diff options
Diffstat (limited to 'sysdeps')
| -rw-r--r-- | sysdeps/generic/math_private.h | 12 | ||||
| -rw-r--r-- | sysdeps/i386/fpu/libm-test-ulps | 596 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/e_gamma_r.c | 140 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/gamma_product.c | 75 | ||||
| -rw-r--r-- | sysdeps/ieee754/dbl-64/gamma_productf.c | 46 | ||||
| -rw-r--r-- | sysdeps/ieee754/flt-32/e_gammaf_r.c | 134 | ||||
| -rw-r--r-- | sysdeps/ieee754/k_standard.c | 2 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/e_gammal_r.c | 145 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128/gamma_productl.c | 75 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c | 144 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-128ibm/gamma_productl.c | 42 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/e_gammal_r.c | 143 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/gamma_product.c | 46 | ||||
| -rw-r--r-- | sysdeps/ieee754/ldbl-96/gamma_productl.c | 75 | ||||
| -rw-r--r-- | sysdeps/x86_64/fpu/libm-test-ulps | 676 |
15 files changed, 2307 insertions, 44 deletions
diff --git a/sysdeps/generic/math_private.h b/sysdeps/generic/math_private.h index 7661788e6d..9d6ecade68 100644 --- a/sysdeps/generic/math_private.h +++ b/sysdeps/generic/math_private.h @@ -371,6 +371,18 @@ extern float __x2y2m1f (float x, float y); extern double __x2y2m1 (double x, double y); extern long double __x2y2m1l (long double x, long double y); +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ +extern float __gamma_productf (float x, float x_eps, int n, float *eps); +extern double __gamma_product (double x, double x_eps, int n, double *eps); +extern long double __gamma_productl (long double x, long double x_eps, + int n, long double *eps); + #ifndef math_opt_barrier # define math_opt_barrier(x) \ ({ __typeof (x) __x = (x); __asm ("" : "+m" (__x)); __x; }) diff --git a/sysdeps/i386/fpu/libm-test-ulps b/sysdeps/i386/fpu/libm-test-ulps index 081559257d..8761d3ac99 100644 --- a/sysdeps/i386/fpu/libm-test-ulps +++ b/sysdeps/i386/fpu/libm-test-ulps @@ -6165,6 +6165,379 @@ idouble: 2 ifloat: 1 ildouble: 1 ldouble: 1 +Test "tgamma (-0x0.ffffffffffffffffp0) == -1.8446744073709551616422784335098467139470e+19": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1.000002p0) == 8.3886075772158332060084424806449513922858e+06": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1.0a32a2p+5) == 1.8125267978155035272941154746083439329912e-37": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1.5800000080001p+7) == -3.1439271448823567326093363350637118195240e-304": +double: 1 +idouble: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x1.fffffffffffffp0) == 2.2517998136852484613921675492337776673289e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x13.ffffep0) == 2.1550026214525536756224040483579183652119e-13": +float: 1 +ifloat: 1 +Test "tgamma (-0x13.ffffffffffffffep0) == 2.3694367893405502075347562184931828448654e-01": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x13.ffffffffffffp0) == 1.1569515572952029402736625857313236848570e-04": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x14.000000000001p0) == -1.1569515572951781096476686854873801225397e-04": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x1d.ffffep0) == 1.9765721589464867957912772592816027583176e-27": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1d.ffffffffffffffep0) == 2.1732499046818166459536268654187775086902e-15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1e.000000000000002p0) == -2.1732499046818166201837145753965837196590e-15": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x1e.00002p0) == -1.9765463890341964384070157599286498212650e-27": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1f4.00000000000002p0) == -2.9528489142763131406565394149878256133744e-1118": +ildouble: 3 +ldouble: 3 +Test "tgamma (-0x1p-24) == -1.6777216577215723853867349114260580375249e+07": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.0000000000000004p0) == -2.3058430092136939515386078324507664305064e+18": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.0000000000002p0) == -1.1258999068426235386078324507668462444260e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.000004p0) == -2.0971515386080557574407223895988378776747e+06": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.fffffcp0) == -6.9905087601970247876992248591045142913324e+05": +double: 1 +idouble: 1 +Test "tgamma (-0x27.ffffcp0) == 3.2129279441390812141195076945616975790225e-43": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x27.fffffffffffep0) == 1.7249032006742266376460389310340465554361e-34": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.000000000002p0) == -1.7249032006741359094184881234822934593822e-34": +double: 1 +idouble: 1 +Test "tgamma (-0x28.00004p0) == -3.2128372159115252365699015758097981155793e-43": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.ffffcp0) == -7.8364103489619817539676737414096652170685e-45": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.fffffffffffep0) == -4.2070809772542120404320040128839297118648e-36": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.ffffffffffffffcp0) == -8.6161018414163982777002940498289948893044e-33": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.000000000000004p0) == 8.6161018414163980549537337663264762179535e-33": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.000000000002p0) == 4.2070809772539892938717205103652583609422e-36": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.00004p0) == 7.8361876024016854597745353972619195760515e-45": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.ffffcp0) == 1.8658121573125798145204120066590953505132e-46": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2a.00004p0) == -1.8657587834931410688246126853566488626385e-46": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2ed.fffffffffffffcp0) == 6.9801511765871818502006905472380418430269e-1817": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3.0000000000002p0) == 3.7529996894754112398038859470009084971438e+14": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3.000004p0) == 6.9905045731381300146131914617735687322025e+05": +double: 1 +idouble: 1 +Test "tgamma (-0x3.fffffcp0) == 1.7476272942159602684441970627092458855771e+05": +float: 1 +ifloat: 1 +Test "tgamma (-0x3.ffffffffffffep0) == 9.3824992236885396088236184658402406857503e+13": +double: 1 +idouble: 1 +Test "tgamma (-0x3.fffffffffffffffcp0) == 1.9215358410114116272942156951799168638773e+17": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x31.fffffffffffep0) == 4.6273774273632946947805289899230181990085e-51": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x32.000000000000004p0) == -9.4768689712397633101385547903658075308777e-48": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x32.000000000002p0) == -4.6273774273630367887073532197576655720178e-51": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3e7.fffffffffffffcp0) == 4.4768809295877296071892611539415773519036e-2552": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3e8.00000000000004p0) == -4.4768809295877261735541135972060089530309e-2552": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.0000000000000008p0) == -9.6076792050570581270578430482008313684602e+16": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.000008p0) == -8.7381270578483499672965708923121931082305e+04": +float: 2 +ifloat: 2 +Test "tgamma (-0x4.fffff8p0) == -1.7476280884325863043793087474680780379554e+04": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.ffffffffffffcp0) == -9.3824992236885475509805702650262155809819e+12": +double: 1 +idouble: 1 +Test "tgamma (-0x4e2.00000000000008p0) == -5.4651488569236421026544487194247355967789e-3315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.0000000000000008p0) == 