mirror of https://github.com/python/cpython
3084 lines
72 KiB
C
3084 lines
72 KiB
C
|
|
/* Long (arbitrary precision) integer object implementation */
|
|
|
|
/* XXX The functional organization of this file is terrible */
|
|
|
|
#include "Python.h"
|
|
#include "longintrepr.h"
|
|
|
|
#include <ctype.h>
|
|
|
|
/* For long multiplication, use the O(N**2) school algorithm unless
|
|
* both operands contain more than KARATSUBA_CUTOFF digits (this
|
|
* being an internal Python long digit, in base BASE).
|
|
*/
|
|
#define KARATSUBA_CUTOFF 70
|
|
#define KARATSUBA_SQUARE_CUTOFF (2 * KARATSUBA_CUTOFF)
|
|
|
|
/* For exponentiation, use the binary left-to-right algorithm
|
|
* unless the exponent contains more than FIVEARY_CUTOFF digits.
|
|
* In that case, do 5 bits at a time. The potential drawback is that
|
|
* a table of 2**5 intermediate results is computed.
|
|
*/
|
|
#define FIVEARY_CUTOFF 8
|
|
|
|
#define ABS(x) ((x) < 0 ? -(x) : (x))
|
|
|
|
#undef MIN
|
|
#undef MAX
|
|
#define MAX(x, y) ((x) < (y) ? (y) : (x))
|
|
#define MIN(x, y) ((x) > (y) ? (y) : (x))
|
|
|
|
/* Forward */
|
|
static PyLongObject *long_normalize(PyLongObject *);
|
|
static PyLongObject *mul1(PyLongObject *, wdigit);
|
|
static PyLongObject *muladd1(PyLongObject *, wdigit, wdigit);
|
|
static PyLongObject *divrem1(PyLongObject *, digit, digit *);
|
|
static PyObject *long_format(PyObject *aa, int base, int addL);
|
|
|
|
#define SIGCHECK(PyTryBlock) \
|
|
if (--_Py_Ticker < 0) { \
|
|
_Py_Ticker = _Py_CheckInterval; \
|
|
if (PyErr_CheckSignals()) { PyTryBlock; } \
|
|
}
|
|
|
|
/* Normalize (remove leading zeros from) a long int object.
|
|
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. */
|
|
|
|
static PyLongObject *
|
|
long_normalize(register PyLongObject *v)
|
|
{
|
|
int j = ABS(v->ob_size);
|
|
register int i = j;
|
|
|
|
while (i > 0 && v->ob_digit[i-1] == 0)
|
|
--i;
|
|
if (i != j)
|
|
v->ob_size = (v->ob_size < 0) ? -(i) : i;
|
|
return v;
|
|
}
|
|
|
|
/* Allocate a new long int object with size digits.
|
|
Return NULL and set exception if we run out of memory. */
|
|
|
|
PyLongObject *
|
|
_PyLong_New(int size)
|
|
{
|
|
return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
|
|
}
|
|
|
|
PyObject *
|
|
_PyLong_Copy(PyLongObject *src)
|
|
{
|
|
PyLongObject *result;
|
|
int i;
|
|
|
|
assert(src != NULL);
|
|
i = src->ob_size;
|
|
if (i < 0)
|
|
i = -(i);
|
|
result = _PyLong_New(i);
|
|
if (result != NULL) {
|
|
result->ob_size = src->ob_size;
|
|
while (--i >= 0)
|
|
result->ob_digit[i] = src->ob_digit[i];
|
|
}
|
|
return (PyObject *)result;
|
|
}
|
|
|
|
/* Create a new long int object from a C long int */
|
|
|
|
PyObject *
|
|
PyLong_FromLong(long ival)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long t; /* unsigned so >> doesn't propagate sign bit */
|
|
int ndigits = 0;
|
|
int negative = 0;
|
|
|
|
if (ival < 0) {
|
|
ival = -ival;
|
|
negative = 1;
|
|
}
|
|
|
|
/* Count the number of Python digits.
|
|
We used to pick 5 ("big enough for anything"), but that's a
|
|
waste of time and space given that 5*15 = 75 bits are rarely
|
|
needed. */
|
|
t = (unsigned long)ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
v->ob_size = negative ? -ndigits : ndigits;
|
|
t = (unsigned long)ival;
|
|
while (t) {
|
|
*p++ = (digit)(t & MASK);
|
|
t >>= SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Create a new long int object from a C unsigned long int */
|
|
|
|
PyObject *
|
|
PyLong_FromUnsignedLong(unsigned long ival)
|
|
{
|
|
PyLongObject *v;
|
|
unsigned long t;
|
|
int ndigits = 0;
|
|
|
|
/* Count the number of Python digits. */
|
|
t = (unsigned long)ival;
|
|
while (t) {
|
|
++ndigits;
|
|
t >>= SHIFT;
|
|
}
|
|
v = _PyLong_New(ndigits);
|
|
if (v != NULL) {
|
|
digit *p = v->ob_digit;
|
|
v->ob_size = ndigits;
|
|
while (ival) {
|
|
*p++ = (digit)(ival & MASK);
|
|
ival >>= SHIFT;
|
|
}
|
|
}
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Create a new long int object from a C double */
|
|
|
|
PyObject *
|
|
PyLong_FromDouble(double dval)
|
|
{
|
|
PyLongObject *v;
|
|
double frac;
|
|
int i, ndig, expo, neg;
|
|
neg = 0;
|
|
if (Py_IS_INFINITY(dval)) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"cannot convert float infinity to long");
|
|
return NULL;
|
|
}
|
|
if (dval < 0.0) {
|
|
neg = 1;
|
|
dval = -dval;
|
|
}
|
|
frac = frexp(dval, &expo); /* dval = frac*2**expo; 0.0 <= frac < 1.0 */
|
|
if (expo <= 0)
|
|
return PyLong_FromLong(0L);
|
|
ndig = (expo-1) / SHIFT + 1; /* Number of 'digits' in result */
|
|
v = _PyLong_New(ndig);
|
|
if (v == NULL)
|
|
return NULL;
|
|
frac = ldexp(frac, (expo-1) % SHIFT + 1);
|
|
for (i = ndig; --i >= 0; ) {
|
|
long bits = (long)frac;
|
|
v->ob_digit[i] = (digit) bits;
|
|
frac = frac - (double)bits;
|
|
frac = ldexp(frac, SHIFT);
|
|
}
|
|
if (neg)
|
|
v->ob_size = -(v->ob_size);
|
|
return (PyObject *)v;
|
|
}
|
|
|
|
/* Get a C long int from a long int object.
|
|
Returns -1 and sets an error condition if overflow occurs. */
|
|
|
|
long
|
|
PyLong_AsLong(PyObject *vv)
|
|
{
|
|
/* This version by Tim Peters */
|
|
register PyLongObject *v;
|
|
unsigned long x, prev;
|
|
int i, sign;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
if (vv != NULL && PyInt_Check(vv))
|
|
return PyInt_AsLong(vv);
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = v->ob_size;
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << SHIFT) + v->ob_digit[i];
|
|
if ((x >> SHIFT) != prev)
|
|
goto overflow;
|
|
}
|
|
/* Haven't lost any bits, but if the sign bit is set we're in
|
|
* trouble *unless* this is the min negative number. So,
|
|
* trouble iff sign bit set && (positive || some bit set other
|
|
* than the sign bit).
|
|
*/
|
|
if ((long)x < 0 && (sign > 0 || (x << 1) != 0))
|
|
goto overflow;
|
|
return (long)x * sign;
|
|
|
|
overflow:
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"long int too large to convert to int");
|
|
return -1;
|
|
}
|
|
|
|
/* Get a C unsigned long int from a long int object.
|
|
Returns -1 and sets an error condition if overflow occurs. */
|
|
|
|
unsigned long
|
|
PyLong_AsUnsignedLong(PyObject *vv)
|
|
{
|
|
register PyLongObject *v;
|
|
unsigned long x, prev;
|
|
int i;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
if (vv != NULL && PyInt_Check(vv)) {
|
|
long val = PyInt_AsLong(vv);
|
|
if (val < 0) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"can't convert negative value to unsigned long");
|
|
return (unsigned long) -1;
|
|
}
|
|
return val;
|
|
}
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long) -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = v->ob_size;
|
|
x = 0;
|
|
if (i < 0) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"can't convert negative value to unsigned long");
|
|
return (unsigned long) -1;
|
|
}
|
|
while (--i >= 0) {
|
|
prev = x;
|
|
x = (x << SHIFT) + v->ob_digit[i];
|
|
if ((x >> SHIFT) != prev) {
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"long int too large to convert");
|
|
return (unsigned long) -1;
|
|
}
|
|
}
|
|
return x;
|
|
}
|
|
|
|
/* Get a C unsigned long int from a long int object, ignoring the high bits.
|
|
Returns -1 and sets an error condition if an error occurs. */
|
|
|
|
unsigned long
|
|
PyLong_AsUnsignedLongMask(PyObject *vv)
|
|
{
|
|
register PyLongObject *v;
|
|
unsigned long x;
|
|
int i, sign;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
if (vv != NULL && PyInt_Check(vv))
|
|
return PyInt_AsUnsignedLongMask(vv);
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long) -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = v->ob_size;
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -i;
|
|
}
|
|
while (--i >= 0) {
|
|
x = (x << SHIFT) + v->ob_digit[i];
|
|
}
|
|
return x * sign;
|
|
}
|
|
|
|
int
|
|
_PyLong_Sign(PyObject *vv)
|
|
{
|
|
PyLongObject *v = (PyLongObject *)vv;
|
|
|
|
assert(v != NULL);
|
|
assert(PyLong_Check(v));
|
|
|
|
return v->ob_size == 0 ? 0 : (v->ob_size < 0 ? -1 : 1);
|
|
}
|
|
|
|
size_t
|
|
_PyLong_NumBits(PyObject *vv)
|
|
{
|
|
PyLongObject *v = (PyLongObject *)vv;
|
|
size_t result = 0;
|
|
int ndigits;
|
|
|
|
assert(v != NULL);
|
|
assert(PyLong_Check(v));
|
|
ndigits = ABS(v->ob_size);
|
|
assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
|
|
if (ndigits > 0) {
|
|
digit msd = v->ob_digit[ndigits - 1];
|
|
|
|
result = (ndigits - 1) * SHIFT;
|
|
if (result / SHIFT != (size_t)ndigits - 1)
|
|
goto Overflow;
|
|
do {
|
|
++result;
|
|
if (result == 0)
|
|
goto Overflow;
|
|
msd >>= 1;
|
|
} while (msd);
|
|
}
|
|
return result;
|
|
|
|
Overflow:
|
|
PyErr_SetString(PyExc_OverflowError, "long has too many bits "
|
|
"to express in a platform size_t");
|
|
return (size_t)-1;
|
|
}
|
|
|
|
PyObject *
|
|
_PyLong_FromByteArray(const unsigned char* bytes, size_t n,
|
|
int little_endian, int is_signed)
|
|
{
|
|
const unsigned char* pstartbyte;/* LSB of bytes */
|
|
int incr; /* direction to move pstartbyte */
|
|
const unsigned char* pendbyte; /* MSB of bytes */
|
|
size_t numsignificantbytes; /* number of bytes that matter */
|
|
size_t ndigits; /* number of Python long digits */
|
|
PyLongObject* v; /* result */
|
|
int idigit = 0; /* next free index in v->ob_digit */
|
|
|
|
if (n == 0)
|
|
return PyLong_FromLong(0L);
|
|
|
|
if (little_endian) {
|
|
pstartbyte = bytes;
|
|
pendbyte = bytes + n - 1;
|
|
incr = 1;
|
|
}
|
|
else {
|
|
pstartbyte = bytes + n - 1;
|
|
pendbyte = bytes;
|
|
incr = -1;
|
|
}
|
|
|
|
if (is_signed)
|
|
is_signed = *pendbyte >= 0x80;
|
|
|
|
/* Compute numsignificantbytes. This consists of finding the most
|
|
significant byte. Leading 0 bytes are insignficant if the number
|
|
is positive, and leading 0xff bytes if negative. */
|
|
{
|
|
size_t i;
|
|
const unsigned char* p = pendbyte;
|
|
const int pincr = -incr; /* search MSB to LSB */
|
|
const unsigned char insignficant = is_signed ? 0xff : 0x00;
|
|
|
|
for (i = 0; i < n; ++i, p += pincr) {
|
|
if (*p != insignficant)
|
|
break;
|
|
}
|
|
numsignificantbytes = n - i;
|
|
/* 2's-comp is a bit tricky here, e.g. 0xff00 == -0x0100, so
|
|
actually has 2 significant bytes. OTOH, 0xff0001 ==
|
|
-0x00ffff, so we wouldn't *need* to bump it there; but we
|
|
do for 0xffff = -0x0001. To be safe without bothering to
|
|
check every case, bump it regardless. */
|
|
if (is_signed && numsignificantbytes < n)
|
|
++numsignificantbytes;
|
|
}
|
|
|
|
/* How many Python long digits do we need? We have
|
|
8*numsignificantbytes bits, and each Python long digit has SHIFT
|
|
bits, so it's the ceiling of the quotient. */
|
|
ndigits = (numsignificantbytes * 8 + SHIFT - 1) / SHIFT;
|
|
if (ndigits > (size_t)INT_MAX)
|
|
return PyErr_NoMemory();
|
|
v = _PyLong_New((int)ndigits);
|
|
if (v == NULL)
|
|
return NULL;
|
|
|
|
/* Copy the bits over. The tricky parts are computing 2's-comp on
|
|
the fly for signed numbers, and dealing with the mismatch between
|
|
8-bit bytes and (probably) 15-bit Python digits.*/
|
|
{
|
|
size_t i;
|
|
twodigits carry = 1; /* for 2's-comp calculation */
|
|
twodigits accum = 0; /* sliding register */
|
|
unsigned int accumbits = 0; /* number of bits in accum */
|
|
const unsigned char* p = pstartbyte;
|
|
|
|
for (i = 0; i < numsignificantbytes; ++i, p += incr) {
|
|
twodigits thisbyte = *p;
|
|
/* Compute correction for 2's comp, if needed. */
|
|
if (is_signed) {
|
|
thisbyte = (0xff ^ thisbyte) + carry;
|
|
carry = thisbyte >> 8;
|
|
thisbyte &= 0xff;
|
|
}
|
|
/* Because we're going LSB to MSB, thisbyte is
|
|
more significant than what's already in accum,
|
|
so needs to be prepended to accum. */
|
|
accum |= thisbyte << accumbits;
|
|
accumbits += 8;
|
|
if (accumbits >= SHIFT) {
|
|
/* There's enough to fill a Python digit. */
|
|
assert(idigit < (int)ndigits);
|
|
v->ob_digit[idigit] = (digit)(accum & MASK);
|
|
++idigit;
|
|
accum >>= SHIFT;
|
|
accumbits -= SHIFT;
|
|
assert(accumbits < SHIFT);
|
|
}
|
|
}
|
|
assert(accumbits < SHIFT);
|
|
if (accumbits) {
|
|
assert(idigit < (int)ndigits);
|
|
v->ob_digit[idigit] = (digit)accum;
|
|
++idigit;
|
|
}
|
|
}
|
|
|
|
v->ob_size = is_signed ? -idigit : idigit;
|
|
return (PyObject *)long_normalize(v);
|
|
}
|
|
|
|
int
|
|
_PyLong_AsByteArray(PyLongObject* v,
|
|
unsigned char* bytes, size_t n,
|
|
int little_endian, int is_signed)
|
|
{
|
|
int i; /* index into v->ob_digit */
|
|
int ndigits; /* |v->ob_size| */
|
|
twodigits accum; /* sliding register */
|
|
unsigned int accumbits; /* # bits in accum */
|
|
int do_twos_comp; /* store 2's-comp? is_signed and v < 0 */
|
|
twodigits carry; /* for computing 2's-comp */
|
|
size_t j; /* # bytes filled */
|
|
unsigned char* p; /* pointer to next byte in bytes */
|
|
int pincr; /* direction to move p */
|
|
|
|
assert(v != NULL && PyLong_Check(v));
|
|
|
|
if (v->ob_size < 0) {
|
|
ndigits = -(v->ob_size);
|
|
if (!is_signed) {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"can't convert negative long to unsigned");
|
|
return -1;
|
|
}
|
|
do_twos_comp = 1;
|
|
}
|
|
else {
|
|
ndigits = v->ob_size;
|
|
do_twos_comp = 0;
|
|
}
|
|
|
|
if (little_endian) {
|
|
p = bytes;
|
|
pincr = 1;
|
|
}
|
|
else {
|
|
p = bytes + n - 1;
|
|
pincr = -1;
|
|
}
|
|
|
|
/* Copy over all the Python digits.
