79 lines
2.2 KiB
Go
79 lines
2.2 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 power function
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//
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// DESCRIPTION:
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//
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// Raises complex A to the complex Zth power.
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// Definition is per AMS55 # 4.2.8,
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// analytically equivalent to cpow(a,z) = cexp(z clog(a)).
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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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// IEEE -10,+10 30000 9.4e-15 1.5e-15
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// Pow returns x**y, the base-x exponential of y.
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// For generalized compatibility with math.Pow:
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// Pow(0, ±0) returns 1+0i
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// Pow(0, c) for real(c)<0 returns Inf+0i if imag(c) is zero, otherwise Inf+Inf i.
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func Pow(x, y complex128) complex128 {
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if x == 0 { // Guaranteed also true for x == -0.
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r, i := real(y), imag(y)
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switch {
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case r == 0:
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return 1
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case r < 0:
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if i == 0 {
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return complex(math.Inf(1), 0)
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}
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return Inf()
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case r > 0:
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return 0
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}
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panic("not reached")
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}
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modulus := Abs(x)
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if modulus == 0 {
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return complex(0, 0)
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}
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r := math.Pow(modulus, real(y))
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arg := Phase(x)
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theta := real(y) * arg
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if imag(y) != 0 {
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r *= math.Exp(-imag(y) * arg)
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theta += imag(y) * math.Log(modulus)
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}
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s, c := math.Sincos(theta)
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return complex(r*c, r*s)
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}
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