1 |
|
|
/* |
2 |
|
|
* ==================================================== |
3 |
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
4 |
|
|
* |
5 |
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business. |
6 |
|
|
* Permission to use, copy, modify, and distribute this |
7 |
|
|
* software is freely granted, provided that this notice |
8 |
|
|
* is preserved. |
9 |
|
|
* ==================================================== |
10 |
|
|
*/ |
11 |
|
|
|
12 |
|
|
/* |
13 |
|
|
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net> |
14 |
|
|
* |
15 |
|
|
* Permission to use, copy, modify, and distribute this software for any |
16 |
|
|
* purpose with or without fee is hereby granted, provided that the above |
17 |
|
|
* copyright notice and this permission notice appear in all copies. |
18 |
|
|
* |
19 |
|
|
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
20 |
|
|
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
21 |
|
|
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR |
22 |
|
|
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
23 |
|
|
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN |
24 |
|
|
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF |
25 |
|
|
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. |
26 |
|
|
*/ |
27 |
|
|
|
28 |
|
|
/* lgammal(x) |
29 |
|
|
* Reentrant version of the logarithm of the Gamma function |
30 |
|
|
* with user provide pointer for the sign of Gamma(x). |
31 |
|
|
* |
32 |
|
|
* Method: |
33 |
|
|
* 1. Argument Reduction for 0 < x <= 8 |
34 |
|
|
* Since gamma(1+s)=s*gamma(s), for x in [0,8], we may |
35 |
|
|
* reduce x to a number in [1.5,2.5] by |
36 |
|
|
* lgamma(1+s) = log(s) + lgamma(s) |
37 |
|
|
* for example, |
38 |
|
|
* lgamma(7.3) = log(6.3) + lgamma(6.3) |
39 |
|
|
* = log(6.3*5.3) + lgamma(5.3) |
40 |
|
|
* = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) |
41 |
|
|
* 2. Polynomial approximation of lgamma around its |
42 |
|
|
* minimun ymin=1.461632144968362245 to maintain monotonicity. |
43 |
|
|
* On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use |
44 |
|
|
* Let z = x-ymin; |
45 |
|
|
* lgamma(x) = -1.214862905358496078218 + z^2*poly(z) |
46 |
|
|
* 2. Rational approximation in the primary interval [2,3] |
47 |
|
|
* We use the following approximation: |
48 |
|
|
* s = x-2.0; |
49 |
|
|
* lgamma(x) = 0.5*s + s*P(s)/Q(s) |
50 |
|
|
* Our algorithms are based on the following observation |
51 |
|
|
* |
52 |
|
|
* zeta(2)-1 2 zeta(3)-1 3 |
53 |
|
|
* lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... |
54 |
|
|
* 2 3 |
55 |
|
|
* |
56 |
|
|
* where Euler = 0.5771... is the Euler constant, which is very |
57 |
|
|
* close to 0.5. |
58 |