|
|
It's crucial that every Python digit except for the MSD contribute
|
|
exactly SHIFT bits to the total, so first assert that the long is
|
|
normalized. */
|
|
assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
|
|
j = 0;
|
|
accum = 0;
|
|
accumbits = 0;
|
|
carry = do_twos_comp ? 1 : 0;
|
|
for (i = 0; i < ndigits; ++i) {
|
|
twodigits thisdigit = v->ob_digit[i];
|
|
if (do_twos_comp) {
|
|
thisdigit = (thisdigit ^ MASK) + carry;
|
|
carry = thisdigit >> SHIFT;
|
|
thisdigit &= MASK;
|
|
}
|
|
/* Because we're going LSB to MSB, thisdigit is more
|
|
significant than what's already in accum, so needs to be
|
|
prepended to accum. */
|
|
accum |= thisdigit << accumbits;
|
|
accumbits += SHIFT;
|
|
|
|
/* The most-significant digit may be (probably is) at least
|
|
partly empty. */
|
|
if (i == ndigits - 1) {
|
|
/* Count # of sign bits -- they needn't be stored,
|
|
* although for signed conversion we need later to
|
|
* make sure at least one sign bit gets stored.
|
|
* First shift conceptual sign bit to real sign bit.
|
|
*/
|
|
stwodigits s = (stwodigits)(thisdigit <<
|
|
(8*sizeof(stwodigits) - SHIFT));
|
|
unsigned int nsignbits = 0;
|
|
while ((s < 0) == do_twos_comp && nsignbits < SHIFT) {
|
|
++nsignbits;
|
|
s <<= 1;
|
|
}
|
|
accumbits -= nsignbits;
|
|
}
|
|
|
|
/* Store as many bytes as possible. */
|
|
while (accumbits >= 8) {
|
|
if (j >= n)
|
|
goto Overflow;
|
|
++j;
|
|
*p = (unsigned char)(accum & 0xff);
|
|
p += pincr;
|
|
accumbits -= 8;
|
|
accum >>= 8;
|
|
}
|
|
}
|
|
|
|
/* Store the straggler (if any). */
|
|
assert(accumbits < 8);
|
|
assert(carry == 0); /* else do_twos_comp and *every* digit was 0 */
|
|
if (accumbits > 0) {
|
|
if (j >= n)
|
|
goto Overflow;
|
|
++j;
|
|
if (do_twos_comp) {
|
|
/* Fill leading bits of the byte with sign bits
|
|
(appropriately pretending that the long had an
|
|
infinite supply of sign bits). */
|
|
accum |= (~(twodigits)0) << accumbits;
|
|
}
|
|
*p = (unsigned char)(accum & 0xff);
|
|
p += pincr;
|
|
}
|
|
else if (j == n && n > 0 && is_signed) {
|
|
/* The main loop filled the byte array exactly, so the code
|
|
just above didn't get to ensure there's a sign bit, and the
|
|
loop below wouldn't add one either. Make sure a sign bit
|
|
exists. */
|
|
unsigned char msb = *(p - pincr);
|
|
int sign_bit_set = msb >= 0x80;
|
|
assert(accumbits == 0);
|
|
if (sign_bit_set == do_twos_comp)
|
|
return 0;
|
|
else
|
|
goto Overflow;
|
|
}
|
|
|
|
/* Fill remaining bytes with copies of the sign bit. */
|
|
{
|
|
unsigned char signbyte = do_twos_comp ? 0xffU : 0U;
|
|
for ( ; j < n; ++j, p += pincr)
|
|
*p = signbyte;
|
|
}
|
|
|
|
return 0;
|
|
|
|
Overflow:
|
|
PyErr_SetString(PyExc_OverflowError, "long too big to convert");
|
|
return -1;
|
|
|
|
}
|
|
|
|
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 << SHIFT);
|
|
int i, sign;
|
|
int nbitsneeded;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = v->ob_size;
|
|
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 -= SHIFT;
|
|
}
|
|
/* There are i digits we didn't shift in. Pretending they're all
|
|
zeroes, the true value is x * 2**(i*SHIFT). */
|
|
*exponent = i;
|
|
assert(x > 0.0);
|
|
return x * sign;
|
|
#undef NBITS_WANTED
|
|
}
|
|
|
|
/* Get a C double from a long int object. */
|
|
|
|
double
|
|
PyLong_AsDouble(PyObject *vv)
|
|
{
|
|
int e;
|
|
double x;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
x = _PyLong_AsScaledDouble(vv, &e);
|
|
if (x == -1.0 && PyErr_Occurred())
|
|
return -1.0;
|
|
if (e > INT_MAX / SHIFT)
|
|
goto overflow;
|
|
errno = 0;
|
|
x = ldexp(x, e * SHIFT);
|
|
if (Py_OVERFLOWED(x))
|
|
goto overflow;
|
|
return x;
|
|
|
|
overflow:
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"long int too large to convert to float");
|
|
return -1.0;
|
|
}
|
|
|
|
/* Create a new long (or int) object from a C pointer */
|
|
|
|
PyObject *
|
|
PyLong_FromVoidPtr(void *p)
|
|
{
|
|
#if SIZEOF_VOID_P <= SIZEOF_LONG
|
|
return PyInt_FromLong((long)p);
|
|
#else
|
|
|
|
#ifndef HAVE_LONG_LONG
|
|
# error "PyLong_FromVoidPtr: sizeof(void*) > sizeof(long), but no long long"
|
|
#endif
|
|
#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
|
|
# error "PyLong_FromVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
|
|
#endif
|
|
/* optimize null pointers */
|
|
if (p == NULL)
|
|
return PyInt_FromLong(0);
|
|
return PyLong_FromLongLong((PY_LONG_LONG)p);
|
|
|
|
#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
|
|
}
|
|
|
|
/* Get a C pointer from a long object (or an int object in some cases) */
|
|
|
|
void *
|
|
PyLong_AsVoidPtr(PyObject *vv)
|
|
{
|
|
/* This function will allow int or long objects. If vv is neither,
|
|
then the PyLong_AsLong*() functions will raise the exception:
|
|
PyExc_SystemError, "bad argument to internal function"
|
|
*/
|
|
#if SIZEOF_VOID_P <= SIZEOF_LONG
|
|
long x;
|
|
|
|
if (PyInt_Check(vv))
|
|
x = PyInt_AS_LONG(vv);
|
|
else
|
|
x = PyLong_AsLong(vv);
|
|
#else
|
|
|
|
#ifndef HAVE_LONG_LONG
|
|
# error "PyLong_AsVoidPtr: sizeof(void*) > sizeof(long), but no long long"
|
|
#endif
|
|
#if SIZEOF_LONG_LONG < SIZEOF_VOID_P
|
|
# error "PyLong_AsVoidPtr: sizeof(PY_LONG_LONG) < sizeof(void*)"
|
|
#endif
|
|
PY_LONG_LONG x;
|
|
|
|
if (PyInt_Check(vv))
|
|
x = PyInt_AS_LONG(vv);
|
|
else
|
|
x = PyLong_AsLongLong(vv);
|
|
|
|
#endif /* SIZEOF_VOID_P <= SIZEOF_LONG */
|
|
|
|
if (x == -1 && PyErr_Occurred())
|
|
return NULL;
|
|
return (void *)x;
|
|
}
|
|
|
|
#ifdef HAVE_LONG_LONG
|
|
|
|
/* Initial PY_LONG_LONG support by Chris Herborth (chrish@qnx.com), later
|
|
* rewritten to use the newer PyLong_{As,From}ByteArray API.
|
|
*/
|
|
|
|
#define IS_LITTLE_ENDIAN (int)*(unsigned char*)&one
|
|
|
|
/* Create a new long int object from a C PY_LONG_LONG int. */
|
|
|
|
PyObject *
|
|
PyLong_FromLongLong(PY_LONG_LONG ival)
|
|
{
|
|
PY_LONG_LONG bytes = ival;
|
|
int one = 1;
|
|
return _PyLong_FromByteArray(
|
|
(unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 1);
|
|
}
|
|
|
|
/* Create a new long int object from a C unsigned PY_LONG_LONG int. */
|
|
|
|
PyObject *
|
|
PyLong_FromUnsignedLongLong(unsigned PY_LONG_LONG ival)
|
|
{
|
|
unsigned PY_LONG_LONG bytes = ival;
|
|
int one = 1;
|
|
return _PyLong_FromByteArray(
|
|
(unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 0);
|
|
}
|
|
|
|
/* Get a C PY_LONG_LONG int from a long int object.
|
|
Return -1 and set an error if overflow occurs. */
|
|
|
|
PY_LONG_LONG
|
|
PyLong_AsLongLong(PyObject *vv)
|
|
{
|
|
PY_LONG_LONG bytes;
|
|
int one = 1;
|
|
int res;
|
|
|
|
if (vv == NULL) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
if (!PyLong_Check(vv)) {
|
|
PyNumberMethods *nb;
|
|
PyObject *io;
|
|
if (PyInt_Check(vv))
|
|
return (PY_LONG_LONG)PyInt_AsLong(vv);
|
|
if ((nb = vv->ob_type->tp_as_number) == NULL ||
|
|
nb->nb_int == NULL) {
|
|
PyErr_SetString(PyExc_TypeError, "an integer is required");
|
|
return -1;
|
|
}
|
|
io = (*nb->nb_int) (vv);
|
|
if (io == NULL)
|
|
return -1;
|
|
if (PyInt_Check(io)) {
|
|
bytes = PyInt_AsLong(io);
|
|
Py_DECREF(io);
|
|
return bytes;
|
|
}
|
|
if (PyLong_Check(io)) {
|
|
bytes = PyLong_AsLongLong(io);
|
|
Py_DECREF(io);
|
|
return bytes;
|
|
}
|
|
Py_DECREF(io);
|
|
PyErr_SetString(PyExc_TypeError, "integer conversion failed");
|
|
return -1;
|
|
}
|
|
|
|
res = _PyLong_AsByteArray(
|
|
(PyLongObject *)vv, (unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 1);
|
|
|
|
/* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
|
|
if (res < 0)
|
|
return (PY_LONG_LONG)-1;
|
|
else
|
|
return bytes;
|
|
}
|
|
|
|
/* Get a C unsigned PY_LONG_LONG int from a long int object.
