mirror of git://gcc.gnu.org/git/gcc.git
65 lines
2.0 KiB
Go
65 lines
2.0 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 natural logarithm
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//
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// DESCRIPTION:
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//
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// Returns complex logarithm to the base e (2.718...) of
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// the complex argument z.
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//
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// If
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// z = x + iy, r = sqrt( x**2 + y**2 ),
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// then
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// w = log(r) + i arctan(y/x).
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//
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// The arctangent ranges from -PI to +PI.
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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 7000 8.5e-17 1.9e-17
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// IEEE -10,+10 30000 5.0e-15 1.1e-16
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//
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// Larger relative error can be observed for z near 1 +i0.
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// In IEEE arithmetic the peak absolute error is 5.2e-16, rms
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// absolute error 1.0e-16.
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// Log returns the natural logarithm of x.
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func Log(x complex128) complex128 {
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return complex(math.Log(Abs(x)), Phase(x))
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}
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// Log10 returns the decimal logarithm of x.
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func Log10(x complex128) complex128 {
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return math.Log10E * Log(x)
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}
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