| 1 | # Tests for the correctly-rounded string -> float conversions
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| 2 | # introduced in Python 2.7 and 3.1.
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| 3 |
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| 4 | import random
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| 5 | import struct
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| 6 | import unittest
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| 7 | import re
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| 8 | import sys
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| 9 | from test import test_support
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| 10 |
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| 11 | if getattr(sys, 'float_repr_style', '') != 'short':
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| 12 | raise unittest.SkipTest('correctly-rounded string->float conversions '
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| 13 | 'not available on this system')
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| 14 |
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| 15 | # Correctly rounded str -> float in pure Python, for comparison.
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| 16 |
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| 17 | strtod_parser = re.compile(r""" # A numeric string consists of:
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| 18 | (?P<sign>[-+])? # an optional sign, followed by
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| 19 | (?=\d|\.\d) # a number with at least one digit
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| 20 | (?P<int>\d*) # having a (possibly empty) integer part
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| 21 | (?:\.(?P<frac>\d*))? # followed by an optional fractional part
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| 22 | (?:E(?P<exp>[-+]?\d+))? # and an optional exponent
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| 23 | \Z
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| 24 | """, re.VERBOSE | re.IGNORECASE).match
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| 25 |
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| 26 | # Pure Python version of correctly rounded string->float conversion.
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| 27 | # Avoids any use of floating-point by returning the result as a hex string.
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| 28 | def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
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| 29 | """Convert a finite decimal string to a hex string representing an
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| 30 | IEEE 754 binary64 float. Return 'inf' or '-inf' on overflow.
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| 31 | This function makes no use of floating-point arithmetic at any
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| 32 | stage."""
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| 33 |
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| 34 | # parse string into a pair of integers 'a' and 'b' such that
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| 35 | # abs(decimal value) = a/b, along with a boolean 'negative'.
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| 36 | m = strtod_parser(s)
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| 37 | if m is None:
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| 38 | raise ValueError('invalid numeric string')
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| 39 | fraction = m.group('frac') or ''
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| 40 | intpart = int(m.group('int') + fraction)
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| 41 | exp = int(m.group('exp') or '0') - len(fraction)
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| 42 | negative = m.group('sign') == '-'
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| 43 | a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
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| 44 |
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| 45 | # quick return for zeros
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| 46 | if not a:
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| 47 | return '-0x0.0p+0' if negative else '0x0.0p+0'
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| 48 |
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| 49 | # compute exponent e for result; may be one too small in the case
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| 50 | # that the rounded value of a/b lies in a different binade from a/b
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| 51 | d = a.bit_length() - b.bit_length()
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| 52 | d += (a >> d if d >= 0 else a << -d) >= b
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| 53 | e = max(d, min_exp) - mant_dig
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| 54 |
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| 55 | # approximate a/b by number of the form q * 2**e; adjust e if necessary
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| 56 | a, b = a << max(-e, 0), b << max(e, 0)
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| 57 | q, r = divmod(a, b)
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| 58 | if 2*r > b or 2*r == b and q & 1:
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| 59 | q += 1
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| 60 | if q.bit_length() == mant_dig+1:
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| 61 | q //= 2
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| 62 | e += 1
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| 63 |
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| 64 | # double check that (q, e) has the right form
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| 65 | assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
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| 66 | assert q.bit_length() == mant_dig or e == min_exp - mant_dig
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| 67 |
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| 68 | # check for overflow and underflow
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| 69 | if e + q.bit_length() > max_exp:
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| 70 | return '-inf' if negative else 'inf'
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| 71 | if not q:
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| 72 | return '-0x0.0p+0' if negative else '0x0.0p+0'
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| 73 |
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| 74 | # for hex representation, shift so # bits after point is a multiple of 4
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| 75 | hexdigs = 1 + (mant_dig-2)//4
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| 76 | shift = 3 - (mant_dig-2)%4
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| 77 | q, e = q << shift, e - shift
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| 78 | return '{}0x{:x}.{:0{}x}p{:+d}'.format(
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| 79 | '-' if negative else '',
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| 80 | q // 16**hexdigs,
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| 81 | q % 16**hexdigs,
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| 82 | hexdigs,
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| 83 | e + 4*hexdigs)
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| 84 |
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| 85 | TEST_SIZE = 10
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| 86 |
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| 87 | class StrtodTests(unittest.TestCase):
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| 88 | def check_strtod(self, s):
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| 89 | """Compare the result of Python's builtin correctly rounded
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| 90 | string->float conversion (using float) to a pure Python
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| 91 | correctly rounded string->float implementation. Fail if the
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| 92 | two methods give different results."""
