sysdeps/ieee754/ldbl-96/s_asinhl.c

   1 /* s_asinhl.c -- long double version of s_asinh.c.
   2  * Conversion to long double by Ulrich Drepper,
   3  * Cygnus Support, drepper@cygnus.com.
   4  */
   5
   6 /*
   7  * ====================================================
   8  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   9  *
  10  * Developed at SunPro, a Sun Microsystems, Inc. business.
  11  * Permission to use, copy, modify, and distribute this
  12  * software is freely granted, provided that this notice
  13  * is preserved.
  14  * ====================================================
  15  */
  16
  17 #if defined(LIBM_SCCS) && !defined(lint)
  18 static char rcsid[] = "$NetBSD: $";
  19 #endif
  20
  21 /* asinhl(x)
  22  * Method :
  23  *      Based on
  24  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  25  *      we have
  26  *      asinhl(x) := x  if  1+x*x=1,
  27  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  28  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  29  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  30  */
  31
  32 #include "math.h"
  33 #include "math_private.h"
  34
  35 #ifdef __STDC__
  36 static const long double
  37 #else
  38 static long double
  39 #endif
  40 one =  1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
  41 ln2 =  6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
  42 huge=  1.000000000000000000e+4900L;
  43
  44 #ifdef __STDC__
  45         long double __asinhl(long double x)
  46 #else
  47         long double __asinhl(x)
  48         long double x;
  49 #endif
  50 {
  51         long double t,w;
  52         int32_t hx,ix;
  53         GET_LDOUBLE_EXP(hx,x);
  54         ix = hx&0x7fff;
  55         if(ix==0x7fff) return x+x;      /* x is inf or NaN */
  56         if(ix< 0x3fde) {        /* |x|<2**-34 */
  57             if(huge+x>one) return x;    /* return x inexact except 0 */
  58         }
  59         if(ix>0x4020) {         /* |x| > 2**34 */
  60             w = __ieee754_logl(fabsl(x))+ln2;
  61         } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
  62             t = fabsl(x);
  63             w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
  64         } else {                /* 2.0 > |x| > 2**-28 */
  65             t = x*x;
  66             w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
  67         }
  68         if(hx&0x8000) return -w; else return w;
  69 }
  70 weak_alias (__asinhl, asinhl)