1
2 /* @(#)e_hypot.c 5.1 93/09/24 */
3 /*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunPro, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 /* hypot(x,y)
15 *
16 * Method :
17 * If (assume round-to-nearest) z=x*x+y*y
18 * has error less than sqrt(2)/2 ulp, than
19 * sqrt(z) has error less than 1 ulp (exercise).
20 *
21 * So, compute sqrt(x*x+y*y) with some care as
22 * follows to get the error below 1 ulp:
23 *
24 * Assume x>y>0;
25 * (if possible, set rounding to round-to-nearest)
26 * 1. if x > 2y use
27 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
28 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
29 * 2. if x <= 2y use
30 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
31 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
32 * y1= y with lower 32 bits chopped, y2 = y-y1.
33 *
34 * NOTE: scaling may be necessary if some argument is too
35 * large or too tiny
36 *
37 * Special cases:
38 * hypot(x,y) is INF if x or y is +INF or -INF; else
39 * hypot(x,y) is NAN if x or y is NAN.
40 *
41 * Accuracy:
42 * hypot(x,y) returns sqrt(x^2+y^2) with error less
43 * than 1 ulps (units in the last place)
44 */
45
46 #include "fdlibm.h"
47
48 #ifdef _NEED_FLOAT64
49
50 __float64
hypot64(__float64 x,__float64 y)51 hypot64(__float64 x, __float64 y)
52 {
53 __float64 a = x, b = y, t1, t2, y1, y2, w;
54 __int32_t j, k, ha, hb;
55
56 GET_HIGH_WORD(ha, x);
57 ha &= 0x7fffffff;
58 GET_HIGH_WORD(hb, y);
59 hb &= 0x7fffffff;
60 if (hb > ha) {
61 a = y;
62 b = x;
63 j = ha;
64 ha = hb;
65 hb = j;
66 } else {
67 a = x;
68 b = y;
69 }
70 SET_HIGH_WORD(a, ha); /* a <- |a| */
71 SET_HIGH_WORD(b, hb); /* b <- |b| */
72 if ((ha - hb) > 0x3c00000) {
73 return a + b;
74 } /* x/y > 2**60 */
75 k = 0;
76 if (ha > 0x5f300000) { /* a>2**500 */
77 if (ha >= 0x7ff00000) { /* Inf or NaN */
78 __uint32_t low;
79 w = a + b; /* for sNaN */
80 GET_LOW_WORD(low, a);
81 if (((ha & 0xfffff) | low) == 0 && !issignaling(b))
82 w = a;
83 GET_LOW_WORD(low, b);
84 if (((hb ^ 0x7ff00000) | low) == 0 && !issignaling(a))
85 w = b;
86 return w;
87 }
88 /* scale a and b by 2**-600 */
89 ha -= 0x25800000;
90 hb -= 0x25800000;
91 k += 600;
92 SET_HIGH_WORD(a, ha);
93 SET_HIGH_WORD(b, hb);
94 }
95 if (hb < 0x20b00000) { /* b < 2**-500 */
96 if (hb <= 0x000fffff) { /* subnormal b or 0 */
97 __uint32_t low;
98 GET_LOW_WORD(low, b);
99 if ((hb | low) == 0)
100 return a;
101 t1 = 0;
102 SET_HIGH_WORD(t1, 0x7fd00000); /* t1=2^1022 */
103 b *= t1;
104 a *= t1;
105 k -= 1022;
106 } else { /* scale a and b by 2^600 */
107 ha += 0x25800000; /* a *= 2^600 */
108 hb += 0x25800000; /* b *= 2^600 */
109 k -= 600;
110 SET_HIGH_WORD(a, ha);
111 SET_HIGH_WORD(b, hb);
112 }
113 }
114 /* medium size a and b */
115 w = a - b;
116 if (w > b) {
117 t1 = 0;
118 SET_HIGH_WORD(t1, ha);
119 t2 = a - t1;
120 w = sqrt64(t1 * t1 - (b * (-b) - t2 * (a + t1)));
121 } else {
122 a = a + a;
123 y1 = 0;
124 SET_HIGH_WORD(y1, hb);
125 y2 = b - y1;
126 t1 = 0;
127 SET_HIGH_WORD(t1, ha + 0x00100000);
128 t2 = a - t1;
129 w = sqrt64(t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
130 }
131 if (k != 0) {
132 __uint32_t high;
133 t1 = _F_64(1.0);
134 GET_HIGH_WORD(high, t1);
135 SET_HIGH_WORD(t1, high + (k << 20));
136 w *= t1;
137 }
138 return check_oflow(w);
139 }
140
141 _MATH_ALIAS_d_dd(hypot)
142
143 #endif /* _NEED_FLOAT64 */
144
