You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
2224 lines
90 KiB
2224 lines
90 KiB
3 years ago
|
# Python test set -- math module
|
||
|
|
# XXXX Should not do tests around zero only
|
||
|
|
|
||
|
|
from test.support import run_unittest, verbose, requires_IEEE_754
|
||
|
|
from test import support
|
||
|
|
import unittest
|
||
|
|
import itertools
|
||
|
|
import decimal
|
||
|
|
import math
|
||
|
|
import os
|
||
|
|
import platform
|
||
|
|
import random
|
||
|
|
import struct
|
||
|
|
import sys
|
||
|
|
|
||
|
|
|
||
|
|
eps = 1E-05
|
||
|
|
NAN = float('nan')
|
||
|
|
INF = float('inf')
|
||
|
|
NINF = float('-inf')
|
||
|
|
FLOAT_MAX = sys.float_info.max
|
||
|
|
FLOAT_MIN = sys.float_info.min
|
||
|
|
|
||
|
|
# 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 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
|
||
|
|
|
||
|
|
|
||
|
|
# Here's a pure Python version of the math.factorial algorithm, for
|
||
|
|
# documentation and comparison purposes.
|
||
|
|
#
|
||
|
|
# Formula:
|
||
|
|
#
|
||
|
|
# factorial(n) = factorial_odd_part(n) << (n - count_set_bits(n))
|
||
|
|
#
|
||
|
|
# where
|
||
|
|
#
|
||
|
|
# factorial_odd_part(n) = product_{i >= 0} product_{0 < j <= n >> i; j odd} j
|
||
|
|
#
|
||
|
|
# The outer product above is an infinite product, but once i >= n.bit_length,
|
||
|
|
# (n >> i) < 1 and the corresponding term of the product is empty. So only the
|
||
|
|
# finitely many terms for 0 <= i < n.bit_length() contribute anything.
|
||
|
|
#
|
||
|
|
# We iterate downwards from i == n.bit_length() - 1 to i == 0. The inner
|
||
|
|
# product in the formula above starts at 1 for i == n.bit_length(); for each i
|
||
|
|
# < n.bit_length() we get the inner product for i from that for i + 1 by
|
||
|
|
# multiplying by all j in {n >> i+1 < j <= n >> i; j odd}. In Python terms,
|
||
|
|
# this set is range((n >> i+1) + 1 | 1, (n >> i) + 1 | 1, 2).
|
||
|
|
|
||
|
|
def count_set_bits(n):
|
||
|
|
"""Number of '1' bits in binary expansion of a nonnnegative integer."""
|
||
|
|
return 1 + count_set_bits(n & n - 1) if n else 0
|
||
|
|
|
||
|
|
def partial_product(start, stop):
|
||
|
|
"""Product of integers in range(start, stop, 2), computed recursively.
|
||
|
|
start and stop should both be odd, with start <= stop.
|
||
|
|
|
||
|
|
"""
|
||
|
|
numfactors = (stop - start) >> 1
|
||
|
|
if not numfactors:
|
||
|
|
return 1
|
||
|
|
elif numfactors == 1:
|
||
|
|
return start
|
||
|
|
else:
|
||
|
|
mid = (start + numfactors) | 1
|
||
|
|
return partial_product(start, mid) * partial_product(mid, stop)
|
||
|
|
|
||
|
|
def py_factorial(n):
|
||
|
|
"""Factorial of nonnegative integer n, via "Binary Split Factorial Formula"
|
||
|
|
described at http://www.luschny.de/math/factorial/binarysplitfact.html
|
||
|
|
|
||
|
|
"""
|
||
|
|
inner = outer = 1
|
||
|
|
for i in reversed(range(n.bit_length())):
|
||
|
|
inner *= partial_product((n >> i + 1) + 1 | 1, (n >> i) + 1 | 1)
|
||
|
|
outer *= inner
|
||
|
|
return outer << (n - count_set_bits(n))
|
||
|
|
|
||
|
|
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.
|
||
|
|
|
||
|
|
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
|
||
|
|
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
|
||
|
|
|
||
|
|
-- 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, encoding="utf-8") 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, encoding="utf-8") 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)
|
||
|
|
|
||
|
|
|
||
|
|
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 FloatLike:
|
||
|
|
def __init__(self, value):
|
||
|
|
self.value = value
|
||
|
|
|
||
|
|
def __float__(self):
|
||
|
|
return self.value
|
||
|
|
|
||
|
|
class IntSubclass(int):
|
||
|
|
pass
|
||
|
|
|
||
|
|
# Class providing an __index__ method.
|
||
|
|
class MyIndexable(object):
|
||
|
|
def __init__(self, value):
|
||
|
|
self.value = value
|
||
|
|
|
||
|
|
def __index__(self):
|
||
|
|
return self.value
|
||
|
|
|
||
|
|
class MathTests(unittest.TestCase):
|
||
|
|
|
||
|
|
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):
|
||
|
|
# 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):
|
||
|
|
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.assertRaises(ValueError, math.acos, 1 + eps)
|
||
|
|
self.assertRaises(ValueError, math.acos, -1 - eps)
|
||
|
|
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.assertRaises(ValueError, math.asin, 1 + eps)
|
||
|
|
self.assertRaises(ValueError, math.asin, -1 - eps)
|
||
|
|
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)
|
||
|
|
self.assertEqual(int, type(math.ceil(0.5)))
|
||
|
|
self.assertEqual(math.ceil(0.5), 1)
|
||
|
|
self.assertEqual(math.ceil(1.0), 1)
|
||
|
|
self.assertEqual(math.ceil(1.5), 2)
|
||
|
|
self.assertEqual(math.ceil(-0.5), 0)
|
||
|
|
self.assertEqual(math.ceil(-1.0), -1)
|
||
|
|
self.assertEqual(math.ceil(-1.5), -1)
|
||
|
|
self.assertEqual(math.ceil(0.0), 0)
|
||
|
|
self.assertEqual(math.ceil(-0.0), 0)
|
||
|
|
#self.assertEqual(math.ceil(INF), INF)
|
||
|
|
#self.assertEqual(math.ceil(NINF), NINF)
|
||
|
|
#self.assertTrue(math.isnan(math.ceil(NAN)))
|
||
|
|
|
||
|
|
class TestCeil:
|
||
|
|
def __ceil__(self):
|
||
|
|
return 42
|
||
|
|
class FloatCeil(float):
|
||
|
|
def __ceil__(self):
|
||
|
|
return 42
|
||
|
|
class TestNoCeil:
|
||
|
|
pass
|
||
|
|
self.assertEqual(math.ceil(TestCeil()), 42)
|
||
|
|
self.assertEqual(math.ceil(FloatCeil()), 42)
|
||
|
|
self.assertEqual(math.ceil(FloatLike(42.5)), 43)
|
||
|
|
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, abs_tol=math.ulp(1))
|
||
|
|
self.ftest('cos(0)', math.cos(0), 1)
|
||
|
|
self.ftest('cos(pi/2)', math.cos(math.pi/2), 0, abs_tol=math.ulp(1))
|
||
|
|
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)))
|
||
|
|
|
||
|
|
@unittest.skipIf(sys.platform == 'win32' and platform.machine() in ('ARM', 'ARM64'),
|
||
|
|
"Windows UCRT is off by 2 ULP this test requires accuracy within 1 ULP")
|
||
|
|
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)
|
||
|
|
self.ftest('degrees(0)', math.degrees(0), 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)))
|
||
|
|
self.assertRaises(OverflowError, math.exp, 1000000)
|
||
|
|
|
||
|
|
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):
|
||
|
|
self.assertEqual(math.factorial(0), 1)
|
||
|
|
total = 1
|
||
|
|
for i in range(1, 1000):
|
||
|
|
total *= i
|
||
|
|
self.assertEqual(math.factorial(i), total)
|
||
|
|
self.assertEqual(math.factorial(i), py_factorial(i))
|
||
|
|
self.assertRaises(ValueError, math.factorial, -1)
|
||
|
|
self.assertRaises(ValueError, math.factorial, -10**100)
|
||
|
|
|
||
|
|
def testFactorialNonIntegers(self):
|
||
|
|
self.assertRaises(TypeError, math.factorial, 5.0)
|
||
|
|
self.assertRaises(TypeError, math.factorial, 5.2)
|
||
|
|
self.assertRaises(TypeError, math.factorial, -1.0)
|
||
|
|
self.assertRaises(TypeError, math.factorial, -1e100)
|
||
|
|
self.assertRaises(TypeError, math.factorial, decimal.Decimal('5'))
|
||
|
|
self.assertRaises(TypeError, math.factorial, decimal.Decimal('5.2'))
|
||
|
|
self.assertRaises(TypeError, math.factorial, "5")
|
||
|
|
|
||
|
|
# Other implementations may place different upper bounds.
|
||
|
|
@support.cpython_only
|
||
|
|
def testFactorialHugeInputs(self):
