libgo/go/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 {
  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
  70 func 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 }