726 lines
30 KiB
V
726 lines
30 KiB
V
module math
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struct Fi {
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f f64
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i int
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}
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const (
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vf_ = [f64(4.9790119248836735e+00), 7.7388724745781045e+00, -2.7688005719200159e-01,
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-5.0106036182710749e+00, 9.6362937071984173e+00, 2.9263772392439646e+00, 5.2290834314593066e+00,
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2.7279399104360102e+00, 1.8253080916808550e+00, -8.6859247685756013e+00]
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// The expected results below were computed by the high precision calculators
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// at https://keisan.casio.com/. More exact input values (array vf_[], above)
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// were obtained by printing them with "%.26f". The answers were calculated
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// to 26 digits (by using the "Digit number" drop-down control of each
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// calculator).
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acos_ = [f64(1.0496193546107222142571536e+00), 6.8584012813664425171660692e-01, 1.5984878714577160325521819e+00,
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2.0956199361475859327461799e+00, 2.7053008467824138592616927e-01, 1.2738121680361776018155625e+00,
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1.0205369421140629186287407e+00, 1.2945003481781246062157835e+00, 1.3872364345374451433846657e+00,
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2.6231510803970463967294145e+00,
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]
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asin_ = [f64(5.2117697218417440497416805e-01), 8.8495619865825236751471477e-01, -2.769154466281941332086016e-02,
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-5.2482360935268931351485822e-01, 1.3002662421166552333051524e+00, 2.9698415875871901741575922e-01,
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5.5025938468083370060258102e-01, 2.7629597861677201301553823e-01, 1.83559892257451475846656e-01,
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-1.0523547536021497774980928e+00,
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]
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atan_ = [f64(1.372590262129621651920085e+00), 1.442290609645298083020664e+00, -2.7011324359471758245192595e-01,
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-1.3738077684543379452781531e+00, 1.4673921193587666049154681e+00, 1.2415173565870168649117764e+00,
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1.3818396865615168979966498e+00, 1.2194305844639670701091426e+00, 1.0696031952318783760193244e+00,
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-1.4561721938838084990898679e+00,
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]
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atan2_ = [f64(1.1088291730037004444527075e+00), 9.1218183188715804018797795e-01, 1.5984772603216203736068915e+00,
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2.0352918654092086637227327e+00, 8.0391819139044720267356014e-01, 1.2861075249894661588866752e+00,
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1.0889904479131695712182587e+00, 1.3044821793397925293797357e+00, 1.3902530903455392306872261e+00,
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2.2859857424479142655411058e+00,
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]
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ceil_ = [f64(5.0000000000000000e+00), 8.0000000000000000e+00, copysign(0, -1),
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-5.0000000000000000e+00, 1.0000000000000000e+01, 3.0000000000000000e+00, 6.0000000000000000e+00,
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3.0000000000000000e+00, 2.0000000000000000e+00, -8.0000000000000000e+00]
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cos_ = [f64(2.634752140995199110787593e-01), 1.148551260848219865642039e-01, 9.6191297325640768154550453e-01,
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2.938141150061714816890637e-01, -9.777138189897924126294461e-01, -9.7693041344303219127199518e-01,
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4.940088096948647263961162e-01, -9.1565869021018925545016502e-01, -2.517729313893103197176091e-01,
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-7.39241351595676573201918e-01,
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]
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// Results for 100000 * pi + vf_[i]
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cos_large_ = [f64(2.634752141185559426744e-01), 1.14855126055543100712e-01, 9.61912973266488928113e-01,
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2.9381411499556122552e-01, -9.777138189880161924641e-01, -9.76930413445147608049e-01, 4.940088097314976789841e-01,
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-9.15658690217517835002e-01, -2.51772931436786954751e-01, -7.3924135157173099849e-01]
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cosh_ = [f64(7.2668796942212842775517446e+01), 1.1479413465659254502011135e+03, 1.0385767908766418550935495e+00,
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7.5000957789658051428857788e+01, 7.655246669605357888468613e+03, 9.3567491758321272072888257e+00,
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9.331351599270605471131735e+01, 7.6833430994624643209296404e+00, 3.1829371625150718153881164e+00,
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2.9595059261916188501640911e+03,
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]
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exp_ = [f64(1.4533071302642137507696589e+02), 2.2958822575694449002537581e+03, 7.5814542574851666582042306e-01,
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6.6668778421791005061482264e-03, 1.5310493273896033740861206e+04, 1.8659907517999328638667732e+01,
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1.8662167355098714543942057e+02, 1.5301332413189378961665788e+01, 6.2047063430646876349125085e+00,
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1.6894712385826521111610438e-04,
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]
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exp2_ = [f64(3.1537839463286288034313104e+01), 2.1361549283756232296144849e+02, 8.2537402562185562902577219e-01,
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3.1021158628740294833424229e-02, 7.9581744110252191462569661e+02, 7.6019905892596359262696423e+00,
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3.7506882048388096973183084e+01, 6.6250893439173561733216375e+00, 3.5438267900243941544605339e+00,
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2.4281533133513300984289196e-03,