|
||
|
|
# Currently raises OverflowError for inputs that are too large
|
||
|
|
# to fit into a C long.
|
||
|
|
self.assertRaises(OverflowError, math.factorial, 10**100)
|
||
|
|
self.assertRaises(TypeError, math.factorial, 1e100)
|
||
|
|
|
||
|
|
def testFloor(self):
|
||
|
|
self.assertRaises(TypeError, math.floor)
|
||
|
|
self.assertEqual(int, type(math.floor(0.5)))
|
||
|
|
self.assertEqual(math.floor(0.5), 0)
|
||
|
|
self.assertEqual(math.floor(1.0), 1)
|
||
|
|
self.assertEqual(math.floor(1.5), 1)
|
||
|
|
self.assertEqual(math.floor(-0.5), -1)
|
||
|
|
self.assertEqual(math.floor(-1.0), -1)
|
||
|
|
self.assertEqual(math.floor(-1.5), -2)
|
||
|
|
#self.assertEqual(math.ceil(INF), INF)
|
||
|
|
#self.assertEqual(math.ceil(NINF), NINF)
|
||
|
|
#self.assertTrue(math.isnan(math.floor(NAN)))
|
||
|
|
|
||
|
|
class TestFloor:
|
||
|
|
def __floor__(self):
|
||
|
|
return 42
|
||
|
|
class FloatFloor(float):
|
||
|
|
def __floor__(self):
|
||
|
|
return 42
|
||
|
|
class TestNoFloor:
|
||
|
|
pass
|
||
|
|
self.assertEqual(math.floor(TestFloor()), 42)
|
||
|
|
self.assertEqual(math.floor(FloatFloor()), 42)
|
||
|
|
self.assertEqual(math.floor(FloatLike(41.9)), 41)
|
||
|
|
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), 0.0)
|
||
|
|
self.ftest('fmod(10, 0.5)', math.fmod(10, 0.5), 0.0)
|
||
|
|
self.ftest('fmod(10, 1.5)', math.fmod(10, 1.5), 1.0)
|
||
|
|
self.ftest('fmod(-10, 1)', math.fmod(-10, 1), -0.0)
|
||
|
|
self.ftest('fmod(-10, 0.5)', math.fmod(-10, 0.5), -0.0)
|
||
|
|
self.ftest('fmod(-10, 1.5)', math.fmod(-10, 1.5), -1.0)
|
||
|
|
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, result, expected))
|
||
|
|
|
||
|
|
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')),
|
||
|
|
([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')),
|
||
|
|
]
|
||
|
|
|
||
|
|
# Telescoping sum, with exact differences (due to Sterbenz)
|
||
|
|
terms = [1.7**i for i in range(1001)]
|
||
|
|
test_values.append((
|
||
|
|
[terms[i+1] - terms[i] for i in range(1000)] + [-terms[1000]],
|
||
|
|
-terms[0]
|
||
|
|
))
|
||
|
|
|
||
|
|
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 range(1000):
|
||
|
|
vals = [7, 1e100, -7, -1e100, -9e-20, 8e-20] * 10
|
||
|
|
s = 0
|
||
|
|
for i in range(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 testGcd(self):
|
||
|
|
gcd = math.gcd
|
||
|
|
self.assertEqual(gcd(0, 0), 0)
|
||
|
|
self.assertEqual(gcd(1, 0), 1)
|
||
|
|
self.assertEqual(gcd(-1, 0), 1)
|
||
|
|
self.assertEqual(gcd(0, 1), 1)
|
||
|
|
self.assertEqual(gcd(0, -1), 1)
|
||
|
|
self.assertEqual(gcd(7, 1), 1)
|
||
|
|
self.assertEqual(gcd(7, -1), 1)
|
||
|
|
self.assertEqual(gcd(-23, 15), 1)
|
||
|
|
self.assertEqual(gcd(120, 84), 12)
|
||
|
|
self.assertEqual(gcd(84, -120), 12)
|
||
|
|
self.assertEqual(gcd(1216342683557601535506311712,
|
||
|
|
436522681849110124616458784), 32)
|
||
|
|
|
||
|
|
x = 434610456570399902378880679233098819019853229470286994367836600566
|
||
|
|
y = 1064502245825115327754847244914921553977
|
||
|
|
for c in (652560,
|
||
|
|
576559230871654959816130551884856912003141446781646602790216406874):
|
||
|
|
a = x * c
|
||
|
|
b = y * c
|
||
|
|
self.assertEqual(gcd(a, b), c)
|
||
|
|
self.assertEqual(gcd(b, a), c)
|
||
|
|
self.assertEqual(gcd(-a, b), c)
|
||
|
|
self.assertEqual(gcd(b, -a), c)
|
||
|
|
self.assertEqual(gcd(a, -b), c)
|
||
|
|
self.assertEqual(gcd(-b, a), c)
|
||
|
|
self.assertEqual(gcd(-a, -b), c)
|
||
|
|
self.assertEqual(gcd(-b, -a), c)
|
||
|
|
|
||
|
|
self.assertEqual(gcd(), 0)
|
||
|
|
self.assertEqual(gcd(120), 120)
|
||
|
|
self.assertEqual(gcd(-120), 120)
|
||
|
|
self.assertEqual(gcd(120, 84, 102), 6)
|
||
|
|
self.assertEqual(gcd(120, 1, 84), 1)
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, gcd, 120.0)
|
||
|
|
self.assertRaises(TypeError, gcd, 120.0, 84)
|
||
|
|
self.assertRaises(TypeError, gcd, 120, 84.0)
|
||
|
|
self.assertRaises(TypeError, gcd, 120, 1, 84.0)
|
||
|
|
self.assertEqual(gcd(MyIndexable(120), MyIndexable(84)), 12)
|
||
|
|
|
||
|
|
def testHypot(self):
|
||
|
|
from decimal import Decimal
|
||
|
|
from fractions import Fraction
|
||
|
|
|
||
|
|
hypot = math.hypot
|
||
|
|
|
||
|
|
# Test different numbers of arguments (from zero to five)
|
||
|
|
# against a straightforward pure python implementation
|
||
|
|
args = math.e, math.pi, math.sqrt(2.0), math.gamma(3.5), math.sin(2.1)
|
||
|
|
for i in range(len(args)+1):
|
||
|
|
self.assertAlmostEqual(
|
||
|
|
hypot(*args[:i]),
|
||
|
|
math.sqrt(sum(s**2 for s in args[:i]))
|
||
|
|
)
|
||
|
|
|
||
|
|
# Test allowable types (those with __float__)
|
||
|
|
self.assertEqual(hypot(12.0, 5.0), 13.0)
|
||
|
|
self.assertEqual(hypot(12, 5), 13)
|
||
|
|
self.assertEqual(hypot(Decimal(12), Decimal(5)), 13)
|
||
|
|
self.assertEqual(hypot(Fraction(12, 32), Fraction(5, 32)), Fraction(13, 32))
|
||
|
|
self.assertEqual(hypot(bool(1), bool(0), bool(1), bool(1)), math.sqrt(3))
|
||
|
|
|
||
|
|
# Test corner cases
|
||
|
|
self.assertEqual(hypot(0.0, 0.0), 0.0) # Max input is zero
|
||
|
|
self.assertEqual(hypot(-10.5), 10.5) # Negative input
|
||
|
|
self.assertEqual(hypot(), 0.0) # Negative input
|
||
|
|
self.assertEqual(1.0,
|
||
|
|
math.copysign(1.0, hypot(-0.0)) # Convert negative zero to positive zero
|
||
|
|
)
|
||
|
|
self.assertEqual( # Handling of moving max to the end
|
||
|
|
hypot(1.5, 1.5, 0.5),
|
||
|
|
hypot(1.5, 0.5, 1.5),
|
||
|
|
)
|
||
|
|
|
||
|
|
# Test handling of bad arguments
|
||
|
|
with self.assertRaises(TypeError): # Reject keyword args
|
||
|
|
hypot(x=1)
|
||
|
|
with self.assertRaises(TypeError): # Reject values without __float__
|
||
|
|
hypot(1.1, 'string', 2.2)
|
||
|
|
int_too_big_for_float = 10 ** (sys.float_info.max_10_exp + 5)
|
||
|
|
with self.assertRaises((ValueError, OverflowError)):
|
||
|
|
hypot(1, int_too_big_for_float)
|
||
|
|
|
||
|
|
# Any infinity gives positive infinity.
|
||
|
|
self.assertEqual(hypot(INF), INF)
|
||
|
|
self.assertEqual(hypot(0, INF), INF)
|
||
|
|
self.assertEqual(hypot(10, INF), INF)
|
||
|
|
self.assertEqual(hypot(-10, INF), INF)
|
||
|
|
self.assertEqual(hypot(NAN, INF), INF)
|
||
|
|
self.assertEqual(hypot(INF, NAN), INF)
|
||
|
|
self.assertEqual(hypot(NINF, NAN), INF)
|
||
|
|
self.assertEqual(hypot(NAN, NINF), INF)
|
||
|
|
self.assertEqual(hypot(-INF, INF), INF)
|
||
|
|
self.assertEqual(hypot(-INF, -INF), INF)
|
||
|
|
self.assertEqual(hypot(10, -INF), INF)
|
||
|
|
|
||
|
|
# If no infinity, any NaN gives a NaN.
|
||
|
|
self.assertTrue(math.isnan(hypot(NAN)))
|
||
|
|
self.assertTrue(math.isnan(hypot(0, NAN)))
|
||
|
|
self.assertTrue(math.isnan(hypot(NAN, 10)))
|
||
|
|
self.assertTrue(math.isnan(hypot(10, NAN)))
|
||
|
|
self.assertTrue(math.isnan(hypot(NAN, NAN)))
|
||
|
|
self.assertTrue(math.isnan(hypot(NAN)))
|
||
|
|
|
||
|
|
# Verify scaling for extremely large values
|
||
|
|
fourthmax = FLOAT_MAX / 4.0
|
||
|
|
for n in range(32):
|
||
|
|
self.assertTrue(math.isclose(hypot(*([fourthmax]*n)),
|
||
|
|
fourthmax * math.sqrt(n)))
|
||
|
|
|
||
|
|
# Verify scaling for extremely small values
|
||
|
|
for exp in range(32):
|
||
|
|
scale = FLOAT_MIN / 2.0 ** exp
|
||
|
|
self.assertEqual(math.hypot(4*scale, 3*scale), 5*scale)
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
@unittest.skipIf(HAVE_DOUBLE_ROUNDING,
|
||
|
|
"hypot() loses accuracy on machines with double rounding")
|
||
|
|
def testHypotAccuracy(self):
