# Python test set -- math module | |
# XXXX Should not do tests around zero only | |
from test.test_support import run_unittest, verbose | |
import unittest | |
import math | |
import os | |
import sys | |
import random | |
import struct | |
eps = 1E-05 | |
NAN = float('nan') | |
INF = float('inf') | |
NINF = float('-inf') | |
# decorator for skipping tests on non-IEEE 754 platforms | |
requires_IEEE_754 = unittest.skipUnless( | |
float.__getformat__("double").startswith("IEEE"), | |
"test requires IEEE 754 doubles") | |
# detect evidence of double-rounding: fsum is not always correctly | |
# rounded on machines that suffer from double rounding. | |
x, y = 1e16, 2.9999 # use temporary values to defeat peephole optimizer | |
HAVE_DOUBLE_ROUNDING = (x + y == 1e16 + 4) | |
# locate file with test values | |
if __name__ == '__main__': | |
file = sys.argv[0] | |
else: | |
file = __file__ | |
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 | |
abs(ulps(x) - ulps(y)) gives the difference in ulps between two | |
floats. | |
The results from this function will only make sense on platforms | |
where C doubles are represented in IEEE 754 binary64 format. | |
""" | |
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.""" | |
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) | |
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.""" | |
# need to special case infinities, since inf - inf gives nan | |
if math.isinf(expected) and got == expected: | |
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) | |
def parse_mtestfile(fname): | |
"""Parse a file with test values | |
-- starts a comment | |
blank lines, or lines containing only a comment, are ignored | |
other lines are expected to have the form | |
id fn arg -> expected [flag]* | |
""" | |
with open(fname) as fp: | |
for line in fp: | |
# strip comments, and skip blank lines | |
if '--' in line: | |
line = line[:line.index('--')] | |
if not line.strip(): | |
continue | |
lhs, rhs = line.split('->') | |
id, fn, arg = lhs.split() | |
rhs_pieces = rhs.split() | |
exp = rhs_pieces[0] | |
flags = rhs_pieces[1:] | |
yield (id, fn, float(arg), float(exp), flags) | |
def parse_testfile(fname): | |
"""Parse a file with test values | |
Empty lines or lines starting with -- are ignored | |
yields id, fn, arg_real, arg_imag, exp_real, exp_imag | |
""" | |
with open(fname) as fp: | |
for line in fp: | |
# skip comment lines and blank lines | |
if line.startswith('--') or not line.strip(): | |
continue | |
lhs, rhs = line.split('->') | |
id, fn, arg_real, arg_imag = lhs.split() | |
rhs_pieces = rhs.split() | |
exp_real, exp_imag = rhs_pieces[0], rhs_pieces[1] | |
flags = rhs_pieces[2:] | |
yield (id, fn, | |
float(arg_real), float(arg_imag), | |
float(exp_real), float(exp_imag), | |
flags | |
) | |
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 testConstants(self): | |
self.ftest('pi', math.pi, 3.1415926) | |
self.ftest('e', math.e, 2.7182818) | |
def testAcos(self): | |
self.assertRaises(TypeError, math.acos) | |
self.ftest('acos(-1)', math.acos(-1), math.pi) | |
self.ftest('acos(0)', math.acos(0), math.pi/2) | |
self.ftest('acos(1)', math.acos(1), 0) | |
self.assertRaises(ValueError, math.acos, INF) | |
self.assertRaises(ValueError, math.acos, NINF) | |
self.assertTrue(math.isnan(math.acos(NAN))) | |
def testAcosh(self): | |
self.assertRaises(TypeError, math.acosh) | |
self.ftest('acosh(1)', math.acosh(1), 0) | |
self.ftest('acosh(2)', math.acosh(2), 1.3169578969248168) | |
self.assertRaises(ValueError, math.acosh, 0) | |
self.assertRaises(ValueError, math.acosh, -1) | |
self.assertEqual(math.acosh(INF), INF) | |
self.assertRaises(ValueError, math.acosh, NINF) | |
self.assertTrue(math.isnan(math.acosh(NAN))) | |
def testAsin(self): | |
self.assertRaises(TypeError, math.asin) | |
self.ftest('asin(-1)', math.asin(-1), -math.pi/2) | |
self.ftest('asin(0)', math.asin(0), 0) | |
self.ftest('asin(1)', math.asin(1), math.pi/2) | |
self.assertRaises(ValueError, math.asin, INF) | |
self.assertRaises(ValueError, math.asin, NINF) | |
self.assertTrue(math.isnan(math.asin(NAN))) | |
def testAsinh(self): | |
self.assertRaises(TypeError, math.asinh) | |
self.ftest('asinh(0)', math.asinh(0), 0) | |
self.ftest('asinh(1)', math.asinh(1), 0.88137358701954305) | |
self.ftest('asinh(-1)', math.asinh(-1), -0.88137358701954305) | |
self.assertEqual(math.asinh(INF), INF) | |
self.assertEqual(math.asinh(NINF), NINF) | |
self.assertTrue(math.isnan(math.asinh(NAN))) | |
def testAtan(self): | |
self.assertRaises(TypeError, math.atan) | |
