o lÇh¼ã@sdZddlZddlZddlmZdejvr ej d¡dejd<dZ ejd d ¡s/ejdZ dd lTddlm Z ddd„Zd\ZZZZZdd„ZdZdd„ZedkrŒzddlmZedƒjZedƒWneysedƒeZYnweƒZe ¡Z eee ƒeƒZ!ede!eƒdSdS)a Torture tests for asymptotics and high precision evaluation of special functions. (Other torture tests may also be placed here.) Running this file (gmpy recommended!) takes several CPU minutes. With Python 2.6+, multiprocessing is used automatically to run tests in parallel if many cores are available. (A single test may take between a second and several minutes; possibly more.) The idea: * We evaluate functions at positive, negative, imaginary, 45- and 135-degree complex values with magnitudes between 10^-20 to 10^20, at precisions between 5 and 150 digits (we can go even higher for fast functions). * Comparing the result from two different precision levels provides a strong consistency check (particularly for functions that use different algorithms at different precision levels). * That the computation finishes at all (without failure), within reasonable time, provides a check that evaluation works at all: that the code runs, that it doesn't get stuck in an infinite loop, and that it doesn't use some extremely slowly algorithm where it could use a faster one. TODO: * Speed up those functions that take long to finish! * Generalize to test more cases; more options. * Implement a timeout mechanism. * Some functions are notably absent, including the following: * inverse trigonometric functions (some become inaccurate for complex arguments) * ci, si (not implemented properly for large complex arguments) * zeta functions (need to modify test not to try too large imaginary values) * and others... éN)Ú default_timerz-nogmpyÚYÚ MPMATH_NOGMPYÚéÿÿÿÿz.py)Ú*)Úexec_é–Fcs|gd¢}‡fdd„|Dƒ}dd„}tddƒ}|r|gd¢7}|D]”}|r*tj d ¡d t_tdƒ|d}|} |t} |d t}|dt}tt|ƒƒD]e} |rZt d|| ƒ|| t_||ƒ|| ƒ|| ƒ||ƒ||ƒf}| dkr±|| d }||d|d||ƒ||d |d || ƒ||d|d|| ƒ||d|d||ƒ||d|d||ƒ|}qNq |r¼t ƒdSdS)N) éééé2éZr iôiÜiˆi'csg|]}|ˆkr|‘qS©r)Ú.0Úp©Úmaxdpsrúh/var/www/html/construction_image-detection-poc/venv/lib/python3.10/site-packages/mpmath/tests/torture.pyÚ 9sztest_asymp..cSs–t||ƒt|ƒtdƒtƒd|dƒkrdStƒtdƒtd|ƒtd|ƒtd|ƒtd|ƒtd t||ƒƒtd t||ƒt|ƒƒt‚)Néé ézError!zInput:zdps =z Result 1:z Result 2:zAbsolute error:zRelative error:)ÚabsÚworkprecÚpowerÚprintÚAssertionError)ÚxÚyrÚinptrrrÚcheck:s, ztest_asymp..checkiìÿÿÿr)iüÿÿiœÿÿÿiÎÿÿÿr édièz. rrgWì/»'ò?rrzTesting dps = %srééé) ÚrangeÚsysÚstdoutÚwriteÚmpÚdpsÚmpfÚjÚlenr)ÚfrÚverboseÚ huge_ranger+r!Ú exponentsÚnÚxposÚxnegÚximagÚ xcomplex1Ú xcomplex2ÚiÚnewrÚprevrrrÚ test_asymp7s@ "ô ÿr<)gø?gÀg @r%r#cCsntdƒ\}}|ddksJ‚|dksJ‚dt_ttddƒƒdks#J‚d t_ttddƒƒd ks2J‚dt_dS)Ni(#ld( l£cÈ|l fTè™-âµÛkfKßx]rrr"zy-2.58183325604736e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623r zœ-2.5818332560473632073252488656039475548106223822913e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623)Úbernfracr*r+ÚstrÚ bernoulli)rÚqrrrÚtest_bernoulli_hugeds rAa test_bernoulli_huge() test_asymp(lambda z: +pi, maxdps=10000) test_asymp(lambda z: +e, maxdps=10000) test_asymp(lambda z: +ln2, maxdps=10000) test_asymp(lambda z: +ln10, maxdps=10000) test_asymp(lambda z: +phi, maxdps=10000) test_asymp(lambda z: +catalan, maxdps=5000) test_asymp(lambda z: +euler, maxdps=5000) test_asymp(lambda z: +glaisher, maxdps=1000) test_asymp(lambda z: +khinchin, maxdps=1000) test_asymp(lambda z: +twinprime, maxdps=150) test_asymp(lambda z: stieltjes(2), maxdps=150) test_asymp(lambda z: +mertens, maxdps=150) test_asymp(lambda z: +apery, maxdps=5000) test_asymp(sqrt, maxdps=10000, huge_range=True) test_asymp(cbrt, maxdps=5000, huge_range=True) test_asymp(lambda z: root(z,4), maxdps=5000, huge_range=True) test_asymp(lambda z: root(z,-5), maxdps=5000, huge_range=True) test_asymp(exp, maxdps=5000, huge_range=True) test_asymp(expm1, maxdps=1500) test_asymp(ln, maxdps=5000, huge_range=True) test_asymp(cosh, maxdps=5000) test_asymp(sinh, maxdps=5000) test_asymp(tanh, maxdps=1500) test_asymp(sin, maxdps=5000, huge_range=True) test_asymp(cos, maxdps=5000, huge_range=True) test_asymp(tan, maxdps=1500) test_asymp(agm, maxdps=1500, huge_range=True) test_asymp(ellipk, maxdps=1500) test_asymp(ellipe, maxdps=1500) test_asymp(lambertw, huge_range=True) test_asymp(lambda z: lambertw(z,-1)) test_asymp(lambda z: lambertw(z,1)) test_asymp(lambda z: lambertw(z,4)) test_asymp(gamma) test_asymp(loggamma) # huge_range=True ? test_asymp(ei) test_asymp(e1) test_asymp(li, huge_range=True) test_asymp(ci) test_asymp(si) test_asymp(chi) test_asymp(shi) test_asymp(erf) test_asymp(erfc) test_asymp(erfi) test_asymp(lambda z: besselj(2, z)) test_asymp(lambda z: bessely(2, z)) test_asymp(lambda z: besseli(2, z)) test_asymp(lambda z: besselk(2, z)) test_asymp(lambda z: besselj(-2.25, z)) test_asymp(lambda z: bessely(-2.25, z)) test_asymp(lambda z: besseli(-2.25, z)) test_asymp(lambda z: besselk(-2.25, z)) test_asymp(airyai) test_asymp(airybi) test_asymp(lambda z: hyp0f1(a1, z)) test_asymp(lambda z: hyp1f1(a1, a2, z)) test_asymp(lambda z: hyp1f2(a1, a2, a3, z)) test_asymp(lambda z: hyp2f0(a1, a2, z)) test_asymp(lambda z: hyperu(a1, a2, z)) test_asymp(lambda z: hyp2f1(a1, a2, a3, z)) test_asymp(lambda z: hyp2f2(a1, a2, a3, a4, z)) test_asymp(lambda z: hyp2f3(a1, a2, a3, a4, a5, z)) test_asymp(lambda z: coulombf(a1, a2, z)) test_asymp(lambda z: coulombg(a1, a2, z)) test_asymp(lambda z: polylog(2,z)) test_asymp(lambda z: polylog(3,z)) test_asymp(lambda z: polylog(-2,z)) test_asymp(lambda z: expint(4, z)) test_asymp(lambda z: expint(-4, z)) test_asymp(lambda z: expint(2.25, z)) test_asymp(lambda z: gammainc(2.5, z, 5)) test_asymp(lambda z: gammainc(2.5, 5, z)) test_asymp(lambda z: hermite(3, z)) test_asymp(lambda z: hermite(2.5, z)) test_asymp(lambda z: legendre(3, z)) test_asymp(lambda z: legendre(4, z)) test_asymp(lambda z: legendre(2.5, z)) test_asymp(lambda z: legenp(a1, a2, z)) test_asymp(lambda z: legenq(a1, a2, z), maxdps=90) # abnormally slow test_asymp(lambda z: jtheta(1, z, 0.5)) test_asymp(lambda z: jtheta(2, z, 0.5)) test_asymp(lambda z: jtheta(3, z, 0.5)) test_asymp(lambda z: jtheta(4, z, 0.5)) test_asymp(lambda z: jtheta(1, z, 0.5, 1)) test_asymp(lambda z: jtheta(2, z, 0.5, 1)) test_asymp(lambda z: jtheta(3, z, 0.5, 1)) test_asymp(lambda z: jtheta(4, z, 0.5, 1)) test_asymp(barnesg, maxdps=90) cCsLt|vr$t|ƒtƒ}t|tƒtƒƒtƒ}||}td|d|dƒdSdS)NzTime:Úforz(OK))ÚfiltrÚclockrÚglobalsÚlocals)ÚlineÚt1Út2ÚelapsedrrrÚtestitËsúrKÚ__main__)ÚPoolz"Running tests with multiprocessingzNot using multiprocessingzCumulative wall time:)r FF)"Ú__doc__r'ÚosÚtimeitrrDÚargvÚremoveÚenvironrCÚendswithÚmpmathÚmpmath.libmp.backendrr<Úa1Úa2Úa3Úa4Úa5rAÚcasesrKÚ__name__ÚmultiprocessingrMÚmapÚmapfrÚImportErrorrHÚ splitlinesÚtasksrIrrrrÚs>( + ] þ ô