394 lines
18 KiB
Python
394 lines
18 KiB
Python
# 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
|
|
|
|
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',
|
|
# 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()
|