// 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
//   [email protected]

// 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 {
	r := math.Exp(real(x))
	s, c := math.Sincos(imag(x))
	return complex(r*c, r*s)
}