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// 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)
}