[Python-checkins] r77493 - python/trunk/Lib/test/test_strtod.py
mark.dickinson
python-checkins at python.org
Thu Jan 14 16:22:33 CET 2010
Author: mark.dickinson
Date: Thu Jan 14 16:22:33 2010
New Revision: 77493
Log:
Issue #7632: add tests for bugs fixed so far.
Added:
python/trunk/Lib/test/test_strtod.py
Added: python/trunk/Lib/test/test_strtod.py
==============================================================================
--- (empty file)
+++ python/trunk/Lib/test/test_strtod.py Thu Jan 14 16:22:33 2010
@@ -0,0 +1,269 @@
+# Tests for the correctly-rounded string -> float conversions
+# introduced in Python 2.7 and 3.1.
+
+import random
+import struct
+import unittest
+import re
+import sys
+from test import test_support
+
+# Correctly rounded str -> float in pure Python, for comparison.
+
+strtod_parser = re.compile(r""" # A numeric string consists of:
+ (?P<sign>[-+])? # an optional sign, followed by
+ (?=\d|\.\d) # a number with at least one digit
+ (?P<int>\d*) # having a (possibly empty) integer part
+ (?:\.(?P<frac>\d*))? # followed by an optional fractional part
+ (?:E(?P<exp>[-+]?\d+))? # and an optional exponent
+ \Z
+""", re.VERBOSE | re.IGNORECASE).match
+
+def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
+ """Convert a finite decimal string to a hex string representing an
+ IEEE 754 binary64 float. Return 'inf' or '-inf' on overflow.
+ This function makes no use of floating-point arithmetic at any
+ stage."""
+
+ # parse string into a pair of integers 'a' and 'b' such that
+ # abs(decimal value) = a/b, along with a boolean 'negative'.
+ m = strtod_parser(s)
+ if m is None:
+ raise ValueError('invalid numeric string')
+ fraction = m.group('frac') or ''
+ intpart = int(m.group('int') + fraction)
+ exp = int(m.group('exp') or '0') - len(fraction)
+ negative = m.group('sign') == '-'
+ a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
+
+ # quick return for zeros
+ if not a:
+ return '-0x0.0p+0' if negative else '0x0.0p+0'
+
+ # compute exponent e for result; may be one too small in the case
+ # that the rounded value of a/b lies in a different binade from a/b
+ d = a.bit_length() - b.bit_length()
+ d += (a >> d if d >= 0 else a << -d) >= b
+ e = max(d, min_exp) - mant_dig
+
+ # approximate a/b by number of the form q * 2**e; adjust e if necessary
+ a, b = a << max(-e, 0), b << max(e, 0)
+ q, r = divmod(a, b)
+ if 2*r > b or 2*r == b and q & 1:
+ q += 1
+ if q.bit_length() == mant_dig+1:
+ q //= 2
+ e += 1
+
+ # double check that (q, e) has the right form
+ assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
+ assert q.bit_length() == mant_dig or e == min_exp - mant_dig
+
+ # check for overflow and underflow
+ if e + q.bit_length() > max_exp:
+ return '-inf' if negative else 'inf'
+ if not q:
+ return '-0x0.0p+0' if negative else '0x0.0p+0'
+
+ # for hex representation, shift so # bits after point is a multiple of 4
+ hexdigs = 1 + (mant_dig-2)//4
+ shift = 3 - (mant_dig-2)%4
+ q, e = q << shift, e - shift
+ return '{}0x{:x}.{:0{}x}p{:+d}'.format(
+ '-' if negative else '',
+ q // 16**hexdigs,
+ q % 16**hexdigs,
+ hexdigs,
+ e + 4*hexdigs)
+
+TEST_SIZE = 10
+
+ at unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
+ "applies only when using short float repr style")
+class StrtodTests(unittest.TestCase):
+ def check_strtod(self, s):
+ """Compare the result of Python's builtin correctly rounded
+ string->float conversion (using float) to a pure Python
+ correctly rounded string->float implementation. Fail if the
+ two methods give different results."""
