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/* __ieee754_hypotl(x,y)
17 *
18 * Method :
19 * If (assume round-to-nearest) z=x*x+y*y
20 * has error less than sqrtl(2)/2 ulp, than
21 * sqrtl(z) has error less than 1 ulp (exercise).
22 *
23 * So, compute sqrtl(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 sqrtl(x^2+y^2) with error less
45 * than 1 ulps (units in the last place)
46 */
47
48#include <math.h>
49#include <math_private.h>
50#include <math-underflow.h>
51#include <libm-alias-finite.h>
52
53_Float128
54__ieee754_hypotl(_Float128 x, _Float128 y)
55{
56 _Float128 a,b,t1,t2,y1,y2,w;
57 int64_t j,k,ha,hb;
58
59 GET_LDOUBLE_MSW64(ha,x);
60 ha &= 0x7fffffffffffffffLL;
61 GET_LDOUBLE_MSW64(hb,y);
62 hb &= 0x7fffffffffffffffLL;
63 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
64 SET_LDOUBLE_MSW64(a,ha); /* a <- |a| */
65 SET_LDOUBLE_MSW64(b,hb); /* b <- |b| */
66 if((ha-hb)>0x78000000000000LL) {return a+b;} /* x/y > 2**120 */
67 k=0;
68 if(ha > 0x5f3f000000000000LL) { /* a>2**8000 */
69 if(ha >= 0x7fff000000000000LL) { /* Inf or NaN */
70 uint64_t low;
71 w = a+b; /* for sNaN */
72 if (issignaling (a) || issignaling (b))
73 return w;
74 GET_LDOUBLE_LSW64(low,a);
75 if(((ha&0xffffffffffffLL)|low)==0) w = a;
76 GET_LDOUBLE_LSW64(low,b);
77 if(((hb^0x7fff000000000000LL)|low)==0) w = b;
78 return w;
79 }
80 /* scale a and b by 2**-9600 */
81 ha -= 0x2580000000000000LL;
82 hb -= 0x2580000000000000LL; k += 9600;
83 SET_LDOUBLE_MSW64(a,ha);
84 SET_LDOUBLE_MSW64(b,hb);
85 }
86 if(hb < 0x20bf000000000000LL) { /* b < 2**-8000 */
87 if(hb <= 0x0000ffffffffffffLL) { /* subnormal b or 0 */
88 uint64_t low;
89 GET_LDOUBLE_LSW64(low,b);
90 if((hb|low)==0) return a;
91 t1=0;
92 SET_LDOUBLE_MSW64(t1,0x7ffd000000000000LL); /* t1=2^16382 */
93 b *= t1;
94 a *= t1;
95 k -= 16382;
96 GET_LDOUBLE_MSW64 (ha, a);
97 GET_LDOUBLE_MSW64 (hb, b);
98 if (hb > ha)
99 {
100 t1 = a;
101 a = b;
102 b = t1;
103 j = ha;
104 ha = hb;
105 hb = j;
106 }
107 } else { /* scale a and b by 2^9600 */
108 ha += 0x2580000000000000LL; /* a *= 2^9600 */
109 hb += 0x2580000000000000LL; /* b *= 2^9600 */
110 k -= 9600;
111 SET_LDOUBLE_MSW64(a,ha);
112 SET_LDOUBLE_MSW64(b,hb);
113 }
114 }
115 /* medium size a and b */
116 w = a-b;
117 if (w>b) {
118 t1 = 0;
119 SET_LDOUBLE_MSW64(t1,ha);
120 t2 = a-t1;
121 w = sqrtl(t1*t1-(b*(-b)-t2*(a+t1)));
122 } else {
123 a = a+a;
124 y1 = 0;
125 SET_LDOUBLE_MSW64(y1,hb);
126 y2 = b - y1;
127 t1 = 0;
128 SET_LDOUBLE_MSW64(t1,ha+0x0001000000000000LL);
129 t2 = a - t1;
130 w = sqrtl(t1*y1-(w*(-w)-(t1*y2+t2*b)));
131 }
132 if(k!=0) {
133 uint64_t high;
134 t1 = 1;
135 GET_LDOUBLE_MSW64(high,t1);
136 SET_LDOUBLE_MSW64(t1,high+(k<<48));
137 w *= t1;
138 math_check_force_underflow_nonneg (w);
139 return w;
140 } else return w;
141}
142libm_alias_finite (__ieee754_hypotl, __hypotl)
143