self.ftest('atan(-1)', math.atan(-1), -math.pi/4) | |
self.ftest('atan(0)', math.atan(0), 0) | |
self.ftest('atan(1)', math.atan(1), math.pi/4) | |
self.ftest('atan(inf)', math.atan(INF), math.pi/2) | |
self.ftest('atan(-inf)', math.atan(NINF), -math.pi/2) | |
self.assertTrue(math.isnan(math.atan(NAN))) | |
def testAtanh(self): | |
self.assertRaises(TypeError, math.atan) | |
self.ftest('atanh(0)', math.atanh(0), 0) | |
self.ftest('atanh(0.5)', math.atanh(0.5), 0.54930614433405489) | |
self.ftest('atanh(-0.5)', math.atanh(-0.5), -0.54930614433405489) | |
self.assertRaises(ValueError, math.atanh, 1) | |
self.assertRaises(ValueError, math.atanh, -1) | |
self.assertRaises(ValueError, math.atanh, INF) | |
self.assertRaises(ValueError, math.atanh, NINF) | |
self.assertTrue(math.isnan(math.atanh(NAN))) | |
def testAtan2(self): | |
self.assertRaises(TypeError, math.atan2) | |
self.ftest('atan2(-1, 0)', math.atan2(-1, 0), -math.pi/2) | |
self.ftest('atan2(-1, 1)', math.atan2(-1, 1), -math.pi/4) | |
self.ftest('atan2(0, 1)', math.atan2(0, 1), 0) | |
self.ftest('atan2(1, 1)', math.atan2(1, 1), math.pi/4) | |
self.ftest('atan2(1, 0)', math.atan2(1, 0), math.pi/2) | |
# math.atan2(0, x) | |
self.ftest('atan2(0., -inf)', math.atan2(0., NINF), math.pi) | |
self.ftest('atan2(0., -2.3)', math.atan2(0., -2.3), math.pi) | |
self.ftest('atan2(0., -0.)', math.atan2(0., -0.), math.pi) | |
self.assertEqual(math.atan2(0., 0.), 0.) | |
self.assertEqual(math.atan2(0., 2.3), 0.) | |
self.assertEqual(math.atan2(0., INF), 0.) | |
self.assertTrue(math.isnan(math.atan2(0., NAN))) | |
# math.atan2(-0, x) | |
self.ftest('atan2(-0., -inf)', math.atan2(-0., NINF), -math.pi) | |
self.ftest('atan2(-0., -2.3)', math.atan2(-0., -2.3), -math.pi) | |
self.ftest('atan2(-0., -0.)', math.atan2(-0., -0.), -math.pi) | |
self.assertEqual(math.atan2(-0., 0.), -0.) | |
self.assertEqual(math.atan2(-0., 2.3), -0.) | |
self.assertEqual(math.atan2(-0., INF), -0.) | |
self.assertTrue(math.isnan(math.atan2(-0., NAN))) | |
# math.atan2(INF, x) | |
self.ftest('atan2(inf, -inf)', math.atan2(INF, NINF), math.pi*3/4) | |
self.ftest('atan2(inf, -2.3)', math.atan2(INF, -2.3), math.pi/2) | |
self.ftest('atan2(inf, -0.)', math.atan2(INF, -0.0), math.pi/2) | |
self.ftest('atan2(inf, 0.)', math.atan2(INF, 0.0), math.pi/2) | |
self.ftest('atan2(inf, 2.3)', math.atan2(INF, 2.3), math.pi/2) | |
self.ftest('atan2(inf, inf)', math.atan2(INF, INF), math.pi/4) | |
self.assertTrue(math.isnan(math.atan2(INF, NAN))) | |
# math.atan2(NINF, x) | |
self.ftest('atan2(-inf, -inf)', math.atan2(NINF, NINF), -math.pi*3/4) | |
self.ftest('atan2(-inf, -2.3)', math.atan2(NINF, -2.3), -math.pi/2) | |
self.ftest('atan2(-inf, -0.)', math.atan2(NINF, -0.0), -math.pi/2) | |
self.ftest('atan2(-inf, 0.)', math.atan2(NINF, 0.0), -math.pi/2) | |
self.ftest('atan2(-inf, 2.3)', math.atan2(NINF, 2.3), -math.pi/2) | |
self.ftest('atan2(-inf, inf)', math.atan2(NINF, INF), -math.pi/4) | |
self.assertTrue(math.isnan(math.atan2(NINF, NAN))) | |
# math.atan2(+finite, x) | |
self.ftest('atan2(2.3, -inf)', math.atan2(2.3, NINF), math.pi) | |
self.ftest('atan2(2.3, -0.)', math.atan2(2.3, -0.), math.pi/2) | |
self.ftest('atan2(2.3, 0.)', math.atan2(2.3, 0.), math.pi/2) | |
self.assertEqual(math.atan2(2.3, INF), 0.) | |
self.assertTrue(math.isnan(math.atan2(2.3, NAN))) | |
# math.atan2(-finite, x) | |
self.ftest('atan2(-2.3, -inf)', math.atan2(-2.3, NINF), -math.pi) | |
self.ftest('atan2(-2.3, -0.)', math.atan2(-2.3, -0.), -math.pi/2) | |
self.ftest('atan2(-2.3, 0.)', math.atan2(-2.3, 0.), -math.pi/2) | |
self.assertEqual(math.atan2(-2.3, INF), -0.) | |
self.assertTrue(math.isnan(math.atan2(-2.3, NAN))) | |
# math.atan2(NAN, x) | |
self.assertTrue(math.isnan(math.atan2(NAN, NINF))) | |
self.assertTrue(math.isnan(math.atan2(NAN, -2.3))) | |
self.assertTrue(math.isnan(math.atan2(NAN, -0.))) | |
self.assertTrue(math.isnan(math.atan2(NAN, 0.))) | |
self.assertTrue(math.isnan(math.atan2(NAN, 2.3))) | |
self.assertTrue(math.isnan(math.atan2(NAN, INF))) | |
self.assertTrue(math.isnan(math.atan2(NAN, NAN))) | |
def testCeil(self): | |
self.assertRaises(TypeError, math.ceil) | |
# These types will be int in py3k. | |
self.assertEqual(float, type(math.ceil(1))) | |
self.assertEqual(float, type(math.ceil(1L))) | |
self.assertEqual(float, type(math.ceil(1.0))) | |
self.ftest('ceil(0.5)', math.ceil(0.5), 1) | |
self.ftest('ceil(1.0)', math.ceil(1.0), 1) | |
self.ftest('ceil(1.5)', math.ceil(1.5), 2) | |
self.ftest('ceil(-0.5)', math.ceil(-0.5), 0) | |
