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      1 # Tests for the correctly-rounded string -> float conversions
      2 # introduced in Python 2.7 and 3.1.
      3 
      4 import random
      5 import struct
      6 import unittest
      7 import re
      8 import sys
      9 from test import test_support
     10 
     11 if getattr(sys, 'float_repr_style', '') != 'short':
     12     raise unittest.SkipTest('correctly-rounded string->float conversions '
     13                             'not available on this system')
     14 
     15 # Correctly rounded str -> float in pure Python, for comparison.
     16 
     17 strtod_parser = re.compile(r"""    # A numeric string consists of:
     18     (?P<sign>[-+])?          # an optional sign, followed by
     19     (?=\d|\.\d)              # a number with at least one digit
     20     (?P<int>\d*)             # having a (possibly empty) integer part
     21     (?:\.(?P<frac>\d*))?     # followed by an optional fractional part
     22     (?:E(?P<exp>[-+]?\d+))?  # and an optional exponent
     23     \Z
     24 """, re.VERBOSE | re.IGNORECASE).match
     25 
     26 # Pure Python version of correctly rounded string->float conversion.
     27 # Avoids any use of floating-point by returning the result as a hex string.
     28 def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
     29     """Convert a finite decimal string to a hex string representing an
     30     IEEE 754 binary64 float.  Return 'inf' or '-inf' on overflow.
     31     This function makes no use of floating-point arithmetic at any
     32     stage."""
     33 
     34     # parse string into a pair of integers 'a' and 'b' such that
     35     # abs(decimal value) = a/b, along with a boolean 'negative'.
     36     m = strtod_parser(s)
     37     if m is None:
     38         raise ValueError('invalid numeric string')
     39     fraction = m.group('frac') or ''
     40     intpart = int(m.group('int') + fraction)
     41     exp = int(m.group('exp') or '0') - len(fraction)
     42     negative = m.group('sign') == '-'
     43     a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
     44 
     45     # quick return for zeros
     46     if not a:
     47         return '-0x0.0p+0' if negative else '0x0.0p+0'
     48 
     49     # compute exponent e for result; may be one too small in the case
     50     # that the rounded value of a/b lies in a different binade from a/b
     51     d = a.bit_length() - b.bit_length()
     52     d += (a >> d if d >= 0 else a << -d) >= b
     53     e = max(d, min_exp) - mant_dig
     54 
     55     # approximate a/b by number of the form q * 2**e; adjust e if necessary
     56     a, b = a << max(-e, 0), b << max(e, 0)
     57     q, r = divmod(a, b)
     58     if 2*r > b or 2*r == b and q & 1:
     59         q += 1
     60         if q.bit_length() == mant_dig+1:
     61             q //= 2
     62             e += 1
     63 
     64     # double check that (q, e) has the right form
     65     assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
     66     assert q.bit_length() == mant_dig or e == min_exp - mant_dig
     67 
     68     # check for overflow and underflow
     69     if e + q.bit_length() > max_exp:
     70         return '-inf' if negative else 'inf'
     71     if not q:
     72         return '-0x0.0p+0' if negative else '0x0.0p+0'
     73 
     74     # for hex representation, shift so # bits after point is a multiple of 4
     75     hexdigs = 1 + (mant_dig-2)//4
     76     shift = 3 - (mant_dig-2)%4
     77     q, e = q << shift, e - shift
     78     return '{}0x{:x}.{:0{}x}p{:+d}'.format(
     79         '-' if negative else '',
     80         q // 16**hexdigs,
     81         q % 16**hexdigs,
     82         hexdigs,
     83         e + 4*hexdigs)
     84 
     85 TEST_SIZE = 10
     86 
     87 class StrtodTests(unittest.TestCase):
     88     def check_strtod(self, s):
     89         """Compare the result of Python's builtin correctly rounded
     90         string->float conversion (using float) to a pure Python
     91         correctly rounded string->float implementation.  Fail if the
     92         two methods give different results."""
     93 
     94         try:
     95             fs = float(s)
     96         except OverflowError:
     97             got = '-inf' if s[0] == '-' else 'inf'
     98         except MemoryError:
     99             got = 'memory error'
    100         else:
    101             got = fs.hex()
    102         expected = strtod(s)
    103         self.assertEqual(expected, got,
    104                          "Incorrectly rounded str->float conversion for {}: "
    105                          "expected {}, got {}".format(s, expected, got))
    106 
    107     def test_short_halfway_cases(self):
    108         # exact halfway cases with a small number of significant digits
    109         for k in 0, 5, 10, 15, 20:
    110             # upper = smallest integer >= 2**54/5**k
    111             upper = -(-2**54//5**k)
    112             # lower = smallest odd number >= 2**53/5**k
    113             lower = -(-2**53//5**k)
    114             if lower % 2 == 0:
    115                 lower += 1
    116             for i in xrange(TEST_SIZE):
    117                 # Select a random odd n in [2**53/5**k,
    118                 # 2**54/5**k). Then n * 10**k gives a halfway case
    119                 # with small number of significant digits.