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]
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fabs_ = [f64(4.9790119248836735e+00), 7.7388724745781045e+00, 2.7688005719200159e-01,
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5.0106036182710749e+00, 9.6362937071984173e+00, 2.9263772392439646e+00, 5.2290834314593066e+00,
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2.7279399104360102e+00, 1.8253080916808550e+00, 8.6859247685756013e+00]
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floor_ = [f64(4.0000000000000000e+00), 7.0000000000000000e+00, -1.0000000000000000e+00,
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-6.0000000000000000e+00, 9.0000000000000000e+00, 2.0000000000000000e+00, 5.0000000000000000e+00,
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2.0000000000000000e+00, 1.0000000000000000e+00, -9.0000000000000000e+00]
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fmod_ = [f64(4.197615023265299782906368e-02), 2.261127525421895434476482e+00, 3.231794108794261433104108e-02,
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4.989396381728925078391512e+00, 3.637062928015826201999516e-01, 1.220868282268106064236690e+00,
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4.770916568540693347699744e+00, 1.816180268691969246219742e+00, 8.734595415957246977711748e-01,
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1.314075231424398637614104e+00,
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]
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gamma_ = [f64(2.3254348370739963835386613898e+01), 2.991153837155317076427529816e+03,
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-4.561154336726758060575129109e+00, 7.719403468842639065959210984e-01, 1.6111876618855418534325755566e+05,
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1.8706575145216421164173224946e+00, 3.4082787447257502836734201635e+01, 1.579733951448952054898583387e+00,
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9.3834586598354592860187267089e-01, -2.093995902923148389186189429e-05]
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log_ = [f64(1.605231462693062999102599e+00), 2.0462560018708770653153909e+00, -1.2841708730962657801275038e+00,
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1.6115563905281545116286206e+00, 2.2655365644872016636317461e+00, 1.0737652208918379856272735e+00,
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1.6542360106073546632707956e+00, 1.0035467127723465801264487e+00, 6.0174879014578057187016475e-01,
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2.161703872847352815363655e+00,
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]
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logb_ = [f64(2.0000000000000000e+00), 2.0000000000000000e+00, -2.0000000000000000e+00,
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2.0000000000000000e+00, 3.0000000000000000e+00, 1.0000000000000000e+00, 2.0000000000000000e+00,
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1.0000000000000000e+00, 0.0000000000000000e+00, 3.0000000000000000e+00]
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log10_ = [f64(6.9714316642508290997617083e-01), 8.886776901739320576279124e-01, -5.5770832400658929815908236e-01,
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6.998900476822994346229723e-01, 9.8391002850684232013281033e-01, 4.6633031029295153334285302e-01,
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7.1842557117242328821552533e-01, 4.3583479968917773161304553e-01, 2.6133617905227038228626834e-01,
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9.3881606348649405716214241e-01,
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]
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log1p_ = [f64(4.8590257759797794104158205e-02), 7.4540265965225865330849141e-02, -2.7726407903942672823234024e-03,
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-5.1404917651627649094953380e-02, 9.1998280672258624681335010e-02, 2.8843762576593352865894824e-02,
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5.0969534581863707268992645e-02, 2.6913947602193238458458594e-02, 1.8088493239630770262045333e-02,
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-9.0865245631588989681559268e-02,
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]
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log2_ = [f64(2.3158594707062190618898251e+00), 2.9521233862883917703341018e+00, -1.8526669502700329984917062e+00,
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2.3249844127278861543568029e+00, 3.268478366538305087466309e+00, 1.5491157592596970278166492e+00,
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2.3865580889631732407886495e+00, 1.447811865817085365540347e+00, 8.6813999540425116282815557e-01,
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3.118679457227342224364709e+00,
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]
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modf_ = [[f64(4.0000000000000000e+00), 9.7901192488367350108546816e-01],
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[f64(7.0000000000000000e+00), 7.3887247457810456552351752e-01],
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[f64(-0.0), -2.7688005719200159404635997e-01], [f64(-5.0000000000000000e+00), -1.060361827107492160848778e-02],
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[f64(9.0000000000000000e+00), 6.3629370719841737980004837e-01],
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[f64(2.0000000000000000e+00), 9.2637723924396464525443662e-01],
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[f64(5.0000000000000000e+00), 2.2908343145930665230025625e-01],
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[f64(2.0000000000000000e+00), 7.2793991043601025126008608e-01],
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[f64(1.0000000000000000e+00), 8.2530809168085506044576505e-01],
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[f64(-8.0000000000000000e+00), -6.8592476857560136238589621e-01],
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]
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nextafter32_ = [4.979012489318848e+00, 7.738873004913330e+00, -2.768800258636475e-01, -5.010602951049805e+00,
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9.636294364929199e+00, 2.926377534866333e+00, 5.229084014892578e+00, 2.727940082550049e+00,
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1.825308203697205e+00, -8.685923576354980e+00]
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nextafter64_ = [f64(4.97901192488367438926388786e+00), 7.73887247457810545370193722e+00, -2.7688005719200153853520874e-01,
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-5.01060361827107403343006808e+00, 9.63629370719841915615688777e+00, 2.92637723924396508934364647e+00,
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5.22908343145930754047867595e+00, 2.72793991043601069534929593e+00, 1.82530809168085528249036997e+00,
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-8.68592476857559958602905681e+00,
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]
