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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.
........
This commit is contained in:
Mark Dickinson 2010-01-14 15:37:49 +00:00
parent ae5465a578
commit 853c3bbc4c
2 changed files with 418 additions and 117 deletions
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269
Lib/test/test_strtod.py Normal file
View File

@ -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()

240
Python/dtoa.c
View File

@ -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 (9 < nd0) {
if (nd <= 9)
return b;
s += 9;
do {
for (i = 9; i < nd0; i++) {
b = multadd(b, 10, *s++ - '0');
if (b == NULL)
return NULL;
} while(++i < nd0);
s += dplen;
}
else
s += dplen + 9;
s++;
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
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;
/* floor(log2(rv)) == bbits - 1 + p2 */
/* Check for denormal case. */
i = P - bbits;
if (i > (j = P - Emin - 1 + p2)) {
i = j;
}
{
/* 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 > 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;
}
have_i:
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
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);
}
for(j = bc->dp1; i++ < nd;) {
if ((dd = s0[j++] - '0' - dig))
dd = *s0++ - '0' - quorem(b, d);
if (dd)
goto ret;
if (!b->x[0] && b->wds == 1) {
if (i < nd)
if (i < nd - 1)
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:
if (dd > 0 || (dd == 0 && odd))
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;
bc.dplen = bc.dp1 - bc.dp0;
dp1 = s - s0;
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)
j = bc.dp0 - 1;
if (--j <= dp1 && j >= dp0)
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. */