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 static const long double one=1.0L, two=2.0L, tiny = 1.0e-300L;
  46
  47 long double __tanhl(long double x)
  48 {
  49         long double t,z;
  50         int64_t jx,ix;
  51         double xhi;
  52
  53     /* High word of |x|. */
  54         xhi = ldbl_high (x);
  55         EXTRACT_WORDS64 (jx, xhi);
  56         ix = jx&0x7fffffffffffffffLL;
  57
  58     /* x is INF or NaN */
  59         if(ix>=0x7ff0000000000000LL) {
  60             if (jx>=0) return one/x+one;    /* tanh(+-inf)=+-1 */
  61             else       return one/x-one;    /* tanh(NaN) = NaN */
  62         }
  63
  64     /* |x| < 22 */
  65         if (ix < 0x4036000000000000LL) {                /* |x|<22 */
  66             if (ix == 0)
  67                 return x;               /* x == +-0 */
  68             if (ix<0x3c60000000000000LL)        /* |x|<2**-57 */
  69                 return x*(one+x);       /* tanh(small) = small */
  70             if (ix>=0x3ff0000000000000LL) {     /* |x|>=1  */
  71                 t = __expm1l(two*fabsl(x));
  72                 z = one - two/(t+two);
  73             } else {
  74                 t = __expm1l(-two*fabsl(x));
  75                 z= -t/(t+two);
  76             }
  77     /* |x| > 22, return +-1 */
  78         } else {
  79             z = one - tiny;             /* raised inexact flag */
  80         }
  81         return (jx>=0)? z: -z;
  82 }
  83 long_double_symbol (libm, __tanhl, tanhl);