Lines Matching +full:0 +full:x70000000
48 * C: For x between 0 and 1
79 * such that 0<x<T. Let k = [x] and z = x-[x]. Define
96 * (I) kpsin(z) = kpsin(t) ... 0<= z < 0.3184
98 * (III) kpsin(z) = kpsin(t) ... 0<= t < 0.3184
101 * approximation for kpsin(t) for 0<=t<0.3184:
104 * return head = t and tail = ks[0]*t^3 + (...) to maintain extra bits.
108 * kpsin(t) = t + ks[0] * t + ks[1] * t + ... + ks[12] * t
110 * ks[ 0] = -1.64493406684822643647241516664602518705158902870e+0000
126 * kpsin(t) = t + ks[0] * t + ks[1] * t + ... + ks[6] * t
128 * ks[0] = -1.644934066848226406065691 (0x3ffa51a6 625307d3)
138 * kpsin(t) = t + ks[0] * t + ks[1] * t + ... + ks[3] * t
140 * ks[0] = -1.64493404985645811354476665052005342839447790544e+0000
146 * return head = t and tail = kc[0]*t^3 + (...) to maintain extra bits
178 * kpcos(t) = kc[0] + kc[1] * t + ... + kc[3] * t
180 * kc[0] = 3.18309886183790671537767526745028724068919291480e-0001
190 * Thus, the computation of gamma(-x), x>0, is:
242 * P1(y) = p1[0] + p1[1]*y + ... + p1[4]*y^4
243 * Q1(y) = q1[0] + q1[1]*y + ... + q1[5]*y^5
245 * P2(y) = p2[0] + p2[1]*y + ... + p2[3]*y^3
246 * Q2(y) = q2[0] + q2[1]*y + ... + q2[6]*y^6
248 * P3(y) = p3[0] + p3[1]*y + ... + p3[4]*y^4
249 * Q3(y) = q3[0] + q3[1]*y + ... + q3[5]*y^5
260 * P1(y) = p1[0] + p1[1]*y + ... + p1[9]*y^9
261 * Q1(y) = q1[0] + q1[1]*y + ... + q1[8]*y^8
263 * P2(y) = p2[0] + p2[1]*y + ... + p2[9]*y^9
264 * Q2(y) = q2[0] + q2[1]*y + ... + q2[9]*y^9
266 * P3(y) = p3[0] + p3[1]*y + ... + p3[9]*y^9
267 * Q3(y) = q3[0] + q3[1]*y + ... + q3[9]*y^9
278 * P1(y) = p1[0] + p1[1]*y + ... + p1[5]*y^5
280 * P2(y) = p2[0] + p2[1]*y + ... + p2[5]*y^5
282 * P3(y) = p3[0] + p3[1]*y + ... + p3[4]*y^4
300 * P1[0] = 7.09087253435088360271451613398019280077561279443e-0001
308 * p2[0] = 4.28486983980295198166056119223984284434264344578e-0001
316 * p3[0] = 3.82409531118807759081121479786092134814808872880e-0001
324 * p1[0] = 0.70908683619977797008004927192814648151397705078125000
329 * q1[0] = 1.0
336 * p2[0] = 0.42848681585558601181418225678498856723308563232421875
340 * q2[0] = 1.0
348 * p3[0] = 0.382409479734567459008331979930517263710498809814453125
353 * q3[0] = 1.0
365 * p1[0] = 0.709086836199777919037185741507610124611513720557
375 * q1[0] = 1.0+0000
386 * p2[0] = 0.428486815855585429730209907810650616737756697477
396 * q2[0] = 1.0
408 * p3[0] = 0.3824094797345675048502747661075355640070439388902
418 * q3[0] = 1.0
429 * (C) For x between 0 and 1.
432 * (1)For 0 <= x <= 2 , gamma(x) is computed by --- rounded to nearest.
443 * 0 < --- - gamma(x) <= --- - ----------- < 0.578
526 * = 0x420C290F (IEEE single)
528 * = 0x406573FAE561F647 (IEEE double)
530 * = 0x4009B6E3180CD66A5C4206F128BA77F4 (quad)
626 * Base on this analysis, we choose Z = {z(i)|z(i)=1+i/64+1/128, 0<=i<=63}.
