| /* @(#)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**-57 : tanh(x) := x*(one+x) |
| * -t |
| * 2**-57 < 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> |
| #include <math_ldbl_opt.h> |
| |
| static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L; |
| |
| long double __tanhl(long double x) |
| { |
| long double t,z; |
| int64_t jx,ix; |
| double xhi; |
| |
| /* High word of |x|. */ |
| xhi = ldbl_high (x); |
| EXTRACT_WORDS64 (jx, xhi); |
| ix = jx&0x7fffffffffffffffLL; |
| |
| /* x is INF or NaN */ |
| if(ix>=0x7ff0000000000000LL) { |
| if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ |
| else return one/x-one; /* tanh(NaN) = NaN */ |
| } |
| |
| /* |x| < 22 */ |
| if (ix < 0x4036000000000000LL) { /* |x|<22 */ |
| if (ix == 0) |
| return x; /* x == +-0 */ |
| if (ix<0x3c60000000000000LL) /* |x|<2**-57 */ |
| return x*(one+x); /* tanh(small) = small */ |
| if (ix>=0x3ff0000000000000LL) { /* |x|>=1 */ |
| t = __expm1l(two*fabsl(x)); |
| z = one - two/(t+two); |
| } else { |
| t = __expm1l(-two*fabsl(x)); |
| z= -t/(t+two); |
| } |
| /* |x| > 22, return +-1 */ |
| } else { |
| z = one - tiny; /* raised inexact flag */ |
| } |
| return (jx>=0)? z: -z; |
| } |
| long_double_symbol (libm, __tanhl, tanhl); |