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 }