667 * (3) Remez approximation for (T3(s)-2s)/s = T3[0]*s + T3[1]*s + ...:
690 * hex 0x3ffe5555 55555555 55555555 55555548
767 +6.66666666666666740682e-01, /* A1=T3[0] */
770 +0.0833333333333333287074040640618477, /* GP[0] */
791 #define one c[0]
826 * T3(s) = 2s + T3[0]s^3 + T3[1]s^5 + T3[2]s^7
836 -1.00000000000000000000e+00, /* 0xBFF00000 0x00000000 */
837 +0.00000000000000000000e+00, /* 0x00000000 0x00000000 */
838 -3.06852817535400390625e-01, /* 0xBFD3A37A 0x00000000 */
839 -1.90465429995776763166e-09, /* 0xBE205C61 0x0CA86C38 */
840 +3.86294305324554443359e-01, /* 0x3FD8B90B 0xC0000000 */
841 +5.57953361754750897367e-08, /* 0x3E6DF473 0xDE6AF279 */
842 +1.07944148778915405273e+00, /* 0x3FF14564 0x70000000 */
843 +5.38906818755173187963e-08, /* 0x3E6CEEAD 0xCDA06BB5 */
844 +1.77258867025375366211e+00, /* 0x3FFC5C85 0xF0000000 */
845 +5.19860275755595544734e-08, /* 0x3E6BE8E7 0xBCD5E4F2 */
846 +2.46573585271835327148e+00, /* 0x4003B9D3 0xB8000000 */
847 +5.00813732756017835330e-08, /* 0x3E6AE321 0xAC0B5E2E */
848 +3.15888303518295288086e+00, /* 0x40094564 0x78000000 */
849 +4.81767189756440192100e-08, /* 0x3E69DD5B 0x9B40D76B */
850 +3.85203021764755249023e+00, /* 0x400ED0F5 0x38000000 */
851 +4.62720646756862482697e-08, /* 0x3E68D795 0x8A7650A7 */
852 +4.54517740011215209961e+00, /* 0x40122E42 0xFC000000 */
853 +4.43674103757284839467e-08, /* 0x3E67D1CF 0x79ABC9E4 */
854 +5.23832458257675170898e+00, /* 0x4014F40B 0x5C000000 */
855 +4.24627560757707130063e-08, /* 0x3E66CC09 0x68E14320 */
856 +5.93147176504135131836e+00, /* 0x4017B9D3 0xBC000000 */
857 +4.05581017758129486834e-08, /* 0x3E65C643 0x5816BC5D */
861 +7.78210163116455078125e-03, /* 0x3F7FE020 0x00000000 */
862 +3.88108903981662140884e-08, /* 0x3E64D620 0xCF11F86F */
863 +2.31670141220092773438e-02, /* 0x3F97B918 0x00000000 */
864 +4.51595251008850513740e-08, /* 0x3E683EAD 0x88D54940 */
865 +3.83188128471374511719e-02, /* 0x3FA39E86 0x00000000 */
866 +5.14549991480218823411e-08, /* 0x3E6B9FEB 0xD5FA9016 */
867 +5.32444715499877929688e-02, /* 0x3FAB42DC 0x00000000 */
868 +4.29688244898971182165e-08, /* 0x3E671197 0x1BEC28D1 */
869 +6.79506063461303710938e-02, /* 0x3FB16536 0x00000000 */
870 +5.55623773783008185114e-08, /* 0x3E6DD46F 0x5C1D0C4C */
871 +8.24436545372009277344e-02, /* 0x3FB51B07 0x00000000 */
872 +1.46738736635337847313e-08, /* 0x3E4F830C 0x1FB493C7 */
873 +9.67295765876770019531e-02, /* 0x3FB8C345 0x00000000 */
874 +4.98708741103424492282e-08, /* 0x3E6AC633 0x641EB597 */
875 +1.10814332962036132812e-01, /* 0x3FBC5E54 0x00000000 */
876 +3.33782539813823062226e-08, /* 0x3E61EB78 0xE862BAC3 */
877 +1.24703466892242431641e-01, /* 0x3FBFEC91 0x00000000 */
878 +1.16087148042227818450e-08, /* 0x3E48EDF5 0x5D551729 */
879 +1.38402283191680908203e-01, /* 0x3FC1B72A 0x80000000 */
880 +3.96674382274822001957e-08, /* 0x3E654BD9 0xE80A4181 */
