||
122
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_noasm.go
generated
vendored
Normal file
122
vendor/gonum.org/v1/gonum/internal/asm/c64/stubs_noasm.go
generated
vendored
Normal file
@@ -0,0 +1,122 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !amd64 || noasm || gccgo || safe
|
||||
// +build !amd64 noasm gccgo safe
|
||||
|
||||
package c64
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha complex64, x, y []complex64) {
|
||||
for i, v := range x {
|
||||
y[i] += alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []complex64, alpha complex64, x, y []complex64) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha*v + y[i]
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
y[iy] += alpha * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []complex64, incDst, idst uintptr, alpha complex64, x, y []complex64, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha*x[ix] + y[iy]
|
||||
ix += incX
|
||||
iy += incY
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
|
||||
// DotcUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * conj(v)
|
||||
// }
|
||||
// return sum
|
||||
func DotcUnitary(x, y []complex64) (sum complex64) {
|
||||
for i, v := range x {
|
||||
sum += y[i] * conj(v)
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotcInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * conj(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotcInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += y[iy] * conj(x[ix])
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotuUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotuUnitary(x, y []complex64) (sum complex64) {
|
||||
for i, v := range x {
|
||||
sum += y[i] * v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotuInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotuInc(x, y []complex64, n, incX, incY, ix, iy uintptr) (sum complex64) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += y[iy] * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return sum
|
||||
}
|
||||
73
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyinc_amd64.s
generated
vendored
Normal file
73
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,73 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyInc(SB), NOSPLIT, $0
|
||||
MOVQ n+56(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JLE axpyi_end
|
||||
MOVQ x_base+8(FP), SI // SI = &x
|
||||
MOVQ y_base+32(FP), DI // DI = &y
|
||||
MOVQ ix+80(FP), R8 // R8 = ix
|
||||
MOVQ iy+88(FP), R9 // R9 = iy
|
||||
LEAQ (SI)(R8*4), SI // SI = &(x[ix])
|
||||
LEAQ (DI)(R9*4), DI // DI = &(y[iy])
|
||||
MOVQ DI, DX // DX = DI Read Pointer for y
|
||||
MOVQ incX+64(FP), R8 // R8 = incX
|
||||
SHLQ $2, R8 // R8 *= sizeof(float32)
|
||||
MOVQ incY+72(FP), R9 // R9 = incY
|
||||
SHLQ $2, R9 // R9 *= sizeof(float32)
|
||||
MOVSS alpha+0(FP), X0 // X0 = alpha
|
||||
MOVSS X0, X1 // X1 = X0 // for pipelining
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, BX // BX = n % 4
|
||||
SHRQ $2, CX // CX = floor( n / 4 )
|
||||
JZ axpyi_tail_start // if CX == 0 { goto axpyi_tail_start }
|
||||
|
||||
axpyi_loop: // Loop unrolled 4x do {
|
||||
MOVSS (SI), X2 // X_i = x[i]
|
||||
MOVSS (SI)(R8*1), X3
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
MOVSS (SI), X4
|
||||
MOVSS (SI)(R8*1), X5
|
||||
MULSS X1, X2 // X_i *= a
|
||||
MULSS X0, X3
|
||||
MULSS X1, X4
|
||||
MULSS X0, X5
|
||||
ADDSS (DX), X2 // X_i += y[i]
|
||||
ADDSS (DX)(R9*1), X3
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
ADDSS (DX), X4
|
||||
ADDSS (DX)(R9*1), X5
|
||||
MOVSS X2, (DI) // y[i] = X_i
|
||||
MOVSS X3, (DI)(R9*1)
|
||||
LEAQ (DI)(R9*2), DI // DI = &(DI[incY*2])
|
||||
MOVSS X4, (DI)
|
||||
MOVSS X5, (DI)(R9*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2]) // Increment addresses
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R9*2), DI // DI = &(DI[incY*2])
|
||||
LOOP axpyi_loop // } while --CX > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail_start: // Reset loop registers
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
|
||||
axpyi_tail: // do {
|
||||
MOVSS (SI), X2 // X2 = x[i]
|
||||
MULSS X1, X2 // X2 *= a
|
||||
ADDSS (DI), X2 // X2 += y[i]
|
||||
MOVSS X2, (DI) // y[i] = X2
|
||||
ADDQ R8, SI // SI = &(SI[incX])
|
||||
ADDQ R9, DI // DI = &(DI[incY])
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
|
||||
78
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyincto_amd64.s
generated
vendored
Normal file
78
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyincto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,78 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyIncTo(SB), NOSPLIT, $0
|
||||
MOVQ n+96(FP), CX // CX = n
|
||||
CMPQ CX, $0 // if n==0 { return }
|
||||
JLE axpyi_end
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+48(FP), SI // SI = &x
|
||||
MOVQ y_base+72(FP), DX // DX = &y
|
||||
MOVQ ix+120(FP), R8 // R8 = ix // Load the first index
|
||||
MOVQ iy+128(FP), R9 // R9 = iy
|
||||
MOVQ idst+32(FP), R10 // R10 = idst
|
||||
LEAQ (SI)(R8*4), SI // SI = &(x[ix])
|
||||
LEAQ (DX)(R9*4), DX // DX = &(y[iy])
|
||||
LEAQ (DI)(R10*4), DI // DI = &(dst[idst])
|
||||
MOVQ incX+104(FP), R8 // R8 = incX
|
||||
SHLQ $2, R8 // R8 *= sizeof(float32)
|
||||
MOVQ incY+112(FP), R9 // R9 = incY
|
||||
SHLQ $2, R9 // R9 *= sizeof(float32)
|
||||
MOVQ incDst+24(FP), R10 // R10 = incDst
|
||||
SHLQ $2, R10 // R10 *= sizeof(float32)
|
||||
MOVSS alpha+40(FP), X0 // X0 = alpha
|
||||
MOVSS X0, X1 // X1 = X0 // for pipelining
|
||||
MOVQ CX, BX
|
||||
ANDQ $3, BX // BX = n % 4
|
||||
SHRQ $2, CX // CX = floor( n / 4 )
|
||||
JZ axpyi_tail_start // if CX == 0 { goto axpyi_tail_start }
|
||||
|
||||
axpyi_loop: // Loop unrolled 4x do {
|
||||
MOVSS (SI), X2 // X_i = x[i]
|
||||
MOVSS (SI)(R8*1), X3
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2])
|
||||
MOVSS (SI), X4
|
||||
MOVSS (SI)(R8*1), X5
|
||||
MULSS X1, X2 // X_i *= a
|
||||
MULSS X0, X3
|
||||
MULSS X1, X4
|
||||
MULSS X0, X5
|
||||
ADDSS (DX), X2 // X_i += y[i]
|
||||
ADDSS (DX)(R9*1), X3
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
ADDSS (DX), X4
|
||||
ADDSS (DX)(R9*1), X5
|
||||
MOVSS X2, (DI) // dst[i] = X_i
|
||||
MOVSS X3, (DI)(R10*1)
|
||||
LEAQ (DI)(R10*2), DI // DI = &(DI[incDst*2])
|
||||
MOVSS X4, (DI)
|
||||
MOVSS X5, (DI)(R10*1)
|
||||
LEAQ (SI)(R8*2), SI // SI = &(SI[incX*2]) // Increment addresses
|
||||
LEAQ (DX)(R9*2), DX // DX = &(DX[incY*2])
|
||||
LEAQ (DI)(R10*2), DI // DI = &(DI[incDst*2])
|
||||
LOOP axpyi_loop // } while --CX > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpyi_end
|
||||
|
||||
axpyi_tail_start: // Reset loop registers
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
|
||||
axpyi_tail: // do {
|
||||
MOVSS (SI), X2 // X2 = x[i]
|
||||
MULSS X1, X2 // X2 *= a
|
||||
ADDSS (DX), X2 // X2 += y[i]
|
||||
MOVSS X2, (DI) // dst[i] = X2
|
||||
ADDQ R8, SI // SI = &(SI[incX])
|
||||
ADDQ R9, DX // DX = &(DX[incY])
|
||||
ADDQ R10, DI // DI = &(DI[incY])
|
||||
LOOP axpyi_tail // } while --CX > 0
|
||||
|
||||
axpyi_end:
|
||||
RET
|
||||
|
||||
97
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitary_amd64.s
generated
vendored
Normal file
97
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,97 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func AxpyUnitary(alpha float32, x, y []float32)
|
||||
TEXT ·AxpyUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SI // SI = &x
|
||||
MOVQ y_base+32(FP), DI // DI = &y
|
||||
MOVQ x_len+16(FP), BX // BX = min( len(x), len(y) )
|
||||
CMPQ y_len+40(FP), BX
|
||||
CMOVQLE y_len+40(FP), BX
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpy_end
|
||||
MOVSS alpha+0(FP), X0
|
||||
SHUFPS $0, X0, X0 // X0 = { a, a, a, a }
|
||||
XORQ AX, AX // i = 0
|
||||
PXOR X2, X2 // 2 NOP instructions (PXOR) to align
|
||||
PXOR X3, X3 // loop to cache line
|
||||
MOVQ DI, CX
|
||||
ANDQ $0xF, CX // Align on 16-byte boundary for ADDPS
|
||||
JZ axpy_no_trim // if CX == 0 { goto axpy_no_trim }
|
||||
|
||||
XORQ $0xF, CX // CX = 4 - floor( BX % 16 / 4 )
|
||||
INCQ CX
|
||||
SHRQ $2, CX
|
||||
|
||||
axpy_align: // Trim first value(s) in unaligned buffer do {
|
||||
MOVSS (SI)(AX*4), X2 // X2 = x[i]
|
||||
MULSS X0, X2 // X2 *= a
|
||||
ADDSS (DI)(AX*4), X2 // X2 += y[i]
|
||||
MOVSS X2, (DI)(AX*4) // y[i] = X2
|
||||
INCQ AX // i++
|
||||
DECQ BX
|
||||
JZ axpy_end // if --BX == 0 { return }
|
||||
LOOP axpy_align // } while --CX > 0
|
||||
|
||||
axpy_no_trim:
|
||||
MOVUPS X0, X1 // Copy X0 to X1 for pipelining
|
||||
MOVQ BX, CX
|
||||
ANDQ $0xF, BX // BX = len % 16
|
||||
SHRQ $4, CX // CX = int( len / 16 )
|
||||
JZ axpy_tail4_start // if CX == 0 { return }
|
||||
|
||||
axpy_loop: // Loop unrolled 16x do {
|
||||
MOVUPS (SI)(AX*4), X2 // X2 = x[i:i+4]
|
||||
MOVUPS 16(SI)(AX*4), X3
|
||||
MOVUPS 32(SI)(AX*4), X4
|
||||
MOVUPS 48(SI)(AX*4), X5
|
||||
MULPS X0, X2 // X2 *= a
|
||||
MULPS X1, X3
|
||||
MULPS X0, X4
|
||||
MULPS X1, X5
|
||||
ADDPS (DI)(AX*4), X2 // X2 += y[i:i+4]
|
||||
ADDPS 16(DI)(AX*4), X3
|
||||
ADDPS 32(DI)(AX*4), X4
|
||||
ADDPS 48(DI)(AX*4), X5
|
||||
MOVUPS X2, (DI)(AX*4) // dst[i:i+4] = X2
|
||||
MOVUPS X3, 16(DI)(AX*4)
|
||||
MOVUPS X4, 32(DI)(AX*4)
|
||||
MOVUPS X5, 48(DI)(AX*4)
|
||||
ADDQ $16, AX // i += 16
|
||||
LOOP axpy_loop // while (--CX) > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpy_end
|
||||
|
||||
axpy_tail4_start: // Reset loop counter for 4-wide tail loop
|
||||
MOVQ BX, CX // CX = floor( BX / 4 )
|
||||
SHRQ $2, CX
|
||||
JZ axpy_tail_start // if CX == 0 { goto axpy_tail_start }
|
||||
|
||||
axpy_tail4: // Loop unrolled 4x do {
|
||||
MOVUPS (SI)(AX*4), X2 // X2 = x[i]
|
||||
MULPS X0, X2 // X2 *= a
|
||||
