1 #include "test/jemalloc_test.h" 2 3 #define MAX_REL_ERR 1.0e-9 4 #define MAX_ABS_ERR 1.0e-9 5 6 #include <float.h> 7 8 #ifdef __PGI 9 #undef INFINITY 10 #endif 11 12 #ifndef INFINITY 13 #define INFINITY (DBL_MAX + DBL_MAX) 14 #endif 15 16 static bool 17 double_eq_rel(double a, double b, double max_rel_err, double max_abs_err) 18 { 19 double rel_err; 20 21 if (fabs(a - b) < max_abs_err) 22 return (true); 23 rel_err = (fabs(b) > fabs(a)) ? fabs((a-b)/b) : fabs((a-b)/a); 24 return (rel_err < max_rel_err); 25 } 26 27 static uint64_t 28 factorial(unsigned x) 29 { 30 uint64_t ret = 1; 31 unsigned i; 32 33 for (i = 2; i <= x; i++) 34 ret *= (uint64_t)i; 35 36 return (ret); 37 } 38 39 TEST_BEGIN(test_ln_gamma_factorial) 40 { 41 unsigned x; 42 43 /* exp(ln_gamma(x)) == (x-1)! for integer x. */ 44 for (x = 1; x <= 21; x++) { 45 assert_true(double_eq_rel(exp(ln_gamma(x)), 46 (double)factorial(x-1), MAX_REL_ERR, MAX_ABS_ERR), 47 "Incorrect factorial result for x=%u", x); 48 } 49 } 50 TEST_END 51 52 /* Expected ln_gamma([0.0..100.0] increment=0.25). */ 53 static const double ln_gamma_misc_expected[] = { 54 INFINITY, 55 1.28802252469807743, 0.57236494292470008, 0.20328095143129538, 56 0.00000000000000000, -0.09827183642181320, -0.12078223763524518, 57 -0.08440112102048555, 0.00000000000000000, 0.12487171489239651, 58 0.28468287047291918, 0.47521466691493719, 0.69314718055994529, 59 0.93580193110872523, 1.20097360234707429, 1.48681557859341718, 60 1.79175946922805496, 2.11445692745037128, 2.45373657084244234, 61 2.80857141857573644, 3.17805383034794575, 3.56137591038669710, 62 3.95781396761871651, 4.36671603662228680, 4.78749174278204581, 63 5.21960398699022932, 5.66256205985714178, 6.11591589143154568, 64 6.57925121201010121, 7.05218545073853953, 7.53436423675873268, 65 8.02545839631598312, 8.52516136106541467, 9.03318691960512332, 66 9.54926725730099690, 10.07315123968123949, 10.60460290274525086, 67 11.14340011995171231, 11.68933342079726856, 12.24220494005076176, 68 12.80182748008146909, 13.36802367147604720, 13.94062521940376342, 69 14.51947222506051816, 15.10441257307551943, 15.69530137706046524, 70 16.29200047656724237, 16.89437797963419285, 17.50230784587389010, 71 18.11566950571089407, 18.73434751193644843, 19.35823122022435427, 72 19.98721449566188468, 20.62119544270163018, 21.26007615624470048, 73 21.90376249182879320, 22.55216385312342098, 23.20519299513386002, 74 23.86276584168908954, 24.52480131594137802, 25.19122118273868338, 75 25.86194990184851861, 26.53691449111561340, 27.21604439872720604, 76 27.89927138384089389, 28.58652940490193828, 29.27775451504081516, 77 29.97288476399884871, 30.67186010608067548, 31.37462231367769050, 78 32.08111489594735843, 32.79128302226991565, 33.50507345013689076, 79 34.22243445715505317, 34.94331577687681545, 35.66766853819134298, 80 36.39544520803305261, 37.12659953718355865, 37.86108650896109395, 81 38.59886229060776230, 39.33988418719949465, 40.08411059791735198, 82 40.83150097453079752, 41.58201578195490100, 42.33561646075348506, 83 43.09226539146988699, 43.85192586067515208, 44.61456202863158893, 84 45.38013889847690052, 46.14862228684032885, 46.91997879580877395, 85 47.69417578616628361, 48.47118135183522014, 49.25096429545256882, 86 50.03349410501914463, 