diff options
Diffstat (limited to 'sysdeps/ieee754/ldbl-128/e_lgammal_r.c')
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_lgammal_r.c | 932 |
1 files changed, 464 insertions, 468 deletions
diff --git a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c index 5b513ea1df..5c50e4616a 100644 --- a/sysdeps/ieee754/ldbl-128/e_lgammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_lgammal_r.c @@ -72,35 +72,31 @@ #include <math_private.h> #include <float.h> -static const long double PIL = 3.1415926535897932384626433832795028841972E0L; -#if LDBL_MANT_DIG == 106 -static const long double MAXLGM = 0x5.d53649e2d469dbc1f01e99fd66p+1012L; -#else -static const long double MAXLGM = 1.0485738685148938358098967157129705071571E4928L; -#endif -static const long double one = 1.0L; -static const long double huge = LDBL_MAX; +static const _Float128 PIL = L(3.1415926535897932384626433832795028841972E0); +static const _Float128 MAXLGM = L(1.0485738685148938358098967157129705071571E4928); +static const _Float128 one = 1; +static const _Float128 huge = LDBL_MAX; /* log gamma(x) = ( x - 0.5 ) * log(x) - x + LS2PI + 1/x P(1/x^2) 1/x <= 0.0741 (x >= 13.495...) Peak relative error 1.5e-36 */ -static const long double ls2pi = 9.1893853320467274178032973640561763986140E-1L; +static const _Float128 ls2pi = L(9.1893853320467274178032973640561763986140E-1); #define NRASY 12 -static const long double RASY[NRASY + 1] = +static const _Float128 RASY[NRASY + 1] = { - 8.333333333333333333333333333310437112111E-2L, - -2.777777777777777777777774789556228296902E-3L, - 7.936507936507936507795933938448586499183E-4L, - -5.952380952380952041799269756378148574045E-4L, - 8.417508417507928904209891117498524452523E-4L, - -1.917526917481263997778542329739806086290E-3L, - 6.410256381217852504446848671499409919280E-3L, - -2.955064066900961649768101034477363301626E-2L, - 1.796402955865634243663453415388336954675E-1L, - -1.391522089007758553455753477688592767741E0L, - 1.326130089598399157988112385013829305510E1L, - -1.420412699593782497803472576479997819149E2L, - 1.218058922427762808938869872528846787020E3L + L(8.333333333333333333333333333310437112111E-2), + L(-2.777777777777777777777774789556228296902E-3), + L(7.936507936507936507795933938448586499183E-4), + L(-5.952380952380952041799269756378148574045E-4), + L(8.417508417507928904209891117498524452523E-4), + L(-1.917526917481263997778542329739806086290E-3), + L(6.410256381217852504446848671499409919280E-3), + L(-2.955064066900961649768101034477363301626E-2), + L(1.796402955865634243663453415388336954675E-1), + L(-1.391522089007758553455753477688592767741E0), + L(1.326130089598399157988112385013829305510E1), + L(-1.420412699593782497803472576479997819149E2), + L(1.218058922427762808938869872528846787020E3) }; @@ -108,30 +104,30 @@ static const long double RASY[NRASY + 1] = -0.5 <= x <= 0.5 12.5 <= x+13 <= 13.5 Peak relative error 1.1e-36 */ -static const long double lgam13a = 1.9987213134765625E1L; -static const long double lgam13b = 1.3608962611495173623870550785125024484248E-6L; +static const _Float128 lgam13a = L(1.9987213134765625E1); +static const _Float128 lgam13b = L(1.3608962611495173623870550785125024484248E-6); #define NRN13 7 -static const long double RN13[NRN13 + 1] = +static const _Float128 RN13[NRN13 + 1] = { - 8.591478354823578150238226576156275285700E11L, - 2.347931159756482741018258864137297157668E11L, - 2.555408396679352028680662433943000804616E10L, - 1.408581709264464345480765758902967123937E9L, - 4.126759849752613822953004114044451046321E7L, - 6.133298899622688505854211579222889943778E5L, - 3.929248056293651597987893340755876578072E3L, - 6.850783280018706668924952057996075215223E0L + L(8.591478354823578150238226576156275285700E11), + L(2.347931159756482741018258864137297157668E11), + L(2.555408396679352028680662433943000804616E10), + L(1.408581709264464345480765758902967123937E9), + L(4.126759849752613822953004114044451046321E7), + L(6.133298899622688505854211579222889943778E5), + L(3.929248056293651597987893340755876578072E3), + L(6.850783280018706668924952057996075215223E0) }; #define NRD13 6 -static const long double RD13[NRD13 + 1] = +static const _Float128 RD13[NRD13 + 1] = { - 3.401225382297342302296607039352935541669E11L, - 8.756765276918037910363513243563234551784E10L, - 8.873913342866613213078554180987647243903E9L, - 4.483797255342763263361893016049310017973E8L, - 1.178186288833066430952276702931512870676E7L, - 1.519928623743264797939103740132278337476E5L, - 7.989298844938119228411117593338850892311E2L + L(3.401225382297342302296607039352935541669E11), + L(8.756765276918037910363513243563234551784E10), + L(8.873913342866613213078554180987647243903E9), + L(4.483797255342763263361893016049310017973E8), + L(1.178186288833066430952276702931512870676E7), + L(1.519928623743264797939103740132278337476E5), + L(7.989298844938119228411117593338850892311E2) /* 1.0E0L */ }; @@ -140,30 +136,30 @@ static const long double RD13[NRD13 + 1] = -0.5 <= x <= 0.5 11.5 <= x+12 <= 12.5 Peak relative error 4.1e-36 */ -static const long double lgam12a = 1.75023040771484375E1L; -static const long double lgam12b = 3.7687254483392876529072161996717039575982E-6L; +static const _Float128 lgam12a = L(1.75023040771484375E1); +static const _Float128 lgam12b = L(3.7687254483392876529072161996717039575982E-6); #define NRN12 7 -static const long double RN12[NRN12 + 1] = +static const _Float128 RN12[NRN12 + 1] = { - 4.709859662695606986110997348630997559137E11L, - 1.398713878079497115037857470168777995230E11L, - 1.654654931821564315970930093932954900867E10L, - 9.916279414876676861193649489207282144036E8L, - 3.159604070526036074112008954113411389879E7L, - 5.109099197547205212294747623977502492861E5L, - 3.563054878276102790183396740969279826988E3L, - 6.769610657004672719224614163196946862747E0L + L(4.709859662695606986110997348630997559137E11), + L(1.398713878079497115037857470168777995230E11), + L(1.654654931821564315970930093932954900867E10), + L(9.916279414876676861193649489207282144036E8), + L(3.159604070526036074112008954113411389879E7), + L(5.109099197547205212294747623977502492861E5), + L(3.563054878276102790183396740969279826988E3), + L(6.769610657004672719224614163196946862747E0) }; #define NRD12 6 -static const long double RD12[NRD12 + 1] = +static const _Float128 RD12[NRD12 + 1] = { - 1.928167007860968063912467318985802726613E11L, - 5.383198282277806237247492369072266389233E10L, - 5.915693215338294477444809323037871058363E9L, - 