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		// 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	}