From 647ed91d5c7360bdb36d909e7057aad8ce19f662 Mon Sep 17 00:00:00 2001
From: Mark Dickinson <dickinsm@gmail.com>
Date: Thu, 14 Jan 2010 15:22:33 +0000
Subject: Issue #7632:  add tests for bugs fixed so far.

---
 Lib/test/test_strtod.py | 269 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 269 insertions(+)
 create mode 100644 Lib/test/test_strtod.py

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()
-- 
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