ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / e_hypot.c
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1
2/* @(#)e_hypot.c 1.3 95/01/18 */
3/* $FreeBSD: head/lib/msun/src/e_hypot.c 226380 2011-10-15 07:00:28Z das $ */
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4/*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
6ff43c94 8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
b34b60bc 9 * Permission to use, copy, modify, and distribute this
6ff43c94 10 * software is freely granted, provided that this notice
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11 * is preserved.
12 * ====================================================
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13 */
14
6ff43c94 15/* __ieee754_hypot(x,y)
b34b60bc 16 *
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17 * Method :
18 * If (assume round-to-nearest) z=x*x+y*y
19 * has error less than sqrt(2)/2 ulp, than
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20 * sqrt(z) has error less than 1 ulp (exercise).
21 *
6ff43c94 22 * So, compute sqrt(x*x+y*y) with some care as
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23 * follows to get the error below 1 ulp:
24 *
25 * Assume x>y>0;
26 * (if possible, set rounding to round-to-nearest)
27 * 1. if x > 2y use
28 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
29 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else
30 * 2. if x <= 2y use
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31 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
32 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
33 * y1= y with lower 32 bits chopped, y2 = y-y1.
34 *
35 * NOTE: scaling may be necessary if some argument is too
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36 * large or too tiny
37 *
38 * Special cases:
39 * hypot(x,y) is INF if x or y is +INF or -INF; else
40 * hypot(x,y) is NAN if x or y is NAN.
41 *
42 * Accuracy:
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43 * hypot(x,y) returns sqrt(x^2+y^2) with error less
44 * than 1 ulps (units in the last place)
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45 */
46
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47#include <float.h>
48
49#include "math.h"
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50#include "math_private.h"
51
52double
6ff43c94 53__ieee754_hypot(double x, double y)
b34b60bc 54{
6ff43c94 55 double a,b,t1,t2,y1,y2,w;
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56 int32_t j,k,ha,hb;
57
58 GET_HIGH_WORD(ha,x);
59 ha &= 0x7fffffff;
60 GET_HIGH_WORD(hb,y);
61 hb &= 0x7fffffff;
62 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
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63 a = fabs(a);
64 b = fabs(b);
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65 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
66 k=0;
67 if(ha > 0x5f300000) { /* a>2**500 */
68 if(ha >= 0x7ff00000) { /* Inf or NaN */
69 u_int32_t low;
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70 /* Use original arg order iff result is NaN; quieten sNaNs. */
71 w = fabs(x+0.0)-fabs(y+0.0);
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72 GET_LOW_WORD(low,a);
73 if(((ha&0xfffff)|low)==0) w = a;
74 GET_LOW_WORD(low,b);
75 if(((hb^0x7ff00000)|low)==0) w = b;
76 return w;
77 }
78 /* scale a and b by 2**-600 */
79 ha -= 0x25800000; hb -= 0x25800000; k += 600;
80 SET_HIGH_WORD(a,ha);
81 SET_HIGH_WORD(b,hb);
82 }
83 if(hb < 0x20b00000) { /* b < 2**-500 */
84 if(hb <= 0x000fffff) { /* subnormal b or 0 */
85 u_int32_t low;
86 GET_LOW_WORD(low,b);
87 if((hb|low)==0) return a;
88 t1=0;
89 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */
90 b *= t1;
91 a *= t1;
92 k -= 1022;
93 } else { /* scale a and b by 2^600 */
94 ha += 0x25800000; /* a *= 2^600 */
95 hb += 0x25800000; /* b *= 2^600 */
96 k -= 600;
97 SET_HIGH_WORD(a,ha);
98 SET_HIGH_WORD(b,hb);
99 }
100 }
101 /* medium size a and b */
102 w = a-b;
103 if (w>b) {
104 t1 = 0;
105 SET_HIGH_WORD(t1,ha);
106 t2 = a-t1;
107 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
108 } else {
109 a = a+a;
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110 y1 = 0;
111 SET_HIGH_WORD(y1,hb);
112 y2 = b - y1;
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113 t1 = 0;
114 SET_HIGH_WORD(t1,ha+0x00100000);
115 t2 = a - t1;
6ff43c94 116 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
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117 }
118 if(k!=0) {
119 u_int32_t high;
120 t1 = 1.0;
121 GET_HIGH_WORD(high,t1);
122 SET_HIGH_WORD(t1,high+(k<<20));
123 return t1*w;
124 } else return w;
125}
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126
127#if LDBL_MANT_DIG == 53
128__weak_reference(hypot, hypotl);
129#endif