| 1 | /* @(#)s_tanh.c 5.1 93/09/24 */
|
|---|
| 2 | /*
|
|---|
| 3 | * ====================================================
|
|---|
| 4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|---|
| 5 | *
|
|---|
| 6 | * Developed at SunPro, a Sun Microsystems, Inc. business.
|
|---|
| 7 | * Permission to use, copy, modify, and distribute this
|
|---|
| 8 | * software is freely granted, provided that this notice
|
|---|
| 9 | * is preserved.
|
|---|
| 10 | * ====================================================
|
|---|
| 11 | */
|
|---|
| 12 |
|
|---|
| 13 | #ifndef lint
|
|---|
| 14 | static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_tanh.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
|
|---|
| 15 | #endif
|
|---|
| 16 |
|
|---|
| 17 | /* Tanh(x)
|
|---|
| 18 | * Return the Hyperbolic Tangent of x
|
|---|
| 19 | *
|
|---|
| 20 | * Method :
|
|---|
| 21 | * x -x
|
|---|
| 22 | * e - e
|
|---|
| 23 | * 0. tanh(x) is defined to be -----------
|
|---|
| 24 | * x -x
|
|---|
| 25 | * e + e
|
|---|
| 26 | * 1. reduce x to non-negative by tanh(-x) = -tanh(x).
|
|---|
| 27 | * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x)
|
|---|
| 28 | * -t
|
|---|
| 29 | * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x)
|
|---|
| 30 | * t + 2
|
|---|
| 31 | * 2
|
|---|
| 32 | * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x)
|
|---|
| 33 | * t + 2
|
|---|
| 34 | * 22.0 < x <= INF : tanh(x) := 1.
|
|---|
| 35 | *
|
|---|
| 36 | * Special cases:
|
|---|
| 37 | * tanh(NaN) is NaN;
|
|---|
| 38 | * only tanh(0)=0 is exact for finite argument.
|
|---|
| 39 | */
|
|---|
| 40 |
|
|---|
| 41 | #include "math.h"
|
|---|
| 42 | #include "math_private.h"
|
|---|
| 43 |
|
|---|
| 44 | static const double one=1.0, two=2.0, tiny = 1.0e-300;
|
|---|
| 45 |
|
|---|
| 46 | double
|
|---|
| 47 | tanh(double x)
|
|---|
| 48 | {
|
|---|
| 49 | double t,z;
|
|---|
| 50 | int32_t jx,ix;
|
|---|
| 51 |
|
|---|
| 52 | /* High word of |x|. */
|
|---|
| 53 | GET_HIGH_WORD(jx,x);
|
|---|
| 54 | ix = jx&0x7fffffff;
|
|---|
| 55 |
|
|---|
| 56 | /* x is INF or NaN */
|
|---|
| 57 | if(ix>=0x7ff00000) {
|
|---|
| 58 | if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */
|
|---|
| 59 | else return one/x-one; /* tanh(NaN) = NaN */
|
|---|
| 60 | }
|
|---|
| 61 |
|
|---|
| 62 | /* |x| < 22 */
|
|---|
| 63 | if (ix < 0x40360000) { /* |x|<22 */
|
|---|
| 64 | if (ix<0x3c800000) /* |x|<2**-55 */
|
|---|
| 65 | return x*(one+x); /* tanh(small) = small */
|
|---|
| 66 | if (ix>=0x3ff00000) { /* |x|>=1 */
|
|---|
| 67 | t = expm1(two*fabs(x));
|
|---|
| 68 | z = one - two/(t+two);
|
|---|
| 69 | } else {
|
|---|
| 70 | t = expm1(-two*fabs(x));
|
|---|
| 71 | z= -t/(t+two);
|
|---|
| 72 | }
|
|---|
| 73 | /* |x| > 22, return +-1 */
|
|---|
| 74 | } else {
|
|---|
| 75 | z = one - tiny; /* raised inexact flag */
|
|---|
| 76 | }
|
|---|
| 77 | return (jx>=0)? z: -z;
|
|---|
| 78 | }
|
|---|