|
|
* |
59 |
|
|
* 3. For x>=8, we have |
60 |
|
|
* lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... |
61 |
|
|
* (better formula: |
62 |
|
|
* lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) |
63 |
|
|
* Let z = 1/x, then we approximation |
64 |
|
|
* f(z) = lgamma(x) - (x-0.5)(log(x)-1) |
65 |
|
|
* by |
66 |
|
|
* 3 5 11 |
67 |
|
|
* w = w0 + w1*z + w2*z + w3*z + ... + w6*z |
68 |
|
|
* |
69 |
|
|
* 4. For negative x, since (G is gamma function) |
70 |
|
|
* -x*G(-x)*G(x) = pi/sin(pi*x), |
71 |
|
|
* we have |
72 |
|
|
* G(x) = pi/(sin(pi*x)*(-x)*G(-x)) |
73 |
|
|
* since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 |
74 |
|
|
* Hence, for x<0, signgam = sign(sin(pi*x)) and |
75 |
|
|
* lgamma(x) = log(|Gamma(x)|) |
76 |
|
|
* = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); |
77 |
|
|
* Note: one should avoid compute pi*(-x) directly in the |
78 |
|
|
* computation of sin(pi*(-x)). |
79 |
|
|
* |
80 |
|
|
* 5. Special Cases |
81 |
|
|
* lgamma(2+s) ~ s*(1-Euler) for tiny s |
82 |
|
|
* lgamma(1)=lgamma(2)=0 |
83 |
|
|
* lgamma(x) ~ -log(x) for tiny x |
84 |
|
|
* lgamma(0) = lgamma(inf) = inf |
85 |
|
|
* lgamma(-integer) = +-inf |
86 |
|
|
* |
87 |
|
|
*/ |
88 |
|
|
|
89 |
|
|
#include <math.h> |
90 |
|
|
|
91 |
|
|
#include "math_private.h" |
92 |
|
|
|
93 |
|
|
static const long double |
94 |
|
|
half = 0.5L, |
95 |
|
|
one = 1.0L, |
96 |
|
|
pi = 3.14159265358979323846264L, |
97 |
|
|
two63 = 9.223372036854775808e18L, |
98 |
|
|
|
99 |
|
|
/* lgam(1+x) = 0.5 x + x a(x)/b(x) |
100 |
|
|
-0.268402099609375 <= x <= 0 |
101 |
|
|
peak relative error 6.6e-22 */ |
102 |
|
|
a0 = -6.343246574721079391729402781192128239938E2L, |
103 |
|
|
a1 = 1.856560238672465796768677717168371401378E3L, |
104 |
|
|
a2 = 2.404733102163746263689288466865843408429E3L, |
105 |
|
|
a3 = 8.804188795790383497379532868917517596322E2L, |
106 |
|
|
a4 = 1.135361354097447729740103745999661157426E2L, |
107 |
|
|
a5 = 3.766956539107615557608581581190400021285E0L, |
108 |
|
|
|
109 |
|
|
b0 = 8.214973713960928795704317259806842490498E3L, |
110 |
|
|
b1 = 1.026343508841367384879065363925870888012E4L, |
111 |
|
|
b2 = 4.553337477045763320522762343132210919277E3L, |
112 |
|
|
b3 = 8.506975785032585797446253359230031874803E2L, |
113 |
|
|
b4 = 6.042447899703295436820744186992189445813E1L, |
114 |
|
|
/* b5 = 1.000000000000000000000000000000000000000E0 */ |
115 |
|
|
|
116 |
|
|
|
117 |
|
|
tc = 1.4616321449683623412626595423257213284682E0L, |
118 |
|
|
tf = -1.2148629053584961146050602565082954242826E-1,/* double precision */ |
119 |
|
|
/* tt = (tail of tf), i.e. tf + tt has extended precision. */ |
120 |
|
|
tt = 3.3649914684731379602768989080467587736363E-18L, |
