Merged revisions 77614-77616,77663 via svnmerge from
svn+ssh://pythondev@svn.python.org/python/trunk ........ r77614 | mark.dickinson | 2010-01-20 17:36:31 +0000 (Wed, 20 Jan 2010) | 5 lines Various dtoa.c cleanups. 1. Despagghetify _Py_dg_strtod parsing code and exit points. 2. Simplify bigcomp comparison loop. 3. Don't set ERANGE on _Py_dg_strtod underflow (it was set inconsistently anyway). 4. Remove unused dsign field from BCinfo struct. ........ r77615 | mark.dickinson | 2010-01-20 18:02:41 +0000 (Wed, 20 Jan 2010) | 1 line Don't try to put a value into a NULL pointer. ........ r77616 | mark.dickinson | 2010-01-20 21:23:25 +0000 (Wed, 20 Jan 2010) | 1 line Additional explanatory comments for _Py_dg_strtod. ........ r77663 | mark.dickinson | 2010-01-21 17:02:53 +0000 (Thu, 21 Jan 2010) | 1 line Additional testcases for strtod. ........
This commit is contained in:
Mark Dickinson
parent
577473fe68
commit
add2823467
|
|
@ -100,6 +100,49 @@ class StrtodTests(unittest.TestCase):
|
|||
"Incorrectly rounded str->float conversion for {}: "
|
||||
"expected {}, got {}".format(s, expected, got))
|
||||
|
||||
def test_short_halfway_cases(self):
|
||||
# exact halfway cases with a small number of significant digits
|
||||
for k in 0, 5, 10, 15, 20:
|
||||
# upper = smallest integer >= 2**54/5**k
|
||||
upper = -(-2**54//5**k)
|
||||
# lower = smallest odd number >= 2**53/5**k
|
||||
lower = -(-2**53//5**k)
|
||||
if lower % 2 == 0:
|
||||
lower += 1
|
||||
for i in range(10 * TEST_SIZE):
|
||||
# Select a random odd n in [2**53/5**k,
|
||||
# 2**54/5**k). Then n * 10**k gives a halfway case
|
||||
# with small number of significant digits.
|
||||
n, e = random.randrange(lower, upper, 2), k
|
||||
|
||||
# Remove any additional powers of 5.
|
||||
while n % 5 == 0:
|
||||
n, e = n // 5, e + 1
|
||||
assert n % 10 in (1, 3, 7, 9)
|
||||
|
||||
# Try numbers of the form n * 2**p2 * 10**e, p2 >= 0,
|
||||
# until n * 2**p2 has more than 20 significant digits.
|
||||
digits, exponent = n, e
|
||||
while digits < 10**20:
|
||||
s = '{}e{}'.format(digits, exponent)
|
||||
self.check_strtod(s)
|
||||
# Same again, but with extra trailing zeros.
|
||||
s = '{}e{}'.format(digits * 10**40, exponent - 40)
|
||||
self.check_strtod(s)
|
||||
digits *= 2
|
||||
|
||||
# Try numbers of the form n * 5**p2 * 10**(e - p5), p5
|
||||
# >= 0, with n * 5**p5 < 10**20.
|
||||
digits, exponent = n, e
|
||||
while digits < 10**20:
|
||||
s = '{}e{}'.format(digits, exponent)
|
||||
self.check_strtod(s)
|
||||
# Same again, but with extra trailing zeros.
|
||||
s = '{}e{}'.format(digits * 10**40, exponent - 40)
|
||||
self.check_strtod(s)
|
||||
digits *= 5
|
||||
exponent -= 1
|
||||
|
||||
def test_halfway_cases(self):
|
||||
# test halfway cases for the round-half-to-even rule
|
||||
for i in range(1000):
|
||||
|
|
@ -164,10 +207,10 @@ class StrtodTests(unittest.TestCase):
|
|||
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)
|
||||
for ndigs in 5, 10, 14, 15, 16, 17, 18, 19, 20, 40, 41, 50:
|
||||
dig10 = 10**ndigs
|
||||
for i in range(100 * TEST_SIZE):
|
||||
digits = random.randrange(dig10)
|
||||
exponent = random.randrange(-400, 400)
|
||||
s = '{}e{}'.format(digits, exponent)
|
||||
self.check_strtod(s)
|
||||
|
|
@ -254,11 +297,59 @@ class StrtodTests(unittest.TestCase):
