exp.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 exponential function
    32  //
    33  // DESCRIPTION:
    34  //
    35  // Returns the complex exponential of the complex argument z.
    36  //
    37  // If
    38  //     z = x + iy,
    39  //     r = exp(x),
    40  // then
    41  //     w = r cos y + i r sin y.
    42  //
    43  // ACCURACY:
    44  //
    45  //                      Relative error:
    46  // arithmetic   domain     # trials      peak         rms
    47  //    DEC       -10,+10      8700       3.7e-17     1.1e-17
    48  //    IEEE      -10,+10     30000       3.0e-16     8.7e-17
    49  
    50  // Exp returns e**x, the base-e exponential of x.
    51  func Exp(x complex128) complex128 {
    52  	switch re, im := real(x), imag(x); {
    53  	case math.IsInf(re, 0):
    54  		switch {
    55  		case re > 0 && im == 0:
    56  			return x
    57  		case math.IsInf(im, 0) || math.IsNaN(im):
    58  			if re < 0 {
    59  				return complex(0, math.Copysign(0, im))
    60  			} else {
    61  				return complex(math.Inf(1.0), math.NaN())
    62  			}
    63  		}
    64  	case math.IsNaN(re):
    65  		if im == 0 {
    66  			return complex(math.NaN(), im)
    67  		}
    68  	}
    69  	r := math.Exp(real(x))
    70  	s, c := math.Sincos(imag(x))
    71  	return complex(r*c, r*s)
    72  }
    73
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