881 +1.51916027069091796875e-01, /* 0x3FC371FC 0x00000000 */
882 +1.49567501781968021494e-08, /* 0x3E500F47 0xBA1DE6CB */
883 +1.65249526500701904297e-01, /* 0x3FC526E5 0x80000000 */
884 +4.63946052585787334062e-08, /* 0x3E68E86D 0x0DE8B900 */
885 +1.78407609462738037109e-01, /* 0x3FC6D60F 0x80000000 */
886 +4.80100802600100279538e-08, /* 0x3E69C674 0x8723551E */
887 +1.91394805908203125000e-01, /* 0x3FC87FA0 0x00000000 */
888 +4.70914263296092971436e-08, /* 0x3E694832 0x44240802 */
889 +2.04215526580810546875e-01, /* 0x3FCA23BC 0x00000000 */
890 +1.48478803446288209001e-08, /* 0x3E4FE2B5 0x63193712 */
891 +2.16873884201049804688e-01, /* 0x3FCBC286 0x00000000 */
892 +5.40995645549315919488e-08, /* 0x3E6D0B63 0x358A7E74 */
893 +2.29374051094055175781e-01, /* 0x3FCD5C21 0x00000000 */
894 +4.99707906542102284117e-08, /* 0x3E6AD3EE 0xE456E443 */
895 +2.41719901561737060547e-01, /* 0x3FCEF0AD 0x80000000 */
896 +3.53254081075974352804e-08, /* 0x3E62F716 0x4D948638 */
897 +2.53915190696716308594e-01, /* 0x3FD04025 0x80000000 */
898 +1.92842471355435739091e-08, /* 0x3E54B4D0 0x40DAE27C */
899 +2.65963494777679443359e-01, /* 0x3FD1058B 0xC0000000 */
900 +5.37194584979797487125e-08, /* 0x3E6CD725 0x6A8C4FD0 */
901 +2.77868449687957763672e-01, /* 0x3FD1C898 0xC0000000 */
902 +1.31549854251447496506e-09, /* 0x3E16999F 0xAFBC68E7 */
903 +2.89633274078369140625e-01, /* 0x3FD2895A 0x00000000 */
904 +1.85046735362538929911e-08, /* 0x3E53DE86 0xA35EB493 */
905 +3.01261305809020996094e-01, /* 0x3FD347DD 0x80000000 */
906 +2.47691407849191245052e-08, /* 0x3E5A987D 0x54D64567 */
907 +3.12755703926086425781e-01, /* 0x3FD40430 0x80000000 */
908 +6.07781046260499658610e-09, /* 0x3E3A1A9F 0x8EF4304A */
909 +3.24119448661804199219e-01, /* 0x3FD4BE5F 0x80000000 */
910 +1.99924077768719198045e-08, /* 0x3E557778 0xA0DB4C99 */
911 +3.35355520248413085938e-01, /* 0x3FD57677 0x00000000 */
912 +2.16727247443196802771e-08, /* 0x3E57455A 0x6C549AB7 */
913 +3.46466720104217529297e-01, /* 0x3FD62C82 0xC0000000 */
914 +4.72419910516215900493e-08, /* 0x3E695CE3 0xCA97B7B0 */
915 +3.57455849647521972656e-01, /* 0x3FD6E08E 0x80000000 */
916 +3.92742818015697624778e-08, /* 0x3E6515D0 0xF1C609CA */
917 +3.68325531482696533203e-01, /* 0x3FD792A5 0x40000000 */
918 +2.96760111198451042238e-08, /* 0x3E5FDD47 0xA27C15DA */
919 +3.79078328609466552734e-01, /* 0x3FD842D1 0xC0000000 */
920 +2.43255029056564770289e-08, /* 0x3E5A1E8B 0x17493B14 */
921 +3.89716744422912597656e-01, /* 0x3FD8F11E 0x80000000 */
922 +6.71711261571421332726e-09, /* 0x3E3CD98B 0x1DF85DA7 */
923 +4.00243163108825683594e-01, /* 0x3FD99D95 0x80000000 */
924 +1.01818702333557515008e-09, /* 0x3E117E08 0xACBA92EF */
925 +4.10659909248352050781e-01, /* 0x3FDA4840 0x80000000 */
926 +1.57369163351530571459e-08, /* 0x3E50E5BB 0x0A2BFCA7 */
927 +4.20969247817993164062e-01, /* 0x3FDAF129 0x00000000 */
928 +4.68261364720663662040e-08, /* 0x3E6923BC 0x358899C2 */
