Source file src/pkg/math/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	
    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 {
    47		case x > 21:
    48			temp = Exp(x) * 0.5
    49	
    50		case x > 0.5:
    51			ex := Exp(x)
    52			temp = (ex - 1/ex) * 0.5
    53	
    54		default:
    55			sq := x * x
    56			temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x
    57			temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0)
    58		}
    59	
    60		if sign {
    61			temp = -temp
    62		}
    63		return temp
    64	}
    65	
    66	// Cosh returns the hyperbolic cosine of x.
    67	//
    68	// Special cases are:
    69	//	Cosh(±0) = 1
    70	//	Cosh(±Inf) = +Inf
    71	//	Cosh(NaN) = NaN
    72	func Cosh(x float64) float64
    73	
    74	func cosh(x float64) float64 {
    75		x = Abs(x)
    76		if x > 21 {
    77			return Exp(x) * 0.5
    78		}
    79		ex := Exp(x)
    80		return (ex + 1/ex) * 0.5
    81	}
    82	

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