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// Copyright 2009 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 math
/*
Floating-point hyperbolic sine and cosine.
The exponential func is called for arguments
greater in magnitude than 0.5.
A series is used for arguments smaller in magnitude than 0.5.
Cosh(x) is computed from the exponential func for
all arguments.
*/
// Sinh returns the hyperbolic sine of x.
//
// Special cases are:
// Sinh(±0) = ±0
// Sinh(±Inf) = ±Inf
// Sinh(NaN) = NaN
func Sinh(x float64) float64
func sinh(x float64) float64 {
// The coefficients are #2029 from Hart & Cheney. (20.36D)
const (
P0 = -0.6307673640497716991184787251e+6
P1 = -0.8991272022039509355398013511e+5
P2 = -0.2894211355989563807284660366e+4
P3 = -0.2630563213397497062819489e+2
Q0 = -0.6307673640497716991212077277e+6
Q1 = 0.1521517378790019070696485176e+5
Q2 = -0.173678953558233699533450911e+3
)
sign := false
if x < 0 {
x = -x
sign = true
}
var temp float64
switch {
case x > 21:
temp = Exp(x) * 0.5
case x > 0.5:
ex := Exp(x)
temp = (ex - 1/ex) * 0.5
default:
sq := x * x
temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
}
if sign {
temp = -temp
}
return temp
}
// Cosh returns the hyperbolic cosine of x.
//
// Special cases are:
// Cosh(±0) = 1
// Cosh(±Inf) = +Inf
// Cosh(NaN) = NaN
func Cosh(x float64) float64
func cosh(x float64) float64 {
x = Abs(x)
if x > 21 {
return Exp(x) * 0.5
}
ex := Exp(x)
return (ex + 1/ex) * 0.5
}
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