|
||
|
|
# Verify improved accuracy in cases that were known to be inaccurate.
|
||
|
|
#
|
||
|
|
# The new algorithm's accuracy depends on IEEE 754 arithmetic
|
||
|
|
# guarantees, on having the usual ROUND HALF EVEN rounding mode, on
|
||
|
|
# the system not having double rounding due to extended precision,
|
||
|
|
# and on the compiler maintaining the specified order of operations.
|
||
|
|
#
|
||
|
|
# This test is known to succeed on most of our builds. If it fails
|
||
|
|
# some build, we either need to add another skipIf if the cause is
|
||
|
|
# identifiable; otherwise, we can remove this test entirely.
|
||
|
|
|
||
|
|
hypot = math.hypot
|
||
|
|
Decimal = decimal.Decimal
|
||
|
|
high_precision = decimal.Context(prec=500)
|
||
|
|
|
||
|
|
for hx, hy in [
|
||
|
|
# Cases with a 1 ulp error in Python 3.7 compiled with Clang
|
||
|
|
('0x1.10e89518dca48p+29', '0x1.1970f7565b7efp+30'),
|
||
|
|
('0x1.10106eb4b44a2p+29', '0x1.ef0596cdc97f8p+29'),
|
||
|
|
('0x1.459c058e20bb7p+30', '0x1.993ca009b9178p+29'),
|
||
|
|
('0x1.378371ae67c0cp+30', '0x1.fbe6619854b4cp+29'),
|
||
|
|
('0x1.f4cd0574fb97ap+29', '0x1.50fe31669340ep+30'),
|
||
|
|
('0x1.494b2cdd3d446p+29', '0x1.212a5367b4c7cp+29'),
|
||
|
|
('0x1.f84e649f1e46dp+29', '0x1.1fa56bef8eec4p+30'),
|
||
|
|
('0x1.2e817edd3d6fap+30', '0x1.eb0814f1e9602p+29'),
|
||
|
|
('0x1.0d3a6e3d04245p+29', '0x1.32a62fea52352p+30'),
|
||
|
|
('0x1.888e19611bfc5p+29', '0x1.52b8e70b24353p+29'),
|
||
|
|
|
||
|
|
# Cases with 2 ulp error in Python 3.8
|
||
|
|
('0x1.538816d48a13fp+29', '0x1.7967c5ca43e16p+29'),
|
||
|
|
('0x1.57b47b7234530p+29', '0x1.74e2c7040e772p+29'),
|
||
|
|
('0x1.821b685e9b168p+30', '0x1.677dc1c1e3dc6p+29'),
|
||
|
|
('0x1.9e8247f67097bp+29', '0x1.24bd2dc4f4baep+29'),
|
||
|
|
('0x1.b73b59e0cb5f9p+29', '0x1.da899ab784a97p+28'),
|
||
|
|
('0x1.94a8d2842a7cfp+30', '0x1.326a51d4d8d8ap+30'),
|
||
|
|
('0x1.e930b9cd99035p+29', '0x1.5a1030e18dff9p+30'),
|
||
|
|
('0x1.1592bbb0e4690p+29', '0x1.a9c337b33fb9ap+29'),
|
||
|
|
('0x1.1243a50751fd4p+29', '0x1.a5a10175622d9p+29'),
|
||
|
|
('0x1.57a8596e74722p+30', '0x1.42d1af9d04da9p+30'),
|
||
|
|
|
||
|
|
# Cases with 1 ulp error in version fff3c28052e6b0
|
||
|
|
('0x1.ee7dbd9565899p+29', '0x1.7ab4d6fc6e4b4p+29'),
|
||
|
|
('0x1.5c6bfbec5c4dcp+30', '0x1.02511184b4970p+30'),
|
||
|
|
('0x1.59dcebba995cap+30', '0x1.50ca7e7c38854p+29'),
|
||
|
|
('0x1.768cdd94cf5aap+29', '0x1.9cfdc5571d38ep+29'),
|
||
|
|
('0x1.dcf137d60262ep+29', '0x1.1101621990b3ep+30'),
|
||
|
|
('0x1.3a2d006e288b0p+30', '0x1.e9a240914326cp+29'),
|
||
|
|
('0x1.62a32f7f53c61p+29', '0x1.47eb6cd72684fp+29'),
|
||
|
|
('0x1.d3bcb60748ef2p+29', '0x1.3f13c4056312cp+30'),
|
||
|
|
('0x1.282bdb82f17f3p+30', '0x1.640ba4c4eed3ap+30'),
|
||
|
|
('0x1.89d8c423ea0c6p+29', '0x1.d35dcfe902bc3p+29'),
|
||
|
|
]:
|
||
|
|
x = float.fromhex(hx)
|
||
|
|
y = float.fromhex(hy)
|
||
|
|
with self.subTest(hx=hx, hy=hy, x=x, y=y):
|
||
|
|
with decimal.localcontext(high_precision):
|
||
|
|
z = float((Decimal(x)**2 + Decimal(y)**2).sqrt())
|
||
|
|
self.assertEqual(hypot(x, y), z)
|
||
|
|
|
||
|
|
def testDist(self):
|
||
|
|
from decimal import Decimal as D
|
||
|
|
from fractions import Fraction as F
|
||
|
|
|
||
|
|
dist = math.dist
|
||
|
|
sqrt = math.sqrt
|
||
|
|
|
||
|
|
# Simple exact cases
|
||
|
|
self.assertEqual(dist((1.0, 2.0, 3.0), (4.0, 2.0, -1.0)), 5.0)
|
||
|
|
self.assertEqual(dist((1, 2, 3), (4, 2, -1)), 5.0)
|
||
|
|
|
||
|
|
# Test different numbers of arguments (from zero to nine)
|
||
|
|
# against a straightforward pure python implementation
|
||
|
|
for i in range(9):
|
||
|
|
for j in range(5):
|
||
|
|
p = tuple(random.uniform(-5, 5) for k in range(i))
|
||
|
|
q = tuple(random.uniform(-5, 5) for k in range(i))
|
||
|
|
self.assertAlmostEqual(
|
||
|
|
dist(p, q),
|
||
|
|
sqrt(sum((px - qx) ** 2.0 for px, qx in zip(p, q)))
|
||
|
|
)
|
||
|
|
|
||
|
|
# Test non-tuple inputs
|
||
|
|
self.assertEqual(dist([1.0, 2.0, 3.0], [4.0, 2.0, -1.0]), 5.0)
|
||
|
|
self.assertEqual(dist(iter([1.0, 2.0, 3.0]), iter([4.0, 2.0, -1.0])), 5.0)
|
||
|
|
|
||
|
|
# Test allowable types (those with __float__)
|
||
|
|
self.assertEqual(dist((14.0, 1.0), (2.0, -4.0)), 13.0)
|
||
|
|
self.assertEqual(dist((14, 1), (2, -4)), 13)
|
||
|
|
self.assertEqual(dist((D(14), D(1)), (D(2), D(-4))), D(13))
|
||
|
|
self.assertEqual(dist((F(14, 32), F(1, 32)), (F(2, 32), F(-4, 32))),
|
||
|
|
F(13, 32))
|
||
|
|
self.assertEqual(dist((True, True, False, True, False),
|
||
|
|
(True, False, True, True, False)),
|
||
|
|
sqrt(2.0))
|
||
|
|
|
||
|
|
# Test corner cases
|
||
|
|
self.assertEqual(dist((13.25, 12.5, -3.25),
|
||
|
|
(13.25, 12.5, -3.25)),
|
||
|
|
0.0) # Distance with self is zero
|
||
|
|
self.assertEqual(dist((), ()), 0.0) # Zero-dimensional case
|
||
|
|
self.assertEqual(1.0, # Convert negative zero to positive zero
|
||
|
|
math.copysign(1.0, dist((-0.0,), (0.0,)))
|
||
|
|
)
|
||
|
|
self.assertEqual(1.0, # Convert negative zero to positive zero
|
||
|
|
math.copysign(1.0, dist((0.0,), (-0.0,)))
|
||
|
|
)
|
||
|
|
self.assertEqual( # Handling of moving max to the end
|
||
|
|
dist((1.5, 1.5, 0.5), (0, 0, 0)),
|
||
|
|
dist((1.5, 0.5, 1.5), (0, 0, 0))
|
||
|
|
)
|
||
|
|
|
||
|
|
# Verify tuple subclasses are allowed
|
||
|
|
class T(tuple):
|
||
|
|
pass
|
||
|
|
self.assertEqual(dist(T((1, 2, 3)), ((4, 2, -1))), 5.0)
|
||
|
|
|
||
|
|
# Test handling of bad arguments
|
||
|
|
with self.assertRaises(TypeError): # Reject keyword args
|
||
|
|
dist(p=(1, 2, 3), q=(4, 5, 6))
|
||
|
|
with self.assertRaises(TypeError): # Too few args
|
||
|
|
dist((1, 2, 3))
|
||
|
|
with self.assertRaises(TypeError): # Too many args
|
||
|
|
dist((1, 2, 3), (4, 5, 6), (7, 8, 9))
|
||
|
|
with self.assertRaises(TypeError): # Scalars not allowed
|
||
|
|
dist(1, 2)
|
||
|
|
with self.assertRaises(TypeError): # Reject values without __float__
|
||
|
|
dist((1.1, 'string', 2.2), (1, 2, 3))
|
||
|
|
with self.assertRaises(ValueError): # Check dimension agree
|
||
|
|
dist((1, 2, 3, 4), (5, 6, 7))
|
||
|
|
with self.assertRaises(ValueError): # Check dimension agree
|
||
|
|
dist((1, 2, 3), (4, 5, 6, 7))
|
||
|
|
with self.assertRaises(TypeError): # Rejects invalid types
|
||
|
|
dist("abc", "xyz")
|
||
|
|
int_too_big_for_float = 10 ** (sys.float_info.max_10_exp + 5)
|
||
|
|
with self.assertRaises((ValueError, OverflowError)):
|
||
|
|
dist((1, int_too_big_for_float), (2, 3))
|
||
|
|
with self.assertRaises((ValueError, OverflowError)):
|
||
|
|
dist((2, 3), (1, int_too_big_for_float))
|
||
|
|
|
||
|
|
# Verify that the one dimensional case is equivalent to abs()
|
||
|
|
for i in range(20):
|
||
|
|
p, q = random.random(), random.random()
|
||
|
|
self.assertEqual(dist((p,), (q,)), abs(p - q))
|
||
|
|
|
||
|
|
# Test special values
|
||
|
|
values = [NINF, -10.5, -0.0, 0.0, 10.5, INF, NAN]
|
||
|
|
for p in itertools.product(values, repeat=3):
|
||
|
|
for q in itertools.product(values, repeat=3):
|
||
|
|
diffs = [px - qx for px, qx in zip(p, q)]
|
||
|
|
if any(map(math.isinf, diffs)):
