434 lines
20 KiB
Python
434 lines
20 KiB
Python
# Tests for the correctly-rounded string -> float conversions
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# introduced in Python 2.7 and 3.1.
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import random
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import unittest
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import re
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import sys
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import test.support
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if getattr(sys, 'float_repr_style', '') != 'short':
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raise unittest.SkipTest('correctly-rounded string->float conversions '
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'not available on this system')
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# Correctly rounded str -> float in pure Python, for comparison.
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strtod_parser = re.compile(r""" # A numeric string consists of:
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(?P<sign>[-+])? # an optional sign, followed by
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(?=\d|\.\d) # a number with at least one digit
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(?P<int>\d*) # having a (possibly empty) integer part
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(?:\.(?P<frac>\d*))? # followed by an optional fractional part
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(?:E(?P<exp>[-+]?\d+))? # and an optional exponent
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\Z
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""", re.VERBOSE | re.IGNORECASE).match
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# Pure Python version of correctly rounded string->float conversion.
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# Avoids any use of floating-point by returning the result as a hex string.
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def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
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"""Convert a finite decimal string to a hex string representing an
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IEEE 754 binary64 float. Return 'inf' or '-inf' on overflow.
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This function makes no use of floating-point arithmetic at any
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stage."""
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# parse string into a pair of integers 'a' and 'b' such that
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# abs(decimal value) = a/b, along with a boolean 'negative'.
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m = strtod_parser(s)
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if m is None:
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raise ValueError('invalid numeric string')
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fraction = m.group('frac') or ''
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intpart = int(m.group('int') + fraction)
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exp = int(m.group('exp') or '0') - len(fraction)
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negative = m.group('sign') == '-'
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a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
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# quick return for zeros
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if not a:
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return '-0x0.0p+0' if negative else '0x0.0p+0'
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# compute exponent e for result; may be one too small in the case
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# that the rounded value of a/b lies in a different binade from a/b
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d = a.bit_length() - b.bit_length()
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d += (a >> d if d >= 0 else a << -d) >= b
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e = max(d, min_exp) - mant_dig
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# approximate a/b by number of the form q * 2**e; adjust e if necessary
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a, b = a << max(-e, 0), b << max(e, 0)
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q, r = divmod(a, b)
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if 2*r > b or 2*r == b and q & 1:
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q += 1
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if q.bit_length() == mant_dig+1:
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q //= 2
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e += 1
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# double check that (q, e) has the right form
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assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
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assert q.bit_length() == mant_dig or e == min_exp - mant_dig
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# check for overflow and underflow
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if e + q.bit_length() > max_exp:
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return '-inf' if negative else 'inf'
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if not q:
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return '-0x0.0p+0' if negative else '0x0.0p+0'
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# for hex representation, shift so # bits after point is a multiple of 4
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hexdigs = 1 + (mant_dig-2)//4
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shift = 3 - (mant_dig-2)%4
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q, e = q << shift, e - shift
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return '{}0x{:x}.{:0{}x}p{:+d}'.format(
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'-' if negative else '',
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q // 16**hexdigs,
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q % 16**hexdigs,
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hexdigs,
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e + 4*hexdigs)
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TEST_SIZE = 10
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class StrtodTests(unittest.TestCase):
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def check_strtod(self, s):
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"""Compare the result of Python's builtin correctly rounded
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string->float conversion (using float) to a pure Python
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correctly rounded string->float implementation. Fail if the
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two methods give different results."""
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try:
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fs = float(s)
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except OverflowError:
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got = '-inf' if s[0] == '-' else 'inf'
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except MemoryError:
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got = 'memory error'
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else:
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got = fs.hex()
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expected = strtod(s)
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self.assertEqual(expected, got,
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"Incorrectly rounded str->float conversion for {}: "
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"expected {}, got {}".format(s, expected, got))
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def test_short_halfway_cases(self):
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# exact halfway cases with a small number of significant digits
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for k in 0, 5, 10, 15, 20:
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# upper = smallest integer >= 2**54/5**k
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upper = -(-2**54//5**k)
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# lower = smallest odd number >= 2**53/5**k
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lower = -(-2**53//5**k)
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if lower % 2 == 0:
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lower += 1
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for i in range(TEST_SIZE):
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# Select a random odd n in [2**53/5**k,
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# 2**54/5**k). Then n * 10**k gives a halfway case
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# with small number of significant digits.
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n, e = random.randrange(lower, upper, 2), k
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# Remove any additional powers of 5.
