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