Lib/test/test_strtod.py

   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 # Correctly rounded str -> float in pure Python, for comparison.
  12
  13 strtod_parser = re.compile(r"""    # A numeric string consists of:
  14     (?P<sign>[-+])?          # an optional sign, followed by
  15     (?=\d|\.\d)              # a number with at least one digit
  16     (?P<int>\d*)             # having a (possibly empty) integer part
  17     (?:\.(?P<frac>\d*))?     # followed by an optional fractional part
  18     (?:E(?P<exp>[-+]?\d+))?  # and an optional exponent
  19     \Z
  20 """, re.VERBOSE | re.IGNORECASE).match
  21
  22 def strtod(s, mant_dig=53, min_exp = -1021, max_exp = 1024):
  23     """Convert a finite decimal string to a hex string representing an
  24     IEEE 754 binary64 float.  Return 'inf' or '-inf' on overflow.
  25     This function makes no use of floating-point arithmetic at any
  26     stage."""
  27
  28     # parse string into a pair of integers 'a' and 'b' such that
  29     # abs(decimal value) = a/b, along with a boolean 'negative'.
  30     m = strtod_parser(s)
  31     if m is None:
  32         raise ValueError('invalid numeric string')
  33     fraction = m.group('frac') or ''
  34     intpart = int(m.group('int') + fraction)
  35     exp = int(m.group('exp') or '0') - len(fraction)
  36     negative = m.group('sign') == '-'
  37     a, b = intpart*10**max(exp, 0), 10**max(0, -exp)
  38
  39     # quick return for zeros
  40     if not a:
  41         return '-0x0.0p+0' if negative else '0x0.0p+0'
  42
  43     # compute exponent e for result; may be one too small in the case
  44     # that the rounded value of a/b lies in a different binade from a/b
  45     d = a.bit_length() - b.bit_length()
  46     d += (a >> d if d >= 0 else a << -d) >= b
  47     e = max(d, min_exp) - mant_dig
  48
  49     # approximate a/b by number of the form q * 2**e; adjust e if necessary
  50     a, b = a << max(-e, 0), b << max(e, 0)
  51     q, r = divmod(a, b)
  52     if 2*r > b or 2*r == b and q & 1:
  53         q += 1
  54         if q.bit_length() == mant_dig+1:
  55             q //= 2
  56             e += 1
  57
  58     # double check that (q, e) has the right form
  59     assert q.bit_length() <= mant_dig and e >= min_exp - mant_dig
  60     assert q.bit_length() == mant_dig or e == min_exp - mant_dig
  61
  62     # check for overflow and underflow
  63     if e + q.bit_length() > max_exp:
  64         return '-inf' if negative else 'inf'
  65     if not q:
  66         return '-0x0.0p+0' if negative else '0x0.0p+0'
  67
  68     # for hex representation, shift so # bits after point is a multiple of 4
  69     hexdigs = 1 + (mant_dig-2)//4
  70     shift = 3 - (mant_dig-2)%4
  71     q, e = q << shift, e - shift
  72     return '{}0x{:x}.{:0{}x}p{:+d}'.format(
  73         '-' if negative else '',
  74         q // 16**hexdigs,
  75         q % 16**hexdigs,
  76         hexdigs,
  77         e + 4*hexdigs)
  78
  79 TEST_SIZE = 10
  80
  81 @unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short',
  82                      "applies only when using short float repr style")
  83 class StrtodTests(unittest.TestCase):
  84     def check_strtod(self, s):
  85         """Compare the result of Python's builtin correctly rounded
  86         string->float conversion (using float) to a pure Python
  87         correctly rounded string->float implementation.  Fail if the
  88         two methods give different results."""