|
|||
# demonstration that original fix for issue 7632 bug 1 was
|
||||
# buggy; the exit condition was too strong
|
||||
'247032822920623295e-341',
|
||||
# demonstrate similar problem to issue 7632 bug1: crash
|
||||
# with 'oversized quotient in quorem' message.
|
||||
'99037485700245683102805043437346965248029601286431e-373',
|
||||
'99617639833743863161109961162881027406769510558457e-373',
|
||||
'98852915025769345295749278351563179840130565591462e-372',
|
||||
'99059944827693569659153042769690930905148015876788e-373',
|
||||
'98914979205069368270421829889078356254059760327101e-372',
|
||||
# issue 7632 bug 5: the following 2 strings convert differently
|
||||
'1000000000000000000000000000000000000000e-16',
|
||||
'10000000000000000000000000000000000000000e-17',
|
||||
# issue 7632 bug 7
|
||||
'991633793189150720000000000000000000000000000000000000000e-33',
|
||||
# And another, similar, failing halfway case
|
||||
'4106250198039490000000000000000000000000000000000000000e-38',
|
||||
# issue 7632 bug 8: the following produced 10.0
|
||||
'10.900000000000000012345678912345678912345',
|
||||
# exercise exit conditions in bigcomp comparison loop
|
||||
'2602129298404963083833853479113577253105939995688e2',
|
||||
'260212929840496308383385347911357725310593999568896e0',
|
||||
'26021292984049630838338534791135772531059399956889601e-2',
|
||||
'260212929840496308383385347911357725310593999568895e0',
|
||||
'260212929840496308383385347911357725310593999568897e0',
|
||||
'260212929840496308383385347911357725310593999568996e0',
|
||||
'260212929840496308383385347911357725310593999568866e0',
|
||||
# 2**53
|
||||
'9007199254740992.00',
|
||||
# 2**1024 - 2**970: exact overflow boundary. All values
|
||||
# smaller than this should round to something finite; any value
|
||||
# greater than or equal to this one overflows.
|
||||
'179769313486231580793728971405303415079934132710037' #...
|
||||
'826936173778980444968292764750946649017977587207096' #...
|
||||
'330286416692887910946555547851940402630657488671505' #...
|
||||
'820681908902000708383676273854845817711531764475730' #...
|
||||
'270069855571366959622842914819860834936475292719074' #...
|
||||
'168444365510704342711559699508093042880177904174497792',
|
||||
# 2**1024 - 2**970 - tiny
|
||||
'179769313486231580793728971405303415079934132710037' #...
|
||||
'826936173778980444968292764750946649017977587207096' #...
|
||||
'330286416692887910946555547851940402630657488671505' #...
|
||||
'820681908902000708383676273854845817711531764475730' #...
|
||||
'270069855571366959622842914819860834936475292719074' #...
|
||||
'168444365510704342711559699508093042880177904174497791.999',
|
||||
# 2**1024 - 2**970 + tiny
|
||||
'179769313486231580793728971405303415079934132710037' #...
|
||||
'826936173778980444968292764750946649017977587207096' #...
|
||||
'330286416692887910946555547851940402630657488671505' #...
|
||||
'820681908902000708383676273854845817711531764475730' #...
|
||||
'270069855571366959622842914819860834936475292719074' #...
