Program: testlnfactorial.c Test Ln_Factorial() Exceptional value: Negative argument return -DBL_MAX, ln(-1)! -1.7976931348623157e+308 Ln_Factorials n! Ln_Factorial(n) ln(Factorial(n)) Relative Error / DBL_EPSILON 0! 0.0000000000000000e+00 0.0000000000000000e+00 1! 0.0000000000000000e+00 0.0000000000000000e+00 2! 6.9314718055994529e-01 6.9314718055994529e-01 0.0000000000000000e+00 3! 1.7917594692280550e+00 1.7917594692280550e+00 0.0000000000000000e+00 4! 3.1780538303479458e+00 3.1780538303479458e+00 0.0000000000000000e+00 5! 4.7874917427820458e+00 4.7874917427820458e+00 0.0000000000000000e+00 6! 6.5792512120101012e+00 6.5792512120101012e+00 0.0000000000000000e+00 7! 8.5251613610654147e+00 8.5251613610654147e+00 0.0000000000000000e+00 8! 1.0604602902745251e+01 1.0604602902745251e+01 0.0000000000000000e+00 9! 1.2801827480081469e+01 1.2801827480081469e+01 0.0000000000000000e+00 10! 1.5104412573075516e+01 1.5104412573075516e+01 0.0000000000000000e+00 11! 1.7502307845873887e+01 1.7502307845873887e+01 0.0000000000000000e+00 12! 1.9987214495661885e+01 1.9987214495661885e+01 0.0000000000000000e+00 13! 2.2552163853123425e+01 2.2552163853123425e+01 0.0000000000000000e+00 14! 2.5191221182738680e+01 2.5191221182738680e+01 0.0000000000000000e+00 15! 2.7899271383840890e+01 2.7899271383840890e+01 0.0000000000000000e+00 16! 3.0671860106080672e+01 3.0671860106080672e+01 0.0000000000000000e+00 17! 3.3505073450136891e+01 3.3505073450136891e+01 0.0000000000000000e+00 18! 3.6395445208033053e+01 3.6395445208033053e+01 0.0000000000000000e+00 19! 3.9339884187199495e+01 3.9339884187199495e+01 0.0000000000000000e+00 20! 4.2335616460753485e+01 4.2335616460753485e+01 0.0000000000000000e+00 21! 4.5380138898476908e+01 4.5380138898476908e+01 0.0000000000000000e+00 22! 4.8471181351835227e+01 4.8471181351835227e+01 0.0000000000000000e+00 23! 5.1606675567764377e+01 5.1606675567764377e+01 0.0000000000000000e+00 24! 5.4784729398112319e+01 5.4784729398112319e+01 0.0000000000000000e+00 25! 5.8003605222980518e+01 5.8003605222980518e+01 0.0000000000000000e+00 26! 6.1261701761002001e+01 6.1261701761002001e+01 0.0000000000000000e+00 27! 6.4557538627006338e+01 6.4557538627006338e+01 0.0000000000000000e+00 28! 6.7889743137181540e+01 6.7889743137181540e+01 0.0000000000000000e+00 29! 7.1257038967168015e+01 7.1257038967168015e+01 0.0000000000000000e+00 30! 7.4658236348830158e+01 7.4658236348830158e+01 0.0000000000000000e+00 31! 7.8092223553315307e+01 7.8092223553315307e+01 0.0000000000000000e+00 32! 8.1557959456115043e+01 8.1557959456115043e+01 0.0000000000000000e+00 33! 8.5054467017581516e+01 8.5054467017581516e+01 0.0000000000000000e+00 34! 8.8580827542197682e+01 8.8580827542197682e+01 0.0000000000000000e+00 35! 9.2136175603687093e+01 9.2136175603687093e+01 0.0000000000000000e+00 36! 9.5719694542143202e+01 9.5719694542143202e+01 0.0000000000000000e+00 37! 9.9330612454787428e+01 9.9330612454787428e+01 0.0000000000000000e+00 38! 1.0296819861451381e+02 1.0296819861451381e+02 0.0000000000000000e+00 39! 1.0663176026064346e+02 1.0663176026064346e+02 0.0000000000000000e+00 40! 1.1032063971475739e+02 1.1032063971475739e+02 0.0000000000000000e+00 41! 1.1403421178146171e+02 1.1403421178146171e+02 0.0000000000000000e+00 42! 1.1777188139974507e+02 1.1777188139974507e+02 0.0000000000000000e+00 43! 