libquadmath/math/hypotq.c

   1 /* e_hypotl.c -- long double version of e_hypot.c.
   2  * Conversion to long double by Jakub Jelinek, jakub@redhat.com.
   3  */
   4
   5 /*
   6  * ====================================================
   7  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   8  *
   9  * Developed at SunPro, a Sun Microsystems, Inc. business.
  10  * Permission to use, copy, modify, and distribute this
  11  * software is freely granted, provided that this notice
  12  * is preserved.
  13  * ====================================================
  14  */
  15
  16 /* hypotq(x,y)
  17  *
  18  * Method :
  19  *      If (assume round-to-nearest) z=x*x+y*y
  20  *      has error less than sqrtq(2)/2 ulp, than
  21  *      sqrtq(z) has error less than 1 ulp (exercise).
  22  *
  23  *      So, compute sqrtq(x*x+y*y) with some care as
  24  *      follows to get the error below 1 ulp:
  25  *
  26  *      Assume x>y>0;
  27  *      (if possible, set rounding to round-to-nearest)
  28  *      1. if x > 2y  use
  29  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  30  *      where x1 = x with lower 64 bits cleared, x2 = x-x1; else
  31  *      2. if x <= 2y use
  32  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  33  *      where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1,
  34  *      y1= y with lower 64 bits chopped, y2 = y-y1.
  35  *
  36  *      NOTE: scaling may be necessary if some argument is too
  37  *            large or too tiny
  38  *
  39  * Special cases:
  40  *      hypotl(x,y) is INF if x or y is +INF or -INF; else
  41  *      hypotl(x,y) is NAN if x or y is NAN.
  42  *
  43  * Accuracy:
  44  *      hypotl(x,y) returns sqrtq(x^2+y^2) with error less
  45  *      than 1 ulps (units in the last place)
  46  */
  47
  48 #include "quadmath-imp.h"
  49
  50 __float128
  51 hypotq(__float128 x, __float128 y)
  52 {
  53         __float128 a,b,t1,t2,y1,y2,w;
  54         int64_t j,k,ha,hb;
  55
  56         GET_FLT128_MSW64(ha,x);
  57         ha &= 0x7fffffffffffffffLL;
  58         GET_FLT128_MSW64(hb,y);
  59         hb &= 0x7fffffffffffffffLL;
  60         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
  61         SET_FLT128_MSW64(a,ha); /* a <- |a| */
  62         SET_FLT128_MSW64(b,hb); /* b <- |b| */
  63         if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
  64         k=0;
  65         if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
  66            if(ha >= 0x7fff000000000000LL) {     /* Inf or NaN */
  67                uint64_t low;
  68                w = a+b;                 /* for sNaN */
  69                if (issignalingq (a) || issignalingq (b))
  70                  return w;
  71                GET_FLT128_LSW64(low,a);
  72                if(((ha&0xffffffffffffLL)|low)==0) w = a;
  73                GET_FLT128_LSW64(low,b);
  74                if(((hb^0x7fff000000000000LL)|low)==0) w = b;
  75                return w;
  76            }
  77            /* scale a and b by 2**-9600 */
  78            ha -= 0x2580000000000000LL;
  79            hb -= 0x2580000000000000LL;  k += 9600;
  80            SET_FLT128_MSW64(a,ha);
  81            SET_FLT128_MSW64(b,hb);
  82         }
  83         if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
  84             if(hb <= 0x0000ffffffffffffLL) {    /* subnormal b or 0 */
  85                 uint64_t low;
  86                 GET_FLT128_LSW64(low,b);
  87                 if((hb|low)==0) return a;
  88                 t1=0;
  89                 SET_FLT128_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
  90                 b *= t1;
  91                 a *= t1;
  92                 k -= 16382;
  93                 GET_FLT128_MSW64 (ha, a);
  94                 GET_FLT128_MSW64 (hb, b);
  95                 if (hb > ha)
  96                   {
  97                     t1 = a;
  98                     a = b;
  99                     b = t1;
 100                     j = ha;
 101                     ha = hb;
 102                     hb = j;
 103                   }
 104             } else {            /* scale a and b by 2^9600 */
 105                 ha += 0x2580000000000000LL;     /* a *= 2^9600 */
 106                 hb += 0x2580000000000000LL;     /* b *= 2^9600 */
 107                 k -= 9600;
 108                 SET_FLT128_MSW64(a,ha);
 109                 SET_FLT128_MSW64(b,hb);
 110             }
 111         }
 112     /* medium size a and b */
 113         w = a-b;
 114         if (w>b) {
 115             t1 = 0;
 116             SET_FLT128_MSW64(t1,ha);
 117             t2 = a-t1;
 118             w  = sqrtq(t1*t1-(b*(-b)-t2*(a+t1)));
 119         } else {
 120             a  = a+a;
 121             y1 = 0;
 122             SET_FLT128_MSW64(y1,hb);
 123             y2 = b - y1;
 124             t1 = 0;
 125             SET_FLT128_MSW64(t1,ha+0x0001000000000000LL);
 126             t2 = a - t1;
 127             w  = sqrtq(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 128         }
 129         if(k!=0) {
 130             uint64_t high;
 131             t1 = 1;
 132             GET_FLT128_MSW64(high,t1);
 133             SET_FLT128_MSW64(t1,high+(k<<48));
 134             w *= t1;
 135             math_check_force_underflow_nonneg (w);
 136             return w;
 137         } else return w;
 138 }