|
||||
'168444365510704342711559699508093042880177904174497792.001',
|
||||
# 1 - 2**-54, +-tiny
|
||||
'999999999999999944488848768742172978818416595458984375e-54',
|
||||
'9999999999999999444888487687421729788184165954589843749999999e-54',
|
||||
'9999999999999999444888487687421729788184165954589843750000001e-54',
|
||||
]
|
||||
for s in test_strings:
|
||||
self.check_strtod(s)
|
||||
|
|
|
|||
396
Python/dtoa.c
396
Python/dtoa.c
|
|
@ -270,7 +270,7 @@ typedef union { double d; ULong L[2]; } U;
|
|||
typedef struct BCinfo BCinfo;
|
||||
struct
|
||||
BCinfo {
|
||||
int dsign, e0, nd, nd0, scale;
|
||||
int e0, nd, nd0, scale;
|
||||
};
|
||||
|
||||
#define FFFFFFFF 0xffffffffUL
|
||||
|
|
@ -967,8 +967,8 @@ diff(Bigint *a, Bigint *b)
|
|||
return c;
|
||||
}
|
||||
|
||||
/* Given a positive normal double x, return the difference between x and the next
|
||||
double up. Doesn't give correct results for subnormals. */
|
||||
/* Given a positive normal double x, return the difference between x and the
|
||||
next double up. Doesn't give correct results for subnormals. */
|
||||
|
||||
static double
|
||||
ulp(U *x)
|
||||
|
|
@ -1276,9 +1276,6 @@ sulp(U *x, BCinfo *bc)
|
|||
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
|
||||
|
||||
|
|
@ -1387,47 +1384,37 @@ bigcomp(U *rv, const char *s0, BCinfo *bc)
|
|||
}
|
||||
}
|
||||
|
||||
/* if b >= d, round down */
|
||||
if (cmp(b, d) >= 0) {
|
||||
/* Compare s0 with b/d: set dd to -1, 0, or 1 according as s0 < b/d, s0 ==
|
||||
* b/d, or s0 > b/d. Here the digits of s0 are thought of as representing
|
||||
* a number in the range [0.1, 1). */
|
||||
if (cmp(b, d) >= 0)
|
||||
/* b/d >= 1 */
|
||||
dd = -1;
|
||||
goto ret;
|
||||
else {
|
||||
i = 0;
|
||||
for(;;) {
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
dd = s0[i < nd0 ? i : i+1] - '0' - quorem(b, d);
|
||||
i++;
|
||||
|
||||
/* Compare b/d with s0 */
|
||||
for(i = 0; i < nd0; i++) {
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
dd = *s0++ - '0' - quorem(b, d);
|
||||
if (dd)
|
||||
goto ret;
|
||||
break;
|
||||
if (!b->x[0] && b->wds == 1) {
|
||||
if (i < nd - 1)
|
||||
dd = 1;
|
||||
goto ret;
|
||||
/* b/d == 0 */
|
||||
dd = i < nd;
|
||||
break;
|
||||
}
|
||||
}
|
||||
s0++;
|
||||
for(; i < nd; i++) {
|
||||
b = multadd(b, 10, 0);
|
||||
if (b == NULL) {
|
||||
Bfree(d);
|
||||
return -1;
|
||||
}
|
||||
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)
|
||||
if (!(i < nd)) {
|
||||
/* b/d != 0, but digits of s0 exhausted */
|
||||
dd = -1;
|
||||
ret:
|
||||
break;
|
||||
}
|
||||
}
|
||||
}
|
||||
Bfree(b);
|
||||
Bfree(d);
|
||||
if (dd > 0 || (dd == 0 && odd))
|
||||
|
|
@ -1438,128 +1425,130 @@ bigcomp(U *rv, const char *s0, BCinfo *bc)
|
|||
double
|
||||
_Py_dg_strtod(const char *s00, char **se)
|
||||
{
|
||||
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, e, e1, error;
|
||||
int esign, i, j, k, nd, nd0, nf, nz, nz0, sign;
|
||||
int bb2, bb5, bbe, bd2, bd5, bbbits, bs2, c, dsign, e, e1, error;
|
||||
int esign, i, j, k, lz, nd, nd0, sign;
|
||||
const char *s, *s0, *s1;
|
||||
double aadj, aadj1;
|
||||
U aadj2, adj, rv, rv0;
|
||||
ULong y, z, abse;
|
||||
ULong y, z, abs_exp;
|
||||
Long L;
|
||||
BCinfo bc;
|
||||
Bigint *bb, *bb1, *bd, *bd0, *bs, *delta;
