author | Jan Vrany <jan.vrany@fit.cvut.cz> |
Tue, 11 Jun 2019 22:03:11 +0100 | |
changeset 3914 | 35aa88fa58c1 |
parent 2380 | 9195eccdcbd9 |
permissions | -rw-r--r-- |
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|
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/* @(#)e_atan2.c 1.3 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
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* is preserved. |
fa7400d022a0
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* ==================================================== |
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* |
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*/ |
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|
fa7400d022a0
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/* __ieee754_atan2(y,x) |
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* Method : |
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* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). |
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* 2. Reduce x to positive by (if x and y are unexceptional): |
fa7400d022a0
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* ARG (x+iy) = arctan(y/x) ... if x > 0, |
fa7400d022a0
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* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, |
fa7400d022a0
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* |
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* Special cases: |
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23 |
* |
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* ATAN2((anything), NaN ) is NaN; |
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* ATAN2(NAN , (anything) ) is NaN; |
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* ATAN2(+-0, +(anything but NaN)) is +-0 ; |
fa7400d022a0
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27 |
* ATAN2(+-0, -(anything but NaN)) is +-pi ; |
fa7400d022a0
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28 |
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; |
fa7400d022a0
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29 |
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; |
fa7400d022a0
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30 |
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi; |
fa7400d022a0
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* ATAN2(+-INF,+INF ) is +-pi/4 ; |
fa7400d022a0
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* ATAN2(+-INF,-INF ) is +-3pi/4; |
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* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; |
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* |
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* Constants: |
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* The hexadecimal values are the intended ones for the following |
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* constants. The decimal values may be used, provided that the |
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* compiler will convert from decimal to binary accurately enough |
fa7400d022a0
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* to produce the hexadecimal values shown. |
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*/ |
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|
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#include "fdlibm.h" |
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|
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#ifdef __STDC__ |
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static const double |
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#else |
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static double |
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#endif |
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tiny = 1.0e-300, |
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zero = 0.0, |
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pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ |
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pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ |
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pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ |
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pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ |
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|
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#ifdef __STDC__ |
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double __ieee754_atan2(double y, double x) |
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#else |
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double __ieee754_atan2(y,x) |
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double y,x; |
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#endif |
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{ |
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double z; |
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int k,m,hx,hy,ix,iy; |
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unsigned lx,ly; |
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66 |
|
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hx = __HI(x); ix = hx&0x7fffffff; |
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lx = __LO(x); |
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hy = __HI(y); iy = hy&0x7fffffff; |
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ly = __LO(y); |
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if(((ix|((lx|-lx)>>31))>0x7ff00000)|| |
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((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ |
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return x+y; |
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if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ |
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m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ |
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|
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/* when y = 0 */ |
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if((iy|ly)==0) { |
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switch(m) { |
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case 0: |
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81 |
case 1: return y; /* atan(+-0,+anything)=+-0 */ |
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case 2: return pi+tiny;/* atan(+0,-anything) = pi */ |
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case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ |
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84 |
} |
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85 |
} |
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/* when x = 0 */ |
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87 |
if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
88 |
|
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
89 |
/* when x is INF */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
90 |
if(ix==0x7ff00000) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
91 |
if(iy==0x7ff00000) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
92 |
switch(m) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
93 |
case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
94 |
case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
95 |
case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
96 |
case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
97 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
98 |
} else { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
99 |
switch(m) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
100 |
case 0: return zero ; /* atan(+...,+INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
101 |
case 1: return -zero ; /* atan(-...,+INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
102 |
case 2: return pi+tiny ; /* atan(+...,-INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
103 |
case 3: return -pi-tiny ; /* atan(-...,-INF) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
104 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
105 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
106 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
107 |
/* when y is INF */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
108 |
if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
109 |
|
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
110 |
/* compute y/x */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
111 |
k = (iy-ix)>>20; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
112 |
if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
113 |
else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
114 |
else z=atan(fabs(y/x)); /* safe to do y/x */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
115 |
switch (m) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
116 |
case 0: return z ; /* atan(+,+) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
117 |
case 1: __HI(z) ^= 0x80000000; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
118 |
return z ; /* atan(-,+) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
119 |
case 2: return pi-(z-pi_lo);/* atan(+,-) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
120 |
default: /* case 3 */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
121 |
return (z-pi_lo)-pi;/* atan(-,-) */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
122 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
123 |
} |