ADDPS (DI)(AX*4), X2 // X2 += y[i]
|
||||
MOVUPS X2, (DI)(AX*4) // y[i] = X2
|
||||
ADDQ $4, AX // i += 4
|
||||
LOOP axpy_tail4 // } while --CX > 0
|
||||
|
||||
axpy_tail_start: // Reset loop counter for 1-wide tail loop
|
||||
MOVQ BX, CX // CX = BX % 4
|
||||
ANDQ $3, CX
|
||||
JZ axpy_end // if CX == 0 { return }
|
||||
|
||||
axpy_tail:
|
||||
MOVSS (SI)(AX*4), X1 // X1 = x[i]
|
||||
MULSS X0, X1 // X1 *= a
|
||||
ADDSS (DI)(AX*4), X1 // X1 += y[i]
|
||||
MOVSS X1, (DI)(AX*4) // y[i] = X1
|
||||
INCQ AX // i++
|
||||
LOOP axpy_tail // } while --CX > 0
|
||||
|
||||
axpy_end:
|
||||
RET
|
||||
98
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitaryto_amd64.s
generated
vendored
Normal file
98
vendor/gonum.org/v1/gonum/internal/asm/f32/axpyunitaryto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,98 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32)
|
||||
TEXT ·AxpyUnitaryTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ x_base+32(FP), SI // SI = &x
|
||||
MOVQ y_base+56(FP), DX // DX = &y
|
||||
MOVQ x_len+40(FP), BX // BX = min( len(x), len(y), len(dst) )
|
||||
CMPQ y_len+64(FP), BX
|
||||
CMOVQLE y_len+64(FP), BX
|
||||
CMPQ dst_len+8(FP), BX
|
||||
CMOVQLE dst_len+8(FP), BX
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpy_end
|
||||
MOVSS alpha+24(FP), X0
|
||||
SHUFPS $0, X0, X0 // X0 = { a, a, a, a, }
|
||||
XORQ AX, AX // i = 0
|
||||
MOVQ DX, CX
|
||||
ANDQ $0xF, CX // Align on 16-byte boundary for ADDPS
|
||||
JZ axpy_no_trim // if CX == 0 { goto axpy_no_trim }
|
||||
|
||||
XORQ $0xF, CX // CX = 4 - floor ( B % 16 / 4 )
|
||||
INCQ CX
|
||||
SHRQ $2, CX
|
||||
|
||||
axpy_align: // Trim first value(s) in unaligned buffer do {
|
||||
MOVSS (SI)(AX*4), X2 // X2 = x[i]
|
||||
MULSS X0, X2 // X2 *= a
|
||||
ADDSS (DX)(AX*4), X2 // X2 += y[i]
|
||||
MOVSS X2, (DI)(AX*4) // y[i] = X2
|
||||
INCQ AX // i++
|
||||
DECQ BX
|
||||
JZ axpy_end // if --BX == 0 { return }
|
||||
LOOP axpy_align // } while --CX > 0
|
||||
|
||||
axpy_no_trim:
|
||||
MOVUPS X0, X1 // Copy X0 to X1 for pipelining
|
||||
MOVQ BX, CX
|
||||
ANDQ $0xF, BX // BX = len % 16
|
||||
SHRQ $4, CX // CX = floor( len / 16 )
|
||||
JZ axpy_tail4_start // if CX == 0 { return }
|
||||
|
||||
axpy_loop: // Loop unrolled 16x do {
|
||||
MOVUPS (SI)(AX*4), X2 // X2 = x[i:i+4]
|
||||
MOVUPS 16(SI)(AX*4), X3
|
||||
MOVUPS 32(SI)(AX*4), X4
|
||||
MOVUPS 48(SI)(AX*4), X5
|
||||
MULPS X0, X2 // X2 *= a
|
||||
MULPS X1, X3
|
||||
MULPS X0, X4
|
||||
MULPS X1, X5
|
||||
ADDPS (DX)(AX*4), X2 // X2 += y[i:i+4]
|
||||
ADDPS 16(DX)(AX*4), X3
|
||||
ADDPS 32(DX)(AX*4), X4
|
||||
ADDPS 48(DX)(AX*4), X5
|
||||
MOVUPS X2, (DI)(AX*4) // dst[i:i+4] = X2
|
||||
MOVUPS X3, 16(DI)(AX*4)
|
||||
MOVUPS X4, 32(DI)(AX*4)
|
||||
MOVUPS X5, 48(DI)(AX*4)
|
||||
ADDQ $16, AX // i += 16
|
||||
LOOP axpy_loop // while (--CX) > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE axpy_end
|
||||
|
||||
axpy_tail4_start: // Reset loop counter for 4-wide tail loop
|
||||
MOVQ BX, CX // CX = floor( BX / 4 )
|
||||
SHRQ $2, CX
|
||||
JZ axpy_tail_start // if CX == 0 { goto axpy_tail_start }
|
||||
|
||||
axpy_tail4: // Loop unrolled 4x do {
|
||||
MOVUPS (SI)(AX*4), X2 // X2 = x[i]
|
||||
MULPS X0, X2 // X2 *= a
|
||||
ADDPS (DX)(AX*4), X2 // X2 += y[i]
|
||||
MOVUPS X2, (DI)(AX*4) // y[i] = X2
|
||||
ADDQ $4, AX // i += 4
|
||||
LOOP axpy_tail4 // } while --CX > 0
|
||||
|
||||
axpy_tail_start: // Reset loop counter for 1-wide tail loop
|
||||
MOVQ BX, CX // CX = BX % 4
|
||||
ANDQ $3, CX
|
||||
JZ axpy_end // if CX == 0 { return }
|
||||
|
||||
axpy_tail:
|
||||
MOVSS (SI)(AX*4), X1 // X1 = x[i]
|
||||
MULSS X0, X1 // X1 *= a
|
||||
ADDSS (DX)(AX*4), X1 // X1 += y[i]
|
||||
MOVSS X1, (DI)(AX*4) // y[i] = X1
|
||||
INCQ AX // i++
|
||||
LOOP axpy_tail // } while --CX > 0
|
||||
|
||||
axpy_end:
|
||||
RET
|
||||
91
vendor/gonum.org/v1/gonum/internal/asm/f32/ddotinc_amd64.s
generated
vendored
Normal file
91
vendor/gonum.org/v1/gonum/internal/asm/f32/ddotinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,91 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC_X R8
|
||||
#define INCx3_X R10
|
||||
#define INC_Y R9
|
||||
#define INCx3_Y R11
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
|
||||
// func DdotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float64)
|
||||
TEXT ·DdotInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
CMPQ LEN, $0
|
||||
JE dot_end
|
||||
|
||||
MOVQ ix+72(FP), INC_X // INC_X = ix
|
||||
MOVQ iy+80(FP), INC_Y // INC_Y = iy
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(x[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(y[iy])
|
||||
|
||||
MOVQ incX+56(FP), INC_X // INC_X = incX * sizeof(float32)
|
||||
SHLQ $2, INC_X
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y = incY * sizeof(float32)
|
||||
SHLQ $2, INC_Y
|
||||
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = LEN % 4
|
||||
SHRQ $2, LEN // LEN = floor( LEN / 4 )
|
||||
JZ dot_tail // if LEN == 0 { goto dot_tail }
|
||||
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0 for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
|
||||
dot_loop: // Loop unrolled 4x do {
|
||||
CVTSS2SD (X_PTR), X2 // X_i = x[i:i+1]
|
||||
CVTSS2SD (X_PTR)(INC_X*1), X3
|
||||
CVTSS2SD (X_PTR)(INC_X*2), X4
|
||||
CVTSS2SD (X_PTR)(INCx3_X*1), X5
|
||||
|
||||
CVTSS2SD (Y_PTR), X6 // X_j = y[i:i+1]
|
||||
CVTSS2SD (Y_PTR)(INC_Y*1), X7
|
||||
CVTSS2SD (Y_PTR)(INC_Y*2), X8
|
||||
CVTSS2SD (Y_PTR)(INCx3_Y*1), X9
|
||||
|
||||
MULSD X6, X2 // X_i *= X_j
|
||||
MULSD X7, X3
|
||||
MULSD X8, X4
|
||||
MULSD X9, X5
|
||||
|
||||
ADDSD X2, SUM // SUM += X_i
|
||||
ADDSD X3, P_SUM
|
||||
ADDSD X4, SUM
|
||||
ADDSD X5, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[INC_X * 4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[INC_Y * 4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
|
||||
ADDSD P_SUM, SUM // SUM += P_SUM
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
CVTSS2SD (X_PTR), X2 // X2 = x[i]
|
||||
CVTSS2SD (Y_PTR), X3 // X2 *= y[i]
|
||||
MULSD X3, X2
|
||||
ADDSD X2, SUM // SUM += X2
|
||||
ADDQ INC_X, X_PTR // X_PTR += INC_X
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += INC_Y
|
||||
DECQ TAIL
|
||||
JNZ dot_tail // } while --TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVSD SUM, sum+88(FP) // return SUM
|
||||
RET
|
||||
110
vendor/gonum.org/v1/gonum/internal/asm/f32/ddotunitary_amd64.s
generated
vendored
Normal file
110
vendor/gonum.org/v1/gonum/internal/asm/f32/ddotunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,110 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define HADDPD_SUM_SUM LONG $0xC07C0F66 // @ HADDPD X0, X0
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define IDX AX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
|
||||
// func DdotUnitary(x, y []float32) (sum float32)
|
||||
TEXT ·DdotUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
PXOR SUM, SUM // psum = 0
|
||||
CMPQ LEN, $0
|
||||
JE dot_end
|
||||
|
||||
XORQ IDX, IDX
|
||||
MOVQ Y_PTR, DX
|
||||
ANDQ $0xF, DX // Align on 16-byte boundary for ADDPS
|
||||
JZ dot_no_trim // if DX == 0 { goto dot_no_trim }
|
||||
|
||||
SUBQ $16, DX
|
||||
|
||||
dot_align: // Trim first value(s) in unaligned buffer do {
|
||||
CVTSS2SD (X_PTR)(IDX*4), X2 // X2 = float64(x[i])
|
||||
CVTSS2SD (Y_PTR)(IDX*4), X3 // X3 = float64(y[i])
|
||||
MULSD X3, X2
|
||||
ADDSD X2, SUM // SUM += X2
|
||||
INCQ IDX // IDX++
|
||||
DECQ LEN
|
||||
JZ dot_end // if --TAIL == 0 { return }
|
||||
ADDQ $4, DX
|
||||
JNZ dot_align // } while --LEN > 0
|
||||
|
||||
dot_no_trim:
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0 for pipelining
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $0x7, TAIL // TAIL = LEN % 8
|
||||
SHRQ $3, LEN // LEN = floor( LEN / 8 )
|
||||
JZ dot_tail_start // if LEN == 0 { goto dot_tail_start }
|
||||
|
||||
dot_loop: // Loop unrolled 8x do {
|
||||
CVTPS2PD (X_PTR)(IDX*4), X2 // X_i = x[i:i+1]
|
||||
CVTPS2PD 8(X_PTR)(IDX*4), X3
|
||||
CVTPS2PD 16(X_PTR)(IDX*4), X4
|
||||
CVTPS2PD 24(X_PTR)(IDX*4), X5
|
||||
|
||||
CVTPS2PD (Y_PTR)(IDX*4), X6 // X_j = y[i:i+1]
|
||||
CVTPS2PD 8(Y_PTR)(IDX*4), X7
|
||||
CVTPS2PD 16(Y_PTR)(IDX*4), X8
|
||||
CVTPS2PD 24(Y_PTR)(IDX*4), X9
|
||||
|
||||
MULPD X6, X2 // X_i *= X_j
|
||||
MULPD X7, X3
|
||||
MULPD X8, X4
|
||||
MULPD X9, X5
|
||||
|
||||
ADDPD X2, SUM // SUM += X_i
|
||||
ADDPD X3, P_SUM
|
||||
ADDPD X4, SUM
|
||||
ADDPD X5, P_SUM
|
||||
|
||||
ADDQ $8, IDX // IDX += 8
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
|
||||
ADDPD P_SUM, SUM // SUM += P_SUM
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail_start:
|
||||
MOVQ TAIL, LEN
|
||||
SHRQ $1, LEN
|
||||
JZ dot_tail_one
|
||||
|
||||
dot_tail_two:
|
||||
CVTPS2PD (X_PTR)(IDX*4), X2 // X_i = x[i:i+1]
|
||||
CVTPS2PD (Y_PTR)(IDX*4), X6 // X_j = y[i:i+1]
|
||||
MULPD X6, X2 // X_i *= X_j
|
||||
ADDPD X2, SUM // SUM += X_i
|
||||
ADDQ $2, IDX // IDX += 2
|
||||
DECQ LEN
|
||||
JNZ dot_tail_two // } while --LEN > 0
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ dot_end
|
||||
|
||||
dot_tail_one:
|
||||
CVTSS2SD (X_PTR)(IDX*4), X2 // X2 = float64(x[i])
|
||||
CVTSS2SD (Y_PTR)(IDX*4), X3 // X3 = float64(y[i])
|
||||
MULSD X3, X2 // X2 *= X3
|
||||
ADDSD X2, SUM // SUM += X2
|
||||
|
||||
dot_end:
|
||||
HADDPD_SUM_SUM // SUM = \sum{ SUM[i] }
|
||||
MOVSD SUM, sum+48(FP) // return SUM
|
||||
RET
|
||||
6
vendor/gonum.org/v1/gonum/internal/asm/f32/doc.go
generated
vendored
Normal file
6
vendor/gonum.org/v1/gonum/internal/asm/f32/doc.go
generated
vendored
Normal file
@@ -0,0 +1,6 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// Package f32 provides float32 vector primitives.