    120                 n, e = random.randrange(lower, upper, 2), k
    121 
    122                 # Remove any additional powers of 5.
    123                 while n % 5 == 0:
    124                     n, e = n // 5, e + 1
    125                 assert n % 10 in (1, 3, 7, 9)
    126 
    127                 # Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
    128                 # until n * 2**p2 has more than 20 significant digits.
    129                 digits, exponent = n, e
    130                 while digits < 10**20:
    131                     s = '{}e{}'.format(digits, exponent)
    132                     self.check_strtod(s)
    133                     # Same again, but with extra trailing zeros.
    134                     s = '{}e{}'.format(digits * 10**40, exponent - 40)
    135                     self.check_strtod(s)
    136                     digits *= 2
    137 
    138                 # Try numbers of the form n * 5**p2 * 10**(e - p5), p5
    139                 # >= 0, with n * 5**p5 < 10**20.
    140                 digits, exponent = n, e
    141                 while digits < 10**20:
    142                     s = '{}e{}'.format(digits, exponent)
    143                     self.check_strtod(s)
    144                     # Same again, but with extra trailing zeros.
    145                     s = '{}e{}'.format(digits * 10**40, exponent - 40)
    146                     self.check_strtod(s)
    147                     digits *= 5
    148                     exponent -= 1
    149 
    150     def test_halfway_cases(self):
    151         # test halfway cases for the round-half-to-even rule
    152         for i in xrange(100 * TEST_SIZE):
    153             # bit pattern for a random finite positive (or +0.0) float
    154             bits = random.randrange(2047*2**52)
    155 
    156             # convert bit pattern to a number of the form m * 2**e
    157             e, m = divmod(bits, 2**52)
    158             if e:
    159                 m, e = m + 2**52, e - 1
    160             e -= 1074
    161 
    162             # add 0.5 ulps
    163             m, e = 2*m + 1, e - 1
    164 
    165             # convert to a decimal string
    166             if e >= 0:
    167                 digits = m << e
    168                 exponent = 0
    169             else:
    170                 # m * 2**e = (m * 5**-e) * 10**e
    171                 digits = m * 5**-e
    172                 exponent = e
    173             s = '{}e{}'.format(digits, exponent)
    174             self.check_strtod(s)
    175 
    176     def test_boundaries(self):
    177         # boundaries expressed as triples (n, e, u), where
    178         # n*10**e is an approximation to the boundary value and
    179         # u*10**e is 1ulp
    180         boundaries = [
    181             (10000000000000000000, -19, 1110),   # a power of 2 boundary (1.0)
    182             (17976931348623159077, 289, 1995),   # overflow boundary (2.**1024)
    183             (22250738585072013831, -327, 4941),  # normal/subnormal (2.**-1022)
    184             (0, -327, 4941),                     # zero
    185             ]
    186         for n, e, u in boundaries:
    187             for j in xrange(1000):
    188                 digits = n + random.randrange(-3*u, 3*u)
    189                 exponent = e
    190                 s = '{}e{}'.format(digits, exponent)
    191                 self.check_strtod(s)
    192                 n *= 10
    193                 u *= 10
    194                 e -= 1
    195 
    196     def test_underflow_boundary(self):
    197         # test values close to 2**-1075, the underflow boundary; similar
    198         # to boundary_tests, except that the random error doesn't scale
    199         # with n
    200         for exponent in xrange(-400, -320):
    201             base = 10**-exponent // 2**1075
    202             for j in xrange(TEST_SIZE):
    203                 digits = base + random.randrange(-1000, 1000)
    204                 s = '{}e{}'.format(digits, exponent)
    205                 self.check_strtod(s)
    206 
    207     def test_bigcomp(self):
    208         for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
    209             dig10 = 10**ndigs
    210             for i in xrange(10 * TEST_SIZE):
    211                 digits = random.randrange(dig10)
    212                 exponent = random.randrange(-400, 400)
    213                 s = '{}e{}'.format(digits, exponent)
    214                 self.check_strtod(s)
    215 
    216     def test_parsing(self):
    217         # make '0' more likely to be chosen than other digits
    218         digits = '000000123456789'
    219         signs = ('+', '-', '')
    220 
    221         # put together random short valid strings
    222         # \d*[.\d*]?e
    223         for i in xrange(1000):
    224             for j in xrange(TEST_SIZE):
    225                 s = random.choice(signs)
    226                 intpart_len = random.randrange(5)
    227                 s += ''.join(random.choice(digits) for _ in xrange(intpart_len))
    228                 if random.choice([True, False]):
    229                     s += '.'