50.81874093156324790, 51.60667556776436982, 87 52.39726942748592364, 53.19049452616926743, 53.98632346204390586, 88 54.78472939811231157, 55.58568604486942633, 56.38916764371992940, 89 57.19514895105859864, 58.00360522298051080, 58.81451220059079787, 90 59.62784609588432261, 60.44358357816834371, 61.26170176100199427, 91 62.08217818962842927, 62.90499082887649962, 63.73011805151035958, 92 64.55753862700632340, 65.38723171073768015, 66.21917683354901385, 93 67.05335389170279825, 67.88974313718154008, 68.72832516833013017, 94 69.56908092082363737, 70.41199165894616385, 71.25703896716800045, 95 72.10420474200799390, 72.95347118416940191, 73.80482079093779646, 96 74.65823634883015814, 75.51370092648485866, 76.37119786778275454, 97 77.23071078519033961, 78.09222355331530707, 78.95572030266725960, 98 79.82118541361435859, 80.68860351052903468, 81.55795945611502873, 99 82.42923834590904164, 83.30242550295004378, 84.17750647261028973, 100 85.05446701758152983, 85.93329311301090456, 86.81397094178107920, 101 87.69648688992882057, 88.58082754219766741, 89.46697967771913795, 102 90.35493026581838194, 91.24466646193963015, 92.13617560368709292, 103 93.02944520697742803, 93.92446296229978486, 94.82121673107967297, 104 95.71969454214321615, 96.61988458827809723, 97.52177522288820910, 105 98.42535495673848800, 99.33061245478741341, 100.23753653310367895, 106 101.14611615586458981, 102.05634043243354370, 102.96819861451382394, 107 103.88168009337621811, 104.79677439715833032, 105.71347118823287303, 108 106.63176026064346047, 107.55163153760463501, 108.47307506906540198, 109 109.39608102933323153, 110.32063971475740516, 111.24674154146920557, 110 112.17437704317786995, 113.10353686902013237, 114.03421178146170689, 111 114.96639265424990128, 115.90007047041454769, 116.83523632031698014, 112 117.77188139974506953, 118.70999700805310795, 119.64957454634490830, 113 120.59060551569974962, 121.53308151543865279, 122.47699424143097247, 114 123.42233548443955726, 124.36909712850338394, 125.31727114935689826, 115 126.26684961288492559, 127.21782467361175861, 128.17018857322420899, 116 129.12393363912724453, 130.07905228303084755, 131.03553699956862033, 117 131.99338036494577864, 132.95257503561629164, 133.91311374698926784, 118 134.87498931216194364, 135.83819462068046846, 136.80272263732638294, 119 137.76856640092901785, 138.73571902320256299, 139.70417368760718091, 120 140.67392364823425055, 141.64496222871400732, 142.61728282114600574, 121 143.59087888505104047, 144.56574394634486680, 145.54187159633210058, 122 146.51925549072063859, 147.49788934865566148, 148.47776695177302031, 123 149.45888214327129617, 150.44122882700193600, 151.42480096657754984, 124 152.40959258449737490, 153.39559776128982094, 154.38281063467164245, 125 155.37122539872302696, 156.36083630307879844, 157.35163765213474107, 126 158.34362380426921391, 159.33678917107920370, 160.33112821663092973, 127 161.32663545672428995, 162.32330545817117695, 163.32113283808695314, 128 164.32011226319519892, 165.32023844914485267, 166.32150615984036790, 129 167.32391020678358018, 168.32744544842768164, 169.33210678954270634, 130 170.33788918059275375, 171.34478761712384198, 172.35279713916281707, 131 173.36191283062726143, 174.37212981874515094, 