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
		 3  // license that can be found in the LICENSE file.
		 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
View as plain text