|
||||
|
||||
sign = nz0 = nz = 0;
|
||||
dval(&rv) = 0.;
|
||||
for(s = s00;;s++) switch(*s) {
|
||||
|
||||
/* Start parsing. */
|
||||
c = *(s = s00);
|
||||
|
||||
/* Parse optional sign, if present. */
|
||||
sign = 0;
|
||||
switch (c) {
|
||||
case '-':
|
||||
sign = 1;
|
||||
/* no break */
|
||||
case '+':
|
||||
if (*++s)
|
||||
goto break2;
|
||||
/* no break */
|
||||
case 0:
|
||||
goto ret0;
|
||||
/* modify original dtoa.c so that it doesn't accept leading whitespace
|
||||
case '\t':
|
||||
case '\n':
|
||||
case '\v':
|
||||
case '\f':
|
||||
case '\r':
|
||||
case ' ':
|
||||
continue;
|
||||
*/
|
||||
default:
|
||||
goto break2;
|
||||
c = *++s;
|
||||
}
|
||||
break2:
|
||||
if (*s == '0') {
|
||||
nz0 = 1;
|
||||
while(*++s == '0') ;
|
||||
if (!*s)
|
||||
goto ret;
|
||||
}
|
||||
s0 = s;
|
||||
for(nd = nf = 0; (c = *s) >= '0' && c <= '9'; nd++, s++)
|
||||
;
|
||||
nd0 = nd;
|
||||
|
||||
/* Skip leading zeros: lz is true iff there were leading zeros. */
|
||||
s1 = s;
|
||||
while (c == '0')
|
||||
c = *++s;
|
||||
lz = s != s1;
|
||||
|
||||
/* Point s0 at the first nonzero digit (if any). nd0 will be the position
|
||||
of the point relative to s0. nd will be the total number of digits
|
||||
ignoring leading zeros. */
|
||||
s0 = s1 = s;
|
||||
while ('0' <= c && c <= '9')
|
||||
c = *++s;
|
||||
nd0 = nd = s - s1;
|
||||
|
||||
/* Parse decimal point and following digits. */
|
||||
if (c == '.') {
|
||||
c = *++s;
|
||||
if (!nd) {
|
||||
for(; c == '0'; c = *++s)
|
||||
nz++;
|
||||
if (c > '0' && c <= '9') {
|
||||
s1 = s;
|
||||
while (c == '0')
|
||||
c = *++s;
|
||||
lz = lz || s != s1;
|
||||
nd0 -= s - s1;
|
||||
s0 = s;
|
||||
nf += nz;
|
||||
nz = 0;
|
||||
goto have_dig;
|
||||
}
|
||||
goto dig_done;
|
||||
s1 = s;
|
||||
while ('0' <= c && c <= '9')
|
||||
c = *++s;
|
||||
nd += s - s1;
|
||||
}
|
||||
for(; c >= '0' && c <= '9'; c = *++s) {
|
||||
have_dig:
|
||||
nz++;
|
||||
if (c -= '0') {
|
||||
nf += nz;
|
||||
nd += nz;
|
||||
nz = 0;
|
||||
|
||||
/* Now lz is true if and only if there were leading zero digits, and nd
|
||||
gives the total number of digits ignoring leading zeros. A valid input
|
||||
must have at least one digit. */
|
||||
if (!nd && !lz) {
|
||||
if (se)
|
||||
*se = (char *)s00;
|
||||
goto parse_error;
|
||||
}
|
||||
}
|
||||
}
|
||||
dig_done:
|
||||
|
||||
/* Parse exponent. */
|
||||
e = 0;
|
||||
if (c == 'e' || c == 'E') {
|
||||
if (!nd && !nz && !nz0) {
|
||||
goto ret0;
|
||||
}
|
||||
s00 = s;
|
||||
c = *++s;
|
||||
|
||||
/* Exponent sign. */
|
||||
esign = 0;
|
||||
switch(c = *++s) {
|
||||
switch (c) {
|
||||
case '-':
|
||||
esign = 1;
|
||||
/* no break */
|
||||
case '+':
|
||||
c = *++s;
|
||||
}
|
||||
if (c >= '0' && c <= '9') {
|
||||
|
||||
/* Skip zeros. lz is true iff there are leading zeros. */
|
||||
s1 = s;
|
||||
while (c == '0')
|
||||
c = *++s;
|
||||
if (c > '0' && c <= '9') {
|
||||
abse = c - '0';
|
||||
lz = s != s1;
|
||||
|
||||
/* Get absolute value of the exponent. */
|
||||
s1 = s;
|
||||
while((c = *++s) >= '0' && c <= '9')
|
||||
abse = 10*abse + c - '0';
|
||||
if (s - s1 > 8 || abse > MAX_ABS_EXP)
|
||||
/* Avoid confusion from exponents
|
||||
* so large that e might overflow.