175.38344327348534080, 132 176.39584840699734514, 177.40934047306160437, 178.42391476654847793, 133 179.43956662288721304, 180.45629141754378111, 181.47408456550741107, 134 182.49294152078630304, 183.51285777591152737, 184.53382886144947861, 135 185.55585034552262869, 186.57891783333786861, 187.60302696672312095, 136 188.62817342367162610, 189.65435291789341932, 190.68156119837468054, 137 191.70979404894376330, 192.73904728784492590, 193.76931676731820176, 138 194.80059837318714244, 195.83288802445184729, 196.86618167288995096, 139 197.90047530266301123, 198.93576492992946214, 199.97204660246373464, 140 201.00931639928148797, 202.04757043027063901, 203.08680483582807597, 141 204.12701578650228385, 205.16819948264117102, 206.21035215404597807, 142 207.25347005962987623, 208.29754948708190909, 209.34258675253678916, 143 210.38857820024875878, 211.43552020227099320, 212.48340915813977858, 144 213.53224149456323744, 214.58201366511514152, 215.63272214993284592, 145 216.68436345542014010, 217.73693411395422004, 218.79043068359703739, 146 219.84484974781133815, 220.90018791517996988, 221.95644181913033322, 147 223.01360811766215875, 224.07168349307951871, 225.13066465172661879, 148 226.19054832372759734, 227.25133126272962159, 228.31301024565024704, 149 229.37558207242807384, 230.43904356577689896, 231.50339157094342113, 150 232.56862295546847008, 233.63473460895144740, 234.70172344281823484, 151 235.76958639009222907, 236.83832040516844586, 237.90792246359117712, 152 238.97838956183431947, 240.04971871708477238, 241.12190696702904802, 153 242.19495136964280846, 243.26884900298270509, 244.34359696498191283, 154 245.41919237324782443, 246.49563236486270057, 247.57291409618682110, 155 248.65103474266476269, 249.72999149863338175, 250.80978157713354904, 156 251.89040220972316320, 252.97185064629374551, 254.05412415488834199, 157 255.13722002152300661, 256.22113555000953511, 257.30586806178126835, 158 258.39141489572085675, 259.47777340799029844, 260.56494097186322279, 159 261.65291497755913497, 262.74169283208021852, 263.83127195904967266, 160 264.92164979855277807, 266.01282380697938379, 267.10479145686849733, 161 268.19755023675537586, 269.29109765101975427, 270.38543121973674488, 162 271.48054847852881721, 272.57644697842033565, 273.67312428569374561, 163 274.77057798174683967, 275.86880566295326389, 276.96780494052313770, 164 278.06757344036617496, 279.16810880295668085, 280.26940868320008349, 165 281.37147075030043197, 282.47429268763045229, 283.57787219260217171, 166 284.68220697654078322, 285.78729476455760050, 286.89313329542699194, 167 287.99972032146268930, 289.10705360839756395, 290.21513093526289140, 168 291.32395009427028754, 292.43350889069523646, 293.54380514276073200, 169 294.65483668152336350, 295.76660135076059532, 296.87909700685889902, 170 297.99232151870342022, 299.10627276756946458, 300.22094864701409733, 171 301.33634706277030091, 302.45246593264130297, 303.56930318639643929, 172 304.68685676566872189, 305.80512462385280514, 306.92410472600477078, 173 308.04379504874236773, 309.16419358014690033, 310.28529831966631036, 174 311.40710727801865687, 312.52961847709792664, 313.65282994987899201, 175 314.77673974032603610, 315.90134590329950015, 317.02664650446632777, 176 