self.ftest('ceil(-1.0)', math.ceil(-1.0), -1) | |
self.ftest('ceil(-1.5)', math.ceil(-1.5), -1) | |
self.assertEqual(math.ceil(INF), INF) | |
self.assertEqual(math.ceil(NINF), NINF) | |
self.assertTrue(math.isnan(math.ceil(NAN))) | |
class TestCeil(object): | |
def __float__(self): | |
return 41.3 | |
class TestNoCeil(object): | |
pass | |
self.ftest('ceil(TestCeil())', math.ceil(TestCeil()), 42) | |
self.assertRaises(TypeError, math.ceil, TestNoCeil()) | |
t = TestNoCeil() | |
t.__ceil__ = lambda *args: args | |
self.assertRaises(TypeError, math.ceil, t) | |
self.assertRaises(TypeError, math.ceil, t, 0) | |
@requires_IEEE_754 | |
def testCopysign(self): | |
self.assertEqual(math.copysign(1, 42), 1.0) | |
self.assertEqual(math.copysign(0., 42), 0.0) | |
self.assertEqual(math.copysign(1., -42), -1.0) | |
self.assertEqual(math.copysign(3, 0.), 3.0) | |
self.assertEqual(math.copysign(4., -0.), -4.0) | |
self.assertRaises(TypeError, math.copysign) | |
# copysign should let us distinguish signs of zeros | |
self.assertEqual(math.copysign(1., 0.), 1.) | |
self.assertEqual(math.copysign(1., -0.), -1.) | |
self.assertEqual(math.copysign(INF, 0.), INF) | |
self.assertEqual(math.copysign(INF, -0.), NINF) | |
self.assertEqual(math.copysign(NINF, 0.), INF) | |
self.assertEqual(math.copysign(NINF, -0.), NINF) | |
# and of infinities | |
self.assertEqual(math.copysign(1., INF), 1.) | |
self.assertEqual(math.copysign(1., NINF), -1.) | |
self.assertEqual(math.copysign(INF, INF), INF) | |
self.assertEqual(math.copysign(INF, NINF), NINF) | |
self.assertEqual(math.copysign(NINF, INF), INF) | |
self.assertEqual(math.copysign(NINF, NINF), NINF) | |
self.assertTrue(math.isnan(math.copysign(NAN, 1.))) | |
self.assertTrue(math.isnan(math.copysign(NAN, INF))) | |
self.assertTrue(math.isnan(math.copysign(NAN, NINF))) | |
self.assertTrue(math.isnan(math.copysign(NAN, NAN))) | |
# copysign(INF, NAN) may be INF or it may be NINF, since | |
# we don't know whether the sign bit of NAN is set on any | |
# given platform. | |
self.assertTrue(math.isinf(math.copysign(INF, NAN))) | |
# similarly, copysign(2., NAN) could be 2. or -2. | |
self.assertEqual(abs(math.copysign(2., NAN)), 2.) | |
def testCos(self): | |
self.assertRaises(TypeError, math.cos) | |
self.ftest('cos(-pi/2)', math.cos(-math.pi/2), 0) | |
self.ftest('cos(0)', math.cos(0), 1) | |
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0) | |
self.ftest('cos(pi)', math.cos(math.pi), -1) | |
try: | |
self.assertTrue(math.isnan(math.cos(INF))) | |
self.assertTrue(math.isnan(math.cos(NINF))) | |
except ValueError: | |
self.assertRaises(ValueError, math.cos, INF) | |
self.assertRaises(ValueError, math.cos, NINF) | |
self.assertTrue(math.isnan(math.cos(NAN))) | |
def testCosh(self): | |
self.assertRaises(TypeError, math.cosh) | |
self.ftest('cosh(0)', math.cosh(0), 1) | |
self.ftest('cosh(2)-2*cosh(1)**2', math.cosh(2)-2*math.cosh(1)**2, -1) # Thanks to Lambert | |
self.assertEqual(math.cosh(INF), INF) | |
self.assertEqual(math.cosh(NINF), INF) | |
self.assertTrue(math.isnan(math.cosh(NAN))) | |
def testDegrees(self): | |
self.assertRaises(TypeError, math.degrees) | |
self.ftest('degrees(pi)', math.degrees(math.pi), 180.0) | |
self.ftest('degrees(pi/2)', math.degrees(math.pi/2), 90.0) | |
self.ftest('degrees(-pi/4)', math.degrees(-math.pi/4), -45.0) | |
def testExp(self): | |
self.assertRaises(TypeError, math.exp) | |
self.ftest('exp(-1)', math.exp(-1), 1/math.e) | |
self.ftest('exp(0)', math.exp(0), 1) | |
self.ftest('exp(1)', math.exp(1), math.e) | |
self.assertEqual(math.exp(INF), INF) | |
self.assertEqual(math.exp(NINF), 0.) | |
self.assertTrue(math.isnan(math.exp(NAN))) | |
def testFabs(self): | |
self.assertRaises(TypeError, math.fabs) | |
self.ftest('fabs(-1)', math.fabs(-1), 1) | |
self.ftest('fabs(0)', math.fabs(0), 0) | |
self.ftest('fabs(1)', math.fabs(1), 1) | |
def testFactorial(self): | |
def fact(n): | |
result = 1 | |
for i in range(1, int(n)+1): | |
result *= i | |
return result | |
values = range(10) + [50, 100, 500] | |
random.shuffle(values) | |
for x in values: | |
for cast in (int, long, float): | |
self.assertEqual(math.factorial(cast(x)), fact(x), (x, fact(x), math.factorial(x))) | |
self.assertRaises(ValueError, math.factorial, -1) | |
self.assertRaises(ValueError, math.factorial, math.pi) | |
def testFloor(self): | |
self.assertRaises(TypeError, math.floor) | |
# These types will be int in py3k. | |
self.assertEqual(float, type(math.floor(1))) | |
self.assertEqual(float, type(math.floor(1L))) | |
