| /* @(#)s_tanh.c 5.1 93/09/24 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * |
| * Developed at SunPro, a Sun Microsystems, Inc. business. |
| * Permission to use, copy, modify, and distribute this |
| * software is freely granted, provided that this notice |
| * is preserved. |
| * ==================================================== |
| */ |
| |
| #if defined(LIBM_SCCS) && !defined(lint) |
| static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $"; |
| #endif |
| |
| /* Tanh(x) |
| * Return the Hyperbolic Tangent of x |
| * |
| * Method : |
| * x -x |
| * e - e |
| * 0. tanh(x) is defined to be ----------- |
| * x -x |
| * e + e |
| * 1. reduce x to non-negative by tanh(-x) = -tanh(x). |
| * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) |
| * -t |
| * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) |
| * t + 2 |
| * 2 |
| * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) |
| * t + 2 |
| * 22.0 < x <= INF : tanh(x) := 1. |
| * |
| * Special cases: |
| * tanh(NaN) is NaN; |
| * only tanh(0)=0 is exact for finite argument. |
| */ |
| |
| #include <math.h> |
| #include <math_private.h> |
| |
| static const double one = 1.0, two = 2.0, tiny = 1.0e-300; |
| |
| double |
| __tanh (double x) |
| { |
| double t, z; |
| int32_t jx, ix, lx; |
| |
| /* High word of |x|. */ |
| EXTRACT_WORDS (jx, lx, x); |
| ix = jx & 0x7fffffff; |
| |
| /* x is INF or NaN */ |
| if (ix >= 0x7ff00000) |
| { |
| if (jx >= 0) |
| return one / x + one; /* tanh(+-inf)=+-1 */ |
| else |
| return one / x - one; /* tanh(NaN) = NaN */ |
| } |
| |
| /* |x| < 22 */ |
| if (ix < 0x40360000) /* |x|<22 */ |
| { |
| if ((ix | lx) == 0) |
| return x; /* x == +-0 */ |
| if (ix < 0x3c800000) /* |x|<2**-55 */ |
| return x * (one + x); /* tanh(small) = small */ |
| if (ix >= 0x3ff00000) /* |x|>=1 */ |
| { |
| t = __expm1 (two * fabs (x)); |
| z = one - two / (t + two); |
| } |
| else |
| { |
| t = __expm1 (-two * fabs (x)); |
| z = -t / (t + two); |
| } |
| /* |x| > 22, return +-1 */ |
| } |
| else |
| { |
| z = one - tiny; /* raised inexact flag */ |
| } |
| return (jx >= 0) ? z : -z; |
| } |
| weak_alias (__tanh, tanh) |
| #ifdef NO_LONG_DOUBLE |
| strong_alias (__tanh, __tanhl) |
| weak_alias (__tanh, tanhl) |
| #endif |