318.15263962020929966, 319.27932333753892635, 320.40669575400545455, 177 321.53475497761127144, 322.66349912672620803, 323.79292633000159185, 178 324.92303472628691452, 326.05382246454587403, 327.18528770377525916, 179 328.31742861292224234, 329.45024337080525356, 330.58373016603343331, 180 331.71788719692847280, 332.85271267144611329, 333.98820480709991898, 181 335.12436183088397001, 336.26118197919845443, 337.39866349777429377, 182 338.53680464159958774, 339.67560367484657036, 340.81505887079896411, 183 341.95516851178109619, 343.09593088908627578, 344.23734430290727460, 184 345.37940706226686416, 346.52211748494903532, 347.66547389743118401, 185 348.80947463481720661, 349.95411804077025408, 351.09940246744753267, 186 352.24532627543504759, 353.39188783368263103, 354.53908551944078908, 187 355.68691771819692349, 356.83538282361303118, 357.98447923746385868, 188 359.13420536957539753 189 }; 190 191 TEST_BEGIN(test_ln_gamma_misc) 192 { 193 unsigned i; 194 195 for (i = 1; i < sizeof(ln_gamma_misc_expected)/sizeof(double); i++) { 196 double x = (double)i * 0.25; 197 assert_true(double_eq_rel(ln_gamma(x), 198 ln_gamma_misc_expected[i], MAX_REL_ERR, MAX_ABS_ERR), 199 "Incorrect ln_gamma result for i=%u", i); 200 } 201 } 202 TEST_END 203 204 /* Expected pt_norm([0.01..0.99] increment=0.01). */ 205 static const double pt_norm_expected[] = { 206 -INFINITY, 207 -2.32634787404084076, -2.05374891063182252, -1.88079360815125085, 208 -1.75068607125216946, -1.64485362695147264, -1.55477359459685305, 209 -1.47579102817917063, -1.40507156030963221, -1.34075503369021654, 210 -1.28155156554460081, -1.22652812003661049, -1.17498679206608991, 211 -1.12639112903880045, -1.08031934081495606, -1.03643338949378938, 212 -0.99445788320975281, -0.95416525314619416, -0.91536508784281390, 213 -0.87789629505122846, -0.84162123357291418, -0.80642124701824025, 214 -0.77219321418868492, -0.73884684918521371, -0.70630256284008752, 215 -0.67448975019608171, -0.64334540539291685, -0.61281299101662701, 216 -0.58284150727121620, -0.55338471955567281, -0.52440051270804067, 217 -0.49585034734745320, -0.46769879911450812, -0.43991316567323380, 218 -0.41246312944140462, -0.38532046640756751, -0.35845879325119373, 219 -0.33185334643681652, -0.30548078809939738, -0.27931903444745404, 220 -0.25334710313579978, -0.22754497664114931, -0.20189347914185077, 221 -0.17637416478086135, -0.15096921549677725, -0.12566134685507399, 222 -0.10043372051146975, -0.07526986209982976, -0.05015358346473352, 223 -0.02506890825871106, 0.00000000000000000, 0.02506890825871106, 224 0.05015358346473366, 0.07526986209982990, 0.10043372051146990, 225 0.12566134685507413, 0.15096921549677739, 0.17637416478086146, 226 0.20189347914185105, 0.22754497664114931, 0.25334710313579978, 227 0.27931903444745404, 0.30548078809939738, 0.33185334643681652, 228 0.35845879325119373, 0.38532046640756762, 0.41246312944140484, 229 0.43991316567323391, 0.46769879911450835, 0.49585034734745348, 230 0.52440051270804111, 0.55338471955567303, 0.58284150727121620, 231 0.61281299101662701, 0.64334540539291685, 0.67448975019608171, 232 0.70630256284008752, 0.73884684918521371, 0.77219321418868492, 233 0.80642124701824036, 0.84162123357291441, 0.87789629505122879, 234 0.91536508784281423, 