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while n % 5 == 0:
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n, e = n // 5, e + 1
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assert n % 10 in (1, 3, 7, 9)
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# Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
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# until n * 2**p2 has more than 20 significant digits.
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digits, exponent = n, e
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while digits < 10**20:
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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# Same again, but with extra trailing zeros.
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s = '{}e{}'.format(digits * 10**40, exponent - 40)
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self.check_strtod(s)
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digits *= 2
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# Try numbers of the form n * 5**p2 * 10**(e - p5), p5
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# >= 0, with n * 5**p5 < 10**20.
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digits, exponent = n, e
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while digits < 10**20:
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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# Same again, but with extra trailing zeros.
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s = '{}e{}'.format(digits * 10**40, exponent - 40)
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self.check_strtod(s)
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digits *= 5
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exponent -= 1
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def test_halfway_cases(self):
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# test halfway cases for the round-half-to-even rule
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for i in range(100 * TEST_SIZE):
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# bit pattern for a random finite positive (or +0.0) float
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bits = random.randrange(2047*2**52)
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# convert bit pattern to a number of the form m * 2**e
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e, m = divmod(bits, 2**52)
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if e:
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m, e = m + 2**52, e - 1
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e -= 1074
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# add 0.5 ulps
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m, e = 2*m + 1, e - 1
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# convert to a decimal string
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if e >= 0:
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digits = m << e
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exponent = 0
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else:
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# m * 2**e = (m * 5**-e) * 10**e
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digits = m * 5**-e
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exponent = e
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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def test_boundaries(self):
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# boundaries expressed as triples (n, e, u), where
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# n*10**e is an approximation to the boundary value and
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# u*10**e is 1ulp
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boundaries = [
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(10000000000000000000, -19, 1110), # a power of 2 boundary (1.0)
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(17976931348623159077, 289, 1995), # overflow boundary (2.**1024)
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(22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022)
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(0, -327, 4941), # zero
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]
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for n, e, u in boundaries:
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for j in range(1000):
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digits = n + random.randrange(-3*u, 3*u)
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exponent = e
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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n *= 10
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u *= 10
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e -= 1
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def test_underflow_boundary(self):
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# test values close to 2**-1075, the underflow boundary; similar
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# to boundary_tests, except that the random error doesn't scale
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# with n
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for exponent in range(-400, -320):
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base = 10**-exponent // 2**1075
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for j in range(TEST_SIZE):
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digits = base + random.randrange(-1000, 1000)
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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def test_bigcomp(self):
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for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
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dig10 = 10**ndigs
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for i in range(10 * TEST_SIZE):
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digits = random.randrange(dig10)
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exponent = random.randrange(-400, 400)
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s = '{}e{}'.format(digits, exponent)
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self.check_strtod(s)
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def test_parsing(self):
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# make '0' more likely to be chosen than other digits
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digits = '000000123456789'
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signs = ('+', '-', '')
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# put together random short valid strings
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# \d*[.\d*]?e
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for i in range(1000):
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for j in range(TEST_SIZE):
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s = random.choice(signs)
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intpart_len = random.randrange(5)
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s += ''.join(random.choice(digits) for _ in range(intpart_len))
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if random.choice([True, False]):
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s += '.'
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fracpart_len = random.randrange(5)
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s += ''.join(random.choice(digits)
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for _ in range(fracpart_len))
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else:
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fracpart_len = 0
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if random.choice([True, False]):
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s += random.choice(['e', 'E'])
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s += random.choice(signs)
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exponent_len = random.randrange(1, 4)
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s += ''.join(random.choice(digits)
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for _ in range(exponent_len))
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if intpart_len + fracpart_len:
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self.check_strtod(s)
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else:
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try:
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float(s)
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except ValueError:
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pass
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else:
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assert False, "expected ValueError"
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@test.support.bigmemtest(size=test.support._2G+10, memuse=3, dry_run=False)
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def test_oversized_digit_strings(self, maxsize):
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# Input string whose length doesn't fit in an INT.
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s = "1." + "1" * maxsize
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with self.assertRaises(ValueError):
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float(s)
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del s
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s = "0." + "0" * maxsize + "1"
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with self.assertRaises(ValueError):
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float(s)
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del s
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def test_large_exponents(self):
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# Verify that the clipping of the exponent in strtod doesn't affect the
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# output values.