    230                     fracpart_len = random.randrange(5)
    231                     s += ''.join(random.choice(digits)
    232                                  for _ in xrange(fracpart_len))
    233                 else:
    234                     fracpart_len = 0
    235                 if random.choice([True, False]):
    236                     s += random.choice(['e', 'E'])
    237                     s += random.choice(signs)
    238                     exponent_len = random.randrange(1, 4)
    239                     s += ''.join(random.choice(digits)
    240                                  for _ in xrange(exponent_len))
    241 
    242                 if intpart_len + fracpart_len:
    243                     self.check_strtod(s)
    244                 else:
    245                     try:
    246                         float(s)
    247                     except ValueError:
    248                         pass
    249                     else:
    250                         assert False, "expected ValueError"
    251 
    252     def test_particular(self):
    253         # inputs that produced crashes or incorrectly rounded results with
    254         # previous versions of dtoa.c, for various reasons
    255         test_strings = [
    256             # issue 7632 bug 1, originally reported failing case
    257             '2183167012312112312312.23538020374420446192e-370',
    258             # 5 instances of issue 7632 bug 2
    259             '12579816049008305546974391768996369464963024663104e-357',
    260             '17489628565202117263145367596028389348922981857013e-357',
    261             '18487398785991994634182916638542680759613590482273e-357',
    262             '32002864200581033134358724675198044527469366773928e-358',
    263             '94393431193180696942841837085033647913224148539854e-358',
    264             '73608278998966969345824653500136787876436005957953e-358',
    265             '64774478836417299491718435234611299336288082136054e-358',
    266             '13704940134126574534878641876947980878824688451169e-357',
    267             '46697445774047060960624497964425416610480524760471e-358',
    268             # failing case for bug introduced by METD in r77451 (attempted
    269             # fix for issue 7632, bug 2), and fixed in r77482.
    270             '28639097178261763178489759107321392745108491825303e-311',
    271             # two numbers demonstrating a flaw in the bigcomp 'dig == 0'
    272             # correction block (issue 7632, bug 3)
    273             '1.00000000000000001e44',
    274             '1.0000000000000000100000000000000000000001e44',
    275             # dtoa.c bug for numbers just smaller than a power of 2 (issue
    276             # 7632, bug 4)
    277             '99999999999999994487665465554760717039532578546e-47',
    278             # failing case for off-by-one error introduced by METD in
    279             # r77483 (dtoa.c cleanup), fixed in r77490
    280             '965437176333654931799035513671997118345570045914469' #...
    281             '6213413350821416312194420007991306908470147322020121018368e0',
    282             # incorrect lsb detection for round-half-to-even when
    283             # bc->scale != 0 (issue 7632, bug 6).
    284             '104308485241983990666713401708072175773165034278685' #...
    285             '682646111762292409330928739751702404658197872319129' #...
    286             '036519947435319418387839758990478549477777586673075' #...
    287             '945844895981012024387992135617064532141489278815239' #...
    288             '849108105951619997829153633535314849999674266169258' #...
    289             '928940692239684771590065027025835804863585454872499' #...
    290             '320500023126142553932654370362024104462255244034053' #...
    291             '203998964360882487378334860197725139151265590832887' #...
    292             '433736189468858614521708567646743455601905935595381' #...
    293             '852723723645799866672558576993978025033590728687206' #...
    294             '296379801363024094048327273913079612469982585674824' #...
    295             '156000783167963081616214710691759864332339239688734' #...
    296             '656548790656486646106983450809073750535624894296242' #...
    297             '072010195710276073042036425579852459556183541199012' #...
    298             '652571123898996574563824424330960027873516082763671875e-1075',
    299             # demonstration that original fix for issue 7632 bug 1 was
    300             # buggy; the exit condition was too strong
    301             '247032822920623295e-341',
    302             # demonstrate similar problem to issue 7632 bug1: crash
    303             # with 'oversized quotient in quorem' message.
    304             '99037485700245683102805043437346965248029601286431e-373',
    305             '99617639833743863161109961162881027406769510558457e-373',
    306             '98852915025769345295749278351563179840130565591462e-372',
    307             '99059944827693569659153042769690930905148015876788e-373',
    308             '98914979205069368270421829889078356254059760327101e-372',
    309             # issue 7632 bug 5: the following 2 strings convert differently
    310             '1000000000000000000000000000000000000000e-16',
    311             '10000000000000000000000000000000000000000e-17',
    312             # issue 7632 bug 7
    313             '991633793189150720000000000000000000000000000000000000000e-33',
    314             # And another, similar, failing halfway case
    315             '4106250198039490000000000000000000000000000000000000000e-38',
    316             # issue 7632 bug 8:  the following produced 10.0
    317             '10.900000000000000012345678912345678912345',
    318 
    319             # two humongous values from issue 7743
    320             '116512874940594195638617907092569881519034793229385' #...
