| // 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 { |
| // 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 true { |
| 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 { |
| x = Abs(x) |
| if x > 21 { |
| return Exp(x) * 0.5 |
| } |
| ex := Exp(x) |
| return (ex + 1/ex) * 0.5 |
| } |