3.241438287570196713148310560147925781342E8L, - 9.236680081763754597872713592701048455890E6L, - 1.292246897881650919242713651166596478850E5L, - 7.366532445427159272584194816076600211171E2L + L(1.928167007860968063912467318985802726613E11), + L(5.383198282277806237247492369072266389233E10), + L(5.915693215338294477444809323037871058363E9), + L(3.241438287570196713148310560147925781342E8), + L(9.236680081763754597872713592701048455890E6), + L(1.292246897881650919242713651166596478850E5), + L(7.366532445427159272584194816076600211171E2) /* 1.0E0L */ }; @@ -172,30 +168,30 @@ static const long double RD12[NRD12 + 1] = -0.5 <= x <= 0.5 10.5 <= x+11 <= 11.5 Peak relative error 1.8e-35 */ -static const long double lgam11a = 1.5104400634765625E1L; -static const long double lgam11b = 1.1938309890295225709329251070371882250744E-5L; +static const _Float128 lgam11a = L(1.5104400634765625E1); +static const _Float128 lgam11b = L(1.1938309890295225709329251070371882250744E-5); #define NRN11 7 -static const long double RN11[NRN11 + 1] = +static const _Float128 RN11[NRN11 + 1] = { - 2.446960438029415837384622675816736622795E11L, - 7.955444974446413315803799763901729640350E10L, - 1.030555327949159293591618473447420338444E10L, - 6.765022131195302709153994345470493334946E8L, - 2.361892792609204855279723576041468347494E7L, - 4.186623629779479136428005806072176490125E5L, - 3.202506022088912768601325534149383594049E3L, - 6.681356101133728289358838690666225691363E0L + L(2.446960438029415837384622675816736622795E11), + L(7.955444974446413315803799763901729640350E10), + L(1.030555327949159293591618473447420338444E10), + L(6.765022131195302709153994345470493334946E8), + L(2.361892792609204855279723576041468347494E7), + L(4.186623629779479136428005806072176490125E5), + L(3.202506022088912768601325534149383594049E3), + L(6.681356101133728289358838690666225691363E0) }; #define NRD11 6 -static const long double RD11[NRD11 + 1] = +static const _Float128 RD11[NRD11 + 1] = { - 1.040483786179428590683912396379079477432E11L, - 3.172251138489229497223696648369823779729E10L, - 3.806961885984850433709295832245848084614E9L, - 2.278070344022934913730015420611609620171E8L, - 7.089478198662651683977290023829391596481E6L, - 1.083246385105903533237139380509590158658E5L, - 6.744420991491385145885727942219463243597E2L + L(1.040483786179428590683912396379079477432E11), + L(3.172251138489229497223696648369823779729E10), + L(3.806961885984850433709295832245848084614E9), + L(2.278070344022934913730015420611609620171E8), + L(7.089478198662651683977290023829391596481E6), + L(1.083246385105903533237139380509590158658E5), + L(6.744420991491385145885727942219463243597E2) /* 1.0E0L */ }; @@ -204,31 +200,31 @@ static const long double RD11[NRD11 + 1] = -0.5 <= x <= 0.5 9.5 <= x+10 <= 10.5 Peak relative error 5.4e-37 */ -static const long double lgam10a = 1.280181884765625E1L; -static const long double lgam10b = 8.6324252196112077178745667061642811492557E-6L; +static const _Float128 lgam10a = L(1.280181884765625E1); +static const _Float128 lgam10b = L(8.6324252196112077178745667061642811492557E-6); #define NRN10 7 -static const long double RN10[NRN10 + 1] = +static const _Float128 RN10[NRN10 + 1] = { - -1.239059737177249934158597996648808363783E14L, - -4.725899566371458992365624673357356908719E13L, - -7.283906268647083312042059082837754850808E12L, - -5.802855515464011422171165179767478794637E11L, - -2.532349691157548788382820303182745897298E10L, - -5.884260178023777312587193693477072061820E8L, - -6.437774864512125749845840472131829114906E6L, - -2.350975266781548931856017239843273049384E4L + L(-1.239059737177249934158597996648808363783E14), + L(-4.725899566371458992365624673357356908719E13), + L(-7.283906268647083312042059082837754850808E12), + L(-5.802855515464011422171165179767478794637E11), + L(-2.532349691157548788382820303182745897298E10), + L(-5.884260178023777312587193693477072061820E8), + L(-6.437774864512125749845840472131829114906E6), + L(-2.350975266781548931856017239843273049384E4) }; #define NRD10 7 -static const long double RD10[NRD10 + 1] = +static const _Float128 RD10[NRD10 + 1] = { - -5.502645997581822567468347817182347679552E13L, - -1.970266640239849804162284805400136473801E13L, - -2.819677689615038489384974042561531409392E12L, - -2.056105863694742752589691183194061265094E11L, - -8.053670086493258693186307810815819662078E9L, - -1.632090155573373286153427982504851867131E8L, - -1.483575879240631280658077826889223634921E6L, - -4.002806669713232271615885826373550502510E3L + L(-5.502645997581822567468347817182347679552E13), + L(-1.970266640239849804162284805400136473801E13), + L(-2.819677689615038489384974042561531409392E12), + L(-2.056105863694742752589691183194061265094E11), + L(-8.053670086493258693186307810815819662078E9), + L(-1.632090155573373286153427982504851867131E8), + L(-1.483575879240631280658077826889223634921E6), + L(-4.002806669713232271615885826373550502510E3) /* 1.0E0L */ }; @@ -237,31 +233,31 @@ static const long double RD10[NRD10 + 1] = -0.5 <= x <= 0.5 8.5 <= x+9 <= 9.5 Peak relative error 3.6e-36 */ -static const long double lgam9a = 1.06045989990234375E1L; -static const long double lgam9b = 3.9037218127284172274007216547549861681400E-6L; +static const _Float128 lgam9a = L(1.06045989990234375E1); +static const _Float128 lgam9b = L(3.9037218127284172274007216547549861681400E-6); #define NRN9 7 -static const long double RN9[NRN9 + 1] = +static const _Float128 RN9[NRN9 + 1] = { - -4.936332264202687973364500998984608306189E13L, - -2.101372682623700967335206138517766274855E13L, - -3.615893404644823888655732817505129444195E12L, - -3.217104993800878891194322691860075472926E11L, - -1.568465330337375725685439173603032921399E10L, - -4.073317518162025744377629219101510217761E8L, - -4.983232096406156139324846656819246974500E6L, - -2.036280038903695980912289722995505277253E4L + L(-4.936332264202687973364500998984608306189E13), + L(-2.101372682623700967335206138517766274855E13), + L(-3.615893404644823888655732817505129444195E12), + L(-3.217104993800878891194322691860075472926E11), + L(-1.568465330337375725685439173603032921399E10), + L(-4.073317518162025744377629219101510217761E8), + L(-4.983232096406156139324846656819246974500E6), + L(-2.036280038903695980912289722995505277253E4) }; #define NRD9 7 -static const long double RD9[NRD9 + 1] = +static const _Float128 RD9[NRD9 + 