11dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* @(#)s_tanh.c 5.1 93/09/24 */ 21dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* 31dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 41dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 51dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 61dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Developed at SunPro, a Sun Microsystems, Inc. business. 71dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Permission to use, copy, modify, and distribute this 81dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * software is freely granted, provided that this notice 91dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * is preserved. 101dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * ==================================================== 111dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 121dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 13a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes#include <sys/cdefs.h> 14a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes__FBSDID("$FreeBSD$"); 151dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 161dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project/* Tanh(x) 171dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Return the Hyperbolic Tangent of x 181dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 191dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Method : 201dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * x -x 211dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * e - e 221dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 0. tanh(x) is defined to be ----------- 231dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * x -x 241dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * e + e 251dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 26a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0 271dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * -t 28a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) 291dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * t + 2 301dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 2 31a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) 321dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * t + 2 33a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes * 22 <= x <= INF : tanh(x) := 1. 341dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * 351dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * Special cases: 361dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * tanh(NaN) is NaN; 371dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project * only tanh(0)=0 is exact for finite argument. 381dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project */ 391dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 40460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes#include <float.h> 41460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes 421dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math.h" 431dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project#include "math_private.h" 441dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 45460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughesstatic const volatile double tiny = 1.0e-300; 46460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughesstatic const double one = 1.0, two = 2.0, huge = 1.0e300; 471dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 481dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projectdouble 491dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Projecttanh(double x) 501dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project{ 511dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project double t,z; 521dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project int32_t jx,ix; 531dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 541dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project GET_HIGH_WORD(jx,x); 551dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project ix = jx&0x7fffffff; 561dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 571dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* x is INF or NaN */ 581dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if(ix>=0x7ff00000) { 591dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 601dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project else return one/x-one; /* tanh(NaN) = NaN */ 611dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 621dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project 631dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project /* |x| < 22 */ 641dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (ix < 0x40360000) { /* |x|<22 */ 65a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if (ix<0x3e300000) { /* |x|<2**-28 */ 66a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ 67a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes } 681dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project if (ix>=0x3ff00000) { /* |x|>=1 */ 691dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = expm1(two*fabs(x)); 701dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z = one - two/(t+two); 711dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 721dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project t = expm1(-two*fabs(x)); 731dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project z= -t/(t+two); 741dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 75a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes /* |x| >= 22, return +-1 */ 761dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } else { 77a0ee07829a9ba7e99ef68e8c12551301cc797f0fElliott Hughes z = one - tiny; /* raise inexact flag */ 781dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project } 791dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project return (jx>=0)? z: -z; 801dc9e472e19acfe6dc7f41e429236e7eef7ceda1The Android Open Source Project} 81460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes 82460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes#if (LDBL_MANT_DIG == 53) 83460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes__weak_reference(tanh, tanhl); 84460ad7454a281470a1938103f099a1e3192fb3d6Elliott Hughes#endif 85