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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))
+}