git://sourceware.org / glibc.git / blame
| Commit | Line | Data |
|---|---|---|
| f7eac6eb RM |
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 | |
| cccda09f | 8 | * software is freely granted, provided that this notice |
| f7eac6eb RM |
9 | * is preserved. |
| 10 | * ==================================================== | |
| 11 | */ | |
| 12 | ||
| 13 | #if defined(LIBM_SCCS) && !defined(lint) | |
| 14 | static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc 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 | ||
| 37d83a08 | 41 | #include <float.h> |
| 1ed0291c RH |
42 | #include <math.h> |
| 43 | #include <math_private.h> | |
| 8f5b00d3 | 44 | #include <math-underflow.h> |
| 1e2bffd0 | 45 | #include <libm-alias-double.h> |
| f7eac6eb | 46 | |
| c5d5d574 | 47 | static const double one = 1.0, two = 2.0, tiny = 1.0e-300; |
| f7eac6eb | 48 | |
| c5d5d574 OB |
49 | double |
| 50 | __tanh (double x) | |
| f7eac6eb | 51 | { |
| c5d5d574 OB |
52 | double t, z; |
| 53 | int32_t jx, ix, lx; | |
| f7eac6eb | 54 | |
| c5d5d574 OB |
55 | /* High word of |x|. */ |
| 56 | EXTRACT_WORDS (jx, lx, x); | |
| 57 | ix = jx & 0x7fffffff; | |
| f7eac6eb | 58 | |
| c5d5d574 OB |
59 | /* x is INF or NaN */ |
| 60 | if (ix >= 0x7ff00000) | |
| 61 | { | |
| 62 | if (jx >= 0) | |
| 63 | return one / x + one; /* tanh(+-inf)=+-1 */ | |
| 64 | else | |
| 65 | return one / x - one; /* tanh(NaN) = NaN */ | |
| 66 | } | |
| f7eac6eb | 67 | |
| c5d5d574 OB |
68 | /* |x| < 22 */ |
| 69 | if (ix < 0x40360000) /* |x|<22 */ | |
| 70 | { | |
| 71 | if ((ix | lx) == 0) | |
| 72 | return x; /* x == +-0 */ | |
| 73 | if (ix < 0x3c800000) /* |x|<2**-55 */ | |
| 37d83a08 | 74 | { |
| d96164c3 | 75 | math_check_force_underflow (x); |
| 37d83a08 JM |
76 | return x * (one + x); /* tanh(small) = small */ |
| 77 | } | |
| c5d5d574 OB |
78 | if (ix >= 0x3ff00000) /* |x|>=1 */ |
| 79 | { | |
| 80 | t = __expm1 (two * fabs (x)); | |
| 81 | z = one - two / (t + two); | |
| 82 | } | |
| 83 | else | |
| 84 | { | |
| 85 | t = __expm1 (-two * fabs (x)); | |
| 86 | z = -t / (t + two); | |
| f7eac6eb | 87 | } |
| c5d5d574 OB |
88 | /* |x| > 22, return +-1 */ |
| 89 | } | |
| 90 | else | |
| 91 | { | |
| 92 | z = one - tiny; /* raised inexact flag */ | |
| 93 | } | |
| 94 | return (jx >= 0) ? z : -z; | |
| f7eac6eb | 95 | } |
| 1e2bffd0 | 96 | libm_alias_double (__tanh, tanh) |