34 piu = LD80C(0xc90fdaa22168c235, 1,  3.14159265358979323851e+00L);
35 #define	pi	(piu.e)
37  * Domain y in [0x1p-70, 0.27], range ~[-4.5264e-22, 4.5264e-22]:
38  * |(lgamma(2 - y) + y / 2) / y - a(y)| < 2**-70.9
41 a0u = LD80C(0x9e233f1bed863d26, -4,  7.72156649015328606028e-02L),
42 a1u = LD80C(0xa51a6625307d3249, -2,  3.22467033424113218889e-01L),
43 a2u = LD80C(0x89f000d2abafda8c, -4,  6.73523010531979398946e-02L),
44 a3u = LD80C(0xa8991563eca75f26, -6,  2.05808084277991211934e-02L),
45 a4u = LD80C(0xf2027e10634ce6b6, -8,  7.38555102796070454026e-03L),
46 a5u = LD80C(0xbd6eb76dd22187f4, -9,  2.89051035162703932972e-03L),
47 a6u = LD80C(0x9c562ab05e0458ed, -10,  1.19275351624639999297e-03L),
48 a7u = LD80C(0x859baed93ee48e46, -11,  5.09674593842117925320e-04L),
49 a8u = LD80C(0xe9f28a4432949af2, -13,  2.23109648015769155122e-04L),
50 a9u = LD80C(0xd12ad0d9b93c6bb0, -14,  9.97387167479808509830e-05L),
51 a10u= LD80C(0xb7522643c78a219b, -15,  4.37071076331030136818e-05L),
52 a11u= LD80C(0xca024dcdece2cb79, -16,  2.40813493372040143061e-05L),
53 a12u= LD80C(0xbb90fb6968ebdbf9, -19,  2.79495621083634031729e-06L),
54 a13u= LD80C(0xba1c9ffeeae07b37, -17,  1.10931287015513924136e-05L);
55 #define	a0	(a0u.e)
56 #define	a1	(a1u.e)
57 #define	a2	(a2u.e)
58 #define	a3	(a3u.e)
59 #define	a4	(a4u.e)
60 #define	a5	(a5u.e)
61 #define	a6	(a6u.e)
62 #define	a7	(a7u.e)
63 #define	a8	(a8u.e)
64 #define	a9	(a9u.e)
65 #define	a10	(a10u.e)
66 #define	a11	(a11u.e)
67 #define	a12	(a12u.e)
68 #define	a13	(a13u.e)
70  * Domain x in [tc-0.24, tc+0.28], range ~[-6.1205e-22, 6.1205e-22]:
71  * |(lgamma(x) - tf) -  t(x - tc)| < 2**-70.5
74 tcu  = LD80C(0xbb16c31ab5f1fb71, 0,  1.46163214496836234128e+00L),
75 tfu  = LD80C(0xf8cdcde61c520e0f, -4, -1.21486290535849608093e-01L),
76 ttu  = LD80C(0xd46ee54b27d4de99, -69, -2.81152980996018785880e-21L),
77 t0u  = LD80C(0x80b9406556a62a6b, -68,  3.40728634996055147231e-21L),
78 t1u  = LD80C(0xc7e9c6f6df3f8c39, -67, -1.05833162742737073665e-20L),
79 t2u  = LD80C(0xf7b95e4771c55d51, -2,  4.83836122723810583532e-01L),
80 t3u  = LD80C(0x97213c6e35e119ff, -3, -1.47587722994530691476e-01L),
81 t4u  = LD80C(0x845a14a6a81dc94b, -4,  6.46249402389135358063e-02L),
82 t5u  = LD80C(0x864d46fa89997796, -5, -3.27885410884846056084e-02L),
83 t6u  = LD80C(0x93373cbd00297438, -6,  1.79706751150707171293e-02L),
84 t7u  = LD80C(0xa8fcfca7eddc8d1d, -7, -1.03142230361450732547e-02L),
85 t8u  = LD80C(0xc7e7015ff4bc45af, -8,  6.10053603296546099193e-03L),
86 t9u  = LD80C(0xf178d2247adc5093, -9, -3.68456964904901200152e-03L),
87 t10u = LD80C(0x94188d58f12e5e9f, -9,  2.25976420273774583089e-03L),
88 t11u = LD80C(0xb7cbaef14e1406f1, -10, -1.40224943666225639823e-03L),
89 t12u = LD80C(0xe63a671e6704ea4d, -11,  8.78250640744776944887e-04L),
90 t13u = LD80C(0x914b6c9cae61783e, -11, -5.54255012657716808811e-04L),
91 t14u = LD80C(0xb858f5bdb79276fe, -12,  3.51614951536825927370e-04L),
92 t15u = LD80C(0xea73e744c34b9591, -13, -2.23591563824520112236e-04L),
93 t16u = LD80C(0x99aeabb0d67ba835, -13,  1.46562869351659194136e-04L),
94 t17u = LD80C(0xd7c6938325db2024, -14, -1.02889866046435680588e-04L),
95 t18u = LD80C(0xe24cb1e3b0474775, -15,  5.39540265505221957652e-05L);
