sinh.go

     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
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