1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22/*
23 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24 */
25/*
26 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27 * Use is subject to license terms.
28 */
29
30#pragma weak __tgammal = tgammal
31
32#include "libm.h"
33#include <sys/isa_defs.h>
34
35#if defined(_BIG_ENDIAN)
36#define	H0_WORD(x)	((unsigned *) &x)[0]
37#define	H3_WORD(x)	((unsigned *) &x)[3]
38#define	CHOPPED(x)	(long double) ((double) (x))
39#else
40#define	H0_WORD(x)	((((int *) &x)[2] << 16) | \
41			(0x0000ffff & (((unsigned *) &x)[1] >> 15)))
42#define	H3_WORD(x)	((unsigned *) &x)[0]
43#define	CHOPPED(x)	(long double) ((float) (x))
44#endif
45
46struct LDouble {
47	long double h, l;
48};
49
50/* INDENT OFF */
51/* Primary interval GTi() */
52static const long double P1[] = {
53	+0.709086836199777919037185741507610124611513720557L,
54	+4.45754781206489035827915969367354835667391606951e-0001L,
55	+3.21049298735832382311662273882632210062918153852e-0002L,
56	-5.71296796342106617651765245858289197369688864350e-0003L,
57	+6.04666892891998977081619174969855831606965352773e-0003L,
58	+8.99106186996888711939627812174765258822658645168e-0004L,
59	-6.96496846144407741431207008527018441810175568949e-0005L,
60	+1.52597046118984020814225409300131445070213882429e-0005L,
61	+5.68521076168495673844711465407432189190681541547e-0007L,
62	+3.30749673519634895220582062520286565610418952979e-0008L,
63};
64static const long double Q1[] = {
65	+1.0+0000L,
66	+1.35806511721671070408570853537257079579490650668e+0000L,
67	+2.97567810153429553405327140096063086994072952961e-0001L,
68	-1.52956835982588571502954372821681851681118097870e-0001L,
69	-2.88248519561420109768781615289082053597954521218e-0002L,
70	+1.03475311719937405219789948456313936302378395955e-0002L,
71	+4.12310203243891222368965360124391297374822742313e-0004L,
72	-3.12653708152290867248931925120380729518332507388e-0004L,
73	+2.36672170850409745237358105667757760527014332458e-0005L,
74};
75static const long double P2[] = {
76	+0.428486815855585429730209907810650135255270600668084114L,
77	+2.62768479103809762805691743305424077975230551176e-0001L,
78	+3.81187532685392297608310837995193946591425896150e-0002L,
79	+3.00063075891811043820666846129131255948527925381e-0003L,
80	+2.47315407812279164228398470797498649142513408654e-0003L,
81	+3.62838199917848372586173483147214880464782938664e-0004L,
82	+3.43991105975492623982725644046473030098172692423e-0006L,
83	+4.56902151569603272237014240794257659159045432895e-0006L,
84	+2.13734755837595695602045100675540011352948958453e-0007L,
85	+9.74123440547918230781670266967882492234877125358e-0009L,
86};
87static const long double Q2[] = {
88	+1.0L,
89	+9.18284118632506842664645516830761489700556179701e-0001L,
90	-6.41430858837830766045202076965923776189154874947e-0003L,
91	-1.24400885809771073213345747437964149775410921376e-0001L,
92	+4.69803798146251757538856567522481979624746875964e-0003L,
93	+7.18309447069495315914284705109868696262662082731e-0003L,
94	-8.75812626987894695112722600697653425786166399105e-0004L,
95	-1.23539972377769277995959339188431498626674835169e-0004L,
96	+3.10019017590151598732360097849672925448587547746e-0005L,
97	-1.77260223349332617658921874288026777465782364070e-0006L,
98};
99static const long double P3[] = {
100	+0.3824094797345675048502747661075355640070439388902L,
101	+3.42198093076618495415854906335908427159833377774e-0001L,
102	+9.63828189500585568303961406863153237440702754858e-0002L,
103	+8.76069421042696384852462044188520252156846768667e-0003L,
104	+1.86477890389161491224872014149309015261897537488e-0003L,
105	+8.16871354540309895879974742853701311541286944191e-0004L,
106	+6.83783483674600322518695090864659381650125625216e-0005L,
107	-1.10168269719261574708565935172719209272190828456e-0006L,
108	+9.66243228508380420159234853278906717065629721016e-0007L,
109	+2.31858885579177250541163820671121664974334728142e-0008L,
110};
111static const long double Q3[] = {
112	+1.0L,
113	+8.25479821168813634632437430090376252512793067339e-0001L,
114	-1.62251363073937769739639623669295110346015576320e-0002L,
115	-1.10621286905916732758745130629426559691187579852e-0001L,
116	+3.48309693970985612644446415789230015515365291459e-0003L,
117	+6.73553737487488333032431261131289672347043401328e-0003L,
118	-7.63222008393372630162743587811004613050245128051e-0004L,
119	-1.35792670669190631476784768961953711773073251336e-0004L,
120	+3.19610150954223587006220730065608156460205690618e-0005L,
121	-1.82096553862822346610109522015129585693354348322e-0006L,
122};
123
124static const long double
125#if defined(__x86)
126GZ1_h 	=  0.938204627909682449364570100414084663498215377L,
127GZ1_l   =  4.518346116624229420055327632718530617227944106e-20L,
128GZ2_h 	=  0.885603194410888700264725126309883762587560340L,
129GZ2_l   =  1.409077427270497062039119290776508217077297169e-20L,
130GZ3_h 	=  0.936781411463652321613537060640553022494714241L,
131GZ3_l   =  5.309836440284827247897772963887219035221996813e-21L,
132#else
133GZ1_h 	=  0.938204627909682449409753561580326910854647031L,
134GZ1_l   =  4.684412162199460089642452580902345976446297037e-35L,
135GZ2_h 	=  0.885603194410888700278815900582588658192658794L,
136GZ2_l   =  7.501529273890253789219935569758713534641074860e-35L,
137GZ3_h 	=  0.936781411463652321618846897080837818855399840L,
138GZ3_l   =  3.088721217404784363585591914529361687403776917e-35L,
139#endif
140TZ1	= -0.3517214357852935791015625L,
141TZ3	=  0.280530631542205810546875L;
142/* INDENT ON */
143
144/* INDENT OFF */
145/*
