mirrors/cpython
1
0
Fork 0
mirror of https://github.com/python/cpython.git synced 2025-08-03 16:39:00 +00:00
Code Issues Projects Releases Packages Wiki Activity Actions 8

Merged revisions 77494 via svnmerge from

Browse source 
svn+ssh://pythondev@svn.python.org/python/branches/py3k

................
  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

  ........
    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 15:43:57 +00:00
parent d16b2a121e
commit 9000c1614d
2 changed files with 418 additions and 117 deletions
Download patch file Download diff file Expand all files Collapse all files

266
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) {
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 @@ 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;
}
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 @@ 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);
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 @@ _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. */