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

   1 /* @(#)s_asinh.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_asinh.c,v 1.9 1995/05/12 04:57:37 jtc Exp $";
  15 #endif
  16
  17 /* asinh(x)
  18  * Method :
  19  *      Based on
  20  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  21  *      we have
  22  *      asinh(x) := x  if  1+x*x=1,
  23  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  24  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  25  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  26  */
  27
  28 #include <float.h>
  29 #include <math.h>
  30 #include <math_private.h>
  31 #include <math-underflow.h>
  32 #include <math_ldbl_opt.h>
  33
  34 static const long double
  35 one =  1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
  36 ln2 =  0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
  37 huge=  1.00000000000000000000e+300L;
  38
  39 long double __asinhl(long double x)
  40 {
  41         long double t,w;
  42         int64_t hx,ix;
  43         double xhi;
  44
  45         xhi = ldbl_high (x);
  46         EXTRACT_WORDS64 (hx, xhi);
  47         ix = hx&0x7fffffffffffffffLL;
  48         if(ix>=0x7ff0000000000000LL) return x+x;        /* x is inf or NaN */
  49         if(ix< 0x3c70000000000000LL) {  /* |x|<2**-56 */
  50             math_check_force_underflow (x);
  51             if(huge+x>one) return x;    /* return x inexact except 0 */
  52         }
  53         if(ix>0x4370000000000000LL) {   /* |x| > 2**56 */
  54             w = __ieee754_logl(fabsl(x))+ln2;
  55         } else if (ix>0x4000000000000000LL) {   /* 2**56 >= |x| > 2.0 */
  56             t = fabs(x);
  57             w = __ieee754_logl(2.0*t+one/(sqrtl(x*x+one)+t));
  58         } else {                /* 2.0 >= |x| >= 2**-56 */
  59             t = x*x;
  60             w =__log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
  61         }
  62         if(hx>0) return w; else return -w;
  63 }
  64 long_double_symbol (libm, __asinhl, asinhl);