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annotate src/libm/e_atan2.c @ 4875:22ce07e8e824

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author Sam Lantinga <slouken@libsdl.org>
date Sun, 29 Aug 2010 21:41:11 -0700
parents 8288636b861d
children
rev   line source
4870
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1 /*
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2 * ====================================================
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3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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4 *
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5 * Developed at SunPro, a Sun Microsystems, Inc. business.
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6 * Permission to use, copy, modify, and distribute this
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7 * software is freely granted, provided that this notice
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8 * is preserved.
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9 * ====================================================
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10 */
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11
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12 /* __ieee754_atan2(y,x)
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13 * Method :
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14 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
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15 * 2. Reduce x to positive by (if x and y are unexceptional):
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16 * ARG (x+iy) = arctan(y/x) ... if x > 0,
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17 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
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18 *
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19 * Special cases:
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20 *
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21 * ATAN2((anything), NaN ) is NaN;
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22 * ATAN2(NAN , (anything) ) is NaN;
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23 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
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24 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
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25 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
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26 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
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27 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
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28 * ATAN2(+-INF,+INF ) is +-pi/4 ;
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29 * ATAN2(+-INF,-INF ) is +-3pi/4;
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30 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
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31 *
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32 * Constants:
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33 * The hexadecimal values are the intended ones for the following
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34 * constants. The decimal values may be used, provided that the
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35 * compiler will convert from decimal to binary accurately enough
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36 * to produce the hexadecimal values shown.
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37 */
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38
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39 #include "math.h"
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40 #include "math_private.h"
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41
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42 static const double
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43 tiny = 1.0e-300,
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44 zero = 0.0,
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45 pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
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46 pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
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47 pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
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48 pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
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49
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50 double attribute_hidden __ieee754_atan2(double y, double x)
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51 {
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52 double z;
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53 int32_t k,m,hx,hy,ix,iy;
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54 u_int32_t lx,ly;
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55
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56 EXTRACT_WORDS(hx,lx,x);
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57 ix = hx&0x7fffffff;
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58 EXTRACT_WORDS(hy,ly,y);
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59 iy = hy&0x7fffffff;
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60 if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)||
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61 ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */
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62 return x+y;
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63 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
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64 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
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65
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66 /* when y = 0 */
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67 if((iy|ly)==0) {
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68 switch(m) {
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69 case 0:
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70 case 1: return y; /* atan(+-0,+anything)=+-0 */
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71 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
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72 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
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73 }
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74 }
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75 /* when x = 0 */
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76 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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77
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78 /* when x is INF */
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79 if(ix==0x7ff00000) {
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80 if(iy==0x7ff00000) {
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81 switch(m) {
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82 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
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83 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
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84 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
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85 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
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86 }
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87 } else {
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88 switch(m) {
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89 case 0: return zero ; /* atan(+...,+INF) */
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90 case 1: return -zero ; /* atan(-...,+INF) */
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91 case 2: return pi+tiny ; /* atan(+...,-INF) */
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92 case 3: return -pi-tiny ; /* atan(-...,-INF) */
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93 }
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94 }
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95 }
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96 /* when y is INF */
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97 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
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98
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99 /* compute y/x */
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100 k = (iy-ix)>>20;
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101 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
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102 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
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103 else z=atan(fabs(y/x)); /* safe to do y/x */
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104 switch (m) {
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105 case 0: return z ; /* atan(+,+) */
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106 case 1: {
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107 u_int32_t zh;
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108 GET_HIGH_WORD(zh,z);
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109 SET_HIGH_WORD(z,zh ^ 0x80000000);
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110 }
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111 return z ; /* atan(-,+) */
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112 case 2: return pi-(z-pi_lo);/* atan(+,-) */
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113 default: /* case 3 */
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114 return (z-pi_lo)-pi;/* atan(-,-) */
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115 }
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116 }