146 * compute gamma(y=yh+yl) for y in GT1 = [1.0000, 1.2845]
147 * ...assume yh got 53 or 24(i386) significant bits
148 */
149/* INDENT ON */
150static struct LDouble
151GT1(long double yh, long double yl) {
152	long double t3, t4, y;
153	int i;
154	struct LDouble r;
155
156	y = yh + yl;
157	for (t4 = Q1[8], t3 = P1[8] + y * P1[9], i = 7; i >= 0; i--) {
158		t4 = t4 * y + Q1[i];
159		t3 = t3 * y + P1[i];
160	}
161	t3 = (y * y) * t3 / t4;
162	t3 += (TZ1 * yl + GZ1_l);
163	t4 = TZ1 * yh;
164	r.h = CHOPPED((t4 + GZ1_h + t3));
165	t3 += (t4 - (r.h - GZ1_h));
166	r.l = t3;
167	return (r);
168}
169
170/* INDENT OFF */
171/*
172 * compute gamma(y=yh+yl) for y in GT2 = [1.2844, 1.6374]
173 * ...assume yh got 53 significant bits
174 */
175/* INDENT ON */
176static struct LDouble
177GT2(long double yh, long double yl) {
178	long double t3, t4, y;
179	int i;
180	struct LDouble r;
181
182	y = yh + yl;
183	for (t4 = Q2[9], t3 = P2[9], i = 8; i >= 0; i--) {
184		t4 = t4 * y + Q2[i];
185		t3 = t3 * y + P2[i];
186	}
187	t3 = GZ2_l + (y * y) * t3 / t4;
188	r.h = CHOPPED((GZ2_h + t3));
189	r.l = t3 - (r.h - GZ2_h);
190	return (r);
191}
192
193/* INDENT OFF */
194/*
195 * compute gamma(y=yh+yl) for y in GT3 = [1.6373, 2.0000]
196 * ...assume yh got 53 significant bits
197 */
198/* INDENT ON */
199static struct LDouble
200GT3(long double yh, long double yl) {
201	long double t3, t4, y;
202	int i;
203	struct LDouble r;
204
205	y = yh + yl;
206	for (t4 = Q3[9], t3 = P3[9], i = 8; i >= 0; i--) {
207		t4 = t4 * y + Q3[i];
208		t3 = t3 * y + P3[i];
209	}
210	t3 = (y * y) * t3 / t4;
211	t3 += (TZ3 * yl + GZ3_l);
212	t4 = TZ3 * yh;
213	r.h = CHOPPED((t4 + GZ3_h + t3));
214	t3 += (t4 - (r.h - GZ3_h));
215	r.l = t3;
216	return (r);
217}
218
219/* INDENT OFF */
220/* Hex value of GP[0] shoule be 3FB55555 55555555 */
221static const long double GP[] = {
222	+0.083333333333333333333333333333333172839171301L,
223	-2.77777777777777777777777777492501211999399424104e-0003L,
224	+7.93650793650793650793635650541638236350020883243e-0004L,
225	-5.95238095238095238057299772679324503339241961704e-0004L,
226	+8.41750841750841696138422987977683524926142600321e-0004L,
227	-1.91752691752686682825032547823699662178842123308e-0003L,
228	+6.41025641022403480921891559356473451161279359322e-0003L,
229	-2.95506535798414019189819587455577003732808185071e-0002L,
230	+1.79644367229970031486079180060923073476568732136e-0001L,
231	-1.39243086487274662174562872567057200255649290646e+0000L,
232	+1.34025874044417962188677816477842265259608269775e+0001L,
233	-1.56803713480127469414495545399982508700748274318e+0002L,
234	+2.18739841656201561694927630335099313968924493891e+0003L,
235	-3.55249848644100338419187038090925410976237921269e+0004L,
236	+6.43464880437835286216768959439484376449179576452e+0005L,
237	-1.20459154385577014992600342782821389605893904624e+0007L,
238	+2.09263249637351298563934942349749718491071093210e+0008L,
239	-2.96247483183169219343745316433899599834685703457e+0009L,
240	+2.88984933605896033154727626086506756972327292981e+0010L,
241	-1.40960434146030007732838382416230610302678063984e+0011L,	/* 19 */
242};
243
244static const long double T3[] = {
245	+0.666666666666666666666666666666666634567834260213L,	/* T3[0] */
246	+0.400000000000000000000000000040853636176634934140L,	/* T3[1] */
247	+0.285714285714285714285696975252753987869020263448L,	/* T3[2] */
248	+0.222222222222222225593221101192317258554772129875L,	/* T3[3] */
249	+0.181818181817850192105847183461778186703779262916L,	/* T3[4] */
250	+0.153846169861348633757101285952333369222567014596L,	/* T3[5] */
251	+0.133033462889260193922261296772841229985047571265L,	/* T3[6] */
252};
253
254static const long double c[] = {
2550.0L,
2561.0L,
2572.0L,
2580.5L,
2591.0e-4930L,							/* tiny */
2604.18937683105468750000e-01L,					/* hln2pim1_h */
2618.50099203991780329736405617639861397473637783412817152e-07L,	/* hln2pim1_l */
2620.418938533204672741780329736405617639861397473637783412817152L, /* hln2pim1 */
2632.16608493865351192653179168701171875e-02L,			/* ln2_32hi */
2645.96317165397058692545083025235937919875797669127130e-12L,	/* ln2_32lo */
26546.16624130844682903551758979206054839765267053289554989233L,	/* invln2_32 */
266#if defined(__x86)
2671.7555483429044629170023839037639845628291e+03L,		/* overflow */
268#else
2691.7555483429044629170038892160702032034177e+03L,		/* overflow */
270#endif
271};
272
273#define	zero		c[0]
274#define	one		c[1]
275#define	two		c[2]
276#define	half		c[3]
277#define	tiny		c[4]
278#define	hln2pim1_h	c[5]
279#define	hln2pim1_l	c[6]
280#define	hln2pim1	c[7]
281#define	ln2_32hi	c[8]
282#define	ln2_32lo	c[9]
283#define	invln2_32	c[10]
284#define	overflow	c[11]
285
286/*
287 * |exp(r) - (1+r+Et0*r^2+...+Et10*r^12)| <= 2^(-128.88) for |r|<=ln2/64
288 */
289static const long double Et[] = {
290	+5.0000000000000000000e-1L,
291	+1.66666666666666666666666666666828835166292152466e-0001L,
292	+4.16666666666666666666666666666693398646592712189e-0002L,
293	+8.33333333333333333333331748774512601775591115951e-0003L,
294	+1.38888888888888888888888845356011511394764753997e-0003L,
295	+1.98412698412698413237140350092993252684198882102e-0004L,
296	+2.48015873015873016080222025357442659895814371694e-0005L,
297	+2.75573192239028921114572986441972140933432317798e-0006L,
298	+2.75573192239448470555548102895526369739856219317e-0007L,
299	+2.50521677867683935940853997995937600214167232477e-0008L,
300	+2.08767928899010367374984448513685566514152147362e-0009L,
301};
302
303/*
304 * long double precision coefficients for computing log(x)-1 in tgamma.