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pow_ = [f64(9.5282232631648411840742957e+04), 5.4811599352999901232411871e+07, 5.2859121715894396531132279e-01,
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9.7587991957286474464259698e-06, 4.328064329346044846740467e+09, 8.4406761805034547437659092e+02,
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1.6946633276191194947742146e+05, 5.3449040147551939075312879e+02, 6.688182138451414936380374e+01,
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2.0609869004248742886827439e-09,
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]
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remainder_ = [f64(4.197615023265299782906368e-02), 2.261127525421895434476482e+00, 3.231794108794261433104108e-02,
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-2.120723654214984321697556e-02, 3.637062928015826201999516e-01, 1.220868282268106064236690e+00,
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-4.581668629186133046005125e-01, -9.117596417440410050403443e-01, 8.734595415957246977711748e-01,
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1.314075231424398637614104e+00,
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]
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round_ = [f64(5), 8, -0.0, -5, 10, 3, 5, 3, 2, -9]
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signbit_ = [false, false, true, true, false, false, false, false, false, true]
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sin_ = [f64(-9.6466616586009283766724726e-01), 9.9338225271646545763467022e-01, -2.7335587039794393342449301e-01,
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9.5586257685042792878173752e-01, -2.099421066779969164496634e-01, 2.135578780799860532750616e-01,
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-8.694568971167362743327708e-01, 4.019566681155577786649878e-01, 9.6778633541687993721617774e-01,
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-6.734405869050344734943028e-01,
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]
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// Results for 100000 * pi + vf_[i]
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sin_large_ = [f64(-9.646661658548936063912e-01), 9.933822527198506903752e-01, -2.7335587036246899796e-01,
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9.55862576853689321268e-01, -2.099421066862688873691e-01, 2.13557878070308981163e-01, -8.694568970959221300497e-01,
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4.01956668098863248917e-01, 9.67786335404528727927e-01, -6.7344058693131973066e-01]
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sinh_ = [f64(7.2661916084208532301448439e+01), 1.1479409110035194500526446e+03, -2.8043136512812518927312641e-01,
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-7.499429091181587232835164e+01, 7.6552466042906758523925934e+03, 9.3031583421672014313789064e+00,
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9.330815755828109072810322e+01, 7.6179893137269146407361477e+00, 3.021769180549615819524392e+00,
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-2.95950575724449499189888e+03,
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]
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sqrt_ = [f64(2.2313699659365484748756904e+00), 2.7818829009464263511285458e+00, 5.2619393496314796848143251e-01,
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2.2384377628763938724244104e+00, 3.1042380236055381099288487e+00, 1.7106657298385224403917771e+00,
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2.286718922705479046148059e+00, 1.6516476350711159636222979e+00, 1.3510396336454586262419247e+00,
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2.9471892997524949215723329e+00,
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]
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tan_ = [f64(-3.661316565040227801781974e+00), 8.64900232648597589369854e+00, -2.8417941955033612725238097e-01,
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3.253290185974728640827156e+00, 2.147275640380293804770778e-01, -2.18600910711067004921551e-01,
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-1.760002817872367935518928e+00, -4.389808914752818126249079e-01, -3.843885560201130679995041e+00,
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9.10988793377685105753416e-01,
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]
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// Results for 100000 * pi + vf_[i]
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tan_large_ = [f64(-3.66131656475596512705e+00), 8.6490023287202547927e+00, -2.841794195104782406e-01,
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3.2532901861033120983e+00, 2.14727564046880001365e-01, -2.18600910700688062874e-01, -1.760002817699722747043e+00,
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-4.38980891453536115952e-01, -3.84388555942723509071e+00, 9.1098879344275101051e-01]
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tanh_ = [f64(9.9990531206936338549262119e-01), 9.9999962057085294197613294e-01, -2.7001505097318677233756845e-01,
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-9.9991110943061718603541401e-01, 9.9999999146798465745022007e-01, 9.9427249436125236705001048e-01,
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9.9994257600983138572705076e-01, 9.9149409509772875982054701e-01, 9.4936501296239685514466577e-01,
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-9.9999994291374030946055701e-01,
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]
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trunc_ = [f64(4.0000000000000000e+00), 7.0000000000000000e+00, copysign(0, -1),
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-5.0000000000000000e+00, 9.0000000000000000e+00, 2.0000000000000000e+00, 5.0000000000000000e+00,
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2.0000000000000000e+00, 1.0000000000000000e+00, -8.0000000000000000e+00]
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)
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fn tolerance(a f64, b f64, tol f64) bool {
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mut ee := tol
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// Multiplying by ee here can underflow denormal values to zero.
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// Check a==b so that at least if a and b are small and identical
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// we say they match.
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if a == b {
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return true
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}
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mut d := a - b
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if d < 0 {
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d = -d
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}
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// note: b is correct (expected) value, a is actual value.
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// make error tolerance a fraction of b, not a.
