# 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() |