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Carl Shapiro
cmucl
Commits
d2e935a5
Commit
d2e935a5
authored
10 years ago
by
Raymond Toy
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Import atan2 function from fdlibm, as is.
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src/lisp/e_atan2.c
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d2e935a5
/* @(#)e_atan2.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
*/
/* __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
"fdlibm.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
__ieee754_atan2
(
double
y
,
double
x
)
#else
double
__ieee754_atan2
(
y
,
x
)
double
y
,
x
;
#endif
{
double
z
;
int
k
,
m
,
hx
,
hy
,
ix
,
iy
;
unsigned
lx
,
ly
;
hx
=
__HI
(
x
);
ix
=
hx
&
0x7fffffff
;
lx
=
__LO
(
x
);
hy
=
__HI
(
y
);
iy
=
hy
&
0x7fffffff
;
ly
=
__LO
(
y
);
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
:
__HI
(
z
)
^=
0x80000000
;
return
z
;
/* atan(-,+) */
case
2
:
return
pi
-
(
z
-
pi_lo
);
/* atan(+,-) */
default:
/* case 3 */
return
(
z
-
pi_lo
)
-
pi
;
/* atan(-,-) */
}
}
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