305 *  See "algorithm" for details
306 *
307 *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
308 *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
309 *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
310 *       T2(j) = T2[2j,2j+1] = log(z[j]),
311 *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + T3[2]s^7 + ... + T3[6]s^15
312 *  Note
313 *  (1) the leading entries are truncated to 24 binary point.
314 *  (2) Remez error for T3(s) is bounded by 2**(-136.54)
315 */
316static const long double T1[] = {
317-1.000000000000000000000000000000000000000000e+00L,
318	+0.000000000000000000000000000000000000000000e+00L,
319-3.068528175354003906250000000000000000000000e-01L,
320-1.904654299957767878541823431924500011926579e-09L,
321	+3.862943053245544433593750000000000000000000e-01L,
322	+5.579533617547508924291635313615100141107647e-08L,
323	+1.079441487789154052734375000000000000000000e+00L,
324	+5.389068187551732136437452970422650211661470e-08L,
325	+1.772588670253753662109375000000000000000000e+00L,
326	+5.198602757555955348583270627230200282215294e-08L,
327	+2.465735852718353271484375000000000000000000e+00L,
328	+5.008137327560178560729088284037750352769117e-08L,
329	+3.158883035182952880859375000000000000000000e+00L,
330	+4.817671897564401772874905940845299849351090e-08L,
331	+3.852030217647552490234375000000000000000000e+00L,
332	+4.627206467568624985020723597652849919904913e-08L,
333	+4.545177400112152099609375000000000000000000e+00L,
334	+4.436741037572848197166541254460399990458737e-08L,
335	+5.238324582576751708984375000000000000000000e+00L,
336	+4.246275607577071409312358911267950061012560e-08L,
337	+5.931471765041351318359375000000000000000000e+00L,
338	+4.055810177581294621458176568075500131566384e-08L,
339};
340
341/*
342 * T2[2i,2i+1] = log(1+i/64+1/128)
343 */
344static const long double T2[] = {
345	+7.7821016311645507812500000000000000000000e-03L,
346	+3.8810890398166212900061136763678127453570e-08L,
347	+2.3167014122009277343750000000000000000000e-02L,
348	+4.5159525100885049160962289916579411752759e-08L,
349	+3.8318812847137451171875000000000000000000e-02L,
350	+5.1454999148021880325123797290345960518164e-08L,
351	+5.3244471549987792968750000000000000000000e-02L,
352	+4.2968824489897120193786528776939573415076e-08L,
353	+6.7950606346130371093750000000000000000000e-02L,
354	+5.5562377378300815277772629414034632394030e-08L,
355	+8.2443654537200927734375000000000000000000e-02L,
356	+1.4673873663533785068668307805914095366600e-08L,
357	+9.6729576587677001953125000000000000000000e-02L,
358	+4.9870874110342446056487463437015041543346e-08L,
359	+1.1081433296203613281250000000000000000000e-01L,
360	+3.3378253981382306169323211928098474801099e-08L,
361	+1.2470346689224243164062500000000000000000e-01L,
362	+1.1608714804222781515380863268491613205318e-08L,
363	+1.3840228319168090820312500000000000000000e-01L,
364	+3.9667438227482200873601649187393160823607e-08L,
365	+1.5191602706909179687500000000000000000000e-01L,
366	+1.4956750178196803424896884511327584958252e-08L,
367	+1.6524952650070190429687500000000000000000e-01L,
368	+4.6394605258578736449277240313729237989366e-08L,
369	+1.7840760946273803710937500000000000000000e-01L,
370	+4.8010080260010025241510941968354682199540e-08L,
371	+1.9139480590820312500000000000000000000000e-01L,
372	+4.7091426329609298807561308873447039132856e-08L,
373	+2.0421552658081054687500000000000000000000e-01L,
374	+1.4847880344628820386196239272213742113867e-08L,
375	+2.1687388420104980468750000000000000000000e-01L,
376	+5.4099564554931589525744347498478964801484e-08L,
377	+2.2937405109405517578125000000000000000000e-01L,
378	+4.9970790654210230725046139871550961365282e-08L,
379	+2.4171990156173706054687500000000000000000e-01L,
380	+3.5325408107597432515913513900103385655073e-08L,
381	+2.5391519069671630859375000000000000000000e-01L,
382	+1.9284247135543573297906606667466299224747e-08L,
383	+2.6596349477767944335937500000000000000000e-01L,
384	+5.3719458497979750926537543389268821141517e-08L,
385	+2.7786844968795776367187500000000000000000e-01L,
386	+1.3154985425144750329234012330820349974537e-09L,
387	+2.8963327407836914062500000000000000000000e-01L,
388	+1.8504673536253893055525668970003860369760e-08L,
389	+3.0126130580902099609375000000000000000000e-01L,
390	+2.4769140784919125538233755492657352680723e-08L,
391	+3.1275570392608642578125000000000000000000e-01L,
392	+6.0778104626049965596883190321597861455475e-09L,
393	+3.2411944866180419921875000000000000000000e-01L,
394	+1.9992407776871920760434987352182336158873e-08L,
395	+3.3535552024841308593750000000000000000000e-01L,
396	+2.1672724744319679579814166199074433006807e-08L,
397	+3.4646672010421752929687500000000000000000e-01L,
398	+4.7241991051621587188425772950711830538414e-08L,
399	+3.5745584964752197265625000000000000000000e-01L,
400	+3.9274281801569759490140904474434669956562e-08L,
401	+3.6832553148269653320312500000000000000000e-01L,
402	+2.9676011119845105154050398826897178765758e-08L,
403	+3.7907832860946655273437500000000000000000e-01L,
404	+2.4325502905656478345631019858881408009210e-08L,
405	+3.8971674442291259765625000000000000000000e-01L,
406	+6.7171126157142136040035208670510556529487e-09L,
407	+4.0024316310882568359375000000000000000000e-01L,
408	+1.0181870233355751019951311700799406124957e-09L,