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| 93 |
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| 94 | try:
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| 95 | fs = float(s)
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| 96 | except OverflowError:
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| 97 | got = '-inf' if s[0] == '-' else 'inf'
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| 98 | except MemoryError:
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| 99 | got = 'memory error'
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| 100 | else:
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| 101 | got = fs.hex()
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| 102 | expected = strtod(s)
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| 103 | self.assertEqual(expected, got,
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| 104 | "Incorrectly rounded str->float conversion for {}: "
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| 105 | "expected {}, got {}".format(s, expected, got))
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| 106 |
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| 107 | def test_short_halfway_cases(self):
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| 108 | # exact halfway cases with a small number of significant digits
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| 109 | for k in 0, 5, 10, 15, 20:
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| 110 | # upper = smallest integer >= 2**54/5**k
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| 111 | upper = -(-2**54//5**k)
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| 112 | # lower = smallest odd number >= 2**53/5**k
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| 113 | lower = -(-2**53//5**k)
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| 114 | if lower % 2 == 0:
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| 115 | lower += 1
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| 116 | for i in xrange(TEST_SIZE):
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| 117 | # Select a random odd n in [2**53/5**k,
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| 118 | # 2**54/5**k). Then n * 10**k gives a halfway case
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| 119 | # with small number of significant digits.
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| 120 | n, e = random.randrange(lower, upper, 2), k
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| 121 |
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| 122 | # Remove any additional powers of 5.
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| 123 | while n % 5 == 0:
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| 124 | n, e = n // 5, e + 1
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| 125 | assert n % 10 in (1, 3, 7, 9)
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| 126 |
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| 127 | # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
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| 128 | # until n * 2**p2 has more than 20 significant digits.
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| 129 | digits, exponent = n, e
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| 130 | while digits < 10**20:
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| 131 | s = '{}e{}'.format(digits, exponent)
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| 132 | self.check_strtod(s)
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| 133 | # Same again, but with extra trailing zeros.
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| 134 | s = '{}e{}'.format(digits * 10**40, exponent - 40)
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| 135 | self.check_strtod(s)
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| 136 | digits *= 2
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| 137 |
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| 138 | # Try numbers of the form n * 5**p2 * 10**(e - p5), p5
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| 139 | # >= 0, with n * 5**p5 < 10**20.
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| 140 | digits, exponent = n, e
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| 141 | while digits < 10**20:
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| 142 | s = '{}e{}'.format(digits, exponent)
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| 143 | self.check_strtod(s)
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| 144 | # Same again, but with extra trailing zeros.
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| 145 | s = '{}e{}'.format(digits * 10**40, exponent - 40)
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| 146 | self.check_strtod(s)
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| 147 | digits *= 5
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| 148 | exponent -= 1
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| 149 |
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| 150 | def test_halfway_cases(self):
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| 151 | # test halfway cases for the round-half-to-even rule
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| 152 | for i in xrange(100 * TEST_SIZE):
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| 153 | # bit pattern for a random finite positive (or +0.0) float
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| 154 | bits = random.randrange(2047*2**52)
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| 155 |
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| 156 | # convert bit pattern to a number of the form m * 2**e
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| 157 | e, m = divmod(bits, 2**52)
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| 158 | if e:
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| 159 | m, e = m + 2**52, e - 1
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| 160 | e -= 1074
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| 161 |
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| 162 | # add 0.5 ulps
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| 163 | m, e = 2*m + 1, e - 1
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| 164 |
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| 165 | # convert to a decimal string
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| 166 | if e >= 0:
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| 167 | digits = m << e
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| 168 | exponent = 0
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| 169 | else:
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| 170 | # m * 2**e = (m * 5**-e) * 10**e
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| 171 | digits = m * 5**-e
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| 172 | exponent = e
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| 173 | s = '{}e{}'.format(digits, exponent)
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| 174 | self.check_strtod(s)
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| 175 |
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| 176 | def test_boundaries(self):
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| 177 | # boundaries expressed as triples (n, e, u), where
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| 178 | # n*10**e is an approximation to the boundary value and
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| 179 | # u*10**e is 1ulp
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| 180 | boundaries = [
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| 181 | (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0)
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| 182 | (17976931348623159077, 289, 1995), # overflow boundary (2.**1024)
