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| author | Mark Dickinson <dickinsm@gmail.com> | 2016-09-03 18:30:22 (GMT) |
|---|---|---|
| committer | Mark Dickinson <dickinsm@gmail.com> | 2016-09-03 18:30:22 (GMT) |
| commit | 96f774d8246e91bc30fc440b65f9c7a435462f45 (patch) | |
| tree | 6692b7c69287ecdce26612c74f0cab812801a17e | |
| parent | 06cf601e4f9ce57d12573943dda90d1ee4330b7a (diff) | |
| download | cpython-96f774d8246e91bc30fc440b65f9c7a435462f45.zip cpython-96f774d8246e91bc30fc440b65f9c7a435462f45.tar.gz cpython-96f774d8246e91bc30fc440b65f9c7a435462f45.tar.bz2 | |
Issue #26040: Improve test_math and test_cmath coverage and rigour. Thanks Jeff Allen.
| -rw-r--r-- | Lib/test/cmath_testcases.txt | 141 | ||||
| -rw-r--r-- | Lib/test/test_math.py | 265 | ||||
| -rw-r--r-- | Misc/NEWS | 3 |
3 files changed, 322 insertions, 87 deletions
diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt index 9b08653..dd7e458 100644 --- a/Lib/test/cmath_testcases.txt +++ b/Lib/test/cmath_testcases.txt @@ -53,6 +53,12 @@ -- MPFR homepage at http://www.mpfr.org for more information about the -- MPFR project. +-- A minority of the test cases were generated with the help of +-- mpmath 0.19 at 100 bit accuracy (http://mpmath.org) to improve +-- coverage of real functions with real-valued arguments. These are +-- used in test.test_math.MathTests.test_testfile, as well as in +-- test_cmath. + -------------------------- -- acos: Inverse cosine -- @@ -848,6 +854,18 @@ atan0302 atan 9.9999999999999999e-161 -1.0 -> 0.78539816339744828 -184.553381029 atan0303 atan -1e-165 1.0 -> -0.78539816339744828 190.30984376228875 atan0304 atan -9.9998886718268301e-321 -1.0 -> -0.78539816339744828 -368.76019403576692 +-- Additional real values (mpmath) +atan0400 atan 1.7976931348623157e+308 0.0 -> 1.5707963267948966192 0.0 +atan0401 atan -1.7976931348623157e+308 0.0 -> -1.5707963267948966192 0.0 +atan0402 atan 1e-17 0.0 -> 1.0000000000000000715e-17 0.0 +atan0403 atan -1e-17 0.0 -> -1.0000000000000000715e-17 0.0 +atan0404 atan 0.0001 0.0 -> 0.000099999999666666673459 0.0 +atan0405 atan -0.0001 0.0 -> -0.000099999999666666673459 0.0 +atan0406 atan 0.999999999999999 0.0 -> 0.78539816339744781002 0.0 +atan0407 atan 1.000000000000001 0.0 -> 0.78539816339744886473 0.0 +atan0408 atan 14.101419947171719 0.0 -> 1.4999999999999999969 0.0 +atan0409 atan 1255.7655915007897 0.0 -> 1.5700000000000000622 0.0 + -- special values atan1000 atan -0.0 0.0 -> -0.0 0.0 atan1001 atan nan 0.0 -> nan 0.0 @@ -1514,6 +1532,11 @@ sqrt0131 sqrt -1.5477066694467245e-310 -0.0 -> 0.0 -1.2440685951533077e-155 sqrt0140 sqrt 1.6999999999999999e+308 -1.6999999999999999e+308 -> 1.4325088230154573e+154 -5.9336458271212207e+153 sqrt0141 sqrt -1.797e+308 -9.9999999999999999e+306 -> 3.7284476432057307e+152 -1.3410406899802901e+154 +-- Additional real values (mpmath) +sqrt0150 sqrt 1.7976931348623157e+308 0.0 -> 1.3407807929942596355e+154 0.0 +sqrt0151 sqrt 2.2250738585072014e-308 0.0 -> 1.4916681462400413487e-154 0.0 +sqrt0152 sqrt 5e-324 0.0 -> 2.2227587494850774834e-162 0.0 + -- special values sqrt1000 sqrt 0.0 0.0 -> 0.0 0.0 sqrt1001 sqrt -0.0 0.0 -> 0.0 0.0 @@ -1616,6 +1639,20 @@ exp0052 exp 710.0 1.5 -> 1.5802653829857376e+307 inf overflow exp0053 exp 710.0 1.6 -> -6.5231579995501372e+306 inf overflow exp0054 exp 710.0 2.8 -> -inf 7.4836177417448528e+307 overflow +-- Additional real values (mpmath) +exp0070 exp 1e-08 0.0 -> 1.00000001000000005 