409	+4.1065990924835205078125000000000000000000e-01L,
410	+1.5736916335153056203175822787661567534220e-08L,
411	+4.2096924781799316406250000000000000000000e-01L,
412	+4.6826136472066367161506795972449857268707e-08L,
413	+4.3117344379425048828125000000000000000000e-01L,
414	+2.1024120852577922478955594998480144051225e-08L,
415	+4.4127452373504638671875000000000000000000e-01L,
416	+3.7069828842770746441661301225362605528786e-08L,
417	+4.5127463340759277343750000000000000000000e-01L,
418	+1.0731865811707192383079012478685922879010e-08L,
419	+4.6117568016052246093750000000000000000000e-01L,
420	+3.4961647705430499925597855358603099030515e-08L,
421	+4.7097969055175781250000000000000000000000e-01L,
422	+2.4667033200046897856056359251373510964634e-08L,
423	+4.8068851232528686523437500000000000000000e-01L,
424	+1.7020465042442243455448011551208861216878e-08L,
425	+4.9030393362045288085937500000000000000000e-01L,
426	+5.4424740957290971159645746860530583309571e-08L,
427	+4.9982786178588867187500000000000000000000e-01L,
428	+7.7705606579463314152470441415126573566105e-09L,
429	+5.0926184654235839843750000000000000000000e-01L,
430	+5.5247449548366574919228323824878565745713e-08L,
431	+5.1860773563385009765625000000000000000000e-01L,
432	+2.8574195534496726996364798698556235730848e-08L,
433	+5.2786707878112792968750000000000000000000e-01L,
434	+1.0839714455426392217778300963558522088193e-08L,
435	+5.3704142570495605468750000000000000000000e-01L,
436	+4.0191927599879229244153832299023744345999e-08L,
437	+5.4613238573074340820312500000000000000000e-01L,
438	+5.1867392242179272209231209163864971792889e-08L,
439	+5.5514144897460937500000000000000000000000e-01L,
440	+5.8565892217715480359515904050170125743178e-08L,
441	+5.6407010555267333984375000000000000000000e-01L,
442	+3.2732129626227634290090190711817681692354e-08L,
443	+5.7291972637176513671875000000000000000000e-01L,
444	+2.7190020372374006726626261068626400393936e-08L,
445	+5.8169168233871459960937500000000000000000e-01L,
446	+5.7295907882911235753725372340709967597394e-08L,
447	+5.9038740396499633789062500000000000000000e-01L,
448	+4.2637180036751291708123598757577783615014e-08L,
449	+5.9900814294815063476562500000000000000000e-01L,
450	+4.6697932764615975024461651502060474048774e-08L,
451	+6.0755521059036254882812500000000000000000e-01L,
452	+3.9634179246672960152791125371893149820625e-08L,
453	+6.1602985858917236328125000000000000000000e-01L,
454	+1.8626341656366315928196700650292529688219e-08L,
455	+6.2443327903747558593750000000000000000000e-01L,
456	+8.9744179151050387440546731199093039879228e-09L,
457	+6.3276666402816772460937500000000000000000e-01L,
458	+5.5428701049364114685035797584887586099726e-09L,
459	+6.4103114604949951171875000000000000000000e-01L,
460	+3.3371431779336851334405392546708949047361e-08L,
461	+6.4922791719436645507812500000000000000000e-01L,
462	+2.9430743363812714969905311122271269100885e-08L,
463	+6.5735805034637451171875000000000000000000e-01L,
464	+2.2361985518423140023245936165514147093250e-08L,
465	+6.6542261838912963867187500000000000000000e-01L,
466	+1.4155960810278217610006660181148303091649e-08L,
467	+6.7342263460159301757812500000000000000000e-01L,
468	+4.0610573702719835388801017264750843477878e-08L,
469	+6.8135917186737060546875000000000000000000e-01L,
470	+5.2940532463479321559568089441735584156689e-08L,
471	+6.8923324346542358398437500000000000000000e-01L,
472	+3.7773385396340539337814603903232796216537e-08L,
473};
474
475/*
476 * S[j],S_trail[j] = 2**(j/32.) for the final computation of exp(t+w)
477 */
478static const long double S[] = {
479#if defined(__x86)
480	+1.0000000000000000000000000e+00L,
481	+1.0218971486541166782081522e+00L,
482	+1.0442737824274138402382006e+00L,
483	+1.0671404006768236181297224e+00L,
484	+1.0905077326652576591003302e+00L,
485	+1.1143867425958925362894369e+00L,
486	+1.1387886347566916536971221e+00L,
487	+1.1637248587775775137938619e+00L,
488	+1.1892071150027210666875674e+00L,
489	+1.2152473599804688780476325e+00L,
490	+1.2418578120734840485256747e+00L,
491	+1.2690509571917332224885722e+00L,
492	+1.2968395546510096659215822e+00L,
493	+1.3252366431597412945939118e+00L,
494	+1.3542555469368927282668852e+00L,
495	+1.3839098819638319548151403e+00L,
496	+1.4142135623730950487637881e+00L,
497	+1.4451808069770466200253470e+00L,
498	+1.4768261459394993113155431e+00L,
499	+1.5091644275934227397133885e+00L,
500	+1.5422108254079408235859630e+00L,
501	+1.5759808451078864864006862e+00L,
502	+1.6104903319492543080837174e+00L,
503	+1.6457554781539648445110730e+00L,
504	+1.6817928305074290860378350e+00L,
505	+1.7186192981224779156032914e+00L,
506	+1.7562521603732994831094730e+00L,
507	+1.7947090750031071864148413e+00L,
508	+1.8340080864093424633989166e+00L,
509	+1.8741676341102999013002103e+00L,
510	+1.9152065613971472938202589e+00L,
511	+1.9571441241754002689657438e+00L,
512#else
513	+1.00000000000000000000000000000000000e+00L,
514	+1.02189714865411667823448013478329942e+00L,
515	+1.04427378242741384032196647873992910e+00L,
516	+1.06714040067682361816952112099280918e+00L,
517	+1.09050773266525765920701065576070789e+00L,
518	+1.11438674259589253630881295691960313e+00L,
519	+1.13878863475669165370383028384151134e+00L,
520	+1.16372485877757751381357359909218536e+00L,
521	+1.18920711500272106671749997056047593e+00L,