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| 183 | (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022)
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| 184 | (0, -327, 4941), # zero
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| 185 | ]
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| 186 | for n, e, u in boundaries:
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| 187 | for j in xrange(1000):
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| 188 | digits = n + random.randrange(-3*u, 3*u)
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| 189 | exponent = e
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| 190 | s = '{}e{}'.format(digits, exponent)
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| 191 | self.check_strtod(s)
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| 192 | n *= 10
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| 193 | u *= 10
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| 194 | e -= 1
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| 195 |
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| 196 | def test_underflow_boundary(self):
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| 197 | # test values close to 2**-1075, the underflow boundary; similar
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| 198 | # to boundary_tests, except that the random error doesn't scale
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| 199 | # with n
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| 200 | for exponent in xrange(-400, -320):
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| 201 | base = 10**-exponent // 2**1075
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| 202 | for j in xrange(TEST_SIZE):
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| 203 | digits = base + random.randrange(-1000, 1000)
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| 204 | s = '{}e{}'.format(digits, exponent)
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| 205 | self.check_strtod(s)
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| 206 |
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| 207 | def test_bigcomp(self):
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| 208 | for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
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| 209 | dig10 = 10**ndigs
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| 210 | for i in xrange(10 * TEST_SIZE):
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| 211 | digits = random.randrange(dig10)
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| 212 | exponent = random.randrange(-400, 400)
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| 213 | s = '{}e{}'.format(digits, exponent)
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| 214 | self.check_strtod(s)
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| 215 |
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| 216 | def test_parsing(self):
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| 217 | # make '0' more likely to be chosen than other digits
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| 218 | digits = '000000123456789'
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| 219 | signs = ('+', '-', '')
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| 220 |
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| 221 | # put together random short valid strings
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| 222 | # \d*[.\d*]?e
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| 223 | for i in xrange(1000):
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| 224 | for j in xrange(TEST_SIZE):
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| 225 | s = random.choice(signs)
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| 226 | intpart_len = random.randrange(5)
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| 227 | s += ''.join(random.choice(digits) for _ in xrange(intpart_len))
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| 228 | if random.choice([True, False]):
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| 229 | s += '.'
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| 230 | fracpart_len = random.randrange(5)
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| 231 | s += ''.join(random.choice(digits)
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| 232 | for _ in xrange(fracpart_len))
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| 233 | else:
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| 234 | fracpart_len = 0
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| 235 | if random.choice([True, False]):
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| 236 | s += random.choice(['e', 'E'])
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| 237 | s += random.choice(signs)
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| 238 | exponent_len = random.randrange(1, 4)
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| 239 | s += ''.join(random.choice(digits)
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| 240 | for _ in xrange(exponent_len))
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| 241 |
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| 242 | if intpart_len + fracpart_len:
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| 243 | self.check_strtod(s)
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| 244 | else:
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| 245 | try:
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| 246 | float(s)
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| 247 | except ValueError:
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| 248 | pass
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| 249 | else:
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| 250 | assert False, "expected ValueError"
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| 251 |
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| 252 | def test_particular(self):
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| 253 | # inputs that produced crashes or incorrectly rounded results with
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| 254 | # previous versions of dtoa.c, for various reasons
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| 255 | test_strings = [
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| 256 | # issue 7632 bug 1, originally reported failing case
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| 257 | '2183167012312112312312.23538020374420446192e-370',
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| 258 | # 5 instances of issue 7632 bug 2
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| 259 | '12579816049008305546974391768996369464963024663104e-357',
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| 260 | '17489628565202117263145367596028389348922981857013e-357',
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| 261 | '18487398785991994634182916638542680759613590482273e-357',
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| 262 | '32002864200581033134358724675198044527469366773928e-358',
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| 263 | '94393431193180696942841837085033647913224148539854e-358',
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| 264 | '73608278998966969345824653500136787876436005957953e-358',
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| 265 | '64774478836417299491718435234611299336288082136054e-358',
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| 266 | '13704940134126574534878641876947980878824688451169e-357',
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| 267 | '46697445774047060960624497964425416610480524760471e-358',
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| 268 | # failing case for bug introduced by METD in r77451 (attempted
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| 269 | # fix for issue 7632, bug 2), and fixed in r77482.