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def positive_exp(n):
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""" Long string with value 1.0 and exponent n"""
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return '0.{}1e+{}'.format('0'*(n-1), n)
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def negative_exp(n):
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""" Long string with value 1.0 and exponent -n"""
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return '1{}e-{}'.format('0'*n, n)
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self.assertEqual(float(positive_exp(10000)), 1.0)
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self.assertEqual(float(positive_exp(20000)), 1.0)
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self.assertEqual(float(positive_exp(30000)), 1.0)
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self.assertEqual(float(negative_exp(10000)), 1.0)
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self.assertEqual(float(negative_exp(20000)), 1.0)
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self.assertEqual(float(negative_exp(30000)), 1.0)
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def test_particular(self):
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# inputs that produced crashes or incorrectly rounded results with
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# previous versions of dtoa.c, for various reasons
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test_strings = [
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# issue 7632 bug 1, originally reported failing case
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'2183167012312112312312.23538020374420446192e-370',
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# 5 instances of issue 7632 bug 2
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'12579816049008305546974391768996369464963024663104e-357',
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'17489628565202117263145367596028389348922981857013e-357',
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'18487398785991994634182916638542680759613590482273e-357',
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'32002864200581033134358724675198044527469366773928e-358',
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'94393431193180696942841837085033647913224148539854e-358',
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'73608278998966969345824653500136787876436005957953e-358',
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'64774478836417299491718435234611299336288082136054e-358',
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'13704940134126574534878641876947980878824688451169e-357',
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'46697445774047060960624497964425416610480524760471e-358',
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# failing case for bug introduced by METD in r77451 (attempted
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# fix for issue 7632, bug 2), and fixed in r77482.
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'28639097178261763178489759107321392745108491825303e-311',
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# two numbers demonstrating a flaw in the bigcomp 'dig == 0'
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# correction block (issue 7632, bug 3)
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'1.00000000000000001e44',
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'1.0000000000000000100000000000000000000001e44',
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# dtoa.c bug for numbers just smaller than a power of 2 (issue
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# 7632, bug 4)
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'99999999999999994487665465554760717039532578546e-47',
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# failing case for off-by-one error introduced by METD in
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# r77483 (dtoa.c cleanup), fixed in r77490
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'965437176333654931799035513671997118345570045914469' #...
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'6213413350821416312194420007991306908470147322020121018368e0',
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# incorrect lsb detection for round-half-to-even when
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# bc->scale != 0 (issue 7632, bug 6).
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'104308485241983990666713401708072175773165034278685' #...
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'682646111762292409330928739751702404658197872319129' #...
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'036519947435319418387839758990478549477777586673075' #...
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'945844895981012024387992135617064532141489278815239' #...
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'849108105951619997829153633535314849999674266169258' #...
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'928940692239684771590065027025835804863585454872499' #...
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'320500023126142553932654370362024104462255244034053' #...
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'203998964360882487378334860197725139151265590832887' #...
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'433736189468858614521708567646743455601905935595381' #...
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'852723723645799866672558576993978025033590728687206' #...
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'296379801363024094048327273913079612469982585674824' #...
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'156000783167963081616214710691759864332339239688734' #...
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'656548790656486646106983450809073750535624894296242' #...
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'072010195710276073042036425579852459556183541199012' #...
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'652571123898996574563824424330960027873516082763671875e-1075',
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# demonstration that original fix for issue 7632 bug 1 was
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# buggy; the exit condition was too strong
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'247032822920623295e-341',
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# demonstrate similar problem to issue 7632 bug1: crash
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# with 'oversized quotient in quorem' message.
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'99037485700245683102805043437346965248029601286431e-373',
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'99617639833743863161109961162881027406769510558457e-373',
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'98852915025769345295749278351563179840130565591462e-372',
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'99059944827693569659153042769690930905148015876788e-373',
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'98914979205069368270421829889078356254059760327101e-372',
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# issue 7632 bug 5: the following 2 strings convert differently
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'1000000000000000000000000000000000000000e-16',
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'10000000000000000000000000000000000000000e-17',
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# issue 7632 bug 7
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'991633793189150720000000000000000000000000000000000000000e-33',
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# And another, similar, failing halfway case
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'4106250198039490000000000000000000000000000000000000000e-38',
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# issue 7632 bug 8: the following produced 10.0
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'10.900000000000000012345678912345678912345',
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# two humongous values from issue 7743
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'116512874940594195638617907092569881519034793229385' #...
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'228569165191541890846564669771714896916084883987920' #...
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'473321268100296857636200926065340769682863349205363' #...
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'349247637660671783209907949273683040397979984107806' #...
