libgo/go/math/cmplx/pow.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 power function
  32 //
  33 // DESCRIPTION:
  34 //
  35 // Raises complex A to the complex Zth power.
  36 // Definition is per AMS55 # 4.2.8,
  37 // analytically equivalent to cpow(a,z) = cexp(z clog(a)).
  38 //
  39 // ACCURACY:
  40 //
  41 //                      Relative error:
  42 // arithmetic   domain     # trials      peak         rms
  43 //    IEEE      -10,+10     30000       9.4e-15     1.5e-15
  44
  45 // Pow returns x**y, the base-x exponential of y.
  46 // For generalized compatibility with math.Pow:
  47 //      Pow(0, ±0) returns 1+0i
  48 //      Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
  49 func Pow(x, y complex128) complex128 {
  50         if x == 0 { // Guaranteed also true for x == -0.
  51                 r, i := real(y), imag(y)
  52                 switch {
  53                 case r == 0:
  54                         return 1
  55                 case r < 0:
  56                         if i == 0 {
  57                                 return complex(math.Inf(1), 0)
  58                         }
  59                         return Inf()
  60                 case r > 0:
  61                         return 0
  62                 }
  63                 panic("not reached")
  64         }
  65         modulus := Abs(x)
  66         if modulus == 0 {
  67                 return complex(0, 0)
  68         }
  69         r := math.Pow(modulus, real(y))
  70         arg := Phase(x)
  71         theta := real(y) * arg
  72         if imag(y) != 0 {
  73                 r *= math.Exp(-imag(y) * arg)
  74                 theta += imag(y) * math.Log(modulus)
  75         }
  76         s, c := math.Sincos(theta)
  77         return complex(r*c, r*s)
  78 }