self.assertEqual(float, type(math.floor(1.0))) | |
self.ftest('floor(0.5)', math.floor(0.5), 0) | |
self.ftest('floor(1.0)', math.floor(1.0), 1) | |
self.ftest('floor(1.5)', math.floor(1.5), 1) | |
self.ftest('floor(-0.5)', math.floor(-0.5), -1) | |
self.ftest('floor(-1.0)', math.floor(-1.0), -1) | |
self.ftest('floor(-1.5)', math.floor(-1.5), -2) | |
# pow() relies on floor() to check for integers | |
# This fails on some platforms - so check it here | |
self.ftest('floor(1.23e167)', math.floor(1.23e167), 1.23e167) | |
self.ftest('floor(-1.23e167)', math.floor(-1.23e167), -1.23e167) | |
self.assertEqual(math.ceil(INF), INF) | |
self.assertEqual(math.ceil(NINF), NINF) | |
self.assertTrue(math.isnan(math.floor(NAN))) | |
class TestFloor(object): | |
def __float__(self): | |
return 42.3 | |
class TestNoFloor(object): | |
pass | |
self.ftest('floor(TestFloor())', math.floor(TestFloor()), 42) | |
self.assertRaises(TypeError, math.floor, TestNoFloor()) | |
t = TestNoFloor() | |
t.__floor__ = lambda *args: args | |
self.assertRaises(TypeError, math.floor, t) | |
self.assertRaises(TypeError, math.floor, t, 0) | |
def testFmod(self): | |
self.assertRaises(TypeError, math.fmod) | |
self.ftest('fmod(10,1)', math.fmod(10,1), 0) | |
self.ftest('fmod(10,0.5)', math.fmod(10,0.5), 0) | |
self.ftest('fmod(10,1.5)', math.fmod(10,1.5), 1) | |
self.ftest('fmod(-10,1)', math.fmod(-10,1), 0) | |
self.ftest('fmod(-10,0.5)', math.fmod(-10,0.5), 0) | |
self.ftest('fmod(-10,1.5)', math.fmod(-10,1.5), -1) | |
self.assertTrue(math.isnan(math.fmod(NAN, 1.))) | |
self.assertTrue(math.isnan(math.fmod(1., NAN))) | |
self.assertTrue(math.isnan(math.fmod(NAN, NAN))) | |
self.assertRaises(ValueError, math.fmod, 1., 0.) | |
self.assertRaises(ValueError, math.fmod, INF, 1.) | |
self.assertRaises(ValueError, math.fmod, NINF, 1.) | |
self.assertRaises(ValueError, math.fmod, INF, 0.) | |
self.assertEqual(math.fmod(3.0, INF), 3.0) | |
self.assertEqual(math.fmod(-3.0, INF), -3.0) | |
self.assertEqual(math.fmod(3.0, NINF), 3.0) | |
self.assertEqual(math.fmod(-3.0, NINF), -3.0) | |
self.assertEqual(math.fmod(0.0, 3.0), 0.0) | |
self.assertEqual(math.fmod(0.0, NINF), 0.0) | |
def testFrexp(self): | |
self.assertRaises(TypeError, math.frexp) | |
def testfrexp(name, result, expected): | |
(mant, exp), (emant, eexp) = result, expected | |
if abs(mant-emant) > eps or exp != eexp: | |
self.fail('%s returned %r, expected %r'%\ | |
(name, (mant, exp), (emant,eexp))) | |
testfrexp('frexp(-1)', math.frexp(-1), (-0.5, 1)) | |
testfrexp('frexp(0)', math.frexp(0), (0, 0)) | |
testfrexp('frexp(1)', math.frexp(1), (0.5, 1)) | |
testfrexp('frexp(2)', math.frexp(2), (0.5, 2)) | |
self.assertEqual(math.frexp(INF)[0], INF) | |
self.assertEqual(math.frexp(NINF)[0], NINF) | |
self.assertTrue(math.isnan(math.frexp(NAN)[0])) | |
@requires_IEEE_754 | |
@unittest.skipIf(HAVE_DOUBLE_ROUNDING, | |
"fsum is not exact on machines with double rounding") | |
def testFsum(self): | |
# math.fsum relies on exact rounding for correct operation. | |
# There's a known problem with IA32 floating-point that causes | |
# inexact rounding in some situations, and will cause the | |
# math.fsum tests below to fail; see issue #2937. On non IEEE | |
# 754 platforms, and on IEEE 754 platforms that exhibit the | |
# problem described in issue #2937, we simply skip the whole | |
# test. | |
# Python version of math.fsum, for comparison. Uses a | |
# different algorithm based on frexp, ldexp and integer | |
# arithmetic. | |
from sys import float_info | |
mant_dig = float_info.mant_dig | |
etiny = float_info.min_exp - mant_dig | |
def msum(iterable): | |
"""Full precision summation. Compute sum(iterable) without any | |
intermediate accumulation of error. Based on the 'lsum' function | |
at http://code.activestate.com/recipes/393090/ | |
""" | |
tmant, texp = 0, 0 | |
for x in iterable: | |
mant, exp = math.frexp(x) | |
mant, exp = int(math.ldexp(mant, mant_dig)), exp - mant_dig | |
if texp > exp: | |
tmant <<= texp-exp | |
texp = exp | |
else: | |
mant <<= exp-texp | |
tmant += mant | |
# Round tmant * 2**texp to a float. The original recipe | |
# used float(str(tmant)) * 2.0**texp for this, but that's | |
# a little unsafe because str -> float conversion can't be | |
# relied upon to do correct rounding on all platforms. | |
tail = max(len(bin(abs(tmant)))-2 - mant_dig, etiny - texp) | |
if tail > 0: | |
h = 1 << (tail-1) | |
tmant = tmant // (2*h) + bool(tmant & h and tmant & 3*h-1) | |
texp += tail | |
return math.ldexp(tmant, texp) | |
test_values = [ | |