1] = { - -2.306006080437656357167128541231915480393E13L, - -9.183606842453274924895648863832233799950E12L, - -1.461857965935942962087907301194381010380E12L, - -1.185728254682789754150068652663124298303E11L, - -5.166285094703468567389566085480783070037E9L, - -1.164573656694603024184768200787835094317E8L, - -1.177343939483908678474886454113163527909E6L, - -3.529391059783109732159524500029157638736E3L + L(-2.306006080437656357167128541231915480393E13), + L(-9.183606842453274924895648863832233799950E12), + L(-1.461857965935942962087907301194381010380E12), + L(-1.185728254682789754150068652663124298303E11), + L(-5.166285094703468567389566085480783070037E9), + L(-1.164573656694603024184768200787835094317E8), + L(-1.177343939483908678474886454113163527909E6), + L(-3.529391059783109732159524500029157638736E3) /* 1.0E0L */ }; @@ -270,32 +266,32 @@ static const long double RD9[NRD9 + 1] = -0.5 <= x <= 0.5 7.5 <= x+8 <= 8.5 Peak relative error 2.4e-37 */ -static const long double lgam8a = 8.525146484375E0L; -static const long double lgam8b = 1.4876690414300165531036347125050759667737E-5L; +static const _Float128 lgam8a = L(8.525146484375E0); +static const _Float128 lgam8b = L(1.4876690414300165531036347125050759667737E-5); #define NRN8 8 -static const long double RN8[NRN8 + 1] = +static const _Float128 RN8[NRN8 + 1] = { - 6.600775438203423546565361176829139703289E11L, - 3.406361267593790705240802723914281025800E11L, - 7.222460928505293914746983300555538432830E10L, - 8.102984106025088123058747466840656458342E9L, - 5.157620015986282905232150979772409345927E8L, - 1.851445288272645829028129389609068641517E7L, - 3.489261702223124354745894067468953756656E5L, - 2.892095396706665774434217489775617756014E3L, - 6.596977510622195827183948478627058738034E0L + L(6.600775438203423546565361176829139703289E11), + L(3.406361267593790705240802723914281025800E11), + L(7.222460928505293914746983300555538432830E10), + L(8.102984106025088123058747466840656458342E9), + L(5.157620015986282905232150979772409345927E8), + L(1.851445288272645829028129389609068641517E7), + L(3.489261702223124354745894067468953756656E5), + L(2.892095396706665774434217489775617756014E3), + L(6.596977510622195827183948478627058738034E0) }; #define NRD8 7 -static const long double RD8[NRD8 + 1] = +static const _Float128 RD8[NRD8 + 1] = { - 3.274776546520735414638114828622673016920E11L, - 1.581811207929065544043963828487733970107E11L, - 3.108725655667825188135393076860104546416E10L, - 3.193055010502912617128480163681842165730E9L, - 1.830871482669835106357529710116211541839E8L, - 5.790862854275238129848491555068073485086E6L, - 9.305213264307921522842678835618803553589E4L, - 6.216974105861848386918949336819572333622E2L + L(3.274776546520735414638114828622673016920E11), + L(1.581811207929065544043963828487733970107E11), + L(3.108725655667825188135393076860104546416E10), + L(3.193055010502912617128480163681842165730E9), + L(1.830871482669835106357529710116211541839E8), + L(5.790862854275238129848491555068073485086E6), + L(9.305213264307921522842678835618803553589E4), + L(6.216974105861848386918949336819572333622E2) /* 1.0E0L */ }; @@ -304,32 +300,32 @@ static const long double RD8[NRD8 + 1] = -0.5 <= x <= 0.5 6.5 <= x+7 <= 7.5 Peak relative error 3.2e-36 */ -static const long double lgam7a = 6.5792388916015625E0L; -static const long double lgam7b = 1.2320408538495060178292903945321122583007E-5L; +static const _Float128 lgam7a = L(6.5792388916015625E0); +static const _Float128 lgam7b = L(1.2320408538495060178292903945321122583007E-5); #define NRN7 8 -static const long double RN7[NRN7 + 1] = +static const _Float128 RN7[NRN7 + 1] = { - 2.065019306969459407636744543358209942213E11L, - 1.226919919023736909889724951708796532847E11L, - 2.996157990374348596472241776917953749106E10L, - 3.873001919306801037344727168434909521030E9L, - 2.841575255593761593270885753992732145094E8L, - 1.176342515359431913664715324652399565551E7L, - 2.558097039684188723597519300356028511547E5L, - 2.448525238332609439023786244782810774702E3L, - 6.460280377802030953041566617300902020435E0L + L(2.065019306969459407636744543358209942213E11), + L(1.226919919023736909889724951708796532847E11), + L(2.996157990374348596472241776917953749106E10), + L(3.873001919306801037344727168434909521030E9), + L(2.841575255593761593270885753992732145094E8), + L(1.176342515359431913664715324652399565551E7), + L(2.558097039684188723597519300356028511547E5), + L(2.448525238332609439023786244782810774702E3), + L(6.460280377802030953041566617300902020435E0) }; #define NRD7 7 -static const long double RD7[NRD7 + 1] = +static const _Float128 RD7[NRD7 + 1] = { - 1.102646614598516998880874785339049304483E11L, - 6.099297512712715445879759589407189290040E10L, - 1.372898136289611312713283201112060238351E10L, - 1.615306270420293159907951633566635172343E9L, - 1.061114435798489135996614242842561967459E8L, - 3.845638971184305248268608902030718674691E6L, - 7.081730675423444975703917836972720495507E4L, - 5.423122582741398226693137276201344096370E2L + L(1.102646614598516998880874785339049304483E11), + L(6.099297512712715445879759589407189290040E10), + L(1.372898136289611312713283201112060238351E10), + L(1.615306270420293159907951633566635172343E9), + L(1.061114435798489135996614242842561967459E8), + L(3.845638971184305248268608902030718674691E6), + L(7.081730675423444975703917836972720495507E4), + L(5.423122582741398226693137276201344096370E2) /* 1.0E0L */ }; @@ -338,33 +334,33 @@ static const long double RD7[NRD7 + 1] = -0.5 <= x <= 0.5 5.5 <= x+6 <= 6.5 Peak relative error 6.2e-37 */ -static const long double lgam6a = 4.7874908447265625E0L; -static const long double lgam6b = 8.9805548349424770093452324304839959231517E-7L; +static const _Float128 lgam6a = L(4.7874908447265625E0); +static const _Float128 lgam6b = L(8.9805548349424770093452324304839959231517E-7); #define NRN6 8 -static const long double RN6[NRN6 + 1] = +static const _Float128 RN6[NRN6 + 1] = { - -3.538412754670746879119162116819571823643E13L, - -2.613432593406849155765698121483394257148E13L, - -8.020670732770461579558867891923784753062E12L, - -1.322227822931250045347591780332435433420E12L, - -1.262809382777272476572558806855377129513E11L, - -7.015006277027660872284922325741197022467E9L, - -2.149320689089020841076532186783055727299E8L, - -3.167210585700002703820077565539658995316E6L, - -1.576834867378554185210279285358586385266E4L + L(-3.538412754670746879119162116819571823643E13), + L(-2.613432593406849155765698121483394257148E13), + L(-8.020670732770461579558867891923784753062E12), + L(-1.322227822931250045347591780332435433420E12), + L(-1.262809382777272476572558806855377129513E11), + L(-7.015006277027660872284922325741197022467E9), + L(-2.149320689089020841076532186783055727299E8), + L(-3.167210585700002703820077565539658995316E6), + L(-1.576834867378554185210279285358586385266E4) }; #define NRD6 8 -static const long double RD6[NRD6 + 1] = +static const _Float128 RD6[NRD6 + 1] = { - -2.073955870771283609792355579558899389085E13L, - -1.421592856111673959642750863283919318175E13L, - -4.012134994918353924219048850264207074949E12L, - -6.013361045800992316498238470888523722431E11L, - -5.145382510136622274784240527039643430628E10L, - -2.510575820013409711678540476918249524123E9L, - -6.564058379709759600836745035871373240904E7L, - -7.861511116647120540275354855221373571536E5L, - -2.821943442729620524365661338459579270561E3L + L(-2.073955870771283609792355579558899389085E13), + L(-1.421592856111673959642750863283919318175E13), + L(-4.012134994918353924219048850264207074949E12), + L(-6.013361045800992316498238470888523722431E11), + L(-5.145382510136622274784240527039643430628E10), + L(-2.510575820013409711678540476918249524123E9), + L(-6.564058379709759600836745035871373240904E7), + L(-7.861511116647120540275354855221373571536E5), + L(-2.821943442729620524365661338459579270561E3) /* 1.0E0L */ }; @@ -373,34 +369,34 @@ static const long double RD6[NRD6 + 1] = -0.5 <= x <= 0.5 4.5 <= x+5 <= 5.5 Peak relative error 3.4e-37 */ -static const long double lgam5a = 3.17803955078125E0L; -static const long double lgam5b = 1.4279566695619646941601297055408873990961E-5L; +static const _Float128 lgam5a = L(3.17803955078125E0); +static const _Float128 lgam5b = L(1.4279566695619646941601297055408873990961E-5); #define NRN5 9 -static const long double RN5[NRN5 + 1] = +static const _Float128 RN5[NRN5 + 1] = { - 2.010952885441805899580403215533972172098E11L, - 1.916132681242540921354921906708215338584E11L, - 7.679102403710581712903937970163206882492E10L, - 1.680514903671382470108010973615268125169E10L, - 2.181011222911537259440775283277711588410E9L, - 1.705361119398837808244780667539728356096E8L, - 7.792391565652481864976147945997033946360E6L, - 1.910741381027985291688667214472560023819E5L, - 2.088138241893612679762260077783794329559E3L, - 6.330318119566998299106803922739066556550E0L + L(2.010952885441805899580403215533972172098E11), + L(1.916132681242540921354921906708215338584E11), + L(7.679102403710581712903937970163206882492E10), + L(1.680514903671382470108010973615268125169E10), + L(2.181011222911537259440775283277711588410E9), + L(1.705361119398837808244780667539728356096E8), + L(7.792391565652481864976147945997033946360E6), + L(1.910741381027985291688667214472560023819E5), + L(2.088138241893612679762260077783794329559E3), + L(6.330318119566998299106803922739066556550E0) }; #define NRD5 8 -static const long double RD5[NRD5 + 1] = +static const _Float128 RD5[NRD5 + 1] = { - 1.335189758138651840605141370223112376176E11L, - 1.174130445739492885895466097516530211283E11L, - 4.308006619274572338118732154886328519910E10L, - 8.547402888692578655814445003283720677468E9L, - 9.934628078575618309542580800421370730906E8L, - 6.847107420092173812998096295422311820672E7L, - 2.698552646016599923609773122139463150403E6L, - 5.526516251532464176412113632726150253215E4L, - 4.772343321713697385780533022595450486932E2L + L(1.335189758138651840605141370223112376176E11), + L(1.174130445739492885895466097516530211283E11), + L(4.308006619274572338118732154886328519910E10), + L(8.547402888692578655814445003283720677468E9), + L(9.934628078575618309542580800421370730906E8), + L(6.847107420092173812998096295422311820672E7), + L(2.698552646016599923609773122139463150403E6), + L(5.526516251532464176412113632726150253215E4), + L(4.772343321713697385780533022595450486932E2) /* 1.0E0L */ }; @@ -409,35 +405,35 @@ static const long double RD5[NRD5 + 1] = -0.5 <= x <= 0.5 3.5 <= x+4 <= 4.5 Peak relative error 6.7e-37 */ -static const long double lgam4a = 1.791748046875E0L; -static const long double lgam4b = 1.1422353055000812477358380702272722990692E-5L; +static const _Float128 lgam4a = L(1.791748046875E0); +static const _Float128 lgam4b = L(1.1422353055000812477358380702272722990692E-5); #define NRN4 9 -static const long double RN4[NRN4 + 1] = +static const _Float128 RN4[NRN4 + 1] = { - -1.026583408246155508572442242188887829208E13L, - -1.306476685384622809290193031208776258809E13L, - -7.051088602207062164232806511992978915508E12L, - -2.100849457735620004967624442027793656108E12L, - -3.767473790774546963588549871673843260569E11L, - -4.156387497364909963498394522336575984206E10L, - -2.764021460668011732047778992419118757746E9L, - -1.036617204107109779944986471142938641399E8L, - -1.895730886640349026257780896972598305443E6L, - -1.180509051468390914200720003907727988201E4L + L(-1.026583408246155508572442242188887829208E13), + L(-1.306476685384622809290193031208776258809E13), + L(-7.051088602207062164232806511992978915508E12), + L(-2.100849457735620004967624442027793656108E12), + L(-3.767473790774546963588549871673843260569E11), + L(-4.156387497364909963498394522336575984206E10), + L(-2.764021460668011732047778992419118757746E9), + L(-1.036617204107109779944986471142938641399E8), + L(-1.895730886640349026257780896972598305443E6), + L(-1.180509051468390914200720003907727988201E4) }; #define NRD4 9 -static const long double RD4[NRD4 + 1] = +static const _Float128 RD4[NRD4 + 1] = { - -8.172669122056002077809119378047536240889E12L, - -9.477592426087986751343695251801814226960E12L, - -4.629448850139318158743900253637212801682E12L, - -1.237965465892012573255370078308035272942E12L, - -1.971624313506929845158062177061297598956E11L, - -1.905434843346570533229942397763361493610E10L, - -1.089409357680461419743730978512856675984E9L, - -3.416703082301143192939774401370222822430E7L, - -4.981791914177103793218433195857635265295E5L, - -2.192507743896742751483055798411231453733E3L + L(-8.172669122056002077809119378047536240889E12), + L(-9.477592426087986751343695251801814226960E12), + L(-4.629448850139318158743900253637212801682E12), + L(-1.237965465892012573255370078308035272942E12), + L(-1.971624313506929845158062177061297598956E11), + L(-1.905434843346570533229942397763361493610E10), + L(-1.089409357680461419743730978512856675984E9), + L(-3.416703082301143192939774401370222822430E7), + L(-4.981791914177103793218433195857635265295E5), + L(-2.192507743896742751483055798411231453733E3) /* 