# 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
if getattr(sys, 'float_repr_style', '') != 'short':
raise unittest.SkipTest('correctly-rounded string->float conversions '
'not available on this system')
# 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
# Pure Python version of correctly rounded string->float conversion.
# Avoids any use of floating-point by returning the result as a hex string.
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
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'
except MemoryError:
got = 'memory error'
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_short_halfway_cases(self):
# exact halfway cases with a small number of significant digits
for k in 0, 5, 10, 15, 20:
# upper = smallest integer >= 2**54/5**k
upper = -(-2**54//5**k)
# lower = smallest odd number >= 2**53/5**k
lower = -(-2**53//5**k)
if lower % 2 == 0:
lower += 1
for i in xrange(TEST_SIZE):
# Select a random odd n in [2**53/5**k,
# 2**54/5**k). Then n * 10**k gives a halfway case
# with small number of significant digits.
n, e = random.randrange(lower, upper, 2), k
# Remove any additional powers of 5.
while n % 5 == 0:
n, e = n // 5, e + 1
assert n % 10 in (1, 3, 7, 9)
# Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
# until n * 2**p2 has more than 20 significant digits.
digits, exponent = n, e
while digits < 10**20:
s = '{}e{}'.format(digits, exponent)
self.check_strtod(s)
# Same again, but with extra trailing zeros.
s = '{}e{}'.format(digits * 10**40, exponent - 40)
self.check_strtod(s)
digits *= 2
# Try numbers of the form n * 5**p2 * 10**(e - p5), p5
# >= 0, with n * 5**p5 < 10**20.
digits, exponent = n, e
while digits < 10**20:
s = '{}e{}'.format(digits, exponent)
self.check_strtod(s)
# Same again, but with extra trailing zeros.
s = '{}e{}'.format(digits * 10**40, exponent - 40)
self.check_strtod(s)
digits *= 5
exponent -= 1
def test_halfway_cases(self):
# test halfway cases for the round-half-to-even rule
for i in xrange(100 * 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)
self.check_strtod(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):
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):
for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
dig10 = 10**ndigs
for i in xrange(10 * TEST_SIZE):
digits = random.randrange(dig10)
exponent = random.randrange(-400, 400)
s = '{}e{}'.format(digits, exponent)
self.check_strtod(s)
def test_parsing(self):
# make '0' more likely to be chosen than other digits
digits = '000000123456789'
signs = ('+', '-', '')
# put together random short valid strings
# \d*[.\d*]?e
for i in 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',
'73608278998966969345824653500136787876436005957953e-358',
'64774478836417299491718435234611299336288082136054e-358',
'13704940134126574534878641876947980878824688451169e-357',
'46697445774047060960624497964425416610480524760471e-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',
# demonstrate similar problem to issue 7632 bug1: crash
# with 'oversized quotient in quorem' message.
'99037485700245683102805043437346965248029601286431e-373',
'99617639833743863161109961162881027406769510558457e-373',
'98852915025769345295749278351563179840130565591462e-372',
'99059944827693569659153042769690930905148015876788e-373',
'98914979205069368270421829889078356254059760327101e-372',
# issue 7632 bug 5: the following 2 strings convert differently
'1000000000000000000000000000000000000000e-16',
'10000000000000000000000000000000000000000e-17',
# issue 7632 bug 7
'991633793189150720000000000000000000000000000000000000000e-33',
# And another, similar, failing halfway case
'4106250198039490000000000000000000000000000000000000000e-38',
# issue 7632 bug 8: the following produced 10.0
'10.900000000000000012345678912345678912345',
# two humongous values from issue 7743
'116512874940594195638617907092569881519034793229385' #...
'228569165191541890846564669771714896916084883987920' #...
'473321268100296857636200926065340769682863349205363' #...
'349247637660671783209907949273683040397979984107806' #...
'461822693332712828397617946036239581632976585100633' #...
'520260770761060725403904123144384571612073732754774' #...
'588211944406465572591022081973828448927338602556287' #...
'851831745419397433012491884869454462440536895047499' #...
'436551974649731917170099387762871020403582994193439' #...
'761933412166821484015883631622539314203799034497982' #...
'130038741741727907429575673302461380386596501187482' #...
'006257527709842179336488381672818798450229339123527' #...
'858844448336815912020452294624916993546388956561522' #...
'161875352572590420823607478788399460162228308693742' #...
'05287663441403533948204085390898399055004119873046875e-1075',
'525440653352955266109661060358202819561258984964913' #...
'892256527849758956045218257059713765874251436193619' #...
'443248205998870001633865657517447355992225852945912' #...
'016668660000210283807209850662224417504752264995360' #...
'631512007753855801075373057632157738752800840302596' #...
'237050247910530538250008682272783660778181628040733' #...
'653121492436408812668023478001208529190359254322340' #...
'397575185248844788515410722958784640926528544043090' #...
'115352513640884988017342469275006999104519620946430' #...
'818767147966495485406577703972687838176778993472989' #...
'561959000047036638938396333146685137903018376496408' #...
'319705333868476925297317136513970189073693314710318' #...
'991252811050501448326875232850600451776091303043715' #...
'157191292827614046876950225714743118291034780466325' #...
'085141343734564915193426994587206432697337118211527' #...
'278968731294639353354774788602467795167875117481660' #...
'4738791256853675690543663283782215866825e-1180',
# exercise exit conditions in bigcomp comparison loop
'2602129298404963083833853479113577253105939995688e2',
'260212929840496308383385347911357725310593999568896e0',
'26021292984049630838338534791135772531059399956889601e-2',
'260212929840496308383385347911357725310593999568895e0',
'260212929840496308383385347911357725310593999568897e0',
'260212929840496308383385347911357725310593999568996e0',
'260212929840496308383385347911357725310593999568866e0',
# 2**53
'9007199254740992.00',
# 2**1024 - 2**970: exact overflow boundary. All values
# smaller than this should round to something finite; any value
# greater than or equal to this one overflows.
'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',
]
for s in test_strings:
self.check_strtod(s)
def test_main():
test_support.run_unittest(StrtodTests)
if __name__ == "__main__":
test_main()