1.2153308151543864e+02 1.2153308151543864e+02 0.0000000000000000e+00 44! 1.2531727114935690e+02 1.2531727114935690e+02 0.0000000000000000e+00 45! 1.2912393363912722e+02 1.2912393363912722e+02 0.0000000000000000e+00 46! 1.3295257503561632e+02 1.3295257503561632e+02 0.0000000000000000e+00 47! 1.3680272263732635e+02 1.3680272263732635e+02 0.0000000000000000e+00 48! 1.4067392364823425e+02 1.4067392364823425e+02 0.0000000000000000e+00 49! 1.4456574394634490e+02 1.4456574394634490e+02 0.0000000000000000e+00 50! 1.4847776695177302e+02 1.4847776695177302e+02 0.0000000000000000e+00 51! 1.5240959258449735e+02 1.5240959258449735e+02 0.0000000000000000e+00 52! 1.5636083630307880e+02 1.5636083630307880e+02 0.0000000000000000e+00 53! 1.6033112821663090e+02 1.6033112821663090e+02 0.0000000000000000e+00 54! 1.6432011226319517e+02 1.6432011226319517e+02 0.0000000000000000e+00 55! 1.6832744544842765e+02 1.6832744544842765e+02 0.0000000000000000e+00 56! 1.7235279713916279e+02 1.7235279713916279e+02 0.0000000000000000e+00 57! 1.7639584840699735e+02 1.7639584840699735e+02 0.0000000000000000e+00 58! 1.8045629141754378e+02 1.8045629141754378e+02 0.0000000000000000e+00 59! 1.8453382886144948e+02 1.8453382886144948e+02 0.0000000000000000e+00 60! 1.8862817342367160e+02 1.8862817342367160e+02 0.0000000000000000e+00 61! 1.9273904728784490e+02 1.9273904728784490e+02 0.0000000000000000e+00 62! 1.9686618167289001e+02 1.9686618167289001e+02 0.0000000000000000e+00 63! 2.0100931639928152e+02 2.0100931639928152e+02 0.0000000000000000e+00 64! 2.0516819948264120e+02 2.0516819948264120e+02 0.0000000000000000e+00 65! 2.0934258675253685e+02 2.0934258675253685e+02 0.0000000000000000e+00 66! 2.1353224149456327e+02 2.1353224149456327e+02 0.0000000000000000e+00 67! 2.1773693411395422e+02 2.1773693411395422e+02 0.0000000000000000e+00 68! 2.2195644181913033e+02 2.2195644181913033e+02 0.0000000000000000e+00 69! 2.2619054832372760e+02 2.2619054832372760e+02 0.0000000000000000e+00 70! 2.3043904356577696e+02 2.3043904356577696e+02 0.0000000000000000e+00 71! 2.3470172344281826e+02 2.3470172344281826e+02 0.0000000000000000e+00 72! 2.3897838956183432e+02 2.3897838956183432e+02 0.0000000000000000e+00 73! 2.4326884900298271e+02 2.4326884900298271e+02 0.0000000000000000e+00 74! 2.4757291409618688e+02 2.4757291409618688e+02 0.0000000000000000e+00 75! 2.5189040220972319e+02 2.5189040220972319e+02 0.0000000000000000e+00 76! 2.5622113555000954e+02 2.5622113555000954e+02 0.0000000000000000e+00 77! 2.6056494097186322e+02 2.6056494097186322e+02 0.0000000000000000e+00 78! 2.6492164979855278e+02 2.6492164979855278e+02 0.0000000000000000e+00 79! 2.6929109765101981e+02 2.6929109765101981e+02 0.0000000000000000e+00 80! 2.7367312428569369e+02 2.7367312428569369e+02 0.0000000000000000e+00 81! 2.7806757344036612e+02 2.7806757344036612e+02 0.0000000000000000e+00 82! 2.8247429268763040e+02 2.8247429268763040e+02 0.0000000000000000e+00 83! 2.8689313329542699e+02 2.8689313329542699e+02 0.0000000000000000e+00 84! 2.9132395009427029e+02 2.9132395009427029e+02 0.0000000000000000e+00 85! 2.9576660135076065e+02 2.9576660135076065e+02 0.0000000000000000e+00 86! 3.0022094864701415e+02 3.0022094864701415e+02 0.0000000000000000e+00 87! 3.0468685676566872e+02 3.0468685676566872e+02 0.0000000000000000e+00 88! 3.0916419358014690e+02 3.0916419358014690e+02 0.0000000000000000e+00 89! 