1.0E0L */ }; @@ -446,36 +442,36 @@ static const long double RD4[NRD4 + 1] = -0.25 <= x <= 0.5 2.75 <= x+3 <= 3.5 Peak relative error 6.0e-37 */ -static const long double lgam3a = 6.93145751953125E-1L; -static const long double lgam3b = 1.4286068203094172321214581765680755001344E-6L; +static const _Float128 lgam3a = L(6.93145751953125E-1); +static const _Float128 lgam3b = L(1.4286068203094172321214581765680755001344E-6); #define NRN3 9 -static const long double RN3[NRN3 + 1] = +static const _Float128 RN3[NRN3 + 1] = { - -4.813901815114776281494823863935820876670E11L, - -8.425592975288250400493910291066881992620E11L, - -6.228685507402467503655405482985516909157E11L, - -2.531972054436786351403749276956707260499E11L, - -6.170200796658926701311867484296426831687E10L, - -9.211477458528156048231908798456365081135E9L, - -8.251806236175037114064561038908691305583E8L, - -4.147886355917831049939930101151160447495E7L, - -1.010851868928346082547075956946476932162E6L, - -8.333374463411801009783402800801201603736E3L + L(-4.813901815114776281494823863935820876670E11), + L(-8.425592975288250400493910291066881992620E11), + L(-6.228685507402467503655405482985516909157E11), + L(-2.531972054436786351403749276956707260499E11), + L(-6.170200796658926701311867484296426831687E10), + L(-9.211477458528156048231908798456365081135E9), + L(-8.251806236175037114064561038908691305583E8), + L(-4.147886355917831049939930101151160447495E7), + L(-1.010851868928346082547075956946476932162E6), + L(-8.333374463411801009783402800801201603736E3) }; #define NRD3 9 -static const long double RD3[NRD3 + 1] = +static const _Float128 RD3[NRD3 + 1] = { - -5.216713843111675050627304523368029262450E11L, - -8.014292925418308759369583419234079164391E11L, - -5.180106858220030014546267824392678611990E11L, - -1.830406975497439003897734969120997840011E11L, - -3.845274631904879621945745960119924118925E10L, - -4.891033385370523863288908070309417710903E9L, - -3.670172254411328640353855768698287474282E8L, - -1.505316381525727713026364396635522516989E7L, - -2.856327162923716881454613540575964890347E5L, - -1.622140448015769906847567212766206894547E3L + L(-5.216713843111675050627304523368029262450E11), + L(-8.014292925418308759369583419234079164391E11), + L(-5.180106858220030014546267824392678611990E11), + L(-1.830406975497439003897734969120997840011E11), + L(-3.845274631904879621945745960119924118925E10), + L(-4.891033385370523863288908070309417710903E9), + L(-3.670172254411328640353855768698287474282E8), + L(-1.505316381525727713026364396635522516989E7), + L(-2.856327162923716881454613540575964890347E5), + L(-1.622140448015769906847567212766206894547E3) /* 1.0E0L */ }; @@ -483,33 +479,33 @@ static const long double RD3[NRD3 + 1] = /* log gamma(x+2.5) = log gamma(2.5) + x P(x)/Q(x) -0.125 <= x <= 0.25 2.375 <= x+2.5 <= 2.75 */ -static const long double lgam2r5a = 2.8466796875E-1L; -static const long double lgam2r5b = 1.4901722919159632494669682701924320137696E-5L; +static const _Float128 lgam2r5a = L(2.8466796875E-1); +static const _Float128 lgam2r5b = L(1.4901722919159632494669682701924320137696E-5); #define NRN2r5 8 -static const long double RN2r5[NRN2r5 + 1] = +static const _Float128 RN2r5[NRN2r5 + 1] = { - -4.676454313888335499356699817678862233205E9L, - -9.361888347911187924389905984624216340639E9L, - -7.695353600835685037920815799526540237703E9L, - -3.364370100981509060441853085968900734521E9L, - -8.449902011848163568670361316804900559863E8L, - -1.225249050950801905108001246436783022179E8L, - -9.732972931077110161639900388121650470926E6L, - -3.695711763932153505623248207576425983573E5L, - -4.717341584067827676530426007495274711306E3L + L(-4.676454313888335499356699817678862233205E9), + L(-9.361888347911187924389905984624216340639E9), + L(-7.695353600835685037920815799526540237703E9), + L(-3.364370100981509060441853085968900734521E9), + L(-8.449902011848163568670361316804900559863E8), + L(-1.225249050950801905108001246436783022179E8), + L(-9.732972931077110161639900388121650470926E6), + L(-3.695711763932153505623248207576425983573E5), + L(-4.717341584067827676530426007495274711306E3) }; #define NRD2r5 8 -static const long double RD2r5[NRD2r5 + 1] = +static const _Float128 RD2r5[NRD2r5 + 1] = { - -6.650657966618993679456019224416926875619E9L, - -1.099511409330635807899718829033488771623E10L, - -7.482546968307837168164311101447116903148E9L, - -2.702967190056506495988922973755870557217E9L, - -5.570008176482922704972943389590409280950E8L, - -6.536934032192792470926310043166993233231E7L, - -4.101991193844953082400035444146067511725E6L, - -1.174082735875715802334430481065526664020E5L, - -9.932840389994157592102947657277692978511E2L + L(-6.650657966618993679456019224416926875619E9), + L(-1.099511409330635807899718829033488771623E10), + L(-7.482546968307837168164311101447116903148E9), + L(-2.702967190056506495988922973755870557217E9), + L(-5.570008176482922704972943389590409280950E8), + L(-6.536934032192792470926310043166993233231E7), + L(-4.101991193844953082400035444146067511725E6), + L(-1.174082735875715802334430481065526664020E5), + L(-9.932840389994157592102947657277692978511E2) /* 1.0E0L */ }; @@ -519,32 +515,32 @@ static const long double RD2r5[NRD2r5 + 1] = 1.875 <= x+2 <= 2.375 Peak relative error 4.6e-36 */ #define NRN2 9 -static const long double RN2[NRN2 + 1] = +static const _Float128 RN2[NRN2 + 1] = { - -3.716661929737318153526921358113793421524E9L, - -1.138816715030710406922819131397532331321E10L, - -1.421017419363526524544402598734013569950E10L, - -9.510432842542519665483662502132010331451E9L, - -3.747528562099410197957514973274474767329E9L, - -8.923565763363912474488712255317033616626E8L, - -1.261396653700237624185350402781338231697E8L, - -9.918402520255661797735331317081425749014E6L, - -3.753996255897143855113273724233104768831E5L, - -4.778761333044147141559311805999540765612E3L + L(-3.716661929737318153526921358113793421524E9), + L(-1.138816715030710406922819131397532331321E10), + L(-1.421017419363526524544402598734013569950E10), + L(-9.510432842542519665483662502132010331451E9), + L(-3.747528562099410197957514973274474767329E9), + L(-8.923565763363912474488712255317033616626E8), + L(-1.261396653700237624185350402781338231697E8), + L(-9.918402520255661797735331317081425749014E6), + L(-3.753996255897143855113273724233104768831E5), + L(-4.778761333044147141559311805999540765612E3) }; #define NRD2 9 -static const long double RD2[NRD2 + 1] = +static const _Float128 RD2[NRD2 + 