libgo/go/math/cmplx/sin.go

   1 // Copyright 2010 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 cmplx
   6
   7 import "math"
   8
   9 // The original C code, the long comment, and the constants
  10 // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
  11 // The go code is a simplified version of the original C.
  12 //
  13 // Cephes Math Library Release 2.8:  June, 2000
  14 // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
  15 //
  16 // The readme file at http://netlib.sandia.gov/cephes/ says:
  17 //    Some software in this archive may be from the book _Methods and
  18 // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
  19 // International, 1989) or from the Cephes Mathematical Library, a
  20 // commercial product. In either event, it is copyrighted by the author.
  21 // What you see here may be used freely but it comes with no support or
  22 // guarantee.
  23 //
  24 //   The two known misprints in the book are repaired here in the
  25 // source listings for the gamma function and the incomplete beta
  26 // integral.
  27 //
  28 //   Stephen L. Moshier
  29 //   moshier@na-net.ornl.gov
  30
  31 // Complex circular sine
  32 //
  33 // DESCRIPTION:
  34 //
  35 // If
  36 //     z = x + iy,
  37 //
  38 // then
  39 //
  40 //     w = sin x  cosh y  +  i cos x sinh y.
  41 //
  42 // csin(z) = -i csinh(iz).
  43 //
  44 // ACCURACY:
  45 //
  46 //                      Relative error:
  47 // arithmetic   domain     # trials      peak         rms
  48 //    DEC       -10,+10      8400       5.3e-17     1.3e-17
  49 //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  50 // Also tested by csin(casin(z)) = z.
  51
  52 // Sin returns the sine of x.
  53 func Sin(x complex128) complex128 {
  54         s, c := math.Sincos(real(x))
  55         sh, ch := sinhcosh(imag(x))
  56         return complex(s*ch, c*sh)
  57 }
  58
  59 // Complex hyperbolic sine
  60 //
  61 // DESCRIPTION:
  62 //
  63 // csinh z = (cexp(z) - cexp(-z))/2
  64 //         = sinh x * cos y  +  i cosh x * sin y .
  65 //
  66 // ACCURACY:
  67 //
  68 //                      Relative error:
  69 // arithmetic   domain     # trials      peak         rms
  70 //    IEEE      -10,+10     30000       3.1e-16     8.2e-17
  71
  72 // Sinh returns the hyperbolic sine of x.
  73 func Sinh(x complex128) complex128 {
  74         s, c := math.Sincos(imag(x))
  75         sh, ch := sinhcosh(real(x))
  76         return complex(c*sh, s*ch)
  77 }
  78
  79 // Complex circular cosine
  80 //
  81 // DESCRIPTION:
  82 //
  83 // If
  84 //     z = x + iy,
  85 //
  86 // then
  87 //
  88 //     w = cos x  cosh y  -  i sin x sinh y.
  89 //
  90 // ACCURACY:
  91 //
  92 //                      Relative error:
  93 // arithmetic   domain     # trials      peak         rms
  94 //    DEC       -10,+10      8400       4.5e-17     1.3e-17
  95 //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
  96
  97 // Cos returns the cosine of x.
  98 func Cos(x complex128) complex128 {
  99         s, c := math.Sincos(real(x))
 100         sh, ch := sinhcosh(imag(x))
 101         return complex(c*ch, -s*sh)
 102 }
 103
 104 // Complex hyperbolic cosine
 105 //
 106 // DESCRIPTION:
 107 //
 108 // ccosh(z) = cosh x  cos y + i sinh x sin y .
 109 //
 110 // ACCURACY:
 111 //
 112 //                      Relative error:
 113 // arithmetic   domain     # trials      peak         rms
 114 //    IEEE      -10,+10     30000       2.9e-16     8.1e-17
 115
 116 // Cosh returns the hyperbolic cosine of x.
 117 func Cosh(x complex128) complex128 {
 118         s, c := math.Sincos(imag(x))
 119         sh, ch := sinhcosh(real(x))
 120         return complex(c*ch, s*sh)
 121 }
 122
 123 // calculate sinh and cosh
 124 func sinhcosh(x float64) (sh, ch float64) {
 125         if math.Abs(x) <= 0.5 {
 126                 return math.Sinh(x), math.Cosh(x)
 127         }
 128         e := math.Exp(x)
 129         ei := 0.5 / e
 130         e *= 0.5
 131         return e - ei, e + ei
 132 }