96 #define	tc	(tcu.e)
97 #define	tf	(tfu.e)
98 #define	tt	(ttu.e)
99 #define	t0	(t0u.e)
100 #define	t1	(t1u.e)
101 #define	t2	(t2u.e)
102 #define	t3	(t3u.e)
103 #define	t4	(t4u.e)
104 #define	t5	(t5u.e)
105 #define	t6	(t6u.e)
106 #define	t7	(t7u.e)
107 #define	t8	(t8u.e)
108 #define	t9	(t9u.e)
109 #define	t10	(t10u.e)
110 #define	t11	(t11u.e)
111 #define	t12	(t12u.e)
112 #define	t13	(t13u.e)
113 #define	t14	(t14u.e)
114 #define	t15	(t15u.e)
115 #define	t16	(t16u.e)
116 #define	t17	(t17u.e)
117 #define	t18	(t18u.e)
119  * Domain y in [-0.1, 0.232], range ~[-8.1938e-22, 8.3815e-22]:
120  * |(lgamma(1 + y) + 0.5 * y) / y - u(y) / v(y)| < 2**-71.2
123 u0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L),
124 u1u = LD80C(0x98280ee45e4ddd3d, -1,  5.94361239198682739769e-01L),
125 u2u = LD80C(0xe330c8ead4130733, 0,  1.77492629495841234275e+00L),
126 u3u = LD80C(0xd4a213f1a002ec52, 0,  1.66119622514818078064e+00L),
127 u4u = LD80C(0xa5a9ca6f5bc62163, -1,  6.47122051417476492989e-01L),
128 u5u = LD80C(0xc980e49cd5b019e6, -4,  9.83903751718671509455e-02L),
129 u6u = LD80C(0xff636a8bdce7025b, -9,  3.89691687802305743450e-03L),
130 v1u = LD80C(0xbd109c533a19fbf5, 1,  2.95413883330948556544e+00L),
131 v2u = LD80C(0xd295cbf96f31f099, 1,  3.29039286955665403176e+00L),
132 v3u = LD80C(0xdab8bcfee40496cb, 0,  1.70876276441416471410e+00L),
133 v4u = LD80C(0xd2f2dc3638567e9f, -2,  4.12009126299534668571e-01L),
134 v5u = LD80C(0xa07d9b0851070f41, -5,  3.91822868305682491442e-02L),
135 v6u = LD80C(0xe3cd8318f7adb2c4, -11,  8.68998648222144351114e-04L);
136 #define	u0	(u0u.e)
137 #define	u1	(u1u.e)
138 #define	u2	(u2u.e)
139 #define	u3	(u3u.e)
140 #define	u4	(u4u.e)
141 #define	u5	(u5u.e)
142 #define	u6	(u6u.e)
143 #define	v1	(v1u.e)
144 #define	v2	(v2u.e)
145 #define	v3	(v3u.e)
146 #define	v4	(v4u.e)
147 #define	v5	(v5u.e)
148 #define	v6	(v6u.e)
150  * Domain x in (2, 3], range ~[-3.3648e-22, 3.4416e-22]:
151  * |(lgamma(y+2) - 0.5 * y) / y - s(y)/r(y)| < 2**-72.3
152  * with y = x - 2.
155 s0u = LD80C(0x9e233f1bed863d27, -4, -7.72156649015328606095e-02L),
156 s1u = LD80C(0xd3ff0dcc7fa91f94, -3,  2.07027640921219389860e-01L),
157 s2u = LD80C(0xb2bb62782478ef31, -2,  3.49085881391362090549e-01L),
158 s3u = LD80C(0xb49f7438c4611a74, -3,  1.76389518704213357954e-01L),
159 s4u = LD80C(0x9a957008fa27ecf9, -5,  3.77401710862930008071e-02L),
160 s5u = LD80C(0xda9b389a6ca7a7ac, -9,  3.33566791452943399399e-03L),
161 s6u = LD80C(0xbc7a2263faf59c14, -14,  8.98728786745638844395e-05L),
162 r1u = LD80C(0xbf5cff5b11477d4d, 0,  1.49502555796294337722e+00L),
163 r2u = LD80C(0xd9aec89de08e3da6, -1,  8.50323236984473285866e-01L),
164 r3u = LD80C(0xeab7ae5057c443f9, -3,  2.29216312078225806131e-01L),
165 r4u = LD80C(0xf29707d9bd2b1e37, -6,  2.96130326586640089145e-02L),
166 r5u = LD80C(0xd376c2f09736c5a3, -10,  1.61334161411590662495e-03L),
167 r6u = LD80C(0xc985983d0cd34e3d, -16,  2.40232770710953450636e-05L),
168 r7u = LD80C(0xe5c7a4f7fc2ef13d, -25, -5.34997929289167573510e-08L);
169 #define	s0	(s0u.e)
170 #define	s1	(s1u.e)
171 #define	s2	(s2u.e)
172 #define	s3	(s3u.e)
173 #define	s4	(s4u.e)
174 #define	s5	(s5u.e)
175 #define	s6	(s6u.e)
176 #define	r1	(r1u.e)
177 #define	r2	(r2u.e)
178 #define	r3	(r3u.e)