1.9215358410114116252449019429734996071487e+16": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.0000000000004p0) == 9.3824992236885191156860964016850034672946e+12": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.000008p0) == 1.7476252449031389167286893378510439443844e+04": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.fffff8p0) == 2.9127137122026653716311560165769071985443e+03": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (-0x5.ffffffffffffcp0) == 1.5637498706147581566449098589862357835505e+12": +double: 1 +idouble: 1 +Test "tgamma (-0x5db.fffffffffffff8p0) == 1.8718211510339187689122114747834510481993e-4099": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x6.0000000000000008p0) == -3.2025597350190193751766884234743511972877e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x6.000008p0) == -2.9127085100239567622341538102130981196910e+03": +double: 1 +idouble: 1 +Test "tgamma (-0x6.fffff8p0) == -4.1610198723079349791939054365613377035519e+02": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x6.ffffffffffffcp0) == -2.2339283865925119357965832452642909859289e+11": +double: 3 +idouble: 3 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x63.fffffffffffcp0) == 7.5400833348840965463348754984345825364294e-145": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x63.ffffffffffffff8p0) == 1.5442090669841618542494279375256856430049e-141": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x64.000000000000008p0) == -1.5442090669841617554527108348771968070612e-141": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x64.000000000004p0) == -7.5400833348831085791638490135462230991587e-145": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x6d6.00000000000008p0) == -4.2925786447266421378134368786479937285900e-4902": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.0000000000000008p0) == 4.5750853357414562499689653215166468353753e+14": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.0000000000004p0) == 2.2339283865925039372192897706214475877342e+11": +double: 4 +idouble: 4 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.000008p0) == 4.1610118737306415004517215226199741948733e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.fffff8p0) == 5.2012751504050764429534086402871289946986e+01": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.ffffffffffffcp0) == 2.7924104832406402297655703264222230055898e+10": +double: 2 +idouble: 2 +Test "tgamma (-0x7.fffffffffffffff8p0) == 5.7188566696768203227694481100089533685959e+13": +ildouble: 4 +ldouble: 4 +Test "tgamma (-0x8.000000000000001p0) == -2.8594283348384101534210280804672371201060e+13": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x8.00001p0) == -2.6006296115134418896533598545925084576702e+01": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x9.ffffffffffff8p0) == 1.5513391573559147700413058496716749249803e+08": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x95.fffffffffff8p0) == 6.1582369322723207086020016423767264008839e-250": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x95.ffffffffffffffp0) == 1.2612069237291916400144732227892704713839e-246": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x96.000000000008p0) == -6.1582369322705655439003240743176243138734e-250": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xa.000000000000001p0) == -3.1771425942649001698860433502350057763905e+11": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xa.0000000000008p0) == -1.5513391573559018084419393002828541166901e+08": +double: 1 +idouble: 1 +Test "tgamma (-0xa.00001p0) == -2.8895878754728051776830454190076999107021e-01": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb4.ffffffffffffffp0) == -1.9816628031468191243385005680879281767694e-315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb5.00000000000001p0) == 1.9816628031468188382579700510291588022368e-315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb5.000000000008p0) == 9.6760879059888966544677044221698800670218e-319": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xb5.ffffffffffffffp0) == 1.0888257160147357826865964233809723297472e-317": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.00000000000001p0) == -1.0888257160147356253334423783317128355514e-317": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.fffffffffff8p0) == -2.9052086428846935908287469917922960610289e-323": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.ffffffffffffffp0) == -5.9498673006269714905418984659220067091260e-320": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb7.fffffffffff8p0) == 1.5789177406982032823826953250736039527543e-325": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb7.ffffffffffffffp0) == 3.2336235329494410277123118903958061569834e-322": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xb8.000000000008p0) == -1.5789177406977349925854817486109369828857e-325": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbb.ffffffffffffffp0) == 2.6730392040715350119087465463119939092815e-331": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xbc.00000000000001p0) == -2.6730392040715346232108532050343031951651e-331": +ildouble: 3 +ldouble: 3 +Test "tgamma (-0xbd.00000000000001p0) == 1.4143064571807061497431633629389135273431e-333": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbe.00000000000001p0) == -7.4437181956879271033676895858841525581153e-336": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbe.ffffffffffffffp0) == -3.8972346574282346536709453101948570578636e-338": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbf.00000000000001p0) == 3.8972346574282340852496542564155275274974e-338": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xf9.ffffffffffffffp0) == 2.2289142548411573883553287678043297937797e-476": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xfa.00000000000001p0) == -2.2289142548411570466476165308364665814265e-476": +ildouble: 1 +ldouble: 1 +Test "tgamma (-1.5) == 2.3632718012073547030642233111215269103967e+00": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-2.5) == -9.4530872048294188122568932444861076415869e-01": +double: 1 +idouble: 1 +Test "tgamma (-4.5) == -6.0019601300504246427027893615784810422774e-02": +ildouble: 1 +ldouble: 1 +Test "tgamma (-5.5) == 1.0912654781909862986732344293779056440504e-02": +float: 1 +ifloat: 1 +Test "tgamma (-6.5) == -1.6788699664476712287280529682737009908468e-03": +float: 1 +ifloat: 1 +Test "tgamma (-7.5) == 2.2384932885968949716374039576982679877958e-04": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-8.5) == -2.6335215159963470254557693619979623385833e-05": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-9.5) == 2.7721279115751021320587045915768024616666e-06": +ildouble: 2 +ldouble: 2 Test "tgamma (0.5) == sqrt (pi)": float: 1 ifloat: 1 @@ -6173,7 +6546,218 @@ double: 1 float: 1 idouble: 1 ifloat: 1 +Test "tgamma (0x1.fffffep0) == 9.9999994960018563231526611134590489120697e-01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x1.fffffffffffffffep0) == 9.9999999999999999995416163053934024243282e-01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x1p-24) == 1.6777215422784394050795179874582764575261e+07": +float: 1 +ifloat: 1 +Test "tgamma (0x1p-53) == 9.0071992547409914227843350984672492007618e+15": +double: 1 +idouble: 1 +Test "tgamma (0x1p-64) == 1.8446744073709551615422784335098467139447e+19": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.0000000000002p0) == 1.0000000000000001877539613108624482361963e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.000004p0) == 1.0000001007996638509889062631687945799175e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.30a43cp+4) == 3.4027979115654976101247558405326779640190e+38": +double: 1 +idouble: 1 +Test "tgamma (0x2.fffffcp0) == 1.9999995599822108706107786027549565954046e+00": +float: 2 +ifloat: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.ffffffffffffep0) == 