+
+ try:
+ fs = float(s)
+ except OverflowError:
+ got = '-inf' if s[0] == '-' else 'inf'
+ else:
+ got = fs.hex()
+ expected = strtod(s)
+ self.assertEqual(expected, got,
+ "Incorrectly rounded str->float conversion for {}: "
+ "expected {}, got {}".format(s, expected, got))
+
+ def test_halfway_cases(self):
+ # test halfway cases for the round-half-to-even rule
+ for i in xrange(1000):
+ for j in xrange(TEST_SIZE):
+ # bit pattern for a random finite positive (or +0.0) float
+ bits = random.randrange(2047*2**52)
+
+ # convert bit pattern to a number of the form m * 2**e
+ e, m = divmod(bits, 2**52)
+ if e:
+ m, e = m + 2**52, e - 1
+ e -= 1074
+
+ # add 0.5 ulps
+ m, e = 2*m + 1, e - 1
+
+ # convert to a decimal string
+ if e >= 0:
+ digits = m << e
+ exponent = 0
+ else:
+ # m * 2**e = (m * 5**-e) * 10**e
+ digits = m * 5**-e
+ exponent = e
+ s = '{}e{}'.format(digits, exponent)
+
+ # for the moment, ignore errors from trailing zeros
+ if digits % 10 == 0:
+ continue
+ self.check_strtod(s)
+
+ # get expected answer via struct, to triple check
+ #fs = struct.unpack('<d', struct.pack('<Q', bits + (bits&1)))[0]
+ #self.assertEqual(fs, float(s))
+
+ def test_boundaries(self):
+ # boundaries expressed as triples (n, e, u), where
+ # n*10**e is an approximation to the boundary value and
+ # u*10**e is 1ulp
+ boundaries = [
+ (10000000000000000000, -19, 1110), # a power of 2 boundary (1.0)
+ (17976931348623159077, 289, 1995), # overflow boundary (2.**1024)
+ (22250738585072013831, -327, 4941), # normal/subnormal (2.**-1022)
+ (0, -327, 4941), # zero
+ ]
+ for n, e, u in boundaries:
+ for j in xrange(1000):
+ for i in xrange(TEST_SIZE):
+ digits = n + random.randrange(-3*u, 3*u)
+ exponent = e
+ s = '{}e{}'.format(digits, exponent)
+ self.check_strtod(s)
+ n *= 10
+ u *= 10
+ e -= 1
+
+ def test_underflow_boundary(self):
+ # test values close to 2**-1075, the underflow boundary; similar
+ # to boundary_tests, except that the random error doesn't scale
+ # with n
+ for exponent in xrange(-400, -320):
+ base = 10**-exponent // 2**1075
+ for j in xrange(TEST_SIZE):
+ digits = base + random.randrange(-1000, 1000)
+ s = '{}e{}'.format(digits, exponent)
+ self.check_strtod(s)
+
+ def test_bigcomp(self):
+ DIG10 = 10**50
+ for i in xrange(1000):
+ for j in xrange(TEST_SIZE):
+ digits = random.randrange(DIG10)
+ exponent = random.randrange(-400, 400)
+ s = '{}e{}'.format(digits, exponent)
+ self.check_strtod(s)
+
+ def test_parsing(self):
+ digits = tuple(map(str, xrange(10)))
+ signs = ('+', '-', '')
+
+ # put together random short valid strings
+ # \d*[.\d*]?e
+ for i in xrange(1000):
+ for j in xrange(TEST_SIZE):
+ s = random.choice(signs)
+ intpart_len = random.randrange(5)
+ s += ''.join(random.choice(digits) for _ in xrange(intpart_len))
+ if random.choice([True, False]):
+ s += '.'
+ fracpart_len = random.randrange(5)
+ s += ''.join(random.choice(digits)
+ for _ in xrange(fracpart_len))
+ else:
+ fracpart_len = 0
+ if random.choice([True, False]):
+ s += random.choice(['e', 'E'])
+ s += random.choice(signs)
+ exponent_len = random.randrange(1, 4)
+ s += ''.join(random.choice(digits)
+ for _ in xrange(exponent_len))
+
+ if intpart_len + fracpart_len:
+ self.check_strtod(s)
+ else:
+ try:
+ float(s)
+ except ValueError:
+ pass
+ else:
+ assert False, "expected ValueError"
+
+ def test_particular(self):
+ # inputs that produced crashes or incorrectly rounded results with
+ # previous versions of dtoa.c, for various reasons
+ test_strings = [
+ # issue 7632 bug 1, originally reported failing case
+ '2183167012312112312312.23538020374420446192e-370',
+ # 5 instances of issue 7632 bug 2
+ '12579816049008305546974391768996369464963024663104e-357',
+ '17489628565202117263145367596028389348922981857013e-357',
+ '18487398785991994634182916638542680759613590482273e-357',
+ '32002864200581033134358724675198044527469366773928e-358',
+ '94393431193180696942841837085033647913224148539854e-358',
+ # failing case for bug introduced by METD in r77451 (attempted
+ # fix for issue 7632, bug 2), and fixed in r77482.
+ '28639097178261763178489759107321392745108491825303e-311',
+ # two numbers demonstrating a flaw in the bigcomp 'dig == 0'
+ # correction block (issue 7632, bug 3)
+ '1.00000000000000001e44',
+ '1.0000000000000000100000000000000000000001e44',
+ # dtoa.c bug for numbers just smaller than a power of 2 (issue
+ # 7632, bug 4)
+ '99999999999999994487665465554760717039532578546e-47',
+ # failing case for off-by-one error introduced by METD in
+ # r77483 (dtoa.c cleanup), fixed in r77490
+ '965437176333654931799035513671997118345570045914469' #...
+ '6213413350821416312194420007991306908470147322020121018368e0',
+ # incorrect lsb detection for round-half-to-even when
+ # bc->scale != 0 (issue 7632, bug 6).
+ '104308485241983990666713401708072175773165034278685' #...
+ '682646111762292409330928739751702404658197872319129' #...
+ '036519947435319418387839758990478549477777586673075' #...
+ '945844895981012024387992135617064532141489278815239' #...
+ '849108105951619997829153633535314849999674266169258' #...
+ '928940692239684771590065027025835804863585454872499' #...
+ '320500023126142553932654370362024104462255244034053' #...
+ '203998964360882487378334860197725139151265590832887' #...
+ '433736189468858614521708567646743455601905935595381' #...
+ '852723723645799866672558576993978025033590728687206' #...
+ '296379801363024094048327273913079612469982585674824' #...
+ '156000783167963081616214710691759864332339239688734' #...
+ '656548790656486646106983450809073750535624894296242' #...
+ '072010195710276073042036425579852459556183541199012' #...
+ '652571123898996574563824424330960027873516082763671875e-1075',
+ # demonstration that original fix for issue 7632 bug 1 was
+ # buggy; the exit condition was too strong
+ '247032822920623295e-341',
+ # issue 7632 bug 5: the following 2 strings convert differently
+ '1000000000000000000000000000000000000000e-16',
+ #'10000000000000000000000000000000000000000e-17',
+ ]
+ for s in test_strings:
+ self.check_strtod(s)
+
+def test_main():
+ test_support.run_unittest(StrtodTests)
+
+if __name__ == "__main__":
+ test_main()
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