Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from

svn+ssh://pythondev@svn.python.org/python/trunk

........
  r77477 | mark.dickinson | 2010-01-13 18:21:53 +0000 (Wed, 13 Jan 2010) | 1 line

  Add comments explaining the role of the bigcomp function in dtoa.c.
........
  r77478 | mark.dickinson | 2010-01-13 19:02:37 +0000 (Wed, 13 Jan 2010) | 1 line

  Clarify that sulp expects a nonnegative input, but that +0.0 is fine.
........
  r77481 | mark.dickinson | 2010-01-13 20:55:03 +0000 (Wed, 13 Jan 2010) | 1 line

  Simplify and annotate the bigcomp function, removing unused special cases.
........
  r77482 | mark.dickinson | 2010-01-13 22:15:53 +0000 (Wed, 13 Jan 2010) | 1 line

  Fix buggy comparison:  LHS of comparison was being treated as unsigned.
........
  r77483 | mark.dickinson | 2010-01-13 22:20:10 +0000 (Wed, 13 Jan 2010) | 1 line

  More dtoa.c cleanup;  remove the need for bc.dplen, bc.dp0 and bc.dp1.
........
  r77490 | mark.dickinson | 2010-01-14 13:02:36 +0000 (Thu, 14 Jan 2010) | 1 line

  Fix off-by-one error introduced in r77483.  I have a test for this, but it currently fails due to a different dtoa.c bug;  I'll add the test once that bug is fixed.
........
  r77491 | mark.dickinson | 2010-01-14 13:14:49 +0000 (Thu, 14 Jan 2010) | 1 line

  Issue 7632: fix a dtoa.c bug (bug 6) causing incorrect rounding.  Tests to follow.
........
  r77492 | mark.dickinson | 2010-01-14 14:40:20 +0000 (Thu, 14 Jan 2010) | 1 line

  Issue 7632:  fix incorrect rounding for long input strings with values very close to a power of 2.  (See Bug 4 in the tracker discussion.)
........
  r77493 | mark.dickinson | 2010-01-14 15:22:33 +0000 (Thu, 14 Jan 2010) | 1 line

  Issue #7632:  add tests for bugs fixed so far.
........

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
+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 range(1000):
+            for j in range(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 range(1000):
+                for i in range(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 range(-400, -320):
+            base = 10**-exponent // 2**1075
+            for j in range(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 range(1000):
+            for j in range(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, range(10)))
+        signs = ('+', '-', '')
+
+        # put together random short valid strings
+        # \d*[.\d*]?e
+        for i in range(1000):
+            for j in range(TEST_SIZE):
+                s = random.choice(signs)
+                intpart_len = random.randrange(5)
+                s += ''.join(random.choice(digits) for _ in range(intpart_len))
+                if random.choice([True, False]):
+                    s += '.'
+                    fracpart_len = random.randrange(5)
+                    s += ''.join(random.choice(digits)
+                                 for _ in range(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 range(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()

Python/dtoa.c

@@ -270,7 +270,7 @@ typedef union { double d; ULong L[2]; } U;
 typedef struct BCinfo BCinfo;
 struct
 BCinfo {
-    int dp0, dp1, dplen, dsign, e0, nd, nd0, scale;
+    int dsign, e0, nd, nd0, scale;
 };
 
 #define FFFFFFFF 0xffffffffUL
@@ -437,7 +437,7 @@ multadd(Bigint *b, int m, int a)       /* multiply by m and add a */
    NULL on failure. */
 
 static Bigint *
-s2b(const char *s, int nd0, int nd, ULong y9, int dplen)
+s2b(const char *s, int nd0, int nd, ULong y9)
 {
     Bigint *b;
     int i, k;
@@ -451,18 +451,16 @@ s2b(const char *s, int nd0, int nd, ULong y9, int dplen)
     b->x[0] = y9;
     b->wds = 1;
 
-    i = 9;
+    if (nd <= 9)
-    if (9 < nd0) {
+      return b;
-        s += 9;
+
-        do {
+    s += 9;
-            b = multadd(b, 10, *s++ - '0');
+    for (i = 9; i < nd0; i++) {
-            if (b == NULL)
+        b = multadd(b, 10, *s++ - '0');
-                return NULL;
+        if (b == NULL)
-        } while(++i < nd0);
+            return NULL;
-        s += dplen;
     }
-    else
+    s++;
-        s += dplen + 9;
     for(; i < nd; i++) {
         b = multadd(b, 10, *s++ - '0');
         if (b == NULL)
@@ -1130,76 +1128,120 @@ quorem(Bigint *b, Bigint *S)
     return q;
 }
 
-/* version of ulp(x) that takes bc.scale into account.
+/* sulp(x) is a version of ulp(x) that takes bc.scale into account.
 
