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path: root/src/math/tanh.c
blob: 2113864380a5930da96c5f441a7538c0bf36f2c5 (plain)
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 /* 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 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 1.0f/x + 1.0f; /* tanh(+-inf)=+-1 */ else return 1.0f/x - 1.0f; /* tanh(NaN) = NaN */ } if (ix < 0x40360000) { /* |x| < 22 */ if (ix < 0x3e300000) { /* |x| < 2**-28 */ /* tanh(tiny) = tiny with inexact */ if (huge+x > 1.0f) return x; } if (ix >= 0x3ff00000) { /* |x| >= 1 */ t = expm1(2.0f*fabs(x)); z = 1.0f - 2.0f/(t+2.0f); } else { t = expm1(-2.0f*fabs(x)); z= -t/(t+2.0f); } } else { /* |x| >= 22, return +-1 */ z = 1.0f - tiny; /* raise inexact */ } return jx >= 0 ? z : -z; }