3.1365282994987905e+02 3.1365282994987905e+02 0.0000000000000000e+00 90! 3.1815263962020930e+02 3.1815263962020930e+02 0.0000000000000000e+00 91! 3.2266349912672615e+02 3.2266349912672615e+02 0.0000000000000000e+00 92! 3.2718528770377520e+02 3.2718528770377520e+02 0.0000000000000000e+00 93! 3.3171788719692847e+02 3.3171788719692847e+02 0.0000000000000000e+00 94! 3.3626118197919845e+02 3.3626118197919845e+02 0.0000000000000000e+00 95! 3.4081505887079902e+02 3.4081505887079902e+02 0.0000000000000000e+00 96! 3.4537940706226686e+02 3.4537940706226686e+02 0.0000000000000000e+00 97! 3.4995411804077025e+02 3.4995411804077025e+02 0.0000000000000000e+00 98! 3.5453908551944079e+02 3.5453908551944079e+02 0.0000000000000000e+00 99! 3.5913420536957540e+02 3.5913420536957540e+02 0.0000000000000000e+00 100! 3.6373937555556347e+02 3.6373937555556347e+02 0.0000000000000000e+00 101! 3.6835449607240474e+02 3.6835449607240474e+02 0.0000000000000000e+00 102! 3.7297946888568902e+02 3.7297946888568902e+02 0.0000000000000000e+00 103! 3.7761419787391867e+02 3.7761419787391867e+02 0.0000000000000000e+00 104! 3.8225858877306001e+02 3.8225858877306001e+02 0.0000000000000000e+00 105! 3.8691254912321756e+02 3.8691254912321756e+02 0.0000000000000000e+00 106! 3.9157598821732961e+02 3.9157598821732961e+02 0.0000000000000000e+00 107! 3.9624881705179155e+02 3.9624881705179155e+02 0.0000000000000000e+00 108! 4.0093094827891576e+02 4.0093094827891576e+02 0.0000000000000000e+00 109! 4.0562229616114490e+02 4.0562229616114490e+02 0.0000000000000000e+00 110! 4.1032277652693733e+02 4.1032277652693733e+02 0.0000000000000000e+00 111! 4.1503230672824964e+02 4.1503230672824964e+02 0.0000000000000000e+00 112! 4.1975080559954472e+02 4.1975080559954472e+02 0.0000000000000000e+00 113! 4.2447819341825709e+02 4.2447819341825709e+02 0.0000000000000000e+00 114! 4.2921439186665157e+02 4.2921439186665157e+02 0.0000000000000000e+00 115! 4.3395932399501481e+02 4.3395932399501481e+02 0.0000000000000000e+00 116! 4.3871291418612117e+02 4.3871291418612117e+02 0.0000000000000000e+00 117! 4.4347508812091894e+02 4.4347508812091894e+02 0.0000000000000000e+00 118! 4.4824577274538461e+02 4.4824577274538461e+02 0.0000000000000000e+00 119! 4.5302489623849613e+02 4.5302489623849613e+02 0.0000000000000000e+00 120! 4.5781238798127816e+02 4.5781238798127816e+02 0.0000000000000000e+00 121! 4.6260817852687489e+02 4.6260817852687489e+02 0.0000000000000000e+00 122! 4.6741219957160820e+02 4.6741219957160820e+02 0.0000000000000000e+00 123! 4.7222438392698058e+02 4.7222438392698058e+02 0.0000000000000000e+00 124! 4.7704466549258564e+02 4.7704466549258564e+02 0.0000000000000000e+00 125! 4.8187297922988796e+02 4.8187297922988796e+02 0.0000000000000000e+00 126! 4.8670926113683942e+02 4.8670926113683942e+02 0.0000000000000000e+00 127! 4.9155344822329801e+02 4.9155344822329801e+02 0.0000000000000000e+00 128! 4.9640547848721764e+02 4.9640547848721764e+02 0.0000000000000000e+00 129! 5.0126529089157930e+02 5.0126529089157930e+02 0.0000000000000000e+00 130! 5.0613282534203489e+02 5.0613282534203489e+02 0.0000000000000000e+00 131! 5.1100802266523601e+02 5.1100802266523601e+02 0.0000000000000000e+00 132! 5.1589082458782241e+02 5.1589082458782241e+02 0.0000000000000000e+00 133! 5.2078117371604412e+02 5.2078117371604412e+02 0.0000000000000000e+00 134! 