|
|
Return -1 and set an error if overflow occurs. */
|
|
|
|
unsigned PY_LONG_LONG
|
|
PyLong_AsUnsignedLongLong(PyObject *vv)
|
|
{
|
|
unsigned PY_LONG_LONG bytes;
|
|
int one = 1;
|
|
int res;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return -1;
|
|
}
|
|
|
|
res = _PyLong_AsByteArray(
|
|
(PyLongObject *)vv, (unsigned char *)&bytes,
|
|
SIZEOF_LONG_LONG, IS_LITTLE_ENDIAN, 0);
|
|
|
|
/* Plan 9 can't handle PY_LONG_LONG in ? : expressions */
|
|
if (res < 0)
|
|
return (unsigned PY_LONG_LONG)res;
|
|
else
|
|
return bytes;
|
|
}
|
|
|
|
/* Get a C unsigned long int from a long int object, ignoring the high bits.
|
|
Returns -1 and sets an error condition if an error occurs. */
|
|
|
|
unsigned PY_LONG_LONG
|
|
PyLong_AsUnsignedLongLongMask(PyObject *vv)
|
|
{
|
|
register PyLongObject *v;
|
|
unsigned PY_LONG_LONG x;
|
|
int i, sign;
|
|
|
|
if (vv == NULL || !PyLong_Check(vv)) {
|
|
PyErr_BadInternalCall();
|
|
return (unsigned long) -1;
|
|
}
|
|
v = (PyLongObject *)vv;
|
|
i = v->ob_size;
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -i;
|
|
}
|
|
while (--i >= 0) {
|
|
x = (x << SHIFT) + v->ob_digit[i];
|
|
}
|
|
return x * sign;
|
|
}
|
|
#undef IS_LITTLE_ENDIAN
|
|
|
|
#endif /* HAVE_LONG_LONG */
|
|
|
|
|
|
static int
|
|
convert_binop(PyObject *v, PyObject *w, PyLongObject **a, PyLongObject **b) {
|
|
if (PyLong_Check(v)) {
|
|
*a = (PyLongObject *) v;
|
|
Py_INCREF(v);
|
|
}
|
|
else if (PyInt_Check(v)) {
|
|
*a = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(v));
|
|
}
|
|
else {
|
|
return 0;
|
|
}
|
|
if (PyLong_Check(w)) {
|
|
*b = (PyLongObject *) w;
|
|
Py_INCREF(w);
|
|
}
|
|
else if (PyInt_Check(w)) {
|
|
*b = (PyLongObject *) PyLong_FromLong(PyInt_AS_LONG(w));
|
|
}
|
|
else {
|
|
Py_DECREF(*a);
|
|
return 0;
|
|
}
|
|
return 1;
|
|
}
|
|
|
|
#define CONVERT_BINOP(v, w, a, b) \
|
|
if (!convert_binop(v, w, a, b)) { \
|
|
Py_INCREF(Py_NotImplemented); \
|
|
return Py_NotImplemented; \
|
|
}
|
|
|
|
/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
|
|
* is modified in place, by adding y to it. Carries are propagated as far as
|
|
* x[m-1], and the remaining carry (0 or 1) is returned.
|
|
*/
|
|
static digit
|
|
v_iadd(digit *x, int m, digit *y, int n)
|
|
{
|
|
int i;
|
|
digit carry = 0;
|
|
|
|
assert(m >= n);
|
|
for (i = 0; i < n; ++i) {
|
|
carry += x[i] + y[i];
|
|
x[i] = carry & MASK;
|
|
carry >>= SHIFT;
|
|
assert((carry & 1) == carry);
|
|
}
|
|
for (; carry && i < m; ++i) {
|
|
carry += x[i];
|
|
x[i] = carry & MASK;
|
|
carry >>= SHIFT;
|
|
assert((carry & 1) == carry);
|
|
}
|
|
return carry;
|
|
}
|
|
|
|
/* x[0:m] and y[0:n] are digit vectors, LSD first, m >= n required. x[0:n]
|
|
* is modified in place, by subtracting y from it. Borrows are propagated as
|
|
* far as x[m-1], and the remaining borrow (0 or 1) is returned.
|
|
*/
|
|
static digit
|
|
v_isub(digit *x, int m, digit *y, int n)
|
|
{
|
|
int i;
|
|
digit borrow = 0;
|
|
|
|
assert(m >= n);
|
|
for (i = 0; i < n; ++i) {
|
|
borrow = x[i] - y[i] - borrow;
|
|
x[i] = borrow & MASK;
|
|
borrow >>= SHIFT;
|
|
borrow &= 1; /* keep only 1 sign bit */
|
|
}
|
|
for (; borrow && i < m; ++i) {
|
|
borrow = x[i] - borrow;
|
|
x[i] = borrow & MASK;
|
|
borrow >>= SHIFT;
|
|
borrow &= 1;
|
|
}
|
|
return borrow;
|
|
}
|
|
|
|
/* Multiply by a single digit, ignoring the sign. */
|
|
|
|
static PyLongObject *
|
|
mul1(PyLongObject *a, wdigit n)
|
|
{
|
|
return muladd1(a, n, (digit)0);
|
|
}
|
|
|
|
/* Multiply by a single digit and add a single digit, ignoring the sign. */
|
|
|
|
static PyLongObject *
|
|
muladd1(PyLongObject *a, wdigit n, wdigit extra)
|
|
{
|
|
int size_a = ABS(a->ob_size);
|
|
PyLongObject *z = _PyLong_New(size_a+1);
|
|
twodigits carry = extra;
|
|
int i;
|
|
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0; i < size_a; ++i) {
|
|
carry += (twodigits)a->ob_digit[i] * n;
|
|
z->ob_digit[i] = (digit) (carry & MASK);
|
|
carry >>= SHIFT;
|
|
}
|
|
z->ob_digit[i] = (digit) carry;
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* Divide long pin, w/ size digits, by non-zero digit n, storing quotient
|
|
in pout, and returning the remainder. pin and pout point at the LSD.
|
|
It's OK for pin == pout on entry, which saves oodles of mallocs/frees in
|
|
long_format, but that should be done with great care since longs are
|
|
immutable. */
|
|
|
|
static digit
|
|
inplace_divrem1(digit *pout, digit *pin, int size, digit n)
|
|
{
|
|
twodigits rem = 0;
|
|
|
|
assert(n > 0 && n <= MASK);
|
|
pin += size;
|
|
pout += size;
|
|
while (--size >= 0) {
|
|
digit hi;
|
|
rem = (rem << SHIFT) + *--pin;
|
|
*--pout = hi = (digit)(rem / n);
|
|
rem -= hi * n;
|
|
}
|
|
return (digit)rem;
|
|
}
|
|
|
|
/* Divide a long integer by a digit, returning both the quotient
|
|
(as function result) and the remainder (through *prem).
|
|
The sign of a is ignored; n should not be zero. */
|
|
|
|
static PyLongObject *
|
|
divrem1(PyLongObject *a, digit n, digit *prem)
|
|
{
|
|
const int size = ABS(a->ob_size);
|
|
PyLongObject *z;
|
|
|
|
assert(n > 0 && n <= MASK);
|
|
z = _PyLong_New(size);
|
|
if (z == NULL)
|
|
return NULL;
|
|
*prem = inplace_divrem1(z->ob_digit, a->ob_digit, size, n);
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* Convert a long int object to a string, using a given conversion base.
|
|
Return a string object.
|
|
If base is 8 or 16, add the proper prefix '0' or '0x'. */
|
|
|
|
static PyObject *
|
|
long_format(PyObject *aa, int base, int addL)
|
|
{
|
|
register PyLongObject *a = (PyLongObject *)aa;
|
|
PyStringObject *str;
|
|
int i;
|
|
const int size_a = ABS(a->ob_size);
|
|
char *p;
|
|
int bits;
|
|
char sign = '\0';
|
|
|
|
if (a == NULL || !PyLong_Check(a)) {
|
|
PyErr_BadInternalCall();
|
|
return NULL;
|
|
}
|
|
assert(base >= 2 && base <= 36);
|
|
|
|
/* Compute a rough upper bound for the length of the string */
|
|
i = base;
|
|
bits = 0;
|
|
while (i > 1) {
|
|
++bits;
|
|
i >>= 1;
|
|
}
|
|
i = 5 + (addL ? 1 : 0) + (size_a*SHIFT + bits-1) / bits;
|
|
str = (PyStringObject *) PyString_FromStringAndSize((char *)0, i);
|
|
if (str == NULL)
|
|
return NULL;
|
|
p = PyString_AS_STRING(str) + i;
|
|
*p = '\0';
|
|
if (addL)
|
|
*--p = 'L';
|
|
if (a->ob_size < 0)
|
|
sign = '-';
|
|
|
|
if (a->ob_size == 0) {
|
|
*--p = '0';
|
|
}
|
|
else if ((base & (base - 1)) == 0) {
|
|
/* JRH: special case for power-of-2 bases */
|
|
twodigits accum = 0;
|
|
int accumbits = 0; /* # of bits in accum */
|
|
int basebits = 1; /* # of bits in base-1 */
|
|
i = base;
|
|
while ((i >>= 1) > 1)
|
|
++basebits;
|
|
|
|
for (i = 0; i < size_a; ++i) {
|
|
accum |= (twodigits)a->ob_digit[i] << accumbits;
|
|
accumbits += SHIFT;
|
|
assert(accumbits >= basebits);
|
|
do {
|
|
char cdigit = (char)(accum & (base - 1));
|
|
cdigit += (cdigit < 10) ? '0' : 'A'-10;
|
|
assert(p > PyString_AS_STRING(str));
|
|
*--p = cdigit;
|
|
accumbits -= basebits;
|
|
accum >>= basebits;
|
|
} while (i < size_a-1 ? accumbits >= basebits :
|
|
accum > 0);
|
|
}
|
|
}
|
|
else {
|
|
/* Not 0, and base not a power of 2. Divide repeatedly by
|
|
base, but for speed use the highest power of base that
|
|
fits in a digit. */
|
|
int size = size_a;
|
|
digit *pin = a->ob_digit;
|
|
PyLongObject *scratch;
|
|
/* powbasw <- largest power of base that fits in a digit. */
|
|
digit powbase = base; /* powbase == base ** power */
|
|
int power = 1;
|
|
for (;;) {
|
|
unsigned long newpow = powbase * (unsigned long)base;
|
|
if (newpow >> SHIFT) /* doesn't fit in a digit */
|
|
break;
|
|
powbase = (digit)newpow;
|
|
++power;
|
|
}
|
|
|
|
/* Get a scratch area for repeated division. */
|
|
scratch = _PyLong_New(size);
|
|
if (scratch == NULL) {
|
|
Py_DECREF(str);
|
|
return NULL;
|
|
}
|
|
|
|
/* Repeatedly divide by powbase. */
|
|
do {
|
|
int ntostore = power;
|
|
digit rem = inplace_divrem1(scratch->ob_digit,
|
|
pin, size, powbase);
|
|
pin = scratch->ob_digit; /* no need to use a again */
|
|
if (pin[size - 1] == 0)
|
|
--size;
|
|
SIGCHECK({
|
|
Py_DECREF(scratch);
|
|
Py_DECREF(str);
|
|
return NULL;
|
|
})
|
|
|
|
/* Break rem into digits. */
|
|
assert(ntostore > 0);
|
|
do {
|
|
digit nextrem = (digit)(rem / base);
|
|
char c = (char)(rem - nextrem * base);
|
|
assert(p > PyString_AS_STRING(str));
|
|
c += (c < 10) ? '0' : 'A'-10;
|
|
*--p = c;
|
|
rem = nextrem;
|
|
--ntostore;
|
|
/* Termination is a bit delicate: must not
|
|
store leading zeroes, so must get out if
|
|
remaining quotient and rem are both 0. */
|
|
} while (ntostore && (size || rem));
|
|
} while (size != 0);
|
|
Py_DECREF(scratch);
|
|
}
|
|
|
|
if (base == 8) {
|
|
if (size_a != 0)
|
|
*--p = '0';
|
|
}
|
|
else if (base == 16) {
|
|
*--p = 'x';
|
|
*--p = '0';
|
|
}
|
|
else if (base != 10) {
|
|
*--p = '#';
|
|
*--p = '0' + base%10;
|
|
if (base > 10)
|
|
*--p = '0' + base/10;
|
|
}
|
|
if (sign)
|
|
*--p = sign;
|
|
if (p != PyString_AS_STRING(str)) {
|
|
char *q = PyString_AS_STRING(str);
|
|
assert(p > q);
|
|
do {
|
|
} while ((*q++ = *p++) != '\0');
|
|
q--;
|
|
_PyString_Resize((PyObject **)&str,
|
|
(int) (q - PyString_AS_STRING(str)));
|
|
}
|
|
return (PyObject *)str;
|
|
}
|
|
|
|
/* *str points to the first digit in a string of base base digits. base
|
|
* is a power of 2 (2, 4, 8, 16, or 32). *str is set to point to the first
|
|
* non-digit (which may be *str!). A normalized long is returned.
