--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/Modules/_decimal/tests/randfloat.py Sat Mar 10 18:12:20 2012 +0100 @@ -0,0 +1,250 @@ +# Copyright (c) 2010 Python Software Foundation. All Rights Reserved. +# Adapted from Python's Lib/test/test_strtod.py (by Mark Dickinson) + +# More test cases for deccheck.py. + +import random + +TEST_SIZE = 2 + + +def test_short_halfway_cases(): + # exact halfway cases with a small number of significant digits + for k in 0, 5, 10, 15, 20: + # upper = smallest integer >= 2**54/5**k + upper = -(-2**54//5**k) + # lower = smallest odd number >= 2**53/5**k + lower = -(-2**53//5**k) + if lower % 2 == 0: + lower += 1 + for i in range(10 * TEST_SIZE): + # Select a random odd n in [2**53/5**k, + # 2**54/5**k). Then n * 10**k gives a halfway case + # with small number of significant digits. + n, e = random.randrange(lower, upper, 2), k + + # Remove any additional powers of 5. + while n % 5 == 0: + n, e = n // 5, e + 1 + assert n % 10 in (1, 3, 7, 9) + + # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0, + # until n * 2**p2 has more than 20 significant digits. + digits, exponent = n, e + while digits < 10**20: + s = '{}e{}'.format(digits, exponent) + yield s + # Same again, but with extra trailing zeros. + s = '{}e{}'.format(digits * 10**40, exponent - 40) + yield s + digits *= 2 + + # Try numbers of the form n * 5**p2 * 10**(e - p5), p5 + # >= 0, with n * 5**p5 < 10**20. + digits, exponent = n, e + while digits < 10**20: + s = '{}e{}'.format(digits, exponent) + yield s + # Same again, but with extra trailing zeros. + s = '{}e{}'.format(digits * 10**40, exponent - 40) + yield s + digits *= 5 + exponent -= 1 + +def test_halfway_cases(): + # test halfway cases for the round-half-to-even rule + for i in range(1000): + for j in range(TEST_SIZE): + # bit pattern for a random finite positive (or +0.0) float + bits = random.randrange(2047*2**52) + + # convert bit pattern to a number of the form m * 2**e + e, m = divmod(bits, 2**52) + if e: + m, e = m + 2**52, e - 1 + e -= 1074 + + # add 0.5 ulps + m, e = 2*m + 1, e - 1 + + # convert to a decimal string + if e >= 0: + digits = m << e + exponent = 0 + else: + # m * 2**e = (m * 5**-e) * 10**e + digits = m * 5**-e + exponent = e + s = '{}e{}'.format(digits, exponent) + yield s + +def test_boundaries(): + # boundaries expressed as triples (n, e, u), where + # n*10**e is an approximation to the boundary value and + # u*10**e is 1ulp + boundaries = [ + (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0) + (17976931348623159077, 289, 1995), # overflow boundary (2.**1024) + (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022) + (0, -327, 4941), # zero + ] + for n, e, u in boundaries: + for j in range(1000): + for i in range(TEST_SIZE): + digits = n + random.randrange(-3*u, 3*u) + exponent = e + s = '{}e{}'.format(digits, exponent) + yield s + n *= 10 + u *= 10 + e -= 1 + +def test_underflow_boundary(): + # test values close to 2**-1075, the underflow boundary; similar + # to boundary_tests, except that the random error doesn't scale + # with n + for exponent in range(-400, -320): + base = 10**-exponent // 2**1075 + for j in range(TEST_SIZE): + digits = base + random.randrange(-1000, 1000) + s = '{}e{}'.format(digits, exponent) + yield s + +def test_bigcomp(): + for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50: + dig10 = 10**ndigs + for i in range(100 * TEST_SIZE): + digits = random.randrange(dig10) + exponent = random.randrange(-400, 400) + s = '{}e{}'.format(digits, exponent) + yield s + +def test_parsing(): + # make '0' more likely to be chosen than other digits + digits = '000000123456789' + signs = ('+', '-', '') + + # put together random short valid strings + # \d*[.