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if b != 0 {
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ee = ee * b
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if ee < 0 {
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ee = -ee
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}
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}
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return d < ee
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}
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fn close(a f64, b f64) bool {
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return tolerance(a, b, 1e-14)
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}
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fn veryclose(a f64, b f64) bool {
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return tolerance(a, b, 4e-16)
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}
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fn soclose(a f64, b f64, e f64) bool {
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return tolerance(a, b, e)
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}
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fn alike(a f64, b f64) bool {
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if is_nan(a) && is_nan(b) {
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return true
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} else if a == b {
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return signbit(a) == signbit(b)
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}
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return false
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}
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fn test_nan() {
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nan_f64 := nan()
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assert nan_f64 != nan_f64
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nan_f32 := f32(nan_f64)
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assert nan_f32 != nan_f32
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}
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fn test_acos() {
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for i := 0; i < math.vf_.len; i++ {
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a := math.vf_[i] / 10
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f := acos(a)
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assert soclose(math.acos_[i], f, 1e-7)
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}
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vfacos_sc_ := [-pi, 1, pi, nan()]
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acos_sc_ := [nan(), 0, nan(), nan()]
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for i := 0; i < vfacos_sc_.len; i++ {
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f := acos(vfacos_sc_[i])
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assert alike(acos_sc_[i], f)
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}
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}
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fn test_asin() {
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for i := 0; i < math.vf_.len; i++ {
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a := math.vf_[i] / 10
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f := asin(a)
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assert veryclose(math.asin_[i], f)
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}
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vfasin_sc_ := [-pi, copysign(0, -1), 0, pi, nan()]
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asin_sc_ := [nan(), copysign(0, -1), 0, nan(), nan()]
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for i := 0; i < vfasin_sc_.len; i++ {
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f := asin(vfasin_sc_[i])
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assert alike(asin_sc_[i], f)
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}
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}
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fn test_atan() {
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for i := 0; i < math.vf_.len; i++ {
|
|
f := atan(math.vf_[i])
|
|
assert veryclose(math.atan_[i], f)
|
|
}
|
|
vfatan_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
atan_sc_ := [f64(-pi / 2), copysign(0, -1), 0, pi / 2, nan()]
|
|
for i := 0; i < vfatan_sc_.len; i++ {
|
|
f := atan(vfatan_sc_[i])
|
|
