1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
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2 | /*
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3 | * ====================================================
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4 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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5 | *
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6 | * Developed at SunSoft, a Sun Microsystems, Inc. business.
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7 | * Permission to use, copy, modify, and distribute this
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8 | * software is freely granted, provided that this notice
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9 | * is preserved.
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10 | * ====================================================
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11 | *
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12 | */
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13 | /* atan2(y,x)
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14 | * Method :
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15 | * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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16 | * 2. Reduce x to positive by (if x and y are unexceptional):
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17 | * ARG (x+iy) = arctan(y/x) ... if x > 0,
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18 | * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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19 | *
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20 | * Special cases:
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21 | *
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22 | * ATAN2((anything), NaN ) is NaN;
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23 | * ATAN2(NAN , (anything) ) is NaN;
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24 | * ATAN2(+-0, +(anything but NaN)) is +-0 ;
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25 | * ATAN2(+-0, -(anything but NaN)) is +-pi ;
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26 | * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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27 | * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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28 | * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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29 | * ATAN2(+-INF,+INF ) is +-pi/4 ;
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30 | * ATAN2(+-INF,-INF ) is +-3pi/4;
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31 | * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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32 | *
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33 | * Constants:
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34 | * The hexadecimal values are the intended ones for the following
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35 | * constants. The decimal values may be used, provided that the
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36 | * compiler will convert from decimal to binary accurately enough
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37 | * to produce the hexadecimal values shown.
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38 | */
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39 |
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40 | #include "libm.h"
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41 |
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42 | static const double
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43 | pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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44 | pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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45 |
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46 | double atan2(double y, double x)
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47 | {
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48 | double z;
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49 | uint32_t m,lx,ly,ix,iy;
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50 |
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51 | if (isnan(x) || isnan(y))
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52 | return x+y;
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53 | EXTRACT_WORDS(ix, lx, x);
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54 | EXTRACT_WORDS(iy, ly, y);
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55 | if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */
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56 | return atan(y);
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57 | m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
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58 | ix = ix & 0x7fffffff;
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59 | iy = iy & 0x7fffffff;
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60 |
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61 | /* when y = 0 */
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62 | if ((iy|ly) == 0) {
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63 | switch(m) {
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64 | case 0:
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65 | case 1: return y; /* atan(+-0,+anything)=+-0 */
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66 | case 2: return pi; /* atan(+0,-anything) = pi */
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67 | case 3: return -pi; /* atan(-0,-anything) =-pi */
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68 | }
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69 | }
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70 | /* when x = 0 */
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71 | if ((ix|lx) == 0)
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72 | return m&1 ? -pi/2 : pi/2;
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73 | /* when x is INF */
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74 | if (ix == 0x7ff00000) {
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75 | if (iy == 0x7ff00000) {
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76 | switch(m) {
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77 | case 0: return pi/4; /* atan(+INF,+INF) */
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78 | case 1: return -pi/4; /* atan(-INF,+INF) */
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79 | case 2: return 3*pi/4; /* atan(+INF,-INF) */
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80 | case 3: return -3*pi/4; /* atan(-INF,-INF) */
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81 | }
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82 | } else {
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83 | switch(m) {
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84 | case 0: return 0.0; /* atan(+...,+INF) */
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85 | case 1: return -0.0; /* atan(-...,+INF) */
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86 | case 2: return pi; /* atan(+...,-INF) */
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87 | case 3: return -pi; /* atan(-...,-INF) */
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88 | }
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89 | }
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90 | }
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91 | /* |y/x| > 0x1p64 */
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92 | if (ix+(64<<20) < iy || iy == 0x7ff00000)
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93 | return m&1 ? -pi/2 : pi/2;
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94 |
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95 | /* z = atan(|y/x|) without spurious underflow */
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96 | if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */
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97 | z = 0;
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98 | else
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99 | z = atan(fabs(y/x));
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100 | switch (m) {
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101 | case 0: return z; /* atan(+,+) */
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102 | case 1: return -z; /* atan(-,+) */
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103 | case 2: return pi - (z-pi_lo); /* atan(+,-) */
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104 | default: /* case 3 */
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105 | return (z-pi_lo) - pi; /* atan(-,-) */
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106 | }
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107 | }
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