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'461822693332712828397617946036239581632976585100633' #...
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'520260770761060725403904123144384571612073732754774' #...
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'588211944406465572591022081973828448927338602556287' #...
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'851831745419397433012491884869454462440536895047499' #...
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'436551974649731917170099387762871020403582994193439' #...
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'761933412166821484015883631622539314203799034497982' #...
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'130038741741727907429575673302461380386596501187482' #...
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'006257527709842179336488381672818798450229339123527' #...
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'858844448336815912020452294624916993546388956561522' #...
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'161875352572590420823607478788399460162228308693742' #...
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'05287663441403533948204085390898399055004119873046875e-1075',
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'525440653352955266109661060358202819561258984964913' #...
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'892256527849758956045218257059713765874251436193619' #...
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'443248205998870001633865657517447355992225852945912' #...
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'016668660000210283807209850662224417504752264995360' #...
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'631512007753855801075373057632157738752800840302596' #...
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'237050247910530538250008682272783660778181628040733' #...
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'653121492436408812668023478001208529190359254322340' #...
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'397575185248844788515410722958784640926528544043090' #...
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'115352513640884988017342469275006999104519620946430' #...
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'818767147966495485406577703972687838176778993472989' #...
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'561959000047036638938396333146685137903018376496408' #...
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'319705333868476925297317136513970189073693314710318' #...
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'991252811050501448326875232850600451776091303043715' #...
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'157191292827614046876950225714743118291034780466325' #...
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'085141343734564915193426994587206432697337118211527' #...
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'278968731294639353354774788602467795167875117481660' #...
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'4738791256853675690543663283782215866825e-1180',
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# exercise exit conditions in bigcomp comparison loop
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'2602129298404963083833853479113577253105939995688e2',
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'260212929840496308383385347911357725310593999568896e0',
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'26021292984049630838338534791135772531059399956889601e-2',
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'260212929840496308383385347911357725310593999568895e0',
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'260212929840496308383385347911357725310593999568897e0',
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'260212929840496308383385347911357725310593999568996e0',
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'260212929840496308383385347911357725310593999568866e0',
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# 2**53
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'9007199254740992.00',
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# 2**1024 - 2**970: exact overflow boundary. All values
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# smaller than this should round to something finite; any value
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# greater than or equal to this one overflows.
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'179769313486231580793728971405303415079934132710037' #...
|
|
'826936173778980444968292764750946649017977587207096' #...
|
|
'330286416692887910946555547851940402630657488671505' #...
|
|
'820681908902000708383676273854845817711531764475730' #...
|
|
'270069855571366959622842914819860834936475292719074' #...
|
|
'168444365510704342711559699508093042880177904174497792',
|
|
# 2**1024 - 2**970 - tiny
|
|
'179769313486231580793728971405303415079934132710037' #...
|
|
'826936173778980444968292764750946649017977587207096' #...
|
|
'330286416692887910946555547851940402630657488671505' #...
|
|
'820681908902000708383676273854845817711531764475730' #...
|
|
'270069855571366959622842914819860834936475292719074' #...
|
|
'168444365510704342711559699508093042880177904174497791.999',
|
|
# 2**1024 - 2**970 + tiny
|
|
'179769313486231580793728971405303415079934132710037' #...
|
|
'826936173778980444968292764750946649017977587207096' #...
|
|
'330286416692887910946555547851940402630657488671505' #...
|
|
'820681908902000708383676273854845817711531764475730' #...
|
|
'270069855571366959622842914819860834936475292719074' #...
|
|
'168444365510704342711559699508093042880177904174497792.001',
|
|
# 1 - 2**-54, +-tiny
|
|
'999999999999999944488848768742172978818416595458984375e-54',
|
|
'9999999999999999444888487687421729788184165954589843749999999e-54',
|
|
'9999999999999999444888487687421729788184165954589843750000001e-54',
|
|
# Value found by Rick Regan that gives a result of 2**-968
|
|
# under Gay's dtoa.c (as of Nov 04, 2010); since fixed.
|
|
# (Fixed some time ago in Python's dtoa.c.)
|
|
'0.0000000000000000000000000000000000000000100000000' #...
|
|
'000000000576129113423785429971690421191214034235435' #...
|
|
'087147763178149762956868991692289869941246658073194' #...
|
|
'51982237978882039897143840789794921875',
|
|
]
|
|
for s in test_strings:
|
|
self.check_strtod(s)
|
|
|
|
if __name__ == "__main__":
|
|
unittest.main()
|