1 /* origin: FreeBSD /usr/src/lib/msun/src/e_lgammaf_r.c */
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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 * ====================================================
19 pi
= 3.1415927410e+00, /* 0x40490fdb */
20 a0
= 7.7215664089e-02, /* 0x3d9e233f */
21 a1
= 3.2246702909e-01, /* 0x3ea51a66 */
22 a2
= 6.7352302372e-02, /* 0x3d89f001 */
23 a3
= 2.0580807701e-02, /* 0x3ca89915 */
24 a4
= 7.3855509982e-03, /* 0x3bf2027e */
25 a5
= 2.8905137442e-03, /* 0x3b3d6ec6 */
26 a6
= 1.1927076848e-03, /* 0x3a9c54a1 */
27 a7
= 5.1006977446e-04, /* 0x3a05b634 */
28 a8
= 2.2086278477e-04, /* 0x39679767 */
29 a9
= 1.0801156895e-04, /* 0x38e28445 */
30 a10
= 2.5214456400e-05, /* 0x37d383a2 */
31 a11
= 4.4864096708e-05, /* 0x383c2c75 */
32 tc
= 1.4616321325e+00, /* 0x3fbb16c3 */
33 tf
= -1.2148628384e-01, /* 0xbdf8cdcd */
34 /* tt = -(tail of tf) */
35 tt
= 6.6971006518e-09, /* 0x31e61c52 */
36 t0
= 4.8383611441e-01, /* 0x3ef7b95e */
37 t1
= -1.4758771658e-01, /* 0xbe17213c */
38 t2
= 6.4624942839e-02, /* 0x3d845a15 */
39 t3
= -3.2788541168e-02, /* 0xbd064d47 */
40 t4
= 1.7970675603e-02, /* 0x3c93373d */
41 t5
= -1.0314224288e-02, /* 0xbc28fcfe */
42 t6
= 6.1005386524e-03, /* 0x3bc7e707 */
43 t7
= -3.6845202558e-03, /* 0xbb7177fe */
44 t8
= 2.2596477065e-03, /* 0x3b141699 */
45 t9
= -1.4034647029e-03, /* 0xbab7f476 */
46 t10
= 8.8108185446e-04, /* 0x3a66f867 */
47 t11
= -5.3859531181e-04, /* 0xba0d3085 */
48 t12
= 3.1563205994e-04, /* 0x39a57b6b */
49 t13
= -3.1275415677e-04, /* 0xb9a3f927 */
50 t14
= 3.3552918467e-04, /* 0x39afe9f7 */
51 u0
= -7.7215664089e-02, /* 0xbd9e233f */
52 u1
= 6.3282704353e-01, /* 0x3f2200f4 */
53 u2
= 1.4549225569e+00, /* 0x3fba3ae7 */
54 u3
= 9.7771751881e-01, /* 0x3f7a4bb2 */
55 u4
= 2.2896373272e-01, /* 0x3e6a7578 */
56 u5
= 1.3381091878e-02, /* 0x3c5b3c5e */
57 v1
= 2.4559779167e+00, /* 0x401d2ebe */
58 v2
= 2.1284897327e+00, /* 0x4008392d */
59 v3
= 7.6928514242e-01, /* 0x3f44efdf */
60 v4
= 1.0422264785e-01, /* 0x3dd572af */
61 v5
= 3.2170924824e-03, /* 0x3b52d5db */
62 s0
= -7.7215664089e-02, /* 0xbd9e233f */
63 s1
= 2.1498242021e-01, /* 0x3e5c245a */
64 s2
= 3.2577878237e-01, /* 0x3ea6cc7a */
65 s3
= 1.4635047317e-01, /* 0x3e15dce6 */
66 s4
= 2.6642270386e-02, /* 0x3cda40e4 */
67 s5
= 1.8402845599e-03, /* 0x3af135b4 */
68 s6
= 3.1947532989e-05, /* 0x3805ff67 */
69 r1
= 1.3920053244e+00, /* 0x3fb22d3b */
70 r2
= 7.2193557024e-01, /* 0x3f38d0c5 */
71 r3
= 1.7193385959e-01, /* 0x3e300f6e */
72 r4
= 1.8645919859e-02, /* 0x3c98bf54 */
73 r5
= 7.7794247773e-04, /* 0x3a4beed6 */
74 r6
= 7.3266842264e-06, /* 0x36f5d7bd */
