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Merged revisions 77234 via svnmerge from 

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

........
  r77234 | mark.dickinson | 2010-01-02 14:45:40 +0000 (Sat, 02 Jan 2010) | 7 lines

  Refactor some longobject internals:  PyLong_AsDouble and _PyLong_AsScaledDouble
  (the latter renamed to _PyLong_Frexp) now use the same core code.  The
  exponent produced by _PyLong_Frexp now has type Py_ssize_t instead of the
  previously used int, and no longer needs scaling by PyLong_SHIFT.  This
  frees the math module from having to know anything about the PyLong
  implementation.  This closes issue #5576.
........
This commit is contained in:
Mark Dickinson 2010-01-02 15:33:56 +00:00
parent 01f748a832
commit 6ecd9e53ce
3 changed files with 168 additions and 240 deletions
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14
Include/longobject.h
View File

@ -44,13 +44,13 @@ PyAPI_FUNC(PyObject *) PyLong_GetInfo(void);
/* For use by intobject.c only */ /* For use by intobject.c only */
PyAPI_DATA(unsigned char) _PyLong_DigitValue[256]; PyAPI_DATA(unsigned char) _PyLong_DigitValue[256];
/* _PyLong_AsScaledDouble returns a double x and an exponent e such that /* _PyLong_Frexp returns a double x and an exponent e such that the
the true value is approximately equal to x * 2**(SHIFT*e). e is >= 0. true value is approximately equal to x * 2**e. e is >= 0. x is
x is 0.0 if and only if the input is 0 (in which case, e and x are both 0.0 if and only if the input is 0 (in which case, e and x are both
zeroes). Overflow is impossible. Note that the exponent returned must zeroes); otherwise, 0.5 <= abs(x) < 1.0. On overflow, which is
be multiplied by SHIFT! There may not be enough room in an int to store possible if the number of bits doesn't fit into a Py_ssize_t, sets
e*SHIFT directly. */ OverflowError and returns -1.0 for x, 0 for e. */
PyAPI_FUNC(double) _PyLong_AsScaledDouble(PyObject *vv, int *e); PyAPI_FUNC(double) _PyLong_Frexp(PyLongObject *a, Py_ssize_t *e);
PyAPI_FUNC(double) PyLong_AsDouble(PyObject *); PyAPI_FUNC(double) PyLong_AsDouble(PyObject *);
PyAPI_FUNC(PyObject *) PyLong_FromVoidPtr(void *); PyAPI_FUNC(PyObject *) PyLong_FromVoidPtr(void *);

27
Modules/mathmodule.c
View File

@ -54,7 +54,6 @@ raised for division by zero and mod by zero.
#include "Python.h" #include "Python.h"
#include "_math.h" #include "_math.h"
#include "longintrepr.h" /* just for SHIFT */
#ifdef _OSF_SOURCE #ifdef _OSF_SOURCE
/* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */ /* OSF1 5.1 doesn't make this available with XOPEN_SOURCE_EXTENDED defined */
@ -1342,11 +1341,12 @@ PyDoc_STRVAR(math_modf_doc,
/* A decent logarithm is easy to compute even for huge longs, but libm can't /* A decent logarithm is easy to compute even for huge longs, but libm can't
do that by itself -- loghelper can. func is log or log10, and name is do that by itself -- loghelper can. func is log or log10, and name is
"log" or "log10". Note that overflow isn't possible: a long can contain "log" or "log10". Note that overflow of the result isn't possible: a long
no more than INT_MAX * SHIFT bits, so has value certainly less than can contain no more than INT_MAX * SHIFT bits, so has value certainly less
2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is than 2**(2**64 * 2**16) == 2**2**80, and log2 of that is 2**80, which is
small enough to fit in an IEEE single. log and log10 are even smaller. small enough to fit in an IEEE single. log and log10 are even smaller.