1.9999999999999991804028675282128956223990e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.0000000000002p0) == 2.0000000000000008195971324717875960213536e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.fffffcp0) == 5.9999982031095793171233994481968816873643e+00": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.fffffffffffffffcp0) == 5.9999999999999999983657373939865784753909e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.0000000000000008p0) == 6.0000000000000000032685252120268430507939e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.000008p0) == 6.0000035937827461765660468073471093546129e+00": +float: 1 +ifloat: 1 +Test "tgamma (0x4.fffff8p0) == 2.3999982763857938712639837029547357501709e+01": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.fffffffffffffff8p0) == 2.3999999999999999984323813937927417165027e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.0000000000000008p0) == 2.4000000000000000015676186062072582846211e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.000008p0) == 2.4000017236155647574166073485628713443799e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.fffff8p0) == 1.1999990237520611552119807476573441975106e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.ffffffffffffcp0) == 1.1999999999999981815957265157389249327533e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.0000000000000008p0) == 1.2000000000000000008878927116622375680433e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.000008p0) == 1.2000009762487825358530770343720418162783e+02": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.fffff8p0) == 7.1999935703082425988147448928288557689866e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.ffffffffffffcp0) == 7.1999999999999880237602554542848858572672e+02": +double: 3 +idouble: 3 +Test "tgamma (0x7.0000000000000008p0) == 7.2000000000000000058477733127664675369681e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.0000000000004p0) == 7.2000000000000119762397445457359071259652e+02": +double: 4 +idouble: 4 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.000008p0) == 7.2000064296977505705636258629805621178587e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.fffff8p0) == 5.0399951558933225045148935487583089307135e+03": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.ffffffffffffcp0) == 5.0399999999999909771437166339103165198442e+03": +double: 2 +idouble: 2 +Test "tgamma (0x7.fffffffffffffff8p0) == 5.0399999999999999955943084553876474508520e+03": +ildouble: 3 +ldouble: 3 +Test "tgamma (0x8.000000000000001p0) == 5.0400000000000000088113830892247051102283e+03": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x8.0000000000008p0) == 5.0400000000000180457125667322294144477136e+03": +double: 1 +idouble: 1 +Test "tgamma (0x8.00001p0) == 5.0400096882277802019946778420223050233915e+03": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0xa.b9fd72b0fb238p+4) == 1.7976931348622298700886249281842651388250e+308": +double: 1 +idouble: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (10) == 362880": +double: 1 +idouble: 1 +Test "tgamma (18.5) == 1.4986120533153361177371791123515513270334e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (19.5) == 2.7724322986333718178137813578503699550119e+16": +double: 1 +idouble: 1 +Test "tgamma (2.5) == 1.3293403881791370204736256125058588870982e+00": +float: 1 +ifloat: 1 +Test "tgamma (23.5) == 5.3613035875444147334274983856108155717836e+21": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (29.5) == 1.6348125198274266444378807806868221866931e+30": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (3) == 2": +float: 1 +ifloat: 1 +Test "tgamma (3.5) == 3.3233509704478425511840640312646472177454e+00": +float: 1 +ifloat: 1 +Test "tgamma (30.5) == 4.8226969334909086010917483030261254507447e+31": +float: 1 +ifloat: 1 +Test "tgamma (31.5) == 1.4709225647147271233329832324229682624771e+33": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (32.5) == 4.6334060788513904384988971821323500268029e+34": +ildouble: 1 +ldouble: 1 +Test "tgamma (34.5) == 5.0446208683494513399156743070465960916817e+37": +ildouble: 1 +ldouble: 1 Test "tgamma (4) == 6": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (4.5) == 1.1631728396567448929144224109426265262109e+01": +double: 1 +idouble: 1 +Test "tgamma (5.5) == 5.2342777784553520181149008492418193679490e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (6.5) == 2.8788527781504436099631954670830006523720e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (7.5) == 1.8712543057977883464760770536039504240418e+03": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (8) == 5040": +ildouble: 1 +ldouble: 1 +Test "tgamma (8.5) == 1.4034407293483412598570577902029628180313e+04": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (9) == 40320": +ildouble: 1 +ldouble: 1 +Test "tgamma (9.5) == 1.1929246199460900708784991216725183953266e+05": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 ildouble: 1 ldouble: 1 @@ -7103,12 +7687,12 @@ ildouble: 2 ldouble: 2 Function: "tgamma": -double: 2 -float: 1 -idouble: 2 -ifloat: 1 -ildouble: 1 -ldouble: 1 +double: 4 +float: 2 +idouble: 4 +ifloat: 2 +ildouble: 4 +ldouble: 4 Function: "y0": double: 2 diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c index 9873551757..5b17f7b5ad 100644 --- a/sysdeps/ieee754/dbl-64/e_gamma_r.c +++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c @@ -19,14 +19,104 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const double gamma_coeff[] = + { + 0x1.5555555555555p-4, + -0xb.60b60b60b60b8p-12, + 0x3.4034034034034p-12, + -0x2.7027027027028p-12, + 0x3.72a3c5631fe46p-12, + -0x7.daac36664f1f4p-12, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 184, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static double +gamma_positive (double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5) + { + *exp2_adj = 0; + return __ieee754_exp (__ieee754_lgamma_r (x, &local_signgam)); + } + else if (x < 6.5) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + double n = __ceil (x - 1.5); + double x_adj = x - n; + double eps; + double prod = __gamma_product (x_adj, 0, n, &eps); + return (__ieee754_exp (__ieee754_lgamma_r (x_adj, &local_signgam)) + * prod * (1.0 + eps)); + } + else + { + double eps = 0; + double x_eps = 0; + double x_adj = x; + double prod = 1; + if (x < 12.0) + { + /* Adjust into the range for applying Stirling's + approximation. */ + double n = __ceil (12.0 - x); +#if FLT_EVAL_METHOD != 0 + volatile +#endif + double x_tmp = x + n; + x_adj = x_tmp; + x_eps = (x - (x_adj - n)); + prod = __gamma_product (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + double exp_adj = -eps; + double x_adj_int = __round (x_adj); + double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + double x_adj_mant = __frexp (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + double ret = (__ieee754_pow (x_adj_mant, x_adj) + * __ieee754_exp2 (x_adj_log2 * x_adj_frac) + * __ieee754_exp (-x_adj) + * __ieee754_sqrt (2 * M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_log (x); + double bsum = gamma_coeff[NCOEFF - 1]; + double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1 (exp_adj); + } +} double __ieee754_gamma_r (double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int32_t hx; u_int32_t lx; @@ -51,8 +141,48 @@ __ieee754_gamma_r (double x, int *signgamp) *signgamp = 0; return x - x; } + if (__builtin_expect ((hx & 0x7ff00000) == 0x7ff00000, 0)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_exp (__ieee754_lgamma_r (x, signgamp)); + if (x >= 172.0) + { + /* Overflow. */ + *signgamp = 0; + return DBL_MAX * DBL_MAX; + } + else if (x > 0.0) + { + *signgamp = 0; + int exp2_adj; + double ret = gamma_positive (x, &exp2_adj); + return __scalbn (ret, exp2_adj); + } + else if (x >= -DBL_EPSILON / 4.0) + { + *signgamp = 0; + return 1.0 / x; + } + else + { + double tx = __trunc (x); + *signgamp = (tx == 2.0 * __trunc (tx / 2.0)) ? -1 : 1; + if (x <= -184.0) + /* Underflow. */ + return DBL_MIN * DBL_MIN; + double frac = tx - x; + if (frac > 0.5) + frac = 1.0 - frac; + double sinpix = (frac <= 0.25 + ? __sin (M_PI * frac) + : __cos (M_PI * (0.5 - frac))); + int exp2_adj; + double ret = M_PI / (-x * sinpix * gamma_positive (-x, &exp2_adj)); + return __scalbn (ret, -exp2_adj); + } } strong_alias (__ieee754_gamma_r, __gamma_r_finite) diff --git a/sysdeps/ieee754/dbl-64/gamma_product.c b/sysdeps/ieee754/dbl-64/gamma_product.c new file mode 100644 index 0000000000..2a3fc1aff8 --- /dev/null +++ b/sysdeps/ieee754/dbl-64/gamma_product.c @@ -0,0 +1,75 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static void +mul_split (double *hi, double *lo, double x, double y) +{ +#ifdef __FP_FAST_FMA + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fma (x, y, -*hi); +#elif defined FP_FAST_FMA + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fma (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1 << (DBL_MANT_DIG + 1) / 2) + 1) + double x1 = x * C; + double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + double x2 = x - x1; + double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +double +__gamma_product (double x, double x_eps, int n, double *eps) +{ + SET_RESTORE_ROUND (FE_TONEAREST); + double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/sysdeps/ieee754/dbl-64/gamma_productf.c b/sysdeps/ieee754/dbl-64/gamma_productf.c new file mode 100644 index 0000000000..46072f16ea --- /dev/null +++ b/sysdeps/ieee754/dbl-64/gamma_productf.c @@ -0,0 +1,46 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +float +__gamma_productf (float x, float x_eps, int n, float *eps) +{ + double x_full = (double) x + (double) x_eps; + double ret = x_full; + for (int i = 1; i < n; i++) + ret *= x_full + i; + +#if FLT_EVAL_METHOD != 0 + volatile +#endif + float fret = ret; + *eps = (ret - fret) / fret; + + return fret; +} diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c index a312957b0a..f58f4c8056 100644 --- a/sysdeps/ieee754/flt-32/e_gammaf_r.c +++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c @@ -19,14 +19,97 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const float gamma_coeff[] = + { + 0x1.555556p-4f, + -0xb.60b61p-12f, + 0x3.403404p-12f, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 42, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static float +gammaf_positive (float x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5f) + { + *exp2_adj = 0; + return __ieee754_expf (__ieee754_lgammaf_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5f) + { + *exp2_adj = 0; + return __ieee754_expf (__ieee754_lgammaf_r (x, &local_signgam)); + } + else if (x < 2.5f) + { + *exp2_adj = 0; + float x_adj = x - 1; + return (__ieee754_expf (__ieee754_lgammaf_r (x_adj, &local_signgam)) + * x_adj); + } + else + { + float eps = 0; + float x_eps = 0; + float x_adj = x; + float prod = 1; + if (x < 4.0f) + { + /* Adjust into the range for applying Stirling's + approximation. */ + float n = __ceilf (4.0f - x); +#if FLT_EVAL_METHOD != 0 + volatile +#endif + float x_tmp = x + n; + x_adj = x_tmp; + x_eps = (x - (x_adj - n)); + prod = __gamma_productf (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + float exp_adj = -eps; + float x_adj_int = __roundf (x_adj); + float x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + float x_adj_mant = __frexpf (x_adj, &x_adj_log2); + if (x_adj_mant < (float) M_SQRT1_2) + { + x_adj_log2--; + x_adj_mant *= 2.0f; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + float ret = (__ieee754_powf (x_adj_mant, x_adj) + * __ieee754_exp2f (x_adj_log2 * x_adj_frac) + * __ieee754_expf (-x_adj) + * __ieee754_sqrtf (2 * (float) M_PI / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logf (x); + float bsum = gamma_coeff[NCOEFF - 1]; + float x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1f (exp_adj); + } +} float __ieee754_gammaf_r (float x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int32_t hx; GET_FLOAT_WORD (hx, x); @@ -50,8 +133,49 @@ __ieee754_gammaf_r (float x, int *signgamp) *signgamp = 0; return x - x; } + if (__builtin_expect ((hx & 0x7f800000) == 0x7f800000, 0)) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_expf (__ieee754_lgammaf_r (x, signgamp)); + if (x >= 36.0f) + { + /* Overflow. */ + *signgamp = 0; + return FLT_MAX * FLT_MAX; + } + else if (x > 0.0f) + { + *signgamp = 0; + int exp2_adj; + float ret = gammaf_positive (x, &exp2_adj); + return __scalbnf (ret, exp2_adj); + } + else if (x >= -FLT_EPSILON / 4.0f) + { + *signgamp = 0; + return 1.0f / x; + } + else + { + float tx = __truncf (x); + *signgamp = (tx == 2.0f * __truncf (tx / 2.0f)) ? -1 : 1; + if (x <= -42.0f) + /* Underflow. */ + return FLT_MIN * FLT_MIN; + float frac = tx - x; + if (frac > 0.5f) + frac = 1.0f - frac; + float sinpix = (frac <= 0.25f + ? __sinf ((float) M_PI * frac) + : __cosf ((float) M_PI * (0.5f - frac))); + int exp2_adj; + float ret = (float) M_PI / (-x * sinpix + * gammaf_positive (-x, &exp2_adj)); + return __scalbnf (ret, -exp2_adj); + } } strong_alias (__ieee754_gammaf_r, __gammaf_r_finite) diff --git a/sysdeps/ieee754/k_standard.c b/sysdeps/ieee754/k_standard.c index cd3123046b..150921f90b 100644 --- a/sysdeps/ieee754/k_standard.c +++ b/sysdeps/ieee754/k_standard.c @@ -837,7 +837,7 @@ __kernel_standard(double x, double y, int type) exc.type = OVERFLOW; exc.name = type < 100 ? "tgamma" : (type < 200 ? "tgammaf" : "tgammal"); - exc.retval = HUGE_VAL; + exc.retval = __copysign (HUGE_VAL, x); if (_LIB_VERSION == _POSIX_) __set_errno (ERANGE); else if (!matherr(&exc)) { diff --git a/sysdeps/ieee754/ldbl-128/e_gammal_r.c b/sysdeps/ieee754/ldbl-128/e_gammal_r.c index b6da31c13e..e8d49e9872 100644 --- a/sysdeps/ieee754/ldbl-128/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-128/e_gammal_r.c @@ -20,14 +20,108 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.5555555555555555555555555555p-4L, + -0xb.60b60b60b60b60b60b60b60b60b8p-12L, + 0x3.4034034034034034034034034034p-12L, + -0x2.7027027027027027027027027028p-12L, + 0x3.72a3c5631fe46ae1d4e700dca8f2p-12L, + -0x7.daac36664f1f207daac36664f1f4p-12L, + 0x1.a41a41a41a41a41a41a41a41a41ap-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5d7p-8L, + 0x2.dfd2c703c0cfff430edfd2c703cp-4L, + -0x1.6476701181f39edbdb9ce625987dp+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e07c8p+4L, + 0x8.911a740da740da740da740da741p+8L, + -0x8.d0cc570e255bf59ff6eec24b49p+12L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 1775, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 12.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 24.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (24.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} long double __ieee754_gammal_r (long double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int64_t hx; u_int64_t lx; @@ -51,8 +145,49 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return x - x; } + if ((hx & 0x7fff000000000000ULL) == 0x7fff000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); + if (x >= 1756.