1// Copyright 2009 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package math
6
7/*
8	Floating-point hyperbolic sine and cosine.
9
10	The exponential func is called for arguments
11	greater in magnitude than 0.5.
12
13	A series is used for arguments smaller in magnitude than 0.5.
14
15	Cosh(x) is computed from the exponential func for
16	all arguments.
17*/
18
19// Sinh returns the hyperbolic sine of x.
20//
21// Special cases are:
22//	Sinh(±0) = ±0
23//	Sinh(±Inf) = ±Inf
24//	Sinh(NaN) = NaN
25func Sinh(x float64) float64 {
26	// The coefficients are #2029 from Hart & Cheney. (20.36D)
27	const (
28		P0 = -0.6307673640497716991184787251e+6
29		P1 = -0.8991272022039509355398013511e+5
30		P2 = -0.2894211355989563807284660366e+4
31		P3 = -0.2630563213397497062819489e+2
32		Q0 = -0.6307673640497716991212077277e+6
33		Q1 = 0.1521517378790019070696485176e+5
34		Q2 = -0.173678953558233699533450911e+3
35	)
36
37	sign := false
38	if x < 0 {
39		x = -x
40		sign = true
41	}
42
43	var temp float64
44	switch {
45	case x > 21:
46		temp = Exp(x) * 0.5
47
48	case x > 0.5:
49		ex := Exp(x)
50		temp = (ex - 1/ex) * 0.5
51
52	default:
53		sq := x * x
54		temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
55		temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
56	}
57
58	if sign {
59		temp = -temp
60	}
61	return temp
62}
63
64// Cosh returns the hyperbolic cosine of x.
65//
66// Special cases are:
67//	Cosh(±0) = 1
68//	Cosh(±Inf) = +Inf
69//	Cosh(NaN) = NaN
70func Cosh(x float64) float64 {
71	x = Abs(x)
72	if x > 21 {
73		return Exp(x) * 0.5
74	}
75	ex := Exp(x)
76	return (ex + 1/ex) * 0.5
77}
78