|
||||
package f32 // import "gonum.org/v1/gonum/internal/asm/f32"
|
||||
85
vendor/gonum.org/v1/gonum/internal/asm/f32/dotinc_amd64.s
generated
vendored
Normal file
85
vendor/gonum.org/v1/gonum/internal/asm/f32/dotinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,85 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC_X R8
|
||||
#define INCx3_X R10
|
||||
#define INC_Y R9
|
||||
#define INCx3_Y R11
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
|
||||
// func DotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float32)
|
||||
TEXT ·DotInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
MOVQ n+48(FP), LEN // LEN = n
|
||||
CMPQ LEN, $0
|
||||
JE dot_end
|
||||
|
||||
MOVQ ix+72(FP), INC_X // INC_X = ix
|
||||
MOVQ iy+80(FP), INC_Y // INC_Y = iy
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(x[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(y[iy])
|
||||
|
||||
MOVQ incX+56(FP), INC_X // INC_X := incX * sizeof(float32)
|
||||
SHLQ $2, INC_X
|
||||
MOVQ incY+64(FP), INC_Y // INC_Y := incY * sizeof(float32)
|
||||
SHLQ $2, INC_Y
|
||||
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $0x3, TAIL // TAIL = LEN % 4
|
||||
SHRQ $2, LEN // LEN = floor( LEN / 4 )
|
||||
JZ dot_tail // if LEN == 0 { goto dot_tail }
|
||||
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0 for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
|
||||
dot_loop: // Loop unrolled 4x do {
|
||||
MOVSS (X_PTR), X2 // X_i = x[i:i+1]
|
||||
MOVSS (X_PTR)(INC_X*1), X3
|
||||
MOVSS (X_PTR)(INC_X*2), X4
|
||||
MOVSS (X_PTR)(INCx3_X*1), X5
|
||||
|
||||
MULSS (Y_PTR), X2 // X_i *= y[i:i+1]
|
||||
MULSS (Y_PTR)(INC_Y*1), X3
|
||||
MULSS (Y_PTR)(INC_Y*2), X4
|
||||
MULSS (Y_PTR)(INCx3_Y*1), X5
|
||||
|
||||
ADDSS X2, SUM // SUM += X_i
|
||||
ADDSS X3, P_SUM
|
||||
ADDSS X4, SUM
|
||||
ADDSS X5, P_SUM
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[INC_X * 4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[INC_Y * 4])
|
||||
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
|
||||
ADDSS P_SUM, SUM // P_SUM += SUM
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail: // do {
|
||||
MOVSS (X_PTR), X2 // X2 = x[i]
|
||||
MULSS (Y_PTR), X2 // X2 *= y[i]
|
||||
ADDSS X2, SUM // SUM += X2
|
||||
ADDQ INC_X, X_PTR // X_PTR += INC_X
|
||||
ADDQ INC_Y, Y_PTR // Y_PTR += INC_Y
|
||||
DECQ TAIL
|
||||
JNZ dot_tail // } while --TAIL > 0
|
||||
|
||||
dot_end:
|
||||
MOVSS SUM, sum+88(FP) // return SUM
|
||||
RET
|
||||
106
vendor/gonum.org/v1/gonum/internal/asm/f32/dotunitary_amd64.s
generated
vendored
Normal file
106
vendor/gonum.org/v1/gonum/internal/asm/f32/dotunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,106 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define HADDPS_SUM_SUM LONG $0xC07C0FF2 // @ HADDPS X0, X0
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define IDX AX
|
||||
#define SUM X0
|
||||
#define P_SUM X1
|
||||
|
||||
// func DotUnitary(x, y []float32) (sum float32)
|
||||
TEXT ·DotUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+24(FP), Y_PTR // Y_PTR = &y
|
||||
PXOR SUM, SUM // SUM = 0
|
||||
MOVQ x_len+8(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+32(FP), LEN
|
||||
CMOVQLE y_len+32(FP), LEN
|
||||
CMPQ LEN, $0
|
||||
JE dot_end
|
||||
|
||||
XORQ IDX, IDX
|
||||
MOVQ Y_PTR, DX
|
||||
ANDQ $0xF, DX // Align on 16-byte boundary for MULPS
|
||||
JZ dot_no_trim // if DX == 0 { goto dot_no_trim }
|
||||
SUBQ $16, DX
|
||||
|
||||
dot_align: // Trim first value(s) in unaligned buffer do {
|
||||
MOVSS (X_PTR)(IDX*4), X2 // X2 = x[i]
|
||||
MULSS (Y_PTR)(IDX*4), X2 // X2 *= y[i]
|
||||
ADDSS X2, SUM // SUM += X2
|
||||
INCQ IDX // IDX++
|
||||
DECQ LEN
|
||||
JZ dot_end // if --TAIL == 0 { return }
|
||||
ADDQ $4, DX
|
||||
JNZ dot_align // } while --DX > 0
|
||||
|
||||
dot_no_trim:
|
||||
PXOR P_SUM, P_SUM // P_SUM = 0 for pipelining
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $0xF, TAIL // TAIL = LEN % 16
|
||||
SHRQ $4, LEN // LEN = floor( LEN / 16 )
|
||||
JZ dot_tail4_start // if LEN == 0 { goto dot_tail4_start }
|
||||
|
||||
dot_loop: // Loop unrolled 16x do {
|
||||
MOVUPS (X_PTR)(IDX*4), X2 // X_i = x[i:i+1]
|
||||
MOVUPS 16(X_PTR)(IDX*4), X3
|
||||
MOVUPS 32(X_PTR)(IDX*4), X4
|
||||
MOVUPS 48(X_PTR)(IDX*4), X5
|
||||
|
||||
MULPS (Y_PTR)(IDX*4), X2 // X_i *= y[i:i+1]
|
||||
MULPS 16(Y_PTR)(IDX*4), X3
|
||||
MULPS 32(Y_PTR)(IDX*4), X4
|
||||
MULPS 48(Y_PTR)(IDX*4), X5
|
||||
|
||||
ADDPS X2, SUM // SUM += X_i
|
||||
ADDPS X3, P_SUM
|
||||
ADDPS X4, SUM
|
||||
ADDPS X5, P_SUM
|
||||
|
||||
ADDQ $16, IDX // IDX += 16
|
||||
DECQ LEN
|
||||
JNZ dot_loop // } while --LEN > 0
|
||||
|
||||
ADDPS P_SUM, SUM // SUM += P_SUM
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE dot_end
|
||||
|
||||
dot_tail4_start: // Reset loop counter for 4-wide tail loop
|
||||
MOVQ TAIL, LEN // LEN = floor( TAIL / 4 )
|
||||
SHRQ $2, LEN
|
||||
JZ dot_tail_start // if LEN == 0 { goto dot_tail_start }
|
||||
|
||||
dot_tail4_loop: // Loop unrolled 4x do {
|
||||
MOVUPS (X_PTR)(IDX*4), X2 // X_i = x[i:i+1]
|
||||
MULPS (Y_PTR)(IDX*4), X2 // X_i *= y[i:i+1]
|
||||
ADDPS X2, SUM // SUM += X_i
|
||||
ADDQ $4, IDX // i += 4
|
||||
DECQ LEN
|
||||
JNZ dot_tail4_loop // } while --LEN > 0
|
||||
|
||||
dot_tail_start: // Reset loop counter for 1-wide tail loop
|
||||
ANDQ $3, TAIL // TAIL = TAIL % 4
|
||||
JZ dot_end // if TAIL == 0 { return }
|
||||
|
||||
dot_tail: // do {
|
||||
MOVSS (X_PTR)(IDX*4), X2 // X2 = x[i]
|
||||
MULSS (Y_PTR)(IDX*4), X2 // X2 *= y[i]
|
||||
ADDSS X2, SUM // psum += X2
|
||||
INCQ IDX // IDX++
|
||||
DECQ TAIL
|
||||
JNZ dot_tail // } while --TAIL > 0
|
||||
|
||||
dot_end:
|
||||
HADDPS_SUM_SUM // SUM = \sum{ SUM[i] }
|
||||
HADDPS_SUM_SUM
|
||||
MOVSS SUM, sum+48(FP) // return SUM
|
||||
RET
|
||||
18
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_amd64.go
generated
vendored
Normal file
18
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_amd64.go
generated
vendored
Normal file
@@ -0,0 +1,18 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !noasm && !gccgo && !safe
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
package f32
|
||||
|
||||
// Ger performs the rank-one operation
|
||||
//
|
||||
// A += alpha * x * yᵀ
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Ger(m, n uintptr, alpha float32,
|
||||
x []float32, incX uintptr,
|
||||
y []float32, incY uintptr,
|
||||
a []float32, lda uintptr)
|
||||
757
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_amd64.s
generated
vendored
Normal file
757
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,757 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define SIZE 4
|
||||
#define BITSIZE 2
|
||||
#define KERNELSIZE 3
|
||||
|
||||
#define M_DIM m+0(FP)
|
||||
#define M CX
|
||||
#define N_DIM n+8(FP)
|
||||
#define N BX
|
||||
|
||||
#define TMP1 R14
|
||||
#define TMP2 R15
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y y_base+56(FP)
|
||||
#define Y_PTR DX
|
||||
#define A_ROW AX
|
||||
#define A_PTR DI
|
||||
|
||||
#define INC_X R8
|
||||
#define INC3_X R9
|
||||
|
||||
#define INC_Y R10
|
||||
#define INC3_Y R11
|
||||
|
||||
#define LDA R12
|
||||
#define LDA3 R13
|
||||
|
||||
#define ALPHA X0
|
||||
#define ALPHA_SPILL al-16(SP)
|
||||
|
||||
#define LOAD_ALPHA \
|
||||
MOVSS alpha+16(FP), ALPHA \
|
||||
SHUFPS $0, ALPHA, ALPHA
|
||||
|
||||
#define LOAD_SCALED4 \
|
||||
PREFETCHNTA 16*SIZE(X_PTR) \
|
||||
MOVDDUP (X_PTR), X1 \
|
||||
MOVDDUP 2*SIZE(X_PTR), X3 \
|
||||
MOVSHDUP X1, X2 \
|
||||
MOVSHDUP X3, X4 \
|
||||
MOVSLDUP X1, X1 \
|
||||
MOVSLDUP X3, X3 \
|
||||
MULPS ALPHA, X1 \
|
||||
MULPS ALPHA, X2 \
|
||||
MULPS ALPHA, X3 \
|
||||
MULPS ALPHA, X4
|
||||
|
||||
#define LOAD_SCALED2 \
|
||||
MOVDDUP (X_PTR), X1 \
|
||||
MOVSHDUP X1, X2 \
|
||||
MOVSLDUP X1, X1 \
|
||||
MULPS ALPHA, X1 \
|
||||
MULPS ALPHA, X2
|
||||
|
||||
#define LOAD_SCALED1 \
|
||||
MOVSS (X_PTR), X1 \
|
||||
SHUFPS $0, X1, X1 \
|
||||
MULPS ALPHA, X1
|
||||
|
||||
#define LOAD_SCALED4_INC \
|
||||
PREFETCHNTA (X_PTR)(INC_X*8) \
|
||||
MOVSS (X_PTR), X1 \
|
||||
MOVSS (X_PTR)(INC_X*1), X2 \
|
||||
MOVSS (X_PTR)(INC_X*2), X3 \
|
||||
MOVSS (X_PTR)(INC3_X*1), X4 \
|
||||
SHUFPS $0, X1, X1 \
|
||||
SHUFPS $0, X2, X2 \
|
||||
SHUFPS $0, X3, X3 \
|
||||
SHUFPS $0, X4, X4 \
|
||||
MULPS ALPHA, X1 \
|
||||
MULPS ALPHA, X2 \
|
||||
MULPS ALPHA, X3 \
|
||||
MULPS ALPHA, X4
|
||||
|
||||
#define LOAD_SCALED2_INC \
|
||||
MOVSS (X_PTR), X1 \
|
||||
MOVSS (X_PTR)(INC_X*1), X2 \
|
||||
SHUFPS $0, X1, X1 \
|
||||
SHUFPS $0, X2, X2 \
|
||||
MULPS ALPHA, X1 \
|
||||
MULPS ALPHA, X2
|
||||
|
||||
#define KERNEL_LOAD8 \
|
||||
MOVUPS (Y_PTR), X5 \
|
||||
MOVUPS 4*SIZE(Y_PTR), X6
|
||||
|
||||
#define KERNEL_LOAD8_INC \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MOVSS (Y_PTR)(INC_Y*1), X6 \
|
||||
MOVSS (Y_PTR)(INC_Y*2), X7 \
|
||||
MOVSS (Y_PTR)(INC3_Y*1), X8 \
|
||||
UNPCKLPS X6, X5 \
|
||||
UNPCKLPS X8, X7 \
|
||||
MOVLHPS X7, X5 \
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR \
|
||||
MOVSS (Y_PTR), X6 \
|
||||
MOVSS (Y_PTR)(INC_Y*1), X7 \
|
||||
MOVSS (Y_PTR)(INC_Y*2), X8 \
|
||||
MOVSS (Y_PTR)(INC3_Y*1), X9 \
|
||||
UNPCKLPS X7, X6 \
|
||||
UNPCKLPS X9, X8 \
|
||||
MOVLHPS X8, X6
|
||||
|
||||
#define KERNEL_LOAD4 \
|
||||
MOVUPS (Y_PTR), X5
|
||||
|
||||
#define KERNEL_LOAD4_INC \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MOVSS (Y_PTR)(INC_Y*1), X6 \
|
||||
MOVSS (Y_PTR)(INC_Y*2), X7 \
|
||||
MOVSS (Y_PTR)(INC3_Y*1), X8 \
|
||||
UNPCKLPS X6, X5 \
|
||||
UNPCKLPS X8, X7 \
|
||||
MOVLHPS X7, X5
|
||||
|
||||