*/ However, intermediate overflow is possible for a long if the number of bits
in that long is larger than PY_SSIZE_T_MAX. */
static PyObject* static PyObject*
loghelper(PyObject* arg, double (*func)(double), char *funcname) loghelper(PyObject* arg, double (*func)(double), char *funcname)
@ -1354,18 +1354,21 @@ loghelper(PyObject* arg, double (*func)(double), char *funcname)
/* If it is long, do it ourselves. */ /* If it is long, do it ourselves. */
if (PyLong_Check(arg)) { if (PyLong_Check(arg)) {
double x; double x;
int e; Py_ssize_t e;
x = _PyLong_AsScaledDouble(arg, &e); x = _PyLong_Frexp((PyLongObject *)arg, &e);
if (x == -1.0 && PyErr_Occurred())
return NULL;
if (x <= 0.0) { if (x <= 0.0) {
PyErr_SetString(PyExc_ValueError, PyErr_SetString(PyExc_ValueError,
"math domain error"); "math domain error");
return NULL; return NULL;
} }
/* Value is ~= x * 2**(e*PyLong_SHIFT), so the log ~= /* Special case for log(1), to make sure we get an
log(x) + log(2) * e * PyLong_SHIFT. exact result there. */
CAUTION: e*PyLong_SHIFT may overflow using int arithmetic, if (e == 1 && x == 0.5)
so force use of double. */ return PyFloat_FromDouble(0.0);
x = func(x) + (e * (double)PyLong_SHIFT) * func(2.0); /* Value is ~= x * 2**e, so the log ~= log(x) + log(2) * e. */
x = func(x) + func(2.0) * e;
return PyFloat_FromDouble(x); return PyFloat_FromDouble(x);
} }

367
Objects/longobject.c
View File

@ -98,9 +98,6 @@ maybe_small_long(PyLongObject *v)
#define SIGCHECK(PyTryBlock) \ #define SIGCHECK(PyTryBlock) \
if (PyErr_CheckSignals()) PyTryBlock \ if (PyErr_CheckSignals()) PyTryBlock \
/* forward declaration */
static int bits_in_digit(digit d);
/* Normalize (remove leading zeros from) a long int object. /* Normalize (remove leading zeros from) a long int object.
Doesn't attempt to free the storage--in most cases, due to the nature Doesn't attempt to free the storage--in most cases, due to the nature
of the algorithms used, this could save at most be one word anyway. */ of the algorithms used, this could save at most be one word anyway. */
@ -911,224 +908,6 @@ Overflow:
} }
double
_PyLong_AsScaledDouble(PyObject *vv, int *exponent)
{
/* NBITS_WANTED should be > the number of bits in a double's precision,
but small enough so that 2**NBITS_WANTED is within the normal double
range. nbitsneeded is set to 1 less than that because the most-significant
Python digit contains at least 1 significant bit, but we don't want to
bother counting them (catering to the worst case cheaply).
57 is one more than VAX-D double precision; I (Tim) don't know of a double
format with more precision than that; it's 1 larger so that we add in at
least one round bit to stand in for the ignored least-significant bits.
*/
#define NBITS_WANTED 57
PyLongObject *v;
double x;
const double multiplier = (double)(1L << PyLong_SHIFT);
Py_ssize_t i;
int sign;
int nbitsneeded;
if (vv == NULL || !PyLong_Check(vv)) {
PyErr_BadInternalCall();
return -1;
}
v = (PyLongObject *)vv;
i = Py_SIZE(v);
sign = 1;
if (i < 0) {
sign = -1;
i = -(i);
}
else if (i == 0) {
*exponent = 0;
return 0.0;
}
--i;
x = (double)v->ob_digit[i];
nbitsneeded = NBITS_WANTED - 1;
/* Invariant: i Python digits remain unaccounted for. */
while (i > 0 && nbitsneeded > 0) {
--i;
x = x * multiplier + (double)v->ob_digit[i];
nbitsneeded -= PyLong_SHIFT;
}
/* There are i digits we didn't shift in. Pretending they're all
zeroes, the true value is x * 2**(i*PyLong_SHIFT). */
*exponent = i;
assert(x > 0.0);
return x * sign;
#undef NBITS_WANTED
}
/* Get a C double from a long int object. Rounds to the nearest double,
using the round-half-to-even rule in the case of a tie. */
double
PyLong_AsDouble(PyObject *vv)
{
PyLongObject *v = (PyLongObject *)vv;
Py_ssize_t rnd_digit, rnd_bit, m, n;
digit lsb, *d;
int round_up = 0;
double x;
if (vv == NULL || !PyLong_Check(vv)) {
PyErr_BadInternalCall();
return -1.0;
}
/* Notes on the method: for simplicity, assume v is positive and >=
2**DBL_MANT_DIG. (For negative v we just ignore the sign until the
end; for small v no rounding is necessary.) Write n for the number
of bits in v, so that 2**(n-1) <= v < 2**n, and n > DBL_MANT_DIG.
