// Copyright 2009 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. package math /* Floating-point hyperbolic sine and cosine. The exponential func is called for arguments greater in magnitude than 0.5. A series is used for arguments smaller in magnitude than 0.5. Cosh(x) is computed from the exponential func for all arguments. */ // Sinh returns the hyperbolic sine of x. // // Special cases are: // Sinh(±0) = ±0 // Sinh(±Inf) = ±Inf // Sinh(NaN) = NaN func Sinh(x float64) float64 func sinh(x float64) float64 { // The coefficients are #2029 from Hart & Cheney. (20.36D) const ( P0 = -0.6307673640497716991184787251e+6 P1 = -0.8991272022039509355398013511e+5 P2 = -0.2894211355989563807284660366e+4 P3 = -0.2630563213397497062819489e+2 Q0 = -0.6307673640497716991212077277e+6 Q1 = 0.1521517378790019070696485176e+5 Q2 = -0.173678953558233699533450911e+3 ) sign := false if x < 0 { x = -x sign = true } var temp float64 switch { case x > 21: temp = Exp(x) * 0.5 case x > 0.5: ex := Exp(x) temp = (ex - 1/ex) * 0.5 default: sq := x * x temp = (((P3*sq+P2)*sq+P1)*sq + P0) * x temp = temp / (((sq+Q2)*sq+Q1)*sq + Q0) } if sign { temp = -temp } return temp } // Cosh returns the hyperbolic cosine of x. // // Special cases are: // Cosh(±0) = 1 // Cosh(±Inf) = +Inf // Cosh(NaN) = NaN func Cosh(x float64) float64 func cosh(x float64) float64 { x = Abs(x) if x > 21 { return Exp(x) * 0.5 } ex := Exp(x) return (ex + 1/ex) * 0.5 }