0.95416525314619460, 0.99445788320975348, 235 1.03643338949378938, 1.08031934081495606, 1.12639112903880045, 236 1.17498679206608991, 1.22652812003661049, 1.28155156554460081, 237 1.34075503369021654, 1.40507156030963265, 1.47579102817917085, 238 1.55477359459685394, 1.64485362695147308, 1.75068607125217102, 239 1.88079360815125041, 2.05374891063182208, 2.32634787404084076 240 }; 241 242 TEST_BEGIN(test_pt_norm) 243 { 244 unsigned i; 245 246 for (i = 1; i < sizeof(pt_norm_expected)/sizeof(double); i++) { 247 double p = (double)i * 0.01; 248 assert_true(double_eq_rel(pt_norm(p), pt_norm_expected[i], 249 MAX_REL_ERR, MAX_ABS_ERR), 250 "Incorrect pt_norm result for i=%u", i); 251 } 252 } 253 TEST_END 254 255 /* 256 * Expected pt_chi2(p=[0.01..0.99] increment=0.07, 257 * df={0.1, 1.1, 10.1, 100.1, 1000.1}). 258 */ 259 static const double pt_chi2_df[] = {0.1, 1.1, 10.1, 100.1, 1000.1}; 260 static const double pt_chi2_expected[] = { 261 1.168926411457320e-40, 1.347680397072034e-22, 3.886980416666260e-17, 262 8.245951724356564e-14, 2.068936347497604e-11, 1.562561743309233e-09, 263 5.459543043426564e-08, 1.114775688149252e-06, 1.532101202364371e-05, 264 1.553884683726585e-04, 1.239396954915939e-03, 8.153872320255721e-03, 265 4.631183739647523e-02, 2.473187311701327e-01, 2.175254800183617e+00, 266 267 0.0003729887888876379, 0.0164409238228929513, 0.0521523015190650113, 268 0.1064701372271216612, 0.1800913735793082115, 0.2748704281195626931, 269 0.3939246282787986497, 0.5420727552260817816, 0.7267265822221973259, 270 0.9596554296000253670, 1.2607440376386165326, 1.6671185084541604304, 271 2.2604828984738705167, 3.2868613342148607082, 6.9298574921692139839, 272 273 2.606673548632508, 4.602913725294877, 5.646152813924212, 274 6.488971315540869, 7.249823275816285, 7.977314231410841, 275 8.700354939944047, 9.441728024225892, 10.224338321374127, 276 11.076435368801061, 12.039320937038386, 13.183878752697167, 277 14.657791935084575, 16.885728216339373, 23.361991680031817, 278 279 70.14844087392152, 80.92379498849355, 85.53325420085891, 280 88.94433120715347, 91.83732712857017, 94.46719943606301, 281 96.96896479994635, 99.43412843510363, 101.94074719829733, 282 104.57228644307247, 107.43900093448734, 110.71844673417287, 283 114.76616819871325, 120.57422505959563, 135.92318818757556, 284 285 899.0072447849649, 937.9271278858220, 953.8117189560207, 286 965.3079371501154, 974.8974061207954, 983.4936235182347, 287 991.5691170518946, 999.4334123954690, 1007.3391826856553, 288 1015.5445154999951, 1024.3777075619569, 1034.3538789836223, 289 1046.4872561869577, 1063.5717461999654, 1107.0741966053859 290 }; 291 292 TEST_BEGIN(test_pt_chi2) 293 { 294 unsigned i, j; 295 unsigned e = 0; 296 297 for (i = 0; i < sizeof(pt_chi2_df)/sizeof(double); i++) { 298 double df = pt_chi2_df[i]; 299 double ln_gamma_df = ln_gamma(df * 0.5); 300 for (j = 1; j < 100; j += 7) { 301 double p = (double)j * 0.01; 302 assert_true(double_eq_rel(pt_chi2(p, df, ln_gamma_df), 303 pt_chi2_expected[e], MAX_REL_ERR, MAX_ABS_ERR), 304 "Incorrect pt_chi2 result for i=%u, j=%u", i, j); 305 e++; 306 } 307 } 308 } 309 TEST_END 310 311 /* 312 * Expected pt_gamma(p=[0.1..0.99] increment=0.07, 313 * shape=[0.5..3.0] increment=0.5). 