|
|
* The point to this routine is that it takes time linear in the number of
|
|
* string characters.
|
|
*/
|
|
static PyLongObject *
|
|
long_from_binary_base(char **str, int base)
|
|
{
|
|
char *p = *str;
|
|
char *start = p;
|
|
int bits_per_char;
|
|
int n;
|
|
PyLongObject *z;
|
|
twodigits accum;
|
|
int bits_in_accum;
|
|
digit *pdigit;
|
|
|
|
assert(base >= 2 && base <= 32 && (base & (base - 1)) == 0);
|
|
n = base;
|
|
for (bits_per_char = -1; n; ++bits_per_char)
|
|
n >>= 1;
|
|
/* n <- total # of bits needed, while setting p to end-of-string */
|
|
n = 0;
|
|
for (;;) {
|
|
int k = -1;
|
|
char ch = *p;
|
|
|
|
if (ch <= '9')
|
|
k = ch - '0';
|
|
else if (ch >= 'a')
|
|
k = ch - 'a' + 10;
|
|
else if (ch >= 'A')
|
|
k = ch - 'A' + 10;
|
|
if (k < 0 || k >= base)
|
|
break;
|
|
++p;
|
|
}
|
|
*str = p;
|
|
n = (p - start) * bits_per_char;
|
|
if (n / bits_per_char != p - start) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"long string too large to convert");
|
|
return NULL;
|
|
}
|
|
/* n <- # of Python digits needed, = ceiling(n/SHIFT). */
|
|
n = (n + SHIFT - 1) / SHIFT;
|
|
z = _PyLong_New(n);
|
|
if (z == NULL)
|
|
return NULL;
|
|
/* Read string from right, and fill in long from left; i.e.,
|
|
* from least to most significant in both.
|
|
*/
|
|
accum = 0;
|
|
bits_in_accum = 0;
|
|
pdigit = z->ob_digit;
|
|
while (--p >= start) {
|
|
int k;
|
|
char ch = *p;
|
|
|
|
if (ch <= '9')
|
|
k = ch - '0';
|
|
else if (ch >= 'a')
|
|
k = ch - 'a' + 10;
|
|
else {
|
|
assert(ch >= 'A');
|
|
k = ch - 'A' + 10;
|
|
}
|
|
assert(k >= 0 && k < base);
|
|
accum |= (twodigits)(k << bits_in_accum);
|
|
bits_in_accum += bits_per_char;
|
|
if (bits_in_accum >= SHIFT) {
|
|
*pdigit++ = (digit)(accum & MASK);
|
|
assert(pdigit - z->ob_digit <= n);
|
|
accum >>= SHIFT;
|
|
bits_in_accum -= SHIFT;
|
|
assert(bits_in_accum < SHIFT);
|
|
}
|
|
}
|
|
if (bits_in_accum) {
|
|
assert(bits_in_accum <= SHIFT);
|
|
*pdigit++ = (digit)accum;
|
|
assert(pdigit - z->ob_digit <= n);
|
|
}
|
|
while (pdigit - z->ob_digit < n)
|
|
*pdigit++ = 0;
|
|
return long_normalize(z);
|
|
}
|
|
|
|
PyObject *
|
|
PyLong_FromString(char *str, char **pend, int base)
|
|
{
|
|
int sign = 1;
|
|
char *start, *orig_str = str;
|
|
PyLongObject *z;
|
|
|
|
if ((base != 0 && base < 2) || base > 36) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"long() arg 2 must be >= 2 and <= 36");
|
|
return NULL;
|
|
}
|
|
while (*str != '\0' && isspace(Py_CHARMASK(*str)))
|
|
str++;
|
|
if (*str == '+')
|
|
++str;
|
|
else if (*str == '-') {
|
|
++str;
|
|
sign = -1;
|
|
}
|
|
while (*str != '\0' && isspace(Py_CHARMASK(*str)))
|
|
str++;
|
|
if (base == 0) {
|
|
if (str[0] != '0')
|
|
base = 10;
|
|
else if (str[1] == 'x' || str[1] == 'X')
|
|
base = 16;
|
|
else
|
|
base = 8;
|
|
}
|
|
if (base == 16 && str[0] == '0' && (str[1] == 'x' || str[1] == 'X'))
|
|
str += 2;
|
|
start = str;
|
|
if ((base & (base - 1)) == 0)
|
|
z = long_from_binary_base(&str, base);
|
|
else {
|
|
z = _PyLong_New(0);
|
|
for ( ; z != NULL; ++str) {
|
|
int k = -1;
|
|
PyLongObject *temp;
|
|
|
|
if (*str <= '9')
|
|
k = *str - '0';
|
|
else if (*str >= 'a')
|
|
k = *str - 'a' + 10;
|
|
else if (*str >= 'A')
|
|
k = *str - 'A' + 10;
|
|
if (k < 0 || k >= base)
|
|
break;
|
|
temp = muladd1(z, (digit)base, (digit)k);
|
|
Py_DECREF(z);
|
|
z = temp;
|
|
}
|
|
}
|
|
if (z == NULL)
|
|
return NULL;
|
|
if (str == start)
|
|
goto onError;
|
|
if (sign < 0 && z != NULL && z->ob_size != 0)
|
|
z->ob_size = -(z->ob_size);
|
|
if (*str == 'L' || *str == 'l')
|
|
str++;
|
|
while (*str && isspace(Py_CHARMASK(*str)))
|
|
str++;
|
|
if (*str != '\0')
|
|
goto onError;
|
|
if (pend)
|
|
*pend = str;
|
|
return (PyObject *) z;
|
|
|
|
onError:
|
|
PyErr_Format(PyExc_ValueError,
|
|
"invalid literal for long(): %.200s", orig_str);
|
|
Py_XDECREF(z);
|
|
return NULL;
|
|
}
|
|
|
|
#ifdef Py_USING_UNICODE
|
|
PyObject *
|
|
PyLong_FromUnicode(Py_UNICODE *u, int length, int base)
|
|
{
|
|
PyObject *result;
|
|
char *buffer = PyMem_MALLOC(length+1);
|
|
|
|
if (buffer == NULL)
|
|
return NULL;
|
|
|
|
if (PyUnicode_EncodeDecimal(u, length, buffer, NULL)) {
|
|
PyMem_FREE(buffer);
|
|
return NULL;
|
|
}
|
|
result = PyLong_FromString(buffer, NULL, base);
|
|
PyMem_FREE(buffer);
|
|
return result;
|
|
}
|
|
#endif
|
|
|
|
/* forward */
|
|
static PyLongObject *x_divrem
|
|
(PyLongObject *, PyLongObject *, PyLongObject **);
|
|
static PyObject *long_pos(PyLongObject *);
|
|
static int long_divrem(PyLongObject *, PyLongObject *,
|
|
PyLongObject **, PyLongObject **);
|
|
|
|
/* Long division with remainder, top-level routine */
|
|
|
|
static int
|
|
long_divrem(PyLongObject *a, PyLongObject *b,
|
|
PyLongObject **pdiv, PyLongObject **prem)
|
|
{
|
|
int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
|
|
PyLongObject *z;
|
|
|
|
if (size_b == 0) {
|
|
PyErr_SetString(PyExc_ZeroDivisionError,
|
|
"long division or modulo by zero");
|
|
return -1;
|
|
}
|
|
if (size_a < size_b ||
|
|
(size_a == size_b &&
|
|
a->ob_digit[size_a-1] < b->ob_digit[size_b-1])) {
|
|
/* |a| < |b|. */
|
|
*pdiv = _PyLong_New(0);
|
|
Py_INCREF(a);
|
|
*prem = (PyLongObject *) a;
|
|
return 0;
|
|
}
|
|
if (size_b == 1) {
|
|
digit rem = 0;
|
|
z = divrem1(a, b->ob_digit[0], &rem);
|
|
if (z == NULL)
|
|
return -1;
|
|
*prem = (PyLongObject *) PyLong_FromLong((long)rem);
|
|
}
|
|
else {
|
|
z = x_divrem(a, b, prem);
|
|
if (z == NULL)
|
|
return -1;
|
|
}
|
|
/* Set the signs.
|
|
The quotient z has the sign of a*b;
|
|
the remainder r has the sign of a,
|
|
so a = b*z + r. */
|
|
if ((a->ob_size < 0) != (b->ob_size < 0))
|
|
z->ob_size = -(z->ob_size);
|
|
if (a->ob_size < 0 && (*prem)->ob_size != 0)
|
|
(*prem)->ob_size = -((*prem)->ob_size);
|
|
*pdiv = z;
|
|
return 0;
|
|
}
|
|
|
|
/* Unsigned long division with remainder -- the algorithm */
|
|
|
|
static PyLongObject *
|
|
x_divrem(PyLongObject *v1, PyLongObject *w1, PyLongObject **prem)
|
|
{
|
|
int size_v = ABS(v1->ob_size), size_w = ABS(w1->ob_size);
|
|
digit d = (digit) ((twodigits)BASE / (w1->ob_digit[size_w-1] + 1));
|
|
PyLongObject *v = mul1(v1, d);
|
|
PyLongObject *w = mul1(w1, d);
|
|
PyLongObject *a;
|
|
int j, k;
|
|
|
|
if (v == NULL || w == NULL) {
|
|
Py_XDECREF(v);
|
|
Py_XDECREF(w);
|
|
return NULL;
|
|
}
|
|
|
|
assert(size_v >= size_w && size_w > 1); /* Assert checks by div() */
|
|
assert(v->ob_refcnt == 1); /* Since v will be used as accumulator! */
|
|
assert(size_w == ABS(w->ob_size)); /* That's how d was calculated */
|
|
|
|
size_v = ABS(v->ob_size);
|
|
a = _PyLong_New(size_v - size_w + 1);
|
|
|
|
for (j = size_v, k = a->ob_size-1; a != NULL && k >= 0; --j, --k) {
|
|
digit vj = (j >= size_v) ? 0 : v->ob_digit[j];
|
|
twodigits q;
|
|
stwodigits carry = 0;
|
|
int i;
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(a);
|
|
a = NULL;
|
|
break;
|
|
})
|
|
if (vj == w->ob_digit[size_w-1])
|
|
q = MASK;
|
|
else
|
|
q = (((twodigits)vj << SHIFT) + v->ob_digit[j-1]) /
|
|
w->ob_digit[size_w-1];
|
|
|
|
while (w->ob_digit[size_w-2]*q >
|
|
((
|
|
((twodigits)vj << SHIFT)
|
|
+ v->ob_digit[j-1]
|
|
- q*w->ob_digit[size_w-1]
|
|
) << SHIFT)
|
|
+ v->ob_digit[j-2])
|
|
--q;
|
|
|
|
for (i = 0; i < size_w && i+k < size_v; ++i) {
|
|
twodigits z = w->ob_digit[i] * q;
|
|
digit zz = (digit) (z >> SHIFT);
|
|
carry += v->ob_digit[i+k] - z
|
|
+ ((twodigits)zz << SHIFT);
|
|
v->ob_digit[i+k] = (digit)(carry & MASK);
|
|
carry = Py_ARITHMETIC_RIGHT_SHIFT(BASE_TWODIGITS_TYPE,
|
|
carry, SHIFT);
|
|
carry -= zz;
|
|
}
|
|
|
|
if (i+k < size_v) {
|
|
carry += v->ob_digit[i+k];
|
|
v->ob_digit[i+k] = 0;
|
|
}
|
|
|
|
if (carry == 0)
|
|
a->ob_digit[k] = (digit) q;
|
|
else {
|
|
assert(carry == -1);
|
|
a->ob_digit[k] = (digit) q-1;
|
|
carry = 0;
|
|
for (i = 0; i < size_w && i+k < size_v; ++i) {
|
|
carry += v->ob_digit[i+k] + w->ob_digit[i];
|
|
v->ob_digit[i+k] = (digit)(carry & MASK);
|
|
carry = Py_ARITHMETIC_RIGHT_SHIFT(
|
|
BASE_TWODIGITS_TYPE,
|
|
carry, SHIFT);
|
|
}
|
|
}
|
|
} /* for j, k */
|
|
|
|
if (a == NULL)
|
|
*prem = NULL;
|
|
else {
|
|
a = long_normalize(a);
|
|
*prem = divrem1(v, d, &d);
|
|
/* d receives the (unused) remainder */
|
|
if (*prem == NULL) {
|
|
Py_DECREF(a);
|
|
a = NULL;
|
|
}
|
|
}
|
|
Py_DECREF(v);
|
|
Py_DECREF(w);
|
|
return a;
|
|
}
|
|
|
|
/* Methods */
|
|
|
|
static void
|
|
long_dealloc(PyObject *v)
|
|
{
|
|
v->ob_type->tp_free(v);
|
|
}
|
|
|
|
static PyObject *
|
|
long_repr(PyObject *v)
|
|
{
|
|
return long_format(v, 10, 1);
|
|
}
|
|
|
|
static PyObject *
|
|
long_str(PyObject *v)
|
|
{
|
|
return long_format(v, 10, 0);
|
|
}
|
|
|
|
static int
|
|
long_compare(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
int sign;
|
|
|
|
if (a->ob_size != b->ob_size) {
|
|
if (ABS(a->ob_size) == 0 && ABS(b->ob_size) == 0)
|
|
sign = 0;
|
|
else
|
|
sign = a->ob_size - b->ob_size;
|
|
}
|
|
else {
|
|
int i = ABS(a->ob_size);
|
|
while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
|
|
;
|
|
if (i < 0)
|
|
sign = 0;
|
|
else {
|
|
sign = (int)a->ob_digit[i] - (int)b->ob_digit[i];
