exp.go

// Copyright 2010 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 cmplx

import "math"

// The original C code, the long comment, and the constants
// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
// The go code is a simplified version of the original C.
//
// Cephes Math Library Release 2.8:  June, 2000
// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
//
// The readme file at http://netlib.sandia.gov/cephes/ says:
//    Some software in this archive may be from the book _Methods and
// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
// International, 1989) or from the Cephes Mathematical Library, a
// commercial product. In either event, it is copyrighted by the author.
// What you see here may be used freely but it comes with no support or
// guarantee.
//
//   The two known misprints in the book are repaired here in the
// source listings for the gamma function and the incomplete beta
// integral.
//
//   Stephen L. Moshier
//   moshier@na-net.ornl.gov

// Complex exponential function
//
// DESCRIPTION:
//
// Returns the complex exponential of the complex argument z.
//
// If
//     z = x + iy,
//     r = exp(x),
// then
//     w = r cos y + i r sin y.
//
// ACCURACY:
//
//                      Relative error:
// arithmetic   domain     # trials      peak         rms
//    DEC       -10,+10      8700       3.7e-17     1.1e-17
//    IEEE      -10,+10     30000       3.0e-16     8.7e-17

// Exp returns e**x, the base-e exponential of x.
func Exp(x complex128) complex128 {
	switch re, im := real(x), imag(x); {
	case math.IsInf(re, 0):
		switch {
		case re > 0 && im == 0:
			return x
		case math.IsInf(im, 0) || math.IsNaN(im):
			if re < 0 {
				return complex(0, math.Copysign(0, im))
			} else {
				return complex(math.Inf(1.0), math.NaN())
			}
		}
	case math.IsNaN(re):
		if im == 0 {
			return complex(math.NaN(), im)
		}
	}
	r := math.Exp(real(x))
	s, c := math.Sincos(imag(x))
	return complex(r*c, r*s)
}