[Python-checkins] cpython: Issue #26040: Improve test_math and test_cmath coverage and rigour. Thanks Jeff
mark.dickinson
python-checkins at python.org
Sat Sep 3 14:30:33 EDT 2016
https://hg.python.org/cpython/rev/e3dbe8b7279a
changeset: 103025:e3dbe8b7279a
parent: 103023:fd4e4fa75260
user: Mark Dickinson <dickinsm at gmail.com>
date: Sat Sep 03 19:30:22 2016 +0100
summary:
Issue #26040: Improve test_math and test_cmath coverage and rigour. Thanks Jeff Allen.
files:
Lib/test/cmath_testcases.txt | 141 ++++++++++++
Lib/test/test_math.py | 261 +++++++++++++++-------
Misc/NEWS | 3 +
3 files changed, 320 insertions(+), 85 deletions(-)
diff --git a/Lib/test/cmath_testcases.txt b/Lib/test/cmath_testcases.txt
--- 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 @@
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 @@
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 @@
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 @@
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 @@
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 @@
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 @@
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 @@
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 @@
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
--- a/Lib/test/test_math.py
+++ b/Lib/test/test_math.py
@@ -29,6 +29,7 @@
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 @@
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 @@
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:
+ Returns None on success and an error message on failure.
+ """
+ ulp_error = abs(to_ulps(expected) - to_ulps(got))
+ abs_error = abs(expected - got)
+
+ # Succeed if either abs_error <= abs_tol or ulp_error <= ulp_tol.
+ if abs_error <= abs_tol or ulp_error <= ulp_tol:
return None
-
- error = got - expected
-
- permitted_error = max(abs_err, rel_err * abs(expected))
- if abs(error) < permitted_error:
- 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 @@
yield (id, fn, float(arg), float(exp), flags)
+
def parse_testfile(fname):
"""Parse a file with test values
@@ -171,8 +186,53 @@
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 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 @@
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 @@
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 @@
@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 @@
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)
+ # Default tolerances
+ ulp_tol, abs_tol = 5, 0.0
- else:
- accuracy_failure = ulps_check(expected, got, 20)
- if accuracy_failure is None:
- continue
+ # 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
- if isinstance(got, str) and isinstance(expected, str):
- if got == expected:
- continue
+ 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
- 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)
+ 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 ' +
diff --git a/Misc/NEWS b/Misc/NEWS
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -135,6 +135,9 @@
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.
--
Repository URL: https://hg.python.org/cpython
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