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Diffstat (limited to 'Lib/test/test_strtod.py')
| -rw-r--r-- | Lib/test/test_strtod.py | 399 |
1 files changed, 399 insertions, 0 deletions
diff --git a/Lib/test/test_strtod.py b/Lib/test/test_strtod.py new file mode 100644 index 0000000000..7bc595daf3 --- /dev/null +++ b/Lib/test/test_strtod.py @@ -0,0 +1,399 @@ +# 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() |