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + long double ret = gammal_positive (x, &exp2_adj); + return __scalbnl (ret, exp2_adj); + } + else if (x >= -LDBL_EPSILON / 4.0L) + { + *signgamp = 0; + return 1.0f / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -1775.0L) + /* Underflow. */ + return LDBL_MIN * LDBL_MIN; + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + long double ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + return __scalbnl (ret, -exp2_adj); + } } strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/sysdeps/ieee754/ldbl-128/gamma_productl.c b/sysdeps/ieee754/ldbl-128/gamma_productl.c new file mode 100644 index 0000000000..157dbab9fb --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/gamma_productl.c @@ -0,0 +1,75 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (long double *hi, long double *lo, long double x, long double y) +{ +#ifdef __FP_FAST_FMAL + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#elif defined FP_FAST_FMAL + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + SET_RESTORE_ROUNDL (FE_TONEAREST); + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + long double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c b/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c index 52ade9e4a1..90d8e3f0d2 100644 --- a/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c @@ -20,14 +20,107 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.555555555555555555555555558p-4L, + -0xb.60b60b60b60b60b60b60b60b6p-12L, + 0x3.4034034034034034034034034p-12L, + -0x2.7027027027027027027027027p-12L, + 0x3.72a3c5631fe46ae1d4e700dca9p-12L, + -0x7.daac36664f1f207daac36664f2p-12L, + 0x1.a41a41a41a41a41a41a41a41a4p-8L, + -0x7.90a1b2c3d4e5f708192a3b4c5ep-8L, + 0x2.dfd2c703c0cfff430edfd2c704p-4L, + -0x1.6476701181f39edbdb9ce625988p+0L, + 0xd.672219167002d3a7a9c886459cp+0L, + -0x9.cd9292e6660d55b3f712eb9e08p+4L, + 0x8.911a740da740da740da740da74p+8L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 191, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 11.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 23.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (23.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} long double __ieee754_gammal_r (long double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ int64_t hx; u_int64_t lx; @@ -51,8 +144,49 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return x - x; } + if ((hx & 0x7ff0000000000000ULL) == 0x7ff0000000000000ULL) + { + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ + *signgamp = 0; + return x + x; + } - /* XXX FIXME. */ - return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); + if (x >= 172.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + long double ret = gammal_positive (x, &exp2_adj); + return __scalbnl (ret, exp2_adj); + } + else if (x >= -0x1p-110L) + { + *signgamp = 0; + return 1.0f / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -191.0L) + /* Underflow. */ + return LDBL_MIN * LDBL_MIN; + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + long double ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + return __scalbnl (ret, -exp2_adj); + } } strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c b/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c new file mode 100644 index 0000000000..7c6186d230 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128ibm/gamma_productl.c @@ -0,0 +1,42 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + ret *= x + i; + /* FIXME: no error estimates for the multiplication. */ + } + return ret; +} diff --git a/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/sysdeps/ieee754/ldbl-96/e_gammal_r.c index 0974351a10..7cb3e8563a 100644 --- a/sysdeps/ieee754/ldbl-96/e_gammal_r.c +++ b/sysdeps/ieee754/ldbl-96/e_gammal_r.c @@ -19,14 +19,102 @@ #include <math.h> #include <math_private.h> +#include <float.h> +/* Coefficients B_2k / 2k(2k-1) of x^-(2k-1) inside exp in Stirling's + approximation to gamma function. */ + +static const long double gamma_coeff[] = + { + 0x1.5555555555555556p-4L, + -0xb.60b60b60b60b60bp-12L, + 0x3.4034034034034034p-12L, + -0x2.7027027027027028p-12L, + 0x3.72a3c5631fe46aep-12L, + -0x7.daac36664f1f208p-12L, + 0x1.a41a41a41a41a41ap-8L, + -0x7.90a1b2c3d4e5f708p-8L, + }; + +#define NCOEFF (sizeof (gamma_coeff) / sizeof (gamma_coeff[0])) + +/* Return gamma (X), for positive X less than 1766, in the form R * + 2^(*EXP2_ADJ), where R is the return value and *EXP2_ADJ is set to + avoid overflow or underflow in intermediate calculations. */ + +static long double +gammal_positive (long double x, int *exp2_adj) +{ + int local_signgam; + if (x < 0.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x + 1, &local_signgam)) / x; + } + else if (x <= 1.5L) + { + *exp2_adj = 0; + return __ieee754_expl (__ieee754_lgammal_r (x, &local_signgam)); + } + else if (x < 7.5L) + { + /* Adjust into the range for using exp (lgamma). */ + *exp2_adj = 0; + long double n = __ceill (x - 1.5L); + long double x_adj = x - n; + long double eps; + long double prod = __gamma_productl (x_adj, 0, n, &eps); + return (__ieee754_expl (__ieee754_lgammal_r (x_adj, &local_signgam)) + * prod * (1.0L + eps)); + } + else + { + long double eps = 0; + long double x_eps = 0; + long double x_adj = x; + long double prod = 1; + if (x < 13.0L) + { + /* Adjust into the range for applying Stirling's + approximation. */ + long double n = __ceill (13.0L - x); + x_adj = x + n; + x_eps = (x - (x_adj - n)); + prod = __gamma_productl (x_adj - n, x_eps, n, &eps); + } + /* The result is now gamma (X_ADJ + X_EPS) / (PROD * (1 + EPS)). + Compute gamma (X_ADJ + X_EPS) using Stirling's approximation, + starting by computing pow (X_ADJ, X_ADJ) with a power of 2 + factored out. */ + long double exp_adj = -eps; + long double x_adj_int = __roundl (x_adj); + long double x_adj_frac = x_adj - x_adj_int; + int x_adj_log2; + long double x_adj_mant = __frexpl (x_adj, &x_adj_log2); + if (x_adj_mant < M_SQRT1_2l) + { + x_adj_log2--; + x_adj_mant *= 2.0L; + } + *exp2_adj = x_adj_log2 * (int) x_adj_int; + long double ret = (__ieee754_powl (x_adj_mant, x_adj) + * __ieee754_exp2l (x_adj_log2 * x_adj_frac) + * __ieee754_expl (-x_adj) + * __ieee754_sqrtl (2 * M_PIl / x_adj) + / prod); + exp_adj += x_eps * __ieee754_logl (x); + long double bsum = gamma_coeff[NCOEFF - 1]; + long double x_adj2 = x_adj * x_adj; + for (size_t i = 1; i <= NCOEFF - 1; i++) + bsum = bsum / x_adj2 + gamma_coeff[NCOEFF - 1 - i]; + exp_adj += bsum / x_adj; + return ret + ret * __expm1l (exp_adj); + } +} long double __ieee754_gammal_r (long double x, int *signgamp) { - /* We don't have a real gamma implementation now. We'll use lgamma - and the exp function. But due to the required boundary - conditions we must check some values separately. */ u_int32_t es, hx, lx; GET_LDOUBLE_WORDS (es, hx, lx, x); @@ -43,22 +131,55 @@ __ieee754_gammal_r (long double x, int *signgamp) *signgamp = 0; return x - x; } - if (__builtin_expect ((es & 0x7fff) == 0x7fff, 0) - && ((hx & 0x7fffffff) | lx) != 0) + if (__builtin_expect ((es & 0x7fff) == 0x7fff, 0)) { - /* NaN, return it. */ + /* Positive infinity (return positive infinity) or NaN (return + NaN). */ *signgamp = 0; - return x; + return x + x; } - if (__builtin_expect ((es & 0x8000) != 0, 0) - && x < 0xffffffff && __rintl (x) == x) + if (__builtin_expect ((es & 0x8000) != 0, 0) && __rintl (x) == x) { /* Return value for integer x < 0 is NaN with invalid exception. */ *signgamp = 0; return (x - x) / (x - x); } - /* XXX FIXME. */ - return __ieee754_expl (__ieee754_lgammal_r (x, signgamp)); + if (x >= 1756.0L) + { + /* Overflow. */ + *signgamp = 0; + return LDBL_MAX * LDBL_MAX; + } + else if (x > 0.0L) + { + *signgamp = 0; + int exp2_adj; + long double ret = gammal_positive (x, &exp2_adj); + return __scalbnl (ret, exp2_adj); + } + else if (x >= -LDBL_EPSILON / 4.0L) + { + *signgamp = 0; + return 1.0f / x; + } + else + { + long double tx = __truncl (x); + *signgamp = (tx == 2.0L * __truncl (tx / 2.0L)) ? -1 : 1; + if (x <= -1766.0L) + /* Underflow. */ + return LDBL_MIN * LDBL_MIN; + long double frac = tx - x; + if (frac > 0.5L) + frac = 1.0L - frac; + long double sinpix = (frac <= 0.25L + ? __sinl (M_PIl * frac) + : __cosl (M_PIl * (0.5L - frac))); + int exp2_adj; + long double ret = M_PIl / (-x * sinpix + * gammal_positive (-x, &exp2_adj)); + return __scalbnl (ret, -exp2_adj); + } } strong_alias (__ieee754_gammal_r, __gammal_r_finite) diff --git a/sysdeps/ieee754/ldbl-96/gamma_product.c