121 |
|
|
/* lgam ( 1.4616321449683623412626595423257213284682E0 ) = |
122 |
|
|
-1.2148629053584960809551455717769158215135617312999903886372437313313530E-1 */ |
123 |
|
|
|
124 |
|
|
/* lgam (x + tc) = tf + tt + x g(x)/h(x) |
125 |
|
|
- 0.230003726999612341262659542325721328468 <= x |
126 |
|
|
<= 0.2699962730003876587373404576742786715318 |
127 |
|
|
peak relative error 2.1e-21 */ |
128 |
|
|
g0 = 3.645529916721223331888305293534095553827E-18L, |
129 |
|
|
g1 = 5.126654642791082497002594216163574795690E3L, |
130 |
|
|
g2 = 8.828603575854624811911631336122070070327E3L, |
131 |
|
|
g3 = 5.464186426932117031234820886525701595203E3L, |
132 |
|
|
g4 = 1.455427403530884193180776558102868592293E3L, |
133 |
|
|
g5 = 1.541735456969245924860307497029155838446E2L, |
134 |
|
|
g6 = 4.335498275274822298341872707453445815118E0L, |
135 |
|
|
|
136 |
|
|
h0 = 1.059584930106085509696730443974495979641E4L, |
137 |
|
|
h1 = 2.147921653490043010629481226937850618860E4L, |
138 |
|
|
h2 = 1.643014770044524804175197151958100656728E4L, |
139 |
|
|
h3 = 5.869021995186925517228323497501767586078E3L, |
140 |
|
|
h4 = 9.764244777714344488787381271643502742293E2L, |
141 |
|
|
h5 = 6.442485441570592541741092969581997002349E1L, |
142 |
|
|
/* h6 = 1.000000000000000000000000000000000000000E0 */ |
143 |
|
|
|
144 |
|
|
|
145 |
|
|
/* lgam (x+1) = -0.5 x + x u(x)/v(x) |
146 |
|
|
-0.100006103515625 <= x <= 0.231639862060546875 |
147 |
|
|
peak relative error 1.3e-21 */ |
148 |
|
|
u0 = -8.886217500092090678492242071879342025627E1L, |
149 |
|
|
u1 = 6.840109978129177639438792958320783599310E2L, |
150 |
|
|
u2 = 2.042626104514127267855588786511809932433E3L, |
151 |
|
|
u3 = 1.911723903442667422201651063009856064275E3L, |
152 |
|
|
u4 = 7.447065275665887457628865263491667767695E2L, |
153 |
|
|
u5 = 1.132256494121790736268471016493103952637E2L, |
154 |
|
|
u6 = 4.484398885516614191003094714505960972894E0L, |
155 |
|
|
|
156 |
|
|
v0 = 1.150830924194461522996462401210374632929E3L, |
157 |
|
|
v1 = 3.399692260848747447377972081399737098610E3L, |
158 |
|
|
v2 = 3.786631705644460255229513563657226008015E3L, |
159 |
|
|
v3 = 1.966450123004478374557778781564114347876E3L, |
160 |
|
|
v4 = 4.741359068914069299837355438370682773122E2L, |
161 |
|
|
v5 = 4.508989649747184050907206782117647852364E1L, |
162 |
|
|
/* v6 = 1.000000000000000000000000000000000000000E0 */ |
163 |
|
|
|
164 |
|
|
|
165 |
|
|
/* lgam (x+2) = .5 x + x s(x)/r(x) |
166 |
|
|
0 <= x <= 1 |
167 |
|
|
peak relative error 7.2e-22 */ |
168 |
|
|
s0 = 1.454726263410661942989109455292824853344E6L, |
169 |
|
|
s1 = -3.901428390086348447890408306153378922752E6L, |
170 |
|
|
s2 = -6.573568698209374121847873064292963089438E6L, |