assert alike(atan_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_atan2() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := atan2(10, math.vf_[i])
|
|
assert veryclose(math.atan2_[i], f)
|
|
}
|
|
vfatan2_sc_ := [[inf(-1), inf(-1)], [inf(-1), -pi], [inf(-1), 0],
|
|
[inf(-1), pi], [inf(-1), inf(1)], [inf(-1), nan()], [-pi, inf(-1)],
|
|
[-pi, 0], [-pi, inf(1)], [-pi, nan()], [f64(-0.0), inf(-1)],
|
|
[f64(-0.0), -pi], [f64(-0.0), -0.0], [f64(-0.0), 0], [f64(-0.0), pi],
|
|
[f64(-0.0), inf(1)], [f64(-0.0), nan()], [f64(0), inf(-1)],
|
|
[f64(0), -pi], [f64(0), -0.0], [f64(0), 0], [f64(0), pi],
|
|
[f64(0), inf(1)], [f64(0), nan()], [pi, inf(-1)], [pi, 0],
|
|
[pi, inf(1)], [pi, nan()], [inf(1), inf(-1)], [inf(1), -pi],
|
|
[inf(1), 0], [inf(1), pi], [inf(1), inf(1)], [inf(1),
|
|
nan(),
|
|
], [nan(), nan()]]
|
|
atan2_sc_ := [f64(-3.0) * pi / 4.0, /* atan2(-inf, -inf) */ -pi / 2, /* atan2(-inf, -pi) */
|
|
-pi / 2,
|
|
/* atan2(-inf, +0) */ -pi / 2, /* atan2(-inf, pi) */ -pi / 4, /* atan2(-inf, +inf) */
|
|
nan(), /* atan2(-inf, nan) */ -pi, /* atan2(-pi, -inf) */ -pi / 2, /* atan2(-pi, +0) */
|
|
-0.0,
|
|
/* atan2(-pi, inf) */ nan(), /* atan2(-pi, nan) */ -pi, /* atan2(-0, -inf) */ -pi,
|
|
/* atan2(-0, -pi) */ -pi, /* atan2(-0, -0) */ -0.0, /* atan2(-0, +0) */ -0.0, /* atan2(-0, pi) */
|
|
-0.0,
|
|
/* atan2(-0, +inf) */ nan(), /* atan2(-0, nan) */ pi, /* atan2(+0, -inf) */ pi, /* atan2(+0, -pi) */
|
|
pi, /* atan2(+0, -0) */ 0, /* atan2(+0, +0) */ 0, /* atan2(+0, pi) */ 0, /* atan2(+0, +inf) */
|
|
nan(), /* atan2(+0, nan) */ pi, /* atan2(pi, -inf) */ pi / 2, /* atan2(pi, +0) */ 0,
|
|
/* atan2(pi, +inf) */ nan(), /* atan2(pi, nan) */ 3.0 * pi / 4, /* atan2(+inf, -inf) */ pi / 2, /* atan2(+inf, -pi) */
|
|
pi / 2, /* atan2(+inf, +0) */ pi / 2, /* atan2(+inf, pi) */ pi / 4, /* atan2(+inf, +inf) */
|
|
nan(), /* atan2(+inf, nan) */ nan(), /* atan2(nan, nan) */]
|
|
for i := 0; i < vfatan2_sc_.len; i++ {
|
|
f := atan2(vfatan2_sc_[i][0], vfatan2_sc_[i][1])
|
|
assert alike(atan2_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_ceil() {
|
|
// for i := 0; i < vf_.len; i++ {
|
|
// f := ceil(vf_[i])
|
|
// assert alike(ceil_[i], f)
|
|
// }
|
|
vfceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
ceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
for i := 0; i < vfceil_sc_.len; i++ {
|
|
f := ceil(vfceil_sc_[i])
|
|
assert alike(ceil_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_cos() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := cos(math.vf_[i])
|
|
assert veryclose(math.cos_[i], f)
|
|
}
|
|
vfcos_sc_ := [inf(-1), inf(1), nan()]
|
|
cos_sc_ := [nan(), nan(), nan()]
|
|
for i := 0; i < vfcos_sc_.len; i++ {
|
|
f := cos(vfcos_sc_[i])
|
|
assert alike(cos_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_cosh() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := cosh(math.vf_[i])
|
|
assert close(math.cosh_[i], f)
|
|
}
|
|
vfcosh_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
cosh_sc_ := [inf(1), 1, 1, inf(1), nan()]
|
|
for i := 0; i < vfcosh_sc_.len; i++ {
|
|
f := cosh(vfcosh_sc_[i])
|
|
assert alike(cosh_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_abs() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := abs(math.vf_[i])
|
|
assert math.fabs_[i] == f
|
|
}
|
|
}
|
|
|
|
fn test_floor() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := floor(math.vf_[i])
|
|
assert alike(math.floor_[i], f)
|
|
}
|
|
vfceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
ceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
for i := 0; i < vfceil_sc_.len; i++ {
|
|
f := floor(vfceil_sc_[i])
|
|
assert alike(ceil_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_max() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := max(math.vf_[i], math.ceil_[i])
|
|
assert math.ceil_[i] == f
|
|
}
|
|
}
|
|
|
|
fn test_min() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := min(math.vf_[i], math.floor_[i])
|
|
assert math.floor_[i] == f
|
|
}
|
|
}
|
|
|
|
fn test_exp() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := exp(math.vf_[i])
|
|
assert veryclose(math.exp_[i], f)
|
|
}
|
|
vfexp_sc_ := [inf(-1), -2000, 2000, inf(1), nan(), /* smallest f64 that overflows Exp(x) */
|
|
7.097827128933841e+02, 1.48852223e+09, 1.4885222e+09, 1, /* near zero */ 3.725290298461915e-09,
|
|
/* denormal */ -740]
|
|
exp_sc_ := [f64(0), 0, inf(1), inf(1), nan(), inf(1), inf(1),
|
|
inf(1), 2.718281828459045, 1.0000000037252903, 4.2e-322]
|
|
for i := 0; i < vfexp_sc_.len; i++ {
|
|
f := exp(vfexp_sc_[i])
|
|