|
||||
*/
|
||||
e = (int)MAX_ABS_EXP; /* safe for 16 bit ints */
|
||||
abs_exp = 0;
|
||||
while ('0' <= c && c <= '9') {
|
||||
abs_exp = 10*abs_exp + (c - '0');
|
||||
c = *++s;
|
||||
}
|
||||
|
||||
/* abs_exp will be correct modulo 2**32. But 10**9 < 2**32, so if
|
||||
there are at most 9 significant exponent digits then overflow is
|
||||
impossible. */
|
||||
if (s - s1 > 9 || abs_exp > MAX_ABS_EXP)
|
||||
e = (int)MAX_ABS_EXP;
|
||||
else
|
||||
e = (int)abse;
|
||||
e = (int)abs_exp;
|
||||
if (esign)
|
||||
e = -e;
|
||||
}
|
||||
else
|
||||
e = 0;
|
||||
}
|
||||
else
|
||||
|
||||
/* A valid exponent must have at least one digit. */
|
||||
if (s == s1 && !lz)
|
||||
s = s00;
|
||||
}
|
||||
if (!nd) {
|
||||
if (!nz && !nz0) {
|
||||
ret0:
|
||||
s = s00;
|
||||
sign = 0;
|
||||
}
|
||||
goto ret;
|
||||
}
|
||||
e -= nf;
|
||||
if (!nd0)
|
||||
|
||||
/* Adjust exponent to take into account position of the point. */
|
||||
e -= nd - nd0;
|
||||
if (nd0 <= 0)
|
||||
nd0 = nd;
|
||||
|
||||
/* strip trailing zeros */
|
||||
/* Finished parsing. Set se to indicate how far we parsed */
|
||||
if (se)
|
||||
*se = (char *)s;
|
||||
|
||||
/* If all digits were zero, exit with return value +-0.0. Otherwise,
|
||||
strip trailing zeros: scan back until we hit a nonzero digit. */
|
||||
if (!nd)
|
||||
goto ret;
|
||||
for (i = nd; i > 0; ) {
|
||||
/* scan back until we hit a nonzero digit. significant digit 'i'
|
||||
is s0[i] if i < nd0, s0[i+1] if i >= nd0. */
|
||||
--i;
|
||||
if (s0[i < nd0 ? i : i+1] != '0') {
|
||||
++i;
|
||||
|
|
@ -1571,28 +1560,21 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
if (nd0 > nd)
|
||||
nd0 = nd;
|
||||
|
||||
/* Now we have nd0 digits, starting at s0, followed by a
|
||||
* decimal point, followed by nd-nd0 digits. The number we're
|
||||
* after is the integer represented by those digits times
|
||||
* 10**e */
|
||||
|
||||
bc.e0 = e1 = e;
|
||||
|
||||
/* Summary of parsing results. The parsing stage gives values
|
||||
* s0, nd0, nd, e, sign, where:
|
||||
/* Summary of parsing results. After parsing, and dealing with zero
|
||||
* inputs, we have values s0, nd0, nd, e, sign, where:
|
||||
*
|
||||
* - s0 points to the first significant digit of the input string s00;
|
||||
* - s0 points to the first significant digit of the input string
|
||||
*
|
||||
* - nd is the total number of significant digits (here, and
|
||||
* below, 'significant digits' means the set of digits of the
|
||||
* significand of the input that remain after ignoring leading
|
||||
* and trailing zeros.
|
||||
* and trailing zeros).
|
||||
*
|
||||
* - nd0 indicates the position of the decimal point (if
|
||||
* present): so the nd significant digits are in s0[0:nd0] and
|
||||
* s0[nd0+1:nd+1] using the usual Python half-open slice
|
||||
* notation. (If nd0 < nd, then s0[nd0] necessarily contains
|
||||
* a '.' character; if nd0 == nd, then it could be anything.)
|
||||
* - nd0 indicates the position of the decimal point, if present; it
|
||||
* satisfies 1 <= nd0 <= nd. The nd significant digits are in
|
||||
* s0[0:nd0] and s0[nd0+1:nd+1] using the usual Python half-open slice
|
||||
* notation. (If nd0 < nd, then s0[nd0] contains a '.' character; if
|
||||
* nd0 == nd, then s0[nd0] could be any non-digit character.)