171 |
|
|
s3 = -3.319055881485044417245964508099095984643E6L, |
172 |
|
|
s4 = -7.094891568758439227560184618114707107977E5L, |
173 |
|
|
s5 = -6.263426646464505837422314539808112478303E4L, |
174 |
|
|
s6 = -1.684926520999477529949915657519454051529E3L, |
175 |
|
|
|
176 |
|
|
r0 = -1.883978160734303518163008696712983134698E7L, |
177 |
|
|
r1 = -2.815206082812062064902202753264922306830E7L, |
178 |
|
|
r2 = -1.600245495251915899081846093343626358398E7L, |
179 |
|
|
r3 = -4.310526301881305003489257052083370058799E6L, |
180 |
|
|
r4 = -5.563807682263923279438235987186184968542E5L, |
181 |
|
|
r5 = -3.027734654434169996032905158145259713083E4L, |
182 |
|
|
r6 = -4.501995652861105629217250715790764371267E2L, |
183 |
|
|
/* r6 = 1.000000000000000000000000000000000000000E0 */ |
184 |
|
|
|
185 |
|
|
|
186 |
|
|
/* lgam(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x w(1/x^2) |
187 |
|
|
x >= 8 |
188 |
|
|
Peak relative error 1.51e-21 |
189 |
|
|
w0 = LS2PI - 0.5 */ |
190 |
|
|
w0 = 4.189385332046727417803e-1L, |
191 |
|
|
w1 = 8.333333333333331447505E-2L, |
192 |
|
|
w2 = -2.777777777750349603440E-3L, |
193 |
|
|
w3 = 7.936507795855070755671E-4L, |
194 |
|
|
w4 = -5.952345851765688514613E-4L, |
195 |
|
|
w5 = 8.412723297322498080632E-4L, |
196 |
|
|
w6 = -1.880801938119376907179E-3L, |
197 |
|
|
w7 = 4.885026142432270781165E-3L; |
198 |
|
|
|
199 |
|
|
static const long double zero = 0.0L; |
200 |
|
|
|
201 |
|
|
static long double |
202 |
|
|
sin_pi(long double x) |
203 |
|
|
{ |
204 |
|
|
long double y, z; |
205 |
|
|
int n, ix; |
206 |
|
|
u_int32_t se, i0, i1; |
207 |
|
|
|
208 |
|
|
GET_LDOUBLE_WORDS (se, i0, i1, x); |
209 |
|
|
ix = se & 0x7fff; |
210 |
|
|
ix = (ix << 16) | (i0 >> 16); |
211 |
|
|
if (ix < 0x3ffd8000) /* 0.25 */ |
212 |
|
|
return sinl (pi * x); |
213 |
|
|
y = -x; /* x is assume negative */ |
214 |
|
|
|
215 |
|
|
/* |
216 |
|
|
* argument reduction, make sure inexact flag not raised if input |
217 |
|
|
* is an integer |
218 |
|
|
*/ |
219 |
|
|
z = floorl (y); |
220 |
|
|
if (z != y) |
221 |
|
|
{ /* inexact anyway */ |
222 |
|
|
y *= 0.5; |
223 |
|
|
y = 2.0*(y - floorl(y)); /* y = |x| mod 2.0 */ |
224 |
|
|
n = (int) (y*4.0); |
225 |
|
|
} |
226 |
|
|
else |
227 |
|
|
{ |
228 |
|
|
if (ix >= 0x403f8000) /* 2^64 */ |
229 |
|
|
{ |
230 |
|
|
y = zero; n = 0; /* y must be even */ |
231 |
|
|
} |
232 |
|
|
else |
233 |
|
|
{ |
234 |
|
|
if (ix < 0x403e8000) /* 2^63 */ |
235 |
|
|
z = y + two63; /* exact */ |
236 |
|
|
GET_LDOUBLE_WORDS (se, i0, i1, z); |
237 |
|
|
n = i1 & 1; |
238 |
|
|
y = n; |
239 |
|
|
n <<= 2; |
240 |
|
|
} |
241 |
|
|
} |
242 |
|
|
|
243 |
|
|
switch (n) |
244 |
|
|
{ |
245 |
|
|
case 0: |
