fixed dependencies

vendor/gonum.org/v1/gonum/num/quat/trig.go

@@ -0,0 +1,171 @@
+// Copyright ©2018 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.
+
+// Copyright 2017 The Go 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 quat
+
+import "math"
+
+// Sin returns the sine of q.
+func Sin(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Sin(w))
+	}
+	v := Abs(uv)
+	s, c := math.Sincos(w)
+	sh, ch := sinhcosh(v)
+	return join(s*ch, Scale(c*sh/v, uv))
+}
+
+// Sinh returns the hyperbolic sine of q.
+func Sinh(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Sinh(w))
+	}
+	v := Abs(uv)
+	s, c := math.Sincos(v)
+	sh, ch := sinhcosh(w)
+	return join(c*sh, scale(s*ch/v, uv))
+}
+
+// Cos returns the cosine of q.
+func Cos(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Cos(w))
+	}
+	v := Abs(uv)
+	s, c := math.Sincos(w)
+	sh, ch := sinhcosh(v)
+	return join(c*ch, Scale(-s*sh/v, uv))
+}
+
+// Cosh returns the hyperbolic cosine of q.
+func Cosh(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Cosh(w))
+	}
+	v := Abs(uv)
+	s, c := math.Sincos(v)
+	sh, ch := sinhcosh(w)
+	return join(c*ch, scale(s*sh/v, uv))
+}
+
+// Tan returns the tangent of q.
+func Tan(q Number) Number {
+	d := Cos(q)
+	if d == zero {
+		return Inf()
+	}
+	return Mul(Sin(q), Inv(d))
+}
+
+// Tanh returns the hyperbolic tangent of q.
+func Tanh(q Number) Number {
+	if math.IsInf(q.Real, 1) {
+		r := Number{Real: 1}
+		// Change signs dependent on imaginary parts.
+		r.Imag *= math.Sin(2 * q.Imag)
+		r.Jmag *= math.Sin(2 * q.Jmag)
+		r.Kmag *= math.Sin(2 * q.Kmag)
+		return r
+	}
+	d := Cosh(q)
+	if d == zero {
+		return Inf()
+	}
+	return Mul(Sinh(q), Inv(d))
+}
+
+// Asin returns the inverse sine of q.
+func Asin(q Number) Number {
+	_, uv := split(q)
+	if uv == zero {
+		return lift(math.Asin(q.Real))
+	}
+	u := unit(uv)
+	return Mul(Scale(-1, u), Log(Add(Mul(u, q), Sqrt(Sub(Number{Real: 1}, Mul(q, q))))))
+}
+
+// Asinh returns the inverse hyperbolic sine of q.
+func Asinh(q Number) Number {
+	return Log(Add(q, Sqrt(Add(Number{Real: 1}, Mul(q, q)))))
+}
+
+// Acos returns the inverse cosine of q.
+func Acos(q Number) Number {
+	w, uv := split(Asin(q))
+	return join(math.Pi/2-w, Scale(-1, uv))
+}
+
+// Acosh returns the inverse hyperbolic cosine of q.
+func Acosh(q Number) Number {
+	w := Acos(q)
+	_, uv := split(w)
+	if uv == zero {
+		return w
+	}
+	w = Mul(w, unit(uv))
+	if w.Real < 0 {
+		w = Scale(-1, w)
+	}
+	return w
+}
+
+// Atan returns the inverse tangent of q.
+func Atan(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Atan(w))
+	}
+	u := unit(uv)
+	return Mul(Mul(lift(0.5), u), Log(Mul(Add(u, q), Inv(Sub(u, q)))))
+}
+
+// Atanh returns the inverse hyperbolic tangent of q.
+func Atanh(q Number) Number {
+	w, uv := split(q)
+	if uv == zero {
+		return lift(math.Atanh(w))
+	}
+	u := unit(uv)
+	return Mul(Scale(-1, u), Atan(Mul(u, q)))
+}
+
+// calculate sinh and cosh
+func sinhcosh(x float64) (sh, ch float64) {
+	if math.Abs(x) <= 0.5 {
+		return math.Sinh(x), math.Cosh(x)
+	}
+	e := math.Exp(x)
+	ei := 0.5 / e
+	e *= 0.5
+	return e - ei, e + ei
+}
+
+// scale returns q scaled by f, except that inf×0 is 0.
+func scale(f float64, q Number) Number {
+	if f == 0 {
+		return Number{}
+	}
+	if q.Real != 0 {
+		q.Real *= f
+	}
+	if q.Imag != 0 {
+		q.Imag *= f
+	}
+	if q.Jmag != 0 {
+		q.Jmag *= f
+	}
+	if q.Kmag != 0 {
+		q.Kmag *= f
+	}
+	return q
+}