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Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk ........ r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line Add comments explaining the role of the bigcomp function in dtoa.c. ........ r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line Clarify that sulp expects a nonnegative input, but that +0.0 is fine. ........ r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line Simplify and annotate the bigcomp function, removing unused special cases. ........ r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line Fix buggy comparison: LHS of comparison was being treated as unsigned. ........ r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line More dtoa.c cleanup; remove the need for bc.dplen, bc.dp0 and bc.dp1. ........ r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line Fix off-by-one error introduced in r77483. I have a test for this, but it currently fails due to a different dtoa.c bug; I'll add the test once that bug is fixed. ........ r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding. Tests to follow. ........ r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line Issue 7632: fix incorrect rounding for long input strings with values very close to a power of 2. (See Bug 4 in the tracker discussion.) ........ r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line Issue #7632: add tests for bugs fixed so far. ........
This commit is contained in:
Mark Dickinson
parent
ae5465a578
commit
853c3bbc4c
269
Lib/test/test_strtod.py
Normal file
269
Lib/test/test_strtod.py
Normal file
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@ -0,0 +1,269 @@
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# 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 struct
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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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# 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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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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@unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
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"applies only when using short float repr style")
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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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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_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(1000):
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for j in range(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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# for the moment, ignore errors from trailing zeros
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if digits % 10 == 0:
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continue
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self.check_strtod(s)
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# get expected answer via struct, to triple check
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#fs = struct.unpack('<d', struct.pack('<Q', bits + (bits&1)))[0]
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#self.assertEqual(fs, float(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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for i in range(TEST_SIZE):
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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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DIG10 = 10**50
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for i in range(1000):
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for j in range(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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digits = tuple(map(str, range(10)))
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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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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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# 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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# 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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]
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for s in test_strings:
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self.check_strtod(s)
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def test_main():
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test.support.run_unittest(StrtodTests)
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if __name__ == "__main__":
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test_main()
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266
Python/dtoa.c
266
Python/dtoa.c
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@ -270,7 +270,7 @@ typedef union { double d; ULong L[2]; } U;
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typedef struct BCinfo BCinfo;
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struct
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BCinfo {
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int dp0, dp1, dplen, dsign, e0, nd, nd0, scale;
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int dsign, e0, nd, nd0, scale;
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};
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#define FFFFFFFF 0xffffffffUL
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@ -437,7 +437,7 @@ multadd(Bigint *b, int m, int a) /* multiply by m and add a */
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NULL on failure. */
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static Bigint *
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s2b(const char *s, int nd0, int nd, ULong y9, int dplen)
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s2b(const char *s, int nd0, int nd, ULong y9)
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{
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Bigint *b;
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int i, k;
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@ -451,18 +451,16 @@ s2b(const char *s, int nd0, int nd, ULong y9, int dplen)
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b->x[0] = y9;
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b->wds = 1;
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i = 9;
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if (9 < nd0) {
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s += 9;
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do {
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b = multadd(b, 10, *s++ - '0');
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||||
if (b == NULL)
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return NULL;
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} while(++i < nd0);
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s += dplen;
|
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if (nd <= 9)
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return b;
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|
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s += 9;
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for (i = 9; i < nd0; i++) {
|
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b = multadd(b, 10, *s++ - '0');
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||||
if (b == NULL)
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return NULL;
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}
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else
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s += dplen + 9;
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s++;
|
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for(; i < nd; i++) {
|
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b = multadd(b, 10, *s++ - '0');
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if (b == NULL)
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|
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@ -1130,76 +1128,120 @@ quorem(Bigint *b, Bigint *S)
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return q;
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}
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/* version of ulp(x) that takes bc.scale into account.
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/* sulp(x) is a version of ulp(x) that takes bc.scale into account.