assert alike(exp_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_exp2() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := exp2(math.vf_[i])
|
|
assert soclose(math.exp2_[i], f, 1e-9)
|
|
}
|
|
vfexp2_sc_ := [f64(-2000), 2000, inf(1), nan(), /* smallest f64 that overflows Exp2(x) */
|
|
1024, /* near underflow */ -1.07399999999999e+03, /* near zero */ 3.725290298461915e-09]
|
|
exp2_sc_ := [f64(0), inf(1), inf(1), nan(), inf(1), 5e-324, 1.0000000025821745]
|
|
for i := 0; i < vfexp2_sc_.len; i++ {
|
|
f := exp2(vfexp2_sc_[i])
|
|
assert alike(exp2_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_gamma() {
|
|
vfgamma_ := [[inf(1), inf(1)], [inf(-1), nan()], [f64(0), inf(1)],
|
|
[f64(-0.0), inf(-1)], [nan(), nan()], [f64(-1), nan()],
|
|
[f64(-2), nan()], [f64(-3), nan()], [f64(-1e+16), nan()],
|
|
[f64(-1e+300), nan()], [f64(1.7e+308), inf(1)], /* Test inputs inspi_red by Python test suite. */
|
|
// Outputs computed at high precision by PARI/GP.
|
|
// If recomputing table entries), be careful to use
|
|
// high-precision (%.1000g) formatting of the f64 inputs.
|
|
// For example), -2.0000000000000004 is the f64 with exact value
|
|
//-2.00000000000000044408920985626161695), and
|
|
// gamma(-2.0000000000000004) = -1249999999999999.5386078562728167651513), while
|
|
// gamma(-2.00000000000000044408920985626161695) = -1125899906826907.2044875028130093136826.
|
|
// Thus the table lists -1.1258999068426235e+15 as the answer.
|
|
[f64(0.5), 1.772453850905516], [f64(1.5), 0.886226925452758],
|
|
[f64(2.5), 1.329340388179137], [f64(3.5), 3.3233509704478426],
|
|
[f64(-0.5), -3.544907701811032], [f64(-1.5), 2.363271801207355],
|
|
[f64(-2.5), -0.9453087204829419], [f64(-3.5), 0.2700882058522691],
|
|
[f64(0.1), 9.51350769866873], [f64(0.01), 99.4325851191506],
|
|
[f64(1e-08), 9.999999942278434e+07], [f64(1e-16), 1e+16],
|
|
[f64(0.001), 999.4237724845955], [f64(1e-16), 1e+16],
|
|
[f64(1e-308), 1e+308], [f64(5.6e-309), 1.7857142857142864e+308],
|
|
[f64(5.5e-309), inf(1)], [f64(1e-309), inf(1)], [f64(1e-323), inf(1)],
|
|
[f64(5e-324), inf(1)], [f64(-0.1), -10.686287021193193],
|
|
[f64(-0.01), -100.58719796441078], [f64(-1e-08), -1.0000000057721567e+08],
|
|
[f64(-1e-16), -1e+16], [f64(-0.001), -1000.5782056293586],
|
|
[f64(-1e-16), -1e+16], [f64(-1e-308), -1e+308], [f64(-5.6e-309), -1.7857142857142864e+308],
|
|
[f64(-5.5e-309), inf(-1)], [f64(-1e-309), inf(-1)], [f64(-1e-323), inf(-1)],
|
|
[f64(-5e-324), inf(-1)], [f64(-0.9999999999999999), -9.007199254740992e+15],
|
|
[f64(-1.0000000000000002), 4.5035996273704955e+15], [f64(-1.9999999999999998), 2.2517998136852485e+15],
|
|
[f64(-2.0000000000000004), -1.1258999068426235e+15], [f64(-100.00000000000001), -7.540083334883109e-145],
|
|
[f64(-99.99999999999999), 7.540083334884096e-145], [f64(17), 2.0922789888e+13],
|
|
[f64(171), 7.257415615307999e+306], [f64(171.6), 1.5858969096672565e+308],
|
|
[f64(171.624), 1.7942117599248104e+308], [f64(171.625), inf(1)],
|
|
[f64(172), inf(1)], [f64(2000), inf(1)], [f64(-100.5), -3.3536908198076787e-159],
|
|
[f64(-160.5), -5.255546447007829e-286], [f64(-170.5), -3.3127395215386074e-308],
|
|
[f64(-171.5), 1.9316265431712e-310], [f64(-176.5), -1.196e-321],
|
|
[f64(-177.5), 5e-324], [f64(-178.5), -0.0], [f64(-179.5), 0],
|
|
[f64(-201.0001), 0], [f64(-202.9999), -0.0], [f64(-1000.5), -0.0],
|
|
[f64(-1.0000000003e+09), -0.0], [f64(-4.5035996273704955e+15), 0],
|
|
[f64(-63.349078729022985), 4.177797167776188e-88], [f64(-127.45117632943295), 1.183111089623681e-214]]
|
|
_ := vfgamma_[0][0]
|
|
// for i := 0; i < math.vf_.len; i++ {
|
|
// f := gamma(math.vf_[i])
|
|
// assert veryclose(math.gamma_[i], f)
|
|
// }
|
|
// for _, g in vfgamma_ {
|
|
// f := gamma(g[0])
|
|
// if is_nan(g[1]) || is_inf(g[1], 0) || g[1] == 0 || f == 0 {
|
|
// assert alike(g[1], f)
|
|
// } else if g[0] > -50 && g[0] <= 171 {
|
|
// assert veryclose(g[1], f)
|
|
// } else {
|
|
// assert soclose(g[1], f, 1e-9)
|
|
// }
|
|
// }
|
|
}
|
|
|
|
fn test_hypot() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
a := abs(1e+200 * math.tanh_[i] * sqrt(2.0))
|
|
f := hypot(1e+200 * math.tanh_[i], 1e+200 * math.tanh_[i])
|
|
assert veryclose(a, f)
|
|
}
|
|
vfhypot_sc_ := [[inf(-1), inf(-1)], [inf(-1), 0], [inf(-1),
|
|
inf(1),
|
|
], [inf(-1), nan()], [f64(-0.0), -0.0], [f64(-0.0), 0], [f64(0), -0.0],
|
|
[f64(0), 0], /* +0,0 */ [f64(0), inf(-1)], [f64(0), inf(1)],
|
|
[f64(0), nan()], [inf(1), inf(-1)], [inf(1), 0], [inf(1),
|
|
inf(1),
|
|
], [inf(1), nan()], [nan(), inf(-1)], [nan(), 0], [nan(),
|
|
inf(1),
|
|
], [nan(), nan()]]
|
|