522	+1.21524735998046887811652025133879836e+00L,
523	+1.24185781207348404859367746872659561e+00L,
524	+1.26905095719173322255441908103233805e+00L,
525	+1.29683955465100966593375411779245118e+00L,
526	+1.32523664315974129462953709549872168e+00L,
527	+1.35425554693689272829801474014070273e+00L,
528	+1.38390988196383195487265952726519287e+00L,
529	+1.41421356237309504880168872420969798e+00L,
530	+1.44518080697704662003700624147167095e+00L,
531	+1.47682614593949931138690748037404985e+00L,
532	+1.50916442759342273976601955103319352e+00L,
533	+1.54221082540794082361229186209073479e+00L,
534	+1.57598084510788648645527016018190504e+00L,
535	+1.61049033194925430817952066735740067e+00L,
536	+1.64575547815396484451875672472582254e+00L,
537	+1.68179283050742908606225095246642969e+00L,
538	+1.71861929812247791562934437645631244e+00L,
539	+1.75625216037329948311216061937531314e+00L,
540	+1.79470907500310718642770324212778174e+00L,
541	+1.83400808640934246348708318958828892e+00L,
542	+1.87416763411029990132999894995444645e+00L,
543	+1.91520656139714729387261127029583086e+00L,
544	+1.95714412417540026901832225162687149e+00L,
545#endif
546};
547static const long double S_trail[] = {
548#if defined(__x86)
549	+0.0000000000000000000000000e+00L,
550	+2.6327965667180882569382524e-20L,
551	+8.3765863521895191129661899e-20L,
552	+3.9798705777454504249209575e-20L,
553	+1.0668046596651558640993042e-19L,
554	+1.9376009847285360448117114e-20L,
555	+6.7081819456112953751277576e-21L,
556	+1.9711680502629186462729727e-20L,
557	+2.9932584438449523689104569e-20L,
558	+6.8887754153039109411061914e-20L,
559	+6.8002718741225378942847820e-20L,
560	+6.5846917376975403439742349e-20L,
561	+1.2171958727511372194876001e-20L,
562	+3.5625253228704087115438260e-20L,
563	+3.1129551559077560956309179e-20L,
564	+5.7519192396164779846216492e-20L,
565	+3.7900651177865141593101239e-20L,
566	+1.1659262405698741798080115e-20L,
567	+7.1364385105284695967172478e-20L,
568	+5.2631003710812203588788949e-20L,
569	+2.6328853788732632868460580e-20L,
570	+5.4583950085438242788190141e-20L,
571	+9.5803254376938269960718656e-20L,
572	+7.6837733983874245823512279e-21L,
573	+2.4415965910835093824202087e-20L,
574	+2.6052966871016580981769728e-20L,
575	+2.6876456344632553875309579e-21L,
576	+1.2861930155613700201703279e-20L,
577	+8.8166633394037485606572294e-20L,
578	+2.9788615389580190940837037e-20L,
579	+5.2352341619805098677422139e-20L,
580	+5.2578463064010463732242363e-20L,
581#else
582	+0.00000000000000000000000000000000000e+00L,
583	+1.80506787420330954745573333054573786e-35L,
584-9.37452029228042742195756741973083214e-35L,
585-1.59696844729275877071290963023149997e-35L,
586	+9.11249341012502297851168610167248666e-35L,
587-6.50422820697854828723037477525938871e-35L,
588-8.14846884452585113732569176748815532e-35L,
589-5.06621457672180031337233074514290335e-35L,
590-1.35983097468881697374987563824591912e-35L,
591	+9.49742763556319647030771056643324660e-35L,
592-3.28317052317699860161506596533391526e-36L,
593-5.01723570938719041029018653045842895e-35L,
594-2.39147479768910917162283430160264014e-35L,
595-8.35057135763390881529889073794408385e-36L,
596	+7.03675688907326504242173719067187644e-35L,
597-5.18248485306464645753689301856695619e-35L,
598	+9.42224254862183206569211673639406488e-35L,
599-3.96750082539886230916730613021641828e-35L,
600	+7.14352899156330061452327361509276724e-35L,
601	+1.15987125286798512424651783410044433e-35L,
602	+4.69693347835811549530973921320187447e-35L,
603-3.38651317599500471079924198499981917e-35L,
604-8.58731877429824706886865593510387445e-35L,
605-9.60595154874935050318549936224606909e-35L,
606	+9.60973393212801278450755869714178581e-35L,
607	+6.37839792144002843924476144978084855e-35L,
608	+7.79243078569586424945646112516927770e-35L,
609	+7.36133776758845652413193083663393220e-35L,
610-6.47299514791334723003521457561217053e-35L,
611	+8.58747441795369869427879806229522962e-35L,
612	+2.37181542282517483569165122830269098e-35L,
613-3.02689168209611877300459737342190031e-37L,
614#endif
615};
616/* INDENT ON */
617
618/* INDENT OFF */
619/*
620 * return tgamma(x) scaled by 2**-m for 8<x<=171.62... using Stirling's formula
621 *     log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + (1/x)*P(1/(x*x))
622 *                = L1 + L2 + L3,
623 */
624/* INDENT ON */
625static struct LDouble
626large_gam(long double x, int *m) {
627	long double z, t1, t2, t3, z2, t5, w, y, u, r, v;
628	long double t24 = 16777216.0L, p24 = 1.0L / 16777216.0L;
629	int n2, j2, k, ix, j, i;
630	struct LDouble zz;
631	long double u2, ss_h, ss_l, r_h, w_h, w_l, t4;
632
633/* INDENT OFF */
634/*
635 * compute ss = ss.h+ss.l = log(x)-1 (see tgamma_log.h for details)
636 *
637 *  log(x) - 1 = T1(n) + T2(j) + T3(s), where x = 2**n * y,  1<=y<2,
638 *  j=[64*y], z[j]=1+j/64+1/128, s = (y-z[j])/(y+z[j]), and
639 *       T1(n) = T1[2n,2n+1] = n*log(2)-1,
640 *       T2(j) = T2[2j,2j+1] = log(z[j]),
641 *       T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + ... + T3[6]s^15
642 *  Note
643 *  (1) the leading entries are truncated to 24 binary point.
644 *  (2) Remez error for T3(s) is bounded by 2**(-72.4)
645 *                                   2**(-24)
646 *                           _________V___________________
647 *               T1(n):     |_________|___________________|
