newlib/libm/ld/e_atanhl.c

   1 /* from: FreeBSD: head/lib/msun/src/e_atanh.c 176451 2008-02-22 02:30:36Z das */
   2
   3 /* @(#)e_atanh.c 1.3 95/01/18 */
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  *
  14  */
  15
  16 #include <sys/cdefs.h>
  17 __FBSDID("$FreeBSD$");
  18
  19 /*
  20  * See e_atanh.c for complete comments.
  21  *
  22  * Converted to long double by David Schultz <das@FreeBSD.ORG> and
  23  * Bruce D. Evans.
  24  */
  25
  26 #include <float.h>
  27 #ifdef __i386__
  28 #include <ieeefp.h>
  29 #endif
  30
  31 #include "fpmath.h"
  32 #include "math.h"
  33 #include "math_private.h"
  34
  35 /* EXP_TINY is the threshold below which we use atanh(x) ~= x. */
  36 #if LDBL_MANT_DIG == 64
  37 #define EXP_TINY        -34
  38 #elif LDBL_MANT_DIG == 113
  39 #define EXP_TINY        -58
  40 #else
  41 #error "Unsupported long double format"
  42 #endif
  43
  44 #if LDBL_MAX_EXP != 0x4000
  45 /* We also require the usual expsign encoding. */
  46 #error "Unsupported long double format"
  47 #endif
  48
  49 #define BIAS    (LDBL_MAX_EXP - 1)
  50
  51 static const double one = 1.0, huge = 1e300;
  52 static const double zero = 0.0;
  53
  54 long double
  55 atanhl(long double x)
  56 {
  57         long double t;
  58         uint16_t hx, ix;
  59
  60         ENTERI();
  61         GET_LDBL_EXPSIGN(hx, x);
  62         ix = hx & 0x7fff;
  63         if (ix >= 0x3fff)               /* |x| >= 1, or NaN or misnormal */
  64             RETURNI(fabsl(x) == 1 ? x / zero : (x - x) / (x - x));
  65         if (ix < BIAS + EXP_TINY && (huge + x) > zero)
  66             RETURNI(x);                 /* x is tiny */
  67         SET_LDBL_EXPSIGN(x, ix);
  68         if (ix < 0x3ffe) {              /* |x| < 0.5, or misnormal */
  69             t = x+x;
  70             t = 0.5*log1pl(t+t*x/(one-x));
  71         } else
  72             t = 0.5*log1pl((x+x)/(one-x));
  73         RETURNI((hx & 0x8000) == 0 ? t : -t);
  74 }