|
||||
*
|
||||
* - e is the adjusted exponent: the absolute value of the number
|
||||
* represented by the original input string is n * 10**e, where
|
||||
|
|
@ -1614,6 +1596,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
* gives the value represented by the first min(16, nd) sig. digits.
|
||||
*/
|
||||
|
||||
bc.e0 = e1 = e;
|
||||
y = z = 0;
|
||||
for (i = 0; i < nd; i++) {
|
||||
if (i < 9)
|
||||
|
|
@ -1666,14 +1649,8 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
if ((i = e1 & 15))
|
||||
dval(&rv) *= tens[i];
|
||||
if (e1 &= ~15) {
|
||||
if (e1 > DBL_MAX_10_EXP) {
|
||||
ovfl:
|
||||
errno = ERANGE;
|
||||
/* Can't trust HUGE_VAL */
|
||||
word0(&rv) = Exp_mask;
|
||||
word1(&rv) = 0;
|
||||
goto ret;
|
||||
}
|
||||
if (e1 > DBL_MAX_10_EXP)
|
||||
goto ovfl;
|
||||
e1 >>= 4;
|
||||
for(j = 0; e1 > 1; j++, e1 >>= 1)
|
||||
if (e1 & 1)
|
||||
|
|
@ -1695,6 +1672,16 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
}
|
||||
}
|
||||
else if (e1 < 0) {
|
||||
/* The input decimal value lies in [10**e1, 10**(e1+16)).
|
||||
|
||||
If e1 <= -512, underflow immediately.
|
||||
If e1 <= -256, set bc.scale to 2*P.
|
||||
|
||||
So for input value < 1e-256, bc.scale is always set;
|
||||
for input value >= 1e-240, bc.scale is never set.
|
||||
For input values in [1e-256, 1e-240), bc.scale may or may
|
||||
not be set. */
|
||||
|
||||
e1 = -e1;
|
||||
if ((i = e1 & 15))
|
||||
dval(&rv) /= tens[i];
|
||||
|
|
@ -1719,12 +1706,8 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
else
|
||||
word1(&rv) &= 0xffffffff << j;
|
||||
}
|
||||
if (!dval(&rv)) {
|
||||
undfl:
|
||||
dval(&rv) = 0.;
|
||||
errno = ERANGE;
|
||||
goto ret;
|
||||
}
|
||||
if (!dval(&rv))
|
||||
goto undfl;
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -1769,7 +1752,34 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
if (bd0 == NULL)
|
||||
goto failed_malloc;
|
||||
|
||||
/* Notation for the comments below. Write:
|
||||
|
||||
- dv for the absolute value of the number represented by the original
|
||||
decimal input string.
|
||||
|
||||
- if we've truncated dv, write tdv for the truncated value.
|
||||
Otherwise, set tdv == dv.
|
||||
|
||||
- srv for the quantity rv/2^bc.scale; so srv is the current binary
|
||||
approximation to tdv (and dv). It should be exactly representable
|
||||
in an IEEE 754 double.
|
||||
*/
|
||||
|
||||
for(;;) {
|
||||
|
||||
/* This is the main correction loop for _Py_dg_strtod.
|
||||
|
||||
We've got a decimal value tdv, and a floating-point approximation
|
||||
srv=rv/2^bc.scale to tdv. The aim is to determine whether srv is
|
||||
close enough (i.e., within 0.5 ulps) to tdv, and to compute a new
|
||||
approximation if not.
|
||||
|
||||
To determine whether srv is close enough to tdv, compute integers
|
||||
bd, bb and bs proportional to tdv, srv and 0.5 ulp(srv)
|
||||
respectively, and then use integer arithmetic to determine whether
|
||||
|tdv - srv| is less than, equal to, or greater than 0.5 ulp(srv).
|
||||
*/
|
||||
|
||||
bd = Balloc(bd0->k);
|
||||
if (bd == NULL) {
|
||||
Bfree(bd0);
|
||||
|
|
@ -1782,6 +1792,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
Bfree(bd0);
|
||||
goto failed_malloc;
|
||||
}
|
||||
/* tdv = bd * 10^e; srv = bb * 2^(bbe - scale) */
|
||||
bs = i2b(1);
|
||||
if (bs == NULL) {
|
||||
Bfree(bb);
|
||||
|
|
@ -1802,6 +1813,17 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
bb2 += bbe;
|
||||
else
|
||||
bd2 -= bbe;
|
||||
|
||||
/* At this stage e = bd2 - bb2 + bbe = bd5 - bb5, so:
|
||||
|
||||
tdv = bd * 2^(bbe + bd2 - bb2) * 5^(bd5 - bb5)
|
||||
srv = bb * 2^(bbe - scale).
