sysdeps/ieee754/ldbl-128ibm/s_tanhl.c

   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 #if defined(LIBM_SCCS) && !defined(lint)
  14 static char rcsid[] = "$NetBSD: s_tanh.c,v 1.7 1995/05/10 20:48:22 jtc Exp $";
  15 #endif
  16
  17 /* Tanh(x)
  18  * Return the Hyperbolic Tangent of x
  19  *
  20  * Method :
  21  *                                     x    -x
  22  *                                    e  - e
  23  *      0. tanh(x) is defined to be -----------
  24  *                                     x    -x
  25  *                                    e  + e
  26  *      1. reduce x to non-negative by tanh(-x) = -tanh(x).
  27  *      2.  0      <= x <= 2**-57 : tanh(x) := x*(one+x)
  28  *                                              -t
  29  *          2**-57 <  x <=  1     : tanh(x) := -----; t = expm1(-2x)
  30  *                                             t + 2
  31  *                                                   2
  32  *          1      <= x <=  22.0  : tanh(x) := 1-  ----- ; t=expm1(2x)
  33  *                                                 t + 2
  34  *          22.0   <  x <= INF    : tanh(x) := 1.
  35  *
  36  * Special cases:
  37  *      tanh(NaN) is NaN;
  38  *      only tanh(0)=0 is exact for finite argument.
  39  */
  40
  41 #include "math.h"
  42 #include "math_private.h"
  43 #include <math_ldbl_opt.h>
  44
  45 #ifdef __STDC__
  46 static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
  47 #else
  48 static long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
  49 #endif
  50
  51 #ifdef __STDC__
  52         long double __tanhl(long double x)
  53 #else
  54         long double __tanhl(x)
  55         long double x;
  56 #endif
  57 {
  58         long double t,z;
  59         int64_t jx,ix,lx;
  60
  61     /* High word of |x|. */
  62         GET_LDOUBLE_WORDS64(jx,lx,x);
  63         ix = jx&0x7fffffffffffffffLL;
  64
  65     /* x is INF or NaN */
  66         if(ix>=0x7ff0000000000000LL) {
  67             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  68             else       return one/x-one;    /* tanh(NaN) = NaN */
  69         }
  70
  71     /* |x| < 22 */
  72         if (ix < 0x4036000000000000LL) {                /* |x|<22 */
  73             if ((ix | (lx&0x7fffffffffffffffLL)) == 0)
  74                 return x;               /* x == +-0 */
  75             if (ix<0x3c60000000000000LL)        /* |x|<2**-57 */
  76                 return x*(one+x);       /* tanh(small) = small */
  77             if (ix>=0x3ff0000000000000LL) {     /* |x|>=1  */
  78                 t = __expm1l(two*fabsl(x));
  79                 z = one - two/(t+two);
  80             } else {
  81                 t = __expm1l(-two*fabsl(x));
  82                 z= -t/(t+two);
  83             }
  84     /* |x| > 22, return +-1 */
  85         } else {
  86             z = one - tiny;             /* raised inexact flag */
  87         }
  88         return (jx>=0)? z: -z;
  89 }
  90 long_double_symbol (libm, __tanhl, tanhl);