1/* @(#)e_hypot.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13/* __ieee754_hypot(x,y)
14 *
15 * Method :
16 * If (assume round-to-nearest) z=x*x+y*y
17 * has error less than sqrt(2)/2 ulp, than
18 * sqrt(z) has error less than 1 ulp (exercise).
19 *
20 * So, compute sqrt(x*x+y*y) with some care as
21 * follows to get the error below 1 ulp:
22 *
23 * Assume x>y>0;
24 * (if possible, set rounding to round-to-nearest)
25 * 1. if x > 2y use
26 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
27 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
28 * 2. if x <= 2y use
29 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
30 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
31 * y1= y with lower 32 bits chopped, y2 = y-y1.
32 *
33 * NOTE: scaling may be necessary if some argument is too
34 * large or too tiny
35 *
36 * Special cases:
37 * hypot(x,y) is INF if x or y is +INF or -INF; else
38 * hypot(x,y) is NAN if x or y is NAN.
39 *
40 * Accuracy:
41 * hypot(x,y) returns sqrt(x^2+y^2) with error less
42 * than 1 ulps (units in the last place)
43 */
44
45#include <math.h>
46#include <math_private.h>
47#include <math-underflow.h>
48#include <libm-alias-finite.h>
49
50double
51__ieee754_hypot (double x, double y)
52{
53 double a, b, 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 {
62 a = y; b = x; j = ha; ha = hb; hb = j;
63 }
64 else
65 {
66 a = x; b = y;
67 }
68 SET_HIGH_WORD (a, ha); /* a <- |a| */
69 SET_HIGH_WORD (b, hb); /* b <- |b| */
70 if ((ha - hb) > 0x3c00000)
71 {
72 return a + b;
73 } /* x/y > 2**60 */
74 k = 0;
75 if (__glibc_unlikely (ha > 0x5f300000)) /* a>2**500 */
76 {
77 if (ha >= 0x7ff00000) /* Inf or NaN */
78 {
79 uint32_t low;
80 w = a + b; /* for sNaN */
81 if (issignaling (a) || issignaling (b))
82 return w;
83 GET_LOW_WORD (low, a);
84 if (((ha & 0xfffff) | low) == 0)
85 w = a;
86 GET_LOW_WORD (low, b);
87 if (((hb ^ 0x7ff00000) | low) == 0)
88 w = b;
89 return w;
90 }
91 /* scale a and b by 2**-600 */
92 ha -= 0x25800000; hb -= 0x25800000; k += 600;
93 SET_HIGH_WORD (a, ha);
94 SET_HIGH_WORD (b, hb);
95 }
96 if (__builtin_expect (hb < 0x23d00000, 0)) /* b < 2**-450 */
97 {
98 if (hb <= 0x000fffff) /* subnormal b or 0 */
99 {
100 uint32_t low;
101 GET_LOW_WORD (low, b);
102 if ((hb | low) == 0)
103 return a;
104 t1 = 0;
105 SET_HIGH_WORD (t1, 0x7fd00000); /* t1=2^1022 */
106 b *= t1;
107 a *= t1;
108 k -= 1022;
109 GET_HIGH_WORD (ha, a);
110 GET_HIGH_WORD (hb, b);
111 if (hb > ha)
112 {
113 t1 = a;
114 a = b;
115 b = t1;
116 j = ha;
117 ha = hb;
118 hb = j;
119 }
120 }
121 else /* scale a and b by 2^600 */
122 {
123 ha += 0x25800000; /* a *= 2^600 */
124 hb += 0x25800000; /* b *= 2^600 */
125 k -= 600;
126 SET_HIGH_WORD (a, ha);
127 SET_HIGH_WORD (b, hb);
128 }
129 }
130 /* medium size a and b */
131 w = a - b;
132 if (w > b)
133 {
134 t1 = 0;
135 SET_HIGH_WORD (t1, ha);
136 t2 = a - t1;
137 w = sqrt (t1 * t1 - (b * (-b) - t2 * (a + t1)));
138 }
139 else
140 {
141 a = a + a;
142 y1 = 0;
143 SET_HIGH_WORD (y1, hb);
144 y2 = b - y1;
145 t1 = 0;
146 SET_HIGH_WORD (t1, ha + 0x00100000);
147 t2 = a - t1;
148 w = sqrt (t1 * y1 - (w * (-w) - (t1 * y2 + t2 * b)));
149 }
150 if (k != 0)
151 {
152 uint32_t high;
153 t1 = 1.0;
154 GET_HIGH_WORD (high, t1);
155 SET_HIGH_WORD (t1, high + (k << 20));
156 w *= t1;
157 math_check_force_underflow_nonneg (w);
158 return w;
159 }
160 else
161 return w;
162}
163#ifndef __ieee754_hypot
164libm_alias_finite (__ieee754_hypot, __hypot)
165#endif
166