b/sysdeps/ieee754/ldbl-96/gamma_product.c new file mode 100644 index 0000000000..d464e70842 --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/gamma_product.c @@ -0,0 +1,46 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +double +__gamma_product (double x, double x_eps, int n, double *eps) +{ + long double x_full = (long double) x + (long double) x_eps; + long double ret = x_full; + for (int i = 1; i < n; i++) + ret *= x_full + i; + +#if FLT_EVAL_METHOD != 0 + volatile +#endif + double fret = ret; + *eps = (ret - fret) / fret; + + return fret; +} diff --git a/sysdeps/ieee754/ldbl-96/gamma_productl.c b/sysdeps/ieee754/ldbl-96/gamma_productl.c new file mode 100644 index 0000000000..157dbab9fb --- /dev/null +++ b/sysdeps/ieee754/ldbl-96/gamma_productl.c @@ -0,0 +1,75 @@ +/* Compute a product of X, X+1, ..., with an error estimate. + Copyright (C) 2013 Free Software Foundation, Inc. + This file is part of the GNU C Library. + + The GNU C Library is free software; you can redistribute it and/or + modify it under the terms of the GNU Lesser General Public + License as published by the Free Software Foundation; either + version 2.1 of the License, or (at your option) any later version. + + The GNU C Library is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with the GNU C Library; if not, see + <http://www.gnu.org/licenses/>. */ + +#include <math.h> +#include <math_private.h> +#include <float.h> + +/* Calculate X * Y exactly and store the result in *HI + *LO. It is + given that the values are small enough that no overflow occurs and + large enough (or zero) that no underflow occurs. */ + +static inline void +mul_split (long double *hi, long double *lo, long double x, long double y) +{ +#ifdef __FP_FAST_FMAL + /* Fast built-in fused multiply-add. */ + *hi = x * y; + *lo = __builtin_fmal (x, y, -*hi); +#elif defined FP_FAST_FMAL + /* Fast library fused multiply-add, compiler before GCC 4.6. */ + *hi = x * y; + *lo = __fmal (x, y, -*hi); +#else + /* Apply Dekker's algorithm. */ + *hi = x * y; +# define C ((1LL << (LDBL_MANT_DIG + 1) / 2) + 1) + long double x1 = x * C; + long double y1 = y * C; +# undef C + x1 = (x - x1) + x1; + y1 = (y - y1) + y1; + long double x2 = x - x1; + long double y2 = y - y1; + *lo = (((x1 * y1 - *hi) + x1 * y2) + x2 * y1) + x2 * y2; +#endif +} + +/* Compute the product of X + X_EPS, X + X_EPS + 1, ..., X + X_EPS + N + - 1, in the form R * (1 + *EPS) where the return value R is an + approximation to the product and *EPS is set to indicate the + approximate error in the return value. X is such that all the + values X + 1, ..., X + N - 1 are exactly representable, and X_EPS / + X is small enough that factors quadratic in it can be + neglected. */ + +long double +__gamma_productl (long double x, long double x_eps, int n, long double *eps) +{ + SET_RESTORE_ROUNDL (FE_TONEAREST); + long double ret = x; + *eps = x_eps / x; + for (int i = 1; i < n; i++) + { + *eps += x_eps / (x + i); + long double lo; + mul_split (&ret, &lo, ret, x + i); + *eps += lo / ret; + } + return ret; +} diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps index d84a898e00..3827b9d764 100644 --- a/sysdeps/x86_64/fpu/libm-test-ulps +++ b/sysdeps/x86_64/fpu/libm-test-ulps @@ -7142,6 +7142,417 @@ idouble: 1 ifloat: 1 ildouble: 1 ldouble: 1 +Test "tgamma (-0x0.fffffffffffff8p0) == -9.0071992547409924227843350984672961392521e+15": +double: 1 +idouble: 1 +Test "tgamma (-0x0.ffffffffffffffffp0) == -1.8446744073709551616422784335098467139470e+19": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x0.ffffffp0) == -1.6777216422784419250710305882992376932423e+07": +float: 1 +ifloat: 1 +Test "tgamma (-0x1.000002p0) == 8.3886075772158332060084424806449513922858e+06": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1.0a32a2p+5) == 1.8125267978155035272941154746083439329912e-37": +float: 2 +ifloat: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1.5800000080001p+7) == -3.1439271448823567326093363350637118195240e-304": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x1.fffffffffffffp0) == 2.2517998136852484613921675492337776673289e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x13.ffffep0) == 2.1550026214525536756224040483579183652119e-13": +float: 2 +ifloat: 2 +Test "tgamma (-0x13.ffffffffffffffep0) == 2.3694367893405502075347562184931828448654e-01": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x13.ffffffffffffp0) == 1.1569515572952029402736625857313236848570e-04": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x14.000000000001p0) == -1.1569515572951781096476686854873801225397e-04": +double: 1 +idouble: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x14.00002p0) == -2.1549777908265594916405421768142757507179e-13": +float: 1 +ifloat: 1 +Test "tgamma (-0x1d.ffffep0) == 1.9765721589464867957912772592816027583176e-27": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1d.ffffffffffffffep0) == 2.1732499046818166459536268654187775086902e-15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1e.000000000000002p0) == -2.1732499046818166201837145753965837196590e-15": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x1e.000000000001p0) == -1.0611571800204053929094168642022073530425e-18": +double: 3 +idouble: 3 +Test "tgamma (-0x1e.00002p0) == -1.9765463890341964384070157599286498212650e-27": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x1f4.00000000000002p0) == -2.9528489142763131406565394149878256133744e-1118": +ildouble: 3 +ldouble: 3 +Test "tgamma (-0x1p-24) == -1.6777216577215723853867349114260580375249e+07": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.0000000000000004p0) == -2.3058430092136939515386078324507664305064e+18": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.0000000000002p0) == -1.1258999068426235386078324507668462444260e+15": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.000004p0) == -2.0971515386080557574407223895988378776747e+06": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2.fffffcp0) == -6.9905087601970247876992248591045142913324e+05": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (-0x27.ffffcp0) == 3.2129279441390812141195076945616975790225e-43": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x27.fffffffffffep0) == 1.7249032006742266376460389310340465554361e-34": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.000000000002p0) == -1.7249032006741359094184881234822934593822e-34": +double: 1 +idouble: 1 +Test "tgamma (-0x28.00004p0) == -3.2128372159115252365699015758097981155793e-43": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.ffffcp0) == -7.8364103489619817539676737414096652170685e-45": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.fffffffffffep0) == -4.2070809772542120404320040128839297118648e-36": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x28.ffffffffffffffcp0) == -8.6161018414163982777002940498289948893044e-33": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.000000000000004p0) == 8.6161018414163980549537337663264762179535e-33": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.000000000002p0) == 4.2070809772539892938717205103652583609422e-36": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.00004p0) == 7.8361876024016854597745353972619195760515e-45": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x29.ffffcp0) == 1.8658121573125798145204120066590953505132e-46": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2a.00004p0) == -1.8657587834931410688246126853566488626385e-46": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x2ed.fffffffffffffcp0) == 6.9801511765871818502006905472380418430269e-1817": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3.0000000000002p0) == 3.7529996894754112398038859470009084971438e+14": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3.000004p0) == 