5.2567901351599505e+02 5.2567901351599505e+02 0.0000000000000000e+00 135! 5.3058428829443346e+02 5.3058428829443346e+02 0.0000000000000000e+00 136! 5.3549694318016952e+02 5.3549694318016952e+02 0.0000000000000000e+00 137! 5.4041692410599762e+02 5.4041692410599762e+02 0.0000000000000000e+00 138! 5.4534417779115483e+02 5.4534417779115483e+02 0.0000000000000000e+00 139! 5.5027865172428551e+02 5.5027865172428551e+02 0.0000000000000000e+00 140! 5.5522029414689484e+02 5.5522029414689484e+02 0.0000000000000000e+00 141! 5.6016905403727299e+02 5.6016905403727299e+02 0.0000000000000000e+00 142! 5.6512488109487435e+02 5.6512488109487435e+02 0.0000000000000000e+00 143! 5.7008772572513419e+02 5.7008772572513419e+02 0.0000000000000000e+00 144! 5.7505753902471020e+02 5.7505753902471020e+02 0.0000000000000000e+00 145! 5.8003427276713080e+02 5.8003427276713080e+02 0.0000000000000000e+00 146! 5.8501787938883911e+02 5.8501787938883911e+02 0.0000000000000000e+00 147! 5.9000831197561786e+02 5.9000831197561786e+02 0.0000000000000000e+00 148! 5.9500552424938201e+02 5.9500552424938201e+02 0.0000000000000000e+00 149! 6.0000947055532743e+02 6.0000947055532743e+02 0.0000000000000000e+00 150! 6.0502010584942366e+02 6.0502010584942366e+02 0.0000000000000000e+00 151! 6.1003738568623862e+02 6.1003738568623862e+02 0.0000000000000000e+00 152! 6.1506126620708494e+02 6.1506126620708494e+02 0.0000000000000000e+00 153! 6.2009170412847732e+02 6.2009170412847732e+02 0.0000000000000000e+00 154! 6.2512865673089095e+02 6.2512865673089095e+02 0.0000000000000000e+00 155! 6.3017208184781020e+02 6.3017208184781020e+02 0.0000000000000000e+00 156! 6.3522193785505976e+02 6.3522193785505976e+02 0.0000000000000000e+00 157! 6.4027818366040799e+02 6.4027818366040799e+02 0.0000000000000000e+00 158! 6.4534077869343503e+02 6.4534077869343503e+02 0.0000000000000000e+00 159! 6.5040968289565524e+02 6.5040968289565524e+02 0.0000000000000000e+00 160! 6.5548485671088906e+02 6.5548485671088906e+02 0.0000000000000000e+00 161! 6.6056626107587351e+02 6.6056626107587351e+02 0.0000000000000000e+00 162! 6.6565385741110595e+02 6.6565385741110595e+02 0.0000000000000000e+00 163! 6.7074760761191271e+02 6.7074760761191271e+02 0.0000000000000000e+00 164! 6.7584747403973688e+02 6.7584747403973688e+02 0.0000000000000000e+00 165! 6.8095341951363741e+02 6.8095341951363741e+02 0.0000000000000000e+00 166! 6.8606540730199401e+02 6.8606540730199401e+02 0.0000000000000000e+00 167! 6.9118340111441080e+02 6.9118340111441080e+02 0.0000000000000000e+00 168! 6.9630736509381404e+02 6.9630736509381404e+02 0.0000000000000000e+00 169! 7.0143726380873704e+02 7.0143726380873704e+02 0.0000000000000000e+00 170! 7.0657306224578736e+02 7.0657306224578736e+02 0.0000000000000000e+00 Large Factorials 171! 7.1171472580228999e+02 7.1171472580228999e+02 0.0000000000000000e+00 172! 7.1686222027910344e+02 7.1686222027910344e+02 0.0000000000000000e+00 Test xLn_Factorial() Exceptional value: Negative argument return -LDBL_MAX, ln(-1)! -1.1897314953572318e+4932 xLn_Factorials n! xLn_Factorial(n) ln(xFactorial(n)) Relative Error / LDBL_EPSILON 0! 0.0000000000000000e+00 0.0000000000000000e+00 1! 0.0000000000000000e+00 0.0000000000000000e+00 2! 6.9314718055994531e-01 6.9314718055994531e-01 0.0000000000000000e+00 3! 1.7917594692280550e+00 1.7917594692280550e+00 0.0000000000000000e+00 4! 