#define KERNEL_LOAD2 \
|
||||
MOVSD (Y_PTR), X5
|
||||
|
||||
#define KERNEL_LOAD2_INC \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MOVSS (Y_PTR)(INC_Y*1), X6 \
|
||||
UNPCKLPS X6, X5
|
||||
|
||||
#define KERNEL_4x8 \
|
||||
MOVUPS X5, X7 \
|
||||
MOVUPS X6, X8 \
|
||||
MOVUPS X5, X9 \
|
||||
MOVUPS X6, X10 \
|
||||
MOVUPS X5, X11 \
|
||||
MOVUPS X6, X12 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X1, X6 \
|
||||
MULPS X2, X7 \
|
||||
MULPS X2, X8 \
|
||||
MULPS X3, X9 \
|
||||
MULPS X3, X10 \
|
||||
MULPS X4, X11 \
|
||||
MULPS X4, X12
|
||||
|
||||
#define STORE_4x8 \
|
||||
MOVUPS ALPHA, ALPHA_SPILL \
|
||||
MOVUPS (A_PTR), X13 \
|
||||
ADDPS X13, X5 \
|
||||
MOVUPS 4*SIZE(A_PTR), X14 \
|
||||
ADDPS X14, X6 \
|
||||
MOVUPS (A_PTR)(LDA*1), X15 \
|
||||
ADDPS X15, X7 \
|
||||
MOVUPS 4*SIZE(A_PTR)(LDA*1), X0 \
|
||||
ADDPS X0, X8 \
|
||||
MOVUPS (A_PTR)(LDA*2), X13 \
|
||||
ADDPS X13, X9 \
|
||||
MOVUPS 4*SIZE(A_PTR)(LDA*2), X14 \
|
||||
ADDPS X14, X10 \
|
||||
MOVUPS (A_PTR)(LDA3*1), X15 \
|
||||
ADDPS X15, X11 \
|
||||
MOVUPS 4*SIZE(A_PTR)(LDA3*1), X0 \
|
||||
ADDPS X0, X12 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
MOVUPS X6, 4*SIZE(A_PTR) \
|
||||
MOVUPS X7, (A_PTR)(LDA*1) \
|
||||
MOVUPS X8, 4*SIZE(A_PTR)(LDA*1) \
|
||||
MOVUPS X9, (A_PTR)(LDA*2) \
|
||||
MOVUPS X10, 4*SIZE(A_PTR)(LDA*2) \
|
||||
MOVUPS X11, (A_PTR)(LDA3*1) \
|
||||
MOVUPS X12, 4*SIZE(A_PTR)(LDA3*1) \
|
||||
MOVUPS ALPHA_SPILL, ALPHA \
|
||||
ADDQ $8*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_4x4 \
|
||||
MOVUPS X5, X6 \
|
||||
MOVUPS X5, X7 \
|
||||
MOVUPS X5, X8 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X2, X6 \
|
||||
MULPS X3, X7 \
|
||||
MULPS X4, X8
|
||||
|
||||
#define STORE_4x4 \
|
||||
MOVUPS (A_PTR), X13 \
|
||||
ADDPS X13, X5 \
|
||||
MOVUPS (A_PTR)(LDA*1), X14 \
|
||||
ADDPS X14, X6 \
|
||||
MOVUPS (A_PTR)(LDA*2), X15 \
|
||||
ADDPS X15, X7 \
|
||||
MOVUPS (A_PTR)(LDA3*1), X13 \
|
||||
ADDPS X13, X8 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
MOVUPS X6, (A_PTR)(LDA*1) \
|
||||
MOVUPS X7, (A_PTR)(LDA*2) \
|
||||
MOVUPS X8, (A_PTR)(LDA3*1) \
|
||||
ADDQ $4*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_4x2 \
|
||||
MOVUPS X5, X6 \
|
||||
MOVUPS X5, X7 \
|
||||
MOVUPS X5, X8 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X2, X6 \
|
||||
MULPS X3, X7 \
|
||||
MULPS X4, X8
|
||||
|
||||
#define STORE_4x2 \
|
||||
MOVSD (A_PTR), X9 \
|
||||
ADDPS X9, X5 \
|
||||
MOVSD (A_PTR)(LDA*1), X10 \
|
||||
ADDPS X10, X6 \
|
||||
MOVSD (A_PTR)(LDA*2), X11 \
|
||||
ADDPS X11, X7 \
|
||||
MOVSD (A_PTR)(LDA3*1), X12 \
|
||||
ADDPS X12, X8 \
|
||||
MOVSD X5, (A_PTR) \
|
||||
MOVSD X6, (A_PTR)(LDA*1) \
|
||||
MOVSD X7, (A_PTR)(LDA*2) \
|
||||
MOVSD X8, (A_PTR)(LDA3*1) \
|
||||
ADDQ $2*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_4x1 \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MOVSS X5, X6 \
|
||||
MOVSS X5, X7 \
|
||||
MOVSS X5, X8 \
|
||||
MULSS X1, X5 \
|
||||
MULSS X2, X6 \
|
||||
MULSS X3, X7 \
|
||||
MULSS X4, X8
|
||||
|
||||
#define STORE_4x1 \
|
||||
ADDSS (A_PTR), X5 \
|
||||
ADDSS (A_PTR)(LDA*1), X6 \
|
||||
ADDSS (A_PTR)(LDA*2), X7 \
|
||||
ADDSS (A_PTR)(LDA3*1), X8 \
|
||||
MOVSS X5, (A_PTR) \
|
||||
MOVSS X6, (A_PTR)(LDA*1) \
|
||||
MOVSS X7, (A_PTR)(LDA*2) \
|
||||
MOVSS X8, (A_PTR)(LDA3*1) \
|
||||
ADDQ $SIZE, A_PTR
|
||||
|
||||
#define KERNEL_2x8 \
|
||||
MOVUPS X5, X7 \
|
||||
MOVUPS X6, X8 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X1, X6 \
|
||||
MULPS X2, X7 \
|
||||
MULPS X2, X8
|
||||
|
||||
#define STORE_2x8 \
|
||||
MOVUPS (A_PTR), X9 \
|
||||
ADDPS X9, X5 \
|
||||
MOVUPS 4*SIZE(A_PTR), X10 \
|
||||
ADDPS X10, X6 \
|
||||
MOVUPS (A_PTR)(LDA*1), X11 \
|
||||
ADDPS X11, X7 \
|
||||
MOVUPS 4*SIZE(A_PTR)(LDA*1), X12 \
|
||||
ADDPS X12, X8 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
MOVUPS X6, 4*SIZE(A_PTR) \
|
||||
MOVUPS X7, (A_PTR)(LDA*1) \
|
||||
MOVUPS X8, 4*SIZE(A_PTR)(LDA*1) \
|
||||
ADDQ $8*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_2x4 \
|
||||
MOVUPS X5, X6 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X2, X6
|
||||
|
||||
#define STORE_2x4 \
|
||||
MOVUPS (A_PTR), X9 \
|
||||
ADDPS X9, X5 \
|
||||
MOVUPS (A_PTR)(LDA*1), X11 \
|
||||
ADDPS X11, X6 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
MOVUPS X6, (A_PTR)(LDA*1) \
|
||||
ADDQ $4*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_2x2 \
|
||||
MOVSD X5, X6 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X2, X6
|
||||
|
||||
#define STORE_2x2 \
|
||||
MOVSD (A_PTR), X7 \
|
||||
ADDPS X7, X5 \
|
||||
MOVSD (A_PTR)(LDA*1), X8 \
|
||||
ADDPS X8, X6 \
|
||||
MOVSD X5, (A_PTR) \
|
||||
MOVSD X6, (A_PTR)(LDA*1) \
|
||||
ADDQ $2*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_2x1 \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MOVSS X5, X6 \
|
||||
MULSS X1, X5 \
|
||||
MULSS X2, X6
|
||||
|
||||
#define STORE_2x1 \
|
||||
ADDSS (A_PTR), X5 \
|
||||
ADDSS (A_PTR)(LDA*1), X6 \
|
||||
MOVSS X5, (A_PTR) \
|
||||
MOVSS X6, (A_PTR)(LDA*1) \
|
||||
ADDQ $SIZE, A_PTR
|
||||
|
||||
#define KERNEL_1x8 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X1, X6
|
||||
|
||||
#define STORE_1x8 \
|
||||
MOVUPS (A_PTR), X7 \
|
||||
ADDPS X7, X5 \
|
||||
MOVUPS 4*SIZE(A_PTR), X8 \
|
||||
ADDPS X8, X6 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
MOVUPS X6, 4*SIZE(A_PTR) \
|
||||
ADDQ $8*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_1x4 \
|
||||
MULPS X1, X5 \
|
||||
MULPS X1, X6
|
||||
|
||||
#define STORE_1x4 \
|
||||
MOVUPS (A_PTR), X7 \
|
||||
ADDPS X7, X5 \
|
||||
MOVUPS X5, (A_PTR) \
|
||||
ADDQ $4*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_1x2 \
|
||||
MULPS X1, X5
|
||||
|
||||
#define STORE_1x2 \
|
||||
MOVSD (A_PTR), X6 \
|
||||
ADDPS X6, X5 \
|
||||
MOVSD X5, (A_PTR) \
|
||||
ADDQ $2*SIZE, A_PTR
|
||||
|
||||
#define KERNEL_1x1 \
|
||||
MOVSS (Y_PTR), X5 \
|
||||
MULSS X1, X5
|
||||
|
||||
#define STORE_1x1 \
|
||||
ADDSS (A_PTR), X5 \
|
||||
MOVSS X5, (A_PTR) \
|
||||
ADDQ $SIZE, A_PTR
|
||||
|
||||
// func Ger(m, n uintptr, alpha float32,
|
||||
// x []float32, incX uintptr,
|
||||
// y []float32, incY uintptr,
|
||||
// a []float32, lda uintptr)
|
||||
TEXT ·Ger(SB), 0, $16-120
|
||||
MOVQ M_DIM, M
|
||||
MOVQ N_DIM, N
|
||||
CMPQ M, $0
|
||||
JE end
|
||||
CMPQ N, $0
|
||||
JE end
|
||||
|
||||
LOAD_ALPHA
|
||||
|
||||
MOVQ x_base+24(FP), X_PTR
|
||||
MOVQ y_base+56(FP), Y_PTR
|
||||
MOVQ a_base+88(FP), A_ROW
|
||||
MOVQ A_ROW, A_PTR
|
||||
MOVQ lda+112(FP), LDA // LDA = LDA * sizeof(float32)
|
||||
SHLQ $BITSIZE, LDA
|
||||
LEAQ (LDA)(LDA*2), LDA3 // LDA3 = LDA * 3
|
||||
|
||||
CMPQ incY+80(FP), $1 // Check for dense vector Y (fast-path)
|
||||
JNE inc
|
||||
CMPQ incX+48(FP), $1 // Check for dense vector X (fast-path)
|
||||
JNE inc
|
||||
|
||||
SHRQ $2, M
|
||||
JZ r2
|
||||
|
||||
r4:
|
||||
|
||||
// LOAD 4
|
||||
LOAD_SCALED4
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ r4c4
|
||||
|
||||
r4c8:
|
||||
// 4x8 KERNEL
|
||||
KERNEL_LOAD8
|
||||
KERNEL_4x8
|
||||
STORE_4x8
|
||||
|
||||
ADDQ $8*SIZE, Y_PTR
|
||||
|
||||
DECQ N
|
||||
JNZ r4c8
|
||||
|
||||
r4c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ r4c2
|
||||
|
||||
// 4x4 KERNEL
|
||||
KERNEL_LOAD4
|
||||
KERNEL_4x4
|
||||
STORE_4x4
|
||||
|
||||
ADDQ $4*SIZE, Y_PTR
|
||||
|
||||
r4c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ r4c1
|
||||
|
||||
// 4x2 KERNEL
|
||||
KERNEL_LOAD2
|
||||
KERNEL_4x2
|
||||
STORE_4x2
|
||||
|
||||
ADDQ $2*SIZE, Y_PTR
|
||||
|
||||
r4c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ r4end
|
||||
|
||||
// 4x1 KERNEL
|
||||
KERNEL_4x1
|
||||
STORE_4x1
|
||||
|
||||
ADDQ $SIZE, Y_PTR
|
||||
|
||||
r4end:
|
||||
ADDQ $4*SIZE, X_PTR
|
||||
MOVQ Y, Y_PTR
|
||||
LEAQ (A_ROW)(LDA*4), A_ROW
|
||||
MOVQ A_ROW, A_PTR
|
||||
|
||||
DECQ M
|
||||
JNZ r4
|
||||
|
||||
r2:
|
||||
TESTQ $2, M_DIM
|
||||
JZ r1
|
||||
|
||||
// LOAD 2
|
||||
LOAD_SCALED2
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ r2c4
|
||||
|
||||
r2c8:
|
||||
// 2x8 KERNEL
|
||||
KERNEL_LOAD8
|
||||
KERNEL_2x8
|
||||
STORE_2x8
|
||||
|
||||
ADDQ $8*SIZE, Y_PTR
|
||||
|
||||
DECQ N
|
||||
JNZ r2c8
|
||||
|
||||
r2c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ r2c2
|
||||
|
||||
// 2x4 KERNEL
|
||||
KERNEL_LOAD4
|
||||
KERNEL_2x4
|
||||
STORE_2x4
|
||||
|
||||
ADDQ $4*SIZE, Y_PTR
|
||||
|
||||
r2c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ r2c1
|
||||
|
||||
// 2x2 KERNEL
|
||||
KERNEL_LOAD2
|
||||
KERNEL_2x2
|
||||
STORE_2x2
|
||||
|
||||
ADDQ $2*SIZE, Y_PTR
|
||||
|
||||
r2c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ r2end
|
||||
|
||||
// 2x1 KERNEL
|
||||
KERNEL_2x1
|
||||
STORE_2x1
|
||||
|
||||
ADDQ $SIZE, Y_PTR
|
||||
|
||||
r2end:
|
||||
ADDQ $2*SIZE, X_PTR
|
||||
MOVQ Y, Y_PTR
|
||||
LEAQ (A_ROW)(LDA*2), A_ROW
|
||||
MOVQ A_ROW, A_PTR
|
||||
|
||||
r1:
|
||||
TESTQ $1, M_DIM
|
||||
JZ end
|
||||
|
||||
// LOAD 1
|
||||
LOAD_SCALED1
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ r1c4
|
||||
|
||||
r1c8:
|
||||
// 1x8 KERNEL
|
||||
KERNEL_LOAD8
|
||||
KERNEL_1x8
|
||||
STORE_1x8
|
||||
|
||||
ADDQ $8*SIZE, Y_PTR
|
||||
|
||||
DECQ N
|
||||
JNZ r1c8
|
||||
|
||||
r1c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ r1c2
|
||||
|
||||
// 1x4 KERNEL
|
||||
KERNEL_LOAD4
|
||||
KERNEL_1x4
|
||||
STORE_1x4
|
||||
|
||||
ADDQ $4*SIZE, Y_PTR
|
||||
|
||||
r1c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ r1c1
|
||||
|
||||
// 1x2 KERNEL
|
||||
KERNEL_LOAD2
|
||||
KERNEL_1x2
|
||||
STORE_1x2
|
||||
|
||||
ADDQ $2*SIZE, Y_PTR
|
||||
|
||||