|
|
if (a->ob_size < 0)
|
|
sign = -sign;
|
|
}
|
|
}
|
|
return sign < 0 ? -1 : sign > 0 ? 1 : 0;
|
|
}
|
|
|
|
static long
|
|
long_hash(PyLongObject *v)
|
|
{
|
|
long x;
|
|
int i, sign;
|
|
|
|
/* This is designed so that Python ints and longs with the
|
|
same value hash to the same value, otherwise comparisons
|
|
of mapping keys will turn out weird */
|
|
i = v->ob_size;
|
|
sign = 1;
|
|
x = 0;
|
|
if (i < 0) {
|
|
sign = -1;
|
|
i = -(i);
|
|
}
|
|
#define LONG_BIT_SHIFT (8*sizeof(long) - SHIFT)
|
|
while (--i >= 0) {
|
|
/* Force a native long #-bits (32 or 64) circular shift */
|
|
x = ((x << SHIFT) & ~MASK) | ((x >> LONG_BIT_SHIFT) & MASK);
|
|
x += v->ob_digit[i];
|
|
}
|
|
#undef LONG_BIT_SHIFT
|
|
x = x * sign;
|
|
if (x == -1)
|
|
x = -2;
|
|
return x;
|
|
}
|
|
|
|
|
|
/* Add the absolute values of two long integers. */
|
|
|
|
static PyLongObject *
|
|
x_add(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
|
|
PyLongObject *z;
|
|
int i;
|
|
digit carry = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
{ int size_temp = size_a;
|
|
size_a = size_b;
|
|
size_b = size_temp; }
|
|
}
|
|
z = _PyLong_New(size_a+1);
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0; i < size_b; ++i) {
|
|
carry += a->ob_digit[i] + b->ob_digit[i];
|
|
z->ob_digit[i] = carry & MASK;
|
|
carry >>= SHIFT;
|
|
}
|
|
for (; i < size_a; ++i) {
|
|
carry += a->ob_digit[i];
|
|
z->ob_digit[i] = carry & MASK;
|
|
carry >>= SHIFT;
|
|
}
|
|
z->ob_digit[i] = carry;
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* Subtract the absolute values of two integers. */
|
|
|
|
static PyLongObject *
|
|
x_sub(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
int size_a = ABS(a->ob_size), size_b = ABS(b->ob_size);
|
|
PyLongObject *z;
|
|
int i;
|
|
int sign = 1;
|
|
digit borrow = 0;
|
|
|
|
/* Ensure a is the larger of the two: */
|
|
if (size_a < size_b) {
|
|
sign = -1;
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
{ int size_temp = size_a;
|
|
size_a = size_b;
|
|
size_b = size_temp; }
|
|
}
|
|
else if (size_a == size_b) {
|
|
/* Find highest digit where a and b differ: */
|
|
i = size_a;
|
|
while (--i >= 0 && a->ob_digit[i] == b->ob_digit[i])
|
|
;
|
|
if (i < 0)
|
|
return _PyLong_New(0);
|
|
if (a->ob_digit[i] < b->ob_digit[i]) {
|
|
sign = -1;
|
|
{ PyLongObject *temp = a; a = b; b = temp; }
|
|
}
|
|
size_a = size_b = i+1;
|
|
}
|
|
z = _PyLong_New(size_a);
|
|
if (z == NULL)
|
|
return NULL;
|
|
for (i = 0; i < size_b; ++i) {
|
|
/* The following assumes unsigned arithmetic
|
|
works module 2**N for some N>SHIFT. */
|
|
borrow = a->ob_digit[i] - b->ob_digit[i] - borrow;
|
|
z->ob_digit[i] = borrow & MASK;
|
|
borrow >>= SHIFT;
|
|
borrow &= 1; /* Keep only one sign bit */
|
|
}
|
|
for (; i < size_a; ++i) {
|
|
borrow = a->ob_digit[i] - borrow;
|
|
z->ob_digit[i] = borrow & MASK;
|
|
borrow >>= SHIFT;
|
|
borrow &= 1; /* Keep only one sign bit */
|
|
}
|
|
assert(borrow == 0);
|
|
if (sign < 0)
|
|
z->ob_size = -(z->ob_size);
|
|
return long_normalize(z);
|
|
}
|
|
|
|
static PyObject *
|
|
long_add(PyLongObject *v, PyLongObject *w)
|
|
{
|
|
PyLongObject *a, *b, *z;
|
|
|
|
CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
|
|
|
|
if (a->ob_size < 0) {
|
|
if (b->ob_size < 0) {
|
|
z = x_add(a, b);
|
|
if (z != NULL && z->ob_size != 0)
|
|
z->ob_size = -(z->ob_size);
|
|
}
|
|
else
|
|
z = x_sub(b, a);
|
|
}
|
|
else {
|
|
if (b->ob_size < 0)
|
|
z = x_sub(a, b);
|
|
else
|
|
z = x_add(a, b);
|
|
}
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_sub(PyLongObject *v, PyLongObject *w)
|
|
{
|
|
PyLongObject *a, *b, *z;
|
|
|
|
CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
|
|
|
|
if (a->ob_size < 0) {
|
|
if (b->ob_size < 0)
|
|
z = x_sub(a, b);
|
|
else
|
|
z = x_add(a, b);
|
|
if (z != NULL && z->ob_size != 0)
|
|
z->ob_size = -(z->ob_size);
|
|
}
|
|
else {
|
|
if (b->ob_size < 0)
|
|
z = x_add(a, b);
|
|
else
|
|
z = x_sub(a, b);
|
|
}
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
/* Grade school multiplication, ignoring the signs.
|
|
* Returns the absolute value of the product, or NULL if error.
|
|
*/
|
|
static PyLongObject *
|
|
x_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
PyLongObject *z;
|
|
int size_a = ABS(a->ob_size);
|
|
int size_b = ABS(b->ob_size);
|
|
int i;
|
|
|
|
z = _PyLong_New(size_a + size_b);
|
|
if (z == NULL)
|
|
return NULL;
|
|
|
|
memset(z->ob_digit, 0, z->ob_size * sizeof(digit));
|
|
if (a == b) {
|
|
/* Efficient squaring per HAC, Algorithm 14.16:
|
|
* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf
|
|
* Gives slightly less than a 2x speedup when a == b,
|
|
* via exploiting that each entry in the multiplication
|
|
* pyramid appears twice (except for the size_a squares).
|
|
*/
|
|
for (i = 0; i < size_a; ++i) {
|
|
twodigits carry;
|
|
twodigits f = a->ob_digit[i];
|
|
digit *pz = z->ob_digit + (i << 1);
|
|
digit *pa = a->ob_digit + i + 1;
|
|
digit *paend = a->ob_digit + size_a;
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(z);
|
|
return NULL;
|
|
})
|
|
|
|
carry = *pz + f * f;
|
|
*pz++ = (digit)(carry & MASK);
|
|
carry >>= SHIFT;
|
|
assert(carry <= MASK);
|
|
|
|
/* Now f is added in twice in each column of the
|
|
* pyramid it appears. Same as adding f<<1 once.
|
|
*/
|
|
f <<= 1;
|
|
while (pa < paend) {
|
|
carry += *pz + *pa++ * f;
|
|
*pz++ = (digit)(carry & MASK);
|
|
carry >>= SHIFT;
|
|
assert(carry <= (MASK << 1));
|
|
}
|
|
if (carry) {
|
|
carry += *pz;
|
|
*pz++ = (digit)(carry & MASK);
|
|
carry >>= SHIFT;
|
|
}
|
|
if (carry)
|
|
*pz += (digit)(carry & MASK);
|
|
assert((carry >> SHIFT) == 0);
|
|
}
|
|
}
|
|
else { /* a is not the same as b -- gradeschool long mult */
|
|
for (i = 0; i < size_a; ++i) {
|
|
twodigits carry = 0;
|
|
twodigits f = a->ob_digit[i];
|
|
digit *pz = z->ob_digit + i;
|
|
digit *pb = b->ob_digit;
|
|
digit *pbend = b->ob_digit + size_b;
|
|
|
|
SIGCHECK({
|
|
Py_DECREF(z);
|
|
return NULL;
|
|
})
|
|
|
|
while (pb < pbend) {
|
|
carry += *pz + *pb++ * f;
|
|
*pz++ = (digit)(carry & MASK);
|
|
carry >>= SHIFT;
|
|
assert(carry <= MASK);
|
|
}
|
|
if (carry)
|
|
*pz += (digit)(carry & MASK);
|
|
assert((carry >> SHIFT) == 0);
|
|
}
|
|
}
|
|
return long_normalize(z);
|
|
}
|
|
|
|
/* A helper for Karatsuba multiplication (k_mul).
|
|
Takes a long "n" and an integer "size" representing the place to
|
|
split, and sets low and high such that abs(n) == (high << size) + low,
|
|
viewing the shift as being by digits. The sign bit is ignored, and
|
|
the return values are >= 0.
|
|
Returns 0 on success, -1 on failure.
|
|
*/
|
|
static int
|
|
kmul_split(PyLongObject *n, int size, PyLongObject **high, PyLongObject **low)
|
|
{
|
|
PyLongObject *hi, *lo;
|
|
int size_lo, size_hi;
|
|
const int size_n = ABS(n->ob_size);
|
|
|
|
size_lo = MIN(size_n, size);
|
|
size_hi = size_n - size_lo;
|
|
|
|
if ((hi = _PyLong_New(size_hi)) == NULL)
|
|
return -1;
|
|
if ((lo = _PyLong_New(size_lo)) == NULL) {
|
|
Py_DECREF(hi);
|
|
return -1;
|
|
}
|
|
|
|
memcpy(lo->ob_digit, n->ob_digit, size_lo * sizeof(digit));
|
|
memcpy(hi->ob_digit, n->ob_digit + size_lo, size_hi * sizeof(digit));
|
|
|
|
*high = long_normalize(hi);
|
|
*low = long_normalize(lo);
|
|
return 0;
|
|
}
|
|
|
|
static PyLongObject *k_lopsided_mul(PyLongObject *a, PyLongObject *b);
|
|
|
|
/* Karatsuba multiplication. Ignores the input signs, and returns the
|
|
* absolute value of the product (or NULL if error).
|
|
* See Knuth Vol. 2 Chapter 4.3.3 (Pp. 294-295).
|
|
*/
|
|
static PyLongObject *
|
|
k_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
int asize = ABS(a->ob_size);
|
|
int bsize = ABS(b->ob_size);
|
|
PyLongObject *ah = NULL;
|
|
PyLongObject *al = NULL;
|
|
PyLongObject *bh = NULL;
|
|
PyLongObject *bl = NULL;
|
|
PyLongObject *ret = NULL;
|
|
PyLongObject *t1, *t2, *t3;
|
|
int shift; /* the number of digits we split off */
|
|
int i;
|
|
|
|
/* (ah*X+al)(bh*X+bl) = ah*bh*X*X + (ah*bl + al*bh)*X + al*bl
|
|
* Let k = (ah+al)*(bh+bl) = ah*bl + al*bh + ah*bh + al*bl
|
|
* Then the original product is
|
|
* ah*bh*X*X + (k - ah*bh - al*bl)*X + al*bl
|
|
* By picking X to be a power of 2, "*X" is just shifting, and it's
|
|
* been reduced to 3 multiplies on numbers half the size.
|
|
*/
|
|
|
|
/* We want to split based on the larger number; fiddle so that b
|
|
* is largest.
|
|
*/
|
|
if (asize > bsize) {
|
|
t1 = a;
|
|
a = b;
|
|
b = t1;
|
|
|
|
i = asize;
|
|
asize = bsize;
|
|
bsize = i;
|
|
}
|
|
|
|
/* Use gradeschool math when either number is too small. */
|
|
i = a == b ? KARATSUBA_SQUARE_CUTOFF : KARATSUBA_CUTOFF;
|
|
if (asize <= i) {
|
|
if (asize == 0)
|
|
return _PyLong_New(0);
|
|
else
|
|
return x_mul(a, b);
|
|
}
|
|
|
|
/* If a is small compared to b, splitting on b gives a degenerate
|
|
* case with ah==0, and Karatsuba may be (even much) less efficient
|
|
* than "grade school" then. However, we can still win, by viewing
|
|
* b as a string of "big digits", each of width a->ob_size. That
|
|
* leads to a sequence of balanced calls to k_mul.