\d*]?e + for i in range(1000): + for j in range(TEST_SIZE): + s = random.choice(signs) + intpart_len = random.randrange(5) + s += ''.join(random.choice(digits) for _ in range(intpart_len)) + if random.choice([True, False]): + s += '.' + fracpart_len = random.randrange(5) + s += ''.join(random.choice(digits) + for _ in range(fracpart_len)) + else: + fracpart_len = 0 + if random.choice([True, False]): + s += random.choice(['e', 'E']) + s += random.choice(signs) + exponent_len = random.randrange(1, 4) + s += ''.join(random.choice(digits) + for _ in range(exponent_len)) + + if intpart_len + fracpart_len: + yield s + +test_particular = [ + # squares + '1.00000000100000000025', + '1.0000000000000000000000000100000000000000000000000' #... + '00025', + '1.0000000000000000000000000000000000000000000010000' #... + '0000000000000000000000000000000000000000025', + '1.0000000000000000000000000000000000000000000000000' #... + '000001000000000000000000000000000000000000000000000' #... + '000000000025', + '0.99999999900000000025', + '0.9999999999999999999999999999999999999999999999999' #... + '999000000000000000000000000000000000000000000000000' #... + '000025', + '0.9999999999999999999999999999999999999999999999999' #... + '999999999999999999999999999999999999999999999999999' #... + '999999999999999999999999999999999999999990000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '0000000000000000000000000000025', + + '1.0000000000000000000000000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '100000000000000000000000000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000001', + '1.0000000000000000000000000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '500000000000000000000000000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000005', + '1.0000000000000000000000000000000000000000000000000' #... + '000000000100000000000000000000000000000000000000000' #... + '000000000000000000250000000000000002000000000000000' #... + '000000000000000000000000000000000000000000010000000' #... + '000000000000000000000000000000000000000000000000000' #... + '0000000000000000001', + '1.0000000000000000000000000000000000000000000000000' #... + '000000000100000000000000000000000000000000000000000' #... + '000000000000000000249999999999999999999999999999999' #... + '999999999999979999999999999999999999999999999999999' #... + '999999999999999999999900000000000000000000000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '00000000000000000000000001', + + '0.9999999999999999999999999999999999999999999999999' #... + '999999999900000000000000000000000000000000000000000' #... + '000000000000000000249999999999999998000000000000000' #... + '000000000000000000000000000000000000000000010000000' #... + '000000000000000000000000000000000000000000000000000' #... + '0000000000000000001', + '0.9999999999999999999999999999999999999999999999999' #... + '999999999900000000000000000000000000000000000000000' #... + '000000000000000000250000001999999999999999999999999' #... + '999999999999999999999999999999999990000000000000000' #... + '000000000000000000000000000000000000000000000000000' #... + '1', + + # tough cases for ln etc. + '1.000000000000000000000000000000000000000000000000' #... + '00000000000000000000000000000000000000000000000000' #... + '00100000000000000000000000000000000000000000000000' #... + '00000000000000000000000000000000000000000000000000' #... + '0001', + '0.999999999999999999999999999999999999999999999999' #... + '99999999999999999999999999999999999999999999999999' #... + '99899999999999999999999999999999999999999999999999' #... + '99999999999999999999999999999999999999999999999999' #... + '99999999999999999999999999999999999999999999999999' #... + '9999' + ] + + +TESTCASES = [ + [x for x in test_short_halfway_cases()], + [x for x in test_halfway_cases()], + [x for x in test_boundaries()], + [x for x in test_underflow_boundary()], + [x for x in test_bigcomp()], + [x for x in test_parsing()], + test_particular +] + +def un_randfloat(): + for i in range(1000): + l = random.choice(TESTCASES[:6]) + yield random.choice(l) + for v in test_particular: + yield v + +def bin_randfloat(): + for i in range(1000): + l1 = random.choice(TESTCASES) + l2 = random.choice(TESTCASES) + yield random.choice(l1), random.choice(l2) + +def tern_randfloat(): + for i in range(1000): + l1 = random.choice(TESTCASES) + l2 = random.choice(TESTCASES) + l3 = random.choice(TESTCASES) + yield random.choice(l1), random.choice(l2), random.choice(l3)