ipiq: Add simple IPI latency measure sysctls (2)
[dragonfly.git] / lib / libm / src / e_atan2.c
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1
2/* @(#)e_atan2.c 1.3 95/01/18 */
3/* $FreeBSD: head/lib/msun/src/e_atan2.c 181204 2008-08-02 19:17:00Z 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 * ====================================================
13 *
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14 */
15
6ff43c94 16/* __ieee754_atan2(y,x)
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17 * Method :
18 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
6ff43c94 19 * 2. Reduce x to positive by (if x and y are unexceptional):
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20 * ARG (x+iy) = arctan(y/x) ... if x > 0,
21 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
22 *
23 * Special cases:
24 *
25 * ATAN2((anything), NaN ) is NaN;
26 * ATAN2(NAN , (anything) ) is NaN;
27 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
28 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
29 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
30 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
31 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
32 * ATAN2(+-INF,+INF ) is +-pi/4 ;
33 * ATAN2(+-INF,-INF ) is +-3pi/4;
34 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
35 *
36 * Constants:
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37 * The hexadecimal values are the intended ones for the following
38 * constants. The decimal values may be used, provided that the
39 * compiler will convert from decimal to binary accurately enough
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40 * to produce the hexadecimal values shown.
41 */
42
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43#include <float.h>
44
45#include "math.h"
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46#include "math_private.h"
47
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48static volatile double
49tiny = 1.0e-300;
b34b60bc 50static const double
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51zero = 0.0,
52pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
53pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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54pi = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
55static volatile double
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56pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
57
58double
6ff43c94 59__ieee754_atan2(double y, double x)
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60{
61 double z;
62 int32_t k,m,hx,hy,ix,iy;
63 u_int32_t lx,ly;
64
65 EXTRACT_WORDS(hx,lx,x);
66 ix = hx&0x7fffffff;
67 EXTRACT_WORDS(hy,ly,y);
68 iy = hy&0x7fffffff;
69 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
70 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
71 return x+y;
6ff43c94 72 if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */
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73 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
74
75 /* when y = 0 */
76 if((iy|ly)==0) {
77 switch(m) {
6ff43c94 78 case 0:
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79 case 1: return y; /* atan(+-0,+anything)=+-0 */
80 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
81 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
82 }
83 }
84 /* when x = 0 */
85 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
6ff43c94 86
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87 /* when x is INF */
88 if(ix==0x7ff00000) {
89 if(iy==0x7ff00000) {
90 switch(m) {
91 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
92 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
93 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
94 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
95 }
96 } else {
97 switch(m) {
98 case 0: return zero ; /* atan(+...,+INF) */
99 case 1: return -zero ; /* atan(-...,+INF) */
100 case 2: return pi+tiny ; /* atan(+...,-INF) */
101 case 3: return -pi-tiny ; /* atan(-...,-INF) */
102 }
103 }
104 }
105 /* when y is INF */
106 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
107
108 /* compute y/x */
109 k = (iy-ix)>>20;
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110 if(k > 60) { /* |y/x| > 2**60 */
111 z=pi_o_2+0.5*pi_lo;
112 m&=1;
113 }
114 else if(hx<0&&k<-60) z=0.0; /* 0 > |y|/x > -2**-60 */
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115 else z=atan(fabs(y/x)); /* safe to do y/x */
116 switch (m) {
117 case 0: return z ; /* atan(+,+) */
6ff43c94 118 case 1: return -z ; /* atan(-,+) */
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119 case 2: return pi-(z-pi_lo);/* atan(+,-) */
120 default: /* case 3 */
121 return (z-pi_lo)-pi;/* atan(-,-) */
122 }
123}
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124
125#if LDBL_MANT_DIG == 53
126__weak_reference(atan2, atan2l);
127#endif