newlib/libm/ld/e_asinl.c

   1
   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 #include <sys/cdefs.h>
  16 __FBSDID("$FreeBSD$");
  17
  18 /*
  19  * See comments in e_asin.c.
  20  * Converted to long double by David Schultz <das@FreeBSD.ORG>.
  21  */
  22
  23 #include <float.h>
  24
  25 #include "invtrig.h"
  26 #include "math.h"
  27 #include "math_private.h"
  28
  29 static const long double
  30 one =  1.00000000000000000000e+00,
  31 huge = 1.000e+300;
  32
  33 long double
  34 asinl(long double x)
  35 {
  36         union IEEEl2bits u;
  37         long double t=0.0,w,p,q,c,r,s;
  38         int16_t expsign, expt;
  39         u.e = x;
  40         expsign = u.xbits.expsign;
  41         expt = expsign & 0x7fff;
  42         if(expt >= BIAS) {              /* |x|>= 1 */
  43                 if(expt==BIAS && ((u.bits.manh&~LDBL_NBIT)|u.bits.manl)==0)
  44                     /* asin(1)=+-pi/2 with inexact */
  45                     return x*pio2_hi+x*pio2_lo;
  46             return (x-x)/(x-x);         /* asin(|x|>1) is NaN */
  47         } else if (expt<BIAS-1) {       /* |x|<0.5 */
  48             if(expt<ASIN_LINEAR) {      /* if |x| is small, asinl(x)=x */
  49                 if(huge+x>one) return x;/* return x with inexact if x!=0*/
  50             }
  51             t = x*x;
  52             p = P(t);
  53             q = Q(t);
  54             w = p/q;
  55             return x+x*w;
  56         }
  57         /* 1> |x|>= 0.5 */
  58         w = one-fabsl(x);
  59         t = w*0.5;
  60         p = P(t);
  61         q = Q(t);
  62         s = sqrtl(t);
  63         if(u.bits.manh>=THRESH) {       /* if |x| is close to 1 */
  64             w = p/q;
  65             t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
  66         } else {
  67             u.e = s;
  68             u.bits.manl = 0;
  69             w = u.e;
  70             c  = (t-w*w)/(s+w);
  71             r  = p/q;
  72             p  = 2.0*s*r-(pio2_lo-2.0*c);
  73             q  = pio4_hi-2.0*w;
  74             t  = pio4_hi-(p-q);
  75         }
  76         if(expsign>0) return t; else return -t;
  77 }