648 *                             _______ ______________________
649 *               T2(j):       |_______|______________________|
650 *                                ____ _______________________
651 *               2s:             |____|_______________________|
652 *                                    __________________________
653 *          +    T3(s)-2s:           |__________________________|
654 *                       -------------------------------------------
655 *                          [leading] + [Trailing]
656 */
657	/* INDENT ON */
658	ix = H0_WORD(x);
659	n2 = (ix >> 16) - 0x3fff;	/* exponent of x, range:3-10 */
660	y = scalbnl(x, -n2);	/* y = scale x to [1,2] */
661	n2 += n2;		/* 2n */
662	j = (ix >> 10) & 0x3f;	/* j */
663	z = 1.0078125L + (long double) j * 0.015625L;	/* z[j]=1+j/64+1/128 */
664	j2 = j + j;
665	t1 = y + z;
666	t2 = y - z;
667	r = one / t1;
668	u = r * t2;		/* u = (y-z)/(y+z) */
669	t1 = CHOPPED(t1);
670	t4 = T2[j2 + 1] + T1[n2 + 1];
671	z2 = u * u;
672	k = H0_WORD(u) & 0x7fffffff;
673	t3 = T2[j2] + T1[n2];
674	for (t5 = T3[6], i = 5; i >= 0; i--)
675		t5 = z2 * t5 + T3[i];
676	if ((k >> 16) < 0x3fec) {	/* |u|<2**-19 */
677		t2 = t4 + u * (two + z2 * t5);
678	} else {
679		t5 = t4 + (u * z2) * t5;
680		u2 = u + u;
681		v = (long double) ((int) (u2 * t24)) * p24;
682		t2 = t5 + r * ((two * t2 - v * t1) - v * (y - (t1 - z)));
683		t3 += v;
684	}
685	ss_h = CHOPPED((t2 + t3));
686	ss_l = t2 - (ss_h - t3);
687/* INDENT OFF */
688/*
689 * compute ww = (x-.5)*(log(x)-1) + .5*(log(2pi)-1) + 1/x*(P(1/x^2)))
690 * where ss = log(x) - 1 in already in extra precision
691 */
692	/* INDENT ON */
693	z = one / x;
694	r = x - half;
695	r_h = CHOPPED((r));
696	w_h = r_h * ss_h + hln2pim1_h;
697	z2 = z * z;
698	w = (r - r_h) * ss_h + r * ss_l;
699	t1 = GP[19];
700	for (i = 18; i > 0; i--)
701		t1 = z2 * t1 + GP[i];
702	w += hln2pim1_l;
703	w_l = z * (GP[0] + z2 * t1) + w;
704	k = (int) ((w_h + w_l) * invln2_32 + half);
705
706	/* compute the exponential of w_h+w_l */
707
708	j = k & 0x1f;
709	*m = k >> 5;
710	t3 = (long double) k;
711
712	/* perform w - k*ln2_32 (represent as w_h - w_l) */
713	t1 = w_h - t3 * ln2_32hi;
714	t2 = t3 * ln2_32lo;
715	w = t2 - w_l;
716	w_h = t1 - w;
717	w_l = w - (t1 - w_h);
718
719	/* compute exp(w_h-w_l) */
720	z = w_h - w_l;
721	for (t1 = Et[10], i = 9; i >= 0; i--)
722		t1 = z * t1 + Et[i];
723	t3 = w_h - (w_l - (z * z) * t1);	/* t3 = expm1(z) */
724	zz.l = S_trail[j] * (one + t3) + S[j] * t3;
725	zz.h = S[j];
726	return (zz);
727}
728
729/* INDENT OFF */
730/*
731 * kpsin(x)= sin(pi*x)/pi
732 *	           3        5        7        9        11                27
733 *	= x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x +ks[4]*x  + ... + ks[12]*x
734 */
735static const long double ks[] = {
736	-1.64493406684822643647241516664602518705158902870e+0000L,
737	+8.11742425283353643637002772405874238094995726160e-0001L,
738	-1.90751824122084213696472111835337366232282723933e-0001L,
739	+2.61478478176548005046532613563241288115395517084e-0002L,
740	-2.34608103545582363750893072647117829448016479971e-0003L,
741	+1.48428793031071003684606647212534027556262040158e-0004L,
742	-6.97587366165638046518462722252768122615952898698e-0006L,
743	+2.53121740413702536928659271747187500934840057929e-0007L,
744	-7.30471182221385990397683641695766121301933621956e-0009L,
745	+1.71653847451163495739958249695549313987973589884e-0010L,
746	-3.34813314714560776122245796929054813458341420565e-0012L,
747	+5.50724992262622033449487808306969135431411753047e-0014L,
748	-7.67678132753577998601234393215802221104236979928e-0016L,
749};
750/* INDENT ON */
751
752/*
753 * assume x is not tiny and positive
754 */
755static struct LDouble
756kpsin(long double x) {
757	long double z, t1, t2;
758	struct LDouble xx;
759	int i;
760
761	z = x * x;
762	xx.h = x;
763	for (t2 = ks[12], i = 11; i > 0; i--)
764		t2 = z * t2 + ks[i];
765	t1 = z * x;
766	t2 *= z * t1;
767	xx.l = t1 * ks[0] + t2;
768	return (xx);
769}
770
771/* INDENT OFF */
772/*
773 * kpcos(x)= cos(pi*x)/pi
774 *                     2        4        6        8        10        12
775 *	= 1/pi +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x +kc[4]*x  +kc[5]*x
776 *
777 *                     2        4        6        8        10            22
778 *	= 1/pi - pi/2*x +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x  +...+kc[9]*x
779 *
780 * -pi/2*x*x = (npi_2_h + npi_2_l) * (x_f+x_l)*(x_f+x_l)
781 *	   =  npi_2_h*(x_f+x_l)*(x_f+x_l) + npi_2_l*x*x
782 *	   =  npi_2_h*x_f*x_f + npi_2_h*(x*x-x_f*x_f) + npi_2_l*x*x
783 *	   =  npi_2_h*x_f*x_f + npi_2_h*(x+x_f)*(x-x_f) + npi_2_l*x*x
784 * Here x_f = (long double) (float)x
785 * Note that pi/2(in hex) =
786 *  1.921FB54442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29
787 * npi_2_h = -pi/2 chopped to 25 bits = -1.921FB50000000000000000000000000 =
788 *  -1.570796310901641845703125000000000 and
789 * npi_2_l =
790 *  -0.0000004442D18469898CC51701B839A252049C1114CF98E804177D4C76273644A29 =
791 *  -.0000000158932547735281966916397514420985846996875529104874722961539 =
792 *  -1.5893254773528196691639751442098584699687552910487472296153e-8
793 * 1/pi(in hex) =
794 *  .517CC1B727220A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
