Merged revisions 77494 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/branches/py3k
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r77494 | mark.dickinson | 2010-01-14 15:37:49 +0000 (Thu, 14 Jan 2010) | 41 lines
Merged revisions 77477-77478,77481-77483,77490-77493 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.)
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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.
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diff --git a/Lib/test/test_strtod.py b/Lib/test/test_strtod.py
new file mode 100644
index 0000000..79cfc88
--- /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
+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()
diff --git a/Python/dtoa.c b/Python/dtoa.c
index 1fe20f4..51895c7 100644
--- a/Python/dtoa.c
+++ b/Python/dtoa.c
@@ -270,7 +270,7 @@
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 @@
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 @@
b->x[0] = y9;
b->wds = 1;
- i = 9;
- if (9 < nd0) {
- s += 9;
- do {
- b = multadd(b, 10, *s++ - '0');
- if (b == NULL)
- return NULL;
- } while(++i < nd0);
- s += dplen;
+ if (nd <= 9)
+ return b;
+
+ s += 9;
+ for (i = 9; i < nd0; i++) {
+ b = multadd(b, 10, *s++ - '0');
+ if (b == NULL)
+ return NULL;
}
- else
- s += dplen + 9;
+ s++;
for(; i < nd; i++) {
b = multadd(b, 10, *s++ - '0');
if (b == NULL)
@@ -1130,76 +1128,120 @@
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
- representable as a double, sulp(x) is equivalent to 2^bc.scale * ulp(x /
- 2^bc.scale). */
+ Assuming that x is finite and nonnegative (positive zero is fine
+ here) and x / 2^bc.scale is exactly representable as a double,
+ 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.) { /* special case: value near underflow-to-zero */
- /* threshold was rounded to zero */
- b = i2b(1);
+ if (rv->d == 0.) {
+ /* special case because d2b doesn't handle 0.0 */
+ b = i2b(0);
if (b == NULL)
return -1;
- p2 = Emin - P + 1;
- bbits = 1;
- word0(rv) = (P+2) << Exp_shift;
- i = 0;
- {
- speccase = 1;
- --p2;
- dsign = 0;
- goto have_i;
- }
+ p2 = Emin - P + 1; /* = -1074 for IEEE 754 binary64 */
+ bbits = 0;
}
- else
- {
+ else {
b = d2b(rv, &p2, &bbits);
if (b == NULL)
return -1;
+ p2 -= bc->scale;
}
- p2 -= bc->scale;
- /* floor(log2(rv)) == bbits - 1 + p2 */
- /* Check for denormal case. */
+ /* now rv/2^(bc->scale) = b * 2**p2, and b has bbits significant bits */
+
+ /* 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)) {
- i = j;
- }
- {
- b = lshift(b, ++i);
- if (b == NULL)
- return -1;
- b->x[0] |= 1;
- }
- have_i:
+ if (i > p2 - (Emin - P + 1))
+ 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);
+ if (b == NULL)
+ return -1;
+ /* record whether the lsb of rv/2^(bc->scale) is odd: in the exact halfway
+ case, this is used for round to even. */
+ odd = b->x[0] & 2;
+ b->x[0] |= 1;
+
p2 -= p5 + i;
d = i2b(1);
if (d == NULL) {
@@ -1247,92 +1289,58 @@
}
}
- /* Now 10*b/d = exactly half-way between the two floating-point values
- on either side of the input string. If b >= d, round down. */
+ /* 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 */
-
- 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;
- }
+ for(i = 0; i < nd0; i++) {
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;) {
- if ((dd = s0[j++] - '0' - dig))
- goto ret;
- if (!b->x[0] && b->wds == 1) {
- if (i < nd)
- dd = 1;
- goto ret;
- }
+ s0++;
+ for(; i < nd; i++) {
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)
- 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;
- }
- }
-
+ if (dd > 0 || (dd == 0 && odd))
+ dval(rv) += sulp(rv, bc);
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 @@
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 @@
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;
- bc.dplen = bc.dp1 - bc.dp0;
+ dp1 = s - s0;
+ dplen = 1;
if (!nd) {
for(; c == '0'; c = *++s)
nz++;
@@ -1587,10 +1595,10 @@
/* in IEEE arithmetic. */
i = j = 18;
if (i > nd0)
- j += bc.dplen;
+ j += dplen;
for(;;) {
- if (--j <= bc.dp1 && j >= bc.dp0)
- j = bc.dp0 - 1;
+ if (--j <= dp1 && j >= dp0)
+ j = dp0 - 1;
if (s0[j] != '0')
break;
--i;
@@ -1603,11 +1611,11 @@
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 @@
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. */