1] = { - -8.790916836764308497770359421351673950111E9L, - -2.023108608053212516399197678553737477486E10L, - -1.958067901852022239294231785363504458367E10L, - -1.035515043621003101254252481625188704529E10L, - -3.253884432621336737640841276619272224476E9L, - -6.186383531162456814954947669274235815544E8L, - -6.932557847749518463038934953605969951466E7L, - -4.240731768287359608773351626528479703758E6L, - -1.197343995089189188078944689846348116630E5L, - -1.004622911670588064824904487064114090920E3L + L(-8.790916836764308497770359421351673950111E9), + L(-2.023108608053212516399197678553737477486E10), + L(-1.958067901852022239294231785363504458367E10), + L(-1.035515043621003101254252481625188704529E10), + L(-3.253884432621336737640841276619272224476E9), + L(-6.186383531162456814954947669274235815544E8), + L(-6.932557847749518463038934953605969951466E7), + L(-4.240731768287359608773351626528479703758E6), + L(-1.197343995089189188078944689846348116630E5), + L(-1.004622911670588064824904487064114090920E3) /* 1.0E0 */ }; @@ -553,33 +549,33 @@ static const long double RD2[NRD2 + 1] = -0.125 <= x <= +0.125 1.625 <= x+1.75 <= 1.875 Peak relative error 9.2e-37 */ -static const long double lgam1r75a = -8.441162109375E-2L; -static const long double lgam1r75b = 1.0500073264444042213965868602268256157604E-5L; +static const _Float128 lgam1r75a = L(-8.441162109375E-2); +static const _Float128 lgam1r75b = L(1.0500073264444042213965868602268256157604E-5); #define NRN1r75 8 -static const long double RN1r75[NRN1r75 + 1] = +static const _Float128 RN1r75[NRN1r75 + 1] = { - -5.221061693929833937710891646275798251513E7L, - -2.052466337474314812817883030472496436993E8L, - -2.952718275974940270675670705084125640069E8L, - -2.132294039648116684922965964126389017840E8L, - -8.554103077186505960591321962207519908489E7L, - -1.940250901348870867323943119132071960050E7L, - -2.379394147112756860769336400290402208435E6L, - -1.384060879999526222029386539622255797389E5L, - -2.698453601378319296159355612094598695530E3L + L(-5.221061693929833937710891646275798251513E7), + L(-2.052466337474314812817883030472496436993E8), + L(-2.952718275974940270675670705084125640069E8), + L(-2.132294039648116684922965964126389017840E8), + L(-8.554103077186505960591321962207519908489E7), + L(-1.940250901348870867323943119132071960050E7), + L(-2.379394147112756860769336400290402208435E6), + L(-1.384060879999526222029386539622255797389E5), + L(-2.698453601378319296159355612094598695530E3) }; #define NRD1r75 8 -static const long double RD1r75[NRD1r75 + 1] = +static const _Float128 RD1r75[NRD1r75 + 1] = { - -2.109754689501705828789976311354395393605E8L, - -5.036651829232895725959911504899241062286E8L, - -4.954234699418689764943486770327295098084E8L, - -2.589558042412676610775157783898195339410E8L, - -7.731476117252958268044969614034776883031E7L, - -1.316721702252481296030801191240867486965E7L, - -1.201296501404876774861190604303728810836E6L, - -5.007966406976106636109459072523610273928E4L, - -6.155817990560743422008969155276229018209E2L + L(-2.109754689501705828789976311354395393605E8), + L(-5.036651829232895725959911504899241062286E8), + L(-4.954234699418689764943486770327295098084E8), + L(-2.589558042412676610775157783898195339410E8), + L(-7.731476117252958268044969614034776883031E7), + L(-1.316721702252481296030801191240867486965E7), + L(-1.201296501404876774861190604303728810836E6), + L(-5.007966406976106636109459072523610273928E4), + L(-6.155817990560743422008969155276229018209E2) /* 1.0E0L */ }; @@ -588,35 +584,35 @@ static const long double RD1r75[NRD1r75 + 1] = -0.0867 <= x <= +0.1634 1.374932... <= x+x0 <= 1.625032... Peak relative error 4.0e-36 */ -static const long double x0a = 1.4616241455078125L; -static const long double x0b = 7.9994605498412626595423257213002588621246E-6L; -static const long double y0a = -1.21490478515625E-1L; -static const long double y0b = 4.1879797753919044854428223084178486438269E-6L; +static const _Float128 x0a = L(1.4616241455078125); +static const _Float128 x0b = L(7.9994605498412626595423257213002588621246E-6); +static const _Float128 y0a = L(-1.21490478515625E-1); +static const _Float128 y0b = L(4.1879797753919044854428223084178486438269E-6); #define NRN1r5 8 -static const long double RN1r5[NRN1r5 + 1] = +static const _Float128 RN1r5[NRN1r5 + 1] = { - 6.827103657233705798067415468881313128066E5L, - 1.910041815932269464714909706705242148108E6L, - 2.194344176925978377083808566251427771951E6L, - 1.332921400100891472195055269688876427962E6L, - 4.589080973377307211815655093824787123508E5L, - 8.900334161263456942727083580232613796141E4L, - 9.053840838306019753209127312097612455236E3L, - 4.053367147553353374151852319743594873771E2L, - 5.040631576303952022968949605613514584950E0L + L(6.827103657233705798067415468881313128066E5), + L(1.910041815932269464714909706705242148108E6), + L(2.194344176925978377083808566251427771951E6), + L(1.332921400100891472195055269688876427962E6), + L(4.589080973377307211815655093824787123508E5), + L(8.900334161263456942727083580232613796141E4), + L(9.053840838306019753209127312097612455236E3), + L(4.053367147553353374151852319743594873771E2), + L(5.040631576303952022968949605613514584950E0) }; #define NRD1r5 8 -static const long double RD1r5[NRD1r5 + 1] = +static const _Float128 RD1r5[NRD1r5 + 1] = { - 1.411036368843183477558773688484699813355E6L, - 4.378121767236251950226362443134306184849E6L, - 5.682322855631723455425929877581697918168E6L, - 3.999065731556977782435009349967042222375E6L, - 1.653651390456781293163585493620758410333E6L, - 4.067774359067489605179546964969435858311E5L, - 5.741463295366557346748361781768833633256E4L, - 4.226404539738182992856094681115746692030E3L, - 1.316980975410327975566999780608618774469E2L, + L(1.411036368843183477558773688484699813355E6), + L(4.378121767236251950226362443134306184849E6), + L(5.682322855631723455425929877581697918168E6), + L(3.999065731556977782435009349967042222375E6), + L(1.653651390456781293163585493620758410333E6), + L(4.067774359067489605179546964969435858311E5), + L(5.741463295366557346748361781768833633256E4), + L(4.226404539738182992856094681115746692030E3), + L(1.316980975410327975566999780608618774469E2), /* 1.0E0L */ }; @@ -625,34 +621,34 @@ static const long double RD1r5[NRD1r5 + 1] = -.125 <= x <= +.125 1.125 <= x+1.25 <= 1.375 Peak relative error = 4.9e-36 */ -static const long double lgam1r25a = -9.82818603515625E-2L; -static const long double lgam1r25b = 