|
|
*/
|
|
if (2 * asize <= bsize)
|
|
return k_lopsided_mul(a, b);
|
|
|
|
/* Split a & b into hi & lo pieces. */
|
|
shift = bsize >> 1;
|
|
if (kmul_split(a, shift, &ah, &al) < 0) goto fail;
|
|
assert(ah->ob_size > 0); /* the split isn't degenerate */
|
|
|
|
if (a == b) {
|
|
bh = ah;
|
|
bl = al;
|
|
Py_INCREF(bh);
|
|
Py_INCREF(bl);
|
|
}
|
|
else if (kmul_split(b, shift, &bh, &bl) < 0) goto fail;
|
|
|
|
/* The plan:
|
|
* 1. Allocate result space (asize + bsize digits: that's always
|
|
* enough).
|
|
* 2. Compute ah*bh, and copy into result at 2*shift.
|
|
* 3. Compute al*bl, and copy into result at 0. Note that this
|
|
* can't overlap with #2.
|
|
* 4. Subtract al*bl from the result, starting at shift. This may
|
|
* underflow (borrow out of the high digit), but we don't care:
|
|
* we're effectively doing unsigned arithmetic mod
|
|
* BASE**(sizea + sizeb), and so long as the *final* result fits,
|
|
* borrows and carries out of the high digit can be ignored.
|
|
* 5. Subtract ah*bh from the result, starting at shift.
|
|
* 6. Compute (ah+al)*(bh+bl), and add it into the result starting
|
|
* at shift.
|
|
*/
|
|
|
|
/* 1. Allocate result space. */
|
|
ret = _PyLong_New(asize + bsize);
|
|
if (ret == NULL) goto fail;
|
|
#ifdef Py_DEBUG
|
|
/* Fill with trash, to catch reference to uninitialized digits. */
|
|
memset(ret->ob_digit, 0xDF, ret->ob_size * sizeof(digit));
|
|
#endif
|
|
|
|
/* 2. t1 <- ah*bh, and copy into high digits of result. */
|
|
if ((t1 = k_mul(ah, bh)) == NULL) goto fail;
|
|
assert(t1->ob_size >= 0);
|
|
assert(2*shift + t1->ob_size <= ret->ob_size);
|
|
memcpy(ret->ob_digit + 2*shift, t1->ob_digit,
|
|
t1->ob_size * sizeof(digit));
|
|
|
|
/* Zero-out the digits higher than the ah*bh copy. */
|
|
i = ret->ob_size - 2*shift - t1->ob_size;
|
|
if (i)
|
|
memset(ret->ob_digit + 2*shift + t1->ob_size, 0,
|
|
i * sizeof(digit));
|
|
|
|
/* 3. t2 <- al*bl, and copy into the low digits. */
|
|
if ((t2 = k_mul(al, bl)) == NULL) {
|
|
Py_DECREF(t1);
|
|
goto fail;
|
|
}
|
|
assert(t2->ob_size >= 0);
|
|
assert(t2->ob_size <= 2*shift); /* no overlap with high digits */
|
|
memcpy(ret->ob_digit, t2->ob_digit, t2->ob_size * sizeof(digit));
|
|
|
|
/* Zero out remaining digits. */
|
|
i = 2*shift - t2->ob_size; /* number of uninitialized digits */
|
|
if (i)
|
|
memset(ret->ob_digit + t2->ob_size, 0, i * sizeof(digit));
|
|
|
|
/* 4 & 5. Subtract ah*bh (t1) and al*bl (t2). We do al*bl first
|
|
* because it's fresher in cache.
|
|
*/
|
|
i = ret->ob_size - shift; /* # digits after shift */
|
|
(void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, t2->ob_size);
|
|
Py_DECREF(t2);
|
|
|
|
(void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, t1->ob_size);
|
|
Py_DECREF(t1);
|
|
|
|
/* 6. t3 <- (ah+al)(bh+bl), and add into result. */
|
|
if ((t1 = x_add(ah, al)) == NULL) goto fail;
|
|
Py_DECREF(ah);
|
|
Py_DECREF(al);
|
|
ah = al = NULL;
|
|
|
|
if (a == b) {
|
|
t2 = t1;
|
|
Py_INCREF(t2);
|
|
}
|
|
else if ((t2 = x_add(bh, bl)) == NULL) {
|
|
Py_DECREF(t1);
|
|
goto fail;
|
|
}
|
|
Py_DECREF(bh);
|
|
Py_DECREF(bl);
|
|
bh = bl = NULL;
|
|
|
|
t3 = k_mul(t1, t2);
|
|
Py_DECREF(t1);
|
|
Py_DECREF(t2);
|
|
if (t3 == NULL) goto fail;
|
|
assert(t3->ob_size >= 0);
|
|
|
|
/* Add t3. It's not obvious why we can't run out of room here.
|
|
* See the (*) comment after this function.
|
|
*/
|
|
(void)v_iadd(ret->ob_digit + shift, i, t3->ob_digit, t3->ob_size);
|
|
Py_DECREF(t3);
|
|
|
|
return long_normalize(ret);
|
|
|
|
fail:
|
|
Py_XDECREF(ret);
|
|
Py_XDECREF(ah);
|
|
Py_XDECREF(al);
|
|
Py_XDECREF(bh);
|
|
Py_XDECREF(bl);
|
|
return NULL;
|
|
}
|
|
|
|
/* (*) Why adding t3 can't "run out of room" above.
|
|
|
|
Let f(x) mean the floor of x and c(x) mean the ceiling of x. Some facts
|
|
to start with:
|
|
|
|
1. For any integer i, i = c(i/2) + f(i/2). In particular,
|
|
bsize = c(bsize/2) + f(bsize/2).
|
|
2. shift = f(bsize/2)
|
|
3. asize <= bsize
|
|
4. Since we call k_lopsided_mul if asize*2 <= bsize, asize*2 > bsize in this
|
|
routine, so asize > bsize/2 >= f(bsize/2) in this routine.
|
|
|
|
We allocated asize + bsize result digits, and add t3 into them at an offset
|
|
of shift. This leaves asize+bsize-shift allocated digit positions for t3
|
|
to fit into, = (by #1 and #2) asize + f(bsize/2) + c(bsize/2) - f(bsize/2) =
|
|
asize + c(bsize/2) available digit positions.
|
|
|
|
bh has c(bsize/2) digits, and bl at most f(size/2) digits. So bh+hl has
|
|
at most c(bsize/2) digits + 1 bit.
|
|
|
|
If asize == bsize, ah has c(bsize/2) digits, else ah has at most f(bsize/2)
|
|
digits, and al has at most f(bsize/2) digits in any case. So ah+al has at
|
|
most (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 1 bit.
|
|
|
|
The product (ah+al)*(bh+bl) therefore has at most
|
|
|
|
c(bsize/2) + (asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits
|
|
|
|
and we have asize + c(bsize/2) available digit positions. We need to show
|
|
this is always enough. An instance of c(bsize/2) cancels out in both, so
|
|
the question reduces to whether asize digits is enough to hold
|
|
(asize == bsize ? c(bsize/2) : f(bsize/2)) digits + 2 bits. If asize < bsize,
|
|
then we're asking whether asize digits >= f(bsize/2) digits + 2 bits. By #4,
|
|
asize is at least f(bsize/2)+1 digits, so this in turn reduces to whether 1
|
|
digit is enough to hold 2 bits. This is so since SHIFT=15 >= 2. If
|
|
asize == bsize, then we're asking whether bsize digits is enough to hold
|
|
c(bsize/2) digits + 2 bits, or equivalently (by #1) whether f(bsize/2) digits
|
|
is enough to hold 2 bits. This is so if bsize >= 2, which holds because
|
|
bsize >= KARATSUBA_CUTOFF >= 2.
|
|
|
|
Note that since there's always enough room for (ah+al)*(bh+bl), and that's
|
|
clearly >= each of ah*bh and al*bl, there's always enough room to subtract
|
|
ah*bh and al*bl too.
|
|
*/
|
|
|
|
/* b has at least twice the digits of a, and a is big enough that Karatsuba
|
|
* would pay off *if* the inputs had balanced sizes. View b as a sequence
|
|
* of slices, each with a->ob_size digits, and multiply the slices by a,
|
|
* one at a time. This gives k_mul balanced inputs to work with, and is
|
|
* also cache-friendly (we compute one double-width slice of the result
|
|
* at a time, then move on, never bactracking except for the helpful
|
|
* single-width slice overlap between successive partial sums).
|
|
*/
|
|
static PyLongObject *
|
|
k_lopsided_mul(PyLongObject *a, PyLongObject *b)
|
|
{
|
|
const int asize = ABS(a->ob_size);
|
|
int bsize = ABS(b->ob_size);
|
|
int nbdone; /* # of b digits already multiplied */
|
|
PyLongObject *ret;
|
|
PyLongObject *bslice = NULL;
|
|
|
|
assert(asize > KARATSUBA_CUTOFF);
|
|
assert(2 * asize <= bsize);
|
|
|
|
/* Allocate result space, and zero it out. */
|
|
ret = _PyLong_New(asize + bsize);
|
|
if (ret == NULL)
|
|
return NULL;
|
|
memset(ret->ob_digit, 0, ret->ob_size * sizeof(digit));
|
|
|
|
/* Successive slices of b are copied into bslice. */
|
|
bslice = _PyLong_New(asize);
|
|
if (bslice == NULL)
|
|
goto fail;
|
|
|
|
nbdone = 0;
|
|
while (bsize > 0) {
|
|
PyLongObject *product;
|
|
const int nbtouse = MIN(bsize, asize);
|
|
|
|
/* Multiply the next slice of b by a. */
|
|
memcpy(bslice->ob_digit, b->ob_digit + nbdone,
|
|
nbtouse * sizeof(digit));
|
|
bslice->ob_size = nbtouse;
|
|
product = k_mul(a, bslice);
|
|
if (product == NULL)
|
|
goto fail;
|
|
|
|
/* Add into result. */
|
|
(void)v_iadd(ret->ob_digit + nbdone, ret->ob_size - nbdone,
|
|
product->ob_digit, product->ob_size);
|
|
Py_DECREF(product);
|
|
|
|
bsize -= nbtouse;
|
|
nbdone += nbtouse;
|
|
}
|
|
|
|
Py_DECREF(bslice);
|
|
return long_normalize(ret);
|
|
|
|
fail:
|
|
Py_DECREF(ret);
|
|
Py_XDECREF(bslice);
|
|
return NULL;
|
|
}
|
|
|
|
static PyObject *
|
|
long_mul(PyLongObject *v, PyLongObject *w)
|
|
{
|
|
PyLongObject *a, *b, *z;
|
|
|
|
if (!convert_binop((PyObject *)v, (PyObject *)w, &a, &b)) {
|
|
Py_INCREF(Py_NotImplemented);
|
|
return Py_NotImplemented;
|
|
}
|
|
|
|
z = k_mul(a, b);
|
|
/* Negate if exactly one of the inputs is negative. */
|
|
if (((a->ob_size ^ b->ob_size) < 0) && z)
|
|
z->ob_size = -(z->ob_size);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
/* The / and % operators are now defined in terms of divmod().
|
|
The expression a mod b has the value a - b*floor(a/b).
|
|
The long_divrem function gives the remainder after division of
|
|
|a| by |b|, with the sign of a. This is also expressed
|
|
as a - b*trunc(a/b), if trunc truncates towards zero.
|
|
Some examples:
|
|
a b a rem b a mod b
|
|
13 10 3 3
|
|
-13 10 -3 7
|
|
13 -10 3 -7
|
|
-13 -10 -3 -3
|
|
So, to get from rem to mod, we have to add b if a and b
|
|
have different signs. We then subtract one from the 'div'
|
|
part of the outcome to keep the invariant intact. */
|
|
|
|
/* Compute
|
|
* *pdiv, *pmod = divmod(v, w)
|
|
* NULL can be passed for pdiv or pmod, in which case that part of
|
|
* the result is simply thrown away. The caller owns a reference to
|
|
* each of these it requests (does not pass NULL for).