795 * will be splitted into:
796 *  one_pi_h = 1/pi chopped to 48 bits = .517CC1B727220000000000...  and
797 *  one_pi_l = .0000000000000A94FE13ABE8FA9A6EE06DB14ACC9E21C820FF28B1D5EF5DE2B
798 */
799
800static const long double
801#if defined(__x86)
802one_pi_h = 0.3183098861481994390487670898437500L,	/* 31 bits */
803one_pi_l = 3.559123248900043690127872406891929148e-11L,
804#else
805one_pi_h = 0.31830988618379052468299050815403461456298828125L,
806one_pi_l = 1.46854777018590994109505931010230912897495334688117e-16L,
807#endif
808npi_2_h = -1.570796310901641845703125000000000L,
809npi_2_l = -1.5893254773528196691639751442098584699687552910e-8L;
810
811static const long double kc[] = {
812	+1.29192819501249250731151312779548918765320728489e+0000L,
813	-4.25027339979557573976029596929319207009444090366e-0001L,
814	+7.49080661650990096109672954618317623888421628613e-0002L,
815	-8.21458866111282287985539464173976555436050215120e-0003L,
816	+6.14202578809529228503205255165761204750211603402e-0004L,
817	-3.33073432691149607007217330302595267179545908740e-0005L,
818	+1.36970959047832085796809745461530865597993680204e-0006L,
819	-4.41780774262583514450246512727201806217271097336e-0008L,
820	+1.14741409212381858820016567664488123478660705759e-0009L,
821	-2.44261236114707374558437500654381006300502749632e-0011L,
822};
823/* INDENT ON */
824
825/*
826 * assume x is not tiny and positive
827 */
828static struct LDouble
829kpcos(long double x) {
830	long double z, t1, t2, t3, t4, x4, x8;
831	int i;
832	struct LDouble xx;
833
834	z = x * x;
835	xx.h = one_pi_h;
836	t1 = (long double) ((float) x);
837	x4 = z * z;
838	t2 = npi_2_l * z + npi_2_h * (x + t1) * (x - t1);
839	for (i = 8, t3 = kc[9]; i >= 0; i--)
840		t3 = z * t3 + kc[i];
841	t3 = one_pi_l + x4 * t3;
842	t4 = t1 * t1 * npi_2_h;
843	x8 = t2 + t3;
844	xx.l = x8 + t4;
845	return (xx);
846}
847
848/* INDENT OFF */
849static const long double
850	/* 0.13486180573279076968979393577465291700642511139552429398233 */
851#if defined(__x86)
852t0z1   =  0.1348618057327907696779385054997035808810L,
853t0z1_l =  1.1855430274949336125392717150257379614654e-20L,
854#else
855t0z1   =  0.1348618057327907696897939357746529168654L,
856t0z1_l =  1.4102088588676879418739164486159514674310e-37L,
857#endif
858	/* 0.46163214496836234126265954232572132846819620400644635129599 */
859#if defined(__x86)
860t0z2   =  0.4616321449683623412538115843295472018326L,
861t0z2_l =  8.84795799617412663558532305039261747030640e-21L,
862#else
863t0z2   =  0.46163214496836234126265954232572132343318L,
864t0z2_l =  5.03501162329616380465302666480916271611101e-36L,
865#endif
866	/* 0.81977310110050060178786870492160699631174407846245179119586 */
867#if defined(__x86)
868t0z3   =  0.81977310110050060178773362329351925836817L,
869t0z3_l =  1.350816280877379435658077052534574556256230e-22L
870#else
871t0z3   =  0.8197731011005006017878687049216069516957449L,
872t0z3_l =  4.461599916947014419045492615933551648857380e-35L
873#endif
874;
875/* INDENT ON */
876
877/*
878 * gamma(x+i) for 0 <= x < 1
879 */
880static struct LDouble
881gam_n(int i, long double x) {
882	struct LDouble rr = {0.0L, 0.0L}, yy;
883	long double r1, r2, t2, z, xh, xl, yh, yl, zh, z1, z2, zl, x5, wh, wl;
884
885	/* compute yy = gamma(x+1) */
886	if (x > 0.2845L) {
887		if (x > 0.6374L) {
888			r1 = x - t0z3;
889			r2 = CHOPPED((r1 - t0z3_l));
890			t2 = r1 - r2;
891			yy = GT3(r2, t2 - t0z3_l);
892		} else {
893			r1 = x - t0z2;
894			r2 = CHOPPED((r1 - t0z2_l));
895			t2 = r1 - r2;
896			yy = GT2(r2, t2 - t0z2_l);
897		}
898	} else {
899		r1 = x - t0z1;
900		r2 = CHOPPED((r1 - t0z1_l));
901		t2 = r1 - r2;
902		yy = GT1(r2, t2 - t0z1_l);
903	}
904	/* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */
905	switch (i) {
906	case 0:		/* yy/x */
907		r1 = one / x;
908		xh = CHOPPED((x));	/* x is not tiny */
909		rr.h = CHOPPED(((yy.h + yy.l) * r1));
910		rr.l = r1 * (yy.h - rr.h * xh) - ((r1 * rr.h) * (x - xh) -
911			r1 * yy.l);
912		break;
913	case 1:		/* yy */
914		rr.h = yy.h;
915		rr.l = yy.l;
916		break;
917	case 2:		/* (x+1)*yy */
918		z = x + one;	/* may not be exact */
919		zh = CHOPPED((z));
920		rr.h = zh * yy.h;
921		rr.l = z * yy.l + (x - (zh - one)) * yy.h;
922		break;
923	case 3:		/* (x+2)*(x+1)*yy */
924		z1 = x + one;
925		z2 = x + 2.0L;
926		z = z1 * z2;
927		xh = CHOPPED((z));
928		zh = CHOPPED((z1));
929		xl = (x - (zh - one)) * (z2 + zh) - (xh - zh * (zh + one));
930
931		rr.h = xh * yy.h;
932		rr.l = z * yy.l + xl * yy.h;
933		break;
934
935	case 4:		/* (x+1)*(x+3)*(x+2)*yy */
936		z1 = x + 2.0L;
937		z2 = (x + one) * (x + 3.0L);
938		zh = CHOPPED(z1);
939		zl = x - (zh - 2.0L);
940		xh = CHOPPED(z2);
941		xl = zl * (zh + z1) - (xh - (zh * zh - one));
942
943		/* wh+wl=(x+2)*yy */
944		wh = CHOPPED((z1 * (yy.h + yy.l)));
945		wl = (zl * yy.h + z1 * yy.l) - (wh - zh * yy.h);
946
947		rr.h = xh * wh;
948		rr.l = z2 * wl + xl * wh;
949
950		break;
951	case 5:		/* ((x+1)*(x+4)*(x+2)*(x+3))*yy */
952		z1 = x + 2.0L;
953		z2 = x + 3.0L;
954		z = z1 * z2;
955		zh = CHOPPED((z1));
956		yh = CHOPPED((z));
957		yl = (x - (zh - 2.0L)) * (z2 + zh) - (yh - zh * (zh + one));
958		z2 = z - 2.0L;
959		z *= z2;
960		xh = CHOPPED((z));
961		xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
962		rr.h = xh * yy.h;
963		rr.l = z * yy.l + xl * yy.h;