246 |
|
|
y = sinl (pi * y); |
247 |
|
|
break; |
248 |
|
|
case 1: |
249 |
|
|
case 2: |
250 |
|
|
y = cosl (pi * (half - y)); |
251 |
|
|
break; |
252 |
|
|
case 3: |
253 |
|
|
case 4: |
254 |
|
|
y = sinl (pi * (one - y)); |
255 |
|
|
break; |
256 |
|
|
case 5: |
257 |
|
|
case 6: |
258 |
|
|
y = -cosl (pi * (y - 1.5)); |
259 |
|
|
break; |
260 |
|
|
default: |
261 |
|
|
y = sinl (pi * (y - 2.0)); |
262 |
|
|
break; |
263 |
|
|
} |
264 |
|
|
return -y; |
265 |
|
|
} |
266 |
|
|
|
267 |
|
|
|
268 |
|
|
long double |
269 |
|
|
lgammal(long double x) |
270 |
|
|
{ |
271 |
|
|
long double t, y, z, nadj, p, p1, p2, q, r, w; |
272 |
|
|
int i, ix; |
273 |
|
|
u_int32_t se, i0, i1; |
274 |
|
|
|
275 |
|
36 |
signgam = 1; |
276 |
|
18 |
GET_LDOUBLE_WORDS (se, i0, i1, x); |
277 |
|
18 |
ix = se & 0x7fff; |
278 |
|
|
|
279 |
✓✓ |
18 |
if ((ix | i0 | i1) == 0) |
280 |
|
|
{ |
281 |
✓✓ |
6 |
if (se & 0x8000) |
282 |
|
3 |
signgam = -1; |
283 |
|
6 |
return one / fabsl (x); |
284 |
|
|
} |
285 |
|
|
|
286 |
|
12 |
ix = (ix << 16) | (i0 >> 16); |
287 |
|
|
|
288 |
|
|
/* purge off +-inf, NaN, +-0, and negative arguments */ |
289 |
✓✓ |
12 |
if (ix >= 0x7fff0000) |
290 |
|
6 |
return x * x; |
291 |
|
|
|
292 |
✗✓ |
6 |
if (ix < 0x3fc08000) /* 2^-63 */ |
293 |
|
|
{ /* |x|<2**-63, return -log(|x|) */ |
294 |
|
|
if (se & 0x8000) |
295 |
|
|
{ |
296 |
|
|
signgam = -1; |
297 |
|
|
return -logl (-x); |
298 |
|
|
} |
299 |
|
|
else |
300 |
|
|
return -logl (x); |
301 |
|
|
} |
302 |
✗✓ |
6 |
if (se & 0x8000) |
303 |
|
|
{ |
304 |
|
|
t = sin_pi (x); |
305 |
|
|
if (t == zero) |
306 |
|
|
return one / fabsl (t); /* -integer */ |
307 |
|
|
nadj = logl (pi / fabsl (t * x)); |
308 |
|
|
if (t < zero) |
309 |
|
|
signgam = -1; |
310 |
|
|
x = -x; |
311 |
|
|
} |
312 |
|
|
|
313 |
|
|
/* purge off 1 and 2 */ |
314 |
✗✓ |
12 |
if ((((ix - 0x3fff8000) | i0 | i1) == 0) |
315 |
✓✗ |
12 |
|| (((ix - 0x40008000) | i0 | i1) == 0)) |
316 |
|
|
r = 0; |
317 |
✓✓ |
6 |
else if (ix < 0x40008000) /* 2.0 */ |
318 |
|
|
{ |
319 |
|
|
/* x < 2.0 */ |
320 |
✗✓ |
3 |
if (ix <= 0x3ffee666) /* 8.99993896484375e-1 */ |
321 |
|
|
{ |
322 |
|
|
/* lgamma(x) = lgamma(x+1) - log(x) */ |
323 |
|
|
r = -logl (x); |
324 |
|
|
if (ix >= 0x3ffebb4a) /* 7.31597900390625e-1 */ |
325 |
|
|
{ |
326 |
|
|
y = x - one; |
327 |
|
|
i = 0; |
328 |
|
|
} |
329 |
|
|
else if (ix >= 0x3ffced33)/* 2.31639862060546875e-1 */ |
330 |
|
|
{ |
331 |
|
|
y = x - (tc - one); |
332 |
|
|
i = 1; |
333 |
|
|
} |
334 |
|
|
else |
335 |
|
|
{ |
336 |
|
|
/* x < 0.23 */ |
337 |
|
|
y = x; |
338 |
|
|
i = 2; |
339 |
|
|
} |
340 |
|
|
} |
341 |
|
|
else |
342 |
|
|
{ |
343 |
|
|
r = zero; |
344 |
✗✓ |
3 |