([], 0.0), | |
([0.0], 0.0), | |
([1e100, 1.0, -1e100, 1e-100, 1e50, -1.0, -1e50], 1e-100), | |
([2.0**53, -0.5, -2.0**-54], 2.0**53-1.0), | |
([2.0**53, 1.0, 2.0**-100], 2.0**53+2.0), | |
([2.0**53+10.0, 1.0, 2.0**-100], 2.0**53+12.0), | |
([2.0**53-4.0, 0.5, 2.0**-54], 2.0**53-3.0), | |
([1./n for n in range(1, 1001)], | |
float.fromhex('0x1.df11f45f4e61ap+2')), | |
([(-1.)**n/n for n in range(1, 1001)], | |
float.fromhex('-0x1.62a2af1bd3624p-1')), | |
([1.7**(i+1)-1.7**i for i in range(1000)] + [-1.7**1000], -1.0), | |
([1e16, 1., 1e-16], 10000000000000002.0), | |
([1e16-2., 1.-2.**-53, -(1e16-2.), -(1.-2.**-53)], 0.0), | |
# exercise code for resizing partials array | |
([2.**n - 2.**(n+50) + 2.**(n+52) for n in range(-1074, 972, 2)] + | |
[-2.**1022], | |
float.fromhex('0x1.5555555555555p+970')), | |
] | |
for i, (vals, expected) in enumerate(test_values): | |
try: | |
actual = math.fsum(vals) | |
except OverflowError: | |
self.fail("test %d failed: got OverflowError, expected %r " | |
"for math.fsum(%.100r)" % (i, expected, vals)) | |
except ValueError: | |
self.fail("test %d failed: got ValueError, expected %r " | |
"for math.fsum(%.100r)" % (i, expected, vals)) | |
self.assertEqual(actual, expected) | |
from random import random, gauss, shuffle | |
for j in xrange(1000): | |
vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10 | |
s = 0 | |
for i in xrange(200): | |
v = gauss(0, random()) ** 7 - s | |
s += v | |
vals.append(v) | |
shuffle(vals) | |
s = msum(vals) | |
self.assertEqual(msum(vals), math.fsum(vals)) | |
def testHypot(self): | |
self.assertRaises(TypeError, math.hypot) | |
self.ftest('hypot(0,0)', math.hypot(0,0), 0) | |
self.ftest('hypot(3,4)', math.hypot(3,4), 5) | |
self.assertEqual(math.hypot(NAN, INF), INF) | |
self.assertEqual(math.hypot(INF, NAN), INF) | |
self.assertEqual(math.hypot(NAN, NINF), INF) | |
self.assertEqual(math.hypot(NINF, NAN), INF) | |
self.assertTrue(math.isnan(math.hypot(1.0, NAN))) | |
self.assertTrue(math.isnan(math.hypot(NAN, -2.0))) | |
def testLdexp(self): | |
self.assertRaises(TypeError, math.ldexp) | |
self.ftest('ldexp(0,1)', math.ldexp(0,1), 0) | |
self.ftest('ldexp(1,1)', math.ldexp(1,1), 2) | |
self.ftest('ldexp(1,-1)', math.ldexp(1,-1), 0.5) | |
self.ftest('ldexp(-1,1)', math.ldexp(-1,1), -2) | |
self.assertRaises(OverflowError, math.ldexp, 1., 1000000) | |
self.assertRaises(OverflowError, math.ldexp, -1., 1000000) | |
self.assertEqual(math.ldexp(1., -1000000), 0.) | |
self.assertEqual(math.ldexp(-1., -1000000), -0.) | |
self.assertEqual(math.ldexp(INF, 30), INF) | |
self.assertEqual(math.ldexp(NINF, -213), NINF) | |
self.assertTrue(math.isnan(math.ldexp(NAN, 0))) | |
# large second argument | |
for n in [10**5, 10L**5, 10**10, 10L**10, 10**20, 10**40]: | |
self.assertEqual(math.ldexp(INF, -n), INF) | |
self.assertEqual(math.ldexp(NINF, -n), NINF) | |
self.assertEqual(math.ldexp(1., -n), 0.) | |
self.assertEqual(math.ldexp(-1., -n), -0.) | |
self.assertEqual(math.ldexp(0., -n), 0.) | |
self.assertEqual(math.ldexp(-0., -n), -0.) | |
self.assertTrue(math.isnan(math.ldexp(NAN, -n))) | |
self.assertRaises(OverflowError, math.ldexp, 1., n) | |
self.assertRaises(OverflowError, math.ldexp, -1., n) | |
self.assertEqual(math.ldexp(0., n), 0.) | |
self.assertEqual(math.ldexp(-0., n), -0.) | |
self.assertEqual(math.ldexp(INF, n), INF) | |
self.assertEqual(math.ldexp(NINF, n), NINF) | |
self.assertTrue(math.isnan(math.ldexp(NAN, n))) | |
def testLog(self): | |
self.assertRaises(TypeError, math.log) | |
self.ftest('log(1/e)', math.log(1/math.e), -1) | |
self.ftest('log(1)', math.log(1), 0) | |
self.ftest('log(e)', math.log(math.e), 1) | |
self.ftest('log(32,2)', math.log(32,2), 5) | |
self.ftest('log(10**40, 10)', math.log(10**40, 10), 40) | |
self.ftest('log(10**40, 10**20)', math.log(10**40, 10**20), 2) | |
self.assertEqual(math.log(INF), INF) | |
self.assertRaises(ValueError, math.log, NINF) | |
self.assertTrue(math.isnan(math.log(NAN))) | |
def testLog1p(self): | |
self.assertRaises(TypeError, math.log1p) | |
self.ftest('log1p(1/e -1)', math.log1p(1/math.e-1), -1) | |
self.ftest('log1p(0)', math.log1p(0), 0) | |
self.ftest('log1p(e-1)', math.log1p(math.e-1), 1) | |
self.ftest('log1p(1)', math.log1p(1), math.log(2)) | |
self.assertEqual(math.log1p(INF), INF) | |
self.assertRaises(ValueError, math.log1p, NINF) | |
self.assertTrue(math.isnan(math.log1p(NAN))) | |
n= 2**90 | |
self.assertAlmostEqual(math.log1p(n), 62.383246250395075) | |
self.assertAlmostEqual(math.log1p(n), math.log1p(float(n))) | |