|
||
|
|
# Any infinite difference gives positive infinity.
|
||
|
|
self.assertEqual(dist(p, q), INF)
|
||
|
|
elif any(map(math.isnan, diffs)):
|
||
|
|
# If no infinity, any NaN gives a NaN.
|
||
|
|
self.assertTrue(math.isnan(dist(p, q)))
|
||
|
|
|
||
|
|
# Verify scaling for extremely large values
|
||
|
|
fourthmax = FLOAT_MAX / 4.0
|
||
|
|
for n in range(32):
|
||
|
|
p = (fourthmax,) * n
|
||
|
|
q = (0.0,) * n
|
||
|
|
self.assertTrue(math.isclose(dist(p, q), fourthmax * math.sqrt(n)))
|
||
|
|
self.assertTrue(math.isclose(dist(q, p), fourthmax * math.sqrt(n)))
|
||
|
|
|
||
|
|
# Verify scaling for extremely small values
|
||
|
|
for exp in range(32):
|
||
|
|
scale = FLOAT_MIN / 2.0 ** exp
|
||
|
|
p = (4*scale, 3*scale)
|
||
|
|
q = (0.0, 0.0)
|
||
|
|
self.assertEqual(math.dist(p, q), 5*scale)
|
||
|
|
self.assertEqual(math.dist(q, p), 5*scale)
|
||
|
|
|
||
|
|
def testIsqrt(self):
|
||
|
|
# Test a variety of inputs, large and small.
|
||
|
|
test_values = (
|
||
|
|
list(range(1000))
|
||
|
|
+ list(range(10**6 - 1000, 10**6 + 1000))
|
||
|
|
+ [2**e + i for e in range(60, 200) for i in range(-40, 40)]
|
||
|
|
+ [3**9999, 10**5001]
|
||
|
|
)
|
||
|
|
|
||
|
|
for value in test_values:
|
||
|
|
with self.subTest(value=value):
|
||
|
|
s = math.isqrt(value)
|
||
|
|
self.assertIs(type(s), int)
|
||
|
|
self.assertLessEqual(s*s, value)
|
||
|
|
self.assertLess(value, (s+1)*(s+1))
|
||
|
|
|
||
|
|
# Negative values
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.isqrt(-1)
|
||
|
|
|
||
|
|
# Integer-like things
|
||
|
|
s = math.isqrt(True)
|
||
|
|
self.assertIs(type(s), int)
|
||
|
|
self.assertEqual(s, 1)
|
||
|
|
|
||
|
|
s = math.isqrt(False)
|
||
|
|
self.assertIs(type(s), int)
|
||
|
|
self.assertEqual(s, 0)
|
||
|
|
|
||
|
|
class IntegerLike(object):
|
||
|
|
def __init__(self, value):
|
||
|
|
self.value = value
|
||
|
|
|
||
|
|
def __index__(self):
|
||
|
|
return self.value
|
||
|
|
|
||
|
|
s = math.isqrt(IntegerLike(1729))
|
||
|
|
self.assertIs(type(s), int)
|
||
|
|
self.assertEqual(s, 41)
|
||
|
|
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.isqrt(IntegerLike(-3))
|
||
|
|
|
||
|
|
# Non-integer-like things
|
||
|
|
bad_values = [
|
||
|
|
3.5, "a string", decimal.Decimal("3.5"), 3.5j,
|
||
|
|
100.0, -4.0,
|
||
|
|
]
|
||
|
|
for value in bad_values:
|
||
|
|
with self.subTest(value=value):
|
||
|
|
with self.assertRaises(TypeError):
|
||
|
|
math.isqrt(value)
|
||
|
|
|
||
|
|
def test_lcm(self):
|
||
|
|
lcm = math.lcm
|
||
|
|
self.assertEqual(lcm(0, 0), 0)
|
||
|
|
self.assertEqual(lcm(1, 0), 0)
|
||
|
|
self.assertEqual(lcm(-1, 0), 0)
|
||
|
|
self.assertEqual(lcm(0, 1), 0)
|
||
|
|
self.assertEqual(lcm(0, -1), 0)
|
||
|
|
self.assertEqual(lcm(7, 1), 7)
|
||
|
|
self.assertEqual(lcm(7, -1), 7)
|
||
|
|
self.assertEqual(lcm(-23, 15), 345)
|
||
|
|
self.assertEqual(lcm(120, 84), 840)
|
||
|
|
self.assertEqual(lcm(84, -120), 840)
|
||
|
|
self.assertEqual(lcm(1216342683557601535506311712,
|
||
|
|
436522681849110124616458784),
|
||
|
|
16592536571065866494401400422922201534178938447014944)
|
||
|
|
|
||
|
|
x = 43461045657039990237
|
||
|
|
y = 10645022458251153277
|
||
|
|
for c in (652560,
|
||
|
|
57655923087165495981):
|
||
|
|
a = x * c
|
||
|
|
b = y * c
|
||
|
|
d = x * y * c
|
||
|
|
self.assertEqual(lcm(a, b), d)
|
||
|
|
self.assertEqual(lcm(b, a), d)
|
||
|
|
self.assertEqual(lcm(-a, b), d)
|
||
|
|
self.assertEqual(lcm(b, -a), d)
|
||
|
|
self.assertEqual(lcm(a, -b), d)
|
||
|
|
self.assertEqual(lcm(-b, a), d)
|
||
|
|
self.assertEqual(lcm(-a, -b), d)
|
||
|
|
self.assertEqual(lcm(-b, -a), d)
|
||
|
|
|
||
|
|
self.assertEqual(lcm(), 1)
|
||
|
|
self.assertEqual(lcm(120), 120)
|
||
|
|
self.assertEqual(lcm(-120), 120)
|
||
|
|
self.assertEqual(lcm(120, 84, 102), 14280)
|
||
|
|
self.assertEqual(lcm(120, 0, 84), 0)
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, lcm, 120.0)
|
||
|
|
self.assertRaises(TypeError, lcm, 120.0, 84)
|
||
|
|
self.assertRaises(TypeError, lcm, 120, 84.0)
|
||
|
|
self.assertRaises(TypeError, lcm, 120, 0, 84.0)
|
||
|
|
self.assertEqual(lcm(MyIndexable(120), MyIndexable(84)), 840)
|
||
|
|
|
||
|
|
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, 10**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.ftest('log(10**1000)', math.log(10**1000),
|
||
|
|
2302.5850929940457)
|
||
|
|
self.assertRaises(ValueError, math.log, -1.5)
|
||
|
|
self.assertRaises(ValueError, math.log, -10**1000)
|
||
|
|
self.assertRaises(ValueError, math.log, NINF)
|
||
|
|
self.assertEqual(math.log(INF), INF)
|
||
|
|
self.assertTrue(math.isnan(math.log(NAN)))
|
||
|
|
|
||
|
|
def testLog1p(self):
|
||
|
|
self.assertRaises(TypeError, math.log1p)
|
||
|
|
for n in [2, 2**90, 2**300]:
|
||
|
|
self.assertAlmostEqual(math.log1p(n), math.log1p(float(n)))
|
||
|
|
self.assertRaises(ValueError, math.log1p, -1)
|
||
|
|
self.assertEqual(math.log1p(INF), INF)
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def testLog2(self):
|
||
|
|
self.assertRaises(TypeError, math.log2)
|
||
|
|
|
||
|
|
# Check some integer values
|
||
|
|
self.assertEqual(math.log2(1), 0.0)
|
||
|
|
self.assertEqual(math.log2(2), 1.0)
|
||
|
|
self.assertEqual(math.log2(4), 2.0)
|
||
|
|
|
||
|
|
# Large integer values
|
||
|
|
self.assertEqual(math.log2(2**1023), 1023.0)
|
||
|
|
self.assertEqual(math.log2(2**1024), 1024.0)
|
||
|
|
self.assertEqual(math.log2(2**2000), 2000.0)
|
||
|
|
|
||
|
|
self.assertRaises(ValueError, math.log2, -1.5)
|
||
|
|
self.assertRaises(ValueError, math.log2, NINF)
|
||
|
|
self.assertTrue(math.isnan(math.log2(NAN)))
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
# log2() is not accurate enough on Mac OS X Tiger (10.4)
|
||
|
|
@support.requires_mac_ver(10, 5)
|
||
|
|
def testLog2Exact(self):
|
||
|
|
# Check that we get exact equality for log2 of powers of 2.
|
||
|
|
actual = [math.log2(math.ldexp(1.0, n)) for n in range(-1074, 1024)]
|
||
|
|
expected = [float(n) for n in range(-1074, 1024)]
|
||
|
|
self.assertEqual(actual, expected)
|
||
|
|
|
||
|
|
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.ftest('log10(10**1000)', math.log10(10**1000), 1000.0)
|
||
|
|
self.assertRaises(ValueError, math.log10, -1.5)
|
||
|
|
self.assertRaises(ValueError, math.log10, -10**1000)
|
||
|
|
self.assertRaises(ValueError, math.log10, NINF)
|
||
|
|
self.assertEqual(math.log(INF), INF)
|
||
|
|
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, result, expected))
|
||
|
|
|
||
|
|
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)
|
||
|
|
self.ftest('radians(0)', math.radians(0), 0)
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def testRemainder(self):
|
||
|
|
from fractions import Fraction
|
||
|
|
|
||
|
|
def validate_spec(x, y, r):
|
||
|
|
"""
|
||
|
|
Check that r matches remainder(x, y) according to the IEEE 754
|
||
|
|
specification. Assumes that x, y and r are finite and y is nonzero.
