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