6.9905045731381300146131914617735687322025e+05": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +Test "tgamma (-0x3.fffffcp0) == 1.7476272942159602684441970627092458855771e+05": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (-0x3.ffffffffffffep0) == 9.3824992236885396088236184658402406857503e+13": +double: 2 +idouble: 2 +Test "tgamma (-0x3.fffffffffffffffcp0) == 1.9215358410114116272942156951799168638773e+17": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x31.fffffffffffep0) == 4.6273774273632946947805289899230181990085e-51": +double: 3 +idouble: 3 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x32.000000000000004p0) == -9.4768689712397633101385547903658075308777e-48": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x32.000000000002p0) == -4.6273774273630367887073532197576655720178e-51": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3e7.fffffffffffffcp0) == 4.4768809295877296071892611539415773519036e-2552": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x3e8.00000000000004p0) == -4.4768809295877261735541135972060089530309e-2552": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.0000000000000008p0) == -9.6076792050570581270578430482008313684602e+16": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.000008p0) == -8.7381270578483499672965708923121931082305e+04": +float: 1 +ifloat: 1 +Test "tgamma (-0x4.fffff8p0) == -1.7476280884325863043793087474680780379554e+04": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x4.ffffffffffffcp0) == -9.3824992236885475509805702650262155809819e+12": +double: 1 +idouble: 1 +Test "tgamma (-0x4e2.00000000000008p0) == -5.4651488569236421026544487194247355967789e-3315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.0000000000000008p0) == 1.9215358410114116252449019429734996071487e+16": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.0000000000004p0) == 9.3824992236885191156860964016850034672946e+12": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.000008p0) == 1.7476252449031389167286893378510439443844e+04": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x5.ffffffffffffcp0) == 1.5637498706147581566449098589862357835505e+12": +double: 1 +idouble: 1 +Test "tgamma (-0x5db.fffffffffffff8p0) == 1.8718211510339187689122114747834510481993e-4099": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x6.0000000000000008p0) == -3.2025597350190193751766884234743511972877e+15": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x6.000008p0) == -2.9127085100239567622341538102130981196910e+03": +float: 2 +ifloat: 2 +Test "tgamma (-0x6.fffff8p0) == -4.1610198723079349791939054365613377035519e+02": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x6.ffffffffffffcp0) == -2.2339283865925119357965832452642909859289e+11": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x63.fffffffffffcp0) == 7.5400833348840965463348754984345825364294e-145": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x63.ffffffffffffff8p0) == 1.5442090669841618542494279375256856430049e-141": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x64.000000000000008p0) == -1.5442090669841617554527108348771968070612e-141": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x64.000000000004p0) == -7.5400833348831085791638490135462230991587e-145": +double: 1 +idouble: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x6d6.00000000000008p0) == -4.2925786447266421378134368786479937285900e-4902": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.0000000000000008p0) == 4.5750853357414562499689653215166468353753e+14": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.0000000000004p0) == 2.2339283865925039372192897706214475877342e+11": +double: 3 +idouble: 3 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.000008p0) == 4.1610118737306415004517215226199741948733e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.fffff8p0) == 5.2012751504050764429534086402871289946986e+01": +double: 3 +float: 1 +idouble: 3 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x7.ffffffffffffcp0) == 2.7924104832406402297655703264222230055898e+10": +double: 3 +idouble: 3 +Test "tgamma (-0x7.fffffffffffffff8p0) == 5.7188566696768203227694481100089533685959e+13": +ildouble: 4 +ldouble: 4 +Test "tgamma (-0x8.000000000000001p0) == -2.8594283348384101534210280804672371201060e+13": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0x8.00001p0) == -2.6006296115134418896533598545925084576702e+01": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x9.ffffffffffff8p0) == 1.5513391573559147700413058496716749249803e+08": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x9.fffffp0) == 2.8896008370721717567612135720915723136310e-01": +float: 1 +ifloat: 1 +Test "tgamma (-0x95.fffffffffff8p0) == 6.1582369322723207086020016423767264008839e-250": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x95.ffffffffffffffp0) == 1.2612069237291916400144732227892704713839e-246": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0x96.000000000008p0) == -6.1582369322705655439003240743176243138734e-250": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xa.000000000000001p0) == -3.1771425942649001698860433502350057763905e+11": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xa.00001p0) == -2.8895878754728051776830454190076999107021e-01": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb4.ffffffffffffffp0) == -1.9816628031468191243385005680879281767694e-315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb5.00000000000001p0) == 1.9816628031468188382579700510291588022368e-315": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb5.000000000008p0) == 9.6760879059888966544677044221698800670218e-319": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xb5.ffffffffffffffp0) == 1.0888257160147357826865964233809723297472e-317": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.00000000000001p0) == -1.0888257160147356253334423783317128355514e-317": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.fffffffffff8p0) == -2.9052086428846935908287469917922960610289e-323": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb6.ffffffffffffffp0) == -5.9498673006269714905418984659220067091260e-320": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb7.fffffffffff8p0) == 1.5789177406982032823826953250736039527543e-325": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xb7.ffffffffffffffp0) == 3.2336235329494410277123118903958061569834e-322": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xb8.000000000008p0) == -1.5789177406977349925854817486109369828857e-325": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbb.ffffffffffffffp0) == 2.6730392040715350119087465463119939092815e-331": +ildouble: 2 +ldouble: 2 +Test "tgamma (-0xbc.00000000000001p0) == -2.6730392040715346232108532050343031951651e-331": +ildouble: 3 +ldouble: 3 +Test "tgamma (-0xbd.00000000000001p0) == 1.4143064571807061497431633629389135273431e-333": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbe.00000000000001p0) == -7.4437181956879271033676895858841525581153e-336": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbe.ffffffffffffffp0) == -3.8972346574282346536709453101948570578636e-338": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xbf.00000000000001p0) == 3.8972346574282340852496542564155275274974e-338": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xf9.ffffffffffffffp0) == 2.2289142548411573883553287678043297937797e-476": +ildouble: 1 +ldouble: 1 +Test "tgamma (-0xfa.00000000000001p0) == -2.2289142548411570466476165308364665814265e-476": +ildouble: 1 +ldouble: 1 +Test "tgamma (-1.5) == 2.3632718012073547030642233111215269103967e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (-2.5) == -9.4530872048294188122568932444861076415869e-01": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +Test "tgamma (-3.5) == 