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|
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Assuming that x is finite and nonzero, and x / 2^bc.scale is exactly
|
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representable as a double, sulp(x) is equivalent to 2^bc.scale * ulp(x /
|
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2^bc.scale). */
|
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Assuming that x is finite and nonnegative (positive zero is fine
|
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here) and x / 2^bc.scale is exactly representable as a double,
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sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */
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|
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static double
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sulp(U *x, BCinfo *bc)
|
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{
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U u;
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|
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if (bc->scale && 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift) > 0) {
|
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if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) {
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/* rv/2^bc->scale is subnormal */
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word0(&u) = (P+2)*Exp_msk1;
|
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word1(&u) = 0;
|
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return u.d;
|
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}
|
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else
|
||||
else {
|
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assert(word0(x) || word1(x)); /* x != 0.0 */
|
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return ulp(x);
|
||||
}
|
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}
|
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|
||||
/* return 0 on success, -1 on failure */
|
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/* The bigcomp function handles some hard cases for strtod, for inputs
|
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with more than STRTOD_DIGLIM digits. It's called once an initial
|
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estimate for the double corresponding to the input string has
|
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already been obtained by the code in _Py_dg_strtod.
|
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|
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The bigcomp function is only called after _Py_dg_strtod has found a
|
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double value rv such that either rv or rv + 1ulp represents the
|
||||
correctly rounded value corresponding to the original string. It
|
||||
determines which of these two values is the correct one by
|
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computing the decimal digits of rv + 0.5ulp and comparing them with
|
||||
the corresponding digits of s0.
|
||||
|
||||
In the following, write dv for the absolute value of the number represented
|
||||
by the input string.
|
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|
||||
Inputs:
|
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|
||||
s0 points to the first significant digit of the input string.
|
||||
|
||||
rv is a (possibly scaled) estimate for the closest double value to the
|
||||
value represented by the original input to _Py_dg_strtod. If
|
||||
bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to
|
||||
the input value.
|
||||
|
||||
bc is a struct containing information gathered during the parsing and
|
||||
estimation steps of _Py_dg_strtod. Description of fields follows:
|
||||
|
||||
bc->dsign is 1 if rv < decimal value, 0 if rv >= decimal value. In
|
||||
normal use, it should almost always be 1 when bigcomp is entered.
|
||||
|
||||
bc->e0 gives the exponent of the input value, such that dv = (integer
|
||||
given by the bd->nd digits of s0) * 10**e0