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| 270 | '28639097178261763178489759107321392745108491825303e-311',
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| 271 | # two numbers demonstrating a flaw in the bigcomp 'dig == 0'
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| 272 | # correction block (issue 7632, bug 3)
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| 273 | '1.00000000000000001e44',
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| 274 | '1.0000000000000000100000000000000000000001e44',
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| 275 | # dtoa.c bug for numbers just smaller than a power of 2 (issue
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| 276 | # 7632, bug 4)
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| 277 | '99999999999999994487665465554760717039532578546e-47',
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| 278 | # failing case for off-by-one error introduced by METD in
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| 279 | # r77483 (dtoa.c cleanup), fixed in r77490
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| 280 | '965437176333654931799035513671997118345570045914469' #...
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| 281 | '6213413350821416312194420007991306908470147322020121018368e0',
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| 282 | # incorrect lsb detection for round-half-to-even when
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| 283 | # bc->scale != 0 (issue 7632, bug 6).
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| 284 | '104308485241983990666713401708072175773165034278685' #...
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| 285 | '682646111762292409330928739751702404658197872319129' #...
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| 286 | '036519947435319418387839758990478549477777586673075' #...
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| 287 | '945844895981012024387992135617064532141489278815239' #...
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| 288 | '849108105951619997829153633535314849999674266169258' #...
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| 289 | '928940692239684771590065027025835804863585454872499' #...
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| 290 | '320500023126142553932654370362024104462255244034053' #...
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| 291 | '203998964360882487378334860197725139151265590832887' #...
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| 292 | '433736189468858614521708567646743455601905935595381' #...
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| 293 | '852723723645799866672558576993978025033590728687206' #...
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| 294 | '296379801363024094048327273913079612469982585674824' #...
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| 295 | '156000783167963081616214710691759864332339239688734' #...
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| 296 | '656548790656486646106983450809073750535624894296242' #...
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| 297 | '072010195710276073042036425579852459556183541199012' #...
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| 298 | '652571123898996574563824424330960027873516082763671875e-1075',
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| 299 | # demonstration that original fix for issue 7632 bug 1 was
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| 300 | # buggy; the exit condition was too strong
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| 301 | '247032822920623295e-341',
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| 302 | # demonstrate similar problem to issue 7632 bug1: crash
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| 303 | # with 'oversized quotient in quorem' message.
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| 304 | '99037485700245683102805043437346965248029601286431e-373',
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| 305 | '99617639833743863161109961162881027406769510558457e-373',
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| 306 | '98852915025769345295749278351563179840130565591462e-372',
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| 307 | '99059944827693569659153042769690930905148015876788e-373',
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| 308 | '98914979205069368270421829889078356254059760327101e-372',
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| 309 | # issue 7632 bug 5: the following 2 strings convert differently
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| 310 | '1000000000000000000000000000000000000000e-16',
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| 311 | '10000000000000000000000000000000000000000e-17',
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| 312 | # issue 7632 bug 7
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| 313 | '991633793189150720000000000000000000000000000000000000000e-33',
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| 314 | # And another, similar, failing halfway case
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| 315 | '4106250198039490000000000000000000000000000000000000000e-38',
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| 316 | # issue 7632 bug 8: the following produced 10.0
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| 317 | '10.900000000000000012345678912345678912345',
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| 318 |
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| 319 | # two humongous values from issue 7743
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| 320 | '116512874940594195638617907092569881519034793229385' #...
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| 321 | '228569165191541890846564669771714896916084883987920' #...
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| 322 | '473321268100296857636200926065340769682863349205363' #...
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| 323 | '349247637660671783209907949273683040397979984107806' #...
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| 324 | '461822693332712828397617946036239581632976585100633' #...
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| 325 | '520260770761060725403904123144384571612073732754774' #...
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| 326 | '588211944406465572591022081973828448927338602556287' #...
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| 327 | '851831745419397433012491884869454462440536895047499' #...
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| 328 | '436551974649731917170099387762871020403582994193439' #...
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| 329 | '761933412166821484015883631622539314203799034497982' #...
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| 330 | '130038741741727907429575673302461380386596501187482' #...
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| 331 | '006257527709842179336488381672818798450229339123527' #...
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| 332 | '858844448336815912020452294624916993546388956561522' #...
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| 333 | '161875352572590420823607478788399460162228308693742' #...
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| 334 | '05287663441403533948204085390898399055004119873046875e-1075',
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| 335 |
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| 336 | '525440653352955266109661060358202819561258984964913' #...