r1c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ end
|
||||
|
||||
// 1x1 KERNEL
|
||||
KERNEL_1x1
|
||||
STORE_1x1
|
||||
|
||||
end:
|
||||
RET
|
||||
|
||||
inc: // Algorithm for incY != 0 ( split loads in kernel )
|
||||
|
||||
MOVQ incX+48(FP), INC_X // INC_X = incX * sizeof(float32)
|
||||
SHLQ $BITSIZE, INC_X
|
||||
MOVQ incY+80(FP), INC_Y // INC_Y = incY * sizeof(float32)
|
||||
SHLQ $BITSIZE, INC_Y
|
||||
LEAQ (INC_X)(INC_X*2), INC3_X // INC3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INC3_Y // INC3_Y = INC_Y * 3
|
||||
|
||||
XORQ TMP2, TMP2
|
||||
MOVQ M, TMP1
|
||||
SUBQ $1, TMP1
|
||||
IMULQ INC_X, TMP1
|
||||
NEGQ TMP1
|
||||
CMPQ INC_X, $0
|
||||
CMOVQLT TMP1, TMP2
|
||||
LEAQ (X_PTR)(TMP2*SIZE), X_PTR
|
||||
|
||||
XORQ TMP2, TMP2
|
||||
MOVQ N, TMP1
|
||||
SUBQ $1, TMP1
|
||||
IMULQ INC_Y, TMP1
|
||||
NEGQ TMP1
|
||||
CMPQ INC_Y, $0
|
||||
CMOVQLT TMP1, TMP2
|
||||
LEAQ (Y_PTR)(TMP2*SIZE), Y_PTR
|
||||
|
||||
SHRQ $2, M
|
||||
JZ inc_r2
|
||||
|
||||
inc_r4:
|
||||
// LOAD 4
|
||||
LOAD_SCALED4_INC
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ inc_r4c4
|
||||
|
||||
inc_r4c8:
|
||||
// 4x4 KERNEL
|
||||
KERNEL_LOAD8_INC
|
||||
KERNEL_4x8
|
||||
STORE_4x8
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
DECQ N
|
||||
JNZ inc_r4c8
|
||||
|
||||
inc_r4c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ inc_r4c2
|
||||
|
||||
// 4x4 KERNEL
|
||||
KERNEL_LOAD4_INC
|
||||
KERNEL_4x4
|
||||
STORE_4x4
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
|
||||
inc_r4c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ inc_r4c1
|
||||
|
||||
// 4x2 KERNEL
|
||||
KERNEL_LOAD2_INC
|
||||
KERNEL_4x2
|
||||
STORE_4x2
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
|
||||
|
||||
inc_r4c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ inc_r4end
|
||||
|
||||
// 4x1 KERNEL
|
||||
KERNEL_4x1
|
||||
STORE_4x1
|
||||
|
||||
ADDQ INC_Y, Y_PTR
|
||||
|
||||
inc_r4end:
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR
|
||||
MOVQ Y, Y_PTR
|
||||
LEAQ (A_ROW)(LDA*4), A_ROW
|
||||
MOVQ A_ROW, A_PTR
|
||||
|
||||
DECQ M
|
||||
JNZ inc_r4
|
||||
|
||||
inc_r2:
|
||||
TESTQ $2, M_DIM
|
||||
JZ inc_r1
|
||||
|
||||
// LOAD 2
|
||||
LOAD_SCALED2_INC
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ inc_r2c4
|
||||
|
||||
inc_r2c8:
|
||||
// 2x8 KERNEL
|
||||
KERNEL_LOAD8_INC
|
||||
KERNEL_2x8
|
||||
STORE_2x8
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
DECQ N
|
||||
JNZ inc_r2c8
|
||||
|
||||
inc_r2c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ inc_r2c2
|
||||
|
||||
// 2x4 KERNEL
|
||||
KERNEL_LOAD4_INC
|
||||
KERNEL_2x4
|
||||
STORE_2x4
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
|
||||
inc_r2c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ inc_r2c1
|
||||
|
||||
// 2x2 KERNEL
|
||||
KERNEL_LOAD2_INC
|
||||
KERNEL_2x2
|
||||
STORE_2x2
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
|
||||
|
||||
inc_r2c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ inc_r2end
|
||||
|
||||
// 2x1 KERNEL
|
||||
KERNEL_2x1
|
||||
STORE_2x1
|
||||
|
||||
ADDQ INC_Y, Y_PTR
|
||||
|
||||
inc_r2end:
|
||||
LEAQ (X_PTR)(INC_X*2), X_PTR
|
||||
MOVQ Y, Y_PTR
|
||||
LEAQ (A_ROW)(LDA*2), A_ROW
|
||||
MOVQ A_ROW, A_PTR
|
||||
|
||||
inc_r1:
|
||||
TESTQ $1, M_DIM
|
||||
JZ end
|
||||
|
||||
// LOAD 1
|
||||
LOAD_SCALED1
|
||||
|
||||
MOVQ N_DIM, N
|
||||
SHRQ $KERNELSIZE, N
|
||||
JZ inc_r1c4
|
||||
|
||||
inc_r1c8:
|
||||
// 1x8 KERNEL
|
||||
KERNEL_LOAD8_INC
|
||||
KERNEL_1x8
|
||||
STORE_1x8
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
DECQ N
|
||||
JNZ inc_r1c8
|
||||
|
||||
inc_r1c4:
|
||||
TESTQ $4, N_DIM
|
||||
JZ inc_r1c2
|
||||
|
||||
// 1x4 KERNEL
|
||||
KERNEL_LOAD4_INC
|
||||
KERNEL_1x4
|
||||
STORE_1x4
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR
|
||||
|
||||
inc_r1c2:
|
||||
TESTQ $2, N_DIM
|
||||
JZ inc_r1c1
|
||||
|
||||
// 1x2 KERNEL
|
||||
KERNEL_LOAD2_INC
|
||||
KERNEL_1x2
|
||||
STORE_1x2
|
||||
|
||||
LEAQ (Y_PTR)(INC_Y*2), Y_PTR
|
||||
|
||||
inc_r1c1:
|
||||
TESTQ $1, N_DIM
|
||||
JZ inc_end
|
||||
|
||||
// 1x1 KERNEL
|
||||
KERNEL_1x1
|
||||
STORE_1x1
|
||||
|
||||
inc_end:
|
||||
RET
|
||||
39
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_noasm.go
generated
vendored
Normal file
39
vendor/gonum.org/v1/gonum/internal/asm/f32/ge_noasm.go
generated
vendored
Normal file
@@ -0,0 +1,39 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !amd64 || noasm || gccgo || safe
|
||||
// +build !amd64 noasm gccgo safe
|
||||
|
||||
package f32
|
||||
|
||||
// Ger performs the rank-one operation
|
||||
//
|
||||
// A += alpha * x * yᵀ
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha is a scalar.
|
||||
func Ger(m, n uintptr, alpha float32, x []float32, incX uintptr, y []float32, incY uintptr, a []float32, lda uintptr) {
|
||||
|
||||
if incX == 1 && incY == 1 {
|
||||
x = x[:m]
|
||||
y = y[:n]
|
||||
for i, xv := range x {
|
||||
AxpyUnitary(alpha*xv, y, a[uintptr(i)*lda:uintptr(i)*lda+n])
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
var ky, kx uintptr
|
||||
if int(incY) < 0 {
|
||||
ky = uintptr(-int(n-1) * int(incY))
|
||||
}
|
||||
if int(incX) < 0 {
|
||||
kx = uintptr(-int(m-1) * int(incX))
|
||||
}
|
||||
|
||||
ix := kx
|
||||
for i := 0; i < int(m); i++ {
|
||||
AxpyInc(alpha*x[ix], y, a[uintptr(i)*lda:uintptr(i)*lda+n], uintptr(n), uintptr(incY), 1, uintptr(ky), 0)
|
||||
ix += incX
|
||||
}
|
||||
}
|
||||
92
vendor/gonum.org/v1/gonum/internal/asm/f32/gemv.go
generated
vendored
Normal file
92
vendor/gonum.org/v1/gonum/internal/asm/f32/gemv.go
generated
vendored
Normal file
@@ -0,0 +1,92 @@
|
||||
// Copyright ©2017 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package f32
|
||||
|
||||
// GemvN computes
|
||||
//
|
||||
// y = alpha * A * x + beta * y
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
func GemvN(m, n uintptr, alpha float32, a []float32, lda uintptr, x []float32, incX uintptr, beta float32, y []float32, incY uintptr) {
|
||||
var kx, ky, i uintptr
|
||||
if int(incX) < 0 {
|
||||
kx = uintptr(-int(n-1) * int(incX))
|
||||
}
|
||||
if int(incY) < 0 {
|
||||
ky = uintptr(-int(m-1) * int(incY))
|
||||
}
|
||||
|
||||
if incX == 1 && incY == 1 {
|
||||
if beta == 0 {
|
||||
for i = 0; i < m; i++ {
|
||||
y[i] = alpha * DotUnitary(a[lda*i:lda*i+n], x)
|
||||
}
|
||||
return
|
||||
}
|
||||
for i = 0; i < m; i++ {
|
||||
y[i] = y[i]*beta + alpha*DotUnitary(a[lda*i:lda*i+n], x)
|
||||
}
|
||||
return
|
||||
}
|
||||
iy := ky
|
||||
if beta == 0 {
|
||||
for i = 0; i < m; i++ {
|
||||
y[iy] = alpha * DotInc(x, a[lda*i:lda*i+n], n, incX, 1, kx, 0)
|
||||
iy += incY
|
||||
}
|
||||
return
|
||||
}
|
||||
for i = 0; i < m; i++ {
|
||||
y[iy] = y[iy]*beta + alpha*DotInc(x, a[lda*i:lda*i+n], n, incX, 1, kx, 0)
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// GemvT computes
|
||||
//
|
||||
// y = alpha * Aᵀ * x + beta * y
|
||||
//
|
||||
// where A is an m×n dense matrix, x and y are vectors, and alpha and beta are scalars.
|
||||
func GemvT(m, n uintptr, alpha float32, a []float32, lda uintptr, x []float32, incX uintptr, beta float32, y []float32, incY uintptr) {
|
||||
var kx, ky, i uintptr
|
||||
if int(incX) < 0 {
|
||||
kx = uintptr(-int(m-1) * int(incX))
|
||||
}
|
||||
if int(incY) < 0 {
|
||||
ky = uintptr(-int(n-1) * int(incY))
|
||||
}
|
||||
switch {
|
||||
case beta == 0: // beta == 0 is special-cased to memclear
|
||||
if incY == 1 {
|
||||
for i := range y {
|
||||
y[i] = 0
|
||||
}
|
||||
} else {
|
||||
iy := ky
|
||||
for i := 0; i < int(n); i++ {
|
||||
y[iy] = 0
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
case int(incY) < 0:
|
||||
ScalInc(beta, y, n, uintptr(int(-incY)))
|
||||
case incY == 1:
|
||||
ScalUnitary(beta, y[:n])
|
||||
default:
|
||||
ScalInc(beta, y, n, incY)
|
||||
}
|
||||
|
||||
if incX == 1 && incY == 1 {
|
||||
for i = 0; i < m; i++ {
|
||||
AxpyUnitaryTo(y, alpha*x[i], a[lda*i:lda*i+n], y)
|
||||
}
|
||||
return
|
||||
}
|
||||
ix := kx
|
||||
for i = 0; i < m; i++ {
|
||||
AxpyInc(alpha*x[ix], a[lda*i:lda*i+n], y, n, 1, incY, 0, ky)
|
||||
ix += incX
|
||||
}
|
||||
}
|
||||
90
vendor/gonum.org/v1/gonum/internal/asm/f32/l2norm.go
generated
vendored
Normal file
90
vendor/gonum.org/v1/gonum/internal/asm/f32/l2norm.go
generated
vendored
Normal file
@@ -0,0 +1,90 @@
|
||||
// Copyright ©2019 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package f32
|
||||
|
||||
import "gonum.org/v1/gonum/internal/math32"
|
||||
|
||||
// L2NormUnitary is the level 2 norm of x.
|
||||
func L2NormUnitary(x []float32) (sum float32) {
|
||||
var scale float32
|
||||
var sumSquares float32 = 1
|
||||
for _, v := range x {
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math32.Abs(v)
|
||||
if math32.IsNaN(absxi) {
|
||||
return math32.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math32.IsInf(scale, 1) {
|
||||
return math32.Inf(1)
|
||||
}
|
||||
return scale * math32.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// L2NormInc is the level 2 norm of x.
|
||||
func L2NormInc(x []float32, n, incX uintptr) (sum float32) {
|
||||
var scale float32
|
||||
var sumSquares float32 = 1
|
||||
for ix := uintptr(0); ix < n*incX; ix += incX {
|
||||
val := x[ix]
|
||||
if val == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math32.Abs(val)
|
||||
if math32.IsNaN(absxi) {
|
||||
return math32.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math32.IsInf(scale, 1) {
|
||||
return math32.Inf(1)
|
||||
}
|
||||
return scale * math32.Sqrt(sumSquares)
|
||||
}
|
||||
|
||||
// L2DistanceUnitary is the L2 norm of x-y.