314 */ 315 static const double pt_gamma_shape[] = {0.5, 1.0, 1.5, 2.0, 2.5, 3.0}; 316 static const double pt_gamma_expected[] = { 317 7.854392895485103e-05, 5.043466107888016e-03, 1.788288957794883e-02, 318 3.900956150232906e-02, 6.913847560638034e-02, 1.093710833465766e-01, 319 1.613412523825817e-01, 2.274682115597864e-01, 3.114117323127083e-01, 320 4.189466220207417e-01, 5.598106789059246e-01, 7.521856146202706e-01, 321 1.036125427911119e+00, 1.532450860038180e+00, 3.317448300510606e+00, 322 323 0.01005033585350144, 0.08338160893905107, 0.16251892949777497, 324 0.24846135929849966, 0.34249030894677596, 0.44628710262841947, 325 0.56211891815354142, 0.69314718055994529, 0.84397007029452920, 326 1.02165124753198167, 1.23787435600161766, 1.51412773262977574, 327 1.89711998488588196, 2.52572864430825783, 4.60517018598809091, 328 329 0.05741590094955853, 0.24747378084860744, 0.39888572212236084, 330 0.54394139997444901, 0.69048812513915159, 0.84311389861296104, 331 1.00580622221479898, 1.18298694218766931, 1.38038096305861213, 332 1.60627736383027453, 1.87396970522337947, 2.20749220408081070, 333 2.65852391865854942, 3.37934630984842244, 5.67243336507218476, 334 335 0.1485547402532659, 0.4657458011640391, 0.6832386130709406, 336 0.8794297834672100, 1.0700752852474524, 1.2629614217350744, 337 1.4638400448580779, 1.6783469900166610, 1.9132338090606940, 338 2.1778589228618777, 2.4868823970010991, 2.8664695666264195, 339 3.3724415436062114, 4.1682658512758071, 6.6383520679938108, 340 341 0.2771490383641385, 0.7195001279643727, 0.9969081732265243, 342 1.2383497880608061, 1.4675206597269927, 1.6953064251816552, 343 1.9291243435606809, 2.1757300955477641, 2.4428032131216391, 344 2.7406534569230616, 3.0851445039665513, 3.5043101122033367, 345 4.0575997065264637, 4.9182956424675286, 7.5431362346944937, 346 347 0.4360451650782932, 0.9983600902486267, 1.3306365880734528, 348 1.6129750834753802, 1.8767241606994294, 2.1357032436097660, 349 2.3988853336865565, 2.6740603137235603, 2.9697561737517959, 350 3.2971457713883265, 3.6731795898504660, 4.1275751617770631, 351 4.7230515633946677, 5.6417477865306020, 8.4059469148854635 352 }; 353 354 TEST_BEGIN(test_pt_gamma_shape) 355 { 356 unsigned i, j; 357 unsigned e = 0; 358 359 for (i = 0; i < sizeof(pt_gamma_shape)/sizeof(double); i++) { 360 double shape = pt_gamma_shape[i]; 361 double ln_gamma_shape = ln_gamma(shape); 362 for (j = 1; j < 100; j += 7) { 363 double p = (double)j * 0.01; 364 assert_true(double_eq_rel(pt_gamma(p, shape, 1.0, 365 ln_gamma_shape), pt_gamma_expected[e], MAX_REL_ERR, 366 MAX_ABS_ERR), 367 "Incorrect pt_gamma result for i=%u, j=%u", i, j); 368 e++; 369 } 370 } 371 } 372 TEST_END 373 374 TEST_BEGIN(test_pt_gamma_scale) 375 { 376 double shape = 1.0; 377 double ln_gamma_shape = ln_gamma(shape); 378 379 assert_true(double_eq_rel( 380 pt_gamma(0.5, shape, 1.0, ln_gamma_shape) * 10.0, 381 pt_gamma(0.5, shape, 10.0, ln_gamma_shape), MAX_REL_ERR, 382 MAX_ABS_ERR), 383 "Scale should be trivially equivalent to external multiplication"); 384 } 385 TEST_END 386 387 int 388 main(void) 389 { 390 391 return (test( 392 test_ln_gamma_factorial, 393 test_ln_gamma_misc, 394 test_pt_norm, 395 test_pt_chi2, 396 test_pt_gamma_shape, 397 test_pt_gamma_scale)); 398 } 399
