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# Source file src/math/sinh.go

## Documentation: math

```     1  // Copyright 2009 The Go Authors. All rights reserved.
2  // Use of this source code is governed by a BSD-style
4
5  package 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
25  func Sinh(x float64) float64 {
26  	if haveArchSinh {
27  		return archSinh(x)
28  	}
29  	return sinh(x)
30  }
31
32  func sinh(x float64) float64 {
33  	// The coefficients are #2029 from Hart & Cheney. (20.36D)
34  	const (
35  		P0 = -0.6307673640497716991184787251e+6
36  		P1 = -0.8991272022039509355398013511e+5
37  		P2 = -0.2894211355989563807284660366e+4
38  		P3 = -0.2630563213397497062819489e+2
39  		Q0 = -0.6307673640497716991212077277e+6
40  		Q1 = 0.1521517378790019070696485176e+5
41  		Q2 = -0.173678953558233699533450911e+3
42  	)
43
44  	sign := false
45  	if x < 0 {
46  		x = -x
47  		sign = true
48  	}
49
50  	var temp float64
51  	switch {
52  	case x > 21:
53  		temp = Exp(x) * 0.5
54
55  	case x > 0.5:
56  		ex := Exp(x)
57  		temp = (ex - 1/ex) * 0.5
58
59  	default:
60  		sq := x * x
61  		temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
62  		temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
63  	}
64
65  	if sign {
66  		temp = -temp
67  	}
68  	return temp
69  }
70
71  // Cosh returns the hyperbolic cosine of x.
72  //
73  // Special cases are:
74  //	Cosh(±0) = 1
75  //	Cosh(±Inf) = +Inf
76  //	Cosh(NaN) = NaN
77  func Cosh(x float64) float64 {
78  	if haveArchCosh {
79  		return archCosh(x)
80  	}
81  	return cosh(x)
82  }
83
84  func cosh(x float64) float64 {
85  	x = Abs(x)
86  	if x > 21 {
87  		return Exp(x) * 0.5
88  	}
89  	ex := Exp(x)
90  	return (ex + 1/ex) * 0.5
91  }
92
```

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