contrib/openbsd_libm/src/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 /* asinh(x)
  14  * Method :
  15  *      Based on
  16  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
  17  *      we have
  18  *      asinh(x) := x  if  1+x*x=1,
  19  *               := sign(x)*(log(x)+ln2)) for large |x|, else
  20  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
  21  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))
  22  */
  23
  24 #include <float.h>
  25 #include <math.h>
  26
  27 #include "math_private.h"
  28
  29 static const double
  30 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
  31 ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
  32 huge=  1.00000000000000000000e+300;
  33
  34 double
  35 asinh(double x)
  36 {
  37         double t,w;
  38         int32_t hx,ix;
  39         GET_HIGH_WORD(hx,x);
  40         ix = hx&0x7fffffff;
  41         if(ix>=0x7ff00000) return x+x;  /* x is inf or NaN */
  42         if(ix< 0x3e300000) {    /* |x|<2**-28 */
  43             if(huge+x>one) return x;    /* return x inexact except 0 */
  44         }
  45         if(ix>0x41b00000) {     /* |x| > 2**28 */
  46             w = log(fabs(x))+ln2;
  47         } else if (ix>0x40000000) {     /* 2**28 > |x| > 2.0 */
  48             t = fabs(x);
  49             w = log(2.0*t+one/(sqrt(x*x+one)+t));
  50         } else {                /* 2.0 > |x| > 2**-28 */
  51             t = x*x;
  52             w =log1p(fabs(x)+t/(one+sqrt(one+t)));
  53         }
  54         if(hx>0) return w; else return -w;
  55 }
  56
  57 #if     LDBL_MANT_DIG == DBL_MANT_DIG
  58 __strong_alias(asinhl, asinh);
  59 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */