compiler/stdc/math/ld80/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 /* asinhl(x)
  14  * Method :
  15  *      Based on
  16  *              asinhl(x) = signl(x) * logl [ |x| + sqrtl(x*x+1) ]
  17  *      we have
  18  *      asinhl(x) := x  if  1+x*x=1,
  19  *                := signl(x)*(logl(x)+ln2)) for large |x|, else
  20  *                := signl(x)*logl(2|x|+1/(|x|+sqrtl(x*x+1))) if|x|>2, else
  21  *                := signl(x)*log1pl(|x| + x^2/(1 + sqrtl(1+x^2)))
  22  */
  23
  24 #include "math.h"
  25
  26 #include "math_private.h"
  27
  28 static const long double
  29 one =  1.000000000000000000000e+00L, /* 0x3FFF, 0x00000000, 0x00000000 */
  30 ln2 =  6.931471805599453094287e-01L, /* 0x3FFE, 0xB17217F7, 0xD1CF79AC */
  31 huge=  1.000000000000000000e+4900L;
  32
  33 long double
  34 asinhl(long double x)
  35 {
  36         long double t,w;
  37         int32_t hx,ix;
  38         GET_LDOUBLE_EXP(hx,x);
  39         ix = hx&0x7fff;
  40         if(ix==0x7fff) return x+x;      /* x is inf or NaN */
  41         if(ix< 0x3fde) {        /* |x|<2**-34 */
  42             if(huge+x>one) return x;    /* return x inexact except 0 */
  43         }
  44         if(ix>0x4020) {         /* |x| > 2**34 */
  45             w = logl(fabsl(x))+ln2;
  46         } else if (ix>0x4000) { /* 2**34 > |x| > 2.0 */
  47             t = fabsl(x);
  48             w = logl(2.0*t+one/(sqrtl(x*x+one)+t));
  49         } else {                /* 2.0 > |x| > 2**-28 */
  50             t = x*x;
  51             w =log1pl(fabsl(x)+t/(one+sqrtl(one+t)));
  52         }
  53         if(hx&0x8000) return -w; else return w;
  54 }