0.0 +exp0071 exp 0.0003 0.0 -> 1.0003000450045003375 0.0 +exp0072 exp 0.2 0.0 -> 1.2214027581601698475 0.0 +exp0073 exp 1.0 0.0 -> 2.7182818284590452354 0.0 +exp0074 exp -1e-08 0.0 -> 0.99999999000000005 0.0 +exp0075 exp -0.0003 0.0 -> 0.99970004499550033751 0.0 +exp0076 exp -1.0 0.0 -> 0.3678794411714423216 0.0 +exp0077 exp 2.220446049250313e-16 0.0 -> 1.000000000000000222 0.0 +exp0078 exp -1.1102230246251565e-16 0.0 -> 0.99999999999999988898 0.0 +exp0079 exp 2.302585092994046 0.0 -> 10.000000000000002171 0.0 +exp0080 exp -2.302585092994046 0.0 -> 0.099999999999999978292 0.0 +exp0081 exp 709.7827 0.0 -> 1.7976699566638014654e+308 0.0 + -- special values exp1000 exp 0.0 0.0 -> 1.0 0.0 exp1001 exp -0.0 0.0 -> 1.0 0.0 @@ -1708,6 +1745,23 @@ cosh0023 cosh 2.218885944363501 2.0015727395883687 -> -1.94294321081968 4.129026 cosh0030 cosh 710.5 2.3519999999999999 -> -1.2967465239355998e+308 1.3076707908857333e+308 cosh0031 cosh -710.5 0.69999999999999996 -> 1.4085466381392499e+308 -1.1864024666450239e+308 +-- Additional real values (mpmath) +cosh0050 cosh 1e-150 0.0 -> 1.0 0.0 +cosh0051 cosh 1e-18 0.0 -> 1.0 0.0 +cosh0052 cosh 1e-09 0.0 -> 1.0000000000000000005 0.0 +cosh0053 cosh 0.0003 0.0 -> 1.0000000450000003375 0.0 +cosh0054 cosh 0.2 0.0 -> 1.0200667556190758485 0.0 +cosh0055 cosh 1.0 0.0 -> 1.5430806348152437785 0.0 +cosh0056 cosh -1e-18 0.0 -> 1.0 -0.0 +cosh0057 cosh -0.0003 0.0 -> 1.0000000450000003375 -0.0 +cosh0058 cosh -1.0 0.0 -> 1.5430806348152437785 -0.0 +cosh0059 cosh 1.3169578969248168 0.0 -> 2.0000000000000001504 0.0 +cosh0060 cosh -1.3169578969248168 0.0 -> 2.0000000000000001504 -0.0 +cosh0061 cosh 17.328679513998633 0.0 -> 16777216.000000021938 0.0 +cosh0062 cosh 18.714973875118524 0.0 -> 67108864.000000043662 0.0 +cosh0063 cosh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0 +cosh0064 cosh -709.7827 0.0 -> 8.9883497833190073272e+307 -0.0 + -- special values cosh1000 cosh 0.0 0.0 -> 1.0 0.0 cosh1001 cosh 0.0 inf -> nan 0.0 invalid ignore-imag-sign @@ -1800,6 +1854,24 @@ sinh0023 sinh 0.043713693678420068 0.22512549887532657 -> 0.042624198673416713 0 sinh0030 sinh 710.5 -2.3999999999999999 -> -1.3579970564885919e+308 -1.24394470907798e+308 sinh0031 sinh -710.5 0.80000000000000004 -> -1.2830671601735164e+308 1.3210954193997678e+308 +-- Additional real values (mpmath) +sinh0050 sinh 1e-100 0.0 -> 1.00000000000000002e-100 0.0 +sinh0051 sinh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0 +sinh0052 sinh 1e-16 0.0 -> 9.999999999999999791e-17 0.0 +sinh0053 sinh 3.7e-08 0.0 -> 3.7000000000000008885e-8 0.0 +sinh0054 sinh 0.001 0.0 -> 0.0010000001666666750208 0.0 +sinh0055 sinh 0.2 0.0 -> 0.20133600254109399895 0.0 +sinh0056 sinh 1.0 0.0 -> 1.1752011936438014569 0.0 +sinh0057 sinh -3.7e-08 0.0 -> -3.7000000000000008885e-8 0.0 +sinh0058 sinh -0.001 0.0 -> -0.0010000001666666750208 0.0 +sinh0059 sinh -1.0 0.0 -> -1.1752011936438014569 0.0 +sinh0060 sinh 1.4436354751788103 0.0 -> 1.9999999999999999078 0.0 +sinh0061 sinh -1.4436354751788103 0.0 -> -1.9999999999999999078 0.0 +sinh0062 sinh 17.328679513998633 0.0 -> 16777215.999999992136 0.0 +sinh0063 sinh 18.714973875118524 0.0 -> 67108864.000000036211 0.0 +sinh0064 sinh 709.7827 0.0 -> 8.9883497833190073272e+307 0.0 +sinh0065 sinh -709.7827 0.0 -> -8.9883497833190073272e+307 0.0 + -- special values sinh1000 sinh 0.0 0.0 -> 0.0 0.0 sinh1001 sinh 0.0 inf -> 0.0 nan invalid ignore-real-sign @@ -1897,6 +1969,24 @@ tanh0031 