if (ix >= 0x3fffdda6) /* 1.73162841796875 */ |
345 |
|
|
{ |
346 |
|
|
/* [1.7316,2] */ |
347 |
|
|
y = x - 2.0; |
348 |
|
|
i = 0; |
349 |
|
|
} |
350 |
✗✓ |
3 |
else if (ix >= 0x3fff9da6)/* 1.23162841796875 */ |
351 |
|
|
{ |
352 |
|
|
/* [1.23,1.73] */ |
353 |
|
|
y = x - tc; |
354 |
|
|
i = 1; |
355 |
|
|
} |
356 |
|
|
else |
357 |
|
|
{ |
358 |
|
|
/* [0.9, 1.23] */ |
359 |
|
3 |
y = x - one; |
360 |
|
|
i = 2; |
361 |
|
|
} |
362 |
|
|
} |
363 |
✗✗✓✓
|
6 |
switch (i) |
364 |
|
|
{ |
365 |
|
|
case 0: |
366 |
|
|
p1 = a0 + y * (a1 + y * (a2 + y * (a3 + y * (a4 + y * a5)))); |
367 |
|
|
p2 = b0 + y * (b1 + y * (b2 + y * (b3 + y * (b4 + y)))); |
368 |
|
|
r += half * y + y * p1/p2; |
369 |
|
|
break; |
370 |
|
|
case 1: |
371 |
|
|
p1 = g0 + y * (g1 + y * (g2 + y * (g3 + y * (g4 + y * (g5 + y * g6))))); |
372 |
|
|
p2 = h0 + y * (h1 + y * (h2 + y * (h3 + y * (h4 + y * (h5 + y))))); |
373 |
|
|
p = tt + y * p1/p2; |
374 |
|
|
r += (tf + p); |
375 |
|
|
break; |
376 |
|
|
case 2: |
377 |
|
3 |
p1 = y * (u0 + y * (u1 + y * (u2 + y * (u3 + y * (u4 + y * (u5 + y * u6)))))); |
378 |
|
3 |
p2 = v0 + y * (v1 + y * (v2 + y * (v3 + y * (v4 + y * (v5 + y))))); |
379 |
|
3 |
r += (-half * y + p1 / p2); |
380 |
|
3 |
} |
381 |
|
|
} |
382 |
✓✗ |
3 |
else if (ix < 0x40028000) /* 8.0 */ |
383 |
|
|
{ |
384 |
|
|
/* x < 8.0 */ |
385 |
|
6 |
i = (int) x; |
386 |
|
|
t = zero; |
387 |
|
6 |
y = x - (double) i; |
388 |
|
6 |
p = y * |
389 |
|
6 |
(s0 + y * (s1 + y * (s2 + y * (s3 + y * (s4 + y * (s5 + y * s6)))))); |
390 |
|
6 |
q = r0 + y * (r1 + y * (r2 + y * (r3 + y * (r4 + y * (r5 + y * (r6 + y)))))); |
391 |
|
6 |
r = half * y + p / q; |
392 |
|
|
z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ |
393 |
✗✗✗✗
✓✓ |
6 |
switch (i) |
394 |
|
|
{ |
395 |
|
|
case 7: |
396 |
|
|
z *= (y + 6.0); /* FALLTHRU */ |
397 |
|
|
case 6: |
398 |
|
|
z *= (y + 5.0); /* FALLTHRU */ |
399 |
|
|
case 5: |
400 |
|
|
z *= (y + 4.0); /* FALLTHRU */ |
401 |
|
|
case 4: |
402 |
|
|
z *= (y + 3.0); /* FALLTHRU */ |
403 |
|
|
case 3: |
404 |
|
3 |
z *= (y + 2.0); /* FALLTHRU */ |
405 |
|
3 |
r += logl (z); |
406 |
|
3 |
break; |
407 |
|
|
} |
408 |
|
|
} |
409 |
|
|
else if (ix < 0x40418000) /* 2^66 */ |
410 |
|
|
{ |
411 |
|
|
/* 8.0 <= x < 2**66 */ |
412 |
|
|
t = logl (x); |
413 |
|
|
z = one / x; |
414 |
|
|
y = z * z; |
415 |
|
|
w = w0 + z * (w1 |
416 |
|
|
+ y * (w2 + y * (w3 + y * (w4 + y * (w5 + y * (w6 + y * w7)))))); |
417 |
|
|
r = (x - half) * (t - one) + w; |
418 |
|
|
} |
419 |
|
|
else |
420 |
|
|
/* 2**66 <= x <= inf */ |
421 |
|
|
r = x * (logl (x) - one); |
422 |
✗✓ |
6 |
if (se & 0x8000) |
423 |
|
|
r = nadj - r; |
424 |
|
6 |
return r; |
425 |
|
18 |
} |
426 |
|
|
DEF_STD(lgammal); |