|
||||
|
||||
bc->nd gives the total number of significant digits of s0. It will
|
||||
be at least 1.
|
||||
|
||||
bc->nd0 gives the number of significant digits of s0 before the
|
||||
decimal separator. If there's no decimal separator, bc->nd0 ==
|
||||
bc->nd.
|
||||
|
||||
bc->scale is the value used to scale rv to avoid doing arithmetic with
|
||||
subnormal values. It's either 0 or 2*P (=106).
|
||||
|
||||
Outputs:
|
||||
|
||||
On successful exit, rv/2^(bc->scale) is the closest double to dv.
|
||||
|
||||
Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */
|
||||
|
||||
static int
|
||||
bigcomp(U *rv, const char *s0, BCinfo *bc)
|
||||
{
|
||||
Bigint *b, *d;
|
||||
int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
|
||||
int b2, bbits, d2, dd, i, nd, nd0, odd, p2, p5;
|
||||
|
||||
dsign = bc->dsign;
|
||||
dd = 0; /* silence compiler warning about possibly unused variable */
|
||||
nd = bc->nd;
|
||||
nd0 = bc->nd0;
|
||||
p5 = nd + bc->e0;
|
||||
speccase = 0;
|
||||
if (rv->d == 0.) { /* special case: value near underflow-to-zero */
|
||||
/* threshold was rounded to zero */
|
||||
b = i2b(1);
|
||||
if (rv->d == 0.) {
|
||||
/* special case because d2b doesn't handle 0.0 */
|
||||
b = i2b(0);
|
||||
if (b == NULL)
|
||||
return -1;
|
||||
p2 = Emin - P + 1;
|
||||
bbits = 1;
|
||||
word0(rv) = (P+2) << Exp_shift;
|
||||
i = 0;
|
||||
{
|
||||
speccase = 1;
|
||||
--p2;
|
||||
dsign = 0;
|
||||
goto have_i;
|
||||
}
|
||||
p2 = Emin - P + 1; /* = -1074 for IEEE 754 binary64 */
|
||||
bbits = 0;
|
||||
}
|
||||
else
|
||||
{
|
||||
else {
|
||||
b = d2b(rv, &p2, &bbits);
|
||||
if (b == NULL)
|
||||
return -1;
|
||||
p2 -= bc->scale;
|
||||
}
|
||||
p2 -= bc->scale;
|
||||
/* floor(log2(rv)) == bbits - 1 + p2 */
|
||||
/* Check for denormal case. */
|
||||
/* now rv/2^(bc->scale) = b * 2**p2, and b has bbits significant bits */
|
||||
|
||||
/* Replace (b, p2) by (b << i, p2 - i), with i the largest integer such
|
||||
that b << i has at most P significant bits and p2 - i >= Emin - P +
|
||||
1. */
|
||||
i = P - bbits;
|
||||
if (i > (j = P - Emin - 1 + p2)) {
|
||||
i = j;
|
||||
}
|
||||
{
|
||||
b = lshift(b, ++i);
|
||||
if (b == NULL)
|
||||
return -1;
|
||||
b->x[0] |= 1;
|
||||
}
|
||||
have_i:
|
||||
if (i > p2 - (Emin - P + 1))
|
||||
i = p2 - (Emin - P + 1);
|
||||
/* increment i so that we shift b by an extra bit; then or-ing a 1 into
|
||||
the lsb of b gives us rv/2^(bc->scale) + 0.5ulp. */
|
||||
b = lshift(b, ++i);
|
||||
if (b == NULL)
|
||||
return -1;
|
||||
/* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway
|
||||
case, this is used for round to even. */
|
||||
odd = b->x[0] & 2;
|
||||
b->x[0] |= 1;
|
||||
|
||||
p2 -= p5 + i;
|
||||
d = i2b(1);
|
||||
if (d == NULL) {
|
||||
|
|
@ -1247,92 +1289,58 @@ bigcomp(U *rv, const char *s0, BCinfo *bc)
|
|||
}
|
||||
}
|
||||
|
||||
/* Now 10*b/d = exactly half-way between the two floating-point values
|
||||
on either side of the input string. If b >= d, round down. */
|
||||
/* if b >= d, round down */
|
||||
if (cmp(b, d) >= 0) {
|
||||
dd = -1;
|
||||
goto ret;
|
||||
}
|
||||
|
||||
/* Compute first digit of 10*b/d. */
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
dig = quorem(b, d);
|
||||
assert(dig < 10);
|
||||
|
||||
/* Compare b/d with s0 */
|
||||
|
||||
assert(nd > 0);
|
||||
dd = 9999; /* silence gcc compiler warning */
|
||||
for(i = 0; i < nd0; ) {
|
||||
if ((dd = s0[i++] - '0' - dig))
|
||||
goto ret;
|
||||
if (!b->x[0] && b->wds == 1) {
|
||||
if (i < nd)
|
||||
dd = 1;
|
||||
goto ret;
|
||||
}
|
||||
for(i = 0; i < nd0; i++) {
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
dig = quorem(b,d);
|
||||
dd = *s0++ - '0' - quorem(b, d);
|
||||
if (dd)
|
||||
goto ret;
|
||||
if (!b->x[0] && b->wds == 1) {
|
||||
if (i < nd - 1)
|
||||
dd = 1;
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
for(j = bc->dp1; i++ < nd;) {
|
||||
if ((dd = s0[j++] - '0' - dig))
|
||||
goto ret;
|
||||
if (!b->x[0] && b->wds == 1) {
|
||||
if (i < nd)
|
||||
dd = 1;
|
||||
goto ret;
|
||||
}
|
||||
s0++;
|
||||
for(; i < nd; i++) {
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
