sysdeps/ieee754/dbl-64/s_asinh.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
  31 #ifdef __STDC__
  32 static const double
  33 #else
  34 static double
  35 #endif
  36 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  37 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  38 huge=  1.00000000000000000000e+300;
  39
  40 #ifdef __STDC__
  41         double __asinh(double x)
  42 #else
  43         double __asinh(x)
  44         double x;
  45 #endif
  46 {
  47         double t,w;
  48         int32_t hx,ix;
  49         GET_HIGH_WORD(hx,x);
  50         ix = hx&0x7fffffff;
  51         if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
  52         if(ix< 0x3e300000) {    /* |x|<2**-28 */
  53             if(huge+x>one) return x;    /* return x inexact except 0 */
  54         }
  55         if(ix>0x41b00000) {     /* |x| > 2**28 */
  56             w = __ieee754_log(fabs(x))+ln2;
  57         } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
  58             t = fabs(x);
  59             w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t));
  60         } else {                /* 2.0 > |x| > 2**-28 */
  61             t = x*x;
  62             w =__log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t)));
  63         }
  64         if(hx>0) return w; else return -w;
  65 }
  66 weak_alias (__asinh, asinh)
  67 #ifdef NO_LONG_DOUBLE
  68 strong_alias (__asinh, __asinhl)
  69 weak_alias (__asinh, asinhl)
  70 #endif