hypot_sc_ := [inf(1), inf(1), inf(1), inf(1), 0, 0, 0, 0, inf(1),
|
|
inf(1), nan(), inf(1), inf(1), inf(1), inf(1), inf(1),
|
|
nan(), inf(1), nan()]
|
|
for i := 0; i < vfhypot_sc_.len; i++ {
|
|
f := hypot(vfhypot_sc_[i][0], vfhypot_sc_[i][1])
|
|
assert alike(hypot_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_log() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
a := abs(math.vf_[i])
|
|
f := log(a)
|
|
assert math.log_[i] == f
|
|
}
|
|
vflog_sc_ := [inf(-1), -pi, copysign(0, -1), 0, 1, inf(1),
|
|
nan(),
|
|
]
|
|
log_sc_ := [nan(), nan(), inf(-1), inf(-1), 0, inf(1), nan()]
|
|
f := log(10)
|
|
assert f == ln10
|
|
for i := 0; i < vflog_sc_.len; i++ {
|
|
g := log(vflog_sc_[i])
|
|
assert alike(log_sc_[i], g)
|
|
}
|
|
}
|
|
|
|
fn test_log10() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
a := abs(math.vf_[i])
|
|
f := log10(a)
|
|
assert veryclose(math.log10_[i], f)
|
|
}
|
|
vflog_sc_ := [inf(-1), -pi, copysign(0, -1), 0, 1, inf(1),
|
|
nan(),
|
|
]
|
|
log_sc_ := [nan(), nan(), inf(-1), inf(-1), 0, inf(1), nan()]
|
|
for i := 0; i < vflog_sc_.len; i++ {
|
|
f := log10(vflog_sc_[i])
|
|
assert alike(log_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_pow() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := pow(10, math.vf_[i])
|
|
assert close(math.pow_[i], f)
|
|
}
|
|
vfpow_sc_ := [[inf(-1), -pi], [inf(-1), -3], [inf(-1), -0.0],
|
|
[inf(-1), 0], [inf(-1), 1], [inf(-1), 3], [inf(-1), pi],
|
|
[inf(-1), 0.5], [inf(-1), nan()], [-pi, inf(-1)], [-pi, -pi],
|
|
[-pi, -0.0], [-pi, 0], [-pi, 1], [-pi, pi], [-pi, inf(1)],
|
|
[-pi, nan()], [f64(-1), inf(-1)], [f64(-1), inf(1)], [f64(-1), nan()],
|
|
[f64(-1 / 2), inf(-1)], [f64(-1 / 2), inf(1)], [f64(-0.0), inf(-1)],
|
|
[f64(-0.0), -pi], [f64(-0.0), -0.5], [f64(-0.0), -3],
|
|
[f64(-0.0), 3], [f64(-0.0), pi], [f64(-0.0), 0.5], [f64(-0.0), inf(1)],
|
|
[f64(0), inf(-1)], [f64(0), -pi], [f64(0), -3], [f64(0), -0.0],
|
|
[f64(0), 0], [f64(0), 3], [f64(0), pi], [f64(0), inf(1)],
|
|
[f64(0), nan()], [f64(1 / 2), inf(-1)], [f64(1 / 2), inf(1)],
|
|
[f64(1), inf(-1)], [f64(1), inf(1)], [f64(1), nan()],
|
|
[pi, inf(-1)], [pi, -0.0], [pi, 0], [pi, 1], [pi, inf(1)],
|
|
[pi, nan()], [inf(1), -pi], [inf(1), -0.0], [inf(1), 0],
|
|
[inf(1), 1], [inf(1), pi], [inf(1), nan()], [nan(), -pi],
|
|
[nan(), -0.0], [nan(), 0], [nan(), 1], [nan(), pi], [
|
|
nan(), nan()]]
|
|
pow_sc_ := [f64(0), /* pow(-inf, -pi) */ -0.0, /* pow(-inf, -3) */ 1, /* pow(-inf, -0) */ 1, /* pow(-inf, +0) */
|
|
inf(-1), /* pow(-inf, 1) */ inf(-1), /* pow(-inf, 3) */
|
|
inf(1), /* pow(-inf, pi) */ inf(1), /* pow(-inf, 0.5) */
|
|
nan(), /* pow(-inf, nan) */ 0, /* pow(-pi, -inf) */ nan(), /* pow(-pi, -pi) */
|
|
1, /* pow(-pi, -0) */ 1, /* pow(-pi, +0) */ -pi, /* pow(-pi, 1) */ nan(), /* pow(-pi, pi) */
|
|
inf(1), /* pow(-pi, +inf) */ nan(), /* pow(-pi, nan) */ 1, /* pow(-1, -inf) IEEE 754-2008 */
|
|
1, /* pow(-1, +inf) IEEE 754-2008 */ nan(), /* pow(-1, nan) */
|
|
inf(1), /* pow(-1/2, -inf) */ 0, /* pow(-1/2, +inf) */ inf(1), /* pow(-0, -inf) */
|
|
inf(1), /* pow(-0, -pi) */ inf(1), /* pow(-0, -0.5) */
|
|
inf(-1), /* pow(-0, -3) IEEE 754-2008 */ -0.0, /* pow(-0, 3) IEEE 754-2008 */ 0, /* pow(-0, pi) */
|
|
0, /* pow(-0, 0.5) */ 0, /* pow(-0, +inf) */ inf(1), /* pow(+0, -inf) */
|
|
inf(1), /* pow(+0, -pi) */ inf(1), /* pow(+0, -3) */ 1, /* pow(+0, -0) */ 1, /* pow(+0, +0) */
|
|
0, /* pow(+0, 3) */ 0,
|
|
/* pow(+0, pi) */ 0, /* pow(+0, +inf) */ nan(), /* pow(+0, nan) */
|
|
inf(1), /* pow(1/2, -inf) */ 0, /* pow(1/2, +inf) */ 1, /* pow(1, -inf) IEEE 754-2008 */
|
|
1, /* pow(1, +inf) IEEE 754-2008 */ 1, /* pow(1, nan) IEEE 754-2008 */ 0, /* pow(pi, -inf) */
|
|
1, /* pow(pi, -0) */ 1, /* pow(pi, +0) */ pi, /* pow(pi, 1) */ inf(1), /* pow(pi, +inf) */
|
|
nan(), /* pow(pi, nan) */ 0, /* pow(+inf, -pi) */ 1, /* pow(+inf, -0) */ 1, /* pow(+inf, +0) */
|
|
inf(1), /* pow(+inf, 1) */ inf(1), /* pow(+inf, pi) */
|
|
nan(), /* pow(+inf, nan) */ nan(), /* pow(nan, -pi) */ 1, /* pow(nan, -0) */ 1, /* pow(nan, +0) */
|
|
nan(), /* pow(nan, 1) */ nan(), /* pow(nan, pi) */ nan(), /* pow(nan, nan) */]
|
|
for i := 0; i < vfpow_sc_.len; i++ {
|
|
f := pow(vfpow_sc_[i][0], vfpow_sc_[i][1])
|
|
assert alike(pow_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_round() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := round(math.vf_[i])
|
|
assert alike(math.round_[i], f)
|
|
}
|
|
vfround_sc_ := [[f64(0), 0], [nan(), nan()], [inf(1), inf(1)]]
|
|
vfround_even_sc_ := [[f64(0), 0], [f64(1.390671161567e-309), 0], /* denormal */
|
|
[f64(0.49999999999999994), 0], /* 0.5-epsilon */ [f64(0.5), 0],
