sysdeps/ieee754/ldbl-96/s_asinhl.c

   1 /* s_asinhl.c -- long double version of s_asinh.c.
   2  */
   3
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunPro, 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 #if defined(LIBM_SCCS) && !defined(lint)
  16 static char rcsid[] = "$NetBSD: $";
  17 #endif
  18
  19 /* asinhl(x)
  20  * Method :
  21  *      Based on
  22  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  23  *      we have
  24  *      asinhl(x) := x  if  1+x*x=1,
  25  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  26  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  27  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  28  */
  29
  30 #include <float.h>
  31 #include <math.h>
  32 #include <math_private.h>
  33 #include <math-underflow.h>
  34 #include <libm-alias-ldouble.h>
  35
  36 static const long double
  37 one =  1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
  38 ln2 =  6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
  39 huge=  1.000000000000000000e+4900L;
  40
  41 long double __asinhl(long double x)
  42 {
  43         long double t,w;
  44         int32_t hx,ix;
  45         GET_LDOUBLE_EXP(hx,x);
  46         ix = hx&0x7fff;
  47         if(__builtin_expect(ix< 0x3fde, 0)) {   /* |x|<2**-34 */
  48             math_check_force_underflow (x);
  49             if(huge+x>one) return x;    /* return x inexact except 0 */
  50         }
  51         if(__builtin_expect(ix>0x4020,0)) {             /* |x| > 2**34 */
  52             if(ix==0x7fff) return x+x;  /* x is inf or NaN */
  53             w = __ieee754_logl(fabsl(x))+ln2;
  54         } else {
  55             long double xa = fabsl(x);
  56             if (ix>0x4000) {    /* 2**34 > |x| > 2.0 */
  57                 w = __ieee754_logl(2.0*xa+one/(sqrtl(xa*xa+one)+xa));
  58             } else {            /* 2.0 > |x| > 2**-28 */
  59                 t = xa*xa;
  60                 w =__log1pl(xa+t/(one+sqrtl(one+t)));
  61             }
  62         }
  63         return copysignl(w, x);
  64 }
  65 libm_alias_ldouble (__asinh, asinh)