179 #define	r4	(r4u.e)
180 #define	r5	(r5u.e)
181 #define	r6	(r6u.e)
182 #define	r7	(r7u.e)
184  * Domain z in [8, 0x1p70], range ~[-3.0235e-22, 3.0563e-22]:
185  * |lgamma(x) - (x - 0.5) * (log(x) - 1) - w(1/x)| < 2**-71.7
188 w0u = LD80C(0xd67f1c864beb4a69, -2,  4.18938533204672741776e-01L),
189 w1u = LD80C(0xaaaaaaaaaaaaaaa1, -4,  8.33333333333333332678e-02L),
190 w2u = LD80C(0xb60b60b60b5491c9, -9, -2.77777777777760927870e-03L),
191 w3u = LD80C(0xd00d00cf58aede4c, -11,  7.93650793490637233668e-04L),
192 w4u = LD80C(0x9c09bf626783d4a5, -11, -5.95238023926039051268e-04L),
193 w5u = LD80C(0xdca7cadc5baa517b, -11,  8.41733700408000822962e-04L),
194 w6u = LD80C(0xfb060e361e1ffd07, -10, -1.91515849570245136604e-03L),
195 w7u = LD80C(0xcbd5101bb58d1f2b, -8,  6.22046743903262649294e-03L),
196 w8u = LD80C(0xad27a668d32c821b, -6, -2.11370706734662081843e-02L);
197 #define	w0	(w0u.e)
198 #define	w1	(w1u.e)
199 #define	w2	(w2u.e)
200 #define	w3	(w3u.e)
201 #define	w4	(w4u.e)
202 #define	w5	(w5u.e)
203 #define	w6	(w6u.e)
204 #define	w7	(w7u.e)
205 #define	w8	(w8u.e)
215 	y = -x;  in sin_pil()
218 	z = vz-0x1p63;  in sin_pil()
224 	z = vz-0x1p61;  in sin_pil()
226 	    z -= 0.25;			/* adjust to round down */  in sin_pil()
227 	    n--;  in sin_pil()
230 	y = y - z + n * 0.25;		/* y mod 2 */  in sin_pil()
235 	    case 2:   y =  __kernel_cosl(pi*(0.5-y),zero); break;  in sin_pil()
237 	    case 4:   y =  __kernel_sinl(pi*(one-y),zero,0); break;  in sin_pil()
239 	    case 6:   y = -__kernel_cosl(pi*(y-1.5),zero); break;  in sin_pil()
240 	    default:  y =  __kernel_sinl(pi*(y-2.0),zero,0); break;  in sin_pil()
242 	return -y;  in sin_pil()
255     /* purge +-Inf and NaNs */  in lgammal_r()
262     /* purge +-0 and tiny arguments */  in lgammal_r()
263 	*signgamp = 1-2*(hx>>15);  in lgammal_r()
264 	if(ix<0x3fff-67) {		/* |x|<2**-(p+3), return -log(|x|) */  in lgammal_r()
267 	    RETURNI(-logl(fabsl(x)));  in lgammal_r()
273 	    if(ix>=0x3fff+63) 		/* |x|>=2**(p-1), must be -integer */  in lgammal_r()
276 	    if(t==zero) RETURNI(one/vzero); /* -integer */  in lgammal_r()
278 	    if(t<zero) *signgamp = -1;  in lgammal_r()
279 	    x = -x;  in lgammal_r()
291      * 8.9999961853027344e-01 3ffe e666600000000000  in lgammal_r()
292      * 7.3159980773925781e-01 3ffe bb4a200000000000  in lgammal_r()
293      * 2.3163998126983643e-01 3ffc ed33080000000000  in lgammal_r()
294      * 1.7316312789916992e+00 3fff dda6180000000000  in lgammal_r()
295      * 1.2316322326660156e+00 3fff 9da6200000000000  in lgammal_r()
297 	    if(x<8.9999961853027344e-01) {  in lgammal_r()
298 		r = -logl(x);  in lgammal_r()
299 		if(x>=7.3159980773925781e-01) {y = 1-x; i= 0;}  in lgammal_r()
300 		else if(x>=2.3163998126983643e-01) {y= x-(tc-1); i=1;}  in lgammal_r()
304 		if(x>=1.7316312789916992e+00) {y=2-x;i=0;}  in lgammal_r()
305 		else if(x>=1.2316322326660156e+00) {y=x-tc;i=1;}  in lgammal_r()
306 		else {y=x-1;i=2;}  in lgammal_r()
314 		r  += p-y/2; break;  in lgammal_r()
323 		r += p1/p2-y/2;  in lgammal_r()
329 	    y = x-i;  in lgammal_r()
348 	    r = (x-half)*(t-one)+w;  in lgammal_r()
351 	    r =  x*(logl(x)-1);  in lgammal_r()
352 	if(hx&0x8000) r = nadj - r;  in lgammal_r()