tanh -711 7.4000000000000004 -> -1.0 0.0 tanh0032 tanh 1000 -2.3199999999999998 -> 1.0 0.0 tanh0033 tanh -1.0000000000000001e+300 -9.6699999999999999 -> -1.0 -0.0 +-- Additional real values (mpmath) +tanh0050 tanh 1e-100 0.0 -> 1.00000000000000002e-100 0.0 +tanh0051 tanh 5e-17 0.0 -> 4.9999999999999998955e-17 0.0 +tanh0052 tanh 1e-16 0.0 -> 9.999999999999999791e-17 0.0 +tanh0053 tanh 3.7e-08 0.0 -> 3.6999999999999983559e-8 0.0 +tanh0054 tanh 0.001 0.0 -> 0.00099999966666680002076 0.0 +tanh0055 tanh 0.2 0.0 -> 0.19737532022490401141 0.0 +tanh0056 tanh 1.0 0.0 -> 0.76159415595576488812 0.0 +tanh0057 tanh -3.7e-08 0.0 -> -3.6999999999999983559e-8 0.0 +tanh0058 tanh -0.001 0.0 -> -0.00099999966666680002076 0.0 +tanh0059 tanh -1.0 0.0 -> -0.76159415595576488812 0.0 +tanh0060 tanh 0.5493061443340549 0.0 -> 0.50000000000000003402 0.0 +tanh0061 tanh -0.5493061443340549 0.0 -> -0.50000000000000003402 0.0 +tanh0062 tanh 17.328679513998633 0.0 -> 0.99999999999999822364 0.0 +tanh0063 tanh 18.714973875118524 0.0 -> 0.99999999999999988898 0.0 +tanh0064 tanh 711 0.0 -> 1.0 0.0 +tanh0065 tanh 1.797e+308 0.0 -> 1.0 0.0 + --special values tanh1000 tanh 0.0 0.0 -> 0.0 0.0 tanh1001 tanh 0.0 inf -> nan nan invalid @@ -1985,6 +2075,22 @@ cos0021 cos 4.8048375263775256 0.0062248852898515658 -> 0.092318702015846243 0.0 cos0022 cos 7.9914515433858515 0.71659966615501436 -> -0.17375439906936566 -0.77217043527294582 cos0023 cos 0.45124351152540226 1.6992693993812158 -> 2.543477948972237 -1.1528193694875477 +-- Additional real values (mpmath) +cos0050 cos 1e-150 0.0 -> 1.0 -0.0 +cos0051 cos 1e-18 0.0 -> 1.0 -0.0 +cos0052 cos 1e-09 0.0 -> 0.9999999999999999995 -0.0 +cos0053 cos 0.0003 0.0 -> 0.9999999550000003375 -0.0 +cos0054 cos 0.2 0.0 -> 0.98006657784124162892 -0.0 +cos0055 cos 1.0 0.0 -> 0.5403023058681397174 -0.0 +cos0056 cos -1e-18 0.0 -> 1.0 0.0 +cos0057 cos -0.0003 0.0 -> 0.9999999550000003375 0.0 +cos0058 cos -1.0 0.0 -> 0.5403023058681397174 0.0 +cos0059 cos 1.0471975511965976 0.0 -> 0.50000000000000009945 -0.0 +cos0060 cos 2.5707963267948966 0.0 -> -0.84147098480789647357 -0.0 +cos0061 cos -2.5707963267948966 0.0 -> -0.84147098480789647357 0.0 +cos0062 cos 7.225663103256523 0.0 -> 0.58778525229247407559 -0.0 +cos0063 cos -8.79645943005142 0.0 -> -0.80901699437494722255 0.0 + -- special values cos1000 cos -0.0 0.0 -> 1.0 0.0 cos1001 cos -inf 0.0 -> nan 0.0 invalid ignore-imag-sign @@ -2073,6 +2179,22 @@ sin0021 sin 1.4342727387492671 0.81361889790284347 -> 1.3370960060947923 0.12336 sin0022 sin 1.1518087354403725 4.8597235966150558 -> 58.919141989603041 26.237003403758852 sin0023 sin 0.00087773078406649192 34.792379211312095 -> 565548145569.38245 644329685822700.62 +-- Additional real values (mpmath) +sin0050 sin 1e-100 0.0 -> 1.00000000000000002e-100 0.0 +sin0051 sin 3.7e-08 0.0 -> 3.6999999999999992001e-8 0.0 +sin0052 sin 0.001 0.0 -> 0.00099999983333334168748 0.0 +sin0053 sin 0.2 0.0 -> 0.19866933079506122634 0.0 +sin0054 sin 1.0 0.0 -> 0.84147098480789650665 0.0 +sin0055 sin -3.7e-08 0.0 -> -3.6999999999999992001e-8 0.0 +sin0056 sin -0.001 0.0 -> -0.00099999983333334168748 0.0 +sin0057 sin -1.0 0.0 -> -0.84147098480789650665 0.0 +sin0058 sin 0.5235987755982989 0.0 -> 0.50000000000000004642 0.0 +sin0059 sin -0.5235987755982989 0.0 -> -0.50000000000000004642 0.0 +sin0060 sin 2.6179938779914944 0.0 -> 0.49999999999999996018 -0.0 +sin0061 sin -2.6179938779914944 0.0 -> -0.49999999999999996018 -0.0 +sin0062 sin 7.225663103256523 0.0 -> 0.80901699437494673648 0.0 +sin0063 sin -8.79645943005142 0.0 -> -0.58778525229247340658 -0.0 + -- special values sin1000 sin -0.0 0.0 -> -0.0 0.0 sin1001 sin -inf 0.0 -> nan 0.0 invalid ignore-imag-sign @@ -2161,6 +2283,25 @@ tan0021 tan 1.7809617968443272 1.5052381702853379 -> -0.044066222118946903 1.093 tan0022 tan 1.1615313900880577 1.7956298728647107 -> 0.041793186826390362 1.0375339546034792 tan0023 tan 0.067014779477908945 5.8517361577457097 -> 2.2088639754800034e-06 0.9999836182420061 +-- Additional real values (mpmath) +tan0050 tan 1e-100 0.0 -> 1.00000000000000002e-100 0.0 +tan0051 tan 3.7e-08 0.0 -> 3.7000000000000017328e-8 0.0 +tan0052 tan 0.001 0.0 -> 0.0010000003333334666875 0.0 +tan0053 tan 0.2 0.0 -> 0.20271003550867249488 0.0 +tan0054 tan 1.0 0.0 -> 1.5574077246549022305 0.0 +tan0055 tan -3.7e-08 0.0 -> -3.7000000000000017328e-8 0.0 +tan0056 tan -0.001 0.0 -> -0.0010000003333334666875 0.0 +tan0057 tan -1.0 0.0 -> -1.5574077246549022305 0.0 +tan0058 tan 0.4636476090008061 0.0 -> 0.49999999999999997163 0.0 +tan0059 tan -0.4636476090008061 0.0 -> -0.49999999999999997163 0.0 +tan0060 tan 1.1071487177940904 0.0 -> 1.9999999999999995298 0.0 +tan0061 tan -1.1071487177940904 0.0 -> -1.9999999999999995298 0.0 +tan0062 tan 1.5 0.0 -> 14.101419947171719388 0.0 +tan0063 tan 1.57 0.0 -> 1255.7655915007896475 0.0 +tan0064 tan 1.5707963267948961 0.0 -> 1978937966095219.0538 0.0 +tan0065 tan 7.225663103256523 0.0 -> 1.3763819204711701522 0.0 +tan0066 tan -8.79645943005142 0.0 -> 0.7265425280053614098 0.0 + -- special values tan1000 tan -0.0 0.0 -> -0.0 0.0 tan1001 tan -inf 0.0 -> nan nan invalid diff --git a/Lib/test/test_math.py b/Lib/test/test_math.py index 48e8007..02d8b47 100644 --- a/Lib/test/test_math.py +++ b/Lib/test/test_math.py @@ -29,6 +29,7 @@ test_dir = os.path.dirname(file) or os.curdir math_testcases = os.path.join(test_dir, 'math_testcases.txt') test_file = os.path.join(test_dir, 'cmath_testcases.txt') + def to_ulps(x): """Convert a non-NaN float x to an integer, in such a way that adjacent floats are converted to adjacent integers. Then @@ -36,25 +37,39 @@ def to_ulps(x): floats. The results from this function will only make sense on platforms - where C doubles are represented in IEEE 754 binary64 format. + where native doubles are represented in IEEE 754 binary64 format. + Note: 0.0 and -0.0 are converted to 0 and -1, respectively. """ n = struct.unpack('<q', struct.pack('<d', x))[0] if n < 0: n = ~(n+2**63) return n -def ulps_check(expected, got, ulps=20): - """Given non-NaN floats `expected` and `got`, - check that they're equal to within the given number of ulps. - Returns None on success and an error message on failure.""" +def ulp(x): + """Return the value of the least significant bit of a + float x, such that the first float bigger than x is x+ulp(x). + Then, given an expected result x and a tolerance of n ulps, + the result y should be such that abs(y-x) <= n * ulp(x). + The results from this function will only make sense on platforms + where native doubles are represented in IEEE 754 binary64 format. + """ + x = abs(float(x)) + if math.isnan(x) or math.isinf(x): + return x - ulps_error = to_ulps(got) - to_ulps(expected) - if abs(ulps_error) <= ulps: - return None - return "error = {} ulps; permitted error = {} ulps".format(ulps_error, - ulps) + # Find next float up from x. + n = struct.unpack('<q', struct.pack('<d', x))[0] + x_next = struct.unpack('<d', struct.pack('<q', n + 1))[0] + if math.isinf(x_next): + # Corner case: x was the largest finite float. Then it's + # not an exact power of two, so we can take the difference + # between x and the previous float. + x_prev = struct.unpack('<d', struct.pack('<q', n - 1))[0] + return x - x_prev + else: + return x_next - x # Here's a pure Python version of the math.factorial algorithm, for # documentation and comparison purposes. @@ -106,24 +121,23 @@ def py_factorial(n): outer *= inner return outer << (n - count_set_bits(n)) -def acc_check(expected, got, rel_err=2e-15, abs_err = 5e-323): - """Determine whether non-NaN floats a and b are equal to within a - (small) rounding error. The default values for rel_err and - abs_err are chosen to be suitable for platforms where a float is - represented by an IEEE 754 double. They allow an error of between - 9 and 19 ulps.""" +def ulp_abs_check(expected, got, ulp_tol, abs_tol): + """Given finite floats `expected` and `got`, check that they're + approximately equal to within the given number of ulps or the + given absolute tolerance, whichever is bigger. - # need to special case infinities, since inf - inf gives nan - if math.isinf(expected) and got == expected: - return None - - error = got - expected + Returns None on success and an error message on failure. + """ + ulp_error = abs(to_ulps(expected) - to_ulps(got)) + abs_error = abs(expected - got) - permitted_error = max(abs_err, rel_err * abs(expected)) - if abs(error) < permitted_error: + # Succeed if either abs_error <= abs_tol or ulp_error <= ulp_tol. + if abs_error <= abs_tol or ulp_error <= ulp_tol: return None - return "error = {}; permitted error = {}".format(error, - permitted_error) + else: + fmt = ("error = {:.3g} ({:d} ulps); " + "permitted error = {:.3g} or {:d} ulps") + return fmt.format(abs_error, ulp_error, abs_tol, ulp_tol) def parse_mtestfile(fname): """Parse a file with test values @@ -150,6 +164,7 @@ def parse_mtestfile(fname): yield (id, fn, float(arg), float(exp), flags) + def parse_testfile(fname): """Parse a file with test values @@ -171,8 +186,53 @@ def parse_testfile(fname): yield (id, fn, float(arg_real), float(arg_imag), float(exp_real), float(exp_imag), - flags - ) + flags) + + +def result_check(expected, got, ulp_tol=5, abs_tol=0.0): + # Common logic of MathTests.(ftest, test_testcases, test_mtestcases) + """Compare arguments expected and got, as floats, if either + is a float, using a tolerance expressed in multiples of + ulp(expected) or absolutely (if given and greater). + + As a convenience, when neither argument is a float, and for + non-finite floats, exact equality is demanded. Also, nan==nan + as far as this function is concerned. + + Returns None on success and an error message on failure. + """ + + # Check exactly equal (applies also to strings representing exceptions) + if got == expected: + return None + + failure = "not equal" + + # Turn mixed float and int comparison (e.g. floor()) to all-float + if isinstance(expected, float) and isinstance(got, int): + got = float(got) + elif isinstance(got, float) and isinstance(expected, int): + expected = float(expected) + + if isinstance(expected, float) and isinstance(got, float): + if math.isnan(expected) and math.isnan(got): + # Pass, since both nan + failure = None + elif math.isinf(expected) or math.isinf(got): + # We already know they're not equal, drop through