    321             '228569165191541890846564669771714896916084883987920' #...
    322             '473321268100296857636200926065340769682863349205363' #...
    323             '349247637660671783209907949273683040397979984107806' #...
    324             '461822693332712828397617946036239581632976585100633' #...
    325             '520260770761060725403904123144384571612073732754774' #...
    326             '588211944406465572591022081973828448927338602556287' #...
    327             '851831745419397433012491884869454462440536895047499' #...
    328             '436551974649731917170099387762871020403582994193439' #...
    329             '761933412166821484015883631622539314203799034497982' #...
    330             '130038741741727907429575673302461380386596501187482' #...
    331             '006257527709842179336488381672818798450229339123527' #...
    332             '858844448336815912020452294624916993546388956561522' #...
    333             '161875352572590420823607478788399460162228308693742' #...
    334             '05287663441403533948204085390898399055004119873046875e-1075',
    335 
    336             '525440653352955266109661060358202819561258984964913' #...
    337             '892256527849758956045218257059713765874251436193619' #...
    338             '443248205998870001633865657517447355992225852945912' #...
    339             '016668660000210283807209850662224417504752264995360' #...
    340             '631512007753855801075373057632157738752800840302596' #...
    341             '237050247910530538250008682272783660778181628040733' #...
    342             '653121492436408812668023478001208529190359254322340' #...
    343             '397575185248844788515410722958784640926528544043090' #...
    344             '115352513640884988017342469275006999104519620946430' #...
    345             '818767147966495485406577703972687838176778993472989' #...
    346             '561959000047036638938396333146685137903018376496408' #...
    347             '319705333868476925297317136513970189073693314710318' #...
    348             '991252811050501448326875232850600451776091303043715' #...
    349             '157191292827614046876950225714743118291034780466325' #...
    350             '085141343734564915193426994587206432697337118211527' #...
    351             '278968731294639353354774788602467795167875117481660' #...
    352             '4738791256853675690543663283782215866825e-1180',
    353 
    354             # exercise exit conditions in bigcomp comparison loop
    355             '2602129298404963083833853479113577253105939995688e2',
    356             '260212929840496308383385347911357725310593999568896e0',
    357             '26021292984049630838338534791135772531059399956889601e-2',
    358             '260212929840496308383385347911357725310593999568895e0',
    359             '260212929840496308383385347911357725310593999568897e0',
    360             '260212929840496308383385347911357725310593999568996e0',
    361             '260212929840496308383385347911357725310593999568866e0',
    362             # 2**53
    363             '9007199254740992.00',
    364             # 2**1024 - 2**970:  exact overflow boundary.  All values
    365             # smaller than this should round to something finite;  any value
    366             # greater than or equal to this one overflows.
    367             '179769313486231580793728971405303415079934132710037' #...
    368             '826936173778980444968292764750946649017977587207096' #...
    369             '330286416692887910946555547851940402630657488671505' #...
    370             '820681908902000708383676273854845817711531764475730' #...
    371             '270069855571366959622842914819860834936475292719074' #...
    372             '168444365510704342711559699508093042880177904174497792',
    373             # 2**1024 - 2**970 - tiny
    374             '179769313486231580793728971405303415079934132710037' #...
    375             '826936173778980444968292764750946649017977587207096' #...
    376             '330286416692887910946555547851940402630657488671505' #...
    377             '820681908902000708383676273854845817711531764475730' #...
    378             '270069855571366959622842914819860834936475292719074' #...
    379             '168444365510704342711559699508093042880177904174497791.999',
    380             # 2**1024 - 2**970 + tiny
    381             '179769313486231580793728971405303415079934132710037' #...
    382             '826936173778980444968292764750946649017977587207096' #...
    383             '330286416692887910946555547851940402630657488671505' #...
    384             '820681908902000708383676273854845817711531764475730' #...
    385             '270069855571366959622842914819860834936475292719074' #...
    386             '168444365510704342711559699508093042880177904174497792.001',
    387             # 1 - 2**-54, +-tiny
    388             '999999999999999944488848768742172978818416595458984375e-54',
    389             '9999999999999999444888487687421729788184165954589843749999999e-54',
    390             '9999999999999999444888487687421729788184165954589843750000001e-54',
    391             ]
    392         for s in test_strings:
    393             self.check_strtod(s)
    394 
    395 def test_main():
    396     test_support.run_unittest(StrtodTests)
    397 
    398 if __name__ == "__main__":
    399     test_main()
    400