2.7008820585226910892162552127103164690248e-01": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (-4.5) == -6.0019601300504246427027893615784810422774e-02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-5.5) == 1.0912654781909862986732344293779056440504e-02": +double: 1 +idouble: 1 +Test "tgamma (-6.5) == -1.6788699664476712287280529682737009908468e-03": +float: 1 +ifloat: 1 +Test "tgamma (-7.5) == 2.2384932885968949716374039576982679877958e-04": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-8.5) == -2.6335215159963470254557693619979623385833e-05": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (-9.5) == 2.7721279115751021320587045915768024616666e-06": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 Test "tgamma (0.5) == sqrt (pi)": float: 1 ifloat: 1 @@ -7150,7 +7561,260 @@ double: 1 float: 1 idouble: 1 ifloat: 1 +Test "tgamma (0x1.fffffep0) == 9.9999994960018563231526611134590489120697e-01": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x1.fffffffffffffffep0) == 9.9999999999999999995416163053934024243282e-01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x1.fffffffffffffp0) == 9.9999999999999990612301934456883679778984e-01": +double: 1 +idouble: 1 +Test "tgamma (0x1p-24) == 1.6777215422784394050795179874582764575261e+07": +float: 1 +ifloat: 1 +Test "tgamma (0x1p-53) == 9.0071992547409914227843350984672492007618e+15": +double: 1 +idouble: 1 +Test "tgamma (0x1p-64) == 1.8446744073709551615422784335098467139447e+19": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.0000000000002p0) == 1.0000000000000001877539613108624482361963e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.000004p0) == 1.0000001007996638509889062631687945799175e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.30a43cp+4) == 3.4027979115654976101247558405326779640190e+38": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +Test "tgamma (0x2.fffffcp0) == 1.9999995599822108706107786027549565954046e+00": +float: 3 +ifloat: 3 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x2.ffffffffffffep0) == 1.9999999999999991804028675282128956223990e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.0000000000002p0) == 2.0000000000000008195971324717875960213536e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.fffffcp0) == 5.9999982031095793171233994481968816873643e+00": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x3.ffffffffffffep0) == 5.9999999999999966530301828845138185025345e+00": +double: 1 +idouble: 1 +Test "tgamma (0x3.fffffffffffffffcp0) == 5.9999999999999999983657373939865784753909e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.0000000000000008p0) == 6.0000000000000000032685252120268430507939e+00": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.0000000000004p0) == 6.0000000000000066939396342309789716341613e+00": +double: 1 +idouble: 1 +Test "tgamma (0x4.fffff8p0) == 2.3999982763857938712639837029547357501709e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x4.ffffffffffffcp0) == 2.3999999999999967895170944875373910918544e+01": +double: 1 +idouble: 1 +Test "tgamma (0x4.fffffffffffffff8p0) == 2.3999999999999999984323813937927417165027e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.0000000000000008p0) == 2.4000000000000000015676186062072582846211e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.0000000000004p0) == 2.4000000000000032104829055124673225982803e+01": +double: 1 +idouble: 1 +Test "tgamma (0x5.000008p0) == 2.4000017236155647574166073485628713443799e+01": +float: 2 +ifloat: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.fffff8p0) == 1.1999990237520611552119807476573441975106e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x5.ffffffffffffcp0) == 1.1999999999999981815957265157389249327533e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.0000000000000008p0) == 1.2000000000000000008878927116622375680433e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.0000000000004p0) == 1.2000000000000018184042734842640022086408e+02": +double: 1 +idouble: 1 +Test "tgamma (0x6.000008p0) == 1.2000009762487825358530770343720418162783e+02": +float: 2 +ifloat: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.fffff8p0) == 7.1999935703082425988147448928288557689866e+02": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x6.ffffffffffffcp0) == 7.1999999999999880237602554542848858572672e+02": +double: 3 +idouble: 3 +Test "tgamma (0x7.0000000000000008p0) == 7.2000000000000000058477733127664675369681e+02": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.0000000000004p0) == 7.2000000000000119762397445457359071259652e+02": +double: 4 +idouble: 4 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.000008p0) == 7.2000064296977505705636258629805621178587e+02": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.fffff8p0) == 5.0399951558933225045148935487583089307135e+03": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (0x7.ffffffffffffcp0) == 5.0399999999999909771437166339103165198442e+03": +double: 2 +idouble: 2 +Test "tgamma (0x7.fffffffffffffff8p0) == 5.0399999999999999955943084553876474508520e+03": +ildouble: 3 +ldouble: 3 +Test "tgamma (0x8.000000000000001p0) == 5.0400000000000000088113830892247051102283e+03": +ildouble: 1 +ldouble: 1 +Test "tgamma (0x8.00001p0) == 5.0400096882277802019946778420223050233915e+03": +double: 2 +idouble: 2 +ildouble: 1 +ldouble: 1 +Test "tgamma (0xa.b9fd72b0fb238p+4) == 1.7976931348622298700886249281842651388250e+308": +double: 1 +idouble: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (10) == 362880": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (18.5) == 1.4986120533153361177371791123515513270334e+15": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (19.5) == 2.7724322986333718178137813578503699550119e+16": +double: 2 +idouble: 2 +Test "tgamma (2.5) == 1.3293403881791370204736256125058588870982e+00": +float: 2 +ifloat: 2 +Test "tgamma (23.5) == 5.3613035875444147334274983856108155717836e+21": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (29.5) == 1.6348125198274266444378807806868221866931e+30": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (3) == 2": +float: 1 +ifloat: 1 +Test "tgamma (3.5) == 3.3233509704478425511840640312646472177454e+00": +float: 2 +ifloat: 2 +Test "tgamma (30.5) == 4.8226969334909086010917483030261254507447e+31": +float: 1 +ifloat: 1 +Test "tgamma (32.5) == 4.6334060788513904384988971821323500268029e+34": +ildouble: 1 +ldouble: 1 +Test "tgamma (33.5) == 1.5058569756267018925121415841930137587110e+36": +float: 1 +ifloat: 1 +Test "tgamma (34.5) == 5.0446208683494513399156743070465960916817e+37": +double: 1 +float: 2 +idouble: 1 +ifloat: 2 +ildouble: 1 +ldouble: 1 Test "tgamma (4) == 6": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (4.5) == 1.1631728396567448929144224109426265262109e+01": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +Test "tgamma (5.5) == 5.2342777784553520181149008492418193679490e+01": +ildouble: 1 +ldouble: 1 +Test "tgamma (6) == 120": +float: 1 +ifloat: 1 +Test "tgamma (6.5) == 2.8788527781504436099631954670830006523720e+02": +float: 1 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (7) == 720": +double: 1 +idouble: 1 +Test "tgamma (7.5) == 1.8712543057977883464760770536039504240418e+03": +double: 2 +float: 1 +idouble: 2 +ifloat: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (8) == 5040": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (8.5) == 1.4034407293483412598570577902029628180313e+04": +double: 1 +float: 1 +idouble: 1 +ifloat: 1 +ildouble: 2 +ldouble: 2 +Test "tgamma (9) == 40320": +double: 1 +idouble: 1 +ildouble: 1 +ldouble: 1 +Test "tgamma (9.5) == 1.1929246199460900708784991216725183953266e+05": +double: 1 +idouble: 1 ildouble: 1 ldouble: 1 @@ -8052,12 +8716,12 @@ ildouble: 2 ldouble: 2 Function: "tgamma": -double: 1 -float: 1 -idouble: 1 -ifloat: 1 -ildouble: 1 -ldouble: 1 +double: 4 +float: 3 +idouble: 4 +ifloat: 3 +ildouble: 4 +ldouble: 4 Function: "y0": double: 2 |