1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * 5 * Developed at SunPro, a Sun Microsystems, Inc. business. 6 * Permission to use, copy, modify, and distribute this 7 * software is freely granted, provided that this notice 8 * is preserved. 9 * ==================================================== 10 */ 11 12 /* Tanh(x) 13 * Return the Hyperbolic Tangent of x 14 * 15 * Method : 16 * x -x 17 * e - e 18 * 0. tanh(x) is defined to be ----------- 19 * x -x 20 * e + e 21 * 1. reduce x to non-negative by tanh(-x) = -tanh(x). 22 * 2. 0 <= x < 2**-28 : tanh(x) := x with inexact if x != 0 23 * -t 24 * 2**-28 <= x < 1 : tanh(x) := -----; t = expm1(-2x) 25 * t + 2 26 * 2 27 * 1 <= x < 22 : tanh(x) := 1 - -----; t = expm1(2x) 28 * t + 2 29 * 22 <= x <= INF : tanh(x) := 1. 30 * 31 * Special cases: 32 * tanh(NaN) is NaN; 33 * only tanh(0)=0 is exact for finite argument. 34 */ 35 36 #include <float.h> 37 38 #include "math.h" 39 #include "math_private.h" 40 41 static const volatile double tiny = 1.0e-300; 42 static const double one = 1.0, two = 2.0, huge = 1.0e300; 43 44 double 45 tanh(double x) 46 { 47 double t,z; 48 int32_t jx,ix; 49 50 GET_HIGH_WORD(jx,x); 51 ix = jx&0x7fffffff; 52 53 /* x is INF or NaN */ 54 if(ix>=0x7ff00000) { 55 if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ 56 else return one/x-one; /* tanh(NaN) = NaN */ 57 } 58 59 /* |x| < 22 */ 60 if (ix < 0x40360000) { /* |x|<22 */ 61 if (ix<0x3e300000) { /* |x|<2**-28 */ 62 if(huge+x>one) return x; /* tanh(tiny) = tiny with inexact */ 63 } 64 if (ix>=0x3ff00000) { /* |x|>=1 */ 65 t = expm1(two*fabs(x)); 66 z = one - two/(t+two); 67 } else { 68 t = expm1(-two*fabs(x)); 69 z= -t/(t+two); 70 } 71 /* |x| >= 22, return +-1 */ 72 } else { 73 z = one - tiny; /* raise inexact flag */ 74 } 75 return (jx>=0)? z: -z; 76 } 77 78 #if (LDBL_MANT_DIG == 53) 79 __weak_reference(tanh, tanhl); 80 #endif 81