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  
    27  func sinh(x float64) float64 {
    28  	// The coefficients are #2029 from Hart & Cheney. (20.36D)
    29  	const (
    30  		P0 = -0.6307673640497716991184787251e+6
    31  		P1 = -0.8991272022039509355398013511e+5
    32  		P2 = -0.2894211355989563807284660366e+4
    33  		P3 = -0.2630563213397497062819489e+2
    34  		Q0 = -0.6307673640497716991212077277e+6
    35  		Q1 = 0.1521517378790019070696485176e+5
    36  		Q2 = -0.173678953558233699533450911e+3
    37  	)
    38  
    39  	sign := false
    40  	if x < 0 {
    41  		x = -x
    42  		sign = true
    43  	}
    44  
    45  	var temp float64
    46  	switch true {
    47  	case x > 21:
    48  		temp = Exp(x) / 2
    49  
    50  	case x > 0.5:
    51  		temp = (Exp(x) - Exp(-x)) / 2
    52  
    53  	default:
    54  		sq := x * x
    55  		temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
    56  		temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
    57  	}
    58  
    59  	if sign {
    60  		temp = -temp
    61  	}
    62  	return temp
    63  }
    64  
    65  // Cosh returns the hyperbolic cosine of x.
    66  //
    67  // Special cases are:
    68  //	Cosh(±0) = 1
    69  //	Cosh(±Inf) = +Inf
    70  //	Cosh(NaN) = NaN
    71  func Cosh(x float64) float64
    72  
    73  func cosh(x float64) float64 {
    74  	if x < 0 {
    75  		x = -x
    76  	}
    77  	if x > 21 {
    78  		return Exp(x) / 2
    79  	}
    80  	return (Exp(x) + Exp(-x)) / 2
    81  }
    82
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