|
||
|
|
"""
|
||
|
|
fx, fy, fr = Fraction(x), Fraction(y), Fraction(r)
|
||
|
|
# r should not exceed y/2 in absolute value
|
||
|
|
self.assertLessEqual(abs(fr), abs(fy/2))
|
||
|
|
# x - r should be an exact integer multiple of y
|
||
|
|
n = (fx - fr) / fy
|
||
|
|
self.assertEqual(n, int(n))
|
||
|
|
if abs(fr) == abs(fy/2):
|
||
|
|
# If |r| == |y/2|, n should be even.
|
||
|
|
self.assertEqual(n/2, int(n/2))
|
||
|
|
|
||
|
|
# triples (x, y, remainder(x, y)) in hexadecimal form.
|
||
|
|
testcases = [
|
||
|
|
# Remainders modulo 1, showing the ties-to-even behaviour.
|
||
|
|
'-4.0 1 -0.0',
|
||
|
|
'-3.8 1 0.8',
|
||
|
|
'-3.0 1 -0.0',
|
||
|
|
'-2.8 1 -0.8',
|
||
|
|
'-2.0 1 -0.0',
|
||
|
|
'-1.8 1 0.8',
|
||
|
|
'-1.0 1 -0.0',
|
||
|
|
'-0.8 1 -0.8',
|
||
|
|
'-0.0 1 -0.0',
|
||
|
|
' 0.0 1 0.0',
|
||
|
|
' 0.8 1 0.8',
|
||
|
|
' 1.0 1 0.0',
|
||
|
|
' 1.8 1 -0.8',
|
||
|
|
' 2.0 1 0.0',
|
||
|
|
' 2.8 1 0.8',
|
||
|
|
' 3.0 1 0.0',
|
||
|
|
' 3.8 1 -0.8',
|
||
|
|
' 4.0 1 0.0',
|
||
|
|
|
||
|
|
# Reductions modulo 2*pi
|
||
|
|
'0x0.0p+0 0x1.921fb54442d18p+2 0x0.0p+0',
|
||
|
|
'0x1.921fb54442d18p+0 0x1.921fb54442d18p+2 0x1.921fb54442d18p+0',
|
||
|
|
'0x1.921fb54442d17p+1 0x1.921fb54442d18p+2 0x1.921fb54442d17p+1',
|
||
|
|
'0x1.921fb54442d18p+1 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1',
|
||
|
|
'0x1.921fb54442d19p+1 0x1.921fb54442d18p+2 -0x1.921fb54442d17p+1',
|
||
|
|
'0x1.921fb54442d17p+2 0x1.921fb54442d18p+2 -0x0.0000000000001p+2',
|
||
|
|
'0x1.921fb54442d18p+2 0x1.921fb54442d18p+2 0x0p0',
|
||
|
|
'0x1.921fb54442d19p+2 0x1.921fb54442d18p+2 0x0.0000000000001p+2',
|
||
|
|
'0x1.2d97c7f3321d1p+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1',
|
||
|
|
'0x1.2d97c7f3321d2p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d18p+1',
|
||
|
|
'0x1.2d97c7f3321d3p+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1',
|
||
|
|
'0x1.921fb54442d17p+3 0x1.921fb54442d18p+2 -0x0.0000000000001p+3',
|
||
|
|
'0x1.921fb54442d18p+3 0x1.921fb54442d18p+2 0x0p0',
|
||
|
|
'0x1.921fb54442d19p+3 0x1.921fb54442d18p+2 0x0.0000000000001p+3',
|
||
|
|
'0x1.f6a7a2955385dp+3 0x1.921fb54442d18p+2 0x1.921fb54442d14p+1',
|
||
|
|
'0x1.f6a7a2955385ep+3 0x1.921fb54442d18p+2 0x1.921fb54442d18p+1',
|
||
|
|
'0x1.f6a7a2955385fp+3 0x1.921fb54442d18p+2 -0x1.921fb54442d14p+1',
|
||
|
|
'0x1.1475cc9eedf00p+5 0x1.921fb54442d18p+2 0x1.921fb54442d10p+1',
|
||
|
|
'0x1.1475cc9eedf01p+5 0x1.921fb54442d18p+2 -0x1.921fb54442d10p+1',
|
||
|
|
|
||
|
|
# Symmetry with respect to signs.
|
||
|
|
' 1 0.c 0.4',
|
||
|
|
'-1 0.c -0.4',
|
||
|
|
' 1 -0.c 0.4',
|
||
|
|
'-1 -0.c -0.4',
|
||
|
|
' 1.4 0.c -0.4',
|
||
|
|
'-1.4 0.c 0.4',
|
||
|
|
' 1.4 -0.c -0.4',
|
||
|
|
'-1.4 -0.c 0.4',
|
||
|
|
|
||
|
|
# Huge modulus, to check that the underlying algorithm doesn't
|
||
|
|
# rely on 2.0 * modulus being representable.
|
||
|
|
'0x1.dp+1023 0x1.4p+1023 0x0.9p+1023',
|
||
|
|
'0x1.ep+1023 0x1.4p+1023 -0x0.ap+1023',
|
||
|
|
'0x1.fp+1023 0x1.4p+1023 -0x0.9p+1023',
|
||
|
|
]
|
||
|
|
|
||
|
|
for case in testcases:
|
||
|
|
with self.subTest(case=case):
|
||
|
|
x_hex, y_hex, expected_hex = case.split()
|
||
|
|
x = float.fromhex(x_hex)
|
||
|
|
y = float.fromhex(y_hex)
|
||
|
|
expected = float.fromhex(expected_hex)
|
||
|
|
validate_spec(x, y, expected)
|
||
|
|
actual = math.remainder(x, y)
|
||
|
|
# Cheap way of checking that the floats are
|
||
|
|
# as identical as we need them to be.
|
||
|
|
self.assertEqual(actual.hex(), expected.hex())
|
||
|
|
|
||
|
|
# Test tiny subnormal modulus: there's potential for
|
||
|
|
# getting the implementation wrong here (for example,
|
||
|
|
# by assuming that modulus/2 is exactly representable).
|
||
|
|
tiny = float.fromhex('1p-1074') # min +ve subnormal
|
||
|
|
for n in range(-25, 25):
|
||
|
|
if n == 0:
|
||
|
|
continue
|
||
|
|
y = n * tiny
|
||
|
|
for m in range(100):
|
||
|
|
x = m * tiny
|
||
|
|
actual = math.remainder(x, y)
|
||
|
|
validate_spec(x, y, actual)
|
||
|
|
actual = math.remainder(-x, y)
|
||
|
|
validate_spec(-x, y, actual)
|
||
|
|
|
||
|
|
# Special values.
|
||
|
|
# NaNs should propagate as usual.
|
||
|
|
for value in [NAN, 0.0, -0.0, 2.0, -2.3, NINF, INF]:
|
||
|
|
self.assertIsNaN(math.remainder(NAN, value))
|
||
|
|
self.assertIsNaN(math.remainder(value, NAN))
|
||
|
|
|
||
|
|
# remainder(x, inf) is x, for non-nan non-infinite x.
|
||
|
|
for value in [-2.3, -0.0, 0.0, 2.3]:
|
||
|
|
self.assertEqual(math.remainder(value, INF), value)
|
||
|
|
self.assertEqual(math.remainder(value, NINF), value)
|
||
|
|
|
||
|
|
# remainder(x, 0) and remainder(infinity, x) for non-NaN x are invalid
|
||
|
|
# operations according to IEEE 754-2008 7.2(f), and should raise.
|
||
|
|
for value in [NINF, -2.3, -0.0, 0.0, 2.3, INF]:
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.remainder(INF, value)
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.remainder(NINF, value)
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.remainder(value, 0.0)
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
math.remainder(value, -0.0)
|
||
|
|
|
||
|
|
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, -1)
|
||
|
|
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,
|
||
|
|
abs_tol=math.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)))
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def testTanhSign(self):
|
||
|
|
# check that tanh(-0.) == -0. on IEEE 754 systems
|
||
|
|
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:
|
||
|
|
def __trunc__(self):
|
||
|
|
return 23
|
||
|
|
class FloatTrunc(float):
|
||
|
|
def __trunc__(self):
|
||
|
|
return 23
|
||
|
|
class TestNoTrunc:
|
||
|
|
pass
|
||
|
|
|
||
|
|
self.assertEqual(math.trunc(TestTrunc()), 23)
|
||
|
|
self.assertEqual(math.trunc(FloatTrunc()), 23)
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, math.trunc)
|
||
|
|
self.assertRaises(TypeError, math.trunc, 1, 2)
|
||
|
|
self.assertRaises(TypeError, math.trunc, FloatLike(23.5))
|
||
|
|
self.assertRaises(TypeError, math.trunc, TestNoTrunc())
|
||
|
|
|
||
|
|
def testIsfinite(self):
|
||
|
|
self.assertTrue(math.isfinite(0.0))
|
||
|
|
self.assertTrue(math.isfinite(-0.0))
|
||
|
|
self.assertTrue(math.isfinite(1.0))
|
||
|
|
self.assertTrue(math.isfinite(-1.0))
|
||
|
|
self.assertFalse(math.isfinite(float("nan")))
|
||
|
|
self.assertFalse(math.isfinite(float("inf")))
|
||
|
|
self.assertFalse(math.isfinite(float("-inf")))
|
||
|
|
|
||
|
|
def testIsnan(self):
|
||
|
|
self.assertTrue(math.isnan(float("nan")))
|
||
|
|
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.))
