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| 2 | /* @(#)e_atan2.c 5.1 93/09/24 */ |
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| 3 | /* |
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| 4 | * ==================================================== |
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| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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| 6 | * |
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| 7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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| 8 | * Permission to use, copy, modify, and distribute this |
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| 9 | * software is freely granted, provided that this notice |
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| 10 | * is preserved. |
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| 11 | * ==================================================== |
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| 12 | * |
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| 13 | */ |
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| 14 | |
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| 15 | /* __ieee754_atan2(y,x) |
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| 16 | * Method : |
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| 17 | * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). |
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| 18 | * 2. Reduce x to positive by (if x and y are unexceptional): |
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| 19 | * ARG (x+iy) = arctan(y/x) ... if x > 0, |
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| 20 | * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, |
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| 21 | * |
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| 22 | * Special cases: |
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| 23 | * |
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| 24 | * ATAN2((anything), NaN ) is NaN; |
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| 25 | * ATAN2(NAN , (anything) ) is NaN; |
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| 26 | * ATAN2(+-0, +(anything but NaN)) is +-0 ; |
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| 27 | * ATAN2(+-0, -(anything but NaN)) is +-pi ; |
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| 28 | * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; |
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| 29 | * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; |
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| 30 | * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; |
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| 31 | * ATAN2(+-INF,+INF ) is +-pi/4 ; |
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| 32 | * ATAN2(+-INF,-INF ) is +-3pi/4; |
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| 33 | * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; |
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| 34 | * |
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| 35 | * Constants: |
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| 36 | * The hexadecimal values are the intended ones for the following |
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| 37 | * constants. The decimal values may be used, provided that the |
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| 38 | * compiler will convert from decimal to binary accurately enough |
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| 39 | * to produce the hexadecimal values shown. |
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| 40 | */ |
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| 41 | |
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| 42 | #include <libm/fdlibm.h> |
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| 43 | |
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| 44 | #ifdef __STDC__ |
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| 45 | static const double |
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| 46 | #else |
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| 47 | static double |
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| 48 | #endif |
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| 49 | tiny = 1.0e-300, |
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| 50 | zero = 0.0, |
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| 51 | one = 1.0, |
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| 52 | pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ |
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| 53 | pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ |
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| 54 | pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ |
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| 55 | pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ |
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| 56 | |
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| 57 | #ifdef __STDC__ |
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| 58 | double __ieee754_atan2(double y, double x) |
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| 59 | #else |
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| 60 | double __ieee754_atan2(y,x) |
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| 61 | double y,x; |
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| 62 | #endif |
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| 63 | { |
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| 64 | double z; |
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| 65 | int k,m,hx,hy,ix,iy,n0; |
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| 66 | unsigned lx,ly; |
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| 67 | |
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| 68 | n0 = ((*(int*)&one)>>29)^1; /* high word index */ |
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| 69 | hx = *(n0+(int*)&x); ix = hx&0x7fffffff; |
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| 70 | lx = *(1-n0+(int*)&x); |
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| 71 | hy = *(n0+(int*)&y); iy = hy&0x7fffffff; |
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| 72 | ly = *(1-n0+(int*)&y); |
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| 73 | if(((ix|((lx|-lx)>>31))>0x7ff00000)|| |
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| 74 | ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ |
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| 75 | return x+y; |
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| 76 | if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ |
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| 77 | m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ |
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| 78 | |
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| 79 | /* when y = 0 */ |
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| 80 | if((iy|ly)==0) { |
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| 81 | switch(m) { |
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| 82 | case 0: |
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| 83 | case 1: return y; /* atan(+-0,+anything)=+-0 */ |
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| 84 | case 2: return pi+tiny;/* atan(+0,-anything) = pi */ |
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| 85 | case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ |
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| 86 | } |
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| 87 | } |
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| 88 | /* when x = 0 */ |
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| 89 | if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
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| 90 | |
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| 91 | /* when x is INF */ |
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| 92 | if(ix==0x7ff00000) { |
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| 93 | if(iy==0x7ff00000) { |
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| 94 | switch(m) { |
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| 95 | case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ |
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| 96 | case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ |
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| 97 | case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
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| 98 | case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ |
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| 99 | } |
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| 100 | } else { |
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| 101 | switch(m) { |
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| 102 | case 0: return zero ; /* atan(+...,+INF) */ |
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| 103 | case 1: return -zero ; /* atan(-...,+INF) */ |
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| 104 | case 2: return pi+tiny ; /* atan(+...,-INF) */ |
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| 105 | case 3: return -pi-tiny ; /* atan(-...,-INF) */ |
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| 106 | } |
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| 107 | } |
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| 108 | } |
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| 109 | /* when y is INF */ |
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| 110 | if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
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| 111 | |
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| 112 | /* compute y/x */ |
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| 113 | k = (iy-ix)>>20; |
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| 114 | if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ |
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| 115 | else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ |
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| 116 | else z=atan(fabs(y/x)); /* safe to do y/x */ |
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| 117 | switch (m) { |
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| 118 | case 0: return z ; /* atan(+,+) */ |
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| 119 | case 1: *(n0+(int*)&z) ^= 0x80000000; |
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| 120 | return z ; /* atan(-,+) */ |
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| 121 | case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
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| 122 | default: /* case 3 */ |
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| 123 | return (z-pi_lo)-pi;/* atan(-,-) */ |
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| 124 | } |
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| 125 | } |
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