| # 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() |