|
|
[f64(0.5000000000000001), 1], /* 0.5+epsilon */ [f64(-1.5), -2],
|
|
[f64(-2.5), -2], [nan(), nan()], [inf(1), inf(1)], [f64(2251799813685249.5), 2251799813685250],
|
|
/* 1 bit fractian */ [f64(2251799813685250.5), 2251799813685250],
|
|
[f64(4503599627370495.5), 4503599627370496], /* 1 bit fraction, rounding to 0 bit fractian */
|
|
[f64(4503599627370497), 4503599627370497], /* large integer */
|
|
]
|
|
_ := vfround_even_sc_[0][0]
|
|
for i := 0; i < vfround_sc_.len; i++ {
|
|
f := round(vfround_sc_[i][0])
|
|
assert alike(vfround_sc_[i][1], f)
|
|
}
|
|
}
|
|
|
|
fn test_sin() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := sin(math.vf_[i])
|
|
assert veryclose(math.sin_[i], f)
|
|
}
|
|
vfsin_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
sin_sc_ := [nan(), copysign(0, -1), 0, nan(), nan()]
|
|
for i := 0; i < vfsin_sc_.len; i++ {
|
|
f := sin(vfsin_sc_[i])
|
|
assert alike(sin_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_sinh() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := sinh(math.vf_[i])
|
|
assert close(math.sinh_[i], f)
|
|
}
|
|
vfsinh_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
sinh_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
for i := 0; i < vfsinh_sc_.len; i++ {
|
|
f := sinh(vfsinh_sc_[i])
|
|
assert alike(sinh_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_sqrt() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
mut a := abs(math.vf_[i])
|
|
mut f := sqrt(a)
|
|
assert veryclose(math.sqrt_[i], f)
|
|
a = abs(math.vf_[i])
|
|
f = sqrt(a)
|
|
assert veryclose(math.sqrt_[i], f)
|
|
}
|
|
vfsqrt_sc_ := [inf(-1), -pi, copysign(0, -1), 0, inf(1), nan()]
|
|
sqrt_sc_ := [nan(), nan(), copysign(0, -1), 0, inf(1), nan()]
|
|
for i := 0; i < vfsqrt_sc_.len; i++ {
|
|
mut f := sqrt(vfsqrt_sc_[i])
|
|
assert alike(sqrt_sc_[i], f)
|
|
f = sqrt(vfsqrt_sc_[i])
|
|
assert alike(sqrt_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_tan() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := tan(math.vf_[i])
|
|
assert veryclose(math.tan_[i], f)
|
|
}
|
|
vfsin_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
sin_sc_ := [nan(), copysign(0, -1), 0, nan(), nan()]
|
|
// same special cases as sin
|
|
for i := 0; i < vfsin_sc_.len; i++ {
|
|
f := tan(vfsin_sc_[i])
|
|
assert alike(sin_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_tanh() {
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f := tanh(math.vf_[i])
|
|
assert veryclose(math.tanh_[i], f)
|
|
}
|
|
vftanh_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
tanh_sc_ := [f64(-1), copysign(0, -1), 0, 1, nan()]
|
|
for i := 0; i < vftanh_sc_.len; i++ {
|
|
f := tanh(vftanh_sc_[i])
|
|
assert alike(tanh_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_trunc() {
|
|
// for i := 0; i < vf_.len; i++ {
|
|
// f := trunc(vf_[i])
|
|
// assert alike(trunc_[i], f)
|
|
// }
|
|
vfceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
ceil_sc_ := [inf(-1), copysign(0, -1), 0, inf(1), nan()]
|
|
for i := 0; i < vfceil_sc_.len; i++ {
|
|
f := trunc(vfceil_sc_[i])
|
|
assert alike(ceil_sc_[i], f)
|
|
}
|
|
}
|
|
|
|
fn test_gcd() {
|
|
assert gcd(6, 9) == 3
|
|
assert gcd(6, -9) == 3
|
|
assert gcd(-6, -9) == 3
|
|
assert gcd(0, 0) == 0
|
|
}
|
|
|
|
fn test_lcm() {
|
|
assert lcm(2, 3) == 6
|
|
assert lcm(-2, 3) == 6
|
|
assert lcm(-2, -3) == 6
|
|
assert lcm(0, 0) == 0
|
|
}
|
|
|
|
fn test_digits() {
|
|
digits_in_10th_base := digits(125, 10)
|
|
assert digits_in_10th_base[0] == 5
|
|
assert digits_in_10th_base[1] == 2
|
|
assert digits_in_10th_base[2] == 1
|
|
digits_in_16th_base := digits(15, 16)
|
|
assert digits_in_16th_base[0] == 15
|
|
negative_digits := digits(-4, 2)
|
|
assert negative_digits[2] == -1
|
|
}
|
|
|
|
// Check that math functions of high angle values
|
|
// return accurate results. [since (vf_[i] + large) - large != vf_[i],
|
|
// testing for Trig(vf_[i] + large) == Trig(vf_[i]), where large is
|
|
// a multiple of 2 * pi, is misleading.]
|
|
fn test_large_cos() {
|
|
large := 100000.0 * pi
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f1 := math.cos_large_[i]
|
|
f2 := cos(math.vf_[i] + large)
|
|
assert soclose(f1, f2, 4e-9)
|
|
}
|
|
}
|
|
|
|
fn test_large_sin() {
|
|
large := 100000.0 * pi
|
|
for i := 0; i < math.vf_.len; i++ {
|
|
f1 := math.sin_large_[i]
|
|
f2 := sin(math.vf_[i] + large)
|
|
assert soclose(f1, f2, 4e-9)
|
|
}
|
|
}
|
|
|
|
fn test_large_tan() {
|
|
large := 100000.0 * pi
|
|
for i := 0; i < vf_.len; i++ {
|
|
f1 := tan_large_[i]
|
|
f2 := tan(vf_[i] + large)
|
|
assert soclose(f1, f2, 4e-9)
|
|
}
|
|
}
|