...
Run Format

Source file src/math/tanh.go

     1	// Copyright 2009 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 math
     6	
     7	// The original C code, the long comment, and the constants
     8	// below were from http://netlib.sandia.gov/cephes/cmath/sin.c,
     9	// available from http://www.netlib.org/cephes/cmath.tgz.
    10	// The go code is a simplified version of the original C.
    11	//      tanh.c
    12	//
    13	//      Hyperbolic tangent
    14	//
    15	// SYNOPSIS:
    16	//
    17	// double x, y, tanh();
    18	//
    19	// y = tanh( x );
    20	//
    21	// DESCRIPTION:
    22	//
    23	// Returns hyperbolic tangent of argument in the range MINLOG to MAXLOG.
    24	//      MAXLOG = 8.8029691931113054295988e+01 = log(2**127)
    25	//      MINLOG = -8.872283911167299960540e+01 = log(2**-128)
    26	//
    27	// A rational function is used for |x| < 0.625.  The form
    28	// x + x**3 P(x)/Q(x) of Cody & Waite is employed.
    29	// Otherwise,
    30	//      tanh(x) = sinh(x)/cosh(x) = 1  -  2/(exp(2x) + 1).
    31	//
    32	// ACCURACY:
    33	//
    34	//                      Relative error:
    35	// arithmetic   domain     # trials      peak         rms
    36	//    IEEE      -2,2        30000       2.5e-16     5.8e-17
    37	//
    38	// Cephes Math Library Release 2.8:  June, 2000
    39	// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
    40	//
    41	// The readme file at http://netlib.sandia.gov/cephes/ says:
    42	//    Some software in this archive may be from the book _Methods and
    43	// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
    44	// International, 1989) or from the Cephes Mathematical Library, a
    45	// commercial product. In either event, it is copyrighted by the author.
    46	// What you see here may be used freely but it comes with no support or
    47	// guarantee.
    48	//
    49	//   The two known misprints in the book are repaired here in the
    50	// source listings for the gamma function and the incomplete beta
    51	// integral.
    52	//
    53	//   Stephen L. Moshier
    54	//   moshier@na-net.ornl.gov
    55	//
    56	
    57	var tanhP = [...]float64{
    58		-9.64399179425052238628E-1,
    59		-9.92877231001918586564E1,
    60		-1.61468768441708447952E3,
    61	}
    62	var tanhQ = [...]float64{
    63		1.12811678491632931402E2,
    64		2.23548839060100448583E3,
    65		4.84406305325125486048E3,
    66	}
    67	
    68	// Tanh returns the hyperbolic tangent of x.
    69	//
    70	// Special cases are:
    71	//	Tanh(±0) = ±0
    72	//	Tanh(±Inf) = ±1
    73	//	Tanh(NaN) = NaN
    74	func Tanh(x float64) float64
    75	
    76	func tanh(x float64) float64 {
    77		const MAXLOG = 8.8029691931113054295988e+01 // log(2**127)
    78		z := Abs(x)
    79		switch {
    80		case z > 0.5*MAXLOG:
    81			if x < 0 {
    82				return -1
    83			}
    84			return 1
    85		case z >= 0.625:
    86			s := Exp(2 * z)
    87			z = 1 - 2/(s+1)
    88			if x < 0 {
    89				z = -z
    90			}
    91		default:
    92			if x == 0 {
    93				return x
    94			}
    95			s := x * x
    96			z = x + x*s*((tanhP[0]*s+tanhP[1])*s+tanhP[2])/(((s+tanhQ[0])*s+tanhQ[1])*s+tanhQ[2])
    97		}
    98		return z
    99	}
   100	

View as plain text