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Kaydet (Commit) 96f774d8 authored tarafından Mark Dickinson's avatar Mark Dickinson
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Issue #26040: Improve test_math and test_cmath coverage and rigour. Thanks Jeff Allen.

üst 06cf601e
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Lib/test/cmath_testcases.txt
Dosyayı görüntüle @ 96f774d8
......@@ -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
......
Lib/test/test_math.py
Dosyayı görüntüle @ 96f774d8
......@@ -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 ' +
......
Misc/NEWS
Dosyayı görüntüle @ 96f774d8
......@@ -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.
......
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