225 lines
7.7 KiB
Python
225 lines
7.7 KiB
Python
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"""
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Torture tests for asymptotics and high precision evaluation of
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special functions.
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(Other torture tests may also be placed here.)
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Running this file (gmpy recommended!) takes several CPU minutes.
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With Python 2.6+, multiprocessing is used automatically to run tests
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in parallel if many cores are available. (A single test may take between
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a second and several minutes; possibly more.)
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The idea:
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* We evaluate functions at positive, negative, imaginary, 45- and 135-degree
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complex values with magnitudes between 10^-20 to 10^20, at precisions between
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5 and 150 digits (we can go even higher for fast functions).
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* Comparing the result from two different precision levels provides
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a strong consistency check (particularly for functions that use
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different algorithms at different precision levels).
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* That the computation finishes at all (without failure), within reasonable
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time, provides a check that evaluation works at all: that the code runs,
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that it doesn't get stuck in an infinite loop, and that it doesn't use
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some extremely slowly algorithm where it could use a faster one.
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TODO:
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* Speed up those functions that take long to finish!
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* Generalize to test more cases; more options.
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* Implement a timeout mechanism.
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* Some functions are notably absent, including the following:
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* inverse trigonometric functions (some become inaccurate for complex arguments)
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* ci, si (not implemented properly for large complex arguments)
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* zeta functions (need to modify test not to try too large imaginary values)
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* and others...
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"""
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import sys, os
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from timeit import default_timer as clock
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if "-nogmpy" in sys.argv:
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sys.argv.remove('-nogmpy')
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os.environ['MPMATH_NOGMPY'] = 'Y'
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filt = ''
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if not sys.argv[-1].endswith(".py"):
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filt = sys.argv[-1]
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from mpmath import *
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from mpmath.libmp.backend import exec_
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def test_asymp(f, maxdps=150, verbose=False, huge_range=False):
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dps = [5,15,25,50,90,150,500,1500,5000,10000]
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dps = [p for p in dps if p <= maxdps]
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def check(x,y,p,inpt):
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if abs(x-y)/abs(y) < workprec(20)(power)(10, -p+1):
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return
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print()
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print("Error!")
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print("Input:", inpt)
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print("dps =", p)
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print("Result 1:", x)
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print("Result 2:", y)
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print("Absolute error:", abs(x-y))
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print("Relative error:", abs(x-y)/abs(y))
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raise AssertionError
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exponents = range(-20,20)
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if huge_range:
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exponents += [-1000, -100, -50, 50, 100, 1000]
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for n in exponents:
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if verbose:
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sys.stdout.write(". ")
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mp.dps = 25
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xpos = mpf(10)**n / 1.1287
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xneg = -xpos
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ximag = xpos*j
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xcomplex1 = xpos*(1+j)
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xcomplex2 = xpos*(-1+j)
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for i in range(len(dps)):
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if verbose:
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print("Testing dps = %s" % dps[i])
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mp.dps = dps[i]
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new = f(xpos), f(xneg), f(ximag), f(xcomplex1), f(xcomplex2)
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if i != 0:
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p = dps[i-1]
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check(prev[0], new[0], p, xpos)
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check(prev[1], new[1], p, xneg)
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check(prev[2], new[2], p, ximag)
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check(prev[3], new[3], p, xcomplex1)
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check(prev[4], new[4], p, xcomplex2)
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prev = new
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if verbose:
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print()
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a1, a2, a3, a4, a5 = 1.5, -2.25, 3.125, 4, 2
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def test_bernoulli_huge():
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p, q = bernfrac(9000)
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assert p % 10**10 == 9636701091
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assert q == 4091851784687571609141381951327092757255270
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mp.dps = 15
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assert str(bernoulli(10**100)) == '-2.58183325604736e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623'
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mp.dps = 50
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assert str(bernoulli(10**100)) == '-2.5818332560473632073252488656039475548106223822913e+987675256497386331227838638980680030172857347883537824464410652557820800494271520411283004120790908623'
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mp.dps = 15
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cases = """\
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test_bernoulli_huge()
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test_asymp(lambda z: +pi, maxdps=10000)
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test_asymp(lambda z: +e, maxdps=10000)
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test_asymp(lambda z: +ln2, maxdps=10000)
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test_asymp(lambda z: +ln10, maxdps=10000)
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test_asymp(lambda z: +phi, maxdps=10000)
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test_asymp(lambda z: +catalan, maxdps=5000)
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test_asymp(lambda z: +euler, maxdps=5000)
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test_asymp(lambda z: +glaisher, maxdps=1000)
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test_asymp(lambda z: +khinchin, maxdps=1000)
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test_asymp(lambda z: +twinprime, maxdps=150)
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test_asymp(lambda z: stieltjes(2), maxdps=150)
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test_asymp(lambda z: +mertens, maxdps=150)
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test_asymp(lambda z: +apery, maxdps=5000)
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test_asymp(sqrt, maxdps=10000, huge_range=True)
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test_asymp(cbrt, maxdps=5000, huge_range=True)
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test_asymp(lambda z: root(z,4), maxdps=5000, huge_range=True)
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test_asymp(lambda z: root(z,-5), maxdps=5000, huge_range=True)
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test_asymp(exp, maxdps=5000, huge_range=True)
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test_asymp(expm1, maxdps=1500)
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test_asymp(ln, maxdps=5000, huge_range=True)
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test_asymp(cosh, maxdps=5000)
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test_asymp(sinh, maxdps=5000)
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test_asymp(tanh, maxdps=1500)
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test_asymp(sin, maxdps=5000, huge_range=True)
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test_asymp(cos, maxdps=5000, huge_range=True)
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test_asymp(tan, maxdps=1500)
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test_asymp(agm, maxdps=1500, huge_range=True)
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test_asymp(ellipk, maxdps=1500)
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test_asymp(ellipe, maxdps=1500)
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test_asymp(lambertw, huge_range=True)
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test_asymp(lambda z: lambertw(z,-1))
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test_asymp(lambda z: lambertw(z,1))
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test_asymp(lambda z: lambertw(z,4))
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test_asymp(gamma)
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test_asymp(loggamma) # huge_range=True ?
