lib/libm/src/e_asinl.c

   1 /*      $OpenBSD: e_asinl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $    */
   2 /* @(#)e_asin.c 1.3 95/01/18 */
   3 /* FreeBSD: head/lib/msun/src/e_asin.c 176451 2008-02-22 02:30:36Z das */
   4 /*
   5  * ====================================================
   6  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   7  *
   8  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   9  * Permission to use, copy, modify, and distribute this
  10  * software is freely granted, provided that this notice
  11  * is preserved.
  12  * ====================================================
  13  */
  14
  15 /*
  16  * See comments in e_asin.c.
  17  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
  18  * Adapted for OpenBSD by Martynas Venckus <martynas@openbsd.org>.
  19  */
  20
  21 #include <float.h>
  22 #include <math.h>
  23
  24 #include "invtrig.h"
  25 #include "math_private.h"
  26
  27 #ifdef EXT_IMPLICIT_NBIT
  28 #define LDBL_NBIT       0
  29 #else /* EXT_IMPLICIT_NBIT */
  30 #define LDBL_NBIT       0x80000000
  31 #endif /* EXT_IMPLICIT_NBIT */
  32
  33 static const long double
  34 one =  1.00000000000000000000e+00,
  35 huge = 1.000e+300;
  36
  37 long double
  38 asinl(long double x)
  39 {
  40         union {
  41                 long double e;
  42                 struct ieee_ext bits;
  43         } u;
  44         long double t=0.0,w,p,q,c,r,s;
  45         int16_t expsign, expt;
  46         u.e = x;
  47         expsign = (u.bits.ext_sign << 15) | u.bits.ext_exp;
  48         expt = expsign & 0x7fff;
  49         if(expt >= BIAS) {              /* |x|>= 1 */
  50                 if(expt==BIAS && ((u.bits.ext_frach&~LDBL_NBIT)
  51 #ifdef EXT_FRACHMBITS
  52                         | u.bits.ext_frachm
  53 #endif /* EXT_FRACHMBITS */
  54 #ifdef EXT_FRACLMBITS
  55                         | u.bits.ext_fraclm
  56 #endif /* EXT_FRACLMBITS */
  57                         | u.bits.ext_fracl)==0)
  58                     /* asin(1)=+-pi/2 with inexact */
  59                     return x*pio2_hi+x*pio2_lo;
  60             return (x-x)/(x-x);         /* asin(|x|>1) is NaN */
  61         } else if (expt<BIAS-1) {       /* |x|<0.5 */
  62             if(expt<ASIN_LINEAR) {      /* if |x| is small, asinl(x)=x */
  63                 if(huge+x>one) return x;/* return x with inexact if x!=0*/
  64             }
  65             t = x*x;
  66             p = P(t);
  67             q = Q(t);
  68             w = p/q;
  69             return x+x*w;
  70         }
  71         /* 1> |x|>= 0.5 */
  72         w = one-fabsl(x);
  73         t = w*0.5;
  74         p = P(t);
  75         q = Q(t);
  76         s = sqrtl(t);
  77 #ifdef EXT_FRACHMBITS
  78         if((((uint64_t)u.bits.ext_frach << EXT_FRACHMBITS)
  79                 | u.bits.ext_frachm) >= THRESH) {
  80                                                 /* if |x| is close to 1 */
  81 #else /* EXT_FRACHMBITS */
  82         if(u.bits.ext_frach>=THRESH) {          /* if |x| is close to 1 */
  83 #endif /* EXT_FRACHMBITS */
  84             w = p/q;
  85             t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
  86         } else {
  87             u.e = s;
  88             u.bits.ext_fracl = 0;
  89 #ifdef EXT_FRACLMBITS
  90             u.bits.ext_fraclm = 0;
  91 #endif /* EXT_FRACLMBITS */
  92             w = u.e;
  93             c  = (t-w*w)/(s+w);
  94             r  = p/q;
  95             p  = 2.0*s*r-(pio2_lo-2.0*c);
  96             q  = pio4_hi-2.0*w;
  97             t  = pio4_hi-(p-q);
  98         }
  99         if(expsign>0) return t; else return -t;
 100 }