964		break;
965	case 6:		/* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5))*yy */
966		z1 = x + 2.0L;
967		z2 = x + 3.0L;
968		z = z1 * z2;
969		zh = CHOPPED((z1));
970		yh = CHOPPED((z));
971		z1 = x - (zh - 2.0L);
972		yl = z1 * (z2 + zh) - (yh - zh * (zh + one));
973		z2 = z - 2.0L;
974		x5 = x + 5.0L;
975		z *= z2;
976		xh = CHOPPED(z);
977		zh += 3.0;
978		xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
979						/* xh+xl=(x+1)*...*(x+4) */
980		/* wh+wl=(x+5)*yy */
981		wh = CHOPPED((x5 * (yy.h + yy.l)));
982		wl = (z1 * yy.h + x5 * yy.l) - (wh - zh * yy.h);
983		rr.h = wh * xh;
984		rr.l = z * wl + xl * wh;
985		break;
986	case 7:		/* ((x+1)*(x+2)*(x+3)*(x+4)*(x+5)*(x+6))*yy */
987		z1 = x + 3.0L;
988		z2 = x + 4.0L;
989		z = z2 * z1;
990		zh = CHOPPED((z1));
991		yh = CHOPPED((z));	/* yh+yl = (x+3)(x+4) */
992		yl = (x - (zh - 3.0L)) * (z2 + zh) - (yh - (zh * (zh + one)));
993		z1 = x + 6.0L;
994		z2 = z - 2.0L;	/* z2 = (x+2)*(x+5) */
995		z *= z2;
996		xh = CHOPPED((z));
997		xl = yl * (z2 + yh) - (xh - yh * (yh - 2.0L));
998						/* xh+xl=(x+2)*...*(x+5) */
999		/* wh+wl=(x+1)(x+6)*yy */
1000		z2 -= 4.0L;	/* z2 = (x+1)(x+6) */
1001		wh = CHOPPED((z2 * (yy.h + yy.l)));
1002		wl = (z2 * yy.l + yl * yy.h) - (wh - (yh - 6.0L) * yy.h);
1003		rr.h = wh * xh;
1004		rr.l = z * wl + xl * wh;
1005	}
1006	return (rr);
1007}
1008
1009long double
1010tgammal(long double x) {
1011	struct LDouble ss, ww;
1012	long double t, t1, t2, t3, t4, t5, w, y, z, z1, z2, z3, z5;
1013	int i, j, m, ix, hx, xk;
1014	unsigned lx;
1015
1016	hx = H0_WORD(x);
1017	lx = H3_WORD(x);
1018	ix = hx & 0x7fffffff;
1019	y = x;
1020	if (ix < 0x3f8e0000) {	/* x < 2**-113 */
1021		return (one / x);
1022	}
1023	if (ix >= 0x7fff0000)
1024		return (x * ((hx < 0)? zero : x));	/* Inf or NaN */
1025	if (x > overflow)	/* overflow threshold */
1026		return (x * 1.0e4932L);
1027	if (hx >= 0x40020000) {	/* x >= 8 */
1028		ww = large_gam(x, &m);
1029		w = ww.h + ww.l;
1030		return (scalbnl(w, m));
1031	}
1032
1033	if (hx > 0) {		/* 0 < x < 8 */
1034		i = (int) x;
1035		ww = gam_n(i, x - (long double) i);
1036		return (ww.h + ww.l);
1037	}
1038	/* INDENT OFF */
1039	/* negative x */
1040	/*
1041	 * compute xk =
1042	 *	-2 ... x is an even int (-inf is considered an even #)
1043	 *	-1 ... x is an odd int
1044	 *	+0 ... x is not an int but chopped to an even int
1045	 *	+1 ... x is not an int but chopped to an odd int
1046	 */
1047	/* INDENT ON */
1048	xk = 0;
1049#if defined(__x86)
1050	if (ix >= 0x403e0000) {	/* x >= 2**63 } */
1051		if (ix >= 0x403f0000)
1052			xk = -2;
1053		else
1054			xk = -2 + (lx & 1);
1055#else
1056	if (ix >= 0x406f0000) {	/* x >= 2**112 */
1057		if (ix >= 0x40700000)
1058			xk = -2;
1059		else
1060			xk = -2 + (lx & 1);
1061#endif
1062	} else if (ix >= 0x3fff0000) {
1063		w = -x;
1064		t1 = floorl(w);
1065		t2 = t1 * half;
1066		t3 = floorl(t2);
1067		if (t1 == w) {
1068			if (t2 == t3)
1069				xk = -2;
1070			else
1071				xk = -1;
1072		} else {
1073			if (t2 == t3)
1074				xk = 0;
1075			else
1076				xk = 1;
1077		}
1078	}
1079
1080	if (xk < 0) {
1081		/* return NaN. Ideally gamma(-n)= (-1)**(n+1) * inf */
1082		return (x - x) / (x - x);
1083	}
1084
1085	/*
1086	 * negative underflow thresold -(1774+9ulp)
1087	 */
1088	if (x < -1774.0000000000000000000000000000017749370L) {
1089		z = tiny / x;
1090		if (xk == 1)
1091			z = -z;
1092		return (z * tiny);
1093	}
1094
1095	/* INDENT OFF */
1096	/*
1097	 * now compute gamma(x) by  -1/((sin(pi*y)/pi)*gamma(1+y)), y = -x
1098	 */
1099	/*
1100	 * First compute ss = -sin(pi*y)/pi so that
1101	 * gamma(x) = 1/(ss*gamma(1+y))
1102	 */
1103	/* INDENT ON */
1104	y = -x;
1105	j = (int) y;
1106	z = y - (long double) j;
1107	if (z > 0.3183098861837906715377675L)
1108		if (z > 0.6816901138162093284622325L)
1109			ss = kpsin(one - z);
1110		else
1111			ss = kpcos(0.5L - z);
1112	else
1113		ss = kpsin(z);
1114	if (xk == 0) {
1115		ss.h = -ss.h;
1116		ss.l = -ss.l;
1117	}
1118
1119	/* Then compute ww = gamma(1+y), note that result scale to 2**m */
1120	m = 0;
1121	if (j < 7) {
1122		ww = gam_n(j + 1, z);
1123	} else {
1124		w = y + one;
1125		if ((lx & 1) == 0) {	/* y+1 exact (note that y<184) */
1126			ww = large_gam(w, &m);
1127		} else {
1128			t = w - one;
1129			if (t == y) {	/* y+one exact */
1130				ww = large_gam(w, &m);
1131			} else {	/* use y*gamma(y) */
1132				if (j == 7)
1133					ww = gam_n(j, z);
1134				else
1135					ww = large_gam(y, &m);
1136				t4 = ww.h + ww.l;
1137				t1 = CHOPPED((y));
1138				t2 = CHOPPED((t4));
1139						/* t4 will not be too large */
1140				ww.l = y * (ww.l - (t2 - ww.h)) + (y - t1) * t2;
1141				ww.h = t1 * t2;
1142			}
1143		}
1144	}
1145
1146	/* compute 1/(ss*ww) */
1147	t3 = ss.h + ss.l;
1148	t4 = ww.h + ww.l;
1149	t1 = CHOPPED((t3));
1150	t2 = CHOPPED((t4));
1151	z1 = ss.l - (t1 - ss.h);	/* (t1,z1) = ss */
1152	z2 = ww.l - (t2 - ww.h);	/* (t2,z2) = ww */
1153	t3 = t3 * t4;			/* t3 = ss*ww */
1154	z3 = one / t3;			/* z3 = 1/(ss*ww) */
1155	t5 = t1 * t2;
1156	z5 = z1 * t4 + t1 * z2;		/* (t5,z5) = ss*ww */
1157	t1 = CHOPPED((t3));		/* (t1,z1) = ss*ww */
1158	z1 = z5 - (t1 - t5);
1159	t2 = CHOPPED((z3));		/* leading 1/(ss*ww) */
1160	z2 = z3 * (t2 * z1 - (one - t2 * t1));
1161	z = t2 - z2;
1162
1163	return (scalbnl(z, -m));
1164}
1165