-   Assuming that x is finite and nonzero, and x / 2^bc.scale is exactly
+   Assuming that x is finite and nonnegative (positive zero is fine
-   representable as a double, sulp(x) is equivalent to 2^bc.scale * ulp(x /
+   here) and x / 2^bc.scale is exactly representable as a double,
-   2^bc.scale). */
+   sulp(x) is equivalent to 2^bc.scale * ulp(x / 2^bc.scale). */
 
 static double
 sulp(U *x, BCinfo *bc)
 {
     U u;
 
-    if (bc->scale && 2*P + 1 - ((word0(x) & Exp_mask) >> Exp_shift) > 0) {
+    if (bc->scale && 2*P + 1 > (int)((word0(x) & Exp_mask) >> Exp_shift)) {
         /* rv/2^bc->scale is subnormal */
         word0(&u) = (P+2)*Exp_msk1;
         word1(&u) = 0;
         return u.d;
     }
-    else
+    else {
+        assert(word0(x) || word1(x)); /* x != 0.0 */
         return ulp(x);
+    }
 }
 
-/* return 0 on success, -1 on failure */
+/* The bigcomp function handles some hard cases for strtod, for inputs
+   with more than STRTOD_DIGLIM digits.  It's called once an initial
+   estimate for the double corresponding to the input string has
+   already been obtained by the code in _Py_dg_strtod.
+
+   The bigcomp function is only called after _Py_dg_strtod has found a
+   double value rv such that either rv or rv + 1ulp represents the
+   correctly rounded value corresponding to the original string.  It
+   determines which of these two values is the correct one by
+   computing the decimal digits of rv + 0.5ulp and comparing them with
+   the corresponding digits of s0.
+
+   In the following, write dv for the absolute value of the number represented
+   by the input string.
+
+   Inputs:
+
+     s0 points to the first significant digit of the input string.
+
+     rv is a (possibly scaled) estimate for the closest double value to the
+        value represented by the original input to _Py_dg_strtod.  If
+        bc->scale is nonzero, then rv/2^(bc->scale) is the approximation to
+        the input value.
+
+     bc is a struct containing information gathered during the parsing and
+        estimation steps of _Py_dg_strtod.  Description of fields follows:
+
+        bc->dsign is 1 if rv < decimal value, 0 if rv >= decimal value.  In
+           normal use, it should almost always be 1 when bigcomp is entered.
+
+        bc->e0 gives the exponent of the input value, such that dv = (integer
+           given by the bd->nd digits of s0) * 10**e0
+
+        bc->nd gives the total number of significant digits of s0.  It will
+           be at least 1.
+
+        bc->nd0 gives the number of significant digits of s0 before the
+           decimal separator.  If there's no decimal separator, bc->nd0 ==
+           bc->nd.
+
+        bc->scale is the value used to scale rv to avoid doing arithmetic with
+           subnormal values.  It's either 0 or 2*P (=106).
+
+   Outputs:
+
+     On successful exit, rv/2^(bc->scale) is the closest double to dv.
+
+     Returns 0 on success, -1 on failure (e.g., due to a failed malloc call). */
 
 static int
 bigcomp(U *rv, const char *s0, BCinfo *bc)
 {
     Bigint *b, *d;
-    int b2, bbits, d2, dd, dig, dsign, i, j, nd, nd0, p2, p5, speccase;
+    int b2, bbits, d2, dd, i, nd, nd0, odd, p2, p5;
 