1.0023929749338536146197303364159774377296E-5L; +static const _Float128 lgam1r25a = L(-9.82818603515625E-2); +static const _Float128 lgam1r25b = L(1.0023929749338536146197303364159774377296E-5); #define NRN1r25 9 -static const long double RN1r25[NRN1r25 + 1] = +static const _Float128 RN1r25[NRN1r25 + 1] = { - -9.054787275312026472896002240379580536760E4L, - -8.685076892989927640126560802094680794471E4L, - 2.797898965448019916967849727279076547109E5L, - 6.175520827134342734546868356396008898299E5L, - 5.179626599589134831538516906517372619641E5L, - 2.253076616239043944538380039205558242161E5L, - 5.312653119599957228630544772499197307195E4L, - 6.434329437514083776052669599834938898255E3L, - 3.385414416983114598582554037612347549220E2L, - 4.907821957946273805080625052510832015792E0L + L(-9.054787275312026472896002240379580536760E4), + L(-8.685076892989927640126560802094680794471E4), + L(2.797898965448019916967849727279076547109E5), + L(6.175520827134342734546868356396008898299E5), + L(5.179626599589134831538516906517372619641E5), + L(2.253076616239043944538380039205558242161E5), + L(5.312653119599957228630544772499197307195E4), + L(6.434329437514083776052669599834938898255E3), + L(3.385414416983114598582554037612347549220E2), + L(4.907821957946273805080625052510832015792E0) }; #define NRD1r25 8 -static const long double RD1r25[NRD1r25 + 1] = +static const _Float128 RD1r25[NRD1r25 + 1] = { - 3.980939377333448005389084785896660309000E5L, - 1.429634893085231519692365775184490465542E6L, - 2.145438946455476062850151428438668234336E6L, - 1.743786661358280837020848127465970357893E6L, - 8.316364251289743923178092656080441655273E5L, - 2.355732939106812496699621491135458324294E5L, - 3.822267399625696880571810137601310855419E4L, - 3.228463206479133236028576845538387620856E3L, - 1.152133170470059555646301189220117965514E2L + L(3.980939377333448005389084785896660309000E5), + L(1.429634893085231519692365775184490465542E6), + L(2.145438946455476062850151428438668234336E6), + L(1.743786661358280837020848127465970357893E6), + L(8.316364251289743923178092656080441655273E5), + L(2.355732939106812496699621491135458324294E5), + L(3.822267399625696880571810137601310855419E4), + L(3.228463206479133236028576845538387620856E3), + L(1.152133170470059555646301189220117965514E2) /* 1.0E0L */ }; @@ -662,29 +658,29 @@ static const long double RD1r25[NRD1r25 + 1] = 1.0 <= x+1 <= 1.125 Peak relative error 1.1e-35 */ #define NRN1 8 -static const long double RN1[NRN1 + 1] = +static const _Float128 RN1[NRN1 + 1] = { - -9.987560186094800756471055681088744738818E3L, - -2.506039379419574361949680225279376329742E4L, - -1.386770737662176516403363873617457652991E4L, - 1.439445846078103202928677244188837130744E4L, - 2.159612048879650471489449668295139990693E4L, - 1.047439813638144485276023138173676047079E4L, - 2.250316398054332592560412486630769139961E3L, - 1.958510425467720733041971651126443864041E2L, - 4.516830313569454663374271993200291219855E0L + L(-9.987560186094800756471055681088744738818E3), + L(-2.506039379419574361949680225279376329742E4), + L(-1.386770737662176516403363873617457652991E4), + L(1.439445846078103202928677244188837130744E4), + L(2.159612048879650471489449668295139990693E4), + L(1.047439813638144485276023138173676047079E4), + L(2.250316398054332592560412486630769139961E3), + L(1.958510425467720733041971651126443864041E2), + L(4.516830313569454663374271993200291219855E0) }; #define NRD1 7 -static const long double RD1[NRD1 + 1] = +static const _Float128 RD1[NRD1 + 1] = { - 1.730299573175751778863269333703788214547E4L, - 6.807080914851328611903744668028014678148E4L, - 1.090071629101496938655806063184092302439E5L, - 9.124354356415154289343303999616003884080E4L, - 4.262071638655772404431164427024003253954E4L, - 1.096981664067373953673982635805821283581E4L, - 1.431229503796575892151252708527595787588E3L, - 7.734110684303689320830401788262295992921E1L + L(1.730299573175751778863269333703788214547E4), + L(6.807080914851328611903744668028014678148E4), + L(1.090071629101496938655806063184092302439E5), + L(9.124354356415154289343303999616003884080E4), + L(4.262071638655772404431164427024003253954E4), + L(1.096981664067373953673982635805821283581E4), + L(1.431229503796575892151252708527595787588E3), + L(7.734110684303689320830401788262295992921E1) /* 1.0E0 */ }; @@ -694,40 +690,40 @@ static const long double RD1[NRD1 + 1] = 0.875 <= x+1 <= 1.0 Peak relative error 7.0e-37 */ #define NRNr9 8 -static const long double RNr9[NRNr9 + 1] = +static const _Float128 RNr9[NRNr9 + 1] = { - 4.441379198241760069548832023257571176884E5L, - 1.273072988367176540909122090089580368732E6L, - 9.732422305818501557502584486510048387724E5L, - -5.040539994443998275271644292272870348684E5L, - -1.208719055525609446357448132109723786736E6L, - -7.434275365370936547146540554419058907156E5L, - -2.075642969983377738209203358199008185741E5L, - -2.565534860781128618589288075109372218042E4L, - -1.032901669542994124131223797515913955938E3L, + L(4.441379198241760069548832023257571176884E5), + L(1.273072988367176540909122090089580368732E6), + L(9.732422305818501557502584486510048387724E5), + L(-5.040539994443998275271644292272870348684E5), + L(-1.208719055525609446357448132109723786736E6), + L(-7.434275365370936547146540554419058907156E5), + L(-2.075642969983377738209203358199008185741E5), + L(-2.565534860781128618589288075109372218042E4), + L(-1.032901669542994124131223797515913955938E3), }; #define NRDr9 8 -static const long double RDr9[NRDr9 + 1] = +static const _Float128 RDr9[NRDr9 + 1] = { - -7.694488331323118759486182246005193998007E5L, - -3.301918855321234414232308938454112213751E6L, - -5.856830900232338906742924836032279404702E6L, - -5.540672519616151584486240871424021377540E6L, - -3.006530901041386626148342989181721176919E6L, - -9.350378280513062139466966374330795935163E5L, - -1.566179100031063346901755685375732739511E5L, - -1.205016539620260779274902967231510804992E4L, - -2.724583156305709733221564484006088794284E2L + L(-7.694488331323118759486182246005193998007E5), + L(-3.301918855321234414232308938454112213751E6), + L(-5.856830900232338906742924836032279404702E6), + L(-5.540672519616151584486240871424021377540E6), + L(-3.006530901041386626148342989181721176919E6), + L(-9.350378280513062139466966374330795935163E5), + L(-1.566179100031063346901755685375732739511E5), + L(-1.205016539620260779274902967231510804992E4), + L(-2.724583156305709733221564484006088794284E2) /* 1.0E0 */ }; /* Evaluate P[n] x^n + P[n-1] x^(n-1) + ... + P[0] */ -static long double -neval (long double x, const long double *p, int n) +static _Float128 +neval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = *p--; @@ -742,10 +738,10 @@ neval (long double x, const long double *p, int n) /* Evaluate x^n+1 + P[n] x^(n) + P[n-1] x^(n-1) + ... + P[0] */ -static long double -deval (long double x, const long double *p, int n) +static _Float128 +deval (_Float128 x, const _Float128 *p, int n) { - long double y; + _Float128 y; p += n; y = x + *p--; @@ -758,10 +754,10 @@ deval (long double x, const long double *p, int n) } -long double -__ieee754_lgammal_r (long double x, int *signgamp) +_Float128 +__ieee754_lgammal_r (_Float128 x, int *signgamp) { - long double p, q, w, z, nx; + _Float128 p, q, w, z, nx; int i, nn; *signgamp = 1; @@ -769,31 +765,31 @@ __ieee754_lgammal_r (long double x, int *signgamp) if (! isfinite (x)) return x * x; - if (x == 0.0L) + if (x == 0) { if (signbit (x)) *signgamp = -1; } - if (x < 0.0L) + if (x < 0) { - if (x < -2.0L && x > (LDBL_MANT_DIG == 106 ? -48.0L : -50.0L)) + if (x < -2 && x > -50) return __lgamma_negl (x, signgamp); q = -x; p = __floorl (q); if (p == q) - return (one / (p - p)); - long double halfp = p * 0.5L; + return (one / fabsl (p - p)); + _Float128 halfp = p * L(0.5); if (halfp == __floorl (halfp)) *signgamp = -1; else *signgamp = 1; - if (q < 0x1p-120L) + if (q < L(0x1p-120)) return -__logl (q); z = q - p; - if (z > 0.5L) + if (z > L(0.5)) { - p += 1.0L; + p += 1; z = p - q; } z = q * __sinl (PIL * z); @@ -802,16 +798,16 @@ __ieee754_lgammal_r (long double x, int *signgamp) return (z); } - if (x < 13.5L) + if (x < L(13.5)) { - p = 0.0L; - nx = __floorl (x + 0.5L); + p = 0; + nx = __floorl (x + L(0.5)); nn = nx; switch (nn) { case 0: /* log gamma (x + 1) = log(x) + log gamma(x) */ - if (x < 0x1p-120L) + if (x < L(0x1p-120)) return -__logl (x); else if (x <= 0.125) { @@ -819,14 +815,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.375) { - z = x - 0.25L; + z = x - L(0.25); p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); p += lgam1r25b; p += lgam1r25a; } else if (x <= 0.625) { - z = x + (1.0L - x0a); + z = x + (1 - x0a); z = z - x0b; p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); p = p * z * z; @@ -835,25 +831,25 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.875) { - z = x - 0.75L; + z = x - L(0.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; p += lgam1r75a; } else { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } p = p - __logl (x); break; case 1: - if (x < 0.875L) + if (x < L(0.875)) { if (x <= 0.625) { - z = x + (1.0L - x0a); + z = x + (1 - x0a); z = z - x0b; p = neval (z, RN1r5, NRN1r5) / deval (z, RD1r5, NRD1r5); p = p * z * z; @@ -862,7 +858,7 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else if (x <= 0.875) { - z = x - 0.75L; + z = x - L(0.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; @@ -870,26 +866,26 @@ __ieee754_lgammal_r (long double x, int *signgamp) } else { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } p = p - __logl (x); } - else if (x < 1.0L) + else if (x < 1) { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RNr9, NRNr9) / deval (z, RDr9, NRDr9); } - else if (x == 1.0L) - p = 0.0L; - else if (x <= 1.125L) + else if (x == 1) + p = 0; + else if (x <= L(1.125)) { - z = x - 1.0L; + z = x - 1; p = z * neval (z, RN1, NRN1) / deval (z, RD1, NRD1); } else if (x <= 1.375) { - z = x - 1.25L; + z = x - L(1.25); p = z * neval (z, RN1r25, NRN1r25) / deval (z, RD1r25, NRD1r25); p += lgam1r25b; p += lgam1r25a; @@ -907,7 +903,7 @@ __ieee754_lgammal_r (long double x, int *signgamp) break; case 2: - if (x < 1.625L) + if (x < L(1.625)) { z = x - x0a; z = z - x0b; @@ -916,23 +912,23 @@ __ieee754_lgammal_r (long double x, int *signgamp) p = p + y0b; p = p + y0a; } - else if (x < 1.875L) + else if (x < L(1.875)) { - z = x - 1.75L; + z = x - L(1.75); p = z * neval (z, RN1r75, NRN1r75) / deval (z, RD1r75, NRD1r75); p += lgam1r75b; p += lgam1r75a; } - else if (x == 2.0L) - p = 0.0L; - else if (x < 2.375L) + else if (x == 2) + p = 0; + else if (x < L(2.375)) { - z = x - 2.0L; + z = x - 2; p = z * neval (z, RN2, NRN2) / deval (z, RD2, NRD2); } else { - z = x - 2.5L; + z = x - L(2.5); p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); p += lgam2r5b; p += lgam2r5a; @@ -942,14 +938,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) case 3: if (x < 2.75) { - z = x - 2.5L; + z = x - L(2.5); p = z * neval (z, RN2r5, NRN2r5) / deval (z, RD2r5, NRD2r5); p += lgam2r5b; p += lgam2r5a; } else { - z = x - 3.0L; + z = x - 3; p = z * neval (z, RN3, NRN3) / deval (z, RD3, NRD3); p += lgam3b; p += lgam3a; @@ -957,70 +953,70 @@ __ieee754_lgammal_r (long double x, int *signgamp) break; case 4: - z = x - 4.0L; + z = x - 4; p = z * neval (z, RN4, NRN4) / deval (z, RD4, NRD4); p += lgam4b; p += lgam4a; break; case 5: - z = x - 5.0L; + z = x - 5; p = z * neval (z, RN5, NRN5) / deval (z, RD5, NRD5); p += lgam5b; p += lgam5a; break; case 6: - z = x - 6.0L; + z = x - 6; p = z * neval (z, RN6, NRN6) / deval (z, RD6, NRD6); p += lgam6b; p += lgam6a; break; case 7: - z = x - 7.0L; + z = x - 7; p = z * neval (z, RN7, NRN7) / deval (z, RD7, NRD7); p += lgam7b; p += lgam7a; break; case 8: - z = x - 8.0L; + z = x - 8; p = z * neval (z, RN8, NRN8) / deval (z, RD8, NRD8); p += lgam8b; p += lgam8a; break; case 9: - z = x - 9.0L; + z = x - 9; p = z * neval (z, RN9, NRN9) / deval (z, RD9, NRD9); p += lgam9b; p += lgam9a; break; case 10: - z = x - 10.0L; + z = x - 10; p = z * neval (z, RN10, NRN10) / deval (z, RD10, NRD10); p += lgam10b; p += lgam10a; break; case 11: - z = x - 11.0L; + z = x - 11; p = z * neval (z, RN11, NRN11) / deval (z, RD11, NRD11); p += lgam11b; p += lgam11a; break; case 12: - z = x - 12.0L; + z = x - 12; p = z * neval (z, RN12, NRN12) / deval (z, RD12, NRD12); p += lgam12b; p += lgam12a; break; case 13: - z = x - 13.0L; + z = x - 13; p = z * neval (z, RN13, NRN13) / deval (z, RD13, NRD13); p += lgam13b; p += lgam13a; @@ -1032,14 +1028,14 @@ __ieee754_lgammal_r (long double x, int *signgamp) if (x > MAXLGM) return (*signgamp * huge * huge); - if (x > 0x1p120L) - return x * (__logl (x) - 1.0L); + if (x > L(0x1p120)) + return x * (__logl (x) - 1); q = ls2pi - x; - q = (x - 0.5L) * __logl (x) + q; - if (x > 1.0e18L) + q = (x - L(0.5)) * __logl (x) + q; + if (x > L(1.0e18)) return (q); - p = 1.0L / (x * x); + p = 1 / (x * x); q += neval (p, RASY, NRASY) / x; return (q); } |