|
||||
|
||||
Compute j such that
|
||||
|
||||
0.5 ulp(srv) = 2^(bbe - scale - j)
|
||||
*/
|
||||
|
||||
bs2 = bb2;
|
||||
j = bbe - bc.scale;
|
||||
i = j + bbbits - 1; /* logb(rv) */
|
||||
|
|
@ -1809,9 +1831,26 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
j += P - Emin;
|
||||
else
|
||||
j = P + 1 - bbbits;
|
||||
|
||||
/* Now we have:
|
||||
|
||||
M * tdv = bd * 2^(bd2 + scale + j) * 5^bd5
|
||||
M * srv = bb * 2^(bb2 + j) * 5^bb5
|
||||
M * 0.5 ulp(srv) = 2^bs2 * 5^bb5
|
||||
|
||||
where M is the constant (currently) represented by 2^(j + scale +
|
||||
bb2 - bbe) * 5^bb5.
|
||||
*/
|
||||
|
||||
bb2 += j;
|
||||
bd2 += j;
|
||||
bd2 += bc.scale;
|
||||
|
||||
/* After the adjustments above, tdv, srv and 0.5 ulp(srv) are
|
||||
proportional to: bd * 2^bd2 * 5^bd5, bb * 2^bb2 * 5^bb5, and
|
||||
bs * 2^bs2 * 5^bb5, respectively. */
|
||||
|
||||
/* Remove excess powers of 2. i = min(bb2, bd2, bs2). */
|
||||
i = bb2 < bd2 ? bb2 : bd2;
|
||||
if (i > bs2)
|
||||
i = bs2;
|
||||
|
|
@ -1820,6 +1859,8 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
bd2 -= i;
|
||||
bs2 -= i;
|
||||
}
|
||||
|
||||
/* Scale bb, bd, bs by the appropriate powers of 2 and 5. */
|
||||
if (bb5 > 0) {
|
||||
bs = pow5mult(bs, bb5);
|
||||
if (bs == NULL) {
|
||||
|
|
@ -1874,6 +1915,11 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
goto failed_malloc;
|
||||
}
|
||||
}
|
||||
|
||||
/* Now bd, bb and bs are scaled versions of tdv, srv and 0.5 ulp(srv),
|
||||
respectively. Compute the difference |tdv - srv|, and compare
|
||||
with 0.5 ulp(srv). */
|
||||
|
||||
delta = diff(bb, bd);
|
||||
if (delta == NULL) {
|
||||
Bfree(bb);
|
||||
|
|
@ -1882,11 +1928,11 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
Bfree(bd0);
|
||||
goto failed_malloc;
|
||||
}
|
||||
bc.dsign = delta->sign;
|
||||
dsign = delta->sign;
|
||||
delta->sign = 0;
|
||||
i = cmp(delta, bs);
|
||||
if (bc.nd > nd && i <= 0) {
|
||||
if (bc.dsign)
|
||||
if (dsign)
|
||||
break; /* Must use bigcomp(). */
|
||||
|
||||
/* Here rv overestimates the truncated decimal value by at most
|
||||
|
|
@ -1908,7 +1954,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
rv / 2^bc.scale >= 2^-1021. */
|
||||
if (j - bc.scale >= 2) {
|
||||
dval(&rv) -= 0.5 * sulp(&rv, &bc);
|
||||
break;
|
||||
break; /* Use bigcomp. */
|
||||
}
|
||||
}
|
||||
|
||||
|
|
@ -1922,7 +1968,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
/* Error is less than half an ulp -- check for
|
||||
* special case of mantissa a power of two.