to failure + pass + else: + # Both are finite floats (now). Are they close enough? + failure = ulp_abs_check(expected, got, ulp_tol, abs_tol) + + # arguments are not equal, and if numeric, are too far apart + if failure is not None: + fail_fmt = "expected {!r}, got {!r}" + fail_msg = fail_fmt.format(expected, got) + fail_msg += ' ({})'.format(failure) + return fail_msg + else: + return None # Class providing an __index__ method. class MyIndexable(object): @@ -184,18 +244,23 @@ class MyIndexable(object): class MathTests(unittest.TestCase): - def ftest(self, name, value, expected): - if abs(value-expected) > eps: - # Use %r instead of %f so the error message - # displays full precision. Otherwise discrepancies - # in the last few bits will lead to very confusing - # error messages - self.fail('%s returned %r, expected %r' % - (name, value, expected)) + def ftest(self, name, got, expected, ulp_tol=5, abs_tol=0.0): + """Compare arguments expected and got, as floats, if either + is a float, using a tolerance expressed in multiples of + ulp(expected) or absolutely, whichever is greater. + + As a convenience, when neither argument is a float, and for + non-finite floats, exact equality is demanded. Also, nan==nan + in this function. + """ + failure = result_check(expected, got, ulp_tol, abs_tol) + if failure is not None: + self.fail("{}: {}".format(name, failure)) def testConstants(self): - self.ftest('pi', math.pi, 3.1415926) - self.ftest('e', math.e, 2.7182818) + # Ref: Abramowitz & Stegun (Dover, 1965) + self.ftest('pi', math.pi, 3.141592653589793238462643) + self.ftest('e', math.e, 2.718281828459045235360287) self.assertEqual(math.tau, 2*math.pi) def testAcos(self): @@ -378,9 +443,9 @@ class MathTests(unittest.TestCase): def testCos(self): self.assertRaises(TypeError, math.cos) - self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0) + self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0, abs_tol=ulp(1)) self.ftest('cos(0)', math.cos(0), 1) - self.ftest('cos(pi/2)', math.cos(math.pi/2), 0) + self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=ulp(1)) self.ftest('cos(pi)', math.cos(math.pi), -1) try: self.assertTrue(math.isnan(math.cos(INF))) @@ -970,7 +1035,8 @@ class MathTests(unittest.TestCase): def testTanh(self): self.assertRaises(TypeError, math.tanh) self.ftest('tanh(0)', math.tanh(0), 0) - self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0) + self.ftest('tanh(1)+tanh(-1)', math.tanh(1)+math.tanh(-1), 0, + abs_tol=ulp(1)) self.ftest('tanh(inf)', math.tanh(INF), 1) self.ftest('tanh(-inf)', math.tanh(NINF), -1) self.assertTrue(math.isnan(math.tanh(NAN))) @@ -1084,30 +1150,48 @@ class MathTests(unittest.TestCase): @requires_IEEE_754 def test_testfile(self): + fail_fmt = "{}: {}({!r}): {}" + + failures = [] for id, fn, ar, ai, er, ei, flags in parse_testfile(test_file): - # Skip if either the input or result is complex, or if - # flags is nonempty - if ai != 0. or ei != 0. or flags: + # Skip if either the input or result is complex + if ai != 0.0 or ei != 0.0: continue if fn in ['rect', 'polar']: # no real versions of rect, polar continue + func = getattr(math, fn) + + if 'invalid' in flags or 'divide-by-zero' in flags: + er = 'ValueError' + elif 'overflow' in flags: + er = 'OverflowError' + try: result = func(ar) - except ValueError as exc: - message = (("Unexpected ValueError: %s\n " + - "in test %s:%s(%r)\n") % (exc.args[0], id, fn, ar)) - self.fail(message) + except