|
||||
func L2DistanceUnitary(x, y []float32) (sum float32) {
|
||||
var scale float32
|
||||
var sumSquares float32 = 1
|
||||
for i, v := range x {
|
||||
v -= y[i]
|
||||
if v == 0 {
|
||||
continue
|
||||
}
|
||||
absxi := math32.Abs(v)
|
||||
if math32.IsNaN(absxi) {
|
||||
return math32.NaN()
|
||||
}
|
||||
if scale < absxi {
|
||||
s := scale / absxi
|
||||
sumSquares = 1 + sumSquares*s*s
|
||||
scale = absxi
|
||||
} else {
|
||||
s := absxi / scale
|
||||
sumSquares += s * s
|
||||
}
|
||||
}
|
||||
if math32.IsInf(scale, 1) {
|
||||
return math32.Inf(1)
|
||||
}
|
||||
return scale * math32.Sqrt(sumSquares)
|
||||
}
|
||||
59
vendor/gonum.org/v1/gonum/internal/asm/f32/scal.go
generated
vendored
Normal file
59
vendor/gonum.org/v1/gonum/internal/asm/f32/scal.go
generated
vendored
Normal file
@@ -0,0 +1,59 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
package f32
|
||||
|
||||
// ScalUnitary is
|
||||
//
|
||||
// for i := range x {
|
||||
// x[i] *= alpha
|
||||
// }
|
||||
func ScalUnitary(alpha float32, x []float32) {
|
||||
for i := range x {
|
||||
x[i] *= alpha
|
||||
}
|
||||
}
|
||||
|
||||
// ScalUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha * v
|
||||
// }
|
||||
func ScalUnitaryTo(dst []float32, alpha float32, x []float32) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// ScalInc is
|
||||
//
|
||||
// var ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// x[ix] *= alpha
|
||||
// ix += incX
|
||||
// }
|
||||
func ScalInc(alpha float32, x []float32, n, incX uintptr) {
|
||||
var ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
x[ix] *= alpha
|
||||
ix += incX
|
||||
}
|
||||
}
|
||||
|
||||
// ScalIncTo is
|
||||
//
|
||||
// var idst, ix uintptr
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha * x[ix]
|
||||
// ix += incX
|
||||
// idst += incDst
|
||||
// }
|
||||
func ScalIncTo(dst []float32, incDst uintptr, alpha float32, x []float32, n, incX uintptr) {
|
||||
var idst, ix uintptr
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha * x[ix]
|
||||
ix += incX
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
86
vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_amd64.go
generated
vendored
Normal file
86
vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_amd64.go
generated
vendored
Normal file
@@ -0,0 +1,86 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !noasm && !gccgo && !safe
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
package f32
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha float32, x, y []float32)
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32)
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr)
|
||||
|
||||
// DdotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += float64(y[i]) * float64(v)
|
||||
// }
|
||||
// return
|
||||
func DdotUnitary(x, y []float32) (sum float64)
|
||||
|
||||
// DdotInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += float64(y[iy]) * float64(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return
|
||||
func DdotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float64)
|
||||
|
||||
// DotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotUnitary(x, y []float32) (sum float32)
|
||||
|
||||
// DotInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float32)
|
||||
|
||||
// Sum is
|
||||
//
|
||||
// var sum float32
|
||||
// for _, v := range x {
|
||||
// sum += v
|
||||
// }
|
||||
// return sum
|
||||
func Sum(x []float32) float32
|
||||
137
vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_noasm.go
generated
vendored
Normal file
137
vendor/gonum.org/v1/gonum/internal/asm/f32/stubs_noasm.go
generated
vendored
Normal file
@@ -0,0 +1,137 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !amd64 || noasm || gccgo || safe
|
||||
// +build !amd64 noasm gccgo safe
|
||||
|
||||
package f32
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha float32, x, y []float32) {
|
||||
for i, v := range x {
|
||||
y[i] += alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []float32, alpha float32, x, y []float32) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha*v + y[i]
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
y[iy] += alpha * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []float32, incDst, idst uintptr, alpha float32, x, y []float32, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha*x[ix] + y[iy]
|
||||
ix += incX
|
||||
iy += incY
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
|
||||
// DotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += y[i] * v
|
||||
// }
|
||||
// return sum
|
||||
func DotUnitary(x, y []float32) (sum float32) {
|
||||
for i, v := range x {
|
||||
sum += y[i] * v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DotInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += y[iy] * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return sum
|
||||
func DotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float32) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += y[iy] * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return sum
|
||||
}
|
||||
|
||||
// DdotUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// sum += float64(y[i]) * float64(v)
|
||||
// }
|
||||
// return
|
||||
func DdotUnitary(x, y []float32) (sum float64) {
|
||||
for i, v := range x {
|
||||
sum += float64(y[i]) * float64(v)
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// DdotInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// sum += float64(y[iy]) * float64(x[ix])
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
// return
|
||||
func DdotInc(x, y []float32, n, incX, incY, ix, iy uintptr) (sum float64) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
sum += float64(y[iy]) * float64(x[ix])
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
return
|
||||
}
|
||||
|
||||
// Sum is
|
||||
//
|
||||
// var sum float32
|
||||
// for _, v := range x {
|
||||
// sum += v
|
||||
// }
|
||||
// return sum
|
||||
func Sum(x []float32) float32 {
|
||||
var sum float32
|
||||
for _, v := range x {
|
||||
sum += v
|
||||
}
|
||||
return sum
|
||||
}
|
||||
100
vendor/gonum.org/v1/gonum/internal/asm/f32/sum_amd64.s
generated
vendored
Normal file
100
vendor/gonum.org/v1/gonum/internal/asm/f32/sum_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,100 @@
|
||||
// Copyright ©2021 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define IDX AX
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define SUM X0
|
||||
#define SUM_1 X1
|
||||
#define SUM_2 X2
|
||||
#define SUM_3 X3
|
||||
|
||||
// func Sum(x []float32) float32
|
||||
TEXT ·Sum(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), X_PTR // X_PTR = &x
|
||||
MOVQ x_len+8(FP), LEN // LEN = len(x)
|
||||
XORQ IDX, IDX // i = 0
|
||||
PXOR SUM, SUM // p_sum_i = 0
|
||||
CMPQ LEN, $0 // if LEN == 0 { return 0 }
|
||||
JE sum_end
|
||||
|
||||
PXOR SUM_1, SUM_1
|
||||
PXOR SUM_2, SUM_2
|
||||
PXOR SUM_3, SUM_3
|
||||
|
||||
MOVQ X_PTR, TAIL // Check memory alignment
|
||||
ANDQ $15, TAIL // TAIL = &x % 16
|
||||
JZ no_trim // if TAIL == 0 { goto no_trim }
|
||||
SUBQ $16, TAIL // TAIL -= 16
|
||||
|
||||
sum_align: // Align on 16-byte boundary do {
|
||||
ADDSS (X_PTR)(IDX*4), SUM // SUM += x[0]
|
||||
INCQ IDX // i++
|
||||
DECQ LEN // LEN--
|
||||
JZ sum_end // if LEN == 0 { return }
|
||||
ADDQ $4, TAIL // TAIL += 4
|
||||
JNZ sum_align // } while TAIL < 0
|
||||
|
||||
no_trim:
|
||||
MOVQ LEN, TAIL
|
||||
SHRQ $4, LEN // LEN = floor( n / 16 )
|
||||
JZ sum_tail8 // if LEN == 0 { goto sum_tail8 }
|
||||
|
||||
|
||||
sum_loop: // sum 16x wide do {
|
||||
ADDPS (X_PTR)(IDX*4), SUM // sum_i += x[i:i+4]
|
||||
ADDPS 16(X_PTR)(IDX*4), SUM_1
|
||||
ADDPS 32(X_PTR)(IDX*4), SUM_2
|
||||
ADDPS 48(X_PTR)(IDX*4), SUM_3
|
||||
|
||||
ADDQ $16, IDX // i += 16
|
||||
DECQ LEN
|
||||
JNZ sum_loop // } while --LEN > 0
|
||||
|
||||
sum_tail8:
|
||||
ADDPS SUM_3, SUM
|
||||
ADDPS SUM_2, SUM_1
|
||||
|
||||
TESTQ $8, TAIL
|
||||
JZ sum_tail4
|
||||
|
||||
ADDPS (X_PTR)(IDX*4), SUM // sum_i += x[i:i+4]
|
||||
ADDPS 16(X_PTR)(IDX*4), SUM_1
|
||||
ADDQ $8, IDX
|
||||
|
||||
sum_tail4:
|
||||
ADDPS SUM_1, SUM
|
||||
|
||||
TESTQ $4, TAIL
|
||||
JZ sum_tail2
|
||||
|
||||
ADDPS (X_PTR)(IDX*4), SUM // sum_i += x[i:i+4]
|
||||
ADDQ $4, IDX
|
||||
|
||||
sum_tail2:
|
||||
HADDPS SUM, SUM // sum_i[:2] += sum_i[2:4]
|
||||
|
||||
TESTQ $2, TAIL
|
||||
JZ sum_tail1
|
||||
|
||||
MOVSD (X_PTR)(IDX*4), SUM_1 // reuse SUM_1
|
||||
ADDPS SUM_1, SUM // sum_i += x[i:i+2]
|
||||
ADDQ $2, IDX
|
||||
|
||||
sum_tail1:
|
||||
HADDPS SUM, SUM // sum_i[0] += sum_i[1]
|
||||
|
||||
TESTQ $1, TAIL
|
||||
JZ sum_end
|
||||
|
||||
ADDSS (X_PTR)(IDX*4), SUM
|
||||
|
||||
sum_end: // return sum
|
||||
MOVSS SUM, ret+24(FP)
|
||||
RET
|
||||
82
vendor/gonum.org/v1/gonum/internal/asm/f64/abssum_amd64.s
generated
vendored
Normal file
82
vendor/gonum.org/v1/gonum/internal/asm/f64/abssum_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,82 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func L1Norm(x []float64) float64
|
||||
TEXT ·L1Norm(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), SI // SI = &x
|
||||
MOVQ x_len+8(FP), CX // CX = len(x)
|
||||
XORQ AX, AX // i = 0
|
||||
PXOR X0, X0 // p_sum_i = 0
|
||||
PXOR X1, X1
|
||||
PXOR X2, X2
|
||||
PXOR X3, X3
|
||||
PXOR X4, X4
|
||||
PXOR X5, X5
|
||||
PXOR X6, X6
|
||||
PXOR X7, X7
|
||||
CMPQ CX, $0 // if CX == 0 { return 0 }
|
||||
JE absum_end
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, BX // BX = len(x) % 8
|
||||
SHRQ $3, CX // CX = floor( len(x) / 8 )
|
||||
JZ absum_tail_start // if CX == 0 { goto absum_tail_start }
|
||||
|
||||
absum_loop: // do {
|
||||
// p_sum += max( p_sum + x[i], p_sum - x[i] )
|
||||
MOVUPS (SI)(AX*8), X8 // X_i = x[i:i+1]
|
||||
MOVUPS 16(SI)(AX*8), X9
|
||||
MOVUPS 32(SI)(AX*8), X10
|
||||
MOVUPS 48(SI)(AX*8), X11
|
||||
ADDPD X8, X0 // p_sum_i += X_i ( positive values )
|
||||
ADDPD X9, X2
|
||||
ADDPD X10, X4
|
||||
ADDPD X11, X6
|
||||
SUBPD X8, X1 // p_sum_(i+1) -= X_i ( negative values )
|
||||
SUBPD X9, X3
|
||||
SUBPD X10, X5
|
||||
SUBPD X11, X7
|
||||
MAXPD X1, X0 // p_sum_i = max( p_sum_i, p_sum_(i+1) )
|
||||
MAXPD X3, X2
|
||||
MAXPD X5, X4
|
||||
MAXPD X7, X6
|
||||
MOVAPS X0, X1 // p_sum_(i+1) = p_sum_i
|
||||
MOVAPS X2, X3
|
||||
MOVAPS X4, X5
|
||||
MOVAPS X6, X7
|
||||
ADDQ $8, AX // i += 8
|
||||
LOOP absum_loop // } while --CX > 0
|
||||
|
||||
// p_sum_0 = \sum_{i=1}^{3}( p_sum_(i*2) )
|
||||
ADDPD X3, X0
|
||||
ADDPD X5, X7
|
||||
ADDPD X7, X0
|
||||
|
||||
// p_sum_0[0] = p_sum_0[0] + p_sum_0[1]
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x3, X0, X0 // lower( p_sum_0 ) = upper( p_sum_0 )
|
||||
ADDSD X1, X0
|
||||
CMPQ BX, $0
|
||||
JE absum_end // if BX == 0 { goto absum_end }
|
||||
|
||||
absum_tail_start: // Reset loop registers
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
XORPS X8, X8 // X_8 = 0
|
||||
|
||||
absum_tail: // do {
|
||||
// p_sum += max( p_sum + x[i], p_sum - x[i] )
|
||||
MOVSD (SI)(AX*8), X8 // X_8 = x[i]
|
||||
MOVSD X0, X1 // p_sum_1 = p_sum_0
|
||||
ADDSD X8, X0 // p_sum_0 += X_8
|
||||
SUBSD X8, X1 // p_sum_1 -= X_8
|
||||
MAXSD X1, X0 // p_sum_0 = max( p_sum_0, p_sum_1 )
|
||||
INCQ AX // i++
|
||||
LOOP absum_tail // } while --CX > 0
|
||||
|
||||
absum_end: // return p_sum_0
|
||||
MOVSD X0, sum+24(FP)
|
||||
RET
|
||||
90
vendor/gonum.org/v1/gonum/internal/asm/f64/abssuminc_amd64.s
generated
vendored
Normal file
90
vendor/gonum.org/v1/gonum/internal/asm/f64/abssuminc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,90 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func L1NormInc(x []float64, n, incX int) (sum float64)
|
||||
TEXT ·L1NormInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+0(FP), SI // SI = &x
|
||||
MOVQ n+24(FP), CX // CX = n
|
||||
MOVQ incX+32(FP), AX // AX = increment * sizeof( float64 )
|
||||
SHLQ $3, AX
|
||||
MOVQ AX, DX // DX = AX * 3
|
||||
IMULQ $3, DX
|
||||
PXOR X0, X0 // p_sum_i = 0
|
||||
PXOR X1, X1
|
||||
PXOR X2, X2
|
||||
PXOR X3, X3
|
||||
PXOR X4, X4
|
||||
PXOR X5, X5
|
||||
PXOR X6, X6
|
||||
PXOR X7, X7
|
||||
CMPQ CX, $0 // if CX == 0 { return 0 }
|
||||
JE absum_end
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, BX // BX = n % 8
|
||||
SHRQ $3, CX // CX = floor( n / 8 )