dig = quorem(b,d);
|
||||
dd = *s0++ - '0' - quorem(b, d);
|
||||
if (dd)
|
||||
goto ret;
|
||||
if (!b->x[0] && b->wds == 1) {
|
||||
if (i < nd - 1)
|
||||
dd = 1;
|
||||
goto ret;
|
||||
}
|
||||
}
|
||||
if (b->x[0] || b->wds > 1)
|
||||
dd = -1;
|
||||
ret:
|
||||
Bfree(b);
|
||||
Bfree(d);
|
||||
if (speccase) {
|
||||
if (dd <= 0)
|
||||
rv->d = 0.;
|
||||
}
|
||||
else if (dd < 0) {
|
||||
if (!dsign) /* does not happen for round-near */
|
||||
retlow1:
|
||||
dval(rv) -= sulp(rv, bc);
|
||||
}
|
||||
else if (dd > 0) {
|
||||
if (dsign) {
|
||||
rethi1:
|
||||
dval(rv) += sulp(rv, bc);
|
||||
}
|
||||
}
|
||||
else {
|
||||
/* Exact half-way case: apply round-even rule. */
|
||||
if (word1(rv) & 1) {
|
||||
if (dsign)
|
||||
goto rethi1;
|
||||
goto retlow1;
|
||||
}
|
||||
}
|
||||
|
||||
if (dd > 0 || (dd == 0 && odd))
|
||||
dval(rv) += sulp(rv, bc);
|
||||
return 0;
|
||||
}
|
||||
|
||||
double
|
||||
_Py_dg_strtod(const char *s00, char **se)
|
||||
{
|
||||
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1, error;
|
||||
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dp0, dp1, dplen, e, e1, error;
|
||||
int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
|
||||
const char *s, *s0, *s1;
|
||||
double aadj, aadj1;
|
||||
|
|
@ -1341,7 +1349,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
BCinfo bc;
|
||||
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
||||
|
||||
sign = nz0 = nz = bc.dplen = 0;
|
||||
sign = nz0 = nz = dplen = 0;
|
||||
dval(&rv) = 0.;
|
||||
for(s = s00;;s++) switch(*s) {
|
||||
case '-':
|
||||
|
|
@ -1380,11 +1388,11 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
else if (nd < 16)
|
||||
z = 10*z + c - '0';
|
||||
nd0 = nd;
|
||||
bc.dp0 = bc.dp1 = s - s0;
|
||||
dp0 = dp1 = s - s0;
|
||||
if (c == '.') {
|
||||
c = *++s;
|
||||
bc.dp1 = s - s0;
|
||||
bc.dplen = bc.dp1 - bc.dp0;
|
||||
dp1 = s - s0;
|
||||
dplen = 1;
|
||||
if (!nd) {
|
||||
for(; c == '0'; c = *++s)
|
||||
nz++;
|
||||
|
|
@ -1587,10 +1595,10 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
/* in IEEE arithmetic. */
|
||||
i = j = 18;
|
||||
if (i > nd0)
|
||||
j += bc.dplen;
|
||||
j += dplen;
|
||||
for(;;) {
|
||||
if (--j <= bc.dp1 && j >= bc.dp0)
|
||||
j = bc.dp0 - 1;
|
||||
if (--j <= dp1 && j >= dp0)
|
||||
j = dp0 - 1;
|
||||
if (s0[j] != '0')
|
||||
break;
|
||||
--i;
|
||||
|
|
@ -1603,11 +1611,11 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
y = 0;
|
||||
for(i = 0; i < nd0; ++i)
|
||||
y = 10*y + s0[i] - '0';
|
||||
for(j = bc.dp1; i < nd; ++i)
|
||||
for(j = dp1; i < nd; ++i)
|
||||
y = 10*y + s0[j++] - '0';
|
||||
}
|
||||
}
|
||||
bd0 = s2b(s0, nd0, nd, y, bc.dplen);
|
||||
bd0 = s2b(s0, nd0, nd, y);
|
||||
if (bd0 == NULL)
|
||||
goto failed_malloc;
|
||||
|
||||
|
|
@ -1730,6 +1738,30 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
if (bc.nd > nd && i <= 0) {
|
||||
if (bc.dsign)
|
||||
break; /* Must use bigcomp(). */
|
||||
|
||||
/* Here rv overestimates the truncated decimal value by at most
|
||||
0.5 ulp(rv). Hence rv either overestimates the true decimal
|
||||
value by <= 0.5 ulp(rv), or underestimates it by some small
|
||||
amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of
|
||||
the true decimal value, so it's possible to exit.
|
||||
|
||||
Exception: if scaled rv is a normal exact power of 2, but not
|
||||
DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the
|
||||
next double, so the correctly rounded result is either rv - 0.5
|
||||
ulp(rv) or rv; in this case, use bigcomp to distinguish. */
|
||||
|
||||
if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) {
|
||||
/* rv can't be 0, since it's an overestimate for some
|
||||
nonzero value. So rv is a normal power of 2. */
|
||||
j = (int)(word0(&rv) & Exp_mask) >> Exp_shift;
|
||||
/* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if
|
||||
rv / 2^bc.scale >= 2^-1021. */
|
||||
if (j - bc.scale >= 2) {
|
||||
dval(&rv) -= 0.5 * sulp(&rv, &bc);
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
||||
{
|
||||
bc.nd = nd;
|
||||
i = -1; /* Discarded digits make delta smaller. */
|
||||
|
|
|
|||
Loading…
Reference in a new issue