|
|
*/
|
|
static int
|
|
l_divmod(PyLongObject *v, PyLongObject *w,
|
|
PyLongObject **pdiv, PyLongObject **pmod)
|
|
{
|
|
PyLongObject *div, *mod;
|
|
|
|
if (long_divrem(v, w, &div, &mod) < 0)
|
|
return -1;
|
|
if ((mod->ob_size < 0 && w->ob_size > 0) ||
|
|
(mod->ob_size > 0 && w->ob_size < 0)) {
|
|
PyLongObject *temp;
|
|
PyLongObject *one;
|
|
temp = (PyLongObject *) long_add(mod, w);
|
|
Py_DECREF(mod);
|
|
mod = temp;
|
|
if (mod == NULL) {
|
|
Py_DECREF(div);
|
|
return -1;
|
|
}
|
|
one = (PyLongObject *) PyLong_FromLong(1L);
|
|
if (one == NULL ||
|
|
(temp = (PyLongObject *) long_sub(div, one)) == NULL) {
|
|
Py_DECREF(mod);
|
|
Py_DECREF(div);
|
|
Py_XDECREF(one);
|
|
return -1;
|
|
}
|
|
Py_DECREF(one);
|
|
Py_DECREF(div);
|
|
div = temp;
|
|
}
|
|
if (pdiv != NULL)
|
|
*pdiv = div;
|
|
else
|
|
Py_DECREF(div);
|
|
|
|
if (pmod != NULL)
|
|
*pmod = mod;
|
|
else
|
|
Py_DECREF(mod);
|
|
|
|
return 0;
|
|
}
|
|
|
|
static PyObject *
|
|
long_div(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b, *div;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
if (l_divmod(a, b, &div, NULL) < 0)
|
|
div = NULL;
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)div;
|
|
}
|
|
|
|
static PyObject *
|
|
long_classic_div(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b, *div;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
if (Py_DivisionWarningFlag &&
|
|
PyErr_Warn(PyExc_DeprecationWarning, "classic long division") < 0)
|
|
div = NULL;
|
|
else if (l_divmod(a, b, &div, NULL) < 0)
|
|
div = NULL;
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)div;
|
|
}
|
|
|
|
static PyObject *
|
|
long_true_divide(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b;
|
|
double ad, bd;
|
|
int aexp, bexp, failed;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
ad = _PyLong_AsScaledDouble((PyObject *)a, &aexp);
|
|
bd = _PyLong_AsScaledDouble((PyObject *)b, &bexp);
|
|
failed = (ad == -1.0 || bd == -1.0) && PyErr_Occurred();
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
if (failed)
|
|
return NULL;
|
|
|
|
if (bd == 0.0) {
|
|
PyErr_SetString(PyExc_ZeroDivisionError,
|
|
"long division or modulo by zero");
|
|
return NULL;
|
|
}
|
|
|
|
/* True value is very close to ad/bd * 2**(SHIFT*(aexp-bexp)) */
|
|
ad /= bd; /* overflow/underflow impossible here */
|
|
aexp -= bexp;
|
|
if (aexp > INT_MAX / SHIFT)
|
|
goto overflow;
|
|
else if (aexp < -(INT_MAX / SHIFT))
|
|
return PyFloat_FromDouble(0.0); /* underflow to 0 */
|
|
errno = 0;
|
|
ad = ldexp(ad, aexp * SHIFT);
|
|
if (Py_OVERFLOWED(ad)) /* ignore underflow to 0.0 */
|
|
goto overflow;
|
|
return PyFloat_FromDouble(ad);
|
|
|
|
overflow:
|
|
PyErr_SetString(PyExc_OverflowError,
|
|
"long/long too large for a float");
|
|
return NULL;
|
|
|
|
}
|
|
|
|
static PyObject *
|
|
long_mod(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b, *mod;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
|
|
if (l_divmod(a, b, NULL, &mod) < 0)
|
|
mod = NULL;
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)mod;
|
|
}
|
|
|
|
static PyObject *
|
|
long_divmod(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b, *div, *mod;
|
|
PyObject *z;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
|
|
if (l_divmod(a, b, &div, &mod) < 0) {
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return NULL;
|
|
}
|
|
z = PyTuple_New(2);
|
|
if (z != NULL) {
|
|
PyTuple_SetItem(z, 0, (PyObject *) div);
|
|
PyTuple_SetItem(z, 1, (PyObject *) mod);
|
|
}
|
|
else {
|
|
Py_DECREF(div);
|
|
Py_DECREF(mod);
|
|
}
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return z;
|
|
}
|
|
|
|
/* pow(v, w, x) */
|
|
static PyObject *
|
|
long_pow(PyObject *v, PyObject *w, PyObject *x)
|
|
{
|
|
PyLongObject *a, *b, *c; /* a,b,c = v,w,x */
|
|
int negativeOutput = 0; /* if x<0 return negative output */
|
|
|
|
PyLongObject *z = NULL; /* accumulated result */
|
|
int i, j, k; /* counters */
|
|
PyLongObject *temp = NULL;
|
|
|
|
/* 5-ary values. If the exponent is large enough, table is
|
|
* precomputed so that table[i] == a**i % c for i in range(32).
|
|
*/
|
|
PyLongObject *table[32] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
|
|
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
|
|
|
|
/* a, b, c = v, w, x */
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
if (PyLong_Check(x)) {
|
|
c = (PyLongObject *)x;
|
|
Py_INCREF(x);
|
|
}
|
|
else if (PyInt_Check(x))
|
|
c = (PyLongObject *)PyLong_FromLong(PyInt_AS_LONG(x));
|
|
else if (x == Py_None)
|
|
c = NULL;
|
|
else {
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
Py_INCREF(Py_NotImplemented);
|
|
return Py_NotImplemented;
|
|
}
|
|
|
|
if (b->ob_size < 0) { /* if exponent is negative */
|
|
if (c) {
|
|
PyErr_SetString(PyExc_TypeError, "pow() 2nd argument "
|
|
"cannot be negative when 3rd argument specified");
|
|
goto Error;
|
|
}
|
|
else {
|
|
/* else return a float. This works because we know
|
|
that this calls float_pow() which converts its
|
|
arguments to double. */
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return PyFloat_Type.tp_as_number->nb_power(v, w, x);
|
|
}
|
|
}
|
|
|
|
if (c) {
|
|
/* if modulus == 0:
|
|
raise ValueError() */
|
|
if (c->ob_size == 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"pow() 3rd argument cannot be 0");
|
|
goto Error;
|
|
}
|
|
|
|
/* if modulus < 0:
|
|
negativeOutput = True
|
|
modulus = -modulus */
|
|
if (c->ob_size < 0) {
|
|
negativeOutput = 1;
|
|
temp = (PyLongObject *)_PyLong_Copy(c);
|
|
if (temp == NULL)
|
|
goto Error;
|
|
Py_DECREF(c);
|
|
c = temp;
|
|
temp = NULL;
|
|
c->ob_size = - c->ob_size;
|
|
}
|
|
|
|
/* if modulus == 1:
|
|
return 0 */
|
|
if ((c->ob_size == 1) && (c->ob_digit[0] == 1)) {
|
|
z = (PyLongObject *)PyLong_FromLong(0L);
|
|
goto Done;
|
|
}
|
|
|
|
/* if base < 0:
|
|
base = base % modulus
|
|
Having the base positive just makes things easier. */
|
|
if (a->ob_size < 0) {
|
|
if (l_divmod(a, c, NULL, &temp) < 0)
|
|
goto Error;
|
|
Py_DECREF(a);
|
|
a = temp;
|
|
temp = NULL;
|
|
}
|
|
}
|
|
|
|
/* At this point a, b, and c are guaranteed non-negative UNLESS
|
|
c is NULL, in which case a may be negative. */
|
|
|
|
z = (PyLongObject *)PyLong_FromLong(1L);
|
|
if (z == NULL)
|
|
goto Error;
|
|
|
|
/* Perform a modular reduction, X = X % c, but leave X alone if c
|
|
* is NULL.
|
|
*/
|
|
#define REDUCE(X) \
|
|
if (c != NULL) { \
|
|
if (l_divmod(X, c, NULL, &temp) < 0) \
|
|
goto Error; \
|
|
Py_XDECREF(X); \
|
|
X = temp; \
|
|
temp = NULL; \
|
|
}
|
|
|
|
/* Multiply two values, then reduce the result:
|
|
result = X*Y % c. If c is NULL, skip the mod. */
|
|
#define MULT(X, Y, result) \
|
|
{ \
|
|
temp = (PyLongObject *)long_mul(X, Y); \
|
|
if (temp == NULL) \
|
|
goto Error; \
|
|
Py_XDECREF(result); \
|
|
result = temp; \
|
|
temp = NULL; \
|
|
REDUCE(result) \
|
|
}
|
|
|
|
if (b->ob_size <= FIVEARY_CUTOFF) {
|
|
/* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
|
|
/* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */
|
|
for (i = b->ob_size - 1; i >= 0; --i) {
|
|
digit bi = b->ob_digit[i];
|
|
|
|
for (j = 1 << (SHIFT-1); j != 0; j >>= 1) {
|
|
MULT(z, z, z)
|
|
if (bi & j)
|
|
MULT(z, a, z)
|
|
}
|
|
}
|
|
}
|
|
else {
|
|
/* Left-to-right 5-ary exponentiation (HAC Algorithm 14.82) */
|
|
Py_INCREF(z); /* still holds 1L */
|
|
table[0] = z;
|
|
for (i = 1; i < 32; ++i)
|
|
MULT(table[i-1], a, table[i])
|
|
|
|
for (i = b->ob_size - 1; i >= 0; --i) {
|
|
const digit bi = b->ob_digit[i];
|
|
|
|
for (j = SHIFT - 5; j >= 0; j -= 5) {
|
|
const int index = (bi >> j) & 0x1f;
|
|
for (k = 0; k < 5; ++k)
|
|
MULT(z, z, z)
|
|
if (index)
|
|
MULT(z, table[index], z)
|
|
}
|
|
}
|
|
}
|
|
|
|
if (negativeOutput && (z->ob_size != 0)) {
|
|
temp = (PyLongObject *)long_sub(z, c);
|
|
if (temp == NULL)
|
|
goto Error;
|
|
Py_DECREF(z);
|
|
z = temp;
|
|
temp = NULL;
|
|
}
|
|
goto Done;
|
|
|
|
Error:
|
|
if (z != NULL) {
|
|
Py_DECREF(z);
|
|
z = NULL;
|
|
}
|
|
/* fall through */
|
|
Done:
|
|
Py_XDECREF(a);
|
|
Py_XDECREF(b);
|
|
Py_XDECREF(c);
|
|
Py_XDECREF(temp);
|
|
if (b->ob_size > FIVEARY_CUTOFF) {
|
|
for (i = 0; i < 32; ++i)
|
|
Py_XDECREF(table[i]);
|
|
}
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_invert(PyLongObject *v)
|
|
{
|
|
/* Implement ~x as -(x+1) */
|
|
PyLongObject *x;
|
|
PyLongObject *w;
|
|
w = (PyLongObject *)PyLong_FromLong(1L);
|
|
if (w == NULL)
|
|
return NULL;
|
|
x = (PyLongObject *) long_add(v, w);
|
|
Py_DECREF(w);
|
|
if (x == NULL)
|
|
return NULL;
|
|
x->ob_size = -(x->ob_size);
|
|
return (PyObject *)x;
|
|
}
|
|
|
|
static PyObject *
|
|
long_pos(PyLongObject *v)
|
|
{
|
|
if (PyLong_CheckExact(v)) {
|
|
Py_INCREF(v);
|
|
return (PyObject *)v;
|
|
}
|
|
else
|
|
return _PyLong_Copy(v);
|
|
}
|
|
|
|
static PyObject *
|
|
long_neg(PyLongObject *v)
|
|
{
|
|
PyLongObject *z;
|
|
if (v->ob_size == 0 && PyLong_CheckExact(v)) {
|
|
/* -0 == 0 */
|
|
Py_INCREF(v);
|
|
return (PyObject *) v;
|
|
}
|
|
z = (PyLongObject *)_PyLong_Copy(v);
|
|
if (z != NULL)
|
|
z->ob_size = -(v->ob_size);
|
|
return (PyObject *)z;
|
|
}
|
|
|
|
static PyObject *
|
|
long_abs(PyLongObject *v)
|
|
{
|
|
if (v->ob_size < 0)
|
|
return long_neg(v);
|
|
else
|
|
return long_pos(v);
|
|
}
|
|
|
|
static int
|
|
long_nonzero(PyLongObject *v)
|
|
{
|
|
return ABS(v->ob_size) != 0;
|
|
}
|
|
|
|
static PyObject *
|
|
long_rshift(PyLongObject *v, PyLongObject *w)
|
|
{
|
|
PyLongObject *a, *b;
|
|
PyLongObject *z = NULL;
|
|
long shiftby;
|
|
int newsize, wordshift, loshift, hishift, i, j;
|
|
digit lomask, himask;
|
|
|
|
CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
|
|
|
|
if (a->ob_size < 0) {
|
|
/* Right shifting negative numbers is harder */
|
|
PyLongObject *a1, *a2;
|
|
a1 = (PyLongObject *) long_invert(a);
|
|
if (a1 == NULL)
|
|
goto rshift_error;
|
|
a2 = (PyLongObject *) long_rshift(a1, b);
|
|
Py_DECREF(a1);
|
|
if (a2 == NULL)
|
|
goto rshift_error;
|
|
z = (PyLongObject *) long_invert(a2);
|
|
Py_DECREF(a2);
|
|
}
|
|
else {
|
|
|
|
shiftby = PyLong_AsLong((PyObject *)b);
|
|
if (shiftby == -1L && PyErr_Occurred())
|
|
goto rshift_error;
|
|
if (shiftby < 0) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"negative shift count");
|
|
goto rshift_error;
|
|
}
|
|