-    dsign = bc->dsign;
+    dd = 0; /* silence compiler warning about possibly unused variable */
     nd = bc->nd;
     nd0 = bc->nd0;
     p5 = nd + bc->e0;
-    speccase = 0;
+    if (rv->d == 0.) {
-    if (rv->d == 0.) {  /* special case: value near underflow-to-zero */
+        /* special case because d2b doesn't handle 0.0 */
-        /* threshold was rounded to zero */
+        b = i2b(0);
-        b = i2b(1);
         if (b == NULL)
             return -1;
-        p2 = Emin - P + 1;
+        p2 = Emin - P + 1; /* = -1074 for IEEE 754 binary64 */
-        bbits = 1;
+        bbits = 0;
-        word0(rv) = (P+2) << Exp_shift;
-        i = 0;
-        {
-            speccase = 1;
-            --p2;
-            dsign = 0;
-            goto have_i;
-        }
     }
-    else
+    else {
-    {
         b = d2b(rv, &p2, &bbits);
         if (b == NULL)
             return -1;
+        p2 -= bc->scale;
     }
-    p2 -= bc->scale;
+    /* now rv/2^(bc->scale) = b * 2**p2, and b has bbits significant bits */
-    /* floor(log2(rv)) == bbits - 1 + p2 */
+
-    /* Check for denormal case. */
+    /* Replace (b, p2) by (b << i, p2 - i), with i the largest integer such
+       that b << i has at most P significant bits and p2 - i >= Emin - P +
+       1. */
     i = P - bbits;
-    if (i > (j = P - Emin - 1 + p2)) {
+    if (i > p2 - (Emin - P + 1))
-        i = j;
+        i = p2 - (Emin - P + 1);
-    }
+    /* increment i so that we shift b by an extra bit;  then or-ing a 1 into
-    {
+       the lsb of b gives us rv/2^(bc->scale) + 0.5ulp. */
-        b = lshift(b, ++i);
+    b = lshift(b, ++i);
-        if (b == NULL)
+    if (b == NULL)
-            return -1;
+        return -1;
-        b->x[0] |= 1;
+    /* record whether the lsb of rv/2^(bc->scale) is odd:  in the exact halfway
-    }
+       case, this is used for round to even. */
-  have_i:
+    odd = b->x[0] & 2;
+    b->x[0] |= 1;
+
     p2 -= p5 + i;
     d = i2b(1);
     if (d == NULL) {
@@ -1247,92 +1289,58 @@ bigcomp(U *rv, const char *s0, BCinfo *bc)
         }
     }
 
-    /* Now 10*b/d = exactly half-way between the two floating-point values
+    /* if b >= d, round down */
-       on either side of the input string.  If b >= d, round down. */
     if (cmp(b, d) >= 0) {
         dd = -1;
         goto ret;
     }
 
-    /* Compute first digit of 10*b/d. */
-    b = multadd(b, 10, 0);
-    if (b == NULL) {
-        Bfree(d);
-        return -1;
-    }
-    dig = quorem(b, d);
-    assert(dig < 10);
-
     /* Compare b/d with s0 */
-
+    for(i = 0; i < nd0; i++) {
-    assert(nd > 0);
-    dd = 9999;  /* silence gcc compiler warning */
-    for(i = 0; i < nd0; ) {
-        if ((dd = s0[i++] - '0' - dig))
-            goto ret;
-        if (!b->x[0] && b->wds == 1) {
-            if (i < nd)
-                dd = 1;
-            goto ret;
-        }
         b = multadd(b, 10, 0);
         if (b == NULL) {
             Bfree(d);
             return -1;
         }
-        dig = quorem(b,d);
+        dd = *s0++ - '0' - quorem(b, d);
+        if (dd)
+            goto ret;
+        if (!b->x[0] && b->wds == 1) {
+            if (i < nd - 1)
+                dd = 1;
+            goto ret;
+        }
     }
-    for(j = bc->dp1; i++ < nd;) {
+    s0++;
-        if ((dd = s0[j++] - '0' - dig))
+    for(; i < nd; i++) {
-            goto ret;
-        if (!b->x[0] && b->wds == 1) {
-            if (i < nd)
-                dd = 1;
-            goto ret;
-        }
         b = multadd(b, 10, 0);
         if (b == NULL) {
             Bfree(d);
             return -1;
         }
-        dig = quorem(b,d);
+        dd = *s0++ - '0' - quorem(b, d);
+        if (dd)
+            goto ret;
+        if (!b->x[0] && b->wds == 1) {
+            if (i < nd - 1)
+                dd = 1;
+            goto ret;
+        }
     }
     if (b->x[0] || b->wds > 1)
         dd = -1;
   ret:
     Bfree(b);
     Bfree(d);
-    if (speccase) {
+    if (dd > 0 || (dd == 0 && odd))
-        if (dd <= 0)
+        dval(rv) += sulp(rv, bc);
-            rv->d = 0.;
-    }
-    else if (dd < 0) {
-        if (!dsign)     /* does not happen for round-near */
-          retlow1:
-            dval(rv) -= sulp(rv, bc);
-    }
-    else if (dd > 0) {
-        if (dsign) {
-          rethi1:
-            dval(rv) += sulp(rv, bc);
-        }
-    }
-    else {
-        /* Exact half-way case:  apply round-even rule. */
-        if (word1(rv) & 1) {
-            if (dsign)
-                goto rethi1;
-            goto retlow1;
-        }
-    }
-
     return 0;
 }
 
