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 "math.h"
  29 #include "math_private.h"
  30 #include <math_ldbl_opt.h>
  31
  32 #ifdef __STDC__
  33 static const long double
  34 #else
  35 static long double
  36 #endif
  37 one =  1.00000000000000000000e+00L, /* 0x3ff0000000000000, 0 */
  38 ln2 =  0.6931471805599453094172321214581766L, /* 0x3fe62e42fefa39ef, 0x3c7abc9e3b398040 */
  39 huge=  1.00000000000000000000e+300L;
  40
  41 #ifdef __STDC__
  42         long double __asinhl(long double x)
  43 #else
  44         long double __asinhl(x)
  45         long double x;
  46 #endif
  47 {
  48         long double t,w;
  49         int64_t hx,ix;
  50         GET_LDOUBLE_MSW64(hx,x);
  51         ix = hx&0x7fffffffffffffffLL;
  52         if(ix>=0x7ff0000000000000LL) return x+x;        /* x is inf or NaN */
  53         if(ix< 0x3e20000000000000LL) {  /* |x|<2**-29 */
  54             if(huge+x>one) return x;    /* return x inexact except 0 */
  55         }
  56         if(ix>0x41b0000000000000LL) {   /* |x| > 2**28 */
  57             w = __ieee754_logl(fabs(x))+ln2;
  58         } else if (ix>0x4000000000000000LL) {   /* 2**28 > |x| > 2.0 */
  59             t = fabs(x);
  60             w = __ieee754_logl(2.0*t+one/(__ieee754_sqrtl(x*x+one)+t));
  61         } else {                /* 2.0 > |x| > 2**-29 */
  62             t = x*x;
  63             w =__log1pl(fabsl(x)+t/(one+__ieee754_sqrtl(one+t)));
  64         }
  65         if(hx>0) return w; else return -w;
  66 }
  67 long_double_symbol (libm, __asinhl, asinhl);