github.com/mdempsky/go@v0.0.0-20151201204031-5dd372bd1e70/src/math/sinh.go (about)

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