| # 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) |