Some terminology: the *rounding bit* of v is the 1st bit of v that
will be rounded away (bit n - DBL_MANT_DIG - 1); the *parity bit*
is the bit immediately above. The round-half-to-even rule says
that we round up if the rounding bit is set, unless v is exactly
halfway between two floats and the parity bit is zero.
Write d[0] ... d[m] for the digits of v, least to most significant.
Let rnd_bit be the index of the rounding bit, and rnd_digit the
index of the PyLong digit containing the rounding bit. Then the
bits of the digit d[rnd_digit] look something like:
rounding bit
|
v
msb -> sssssrttttttttt <- lsb
^
|
parity bit
where 's' represents a 'significant bit' that will be included in
the mantissa of the result, 'r' is the rounding bit, and 't'
represents a 'trailing bit' following the rounding bit. Note that
if the rounding bit is at the top of d[rnd_digit] then the parity
bit will be the lsb of d[rnd_digit+1]. If we set
lsb = 1 << (rnd_bit % PyLong_SHIFT)
then d[rnd_digit] & (PyLong_BASE - 2*lsb) selects just the
significant bits of d[rnd_digit], d[rnd_digit] & (lsb-1) gets the
trailing bits, and d[rnd_digit] & lsb gives the rounding bit.
We initialize the double x to the integer given by digits
d[rnd_digit:m-1], but with the rounding bit and trailing bits of
d[rnd_digit] masked out. So the value of x comes from the top
DBL_MANT_DIG bits of v, multiplied by 2*lsb. Note that in the loop
that produces x, all floating-point operations are exact (assuming
that FLT_RADIX==2). Now if we're rounding down, the value we want
to return is simply
x * 2**(PyLong_SHIFT * rnd_digit).
and if we're rounding up, it's
(x + 2*lsb) * 2**(PyLong_SHIFT * rnd_digit).
Under the round-half-to-even rule, we round up if, and only
if, the rounding bit is set *and* at least one of the
following three conditions is satisfied:
(1) the parity bit is set, or
(2) at least one of the trailing bits of d[rnd_digit] is set, or
(3) at least one of the digits d[i], 0 <= i < rnd_digit
is nonzero.
Finally, we have to worry about overflow. If v >= 2**DBL_MAX_EXP,
or equivalently n > DBL_MAX_EXP, then overflow occurs. If v <
2**DBL_MAX_EXP then we're usually safe, but there's a corner case
to consider: if v is very close to 2**DBL_MAX_EXP then it's
possible that v is rounded up to exactly 2**DBL_MAX_EXP, and then
again overflow occurs.
