1 /* @(#)s_tanh.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 __FBSDID("$FreeBSD$"); 15 16 /* Tanh(x) 17 * Return the Hyperbolic Tangent of x 18 * 19 * Method : 20 * x -x 21 * e - e 22 * 0. tanh(x) is defined to be ----------- 23 * x -x 24 * e + e 25 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 26 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0 27 * -t 28 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) 29 * t + 2 30 * 2 31 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) 32 * t + 2 33 * 22 <= x <= INF : tanh(x) := 1. 34 * 35 * Special cases: 36 * tanh(NaN) is NaN; 37 * only tanh(0)=0 is exact for finite argument. 38 */ 39 40 #include "math.h" 41 #include "math_private.h" 42 43 static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300; 44 45 double 46 tanh(double x) 47 { 48 double t,z; 49 int32_t jx,ix; 50 51 GET_HIGH_WORD(jx,x); 52 ix = jx&0x7fffffff; 53 54 /* x is INF or NaN */ 55 if(ix>=0x7ff00000) { 56 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 57 else return one/x-one; /* tanh(NaN) = NaN */ 58 } 59 60 /* |x| < 22 */ 61 if (ix < 0x40360000) { /* |x|<22 */ 62 if (ix<0x3e300000) { /* |x|<2**-28 */ 63 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ 64 } 65 if (ix>=0x3ff00000) { /* |x|>=1 */ 66 t = expm1(two*fabs(x)); 67 z = one - two/(t+two); 68 } else { 69 t = expm1(-two*fabs(x)); 70 z= -t/(t+two); 71 } 72 /* |x| >= 22, return +-1 */ 73 } else { 74 z = one - tiny; /* raise inexact flag */ 75 } 76 return (jx>=0)? z: -z; 77 } 78