75 w0
= 4.1893854737e-01, /* 0x3ed67f1d */
76 w1
= 8.3333335817e-02, /* 0x3daaaaab */
77 w2
= -2.7777778450e-03, /* 0xbb360b61 */
78 w3
= 7.9365057172e-04, /* 0x3a500cfd */
79 w4
= -5.9518753551e-04, /* 0xba1c065c */
80 w5
= 8.3633989561e-04, /* 0x3a5b3dd2 */
81 w6
= -1.6309292987e-03; /* 0xbad5c4e8 */
83 /* sin(pi*x) assuming x > 2^-100, if sin(pi*x)==0 the sign is arbitrary */
84 static float sin_pi(float x
)
89 /* spurious inexact if odd int */
90 x
= 2*(x
*0.5f
- floorf(x
*0.5f
)); /* x mod 2.0 */
95 y
*= 3.14159265358979323846;
97 default: /* case 4: */
98 case 0: return __sindf(y
);
99 case 1: return __cosdf(y
);
100 case 2: return __sindf(-y
);
101 case 3: return -__cosdf(y
);
105 float __lgammaf_r(float x
, int *signgamp
)
107 union {float f
; uint32_t i
;} u
= {x
};
108 float t
,y
,z
,nadj
,p
,p1
,p2
,p3
,q
,r
,w
;
112 /* purge off +-inf, NaN, +-0, tiny and negative arguments */
115 ix
= u
.i
& 0x7fffffff;
116 if (ix
>= 0x7f800000)
118 if (ix
< 0x35000000) { /* |x| < 2**-21, return -log(|x|) */
128 if (t
== 0.0f
) /* -integer */
134 nadj
= logf(pi
/(t
*x
));
137 /* purge off 1 and 2 */
138 if (ix
== 0x3f800000 || ix
== 0x40000000)
141 else if (ix
< 0x40000000) {
142 if (ix
<= 0x3f666666) { /* lgamma(x) = lgamma(x+1)-log(x) */
144 if (ix
>= 0x3f3b4a20) {
147 } else if (ix
>= 0x3e6d3308) {
156 if (ix
>= 0x3fdda618) { /* [1.7316,2] */
159 } else if (ix
>= 0x3F9da620) { /* [1.23,1.73] */
170 p1
= a0
+z
*(a2
+z
*(a4
+z
*(a6
+z
*(a8
+z
*a10
))));
171 p2
= z
*(a1
+z
*(a3
+z
*(a5
+z
*(a7
+z
*(a9
+z
*a11
)))));
178 p1
= t0
+w
*(t3
+w
*(t6
+w
*(t9
+w
*t12
))); /* parallel comp */
179 p2
= t1
+w
*(t4
+w
*(t7
+w
*(t10
+w
*t13
)));
180 p3
= t2
+w
*(t5
+w
*(t8
+w
*(t11
+w
*t14
)));
181 p
= z
*p1
-(tt
-w
*(p2
+y
*p3
));
185 p1
= y
*(u0
+y
*(u1
+y
*(u2
+y
*(u3
+y
*(u4
+y
*u5
)))));
186 p2
= 1.0f
+y
*(v1
+y
*(v2
+y
*(v3
+y
*(v4
+y
*v5
))));
187 r
+= -0.5f
*y
+ p1
/p2
;
189 } else if (ix
< 0x41000000) { /* x < 8.0 */
192 p
= y
*(s0
+y
*(s1
+y
*(s2
+y
*(s3
+y
*(s4
+y
*(s5
+y
*s6
))))));
193 q
= 1.0f
+y
*(r1
+y
*(r2
+y
*(r3
+y
*(r4
+y
*(r5
+y
*r6
)))));
195 z
= 1.0f
; /* lgamma(1+s) = log(s) + lgamma(s) */
197 case 7: z
*= y
+ 6.0f
; /* FALLTHRU */
198 case 6: z
*= y
+ 5.0f
; /* FALLTHRU */
199 case 5: z
*= y
+ 4.0f
; /* FALLTHRU */
200 case 4: z
*= y
+ 3.0f
; /* FALLTHRU */
201 case 3: z
*= y
+ 2.0f
; /* FALLTHRU */
205 } else if (ix
< 0x5c800000) { /* 8.0 <= x < 2**58 */
209 w
= w0
+z
*(w1
+y
*(w2
+y
*(w3
+y
*(w4
+y
*(w5
+y
*w6
)))));
210 r
= (x
-0.5f
)*(t
-1.0f
)+w
;
211 } else /* 2**58 <= x <= inf */
212 r
= x
*(logf(x
)-1.0f
);
218 weak_alias(__lgammaf_r
, lgammaf_r
);