1 /* e_atan2l.c -- long double version of e_atan2.c.
2 * Conversion to long double by Jakub Jelinek, jj@ultra.linux.cz.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
13 * ====================================================
16 /* __ieee754_atan2l(y,x)
18 * 1. Reduce y to positive by atan2l(y,x)=-atan2l(-y,x).
19 * 2. Reduce x to positive by (if x and y are unexceptional):
20 * ARG (x+iy) = arctan(y/x) ... if x > 0,
21 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
25 * ATAN2((anything), NaN ) is NaN;
26 * ATAN2(NAN , (anything) ) is NaN;
27 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
28 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
29 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
30 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
31 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
32 * ATAN2(+-INF,+INF ) is +-pi/4 ;
33 * ATAN2(+-INF,-INF ) is +-3pi/4;
34 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
37 * The hexadecimal values are the intended ones for the following
38 * constants. The decimal values may be used, provided that the
39 * compiler will convert from decimal to binary accurately enough
40 * to produce the hexadecimal values shown.
44 #include "math_private.h"
47 static const long double
53 pi_o_4
= 7.85398163397448309615660845819875699e-01L, /* 3ffe921fb54442d18469898cc51701b8 */
54 pi_o_2
= 1.57079632679489661923132169163975140e+00L, /* 3fff921fb54442d18469898cc51701b8 */
55 pi
= 3.14159265358979323846264338327950280e+00L, /* 4000921fb54442d18469898cc51701b8 */
56 pi_lo
= 8.67181013012378102479704402604335225e-35L; /* 3f8dcd129024e088a67cc74020bbea64 */
59 long double __ieee754_atan2l(long double y
, long double x
)
61 long double __ieee754_atan2l(y
,x
)
66 int64_t k
,m
,hx
,hy
,ix
,iy
;
69 GET_LDOUBLE_WORDS64(hx
,lx
,x
);
70 ix
= hx
&0x7fffffffffffffffLL
;
71 GET_LDOUBLE_WORDS64(hy
,ly
,y
);
72 iy
= hy
&0x7fffffffffffffffLL
;
73 if(((ix
)>0x7ff0000000000000LL
)||
74 ((iy
)>0x7ff0000000000000LL
)) /* x or y is NaN */
76 if(((hx
-0x3ff0000000000000LL
))==0) return __atanl(y
); /* x=1.0L */
77 m
= ((hy
>>63)&1)|((hx
>>62)&2); /* 2*sign(x)+sign(y) */
80 if((iy
|(ly
&0x7fffffffffffffffLL
))==0) {
83 case 1: return y
; /* atan(+-0,+anything)=+-0 */
84 case 2: return pi
+tiny
;/* atan(+0,-anything) = pi */
85 case 3: return -pi
-tiny
;/* atan(-0,-anything) =-pi */
89 if((ix
|(lx
&0x7fffffffffffffff))==0) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
92 if(ix
==0x7ff0000000000000LL
) {
93 if(iy
==0x7ff0000000000000LL
) {
95 case 0: return pi_o_4
+tiny
;/* atan(+INF,+INF) */
96 case 1: return -pi_o_4
-tiny
;/* atan(-INF,+INF) */
97 case 2: return 3.0L*pi_o_4
+tiny
;/*atan(+INF,-INF)*/
98 case 3: return -3.0L*pi_o_4
-tiny
;/*atan(-INF,-INF)*/
102 case 0: return zero
; /* atan(+...,+INF) */
103 case 1: return -zero
; /* atan(-...,+INF) */
104 case 2: return pi
+tiny
; /* atan(+...,-INF) */
105 case 3: return -pi
-tiny
; /* atan(-...,-INF) */
110 if(iy
==0x7ff0000000000000LL
) return (hy
<0)? -pi_o_2
-tiny
: pi_o_2
+tiny
;
114 if(k
> 120) z
=pi_o_2
+0.5L*pi_lo
; /* |y/x| > 2**120 */
115 else if(hx
<0&&k
<-120) z
=0.0L; /* |y|/x < -2**120 */
116 else z
=__atanl(fabsl(y
/x
)); /* safe to do y/x */
118 case 0: return z
; /* atan(+,+) */
119 case 1: return -z
; /* atan(-,+) */
120 case 2: return pi
-(z
-pi_lo
);/* atan(+,-) */
121 default: /* case 3 */
122 return (z
-pi_lo
)-pi
;/* atan(-,-) */