 double
 _Py_dg_strtod(const char *s00, char **se)
 {
-    int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1, error;
+    int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dp0, dp1, dplen, e, e1, error;
     int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
     const char *s, *s0, *s1;
     double aadj, aadj1;
@@ -1341,7 +1349,7 @@ _Py_dg_strtod(const char *s00, char **se)
     BCinfo bc;
     Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
 
-    sign = nz0 = nz = bc.dplen = 0;
+    sign = nz0 = nz = dplen = 0;
     dval(&rv) = 0.;
     for(s = s00;;s++) switch(*s) {
         case '-':
@@ -1380,11 +1388,11 @@ _Py_dg_strtod(const char *s00, char **se)
         else if (nd < 16)
             z = 10*z + c - '0';
     nd0 = nd;
-    bc.dp0 = bc.dp1 = s - s0;
+    dp0 = dp1 = s - s0;
     if (c == '.') {
         c = *++s;
-        bc.dp1 = s - s0;
+        dp1 = s - s0;
-        bc.dplen = bc.dp1 - bc.dp0;
+        dplen = 1;
         if (!nd) {
             for(; c == '0'; c = *++s)
                 nz++;
@@ -1587,10 +1595,10 @@ _Py_dg_strtod(const char *s00, char **se)
         /* in IEEE arithmetic. */
         i = j = 18;
         if (i > nd0)
-            j += bc.dplen;
+            j += dplen;
         for(;;) {
-            if (--j <= bc.dp1 && j >= bc.dp0)
+            if (--j <= dp1 && j >= dp0)
-                j = bc.dp0 - 1;
+                j = dp0 - 1;
             if (s0[j] != '0')
                 break;
             --i;
@@ -1603,11 +1611,11 @@ _Py_dg_strtod(const char *s00, char **se)
             y = 0;
             for(i = 0; i < nd0; ++i)
                 y = 10*y + s0[i] - '0';
-            for(j = bc.dp1; i < nd; ++i)
+            for(j = dp1; i < nd; ++i)
                 y = 10*y + s0[j++] - '0';
         }
     }
-    bd0 = s2b(s0, nd0, nd, y, bc.dplen);
+    bd0 = s2b(s0, nd0, nd, y);
     if (bd0 == NULL)
         goto failed_malloc;
 
@@ -1730,6 +1738,30 @@ _Py_dg_strtod(const char *s00, char **se)
         if (bc.nd > nd && i <= 0) {
             if (bc.dsign)
                 break;  /* Must use bigcomp(). */
+
+            /* Here rv overestimates the truncated decimal value by at most
+               0.5 ulp(rv).  Hence rv either overestimates the true decimal
+               value by <= 0.5 ulp(rv), or underestimates it by some small
+               amount (< 0.1 ulp(rv)); either way, rv is within 0.5 ulps of
+               the true decimal value, so it's possible to exit.
+
+               Exception: if scaled rv is a normal exact power of 2, but not
+               DBL_MIN, then rv - 0.5 ulp(rv) takes us all the way down to the
+               next double, so the correctly rounded result is either rv - 0.5
+               ulp(rv) or rv; in this case, use bigcomp to distinguish. */
+
+            if (!word1(&rv) && !(word0(&rv) & Bndry_mask)) {
+                /* rv can't be 0, since it's an overestimate for some
+                   nonzero value.  So rv is a normal power of 2. */
+                j = (int)(word0(&rv) & Exp_mask) >> Exp_shift;
+                /* rv / 2^bc.scale = 2^(j - 1023 - bc.scale); use bigcomp if
+                   rv / 2^bc.scale >= 2^-1021. */
+                if (j - bc.scale >= 2) {
+                    dval(&rv) -= 0.5 * sulp(&rv, &bc);
+                    break;
+                }
+            }
+
             {
                 bc.nd = nd;
                 i = -1; /* Discarded digits make delta smaller. */