  89
  90         try:
  91             fs = float(s)
  92         except OverflowError:
  93             got = '-inf' if s[0] == '-' else 'inf'
  94         except MemoryError:
  95             got = 'memory error'
  96         else:
  97             got = fs.hex()
  98         expected = strtod(s)
  99         self.assertEqual(expected, got,
 100                          "Incorrectly rounded str->float conversion for {}: "
 101                          "expected {}, got {}".format(s, expected, got))
 102
 103     def test_halfway_cases(self):
 104         # test halfway cases for the round-half-to-even rule
 105         for i in xrange(1000):
 106             for j in xrange(TEST_SIZE):
 107                 # bit pattern for a random finite positive (or +0.0) float
 108                 bits = random.randrange(2047*2**52)
 109
 110                 # convert bit pattern to a number of the form m * 2**e
 111                 e, m = divmod(bits, 2**52)
 112                 if e:
 113                     m, e = m + 2**52, e - 1
 114                 e -= 1074
 115
 116                 # add 0.5 ulps
 117                 m, e = 2*m + 1, e - 1
 118
 119                 # convert to a decimal string
 120                 if e >= 0:
 121                     digits = m << e
 122                     exponent = 0
 123                 else:
 124                     # m * 2**e = (m * 5**-e) * 10**e
 125                     digits = m * 5**-e
 126                     exponent = e
 127                 s = '{}e{}'.format(digits, exponent)
 128                 self.check_strtod(s)
 129
 130                 # get expected answer via struct, to triple check
 131                 #fs = struct.unpack('<d', struct.pack('<Q', bits + (bits&1)))[0]
 132                 #self.assertEqual(fs, float(s))
 133
 134     def test_boundaries(self):
 135         # boundaries expressed as triples (n, e, u), where
 136         # n*10**e is an approximation to the boundary value and
 137         # u*10**e is 1ulp
 138         boundaries = [
 139             (10000000000000000000, -19, 1110),   # a power of 2 boundary (1.0)
 140             (17976931348623159077, 289, 1995),   # overflow boundary (2.**1024)
 141             (22250738585072013831, -327, 4941),  # normal/subnormal (2.**-1022)
 142             (0, -327, 4941),                     # zero
 143             ]
 144         for n, e, u in boundaries:
 145             for j in xrange(1000):
 146                 for i in xrange(TEST_SIZE):
 147                     digits = n + random.randrange(-3*u, 3*u)
 148                     exponent = e
 149                     s = '{}e{}'.format(digits, exponent)
 150                     self.check_strtod(s)
 151                 n *= 10
 152                 u *= 10
 153                 e -= 1
 154
 155     def test_underflow_boundary(self):
 156         # test values close to 2**-1075, the underflow boundary; similar
 157         # to boundary_tests, except that the random error doesn't scale
 158         # with n
 159         for exponent in xrange(-400, -320):
 160             base = 10**-exponent // 2**1075
 161             for j in xrange(TEST_SIZE):
 162                 digits = base + random.randrange(-1000, 1000)
 163                 s = '{}e{}'.format(digits, exponent)
 164                 self.check_strtod(s)
 165
 166     def test_bigcomp(self):
 167         DIG10 = 10**50
 168         for i in xrange(1000):
 169             for j in xrange(TEST_SIZE):
 170                 digits = random.randrange(DIG10)
 171                 exponent = random.randrange(-400, 400)
 172                 s = '{}e{}'.format(digits, exponent)
 173                 self.check_strtod(s)
 174
 175     def test_parsing(self):
 176         # make '0' more likely to be chosen than other digits
 177         digits = '000000123456789'
 178         signs = ('+', '-', '')
 179
 180         # put together random short valid strings
 181         # \d*[.\d*]?e
 182         for i in xrange(1000):
 183             for j in xrange(TEST_SIZE):
 184                 s = random.choice(signs)
 185                 intpart_len = random.randrange(5)
 186                 s += ''.join(random.choice(digits) for _ in xrange(intpart_len))
 187                 if random.choice([True, False]):
 188                     s += '.'
