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