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 5package 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 25func 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 { 45 case x > 21: 46 temp = Exp(x) * 0.5 47 48 case x > 0.5: 49 ex := Exp(x) 50 temp = (ex - 1/ex) * 0.5 51 52 default: 53 sq := x * x 54 temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x 55 temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0) 56 } 57 58 if sign { 59 temp = -temp 60 } 61 return temp 62} 63 64// Cosh returns the hyperbolic cosine of x. 65// 66// Special cases are: 67// Cosh(±0) = 1 68// Cosh(±Inf) = +Inf 69// Cosh(NaN) = NaN 70func Cosh(x float64) float64 { 71 x = Abs(x) 72 if x > 21 { 73 return Exp(x) * 0.5 74 } 75 ex := Exp(x) 76 return (ex + 1/ex) * 0.5 77} 78