*/
if (Py_SIZE(v) == 0)
return 0.0;
m = ABS(Py_SIZE(v)) - 1;
d = v->ob_digit;
assert(d[m]); /* v should be normalized */
/* fast path for case where 0 < abs(v) < 2**DBL_MANT_DIG */
if (m < DBL_MANT_DIG / PyLong_SHIFT ||
(m == DBL_MANT_DIG / PyLong_SHIFT &&
d[m] < (digit)1 << DBL_MANT_DIG%PyLong_SHIFT)) {
x = d[m];
while (--m >= 0)
x = x*PyLong_BASE + d[m];
return Py_SIZE(v) < 0 ? -x : x;
}
/* if m is huge then overflow immediately; otherwise, compute the
number of bits n in v. The condition below implies n (= #bits) >=
m * PyLong_SHIFT + 1 > DBL_MAX_EXP, hence v >= 2**DBL_MAX_EXP. */
if (m > (DBL_MAX_EXP-1)/PyLong_SHIFT)
goto overflow;
n = m * PyLong_SHIFT + bits_in_digit(d[m]);
if (n > DBL_MAX_EXP)
goto overflow;
/* find location of rounding bit */
assert(n > DBL_MANT_DIG); /* dealt with |v| < 2**DBL_MANT_DIG above */
rnd_bit = n - DBL_MANT_DIG - 1;
rnd_digit = rnd_bit/PyLong_SHIFT;
lsb = (digit)1 << (rnd_bit%PyLong_SHIFT);
/* Get top DBL_MANT_DIG bits of v. Assumes PyLong_SHIFT <
DBL_MANT_DIG, so we'll need bits from at least 2 digits of v. */
x = d[m];
assert(m > rnd_digit);
while (--m > rnd_digit)
x = x*PyLong_BASE + d[m];
x = x*PyLong_BASE + (d[m] & (PyLong_BASE-2*lsb));
/* decide whether to round up, using round-half-to-even */
assert(m == rnd_digit);
if (d[m] & lsb) { /* if (rounding bit is set) */
digit parity_bit;
if (lsb == PyLong_BASE/2)
parity_bit = d[m+1] & 1;
else
parity_bit = d[m] & 2*lsb;
if (parity_bit)
round_up = 1;
else if (d[m] & (lsb-1))
round_up = 1;
else {
while (--m >= 0) {
if (d[m]) {
round_up = 1;
break;
}
}
}
}
/* and round up if necessary */
if (round_up) {
x += 2*lsb;
if (n == DBL_MAX_EXP &&
x == ldexp((double)(2*lsb), DBL_MANT_DIG)) {
/* overflow corner case */
goto overflow;
}
}
/* shift, adjust for sign, and return */
x = ldexp(x, rnd_digit*PyLong_SHIFT);
return Py_SIZE(v) < 0 ? -x : x;
overflow:
PyErr_SetString(PyExc_OverflowError,
"Python int too large to convert to C double");
return -1.0;
}
/* Create a new long (or int) object from a C pointer */ /* Create a new long (or int) object from a C pointer */
PyObject * PyObject *
@ -2442,6 +2221,152 @@ x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
return long_normalize(a); return long_normalize(a);
} }
/* For a nonzero PyLong a, express a in the form x * 2**e, with 0.5 <=
abs(x) < 1.0 and e >= 0; return x and put e in *e. Here x is
rounded to DBL_MANT_DIG significant bits using round-half-to-even.
If a == 0, return 0.0 and set *e = 0. If the resulting exponent
e is larger than PY_SSIZE_T_MAX, raise OverflowError and return
-1.0. */
/* attempt to define 2.0**DBL_MANT_DIG as a compile-time constant */
#if DBL_MANT_DIG == 53
#define EXP2_DBL_MANT_DIG 9007199254740992.0
#else
#define EXP2_DBL_MANT_DIG (ldexp(1.0, DBL_MANT_DIG))
#endif
double
_PyLong_Frexp(PyLongObject *a, Py_ssize_t *e)
{
Py_ssize_t a_size, a_bits, shift_digits, shift_bits, x_size;
/* See below for why x_digits is always large enough. */
digit rem, x_digits[2 + (DBL_MANT_DIG + 1) / PyLong_SHIFT];
double dx;
/* Correction term for round-half-to-even rounding. For a digit x,
"x + half_even_correction[x & 7]" gives x rounded to the nearest
multiple of 4, rounding ties to a multiple of 8. */
static const int half_even_correction[8] = {0, -1, -2, 1, 0, -1, 2, 1};
a_size = ABS(Py_SIZE(a));
if (a_size == 0) {
/* Special case for 0: significand 0.0, exponent 0. */
*e = 0;
return 0.0;
}
a_bits = bits_in_digit(a->ob_digit[a_size-1]);
/* The following is an overflow-free version of the check
"if ((a_size - 1) * PyLong_SHIFT + a_bits > PY_SSIZE_T_MAX) ..." */
if (a_size >= (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 &&
(a_size > (PY_SSIZE_T_MAX - 1) / PyLong_SHIFT + 1 ||
a_bits > (PY_SSIZE_T_MAX - 1) % PyLong_SHIFT + 1))
goto overflow;
a_bits = (a_size - 1) * PyLong_SHIFT + a_bits;
/* Shift the first DBL_MANT_DIG + 2 bits of a into x_digits[0:x_size]
(shifting left if a_bits <= DBL_MANT_DIG + 2).