def testLog10(self): | |
self.assertRaises(TypeError, math.log10) | |
self.ftest('log10(0.1)', math.log10(0.1), -1) | |
self.ftest('log10(1)', math.log10(1), 0) | |
self.ftest('log10(10)', math.log10(10), 1) | |
self.assertEqual(math.log(INF), INF) | |
self.assertRaises(ValueError, math.log10, NINF) | |
self.assertTrue(math.isnan(math.log10(NAN))) | |
def testModf(self): | |
self.assertRaises(TypeError, math.modf) | |
def testmodf(name, result, expected): | |
(v1, v2), (e1, e2) = result, expected | |
if abs(v1-e1) > eps or abs(v2-e2): | |
self.fail('%s returned %r, expected %r'%\ | |
(name, (v1,v2), (e1,e2))) | |
testmodf('modf(1.5)', math.modf(1.5), (0.5, 1.0)) | |
testmodf('modf(-1.5)', math.modf(-1.5), (-0.5, -1.0)) | |
self.assertEqual(math.modf(INF), (0.0, INF)) | |
self.assertEqual(math.modf(NINF), (-0.0, NINF)) | |
modf_nan = math.modf(NAN) | |
self.assertTrue(math.isnan(modf_nan[0])) | |
self.assertTrue(math.isnan(modf_nan[1])) | |
def testPow(self): | |
self.assertRaises(TypeError, math.pow) | |
self.ftest('pow(0,1)', math.pow(0,1), 0) | |
self.ftest('pow(1,0)', math.pow(1,0), 1) | |
self.ftest('pow(2,1)', math.pow(2,1), 2) | |
self.ftest('pow(2,-1)', math.pow(2,-1), 0.5) | |
self.assertEqual(math.pow(INF, 1), INF) | |
self.assertEqual(math.pow(NINF, 1), NINF) | |
self.assertEqual((math.pow(1, INF)), 1.) | |
self.assertEqual((math.pow(1, NINF)), 1.) | |
self.assertTrue(math.isnan(math.pow(NAN, 1))) | |
self.assertTrue(math.isnan(math.pow(2, NAN))) | |
self.assertTrue(math.isnan(math.pow(0, NAN))) | |
self.assertEqual(math.pow(1, NAN), 1) | |
# pow(0., x) | |
self.assertEqual(math.pow(0., INF), 0.) | |
self.assertEqual(math.pow(0., 3.), 0.) | |
self.assertEqual(math.pow(0., 2.3), 0.) | |
self.assertEqual(math.pow(0., 2.), 0.) | |
self.assertEqual(math.pow(0., 0.), 1.) | |
self.assertEqual(math.pow(0., -0.), 1.) | |
self.assertRaises(ValueError, math.pow, 0., -2.) | |
self.assertRaises(ValueError, math.pow, 0., -2.3) | |
self.assertRaises(ValueError, math.pow, 0., -3.) | |
self.assertRaises(ValueError, math.pow, 0., NINF) | |
self.assertTrue(math.isnan(math.pow(0., NAN))) | |
# pow(INF, x) | |
self.assertEqual(math.pow(INF, INF), INF) | |
self.assertEqual(math.pow(INF, 3.), INF) | |
self.assertEqual(math.pow(INF, 2.3), INF) | |
self.assertEqual(math.pow(INF, 2.), INF) | |
self.assertEqual(math.pow(INF, 0.), 1.) | |
self.assertEqual(math.pow(INF, -0.), 1.) | |
self.assertEqual(math.pow(INF, -2.), 0.) | |
self.assertEqual(math.pow(INF, -2.3), 0.) | |
self.assertEqual(math.pow(INF, -3.), 0.) | |
self.assertEqual(math.pow(INF, NINF), 0.) | |
self.assertTrue(math.isnan(math.pow(INF, NAN))) | |
# pow(-0., x) | |
self.assertEqual(math.pow(-0., INF), 0.) | |
self.assertEqual(math.pow(-0., 3.), -0.) | |
self.assertEqual(math.pow(-0., 2.3), 0.) | |
self.assertEqual(math.pow(-0., 2.), 0.) | |
self.assertEqual(math.pow(-0., 0.), 1.) | |
self.assertEqual(math.pow(-0., -0.), 1.) | |
self.assertRaises(ValueError, math.pow, -0., -2.) | |
self.assertRaises(ValueError, math.pow, -0., -2.3) | |
self.assertRaises(ValueError, math.pow, -0., -3.) | |
self.assertRaises(ValueError, math.pow, -0., NINF) | |
self.assertTrue(math.isnan(math.pow(-0., NAN))) | |
# pow(NINF, x) | |
self.assertEqual(math.pow(NINF, INF), INF) | |
self.assertEqual(math.pow(NINF, 3.), NINF) | |
self.assertEqual(math.pow(NINF, 2.3), INF) | |
self.assertEqual(math.pow(NINF, 2.), INF) | |
self.assertEqual(math.pow(NINF, 0.), 1.) | |
self.assertEqual(math.pow(NINF, -0.), 1.) | |
self.assertEqual(math.pow(NINF, -2.), 0.) | |
self.assertEqual(math.pow(NINF, -2.3), 0.) | |
self.assertEqual(math.pow(NINF, -3.), -0.) | |
self.assertEqual(math.pow(NINF, NINF), 0.) | |
self.assertTrue(math.isnan(math.pow(NINF, NAN))) | |
# pow(-1, x) | |
self.assertEqual(math.pow(-1., INF), 1.) | |
self.assertEqual(math.pow(-1., 3.), -1.) | |
self.assertRaises(ValueError, math.pow, -1., 2.3) | |
self.assertEqual(math.pow(-1., 2.), 1.) | |
self.assertEqual(math.pow(-1., 0.), 1.) | |
self.assertEqual(math.pow(-1., -0.), 1.) | |
self.assertEqual(math.pow(-1., -2.), 1.) | |
self.assertRaises(ValueError, math.pow, -1., -2.3) | |
self.assertEqual(math.pow(-1., -3.), -1.) | |
self.assertEqual(math.pow(-1., NINF), 1.) | |
self.assertTrue(math.isnan(math.pow(-1., NAN))) | |
# pow(1, x) | |
self.assertEqual(math.pow(1., INF), 1.) | |
self.assertEqual(math.pow(1., 3.), 1.) | |
self.assertEqual(math.pow(1., 2.3), 1.) | |
self.assertEqual(math.pow(1., 2.), 1.) | |
self.assertEqual(math.pow(1., 0.), 1.) | |
self.assertEqual(math.pow(1., -0.), 1.) | |
