gonzui

    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: /* LINTLIBRARY */
   14: 
   15: /* asinh(x)
   16:  * Method :
   17:  *      Based on 
   18:  *              asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ]
   19:  *      we have
   20:  *      asinh(x) := x  if  1+x*x=1,
   21:  *               := sign(x)*(log(x)+ln2)) for large |x|, else
   22:  *               := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else
   23:  *               := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2)))  
   24:  */
   25: 
   26: #include <sys/cdefs.h>
   27: #include <float.h>
   28: #include <math.h>
   29: 
   30: #include "math_private.h"
   31: 
   32: static const double 
   33: one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
   34: ln2 =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
   35: huge=  1.00000000000000000000e+300; 
   36: 
   37: double
   38: asinh(double x)
   39: {       
   40:         double t,w;
   41:         int32_t hx,ix;
   42:         GET_HIGH_WORD(hx,x);
   43:         ix = hx&0x7fffffff;
   44:         if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */
   45:         if(ix< 0x3e300000) {   /* |x|<2**-28 */
   46:             if(huge+x>one) return x;   /* return x inexact except 0 */
   47:         } 
   48:         if(ix>0x41b00000) {    /* |x| > 2**28 */
   49:             w = log(fabs(x))+ln2;
   50:         } else if (ix>0x40000000) {    /* 2**28 > |x| > 2.0 */
   51:             t = fabs(x);
   52:             w = log(2.0*t+one/(sqrt(x*x+one)+t));
   53:         } else {               /* 2.0 > |x| > 2**-28 */
   54:             t = x*x;
   55:             w =log1p(fabs(x)+t/(one+sqrt(one+t)));
   56:         }
   57:         if(hx>0) return w; else return -w;
   58: }
   59: 
   60: #if     LDBL_MANT_DIG == 53
   61: #ifdef  lint
   62: /* PROTOLIB1 */
   63: long double asinhl(long double);
   64: #else   /* lint */
   65: __weak_alias(asinhl, asinh);
   66: #endif  /* lint */
   67: #endif  /* LDBL_MANT_DIG == 53 */