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Þ'¯°ÌME[YéïĵÂCå½ Ué©Áû'Ê9%eÔðNU”ë‘ÌsD3/®+UI˜9h.WC”빓$#:pz:YÓ ¿xž* ³$Í +$kñAŠ‹†¢ Uê>¸)_š¬÷©ßAÂÔb9ÇU ¯¾á•9¯ÏÏ÷O÷¼¼Fähal1‰3Ì[Ïr•´UCksNÐ] R‘¸¥H+§Šé†c©vÖÞ0iÓ76s†î!§=ß ¼~Ô'°Ãmäoäš³ªøi1úÉ)³yV8 CLÄØÁ‘WYïi€H6ÖÑiámø^ÈY´°Ñ7¥Û*—Ñ©L«Qƒï—Ùrÿ ›£Ð*š¸ˆL©ˆ$ˆ ÷¾D§9È®«qbqC)–ˆïv´çñsÑVT­Ø, <àïºÀO«Jý·õ àfPìð .wFšir´þ’2_Y *Æ€x\« ì€9š@ Ž|F⇥ˆkZ@hÖÄ0t¿-<“‹qµ¾*ZL¤Ú)&BJpÓF5=$„at*Zš$’ÑtdûÝRI1 2Ž‰$€$I$#‰SÞ’Hë¬ï;Á$¡t$’`<(ñÇt)$‡Ð.Êf¢X’Kt=Éé$‚ˆªè¢oÝëòI%Rgcª÷ŠyI%¡‰ÿ !ñ)´õ $¤ Ô’IIGÿÙ# Tests for the correctly-rounded string -> float conversions # introduced in Python 2.7 and 3.1. import random import unittest import re import sys 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[-+])? # an optional sign, followed by (?=\d|\.\d) # a number with at least one digit (?P\d*) # having a (possibly empty) integer part (?:\.(?P\d*))? # followed by an optional fractional part (?:E(?P[-+]?\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 range(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 range(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 range(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 range(-400, -320): base = 10**-exponent // 2**1075 for j in range(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 range(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 range(1000): for j in range(TEST_SIZE): s = random.choice(signs) intpart_len = random.randrange(5) s += ''.join(random.choice(digits) for _ in range(intpart_len)) if random.choice([True, False]): s += '.' fracpart_len = random.randrange(5) s += ''.join(random.choice(digits) for _ in range(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 range(exponent_len)) if intpart_len + fracpart_len: self.check_strtod(s) else: try: float(s) except ValueError: pass else: assert False, "expected ValueError" @test.support.bigmemtest(size=test.support._2G+10, memuse=3, dry_run=False) def test_oversized_digit_strings(self, maxsize): # Input string whose length doesn't fit in an INT. s = "1." + "1" * maxsize with self.assertRaises(ValueError): float(s) del s s = "0." + "0" * maxsize + "1" with self.assertRaises(ValueError): float(s) del s def test_large_exponents(self): # Verify that the clipping of the exponent in strtod doesn't affect the # output values. def positive_exp(n): """ Long string with value 1.0 and exponent n""" return '0.{}1e+{}'.format('0'*(n-1), n) def negative_exp(n): """ Long string with value 1.0 and exponent -n""" return '1{}e-{}'.format('0'*n, n) self.assertEqual(float(positive_exp(10000)), 1.0) self.assertEqual(float(positive_exp(20000)), 1.0) self.assertEqual(float(positive_exp(30000)), 1.0) self.assertEqual(float(negative_exp(10000)), 1.0) self.assertEqual(float(negative_exp(20000)), 1.0) self.assertEqual(float(negative_exp(30000)), 1.0) 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', # Value found by Rick Regan that gives a result of 2**-968 # under Gay's dtoa.c (as of Nov 04, 2010); since fixed. # (Fixed some time ago in Python's dtoa.c.) '0.0000000000000000000000000000000000000000100000000' #... '000000000576129113423785429971690421191214034235435' #... '087147763178149762956868991692289869941246658073194' #... '51982237978882039897143840789794921875', ] for s in test_strings: self.check_strtod(s) if __name__ == "__main__": unittest.main()