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/* @(#)e_atan2.c 5.1 93/09/24 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunPro, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
#ifndef lint
static char rcsid
[] = "$\Id: e_atan2.c,v 1.3.2.1 1997/02/23 11:03:01 joerg Exp $";
#endif
/* __ieee754_atan2(y,x)
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-pi ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
* ATAN2(+-INF,+INF ) is +-pi/4 ;
* ATAN2(+-INF,-INF ) is +-3pi/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following
* constants. The decimal values may be used, provided that the
* compiler will convert from decimal to binary accurately enough
* to produce the hexadecimal values shown.
*/
#include "math.h"
#include "math_private.h"
#ifdef __STDC__
static const double
#else
static double
#endif
tiny
= 1.0e-300,
zero
= 0.0,
pi_o_4
= 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
pi_o_2
= 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
pi
= 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
pi_lo
= 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
#ifdef __STDC__
double __generic___ieee754_atan2
(double y
, double x
)
#else
double __generic___ieee754_atan2
(y
,x
)
double y
,x
;
#endif
{
double z
;
int32_t k
,m
,hx
,hy
,ix
,iy
;
u_int32_t lx
,ly
;
EXTRACT_WORDS
(hx
,lx
,x
);
ix
= hx
&0x7fffffff;
EXTRACT_WORDS
(hy
,ly
,y
);
iy
= hy
&0x7fffffff;
if(((ix
|((lx
|-lx
)>>31))>0x7ff00000)||
((iy
|((ly
|-ly
)>>31))>0x7ff00000)) /* x or y is NaN */
return x
+y
;
if(((hx
-0x3ff00000)|lx
)==0) return atan(y
); /* x=1.0 */
m
= ((hy
>>31)&1)|((hx
>>30)&2); /* 2*sign(x)+sign(y) */
/* when y = 0 */
if((iy
|ly
)==0) {
switch(m
) {
case 0:
case 1: return y
; /* atan(+-0,+anything)=+-0 */
case 2: return pi
+tiny
;/* atan(+0,-anything) = pi */
case 3: return -pi
-tiny
;/* atan(-0,-anything) =-pi */
}
}
/* when x = 0 */
if((ix
|lx
)==0) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
/* when x is INF */
if(ix
==0x7ff00000) {
if(iy
==0x7ff00000) {
switch(m
) {
case 0: return pi_o_4
+tiny
;/* atan(+INF,+INF) */
case 1: return -pi_o_4
-tiny
;/* atan(-INF,+INF) */
case 2: return 3.0*pi_o_4
+tiny
;/*atan(+INF,-INF)*/
case 3: return -3.0*pi_o_4
-tiny
;/*atan(-INF,-INF)*/
}
} else {
switch(m
) {
case 0: return zero
; /* atan(+...,+INF) */
case 1: return -zero
; /* atan(-...,+INF) */
case 2: return pi
+tiny
; /* atan(+...,-INF) */
case 3: return -pi
-tiny
; /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if(iy
==0x7ff00000) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
/* compute y/x */
k
= (iy
-ix
)>>20;
if(k
> 60) z
=pi_o_2
+0.5*pi_lo
; /* |y/x| > 2**60 */
else if(hx
<0&&k
<-60) z
=0.0; /* |y|/x < -2**60 */
else z
=atan(fabs(y
/x
)); /* safe to do y/x */
switch (m
) {
case 0: return z
; /* atan(+,+) */
case 1: {
u_int32_t zh
;
GET_HIGH_WORD
(zh
,z
);
SET_HIGH_WORD
(z
,zh
^ 0x80000000);
}
return z
; /* atan(-,+) */
case 2: return pi
-(z
-pi_lo
);/* atan(+,-) */
default: /* case 3 */
return (z
-pi_lo
)-pi
;/* atan(-,-) */
}
}