self.assertEqual(math.pow(1., -2.), 1.) | |
self.assertEqual(math.pow(1., -2.3), 1.) | |
self.assertEqual(math.pow(1., -3.), 1.) | |
self.assertEqual(math.pow(1., NINF), 1.) | |
self.assertEqual(math.pow(1., NAN), 1.) | |
# pow(x, 0) should be 1 for any x | |
self.assertEqual(math.pow(2.3, 0.), 1.) | |
self.assertEqual(math.pow(-2.3, 0.), 1.) | |
self.assertEqual(math.pow(NAN, 0.), 1.) | |
self.assertEqual(math.pow(2.3, -0.), 1.) | |
self.assertEqual(math.pow(-2.3, -0.), 1.) | |
self.assertEqual(math.pow(NAN, -0.), 1.) | |
# pow(x, y) is invalid if x is negative and y is not integral | |
self.assertRaises(ValueError, math.pow, -1., 2.3) | |
self.assertRaises(ValueError, math.pow, -15., -3.1) | |
# pow(x, NINF) | |
self.assertEqual(math.pow(1.9, NINF), 0.) | |
self.assertEqual(math.pow(1.1, NINF), 0.) | |
self.assertEqual(math.pow(0.9, NINF), INF) | |
self.assertEqual(math.pow(0.1, NINF), INF) | |
self.assertEqual(math.pow(-0.1, NINF), INF) | |
self.assertEqual(math.pow(-0.9, NINF), INF) | |
self.assertEqual(math.pow(-1.1, NINF), 0.) | |
self.assertEqual(math.pow(-1.9, NINF), 0.) | |
# pow(x, INF) | |
self.assertEqual(math.pow(1.9, INF), INF) | |
self.assertEqual(math.pow(1.1, INF), INF) | |
self.assertEqual(math.pow(0.9, INF), 0.) | |
self.assertEqual(math.pow(0.1, INF), 0.) | |
self.assertEqual(math.pow(-0.1, INF), 0.) | |
self.assertEqual(math.pow(-0.9, INF), 0.) | |
self.assertEqual(math.pow(-1.1, INF), INF) | |
self.assertEqual(math.pow(-1.9, INF), INF) | |
# pow(x, y) should work for x negative, y an integer | |
self.ftest('(-2.)**3.', math.pow(-2.0, 3.0), -8.0) | |
self.ftest('(-2.)**2.', math.pow(-2.0, 2.0), 4.0) | |
self.ftest('(-2.)**1.', math.pow(-2.0, 1.0), -2.0) | |
self.ftest('(-2.)**0.', math.pow(-2.0, 0.0), 1.0) | |
self.ftest('(-2.)**-0.', math.pow(-2.0, -0.0), 1.0) | |
self.ftest('(-2.)**-1.', math.pow(-2.0, -1.0), -0.5) | |
self.ftest('(-2.)**-2.', math.pow(-2.0, -2.0), 0.25) | |
self.ftest('(-2.)**-3.', math.pow(-2.0, -3.0), -0.125) | |
self.assertRaises(ValueError, math.pow, -2.0, -0.5) | |
self.assertRaises(ValueError, math.pow, -2.0, 0.5) | |
# the following tests have been commented out since they don't | |
# really belong here: the implementation of ** for floats is | |
# independent of the implementation of math.pow | |
#self.assertEqual(1**NAN, 1) | |
#self.assertEqual(1**INF, 1) | |
#self.assertEqual(1**NINF, 1) | |
#self.assertEqual(1**0, 1) | |
#self.assertEqual(1.**NAN, 1) | |
#self.assertEqual(1.**INF, 1) | |
#self.assertEqual(1.**NINF, 1) | |
#self.assertEqual(1.**0, 1) | |
def testRadians(self): | |
self.assertRaises(TypeError, math.radians) | |
self.ftest('radians(180)', math.radians(180), math.pi) | |
self.ftest('radians(90)', math.radians(90), math.pi/2) | |
self.ftest('radians(-45)', math.radians(-45), -math.pi/4) | |
def testSin(self): | |
self.assertRaises(TypeError, math.sin) | |
self.ftest('sin(0)', math.sin(0), 0) | |
self.ftest('sin(pi/2)', math.sin(math.pi/2), 1) | |
self.ftest('sin(-pi/2)', math.sin(-math.pi/2), -1) | |
try: | |
self.assertTrue(math.isnan(math.sin(INF))) | |
self.assertTrue(math.isnan(math.sin(NINF))) | |
except ValueError: | |
self.assertRaises(ValueError, math.sin, INF) | |
self.assertRaises(ValueError, math.sin, NINF) | |
self.assertTrue(math.isnan(math.sin(NAN))) | |
def testSinh(self): | |
self.assertRaises(TypeError, math.sinh) | |
self.ftest('sinh(0)', math.sinh(0), 0) | |
self.ftest('sinh(1)**2-cosh(1)**2', math.sinh(1)**2-math.cosh(1)**2, -1) | |
self.ftest('sinh(1)+sinh(-1)', math.sinh(1)+math.sinh(-1), 0) | |
self.assertEqual(math.sinh(INF), INF) | |
self.assertEqual(math.sinh(NINF), NINF) | |
self.assertTrue(math.isnan(math.sinh(NAN))) | |
def testSqrt(self): | |
self.assertRaises(TypeError, math.sqrt) | |
self.ftest('sqrt(0)', math.sqrt(0), 0) | |
self.ftest('sqrt(1)', math.sqrt(1), 1) | |
self.ftest('sqrt(4)', math.sqrt(4), 2) | |
self.assertEqual(math.sqrt(INF), INF) | |
self.assertRaises(ValueError, math.sqrt, NINF) | |
self.assertTrue(math.isnan(math.sqrt(NAN))) | |
def testTan(self): | |
self.assertRaises(TypeError, math.tan) | |
self.ftest('tan(0)', math.tan(0), 0) | |
self.ftest('tan(pi/4)', math.tan(math.pi/4), 1) | |
self.ftest('tan(-pi/4)', math.tan(-math.pi/4), -1) | |
try: | |
self.assertTrue(math.isnan(math.tan(INF))) | |
self.assertTrue(math.isnan(math.tan(NINF))) | |
except: | |
self.assertRaises(ValueError, math.tan, INF) | |
self.assertRaises(ValueError, math.tan, NINF) | |
self.assertTrue(math.isnan(math.tan(NAN))) | |
