diff options
Diffstat (limited to 'Lib')
| -rw-r--r-- | Lib/test/test_strtod.py | 269 |
1 files changed, 269 insertions, 0 deletions
diff --git a/Lib/test/test_strtod.py b/Lib/test/test_strtod.py new file mode 100644 index 0000000..7800a73 --- /dev/null +++ b/Lib/test/test_strtod.py @@ -0,0 +1,269 @@ +# 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 + +# 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 + +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 + +@unittest.skipUnless(getattr(sys, 'float_repr_style', '') == 'short', + "applies only when using short float repr style") +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' + 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_halfway_cases(self): + # test halfway cases for the round-half-to-even rule + for i in xrange(1000): + for j in xrange(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) + + # for the moment, ignore errors from trailing zeros + if digits % 10 == 0: + continue + self.check_strtod(s) + + # get expected answer via struct, to triple check + #fs = struct.unpack('<d', struct.pack('<Q', bits + (bits&1)))[0] + #self.assertEqual(fs, float(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): + for i in xrange(TEST_SIZE): + 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): + DIG10 = 10**50 + for i in xrange(1000): + for j in xrange(TEST_SIZE): + digits = random.randrange(DIG10) + exponent = random.randrange(-400, 400) + s = '{}e{}'.format(digits, exponent) + self.check_strtod(s) + + def test_parsing(self): + digits = tuple(map(str, xrange(10))) + 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', + # 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', + # issue 7632 bug 5: the following 2 strings convert differently + '1000000000000000000000000000000000000000e-16', + #'10000000000000000000000000000000000000000e-17', + ] + for s in test_strings: + self.check_strtod(s) + +def test_main(): + test_support.run_unittest(StrtodTests) + +if __name__ == "__main__": + test_main() |