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test_asymp(ei)
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test_asymp(e1)
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test_asymp(li, huge_range=True)
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test_asymp(ci)
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test_asymp(si)
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test_asymp(chi)
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test_asymp(shi)
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test_asymp(erf)
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test_asymp(erfc)
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test_asymp(erfi)
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test_asymp(lambda z: besselj(2, z))
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test_asymp(lambda z: bessely(2, z))
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test_asymp(lambda z: besseli(2, z))
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test_asymp(lambda z: besselk(2, z))
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test_asymp(lambda z: besselj(-2.25, z))
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test_asymp(lambda z: bessely(-2.25, z))
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test_asymp(lambda z: besseli(-2.25, z))
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test_asymp(lambda z: besselk(-2.25, z))
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test_asymp(airyai)
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test_asymp(airybi)
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test_asymp(lambda z: hyp0f1(a1, z))
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test_asymp(lambda z: hyp1f1(a1, a2, z))
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test_asymp(lambda z: hyp1f2(a1, a2, a3, z))
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test_asymp(lambda z: hyp2f0(a1, a2, z))
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test_asymp(lambda z: hyperu(a1, a2, z))
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test_asymp(lambda z: hyp2f1(a1, a2, a3, z))
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test_asymp(lambda z: hyp2f2(a1, a2, a3, a4, z))
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test_asymp(lambda z: hyp2f3(a1, a2, a3, a4, a5, z))
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test_asymp(lambda z: coulombf(a1, a2, z))
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test_asymp(lambda z: coulombg(a1, a2, z))
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test_asymp(lambda z: polylog(2,z))
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test_asymp(lambda z: polylog(3,z))
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test_asymp(lambda z: polylog(-2,z))
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test_asymp(lambda z: expint(4, z))
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test_asymp(lambda z: expint(-4, z))
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test_asymp(lambda z: expint(2.25, z))
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test_asymp(lambda z: gammainc(2.5, z, 5))
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test_asymp(lambda z: gammainc(2.5, 5, z))
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test_asymp(lambda z: hermite(3, z))
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test_asymp(lambda z: hermite(2.5, z))
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test_asymp(lambda z: legendre(3, z))
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test_asymp(lambda z: legendre(4, z))
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test_asymp(lambda z: legendre(2.5, z))
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test_asymp(lambda z: legenp(a1, a2, z))
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test_asymp(lambda z: legenq(a1, a2, z), maxdps=90) # abnormally slow
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test_asymp(lambda z: jtheta(1, z, 0.5))
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test_asymp(lambda z: jtheta(2, z, 0.5))
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test_asymp(lambda z: jtheta(3, z, 0.5))
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test_asymp(lambda z: jtheta(4, z, 0.5))
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test_asymp(lambda z: jtheta(1, z, 0.5, 1))
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test_asymp(lambda z: jtheta(2, z, 0.5, 1))
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test_asymp(lambda z: jtheta(3, z, 0.5, 1))
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test_asymp(lambda z: jtheta(4, z, 0.5, 1))
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test_asymp(barnesg, maxdps=90)
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"""
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def testit(line):
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if filt in line:
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print(line)
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t1 = clock()
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exec_(line, globals(), locals())
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t2 = clock()
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elapsed = t2-t1
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print("Time:", elapsed, "for", line, "(OK)")
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if __name__ == '__main__':
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try:
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from multiprocessing import Pool
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mapf = Pool(None).map
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print("Running tests with multiprocessing")
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except ImportError:
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print("Not using multiprocessing")
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mapf = map
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t1 = clock()
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tasks = cases.splitlines()
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mapf(testit, tasks)
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t2 = clock()
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print("Cumulative wall time:", t2-t1)
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