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def test_nan_constant(self):
|
||
|
|
self.assertTrue(math.isnan(math.nan))
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def test_inf_constant(self):
|
||
|
|
self.assertTrue(math.isinf(math.inf))
|
||
|
|
self.assertGreater(math.inf, 0.0)
|
||
|
|
self.assertEqual(math.inf, float("inf"))
|
||
|
|
self.assertEqual(-math.inf, float("-inf"))
|
||
|
|
|
||
|
|
# 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.
|
||
|
|
@unittest.skipUnless(verbose, 'requires verbose mode')
|
||
|
|
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):
|
||
|
|
# Some tests need to be skipped on ancient OS X versions.
|
||
|
|
# See issue #27953.
|
||
|
|
SKIP_ON_TIGER = {'tan0064'}
|
||
|
|
|
||
|
|
osx_version = None
|
||
|
|
if sys.platform == 'darwin':
|
||
|
|
version_txt = platform.mac_ver()[0]
|
||
|
|
try:
|
||
|
|
osx_version = tuple(map(int, version_txt.split('.')))
|
||
|
|
except ValueError:
|
||
|
|
pass
|
||
|
|
|
||
|
|
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
|
||
|
|
if ai != 0.0 or ei != 0.0:
|
||
|
|
continue
|
||
|
|
if fn in ['rect', 'polar']:
|
||
|
|
# no real versions of rect, polar
|
||
|
|
continue
|
||
|
|
# Skip certain tests on OS X 10.4.
|
||
|
|
if osx_version is not None and osx_version < (10, 5):
|
||
|
|
if id in SKIP_ON_TIGER:
|
||
|
|
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:
|
||
|
|
result = 'ValueError'
|
||
|
|
except OverflowError:
|
||
|
|
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}): {}"
|
||
|
|
|
||
|
|
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'
|
||
|
|
|
||
|
|
# 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 ' +
|
||
|
|
'\n '.join(failures))
|
||
|
|
|
||
|
|
def test_prod(self):
|
||
|
|
prod = math.prod
|
||
|
|
self.assertEqual(prod([]), 1)
|
||
|
|
self.assertEqual(prod([], start=5), 5)
|
||
|
|
self.assertEqual(prod(list(range(2,8))), 5040)
|
||
|
|
self.assertEqual(prod(iter(list(range(2,8)))), 5040)
|
||
|
|
self.assertEqual(prod(range(1, 10), start=10), 3628800)
|
||
|
|
|
||
|
|
self.assertEqual(prod([1, 2, 3, 4, 5]), 120)
|
||
|
|
self.assertEqual(prod([1.0, 2.0, 3.0, 4.0, 5.0]), 120.0)
|
||
|
|
self.assertEqual(prod([1, 2, 3, 4.0, 5.0]), 120.0)
|
||
|
|
self.assertEqual(prod([1.0, 2.0, 3.0, 4, 5]), 120.0)
|
||
|
|
|
||
|
|
# Test overflow in fast-path for integers
|
||
|
|
self.assertEqual(prod([1, 1, 2**32, 1, 1]), 2**32)
|
||
|
|
# Test overflow in fast-path for floats
|
||
|
|
self.assertEqual(prod([1.0, 1.0, 2**32, 1, 1]), float(2**32))
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, prod)
|
||
|
|
self.assertRaises(TypeError, prod, 42)
|
||
|
|
self.assertRaises(TypeError, prod, ['a', 'b', 'c'])
|
||
|
|
self.assertRaises(TypeError, prod, ['a', 'b', 'c'], start='')
|
||
|
|
self.assertRaises(TypeError, prod, [b'a', b'c'], start=b'')
|
||
|
|
values = [bytearray(b'a'), bytearray(b'b')]
|
||
|
|
self.assertRaises(TypeError, prod, values, start=bytearray(b''))
|
||
|
|
self.assertRaises(TypeError, prod, [[1], [2], [3]])
|
||
|
|
self.assertRaises(TypeError, prod, [{2:3}])
|
||
|
|
self.assertRaises(TypeError, prod, [{2:3}]*2, start={2:3})
|
||
|
|
self.assertRaises(TypeError, prod, [[1], [2], [3]], start=[])
|
||
|
|
|
||
|
|
# Some odd cases
|
||
|
|
self.assertEqual(prod([2, 3], start='ab'), 'abababababab')
|
||
|
|
self.assertEqual(prod([2, 3], start=[1, 2]), [1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2])
|
||
|
|
self.assertEqual(prod([], start={2: 3}), {2:3})
|
||
|
|
|
||
|
|
with self.assertRaises(TypeError):
|
||
|
|
prod([10, 20], 1) # start is a keyword-only argument
|
||
|
|
|
||
|
|
self.assertEqual(prod([0, 1, 2, 3]), 0)
|
||
|
|
self.assertEqual(prod([1, 0, 2, 3]), 0)
|
||
|
|
self.assertEqual(prod([1, 2, 3, 0]), 0)
|
||
|
|
|
||
|
|
def _naive_prod(iterable, start=1):
|
||
|
|
for elem in iterable:
|
||
|
|
start *= elem
|
||
|
|
return start
|
||
|
|
|
||
|
|
# Big integers
|
||
|
|
|
||
|
|
iterable = range(1, 10000)
|
||
|
|
self.assertEqual(prod(iterable), _naive_prod(iterable))
|
||
|
|
iterable = range(-10000, -1)
|
||
|
|
self.assertEqual(prod(iterable), _naive_prod(iterable))
|
||
|
|
iterable = range(-1000, 1000)
|
||
|
|
self.assertEqual(prod(iterable), 0)
|
||
|
|
|
||
|
|
# Big floats
|
||
|
|
|
||
|
|
iterable = [float(x) for x in range(1, 1000)]
|
||
|
|
self.assertEqual(prod(iterable), _naive_prod(iterable))
|
||
|
|
iterable = [float(x) for x in range(-1000, -1)]
|
||
|
|
self.assertEqual(prod(iterable), _naive_prod(iterable))
|
||
|
|
iterable = [float(x) for x in range(-1000, 1000)]
|
||
|
|
self.assertIsNaN(prod(iterable))
|
||
|
|
|
||
|
|
# Float tests
|
||
|
|
|
||
|
|
self.assertIsNaN(prod([1, 2, 3, float("nan"), 2, 3]))
|
||
|
|
self.assertIsNaN(prod([1, 0, float("nan"), 2, 3]))
|
||
|
|
self.assertIsNaN(prod([1, float("nan"), 0, 3]))
|
||
|
|
self.assertIsNaN(prod([1, float("inf"), float("nan"),3]))
|
||
|
|
self.assertIsNaN(prod([1, float("-inf"), float("nan"),3]))
|
||
|
|
self.assertIsNaN(prod([1, float("nan"), float("inf"),3]))
|
||
|
|
self.assertIsNaN(prod([1, float("nan"), float("-inf"),3]))
|
||
|
|
|
||
|
|
self.assertEqual(prod([1, 2, 3, float('inf'),-3,4]), float('-inf'))
|
||
|
|
self.assertEqual(prod([1, 2, 3, float('-inf'),-3,4]), float('inf'))
|
||
|
|
|
||
|
|
self.assertIsNaN(prod([1,2,0,float('inf'), -3, 4]))
|
||
|
|
self.assertIsNaN(prod([1,2,0,float('-inf'), -3, 4]))
|
||
|
|
self.assertIsNaN(prod([1, 2, 3, float('inf'), -3, 0, 3]))
|
||
|
|
self.assertIsNaN(prod([1, 2, 3, float('-inf'), -3, 0, 2]))
|
||
|
|
|
||
|
|
# Type preservation
|
||
|
|
|
||
|
|
self.assertEqual(type(prod([1, 2, 3, 4, 5, 6])), int)
|
||
|
|
self.assertEqual(type(prod([1, 2.0, 3, 4, 5, 6])), float)
|
||
|
|
self.assertEqual(type(prod(range(1, 10000))), int)
|
||
|
|
self.assertEqual(type(prod(range(1, 10000), start=1.0)), float)
|
||
|
|
self.assertEqual(type(prod([1, decimal.Decimal(2.0), 3, 4, 5, 6])),
|
||
|
|
decimal.Decimal)
|
||
|
|
|
||
|
|
def testPerm(self):
|
||
|
|
perm = math.perm
|
||
|
|
factorial = math.factorial
|
||
|
|
# Test if factorial definition is satisfied
|
||
|
|
for n in range(100):
|
||
|
|
for k in range(n + 1):
|
||
|
|
self.assertEqual(perm(n, k),
|
||
|
|
factorial(n) // factorial(n - k))
|
||
|
|
|
||
|
|
# Test for Pascal's identity
|
||
|
|
for n in range(1, 100):
|
||
|
|
for k in range(1, n):
|
||
|
|
self.assertEqual(perm(n, k), perm(n - 1, k - 1) * k + perm(n - 1, k))
|
||
|
|
|
||
|
|
# Test corner cases
|
||
|
|
for n in range(1, 100):
|
||
|
|
self.assertEqual(perm(n, 0), 1)
|
||
|
|
self.assertEqual(perm(n, 1), n)
|
||
|
|
self.assertEqual(perm(n, n), factorial(n))
|
||
|
|
|
||
|
|
# Test one argument form
|
||
|
|
for n in range(20):
|
||
|
|
self.assertEqual(perm(n), factorial(n))
|
||
|
|
self.assertEqual(perm(n, None), factorial(n))
|
||
|
|
|
||
|
|
# Raises TypeError if any argument is non-integer or argument count is
|
||
|
|
# not 1 or 2
|
||
|
|
self.assertRaises(TypeError, perm, 10, 1.0)
|
||
|
|
self.assertRaises(TypeError, perm, 10, decimal.Decimal(1.0))
|
||
|
|
self.assertRaises(TypeError, perm, 10, "1")
|
||
|
|
self.assertRaises(TypeError, perm, 10.0, 1)
|
||
|
|
self.assertRaises(TypeError, perm, decimal.Decimal(10.0), 1)
|
||
|
|
self.assertRaises(TypeError, perm, "10", 1)
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, perm)