3.1780538303479456e+00 3.1780538303479456e+00 0.0000000000000000e+00 5! 4.7874917427820460e+00 4.7874917427820460e+00 0.0000000000000000e+00 6! 6.5792512120101010e+00 6.5792512120101010e+00 0.0000000000000000e+00 7! 8.5251613610654143e+00 8.5251613610654143e+00 0.0000000000000000e+00 8! 1.0604602902745250e+01 1.0604602902745250e+01 -7.5438939801593253e-01 9! 1.2801827480081470e+01 1.2801827480081470e+01 0.0000000000000000e+00 10! 1.5104412573075515e+01 1.5104412573075515e+01 0.0000000000000000e+00 11! 1.7502307845873886e+01 1.7502307845873886e+01 0.0000000000000000e+00 12! 1.9987214495661886e+01 1.9987214495661886e+01 0.0000000000000000e+00 13! 2.2552163853123423e+01 2.2552163853123423e+01 0.0000000000000000e+00 14! 2.5191221182738681e+01 2.5191221182738681e+01 0.0000000000000000e+00 15! 2.7899271383840892e+01 2.7899271383840892e+01 -5.7349167940160309e-01 16! 3.0671860106080673e+01 3.0671860106080673e+01 0.0000000000000000e+00 17! 3.3505073450136889e+01 3.3505073450136889e+01 -9.5507923740633556e-01 18! 3.6395445208033054e+01 3.6395445208033054e+01 0.0000000000000000e+00 19! 3.9339884187199494e+01 3.9339884187199494e+01 0.0000000000000000e+00 20! 4.2335616460753485e+01 4.2335616460753485e+01 0.0000000000000000e+00 21! 4.5380138898476908e+01 4.5380138898476908e+01 0.0000000000000000e+00 22! 4.8471181351835224e+01 4.8471181351835224e+01 0.0000000000000000e+00 23! 5.1606675567764374e+01 5.1606675567764374e+01 0.0000000000000000e+00 24! 5.4784729398112319e+01 5.4784729398112319e+01 0.0000000000000000e+00 25! 5.8003605222980520e+01 5.8003605222980520e+01 -5.5168984543260564e-01 26! 6.1261701761002002e+01 6.1261701761002002e+01 -5.2234918521918326e-01 27! 6.4557538627006331e+01 6.4557538627006331e+01 -9.9136369448303136e-01 28! 6.7889743137181535e+01 6.7889743137181535e+01 0.0000000000000000e+00 29! 7.1257038967168009e+01 7.1257038967168009e+01 0.0000000000000000e+00 30! 7.4658236348830164e+01 7.4658236348830164e+01 0.0000000000000000e+00 31! 7.8092223553315311e+01 7.8092223553315311e+01 0.0000000000000000e+00 32! 8.1557959456115037e+01 8.1557959456115037e+01 0.0000000000000000e+00 33! 8.5054467017581517e+01 8.5054467017581517e+01 0.0000000000000000e+00 34! 8.8580827542197679e+01 8.8580827542197679e+01 0.0000000000000000e+00 35! 9.2136175603687092e+01 9.2136175603687092e+01 0.0000000000000000e+00 36! 9.5719694542143202e+01 9.5719694542143202e+01 0.0000000000000000e+00 37! 9.9330612454787427e+01 9.9330612454787427e+01 0.0000000000000000e+00 38! 1.0296819861451381e+02 1.0296819861451381e+02 0.0000000000000000e+00 39! 1.0663176026064346e+02 1.0663176026064346e+02 -6.0019641280949251e-01 40! 1.1032063971475740e+02 1.1032063971475740e+02 0.0000000000000000e+00 41! 1.1403421178146170e+02 1.1403421178146170e+02 0.0000000000000000e+00 42! 1.1777188139974507e+02 1.1777188139974507e+02 0.0000000000000000e+00 43! 1.2153308151543863e+02 1.2153308151543863e+02 0.0000000000000000e+00 44! 1.2531727114935690e+02 1.2531727114935690e+02 0.0000000000000000e+00 45! 1.2912393363912721e+02 1.2912393363912721e+02 -9.9129569857848073e-01 46! 1.3295257503561631e+02 1.3295257503561631e+02 0.0000000000000000e+00 47! 1.3680272263732637e+02 1.3680272263732637e+02 -9.3565389293703602e-01 48! 1.4067392364823426e+02 1.4067392364823426e+02 0.0000000000000000e+00 49! 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