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      1 /* e_hypotl.c -- long double version of e_hypot.c.
      2  * Conversion to long double by Jakub Jelinek, jakub (at) 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 }
    139