/* origin: FreeBSD /usr/src/lib/msun/src/s_tanh.c */ /* * ==================================================== * 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. * ==================================================== */ /* 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 "libm.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 */ } if (ix < 0x40360000) { /* |x| < 22 */ if (ix < 0x3e300000) { /* |x| < 2**-28 */ /* tanh(tiny) = tiny with inexact */ if (huge+x > one) return x; } 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); } } else { /* |x| >= 22, return +-1 */ z = one - tiny; /* raise inexact */ } return jx >= 0 ? z : -z; }