72 lines
2.1 KiB
Go
72 lines
2.1 KiB
Go
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package cmplx
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import "math"
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// The original C code, the long comment, and the constants
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// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
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// The go code is a simplified version of the original C.
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//
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// Cephes Math Library Release 2.8: June, 2000
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// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
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//
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// The readme file at http://netlib.sandia.gov/cephes/ says:
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// Some software in this archive may be from the book _Methods and
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// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
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// International, 1989) or from the Cephes Mathematical Library, a
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// commercial product. In either event, it is copyrighted by the author.
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// What you see here may be used freely but it comes with no support or
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// guarantee.
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//
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// The two known misprints in the book are repaired here in the
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// source listings for the gamma function and the incomplete beta
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// integral.
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//
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// Stephen L. Moshier
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// moshier@na-net.ornl.gov
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// Complex exponential function
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//
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// DESCRIPTION:
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//
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// Returns the complex exponential of the complex argument z.
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//
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// If
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// z = x + iy,
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// r = exp(x),
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// then
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// w = r cos y + i r sin y.
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//
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// ACCURACY:
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//
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// Relative error:
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// arithmetic domain # trials peak rms
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// DEC -10,+10 8700 3.7e-17 1.1e-17
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// IEEE -10,+10 30000 3.0e-16 8.7e-17
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// Exp returns e**x, the base-e exponential of x.
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func Exp(x complex128) complex128 {
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switch re, im := real(x), imag(x); {
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case math.IsInf(re, 0):
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switch {
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case re > 0 && im == 0:
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return x
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case math.IsInf(im, 0) || math.IsNaN(im):
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if re < 0 {
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return complex(0, math.Copysign(0, im))
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} else {
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return complex(math.Inf(1.0), math.NaN())
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}
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}
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case math.IsNaN(re):
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if im == 0 {
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return complex(math.NaN(), im)
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}
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}
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r := math.Exp(real(x))
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s, c := math.Sincos(imag(x))
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return complex(r*c, r*s)
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}
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