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| 337 | '892256527849758956045218257059713765874251436193619' #...
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| 338 | '443248205998870001633865657517447355992225852945912' #...
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| 339 | '016668660000210283807209850662224417504752264995360' #...
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| 340 | '631512007753855801075373057632157738752800840302596' #...
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| 341 | '237050247910530538250008682272783660778181628040733' #...
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| 342 | '653121492436408812668023478001208529190359254322340' #...
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| 343 | '397575185248844788515410722958784640926528544043090' #...
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| 344 | '115352513640884988017342469275006999104519620946430' #...
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| 345 | '818767147966495485406577703972687838176778993472989' #...
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| 346 | '561959000047036638938396333146685137903018376496408' #...
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| 347 | '319705333868476925297317136513970189073693314710318' #...
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|---|
| 348 | '991252811050501448326875232850600451776091303043715' #...
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|---|
| 349 | '157191292827614046876950225714743118291034780466325' #...
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|---|
| 350 | '085141343734564915193426994587206432697337118211527' #...
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|---|
| 351 | '278968731294639353354774788602467795167875117481660' #...
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| 352 | '4738791256853675690543663283782215866825e-1180',
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| 353 |
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| 354 | # exercise exit conditions in bigcomp comparison loop
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| 355 | '2602129298404963083833853479113577253105939995688e2',
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| 356 | '260212929840496308383385347911357725310593999568896e0',
|
|---|
| 357 | '26021292984049630838338534791135772531059399956889601e-2',
|
|---|
| 358 | '260212929840496308383385347911357725310593999568895e0',
|
|---|
| 359 | '260212929840496308383385347911357725310593999568897e0',
|
|---|
| 360 | '260212929840496308383385347911357725310593999568996e0',
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| 361 | '260212929840496308383385347911357725310593999568866e0',
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| 362 | # 2**53
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| 363 | '9007199254740992.00',
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| 364 | # 2**1024 - 2**970: exact overflow boundary. All values
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| 365 | # smaller than this should round to something finite; any value
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| 366 | # greater than or equal to this one overflows.
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| 367 | '179769313486231580793728971405303415079934132710037' #...
|
|---|
| 368 | '826936173778980444968292764750946649017977587207096' #...
|
|---|
| 369 | '330286416692887910946555547851940402630657488671505' #...
|
|---|
| 370 | '820681908902000708383676273854845817711531764475730' #...
|
|---|
| 371 | '270069855571366959622842914819860834936475292719074' #...
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| 372 | '168444365510704342711559699508093042880177904174497792',
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| 373 | # 2**1024 - 2**970 - tiny
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|---|
| 374 | '179769313486231580793728971405303415079934132710037' #...
|
|---|
| 375 | '826936173778980444968292764750946649017977587207096' #...
|
|---|
| 376 | '330286416692887910946555547851940402630657488671505' #...
|
|---|
| 377 | '820681908902000708383676273854845817711531764475730' #...
|
|---|
| 378 | '270069855571366959622842914819860834936475292719074' #...
|
|---|
| 379 | '168444365510704342711559699508093042880177904174497791.999',
|
|---|
| 380 | # 2**1024 - 2**970 + tiny
|
|---|
| 381 | '179769313486231580793728971405303415079934132710037' #...
|
|---|
| 382 | '826936173778980444968292764750946649017977587207096' #...
|
|---|
| 383 | '330286416692887910946555547851940402630657488671505' #...
|
|---|
| 384 | '820681908902000708383676273854845817711531764475730' #...
|
|---|
| 385 | '270069855571366959622842914819860834936475292719074' #...
|
|---|
| 386 | '168444365510704342711559699508093042880177904174497792.001',
|
|---|
| 387 | # 1 - 2**-54, +-tiny
|
|---|
| 388 | '999999999999999944488848768742172978818416595458984375e-54',
|
|---|
| 389 | '9999999999999999444888487687421729788184165954589843749999999e-54',
|
|---|
| 390 | '9999999999999999444888487687421729788184165954589843750000001e-54',
|
|---|
| 391 | ]
|
|---|
| 392 | for s in test_strings:
|
|---|
| 393 | self.check_strtod(s)
|
|---|
| 394 |
|
|---|
| 395 | def test_main():
|
|---|
| 396 | test_support.run_unittest(StrtodTests)
|
|---|
| 397 |
|
|---|
| 398 | if __name__ == "__main__":
|
|---|
| 399 | test_main()
|
|---|