929 +4.31173443794250488281e-01, /* 0x3FDB9858 0x80000000 */
930 +2.10241208525779214510e-08, /* 0x3E569310 0xFB598FB1 */
931 +4.41274523735046386719e-01, /* 0x3FDC3DD7 0x80000000 */
932 +3.70698288427707487748e-08, /* 0x3E63E6D6 0xA6B9D9E1 */
933 +4.51274633407592773438e-01, /* 0x3FDCE1AF 0x00000000 */
934 +1.07318658117071930723e-08, /* 0x3E470BE7 0xD6F6FA58 */
935 +4.61175680160522460938e-01, /* 0x3FDD83E7 0x00000000 */
936 +3.49616477054305011286e-08, /* 0x3E62C517 0x9F2828AE */
937 +4.70979690551757812500e-01, /* 0x3FDE2488 0x00000000 */
938 +2.46670332000468969567e-08, /* 0x3E5A7C6C 0x261CBD8F */
939 +4.80688512325286865234e-01, /* 0x3FDEC399 0xC0000000 */
940 +1.70204650424422423704e-08, /* 0x3E52468C 0xC0175CEE */
941 +4.90303933620452880859e-01, /* 0x3FDF6123 0xC0000000 */
942 +5.44247409572909703749e-08, /* 0x3E6D3814 0x5630A2B6 */
943 +4.99827861785888671875e-01, /* 0x3FDFFD2E 0x00000000 */
944 +7.77056065794633071345e-09, /* 0x3E40AFE9 0x30AB2FA0 */
945 +5.09261846542358398438e-01, /* 0x3FE04BDF 0x80000000 */
946 +5.52474495483665749052e-08, /* 0x3E6DA926 0xD265FCC1 */
947 +5.18607735633850097656e-01, /* 0x3FE0986F 0x40000000 */
948 +2.85741955344967264536e-08, /* 0x3E5EAE6A 0x41723FB5 */
949 +5.27867078781127929688e-01, /* 0x3FE0E449 0x80000000 */
950 +1.08397144554263914271e-08, /* 0x3E474732 0x2FDBAB97 */
951 +5.37041425704956054688e-01, /* 0x3FE12F71 0x80000000 */
952 +4.01919275998792285777e-08, /* 0x3E6593EF 0xBC530123 */
953 +5.46132385730743408203e-01, /* 0x3FE179EA 0xA0000000 */
954 +5.18673922421792693237e-08, /* 0x3E6BD899 0xA0BFC60E */
955 +5.55141448974609375000e-01, /* 0x3FE1C3B8 0x00000000 */
956 +5.85658922177154808539e-08, /* 0x3E6F713C 0x24BC94F9 */
957 +5.64070105552673339844e-01, /* 0x3FE20CDC 0xC0000000 */
958 +3.27321296262276338905e-08, /* 0x3E6192AB 0x6D93503D */
959 +5.72919726371765136719e-01, /* 0x3FE2555B 0xC0000000 */
960 +2.71900203723740076878e-08, /* 0x3E5D31EF 0x96780876 */
961 +5.81691682338714599609e-01, /* 0x3FE29D37 0xE0000000 */
962 +5.72959078829112371070e-08, /* 0x3E6EC2B0 0x8AC85CD7 */
963 +5.90387403964996337891e-01, /* 0x3FE2E474 0x20000000 */
964 +4.26371800367512948470e-08, /* 0x3E66E402 0x68405422 */
965 +5.99008142948150634766e-01, /* 0x3FE32B13 0x20000000 */
966 +4.66979327646159769249e-08, /* 0x3E69121D 0x71320557 */
967 +6.07555210590362548828e-01, /* 0x3FE37117 0xA0000000 */
968 +3.96341792466729582847e-08, /* 0x3E654747 0xB5C5DD02 */
969 +6.16029858589172363281e-01, /* 0x3FE3B684 0x40000000 */
970 +1.86263416563663175432e-08, /* 0x3E53FFF8 0x455F1DBE */
971 +6.24433279037475585938e-01, /* 0x3FE3FB5B 0x80000000 */
972 +8.97441791510503832111e-09, /* 0x3E4345BD 0x096D3A75 */
973 +6.32766664028167724609e-01, /* 0x3FE43F9F 0xE0000000 */
974 +5.54287010493641158796e-09, /* 0x3E37CE73 0x3BD393DD */
975 +6.41031146049499511719e-01, /* 0x3FE48353 0xC0000000 */