|
||||
JZ absum_tail_start // if CX == 0 { goto absum_tail_start }
|
||||
|
||||
absum_loop: // do {
|
||||
// p_sum = max( p_sum + x[i], p_sum - x[i] )
|
||||
MOVSD (SI), X8 // X_i[0] = x[i]
|
||||
MOVSD (SI)(AX*1), X9
|
||||
MOVSD (SI)(AX*2), X10
|
||||
MOVSD (SI)(DX*1), X11
|
||||
LEAQ (SI)(AX*4), SI // SI = SI + 4
|
||||
MOVHPD (SI), X8 // X_i[1] = x[i+4]
|
||||
MOVHPD (SI)(AX*1), X9
|
||||
MOVHPD (SI)(AX*2), X10
|
||||
MOVHPD (SI)(DX*1), X11
|
||||
ADDPD X8, X0 // p_sum_i += X_i ( positive values )
|
||||
ADDPD X9, X2
|
||||
ADDPD X10, X4
|
||||
ADDPD X11, X6
|
||||
SUBPD X8, X1 // p_sum_(i+1) -= X_i ( negative values )
|
||||
SUBPD X9, X3
|
||||
SUBPD X10, X5
|
||||
SUBPD X11, X7
|
||||
MAXPD X1, X0 // p_sum_i = max( p_sum_i, p_sum_(i+1) )
|
||||
MAXPD X3, X2
|
||||
MAXPD X5, X4
|
||||
MAXPD X7, X6
|
||||
MOVAPS X0, X1 // p_sum_(i+1) = p_sum_i
|
||||
MOVAPS X2, X3
|
||||
MOVAPS X4, X5
|
||||
MOVAPS X6, X7
|
||||
LEAQ (SI)(AX*4), SI // SI = SI + 4
|
||||
LOOP absum_loop // } while --CX > 0
|
||||
|
||||
// p_sum_0 = \sum_{i=1}^{3}( p_sum_(i*2) )
|
||||
ADDPD X3, X0
|
||||
ADDPD X5, X7
|
||||
ADDPD X7, X0
|
||||
|
||||
// p_sum_0[0] = p_sum_0[0] + p_sum_0[1]
|
||||
MOVAPS X0, X1
|
||||
SHUFPD $0x3, X0, X0 // lower( p_sum_0 ) = upper( p_sum_0 )
|
||||
ADDSD X1, X0
|
||||
CMPQ BX, $0
|
||||
JE absum_end // if BX == 0 { goto absum_end }
|
||||
|
||||
absum_tail_start: // Reset loop registers
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
XORPS X8, X8 // X_8 = 0
|
||||
|
||||
absum_tail: // do {
|
||||
// p_sum += max( p_sum + x[i], p_sum - x[i] )
|
||||
MOVSD (SI), X8 // X_8 = x[i]
|
||||
MOVSD X0, X1 // p_sum_1 = p_sum_0
|
||||
ADDSD X8, X0 // p_sum_0 += X_8
|
||||
SUBSD X8, X1 // p_sum_1 -= X_8
|
||||
MAXSD X1, X0 // p_sum_0 = max( p_sum_0, p_sum_1 )
|
||||
ADDQ AX, SI // i++
|
||||
LOOP absum_tail // } while --CX > 0
|
||||
|
||||
absum_end: // return p_sum_0
|
||||
MOVSD X0, sum+40(FP)
|
||||
RET
|
||||
66
vendor/gonum.org/v1/gonum/internal/asm/f64/add_amd64.s
generated
vendored
Normal file
66
vendor/gonum.org/v1/gonum/internal/asm/f64/add_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,66 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func Add(dst, s []float64)
|
||||
TEXT ·Add(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DI // DI = &dst
|
||||
MOVQ dst_len+8(FP), CX // CX = len(dst)
|
||||
MOVQ s_base+24(FP), SI // SI = &s
|
||||
CMPQ s_len+32(FP), CX // CX = max( CX, len(s) )
|
||||
CMOVQLE s_len+32(FP), CX
|
||||
CMPQ CX, $0 // if CX == 0 { return }
|
||||
JE add_end
|
||||
XORQ AX, AX
|
||||
MOVQ DI, BX
|
||||
ANDQ $0x0F, BX // BX = &dst & 15
|
||||
JZ add_no_trim // if BX == 0 { goto add_no_trim }
|
||||
|
||||
// Align on 16-bit boundary
|
||||
MOVSD (SI)(AX*8), X0 // X0 = s[i]
|
||||
ADDSD (DI)(AX*8), X0 // X0 += dst[i]
|
||||
MOVSD X0, (DI)(AX*8) // dst[i] = X0
|
||||
INCQ AX // i++
|
||||
DECQ CX // --CX
|
||||
JE add_end // if CX == 0 { return }
|
||||
|
||||
add_no_trim:
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, BX // BX = len(dst) % 8
|
||||
SHRQ $3, CX // CX = floor( len(dst) / 8 )
|
||||
JZ add_tail_start // if CX == 0 { goto add_tail_start }
|
||||
|
||||
add_loop: // Loop unrolled 8x do {
|
||||
MOVUPS (SI)(AX*8), X0 // X_i = s[i:i+1]
|
||||
MOVUPS 16(SI)(AX*8), X1
|
||||
MOVUPS 32(SI)(AX*8), X2
|
||||
MOVUPS 48(SI)(AX*8), X3
|
||||
ADDPD (DI)(AX*8), X0 // X_i += dst[i:i+1]
|
||||
ADDPD 16(DI)(AX*8), X1
|
||||
ADDPD 32(DI)(AX*8), X2
|
||||
ADDPD 48(DI)(AX*8), X3
|
||||
MOVUPS X0, (DI)(AX*8) // dst[i:i+1] = X_i
|
||||
MOVUPS X1, 16(DI)(AX*8)
|
||||
MOVUPS X2, 32(DI)(AX*8)
|
||||
MOVUPS X3, 48(DI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
LOOP add_loop // } while --CX > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE add_end
|
||||
|
||||
add_tail_start: // Reset loop registers
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
|
||||
add_tail: // do {
|
||||
MOVSD (SI)(AX*8), X0 // X0 = s[i]
|
||||
ADDSD (DI)(AX*8), X0 // X0 += dst[i]
|
||||
MOVSD X0, (DI)(AX*8) // dst[i] = X0
|
||||
INCQ AX // ++i
|
||||
LOOP add_tail // } while --CX > 0
|
||||
|
||||
add_end:
|
||||
RET
|
||||
53
vendor/gonum.org/v1/gonum/internal/asm/f64/addconst_amd64.s
generated
vendored
Normal file
53
vendor/gonum.org/v1/gonum/internal/asm/f64/addconst_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,53 @@
|
||||
// Copyright ©2016 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
// func Addconst(alpha float64, x []float64)
|
||||
TEXT ·AddConst(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), SI // SI = &x
|
||||
MOVQ x_len+16(FP), CX // CX = len(x)
|
||||
CMPQ CX, $0 // if len(x) == 0 { return }
|
||||
JE ac_end
|
||||
MOVSD alpha+0(FP), X4 // X4 = { a, a }
|
||||
SHUFPD $0, X4, X4
|
||||
MOVUPS X4, X5 // X5 = X4
|
||||
XORQ AX, AX // i = 0
|
||||
MOVQ CX, BX
|
||||
ANDQ $7, BX // BX = len(x) % 8
|
||||
SHRQ $3, CX // CX = floor( len(x) / 8 )
|
||||
JZ ac_tail_start // if CX == 0 { goto ac_tail_start }
|
||||
|
||||
ac_loop: // Loop unrolled 8x do {
|
||||
MOVUPS (SI)(AX*8), X0 // X_i = s[i:i+1]
|
||||
MOVUPS 16(SI)(AX*8), X1
|
||||
MOVUPS 32(SI)(AX*8), X2
|
||||
MOVUPS 48(SI)(AX*8), X3
|
||||
ADDPD X4, X0 // X_i += a
|
||||
ADDPD X5, X1
|
||||
ADDPD X4, X2
|
||||
ADDPD X5, X3
|
||||
MOVUPS X0, (SI)(AX*8) // s[i:i+1] = X_i
|
||||
MOVUPS X1, 16(SI)(AX*8)
|
||||
MOVUPS X2, 32(SI)(AX*8)
|
||||
MOVUPS X3, 48(SI)(AX*8)
|
||||
ADDQ $8, AX // i += 8
|
||||
LOOP ac_loop // } while --CX > 0
|
||||
CMPQ BX, $0 // if BX == 0 { return }
|
||||
JE ac_end
|
||||
|
||||
ac_tail_start: // Reset loop counters
|
||||
MOVQ BX, CX // Loop counter: CX = BX
|
||||
|
||||
ac_tail: // do {
|
||||
MOVSD (SI)(AX*8), X0 // X0 = s[i]
|
||||
ADDSD X4, X0 // X0 += a
|
||||
MOVSD X0, (SI)(AX*8) // s[i] = X0
|
||||
INCQ AX // ++i
|
||||
LOOP ac_tail // } while --CX > 0
|
||||
|
||||
ac_end:
|
||||
RET
|
||||
62
vendor/gonum.org/v1/gonum/internal/asm/f64/axpy.go
generated
vendored
Normal file
62
vendor/gonum.org/v1/gonum/internal/asm/f64/axpy.go
generated
vendored
Normal file
@@ -0,0 +1,62 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
|
||||
//go:build !amd64 || noasm || gccgo || safe
|
||||
// +build !amd64 noasm gccgo safe
|
||||
|
||||
package f64
|
||||
|
||||
// AxpyUnitary is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// y[i] += alpha * v
|
||||
// }
|
||||
func AxpyUnitary(alpha float64, x, y []float64) {
|
||||
for i, v := range x {
|
||||
y[i] += alpha * v
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyUnitaryTo is
|
||||
//
|
||||
// for i, v := range x {
|
||||
// dst[i] = alpha*v + y[i]
|
||||
// }
|
||||
func AxpyUnitaryTo(dst []float64, alpha float64, x, y []float64) {
|
||||
for i, v := range x {
|
||||
dst[i] = alpha*v + y[i]
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyInc is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// y[iy] += alpha * x[ix]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// }
|
||||
func AxpyInc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
y[iy] += alpha * x[ix]
|
||||
ix += incX
|
||||
iy += incY
|
||||
}
|
||||
}
|
||||
|
||||
// AxpyIncTo is
|
||||
//
|
||||
// for i := 0; i < int(n); i++ {
|
||||
// dst[idst] = alpha*x[ix] + y[iy]
|
||||
// ix += incX
|
||||
// iy += incY
|
||||
// idst += incDst
|
||||
// }
|
||||
func AxpyIncTo(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr) {
|
||||
for i := 0; i < int(n); i++ {
|
||||
dst[idst] = alpha*x[ix] + y[iy]
|
||||
ix += incX
|
||||
iy += incY
|
||||
idst += incDst
|
||||
}
|
||||
}
|
||||
142
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyinc_amd64.s
generated
vendored
Normal file
142
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyinc_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,142 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
//
|
||||
// Some of the loop unrolling code is copied from:
|
||||
// http://golang.org/src/math/big/arith_amd64.s
|
||||
// which is distributed under these terms:
|
||||
//
|
||||
// Copyright (c) 2012 The Go Authors. All rights reserved.
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are
|
||||
// met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright
|
||||
// notice, this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above
|
||||
// copyright notice, this list of conditions and the following disclaimer
|
||||
// in the documentation and/or other materials provided with the
|
||||
// distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its
|
||||
// contributors may be used to endorse or promote products derived from
|
||||
// this software without specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define DST_PTR DI
|
||||
#define IDX AX
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC_X R8
|
||||
#define INCx3_X R11
|
||||
#define INC_Y R9
|
||||
#define INCx3_Y R12
|
||||
#define INC_DST R9
|
||||
#define INCx3_DST R12
|
||||
#define ALPHA X0
|
||||
#define ALPHA_2 X1
|
||||
|
||||
// func AxpyInc(alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyInc(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), X_PTR // X_PTR = &x
|
||||
MOVQ y_base+32(FP), Y_PTR // Y_PTR = &y
|
||||
MOVQ n+56(FP), LEN // LEN = n
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE end
|
||||
|
||||
MOVQ ix+80(FP), INC_X
|
||||
MOVQ iy+88(FP), INC_Y
|
||||
LEAQ (X_PTR)(INC_X*8), X_PTR // X_PTR = &(x[ix])
|
||||
LEAQ (Y_PTR)(INC_Y*8), Y_PTR // Y_PTR = &(y[iy])
|
||||
MOVQ Y_PTR, DST_PTR // DST_PTR = Y_PTR // Write pointer
|
||||
|
||||
MOVQ incX+64(FP), INC_X // INC_X = incX * sizeof(float64)
|
||||
SHLQ $3, INC_X
|
||||
MOVQ incY+72(FP), INC_Y // INC_Y = incY * sizeof(float64)
|
||||
SHLQ $3, INC_Y
|
||||
|
||||
MOVSD alpha+0(FP), ALPHA // ALPHA = alpha
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = n % 4
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ tail_start // if LEN == 0 { goto tail_start }
|
||||
|
||||
MOVAPS ALPHA, ALPHA_2 // ALPHA_2 = ALPHA for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
|
||||
loop: // do { // y[i] += alpha * x[i] unrolled 4x.
|
||||
MOVSD (X_PTR), X2 // X_i = x[i]
|
||||
MOVSD (X_PTR)(INC_X*1), X3
|
||||
MOVSD (X_PTR)(INC_X*2), X4
|
||||
MOVSD (X_PTR)(INCx3_X*1), X5
|
||||
|
||||
MULSD ALPHA, X2 // X_i *= a
|
||||
MULSD ALPHA_2, X3
|
||||
MULSD ALPHA, X4
|
||||
MULSD ALPHA_2, X5
|
||||
|
||||
ADDSD (Y_PTR), X2 // X_i += y[i]
|
||||
ADDSD (Y_PTR)(INC_Y*1), X3
|
||||
ADDSD (Y_PTR)(INC_Y*2), X4
|
||||
ADDSD (Y_PTR)(INCx3_Y*1), X5
|
||||
|
||||
MOVSD X2, (DST_PTR) // y[i] = X_i
|
||||
MOVSD X3, (DST_PTR)(INC_DST*1)
|
||||
MOVSD X4, (DST_PTR)(INC_DST*2)
|
||||
MOVSD X5, (DST_PTR)(INCx3_DST*1)
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[incY*4])
|
||||
DECQ LEN
|
||||
JNZ loop // } while --LEN > 0
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE end
|
||||
|
||||
tail_start: // Reset Loop registers
|
||||
MOVQ TAIL, LEN // Loop counter: LEN = TAIL
|
||||
SHRQ $1, LEN // LEN = floor( LEN / 2 )
|
||||
JZ tail_one
|
||||
|
||||
tail_two:
|
||||
MOVSD (X_PTR), X2 // X_i = x[i]
|
||||
MOVSD (X_PTR)(INC_X*1), X3
|
||||
MULSD ALPHA, X2 // X_i *= a
|
||||
MULSD ALPHA, X3
|
||||
ADDSD (Y_PTR), X2 // X_i += y[i]
|
||||
ADDSD (Y_PTR)(INC_Y*1), X3
|
||||
MOVSD X2, (DST_PTR) // y[i] = X_i
|
||||
MOVSD X3, (DST_PTR)(INC_DST*1)
|
||||
|
||||
LEAQ (X_PTR)(INC_X*2), X_PTR // X_PTR = &(X_PTR[incX*2])
|
||||
LEAQ (Y_PTR)(INC_Y*2), Y_PTR // Y_PTR = &(Y_PTR[incY*2])
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ end // if TAIL == 0 { goto end }
|
||||
|
||||
tail_one:
|
||||
// y[i] += alpha * x[i] for the last n % 4 iterations.
|
||||
MOVSD (X_PTR), X2 // X2 = x[i]
|
||||
MULSD ALPHA, X2 // X2 *= a
|
||||
ADDSD (Y_PTR), X2 // X2 += y[i]
|
||||
MOVSD X2, (DST_PTR) // y[i] = X2
|
||||
|
||||
end:
|
||||
RET
|
||||
148
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyincto_amd64.s
generated
vendored
Normal file
148
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyincto_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,148 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
//
|
||||
// Some of the loop unrolling code is copied from:
|
||||
// http://golang.org/src/math/big/arith_amd64.s
|
||||
// which is distributed under these terms:
|
||||
//
|
||||
// Copyright (c) 2012 The Go Authors. All rights reserved.
