Source file src/pkg/math/cmplx/log.go

     1	// Copyright 2010 The Go Authors. All rights reserved.
     2	// Use of this source code is governed by a BSD-style
     3	// license that can be found in the LICENSE file.
     4	
     5	package cmplx
     6	
     7	import "math"
     8	
     9	// The original C code, the long comment, and the constants
    10	// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
    11	// The go code is a simplified version of the original C.
    12	//
    13	// Cephes Math Library Release 2.8:  June, 2000
    14	// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
    15	//
    16	// The readme file at http://netlib.sandia.gov/cephes/ says:
    17	//    Some software in this archive may be from the book _Methods and
    18	// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
    19	// International, 1989) or from the Cephes Mathematical Library, a
    20	// commercial product. In either event, it is copyrighted by the author.
    21	// What you see here may be used freely but it comes with no support or
    22	// guarantee.
    23	//
    24	//   The two known misprints in the book are repaired here in the
    25	// source listings for the gamma function and the incomplete beta
    26	// integral.
    27	//
    28	//   Stephen L. Moshier
    29	//   [email protected]
    30	
    31	// Complex natural logarithm
    32	//
    33	// DESCRIPTION:
    34	//
    35	// Returns complex logarithm to the base e (2.718...) of
    36	// the complex argument z.
    37	//
    38	// If
    39	//       z = x + iy, r = sqrt( x**2 + y**2 ),
    40	// then
    41	//       w = log(r) + i arctan(y/x).
    42	//
    43	// The arctangent ranges from -PI to +PI.
    44	//
    45	// ACCURACY:
    46	//
    47	//                      Relative error:
    48	// arithmetic   domain     # trials      peak         rms
    49	//    DEC       -10,+10      7000       8.5e-17     1.9e-17
    50	//    IEEE      -10,+10     30000       5.0e-15     1.1e-16
    51	//
    52	// Larger relative error can be observed for z near 1 +i0.
    53	// In IEEE arithmetic the peak absolute error is 5.2e-16, rms
    54	// absolute error 1.0e-16.
    55	
    56	// Log returns the natural logarithm of x.
    57	func Log(x complex128) complex128 {
    58		return complex(math.Log(Abs(x)), Phase(x))
    59	}
    60	
    61	// Log10 returns the decimal logarithm of x.
    62	func Log10(x complex128) complex128 {
    63		return math.Log10E * Log(x)
    64	}