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(inf)', math.tanh(INF), 1) | |
self.ftest('tanh(-inf)', math.tanh(NINF), -1) | |
self.assertTrue(math.isnan(math.tanh(NAN))) | |
# check that tanh(-0.) == -0. on IEEE 754 systems | |
if float.__getformat__("double").startswith("IEEE"): | |
self.assertEqual(math.tanh(-0.), -0.) | |
self.assertEqual(math.copysign(1., math.tanh(-0.)), | |
math.copysign(1., -0.)) | |
def test_trunc(self): | |
self.assertEqual(math.trunc(1), 1) | |
self.assertEqual(math.trunc(-1), -1) | |
self.assertEqual(type(math.trunc(1)), int) | |
self.assertEqual(type(math.trunc(1.5)), int) | |
self.assertEqual(math.trunc(1.5), 1) | |
self.assertEqual(math.trunc(-1.5), -1) | |
self.assertEqual(math.trunc(1.999999), 1) | |
self.assertEqual(math.trunc(-1.999999), -1) | |
self.assertEqual(math.trunc(-0.999999), -0) | |
self.assertEqual(math.trunc(-100.999), -100) | |
class TestTrunc(object): | |
def __trunc__(self): | |
return 23 | |
class TestNoTrunc(object): | |
pass | |
self.assertEqual(math.trunc(TestTrunc()), 23) | |
self.assertRaises(TypeError, math.trunc) | |
self.assertRaises(TypeError, math.trunc, 1, 2) | |
self.assertRaises((AttributeError, TypeError), math.trunc, | |
TestNoTrunc()) | |
def testIsnan(self): | |
self.assertTrue(math.isnan(float("nan"))) | |
self.assertTrue(math.isnan(float("inf")* 0.)) | |
self.assertFalse(math.isnan(float("inf"))) | |
self.assertFalse(math.isnan(0.)) | |
self.assertFalse(math.isnan(1.)) | |
def testIsinf(self): | |
self.assertTrue(math.isinf(float("inf"))) | |
self.assertTrue(math.isinf(float("-inf"))) | |
self.assertTrue(math.isinf(1E400)) | |
self.assertTrue(math.isinf(-1E400)) | |
self.assertFalse(math.isinf(float("nan"))) | |
self.assertFalse(math.isinf(0.)) | |
self.assertFalse(math.isinf(1.)) | |
# RED_FLAG 16-Oct-2000 Tim | |
# While 2.0 is more consistent about exceptions than previous releases, it | |
# still fails this part of the test on some platforms. For now, we only | |
# *run* test_exceptions() in verbose mode, so that this isn't normally | |
# tested. | |
if verbose: | |
def test_exceptions(self): | |
try: | |
x = math.exp(-1000000000) | |
except: | |
# mathmodule.c is failing to weed out underflows from libm, or | |
# we've got an fp format with huge dynamic range | |
self.fail("underflowing exp() should not have raised " | |
"an exception") | |
if x != 0: | |
self.fail("underflowing exp() should have returned 0") | |
# If this fails, probably using a strict IEEE-754 conforming libm, and x | |
# is +Inf afterwards. But Python wants overflows detected by default. | |
try: | |
x = math.exp(1000000000) | |
except OverflowError: | |
pass | |
else: | |
self.fail("overflowing exp() didn't trigger OverflowError") | |
# If this fails, it could be a puzzle. One odd possibility is that | |
# mathmodule.c's macros are getting confused while comparing | |
# Inf (HUGE_VAL) to a NaN, and artificially setting errno to ERANGE | |
# as a result (and so raising OverflowError instead). | |
try: | |
x = math.sqrt(-1.0) | |
except ValueError: | |
pass | |
else: | |
self.fail("sqrt(-1) didn't raise ValueError") | |
@requires_IEEE_754 | |
def test_testfile(self): | |
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: | |
continue | |
if fn in ['rect', 'polar']: | |
# no real versions of rect, polar | |
continue | |
func = getattr(math, fn) | |
try: | |
result = func(ar) | |
except ValueError: | |
message = ("Unexpected ValueError in " + | |
"test %s:%s(%r)\n" % (id, fn, ar)) | |
self.fail(message) | |
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) | |
@unittest.skipUnless(float.__getformat__("double").startswith("IEEE"), | |
"test requires IEEE 754 doubles") | |
def test_mtestfile(self): | |
ALLOWED_ERROR = 20 # permitted error, in ulps | |
fail_fmt = "{}:{}({!r}): expected {!r}, got {!r}" | |
failures = [] | |
for id, fn, arg, expected, flags in parse_mtestfile(math_testcases): | |
func = getattr(math, fn) | |
if 'invalid' in flags or 'divide-by-zero' in flags: | |
expected = 'ValueError' | |
elif 'overflow' in flags: | |
expected = 'OverflowError' | |
try: | |
got = func(arg) | |
except ValueError: | |
got = 'ValueError' | |
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) | |
if failures: | |
self.fail('Failures in test_mtestfile:\n ' + | |
'\n '.join(failures)) | |
def test_main(): | |
from doctest import DocFileSuite | |
suite = unittest.TestSuite() | |
suite.addTest(unittest.makeSuite(MathTests)) | |
suite.addTest(DocFileSuite("ieee754.txt")) | |
run_unittest(suite) | |
if __name__ == '__main__': | |
test_main() |