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//
23//	Sinh(±0) = ±0
24//	Sinh(±Inf) = ±Inf
25//	Sinh(NaN) = NaN
26func Sinh(x float64) float64 {
27	if haveArchSinh {
28		return archSinh(x)
29	}
30	return sinh(x)
31}
32
33func sinh(x float64) float64 {
34	// The coefficients are #2029 from Hart & Cheney. (20.36D)
35	const (
36		P0 = -0.6307673640497716991184787251e+6
37		P1 = -0.8991272022039509355398013511e+5
38		P2 = -0.2894211355989563807284660366e+4
39		P3 = -0.2630563213397497062819489e+2
40		Q0 = -0.6307673640497716991212077277e+6
41		Q1 = 0.1521517378790019070696485176e+5
42		Q2 = -0.173678953558233699533450911e+3
43	)
44
45	sign := false
46	if x < 0 {
47		x = -x
48		sign = true
49	}
50
51	var temp float64
52	switch {
53	case x > 21:
54		temp = Exp(x) * 0.5
55
56	case x > 0.5:
57		ex := Exp(x)
58		temp = (ex - 1/ex) * 0.5
59
60	default:
61		sq := x * x
62		temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
63		temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
64	}
65
66	if sign {
67		temp = -temp
68	}
69	return temp
70}
71
72// Cosh returns the hyperbolic cosine of x.
73//
74// Special cases are:
75//
76//	Cosh(±0) = 1
77//	Cosh(±Inf) = +Inf
78//	Cosh(NaN) = NaN
79func Cosh(x float64) float64 {
80	if haveArchCosh {
81		return archCosh(x)
82	}
83	return cosh(x)
84}
85
86func cosh(x float64) float64 {
87	x = Abs(x)
88	if x > 21 {
89		return Exp(x) * 0.5
90	}
91	ex := Exp(x)
92	return (ex + 1/ex) * 0.5
93}
94