|
||
|
|
self.assertRaises(TypeError, perm, 10, 1, 3)
|
||
|
|
self.assertRaises(TypeError, perm)
|
||
|
|
|
||
|
|
# Raises Value error if not k or n are negative numbers
|
||
|
|
self.assertRaises(ValueError, perm, -1, 1)
|
||
|
|
self.assertRaises(ValueError, perm, -2**1000, 1)
|
||
|
|
self.assertRaises(ValueError, perm, 1, -1)
|
||
|
|
self.assertRaises(ValueError, perm, 1, -2**1000)
|
||
|
|
|
||
|
|
# Returns zero if k is greater than n
|
||
|
|
self.assertEqual(perm(1, 2), 0)
|
||
|
|
self.assertEqual(perm(1, 2**1000), 0)
|
||
|
|
|
||
|
|
n = 2**1000
|
||
|
|
self.assertEqual(perm(n, 0), 1)
|
||
|
|
self.assertEqual(perm(n, 1), n)
|
||
|
|
self.assertEqual(perm(n, 2), n * (n-1))
|
||
|
|
if support.check_impl_detail(cpython=True):
|
||
|
|
self.assertRaises(OverflowError, perm, n, n)
|
||
|
|
|
||
|
|
for n, k in (True, True), (True, False), (False, False):
|
||
|
|
self.assertEqual(perm(n, k), 1)
|
||
|
|
self.assertIs(type(perm(n, k)), int)
|
||
|
|
self.assertEqual(perm(IntSubclass(5), IntSubclass(2)), 20)
|
||
|
|
self.assertEqual(perm(MyIndexable(5), MyIndexable(2)), 20)
|
||
|
|
for k in range(3):
|
||
|
|
self.assertIs(type(perm(IntSubclass(5), IntSubclass(k))), int)
|
||
|
|
self.assertIs(type(perm(MyIndexable(5), MyIndexable(k))), int)
|
||
|
|
|
||
|
|
def testComb(self):
|
||
|
|
comb = math.comb
|
||
|
|
factorial = math.factorial
|
||
|
|
# Test if factorial definition is satisfied
|
||
|
|
for n in range(100):
|
||
|
|
for k in range(n + 1):
|
||
|
|
self.assertEqual(comb(n, k), factorial(n)
|
||
|
|
// (factorial(k) * factorial(n - k)))
|
||
|
|
|
||
|
|
# Test for Pascal's identity
|
||
|
|
for n in range(1, 100):
|
||
|
|
for k in range(1, n):
|
||
|
|
self.assertEqual(comb(n, k), comb(n - 1, k - 1) + comb(n - 1, k))
|
||
|
|
|
||
|
|
# Test corner cases
|
||
|
|
for n in range(100):
|
||
|
|
self.assertEqual(comb(n, 0), 1)
|
||
|
|
self.assertEqual(comb(n, n), 1)
|
||
|
|
|
||
|
|
for n in range(1, 100):
|
||
|
|
self.assertEqual(comb(n, 1), n)
|
||
|
|
self.assertEqual(comb(n, n - 1), n)
|
||
|
|
|
||
|
|
# Test Symmetry
|
||
|
|
for n in range(100):
|
||
|
|
for k in range(n // 2):
|
||
|
|
self.assertEqual(comb(n, k), comb(n, n - k))
|
||
|
|
|
||
|
|
# Raises TypeError if any argument is non-integer or argument count is
|
||
|
|
# not 2
|
||
|
|
self.assertRaises(TypeError, comb, 10, 1.0)
|
||
|
|
self.assertRaises(TypeError, comb, 10, decimal.Decimal(1.0))
|
||
|
|
self.assertRaises(TypeError, comb, 10, "1")
|
||
|
|
self.assertRaises(TypeError, comb, 10.0, 1)
|
||
|
|
self.assertRaises(TypeError, comb, decimal.Decimal(10.0), 1)
|
||
|
|
self.assertRaises(TypeError, comb, "10", 1)
|
||
|
|
|
||
|
|
self.assertRaises(TypeError, comb, 10)
|
||
|
|
self.assertRaises(TypeError, comb, 10, 1, 3)
|
||
|
|
self.assertRaises(TypeError, comb)
|
||
|
|
|
||
|
|
# Raises Value error if not k or n are negative numbers
|
||
|
|
self.assertRaises(ValueError, comb, -1, 1)
|
||
|
|
self.assertRaises(ValueError, comb, -2**1000, 1)
|
||
|
|
self.assertRaises(ValueError, comb, 1, -1)
|
||
|
|
self.assertRaises(ValueError, comb, 1, -2**1000)
|
||
|
|
|
||
|
|
# Returns zero if k is greater than n
|
||
|
|
self.assertEqual(comb(1, 2), 0)
|
||
|
|
self.assertEqual(comb(1, 2**1000), 0)
|
||
|
|
|
||
|
|
n = 2**1000
|
||
|
|
self.assertEqual(comb(n, 0), 1)
|
||
|
|
self.assertEqual(comb(n, 1), n)
|
||
|
|
self.assertEqual(comb(n, 2), n * (n-1) // 2)
|
||
|
|
self.assertEqual(comb(n, n), 1)
|
||
|
|
self.assertEqual(comb(n, n-1), n)
|
||
|
|
self.assertEqual(comb(n, n-2), n * (n-1) // 2)
|
||
|
|
if support.check_impl_detail(cpython=True):
|
||
|
|
self.assertRaises(OverflowError, comb, n, n//2)
|
||
|
|
|
||
|
|
for n, k in (True, True), (True, False), (False, False):
|
||
|
|
self.assertEqual(comb(n, k), 1)
|
||
|
|
self.assertIs(type(comb(n, k)), int)
|
||
|
|
self.assertEqual(comb(IntSubclass(5), IntSubclass(2)), 10)
|
||
|
|
self.assertEqual(comb(MyIndexable(5), MyIndexable(2)), 10)
|
||
|
|
for k in range(3):
|
||
|
|
self.assertIs(type(comb(IntSubclass(5), IntSubclass(k))), int)
|
||
|
|
self.assertIs(type(comb(MyIndexable(5), MyIndexable(k))), int)
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def test_nextafter(self):
|
||
|
|
# around 2^52 and 2^63
|
||
|
|
self.assertEqual(math.nextafter(4503599627370496.0, -INF),
|
||
|
|
4503599627370495.5)
|
||
|
|
self.assertEqual(math.nextafter(4503599627370496.0, INF),
|
||
|
|
4503599627370497.0)
|
||
|
|
self.assertEqual(math.nextafter(9223372036854775808.0, 0.0),
|
||
|
|
9223372036854774784.0)
|
||
|
|
self.assertEqual(math.nextafter(-9223372036854775808.0, 0.0),
|
||
|
|
-9223372036854774784.0)
|
||
|
|
|
||
|
|
# around 1.0
|
||
|
|
self.assertEqual(math.nextafter(1.0, -INF),
|
||
|
|
float.fromhex('0x1.fffffffffffffp-1'))
|
||
|
|
self.assertEqual(math.nextafter(1.0, INF),
|
||
|
|
float.fromhex('0x1.0000000000001p+0'))
|
||
|
|
|
||
|
|
# x == y: y is returned
|
||
|
|
self.assertEqual(math.nextafter(2.0, 2.0), 2.0)
|
||
|
|
self.assertEqualSign(math.nextafter(-0.0, +0.0), +0.0)
|
||
|
|
self.assertEqualSign(math.nextafter(+0.0, -0.0), -0.0)
|
||
|
|
|
||
|
|
# around 0.0
|
||
|
|
smallest_subnormal = sys.float_info.min * sys.float_info.epsilon
|
||
|
|
self.assertEqual(math.nextafter(+0.0, INF), smallest_subnormal)
|
||
|
|
self.assertEqual(math.nextafter(-0.0, INF), smallest_subnormal)
|
||
|
|
self.assertEqual(math.nextafter(+0.0, -INF), -smallest_subnormal)
|
||
|
|
self.assertEqual(math.nextafter(-0.0, -INF), -smallest_subnormal)
|
||
|
|
self.assertEqualSign(math.nextafter(smallest_subnormal, +0.0), +0.0)
|
||
|
|
self.assertEqualSign(math.nextafter(-smallest_subnormal, +0.0), -0.0)
|
||
|
|
self.assertEqualSign(math.nextafter(smallest_subnormal, -0.0), +0.0)
|
||
|
|
self.assertEqualSign(math.nextafter(-smallest_subnormal, -0.0), -0.0)
|
||
|
|
|
||
|
|
# around infinity
|
||
|
|
largest_normal = sys.float_info.max
|
||
|
|
self.assertEqual(math.nextafter(INF, 0.0), largest_normal)
|
||
|
|
self.assertEqual(math.nextafter(-INF, 0.0), -largest_normal)
|
||
|
|
self.assertEqual(math.nextafter(largest_normal, INF), INF)
|
||
|
|
self.assertEqual(math.nextafter(-largest_normal, -INF), -INF)
|
||
|
|
|
||
|
|
# NaN
|
||
|
|
self.assertIsNaN(math.nextafter(NAN, 1.0))
|
||
|
|
self.assertIsNaN(math.nextafter(1.0, NAN))
|
||
|
|
self.assertIsNaN(math.nextafter(NAN, NAN))
|
||
|
|
|
||
|
|
@requires_IEEE_754
|
||
|
|
def test_ulp(self):
|
||
|
|
self.assertEqual(math.ulp(1.0), sys.float_info.epsilon)
|
||
|
|
# use int ** int rather than float ** int to not rely on pow() accuracy
|
||
|
|
self.assertEqual(math.ulp(2 ** 52), 1.0)
|
||
|
|
self.assertEqual(math.ulp(2 ** 53), 2.0)
|
||
|
|
self.assertEqual(math.ulp(2 ** 64), 4096.0)
|
||
|
|
|
||
|
|
# min and max
|
||
|
|
self.assertEqual(math.ulp(0.0),
|
||
|
|
sys.float_info.min * sys.float_info.epsilon)
|
||
|
|
self.assertEqual(math.ulp(FLOAT_MAX),
|
||
|
|
FLOAT_MAX - math.nextafter(FLOAT_MAX, -INF))
|
||
|
|
|
||
|
|
# special cases
|
||
|
|
self.assertEqual(math.ulp(INF), INF)
|
||
|
|
self.assertIsNaN(math.ulp(math.nan))
|
||
|
|
|
||
|
|
# negative number: ulp(-x) == ulp(x)
|
||
|
|
for x in (0.0, 1.0, 2 ** 52, 2 ** 64, INF):
|
||
|
|
with self.subTest(x=x):
|
||
|
|
self.assertEqual(math.ulp(-x), math.ulp(x))
|
||
|
|
|
||
|
|
def test_issue39871(self):