 189                     fracpart_len = random.randrange(5)
 190                     s += ''.join(random.choice(digits)
 191                                  for _ in xrange(fracpart_len))
 192                 else:
 193                     fracpart_len = 0
 194                 if random.choice([True, False]):
 195                     s += random.choice(['e', 'E'])
 196                     s += random.choice(signs)
 197                     exponent_len = random.randrange(1, 4)
 198                     s += ''.join(random.choice(digits)
 199                                  for _ in xrange(exponent_len))
 200
 201                 if intpart_len + fracpart_len:
 202                     self.check_strtod(s)
 203                 else:
 204                     try:
 205                         float(s)
 206                     except ValueError:
 207                         pass
 208                     else:
 209                         assert False, "expected ValueError"
 210
 211     def test_particular(self):
 212         # inputs that produced crashes or incorrectly rounded results with
 213         # previous versions of dtoa.c, for various reasons
 214         test_strings = [
 215             # issue 7632 bug 1, originally reported failing case
 216             '2183167012312112312312.23538020374420446192e-370',
 217             # 5 instances of issue 7632 bug 2
 218             '12579816049008305546974391768996369464963024663104e-357',
 219             '17489628565202117263145367596028389348922981857013e-357',
 220             '18487398785991994634182916638542680759613590482273e-357',
 221             '32002864200581033134358724675198044527469366773928e-358',
 222             '94393431193180696942841837085033647913224148539854e-358',
 223             # failing case for bug introduced by METD in r77451 (attempted
 224             # fix for issue 7632, bug 2), and fixed in r77482.
 225             '28639097178261763178489759107321392745108491825303e-311',
 226             # two numbers demonstrating a flaw in the bigcomp 'dig == 0'
 227             # correction block (issue 7632, bug 3)
 228             '1.00000000000000001e44',
 229             '1.0000000000000000100000000000000000000001e44',
 230             # dtoa.c bug for numbers just smaller than a power of 2 (issue
 231             # 7632, bug 4)
 232             '99999999999999994487665465554760717039532578546e-47',
 233             # failing case for off-by-one error introduced by METD in
 234             # r77483 (dtoa.c cleanup), fixed in r77490
 235             '965437176333654931799035513671997118345570045914469' #...
 236             '6213413350821416312194420007991306908470147322020121018368e0',
 237             # incorrect lsb detection for round-half-to-even when
 238             # bc->scale != 0 (issue 7632, bug 6).
 239             '104308485241983990666713401708072175773165034278685' #...
 240             '682646111762292409330928739751702404658197872319129' #...
 241             '036519947435319418387839758990478549477777586673075' #...
 242             '945844895981012024387992135617064532141489278815239' #...
 243             '849108105951619997829153633535314849999674266169258' #...
 244             '928940692239684771590065027025835804863585454872499' #...
 245             '320500023126142553932654370362024104462255244034053' #...
 246             '203998964360882487378334860197725139151265590832887' #...
 247             '433736189468858614521708567646743455601905935595381' #...
 248             '852723723645799866672558576993978025033590728687206' #...
 249             '296379801363024094048327273913079612469982585674824' #...
 250             '156000783167963081616214710691759864332339239688734' #...
 251             '656548790656486646106983450809073750535624894296242' #...
 252             '072010195710276073042036425579852459556183541199012' #...
 253             '652571123898996574563824424330960027873516082763671875e-1075',
 254             # demonstration that original fix for issue 7632 bug 1 was
 255             # buggy; the exit condition was too strong
 256             '247032822920623295e-341',
 257             # issue 7632 bug 5: the following 2 strings convert differently
 258             '1000000000000000000000000000000000000000e-16',
 259             '10000000000000000000000000000000000000000e-17',
 260             # issue 7632 bug 8:  the following produced 10.0
 261             '10.900000000000000012345678912345678912345',
 262             ]
 263         for s in test_strings:
 264             self.check_strtod(s)
 265
 266 def test_main():
 267     test_support.run_unittest(StrtodTests)
 268
 269 if __name__ == "__main__":
 270     test_main()