| /* @(#)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. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* 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**-28 : tanh(x) := x with inexact if x != 0 |
| * -t |
| * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) |
| * t + 2 |
| * 2 |
| * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) |
| * t + 2 |
| * 22 <= 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, huge = 1.0e300; |
| |
| double |
| tanh(double x) |
| { |
| double t,z; |
| int32_t jx,ix; |
| |
| GET_HIGH_WORD(jx,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<0x3e300000) { /* |x|<2**-28 */ |
| if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ |
| } |
| 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; /* raise inexact flag */ |
| } |
| return (jx>=0)? z: -z; |
| } |