|
||
|
|
# A SystemError should not be raised if the first arg to atan2(),
|
||
|
|
# copysign(), or remainder() cannot be converted to a float.
|
||
|
|
class F:
|
||
|
|
def __float__(self):
|
||
|
|
self.converted = True
|
||
|
|
1/0
|
||
|
|
for func in math.atan2, math.copysign, math.remainder:
|
||
|
|
y = F()
|
||
|
|
with self.assertRaises(TypeError):
|
||
|
|
func("not a number", y)
|
||
|
|
|
||
|
|
# There should not have been any attempt to convert the second
|
||
|
|
# argument to a float.
|
||
|
|
self.assertFalse(getattr(y, "converted", False))
|
||
|
|
|
||
|
|
# Custom assertions.
|
||
|
|
|
||
|
|
def assertIsNaN(self, value):
|
||
|
|
if not math.isnan(value):
|
||
|
|
self.fail("Expected a NaN, got {!r}.".format(value))
|
||
|
|
|
||
|
|
def assertEqualSign(self, x, y):
|
||
|
|
"""Similar to assertEqual(), but compare also the sign with copysign().
|
||
|
|
|
||
|
|
Function useful to compare signed zeros.
|
||
|
|
"""
|
||
|
|
self.assertEqual(x, y)
|
||
|
|
self.assertEqual(math.copysign(1.0, x), math.copysign(1.0, y))
|
||
|
|
|
||
|
|
|
||
|
|
class IsCloseTests(unittest.TestCase):
|
||
|
|
isclose = math.isclose # subclasses should override this
|
||
|
|
|
||
|
|
def assertIsClose(self, a, b, *args, **kwargs):
|
||
|
|
self.assertTrue(self.isclose(a, b, *args, **kwargs),
|
||
|
|
msg="%s and %s should be close!" % (a, b))
|
||
|
|
|
||
|
|
def assertIsNotClose(self, a, b, *args, **kwargs):
|
||
|
|
self.assertFalse(self.isclose(a, b, *args, **kwargs),
|
||
|
|
msg="%s and %s should not be close!" % (a, b))
|
||
|
|
|
||
|
|
def assertAllClose(self, examples, *args, **kwargs):
|
||
|
|
for a, b in examples:
|
||
|
|
self.assertIsClose(a, b, *args, **kwargs)
|
||
|
|
|
||
|
|
def assertAllNotClose(self, examples, *args, **kwargs):
|
||
|
|
for a, b in examples:
|
||
|
|
self.assertIsNotClose(a, b, *args, **kwargs)
|
||
|
|
|
||
|
|
def test_negative_tolerances(self):
|
||
|
|
# ValueError should be raised if either tolerance is less than zero
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
self.assertIsClose(1, 1, rel_tol=-1e-100)
|
||
|
|
with self.assertRaises(ValueError):
|
||
|
|
self.assertIsClose(1, 1, rel_tol=1e-100, abs_tol=-1e10)
|
||
|
|
|
||
|
|
def test_identical(self):
|
||
|
|
# identical values must test as close
|
||
|
|
identical_examples = [(2.0, 2.0),
|
||
|
|
(0.1e200, 0.1e200),
|
||
|
|
(1.123e-300, 1.123e-300),
|
||
|
|
(12345, 12345.0),
|
||
|
|
(0.0, -0.0),
|
||
|
|
(345678, 345678)]
|
||
|
|
self.assertAllClose(identical_examples, rel_tol=0.0, abs_tol=0.0)
|
||
|
|
|
||
|
|
def test_eight_decimal_places(self):
|
||
|
|
# examples that are close to 1e-8, but not 1e-9
|
||
|
|
eight_decimal_places_examples = [(1e8, 1e8 + 1),
|
||
|
|
(-1e-8, -1.000000009e-8),
|
||
|
|
(1.12345678, 1.12345679)]
|
||
|
|
self.assertAllClose(eight_decimal_places_examples, rel_tol=1e-8)
|
||
|
|
self.assertAllNotClose(eight_decimal_places_examples, rel_tol=1e-9)
|
||
|
|
|
||
|
|
def test_near_zero(self):
|
||
|
|
# values close to zero
|
||
|
|
near_zero_examples = [(1e-9, 0.0),
|
||
|
|
(-1e-9, 0.0),
|
||
|
|
(-1e-150, 0.0)]
|
||
|
|
# these should not be close to any rel_tol
|
||
|
|
self.assertAllNotClose(near_zero_examples, rel_tol=0.9)
|
||
|
|
# these should be close to abs_tol=1e-8
|
||
|
|
self.assertAllClose(near_zero_examples, abs_tol=1e-8)
|
||
|
|
|
||
|
|
def test_identical_infinite(self):
|
||
|
|
# these are close regardless of tolerance -- i.e. they are equal
|
||
|
|
self.assertIsClose(INF, INF)
|
||
|
|
self.assertIsClose(INF, INF, abs_tol=0.0)
|
||
|
|
self.assertIsClose(NINF, NINF)
|
||
|
|
self.assertIsClose(NINF, NINF, abs_tol=0.0)
|
||
|
|
|
||
|
|
def test_inf_ninf_nan(self):
|
||
|
|
# these should never be close (following IEEE 754 rules for equality)
|
||
|
|
not_close_examples = [(NAN, NAN),
|
||
|
|
(NAN, 1e-100),
|
||
|
|
(1e-100, NAN),
|
||
|
|
(INF, NAN),
|
||
|
|
(NAN, INF),
|
||
|
|
(INF, NINF),
|
||
|
|
(INF, 1.0),
|
||
|
|
(1.0, INF),
|
||
|
|
(INF, 1e308),
|
||
|
|
(1e308, INF)]
|
||
|
|
# use largest reasonable tolerance
|
||
|
|
self.assertAllNotClose(not_close_examples, abs_tol=0.999999999999999)
|
||
|
|
|
||
|
|
def test_zero_tolerance(self):
|
||
|
|
# test with zero tolerance
|
||
|
|
zero_tolerance_close_examples = [(1.0, 1.0),
|
||
|
|
(-3.4, -3.4),
|
||
|
|
(-1e-300, -1e-300)]
|
||
|
|
self.assertAllClose(zero_tolerance_close_examples, rel_tol=0.0)
|
||
|
|
|
||
|
|
zero_tolerance_not_close_examples = [(1.0, 1.000000000000001),
|
||
|
|
(0.99999999999999, 1.0),
|
||
|
|
(1.0e200, .999999999999999e200)]
|
||
|
|
self.assertAllNotClose(zero_tolerance_not_close_examples, rel_tol=0.0)
|
||
|
|
|
||
|
|
def test_asymmetry(self):
|
||
|
|
# test the asymmetry example from PEP 485
|
||
|
|
self.assertAllClose([(9, 10), (10, 9)], rel_tol=0.1)
|
||
|
|
|
||
|
|
def test_integers(self):
|
||
|
|
# test with integer values
|
||
|
|
integer_examples = [(100000001, 100000000),
|
||
|
|
(123456789, 123456788)]
|
||
|
|
|
||
|
|
self.assertAllClose(integer_examples, rel_tol=1e-8)
|
||
|
|
self.assertAllNotClose(integer_examples, rel_tol=1e-9)
|
||
|
|
|
||
|
|
def test_decimals(self):
|
||
|
|
# test with Decimal values
|
||
|
|
from decimal import Decimal
|
||
|
|
|
||
|
|
decimal_examples = [(Decimal('1.00000001'), Decimal('1.0')),
|
||
|
|
(Decimal('1.00000001e-20'), Decimal('1.0e-20')),
|
||
|
|
(Decimal('1.00000001e-100'), Decimal('1.0e-100')),
|
||
|
|
(Decimal('1.00000001e20'), Decimal('1.0e20'))]
|
||
|
|
self.assertAllClose(decimal_examples, rel_tol=1e-8)
|
||
|
|
self.assertAllNotClose(decimal_examples, rel_tol=1e-9)
|
||
|
|
|
||
|
|
def test_fractions(self):
|
||
|
|
# test with Fraction values
|
||
|
|
from fractions import Fraction
|
||
|
|
|
||
|
|
fraction_examples = [
|
||
|
|
(Fraction(1, 100000000) + 1, Fraction(1)),
|
||
|
|
(Fraction(100000001), Fraction(100000000)),
|
||
|
|
(Fraction(10**8 + 1, 10**28), Fraction(1, 10**20))]
|
||
|
|
self.assertAllClose(fraction_examples, rel_tol=1e-8)
|
||
|
|
self.assertAllNotClose(fraction_examples, rel_tol=1e-9)
|
||
|
|
|
||
|
|
|
||
|
|
def test_main():
|
||
|
|
from doctest import DocFileSuite
|
||
|
|
suite = unittest.TestSuite()
|
||
|
|
suite.addTest(unittest.makeSuite(MathTests))
|
||
|
|
suite.addTest(unittest.makeSuite(IsCloseTests))
|
||
|
|
suite.addTest(DocFileSuite("ieee754.txt"))
|
||
|
|
run_unittest(suite)
|
||
|
|
|
||
|
|
if __name__ == '__main__':
|
||
|
|
test_main()
|