|
||||
*/
|
||||
if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask
|
||||
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask
|
||||
|| (word0(&rv) & Exp_mask) <= (2*P+1)*Exp_msk1
|
||||
) {
|
||||
break;
|
||||
|
|
@ -1945,7 +1991,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
}
|
||||
if (i == 0) {
|
||||
/* exactly half-way between */
|
||||
if (bc.dsign) {
|
||||
if (dsign) {
|
||||
if ((word0(&rv) & Bndry_mask1) == Bndry_mask1
|
||||
&& word1(&rv) == (
|
||||
(bc.scale &&
|
||||
|
|
@ -1957,7 +2003,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
+ Exp_msk1
|
||||
;
|
||||
word1(&rv) = 0;
|
||||
bc.dsign = 0;
|
||||
dsign = 0;
|
||||
break;
|
||||
}
|
||||
}
|
||||
|
|
@ -1984,7 +2030,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
}
|
||||
if (!(word1(&rv) & LSB))
|
||||
break;
|
||||
if (bc.dsign)
|
||||
if (dsign)
|
||||
dval(&rv) += ulp(&rv);
|
||||
else {
|
||||
dval(&rv) -= ulp(&rv);
|
||||
|
|
@ -1994,11 +2040,11 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
goto undfl;
|
||||
}
|
||||
}
|
||||
bc.dsign = 1 - bc.dsign;
|
||||
dsign = 1 - dsign;
|
||||
break;
|
||||
}
|
||||
if ((aadj = ratio(delta, bs)) <= 2.) {
|
||||
if (bc.dsign)
|
||||
if (dsign)
|
||||
aadj = aadj1 = 1.;
|
||||
else if (word1(&rv) || word0(&rv) & Bndry_mask) {
|
||||
if (word1(&rv) == Tiny1 && !word0(&rv)) {
|
||||
|
|
@ -2022,7 +2068,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
}
|
||||
else {
|
||||
aadj *= 0.5;
|
||||
aadj1 = bc.dsign ? aadj : -aadj;
|
||||
aadj1 = dsign ? aadj : -aadj;
|
||||
if (Flt_Rounds == 0)
|
||||
aadj1 += 0.5;
|
||||
}
|
||||
|
|
@ -2058,7 +2104,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
if ((z = (ULong)aadj) <= 0)
|
||||
z = 1;
|
||||
aadj = z;
|
||||
aadj1 = bc.dsign ? aadj : -aadj;
|
||||
aadj1 = dsign ? aadj : -aadj;
|
||||
}
|
||||
dval(&aadj2) = aadj1;
|
||||
word0(&aadj2) += (2*P+1)*Exp_msk1 - y;
|
||||
|
|
@ -2075,7 +2121,7 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
L = (Long)aadj;
|
||||
aadj -= L;
|
||||
/* The tolerances below are conservative. */
|
||||
if (bc.dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
||||
if (dsign || word1(&rv) || word0(&rv) & Bndry_mask) {
|
||||
if (aadj < .4999999 || aadj > .5000001)
|
||||
break;
|
||||
}
|
||||
|
|
@ -2104,20 +2150,28 @@ _Py_dg_strtod(const char *s00, char **se)
|
|||
word0(&rv0) = Exp_1 - 2*P*Exp_msk1;
|
||||
word1(&rv0) = 0;
|
||||
dval(&rv) *= dval(&rv0);
|
||||
/* try to avoid the bug of testing an 8087 register value */
|
||||
if (!(word0(&rv) & Exp_mask))
|
||||
errno = ERANGE;
|
||||
}
|
||||
|
||||
ret:
|
||||
if (se)
|
||||
*se = (char *)s;
|
||||
return sign ? -dval(&rv) : dval(&rv);
|
||||
|
||||
parse_error:
|
||||
return 0.0;
|
||||
|
||||
failed_malloc:
|
||||
if (se)
|
||||
*se = (char *)s00;
|
||||
errno = ENOMEM;
|
||||
return -1.0;
|
||||
|
||||
undfl:
|
||||
return sign ? -0.0 : 0.0;
|
||||
|
||||
ovfl:
|
||||
errno = ERANGE;
|
||||
/* Can't trust HUGE_VAL */
|
||||
word0(&rv) = Exp_mask;
|
||||
word1(&rv) = 0;
|
||||
return sign ? -dval(&rv) : dval(&rv);
|
||||
|
||||
}
|
||||
|
||||
static char *
|
||||
|
|
|
|||
Loading…
Reference in New Issue