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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))
}