976 +3.33714317793368531132e-08, /* 0x3E61EA88 0xDF73D5E9 */
977 +6.49227917194366455078e-01, /* 0x3FE4C679 0xA0000000 */
978 +2.94307433638127158696e-08, /* 0x3E5F99DC 0x7362D1DA */
979 +6.57358050346374511719e-01, /* 0x3FE50913 0xC0000000 */
980 +2.23619855184231409785e-08, /* 0x3E5802D0 0xD6979675 */
981 +6.65422618389129638672e-01, /* 0x3FE54B24 0x60000000 */
982 +1.41559608102782173188e-08, /* 0x3E4E6652 0x5EA4550A */
983 +6.73422634601593017578e-01, /* 0x3FE58CAD 0xA0000000 */
984 +4.06105737027198329700e-08, /* 0x3E65CD79 0x893092F2 */
985 +6.81359171867370605469e-01, /* 0x3FE5CDB1 0xC0000000 */
986 +5.29405324634793230630e-08, /* 0x3E6C6C17 0x648CF6E4 */
987 +6.89233243465423583984e-01, /* 0x3FE60E32 0xE0000000 */
988 +3.77733853963405370102e-08, /* 0x3E644788 0xD8CA7C89 */
1102 #define P10 cr[0]
1226 * T3(s) = 2s + A1[0]s^3 + A2[1]s^5 + A3[2]s^7 in large_gam()
1245 n2 = (ix >> 20) - 0x3ff; /* exponent of x, range:3-7 */ in large_gam()
1247 ix = (ix & 0x000fffff) | 0x3ff00000; /* y = scale x to [1,2] */ in large_gam()
1250 __HI(z) = (ix & 0xffffc000) | 0x2000; /* z[j]=1+j/64+1/128 */ in large_gam()
1251 __LO(z) = 0; in large_gam()
1252 j2 = (ix >> 13) & 0x7e; /* 2j */ in large_gam()
1260 k = __HI(u) & 0x7fffffff; in large_gam()
1262 if ((k >> 20) < 0x3ec) { /* |u|<2**-19 */ in large_gam()
1293 j = k & 0x1f; in large_gam()
1319 * = x+ks[0]*x +ks[1]*x +ks[2]*x +ks[3]*x +ks[4]*x +ks[5]*x +ks[6]*x
1342 t4 = t1 * ks[0]; in kpsin()
1353 * = 1/pi +kc[0]*x +kc[1]*x +kc[2]*x +kc[3]*x +kc[4]*x +kc[5]*x
1404 /* gamma(x+i) for 0 <= x < 1 */
1430 /* compute gamma(x+i) = (x+i-1)*...*(x+1)*yy, 0<i<8 */ in gam_n()
1432 case 0: /* yy/x */ in gam_n()
1464 __LO(zh) = 0; in gam_n()
1465 __HI(zh) &= 0xfffffff8; /* zh 18 bits mantissa */ in gam_n()
1540 ix = hx & 0x7fffffff; in tgamma()
1543 if (ix < 0x3ca00000) in tgamma()
1545 if (ix >= 0x7ff00000) in tgamma()
1547 return (x * ((hx < 0)? 0.0 : x)); in tgamma()
1548 if (hx > 0x406573fa || /* x > 171.62... overflow to +inf */ in tgamma()
1549 (hx == 0x406573fa && lx > 0xE561F647)) { in tgamma()
1553 if (hx >= 0x40200000) { /* x >= 8 */ in tgamma()
1559 if (hx > 0) { /* 0 < x < 8 */ in tgamma()
1571 * +0 ... x is not an int but chopped to an even int in tgamma()
1575 xk = 0; in tgamma()
1576 if (ix >= 0x43300000) { in tgamma()
1577 if (ix >= 0x43400000) in tgamma()
1581 } else if (ix >= 0x3ff00000) { in tgamma()
1582 k = (ix >> 20) - 0x3ff; in tgamma()
1591 if ((j << (20 - k)) == ix && lx == 0) in tgamma()
1597 if (xk < 0) in tgamma()
1599 return ((x - x) / (x - x)); /* 0/0 = NaN */ in tgamma()
1603 if (ix > 0x4066e000 || (ix == 0x4066e000 && lx > 11)) { in tgamma()
1627 if (xk == 0) { in tgamma()
1633 m = 0; in tgamma()
1638 if ((lx & 1) == 0) { /* y+1 exact (note that y<184) */ in tgamma()
1677 if (m != 0) { in tgamma()
1679 i = hx & 0x80000000; in tgamma()
1687 if (xk == 0) in tgamma()