ValueError: + result = 'ValueError' except OverflowError: - message = ("Unexpected OverflowError in " + - "test %s:%s(%r)\n" % (id, fn, ar)) - self.fail(message) - self.ftest("%s:%s(%r)" % (id, fn, ar), result, er) + result = 'OverflowError' + + # Default tolerances + ulp_tol, abs_tol = 5, 0.0 + + failure = result_check(er, result, ulp_tol, abs_tol) + if failure is None: + continue + + msg = fail_fmt.format(id, fn, ar, failure) + failures.append(msg) + + if failures: + self.fail('Failures in test_testfile:\n ' + + '\n '.join(failures)) @requires_IEEE_754 def test_mtestfile(self): - fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}" + fail_fmt = "{}: {}({!r}): {}" failures = [] for id, fn, arg, expected, flags in parse_mtestfile(math_testcases): @@ -1125,41 +1209,48 @@ class MathTests(unittest.TestCase): except OverflowError: got = 'OverflowError' - accuracy_failure = None - if isinstance(got, float) and isinstance(expected, float): - if math.isnan(expected) and math.isnan(got): - continue - if not math.isnan(expected) and not math.isnan(got): - if fn == 'lgamma': - # we use a weaker accuracy test for lgamma; - # lgamma only achieves an absolute error of - # a few multiples of the machine accuracy, in - # general. - accuracy_failure = acc_check(expected, got, - rel_err = 5e-15, - abs_err = 5e-15) - elif fn == 'erfc': - # erfc has less-than-ideal accuracy for large - # arguments (x ~ 25 or so), mainly due to the - # error involved in computing exp(-x*x). - # - # XXX Would be better to weaken this test only - # for large x, instead of for all x. - accuracy_failure = ulps_check(expected, got, 2000) - - else: - accuracy_failure = ulps_check(expected, got, 20) - if accuracy_failure is None: - continue - - if isinstance(got, str) and isinstance(expected, str): - if got == expected: - continue - - fail_msg = fail_fmt.format(id, fn, arg, expected, got) - if accuracy_failure is not None: - fail_msg += ' ({})'.format(accuracy_failure) - failures.append(fail_msg) + # Default tolerances + ulp_tol, abs_tol = 5, 0.0 + + # Exceptions to the defaults + if fn == 'gamma': + # Experimental results on one platform gave + # an accuracy of <= 10 ulps across the entire float + # domain. We weaken that to require 20 ulp accuracy. + ulp_tol = 20 + + elif fn == 'lgamma': + # we use a weaker accuracy test for lgamma; + # lgamma only achieves an absolute error of + # a few multiples of the machine accuracy, in + # general. + abs_tol = 1e-15 + + elif fn == 'erfc' and arg >= 0.0: + # erfc has less-than-ideal accuracy for large + # arguments (x ~ 25 or so), mainly due to the + # error involved in computing exp(-x*x). + # + # Observed between CPython and mpmath at 25 dp: + # x < 0 : err <= 2 ulp + # 0 <= x < 1 : err <= 10 ulp + # 1 <= x < 10 : err <= 100 ulp + # 10 <= x < 20 : err <= 300 ulp + # 20 <= x : < 600 ulp + # + if arg < 1.0: + ulp_tol = 10 + elif arg < 10.0: + ulp_tol = 100 + else: + ulp_tol = 1000 + + failure = result_check(expected, got, ulp_tol, abs_tol) + if failure is None: + continue + + msg = fail_fmt.format(id, fn, arg, failure) + failures.append(msg) if failures: self.fail('Failures in test_mtestfile:\n ' + @@ -135,6 +135,9 @@ Library Tests ----- +- Issue #26040: Improve test_math and test_cmath coverage and rigour. Patch by + Jeff Allen. + - Issue #27787: Call gc.collect() before checking each test for "dangling threads", since the dangling threads are weak references. |