Number of digits needed for result: write // for floor division.
Then if shifting left, we end up using
1 + a_size + (DBL_MANT_DIG + 2 - a_bits) // PyLong_SHIFT
digits. If shifting right, we use
a_size - (a_bits - DBL_MANT_DIG - 2) // PyLong_SHIFT
digits. Using a_size = 1 + (a_bits - 1) // PyLong_SHIFT along with
the inequalities
m // PyLong_SHIFT + n // PyLong_SHIFT <= (m + n) // PyLong_SHIFT
m // PyLong_SHIFT - n // PyLong_SHIFT <=
1 + (m - n - 1) // PyLong_SHIFT,
valid for any integers m and n, we find that x_size satisfies
x_size <= 2 + (DBL_MANT_DIG + 1) // PyLong_SHIFT
in both cases.
*/
if (a_bits <= DBL_MANT_DIG + 2) {
shift_digits = (DBL_MANT_DIG + 2 - a_bits) / PyLong_SHIFT;
shift_bits = (DBL_MANT_DIG + 2 - a_bits) % PyLong_SHIFT;
x_size = 0;
while (x_size < shift_digits)
x_digits[x_size++] = 0;
rem = v_lshift(x_digits + x_size, a->ob_digit, a_size,
shift_bits);
x_size += a_size;
x_digits[x_size++] = rem;
}
else {
shift_digits = (a_bits - DBL_MANT_DIG - 2) / PyLong_SHIFT;
shift_bits = (a_bits - DBL_MANT_DIG - 2) % PyLong_SHIFT;
rem = v_rshift(x_digits, a->ob_digit + shift_digits,
a_size - shift_digits, shift_bits);
x_size = a_size - shift_digits;
/* For correct rounding below, we need the least significant
bit of x to be 'sticky' for this shift: if any of the bits
shifted out was nonzero, we set the least significant bit
of x. */
if (rem)
x_digits[0] |= 1;
else
while (shift_digits > 0)
if (a->ob_digit[--shift_digits]) {
x_digits[0] |= 1;
break;
}
}
assert(1 <= x_size && x_size <= sizeof(x_digits)/sizeof(digit));
/* Round, and convert to double. */
x_digits[0] += half_even_correction[x_digits[0] & 7];
dx = x_digits[--x_size];
while (x_size > 0)
dx = dx * PyLong_BASE + x_digits[--x_size];
/* Rescale; make correction if result is 1.0. */
dx /= 4.0 * EXP2_DBL_MANT_DIG;
if (dx == 1.0) {
if (a_bits == PY_SSIZE_T_MAX)
goto overflow;
dx = 0.5;
a_bits += 1;
}
*e = a_bits;
return Py_SIZE(a) < 0 ? -dx : dx;
overflow:
/* exponent > PY_SSIZE_T_MAX */
PyErr_SetString(PyExc_OverflowError,
"huge integer: number of bits overflows a Py_ssize_t");
*e = 0;
return -1.0;
}
/* Get a C double from a long int object. Rounds to the nearest double,
using the round-half-to-even rule in the case of a tie. */
double
PyLong_AsDouble(PyObject *v)
{
Py_ssize_t exponent;
double x;
if (v == NULL || !PyLong_Check(v)) {
PyErr_BadInternalCall();
return -1.0;
}
x = _PyLong_Frexp((PyLongObject *)v, &exponent);
if ((x == -1.0 && PyErr_Occurred()) || exponent > DBL_MAX_EXP) {
PyErr_SetString(PyExc_OverflowError,
"long int too large to convert to float");
return -1.0;
}
return ldexp(x, exponent);
}
/* Methods */ /* Methods */
static void static void