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are
|
||||
// met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright
|
||||
// notice, this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above
|
||||
// copyright notice, this list of conditions and the following disclaimer
|
||||
// in the documentation and/or other materials provided with the
|
||||
// distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its
|
||||
// contributors may be used to endorse or promote products derived from
|
||||
// this software without specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define DST_PTR DX
|
||||
#define IDX AX
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define INC_X R8
|
||||
#define INCx3_X R11
|
||||
#define INC_Y R9
|
||||
#define INCx3_Y R12
|
||||
#define INC_DST R10
|
||||
#define INCx3_DST R13
|
||||
#define ALPHA X0
|
||||
#define ALPHA_2 X1
|
||||
|
||||
// func AxpyIncTo(dst []float64, incDst, idst uintptr, alpha float64, x, y []float64, n, incX, incY, ix, iy uintptr)
|
||||
TEXT ·AxpyIncTo(SB), NOSPLIT, $0
|
||||
MOVQ dst_base+0(FP), DST_PTR // DST_PTR := &dst
|
||||
MOVQ x_base+48(FP), X_PTR // X_PTR := &x
|
||||
MOVQ y_base+72(FP), Y_PTR // Y_PTR := &y
|
||||
MOVQ n+96(FP), LEN // LEN := n
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE end
|
||||
|
||||
MOVQ ix+120(FP), INC_X
|
||||
LEAQ (X_PTR)(INC_X*8), X_PTR // X_PTR = &(x[ix])
|
||||
MOVQ iy+128(FP), INC_Y
|
||||
LEAQ (Y_PTR)(INC_Y*8), Y_PTR // Y_PTR = &(dst[idst])
|
||||
MOVQ idst+32(FP), INC_DST
|
||||
LEAQ (DST_PTR)(INC_DST*8), DST_PTR // DST_PTR = &(y[iy])
|
||||
|
||||
MOVQ incX+104(FP), INC_X // INC_X = incX * sizeof(float64)
|
||||
SHLQ $3, INC_X
|
||||
MOVQ incY+112(FP), INC_Y // INC_Y = incY * sizeof(float64)
|
||||
SHLQ $3, INC_Y
|
||||
MOVQ incDst+24(FP), INC_DST // INC_DST = incDst * sizeof(float64)
|
||||
SHLQ $3, INC_DST
|
||||
MOVSD alpha+40(FP), ALPHA
|
||||
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $3, TAIL // TAIL = n % 4
|
||||
SHRQ $2, LEN // LEN = floor( n / 4 )
|
||||
JZ tail_start // if LEN == 0 { goto tail_start }
|
||||
|
||||
MOVSD ALPHA, ALPHA_2 // ALPHA_2 = ALPHA for pipelining
|
||||
LEAQ (INC_X)(INC_X*2), INCx3_X // INCx3_X = INC_X * 3
|
||||
LEAQ (INC_Y)(INC_Y*2), INCx3_Y // INCx3_Y = INC_Y * 3
|
||||
LEAQ (INC_DST)(INC_DST*2), INCx3_DST // INCx3_DST = INC_DST * 3
|
||||
|
||||
loop: // do { // y[i] += alpha * x[i] unrolled 2x.
|
||||
MOVSD (X_PTR), X2 // X_i = x[i]
|
||||
MOVSD (X_PTR)(INC_X*1), X3
|
||||
MOVSD (X_PTR)(INC_X*2), X4
|
||||
MOVSD (X_PTR)(INCx3_X*1), X5
|
||||
|
||||
MULSD ALPHA, X2 // X_i *= a
|
||||
MULSD ALPHA_2, X3
|
||||
MULSD ALPHA, X4
|
||||
MULSD ALPHA_2, X5
|
||||
|
||||
ADDSD (Y_PTR), X2 // X_i += y[i]
|
||||
ADDSD (Y_PTR)(INC_Y*1), X3
|
||||
ADDSD (Y_PTR)(INC_Y*2), X4
|
||||
ADDSD (Y_PTR)(INCx3_Y*1), X5
|
||||
|
||||
MOVSD X2, (DST_PTR) // y[i] = X_i
|
||||
MOVSD X3, (DST_PTR)(INC_DST*1)
|
||||
MOVSD X4, (DST_PTR)(INC_DST*2)
|
||||
MOVSD X5, (DST_PTR)(INCx3_DST*1)
|
||||
|
||||
LEAQ (X_PTR)(INC_X*4), X_PTR // X_PTR = &(X_PTR[incX*4])
|
||||
LEAQ (Y_PTR)(INC_Y*4), Y_PTR // Y_PTR = &(Y_PTR[incY*4])
|
||||
LEAQ (DST_PTR)(INC_DST*4), DST_PTR // DST_PTR = &(DST_PTR[incDst*4]
|
||||
DECQ LEN
|
||||
JNZ loop // } while --LEN > 0
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE end
|
||||
|
||||
tail_start: // Reset Loop registers
|
||||
MOVQ TAIL, LEN // Loop counter: LEN = TAIL
|
||||
SHRQ $1, LEN // LEN = floor( LEN / 2 )
|
||||
JZ tail_one
|
||||
|
||||
tail_two:
|
||||
MOVSD (X_PTR), X2 // X_i = x[i]
|
||||
MOVSD (X_PTR)(INC_X*1), X3
|
||||
MULSD ALPHA, X2 // X_i *= a
|
||||
MULSD ALPHA, X3
|
||||
ADDSD (Y_PTR), X2 // X_i += y[i]
|
||||
ADDSD (Y_PTR)(INC_Y*1), X3
|
||||
MOVSD X2, (DST_PTR) // y[i] = X_i
|
||||
MOVSD X3, (DST_PTR)(INC_DST*1)
|
||||
|
||||
LEAQ (X_PTR)(INC_X*2), X_PTR // X_PTR = &(X_PTR[incX*2])
|
||||
LEAQ (Y_PTR)(INC_Y*2), Y_PTR // Y_PTR = &(Y_PTR[incY*2])
|
||||
LEAQ (DST_PTR)(INC_DST*2), DST_PTR // DST_PTR = &(DST_PTR[incY*2]
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ end // if TAIL == 0 { goto end }
|
||||
|
||||
tail_one:
|
||||
MOVSD (X_PTR), X2 // X2 = x[i]
|
||||
MULSD ALPHA, X2 // X2 *= a
|
||||
ADDSD (Y_PTR), X2 // X2 += y[i]
|
||||
MOVSD X2, (DST_PTR) // y[i] = X2
|
||||
|
||||
end:
|
||||
RET
|
||||
134
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitary_amd64.s
generated
vendored
Normal file
134
vendor/gonum.org/v1/gonum/internal/asm/f64/axpyunitary_amd64.s
generated
vendored
Normal file
@@ -0,0 +1,134 @@
|
||||
// Copyright ©2015 The Gonum Authors. All rights reserved.
|
||||
// Use of this source code is governed by a BSD-style
|
||||
// license that can be found in the LICENSE file.
|
||||
//
|
||||
// Some of the loop unrolling code is copied from:
|
||||
// http://golang.org/src/math/big/arith_amd64.s
|
||||
// which is distributed under these terms:
|
||||
//
|
||||
// Copyright (c) 2012 The Go Authors. All rights reserved.
|
||||
//
|
||||
// Redistribution and use in source and binary forms, with or without
|
||||
// modification, are permitted provided that the following conditions are
|
||||
// met:
|
||||
//
|
||||
// * Redistributions of source code must retain the above copyright
|
||||
// notice, this list of conditions and the following disclaimer.
|
||||
// * Redistributions in binary form must reproduce the above
|
||||
// copyright notice, this list of conditions and the following disclaimer
|
||||
// in the documentation and/or other materials provided with the
|
||||
// distribution.
|
||||
// * Neither the name of Google Inc. nor the names of its
|
||||
// contributors may be used to endorse or promote products derived from
|
||||
// this software without specific prior written permission.
|
||||
//
|
||||
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
||||
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
||||
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
||||
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
|
||||
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
|
||||
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
|
||||
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
|
||||
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
|
||||
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
|
||||
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
|
||||
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
||||
|
||||
// +build !noasm,!gccgo,!safe
|
||||
|
||||
#include "textflag.h"
|
||||
|
||||
#define X_PTR SI
|
||||
#define Y_PTR DI
|
||||
#define DST_PTR DI
|
||||
#define IDX AX
|
||||
#define LEN CX
|
||||
#define TAIL BX
|
||||
#define ALPHA X0
|
||||
#define ALPHA_2 X1
|
||||
|
||||
// func AxpyUnitary(alpha float64, x, y []float64)
|
||||
TEXT ·AxpyUnitary(SB), NOSPLIT, $0
|
||||
MOVQ x_base+8(FP), X_PTR // X_PTR := &x
|
||||
MOVQ y_base+32(FP), Y_PTR // Y_PTR := &y
|
||||
MOVQ x_len+16(FP), LEN // LEN = min( len(x), len(y) )
|
||||
CMPQ y_len+40(FP), LEN
|
||||
CMOVQLE y_len+40(FP), LEN
|
||||
CMPQ LEN, $0 // if LEN == 0 { return }
|
||||
JE end
|
||||
XORQ IDX, IDX
|
||||
MOVSD alpha+0(FP), ALPHA // ALPHA := { alpha, alpha }
|
||||
SHUFPD $0, ALPHA, ALPHA
|
||||
MOVUPS ALPHA, ALPHA_2 // ALPHA_2 := ALPHA for pipelining
|
||||
MOVQ Y_PTR, TAIL // Check memory alignment
|
||||
ANDQ $15, TAIL // TAIL = &y % 16
|
||||
JZ no_trim // if TAIL == 0 { goto no_trim }
|
||||
|
||||
// Align on 16-byte boundary
|
||||
MOVSD (X_PTR), X2 // X2 := x[0]
|
||||
MULSD ALPHA, X2 // X2 *= a
|
||||
ADDSD (Y_PTR), X2 // X2 += y[0]
|
||||
MOVSD X2, (DST_PTR) // y[0] = X2
|
||||
INCQ IDX // i++
|
||||
DECQ LEN // LEN--
|
||||
JZ end // if LEN == 0 { return }
|
||||
|
||||
no_trim:
|
||||
MOVQ LEN, TAIL
|
||||
ANDQ $7, TAIL // TAIL := n % 8
|
||||
SHRQ $3, LEN // LEN = floor( n / 8 )
|
||||
JZ tail_start // if LEN == 0 { goto tail2_start }
|
||||
|
||||
loop: // do {
|
||||
// y[i] += alpha * x[i] unrolled 8x.
|
||||
MOVUPS (X_PTR)(IDX*8), X2 // X_i = x[i]
|
||||
MOVUPS 16(X_PTR)(IDX*8), X3
|
||||
MOVUPS 32(X_PTR)(IDX*8), X4
|
||||
MOVUPS 48(X_PTR)(IDX*8), X5
|
||||
|
||||
MULPD ALPHA, X2 // X_i *= a
|
||||
MULPD ALPHA_2, X3
|
||||
MULPD ALPHA, X4
|
||||
MULPD ALPHA_2, X5
|
||||
|
||||
ADDPD (Y_PTR)(IDX*8), X2 // X_i += y[i]
|
||||
ADDPD 16(Y_PTR)(IDX*8), X3
|
||||
ADDPD 32(Y_PTR)(IDX*8), X4
|
||||
ADDPD 48(Y_PTR)(IDX*8), X5
|
||||
|
||||
MOVUPS X2, (DST_PTR)(IDX*8) // y[i] = X_i
|
||||
MOVUPS X3, 16(DST_PTR)(IDX*8)
|
||||
MOVUPS X4, 32(DST_PTR)(IDX*8)
|
||||
MOVUPS X5, 48(DST_PTR)(IDX*8)
|
||||
|
||||
ADDQ $8, IDX // i += 8
|
||||
DECQ LEN
|
||||
JNZ loop // } while --LEN > 0
|
||||
CMPQ TAIL, $0 // if TAIL == 0 { return }
|
||||
JE end
|
||||
|
||||
tail_start: // Reset loop registers
|
||||
MOVQ TAIL, LEN // Loop counter: LEN = TAIL
|
||||
SHRQ $1, LEN // LEN = floor( TAIL / 2 )
|
||||
JZ tail_one // if TAIL == 0 { goto tail }
|
||||
|
||||
tail_two: // do {
|
||||
MOVUPS (X_PTR)(IDX*8), X2 // X2 = x[i]
|
||||
MULPD ALPHA, X2 // X2 *= a
|
||||
ADDPD (Y_PTR)(IDX*8), X2 // X2 += y[i]
|
||||
MOVUPS X2, (DST_PTR)(IDX*8) // y[i] = X2
|
||||
ADDQ $2, IDX // i += 2
|
||||
DECQ LEN
|
||||
JNZ tail_two // } while --LEN > 0
|
||||
|
||||
ANDQ $1, TAIL
|
||||
JZ end // if TAIL == 0 { goto end }
|
||||
|
||||
tail_one:
|
||||
MOVSD (X_PTR)(IDX*8), X2 // X2 = x[i]
|
||||
MULSD ALPHA, X2 // X2 *= a
|
||||
ADDSD (Y_PTR)(IDX*8), X2 // X2 += y[i]
|
||||
MOVSD X2, (DST_PTR)(IDX*8) // y[i] = X2
|
||||
|
||||
end:
|
||||
RET
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user