wordshift = shiftby / SHIFT;
|
|
newsize = ABS(a->ob_size) - wordshift;
|
|
if (newsize <= 0) {
|
|
z = _PyLong_New(0);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *)z;
|
|
}
|
|
loshift = shiftby % SHIFT;
|
|
hishift = SHIFT - loshift;
|
|
lomask = ((digit)1 << hishift) - 1;
|
|
himask = MASK ^ lomask;
|
|
z = _PyLong_New(newsize);
|
|
if (z == NULL)
|
|
goto rshift_error;
|
|
if (a->ob_size < 0)
|
|
z->ob_size = -(z->ob_size);
|
|
for (i = 0, j = wordshift; i < newsize; i++, j++) {
|
|
z->ob_digit[i] = (a->ob_digit[j] >> loshift) & lomask;
|
|
if (i+1 < newsize)
|
|
z->ob_digit[i] |=
|
|
(a->ob_digit[j+1] << hishift) & himask;
|
|
}
|
|
z = long_normalize(z);
|
|
}
|
|
rshift_error:
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *) z;
|
|
|
|
}
|
|
|
|
static PyObject *
|
|
long_lshift(PyObject *v, PyObject *w)
|
|
{
|
|
/* This version due to Tim Peters */
|
|
PyLongObject *a, *b;
|
|
PyLongObject *z = NULL;
|
|
long shiftby;
|
|
int oldsize, newsize, wordshift, remshift, i, j;
|
|
twodigits accum;
|
|
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
|
|
shiftby = PyLong_AsLong((PyObject *)b);
|
|
if (shiftby == -1L && PyErr_Occurred())
|
|
goto lshift_error;
|
|
if (shiftby < 0) {
|
|
PyErr_SetString(PyExc_ValueError, "negative shift count");
|
|
goto lshift_error;
|
|
}
|
|
if ((long)(int)shiftby != shiftby) {
|
|
PyErr_SetString(PyExc_ValueError,
|
|
"outrageous left shift count");
|
|
goto lshift_error;
|
|
}
|
|
/* wordshift, remshift = divmod(shiftby, SHIFT) */
|
|
wordshift = (int)shiftby / SHIFT;
|
|
remshift = (int)shiftby - wordshift * SHIFT;
|
|
|
|
oldsize = ABS(a->ob_size);
|
|
newsize = oldsize + wordshift;
|
|
if (remshift)
|
|
++newsize;
|
|
z = _PyLong_New(newsize);
|
|
if (z == NULL)
|
|
goto lshift_error;
|
|
if (a->ob_size < 0)
|
|
z->ob_size = -(z->ob_size);
|
|
for (i = 0; i < wordshift; i++)
|
|
z->ob_digit[i] = 0;
|
|
accum = 0;
|
|
for (i = wordshift, j = 0; j < oldsize; i++, j++) {
|
|
accum |= (twodigits)a->ob_digit[j] << remshift;
|
|
z->ob_digit[i] = (digit)(accum & MASK);
|
|
accum >>= SHIFT;
|
|
}
|
|
if (remshift)
|
|
z->ob_digit[newsize-1] = (digit)accum;
|
|
else
|
|
assert(!accum);
|
|
z = long_normalize(z);
|
|
lshift_error:
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return (PyObject *) z;
|
|
}
|
|
|
|
|
|
/* Bitwise and/xor/or operations */
|
|
|
|
static PyObject *
|
|
long_bitwise(PyLongObject *a,
|
|
int op, /* '&', '|', '^' */
|
|
PyLongObject *b)
|
|
{
|
|
digit maska, maskb; /* 0 or MASK */
|
|
int negz;
|
|
int size_a, size_b, size_z;
|
|
PyLongObject *z;
|
|
int i;
|
|
digit diga, digb;
|
|
PyObject *v;
|
|
|
|
if (a->ob_size < 0) {
|
|
a = (PyLongObject *) long_invert(a);
|
|
maska = MASK;
|
|
}
|
|
else {
|
|
Py_INCREF(a);
|
|
maska = 0;
|
|
}
|
|
if (b->ob_size < 0) {
|
|
b = (PyLongObject *) long_invert(b);
|
|
maskb = MASK;
|
|
}
|
|
else {
|
|
Py_INCREF(b);
|
|
maskb = 0;
|
|
}
|
|
|
|
negz = 0;
|
|
switch (op) {
|
|
case '^':
|
|
if (maska != maskb) {
|
|
maska ^= MASK;
|
|
negz = -1;
|
|
}
|
|
break;
|
|
case '&':
|
|
if (maska && maskb) {
|
|
op = '|';
|
|
maska ^= MASK;
|
|
maskb ^= MASK;
|
|
negz = -1;
|
|
}
|
|
break;
|
|
case '|':
|
|
if (maska || maskb) {
|
|
op = '&';
|
|
maska ^= MASK;
|
|
maskb ^= MASK;
|
|
negz = -1;
|
|
}
|
|
break;
|
|
}
|
|
|
|
/* JRH: The original logic here was to allocate the result value (z)
|
|
as the longer of the two operands. However, there are some cases
|
|
where the result is guaranteed to be shorter than that: AND of two
|
|
positives, OR of two negatives: use the shorter number. AND with
|
|
mixed signs: use the positive number. OR with mixed signs: use the
|
|
negative number. After the transformations above, op will be '&'
|
|
iff one of these cases applies, and mask will be non-0 for operands
|
|
whose length should be ignored.
|
|
*/
|
|
|
|
size_a = a->ob_size;
|
|
size_b = b->ob_size;
|
|
size_z = op == '&'
|
|
? (maska
|
|
? size_b
|
|
: (maskb ? size_a : MIN(size_a, size_b)))
|
|
: MAX(size_a, size_b);
|
|
z = _PyLong_New(size_z);
|
|
if (a == NULL || b == NULL || z == NULL) {
|
|
Py_XDECREF(a);
|
|
Py_XDECREF(b);
|
|
Py_XDECREF(z);
|
|
return NULL;
|
|
}
|
|
|
|
for (i = 0; i < size_z; ++i) {
|
|
diga = (i < size_a ? a->ob_digit[i] : 0) ^ maska;
|
|
digb = (i < size_b ? b->ob_digit[i] : 0) ^ maskb;
|
|
switch (op) {
|
|
case '&': z->ob_digit[i] = diga & digb; break;
|
|
case '|': z->ob_digit[i] = diga | digb; break;
|
|
case '^': z->ob_digit[i] = diga ^ digb; break;
|
|
}
|
|
}
|
|
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
z = long_normalize(z);
|
|
if (negz == 0)
|
|
return (PyObject *) z;
|
|
v = long_invert(z);
|
|
Py_DECREF(z);
|
|
return v;
|
|
}
|
|
|
|
static PyObject *
|
|
long_and(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b;
|
|
PyObject *c;
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
c = long_bitwise(a, '&', b);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return c;
|
|
}
|
|
|
|
static PyObject *
|
|
long_xor(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b;
|
|
PyObject *c;
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
c = long_bitwise(a, '^', b);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return c;
|
|
}
|
|
|
|
static PyObject *
|
|
long_or(PyObject *v, PyObject *w)
|
|
{
|
|
PyLongObject *a, *b;
|
|
PyObject *c;
|
|
CONVERT_BINOP(v, w, &a, &b);
|
|
c = long_bitwise(a, '|', b);
|
|
Py_DECREF(a);
|
|
Py_DECREF(b);
|
|
return c;
|
|
}
|
|
|
|
static int
|
|
long_coerce(PyObject **pv, PyObject **pw)
|
|
{
|
|
if (PyInt_Check(*pw)) {
|
|
*pw = PyLong_FromLong(PyInt_AS_LONG(*pw));
|
|
Py_INCREF(*pv);
|
|
return 0;
|
|
}
|
|
else if (PyLong_Check(*pw)) {
|
|
Py_INCREF(*pv);
|
|
Py_INCREF(*pw);
|
|
return 0;
|
|
}
|
|
return 1; /* Can't do it */
|
|
}
|
|
|
|
static PyObject *
|
|
long_long(PyObject *v)
|
|
{
|
|
if (PyLong_CheckExact(v))
|
|
Py_INCREF(v);
|
|
else
|
|
v = _PyLong_Copy((PyLongObject *)v);
|
|
return v;
|
|
}
|
|
|
|
static PyObject *
|
|
long_int(PyObject *v)
|
|
{
|
|
long x;
|
|
x = PyLong_AsLong(v);
|
|
if (PyErr_Occurred()) {
|
|
if (PyErr_ExceptionMatches(PyExc_OverflowError)) {
|
|
PyErr_Clear();
|
|
if (PyLong_CheckExact(v)) {
|
|
Py_INCREF(v);
|
|
return v;
|
|
}
|
|
else
|
|
return _PyLong_Copy((PyLongObject *)v);
|
|
}
|
|
else
|
|
return NULL;
|
|
}
|
|
return PyInt_FromLong(x);
|
|
}
|
|
|
|
static PyObject *
|
|
long_float(PyObject *v)
|
|
{
|
|
double result;
|
|
result = PyLong_AsDouble(v);
|
|
if (result == -1.0 && PyErr_Occurred())
|
|
return NULL;
|
|
return PyFloat_FromDouble(result);
|
|
}
|
|
|
|
static PyObject *
|
|
long_oct(PyObject *v)
|
|
{
|
|
return long_format(v, 8, 1);
|
|
}
|
|
|
|
static PyObject *
|
|
long_hex(PyObject *v)
|
|
{
|
|
return long_format(v, 16, 1);
|
|
}
|
|
|
|
static PyObject *
|
|
long_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);
|
|
|
|
static PyObject *
|
|
long_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
|
|
{
|
|
PyObject *x = NULL;
|
|
int base = -909; /* unlikely! */
|
|
static char *kwlist[] = {"x", "base", 0};
|
|
|
|
if (type != &PyLong_Type)
|
|
return long_subtype_new(type, args, kwds); /* Wimp out */
|
|
if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:long", kwlist,
|
|
&x, &base))
|
|
return NULL;
|
|
if (x == NULL)
|
|
return PyLong_FromLong(0L);
|
|
if (base == -909)
|
|
return PyNumber_Long(x);
|
|
else if (PyString_Check(x))
|
|
return PyLong_FromString(PyString_AS_STRING(x), NULL, base);
|
|
#ifdef Py_USING_UNICODE
|
|
else if (PyUnicode_Check(x))
|
|
return PyLong_FromUnicode(PyUnicode_AS_UNICODE(x),
|
|
PyUnicode_GET_SIZE(x),
|
|
base);
|
|
#endif
|
|
else {
|
|
PyErr_SetString(PyExc_TypeError,
|
|
"long() can't convert non-string with explicit base");
|
|
return NULL;
|
|
}
|
|
}
|
|
|
|
/* Wimpy, slow approach to tp_new calls for subtypes of long:
|
|
first create a regular long from whatever arguments we got,
|
|
then allocate a subtype instance and initialize it from
|
|
the regular long. The regular long is then thrown away.
|
|
*/
|
|
static PyObject *
|
|
long_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
|
|
{
|
|
PyLongObject *tmp, *new;
|
|
int i, n;
|
|
|
|
assert(PyType_IsSubtype(type, &PyLong_Type));
|
|
tmp = (PyLongObject *)long_new(&PyLong_Type, args, kwds);
|
|
if (tmp == NULL)
|
|
return NULL;
|
|
assert(PyLong_CheckExact(tmp));
|
|
n = tmp->ob_size;
|
|
if (n < 0)
|
|
n = -n;
|
|
new = (PyLongObject *)type->tp_alloc(type, n);
|
|
if (new == NULL) {
|
|
Py_DECREF(tmp);
|
|
return NULL;
|
|
}
|
|
assert(PyLong_Check(new));
|
|
new->ob_size = tmp->ob_size;
|
|
for (i = 0; i < n; i++)
|
|
new->ob_digit[i] = tmp->ob_digit[i];
|
|
Py_DECREF(tmp);
|
|
return (PyObject *)new;
|
|
}
|
|
|
|
static PyObject *
|
|
long_getnewargs(PyLongObject *v)
|
|
{
|
|
return Py_BuildValue("(N)", _PyLong_Copy(v));
|
|
}
|
|
|
|
static PyMethodDef long_methods[] = {
|
|
{"__getnewargs__", (PyCFunction)long_getnewargs, METH_NOARGS},
|
|
{NULL, NULL} /* sentinel */
|
|
};
|
|
|
|
PyDoc_STRVAR(long_doc,
|
|
"long(x[, base]) -> integer\n\
|
|
\n\
|
|
Convert a string or number to a long integer, if possible. A floating\n\
|
|
point argument will be truncated towards zero (this does not include a\n\
|
|
string representation of a floating point number!) When converting a\n\
|
|
string, use the optional base. It is an error to supply a base when\n\
|
|
converting a non-string.");
|
|
|
|
static PyNumberMethods long_as_number = {
|
|
(binaryfunc) long_add, /*nb_add*/
|
|
(binaryfunc) long_sub, /*nb_subtract*/
|
|
(binaryfunc) long_mul, /*nb_multiply*/
|
|
(binaryfunc) long_classic_div, /*nb_divide*/
|
|
(binaryfunc) long_mod, /*nb_remainder*/
|
|
(binaryfunc) long_divmod, /*nb_divmod*/
|
|
(ternaryfunc) long_pow, /*nb_power*/
|
|
(unaryfunc) long_neg, /*nb_negative*/
|
|
(unaryfunc) long_pos, /*tp_positive*/
|
|
(unaryfunc) long_abs, /*tp_absolute*/
|
|
(inquiry) long_nonzero, /*tp_nonzero*/
|
|
(unaryfunc) long_invert, /*nb_invert*/
|
|
(binaryfunc) long_lshift, /*nb_lshift*/
|
|
(binaryfunc) long_rshift, /*nb_rshift*/
|
|
(binaryfunc) long_and, /*nb_and*/
|
|
(binaryfunc) long_xor, /*nb_xor*/
|
|
(binaryfunc) long_or, /*nb_or*/
|
|
(coercion) long_coerce, /*nb_coerce*/
|
|
(unaryfunc) long_int, /*nb_int*/
|
|
(unaryfunc) long_long, /*nb_long*/
|
|
(unaryfunc) long_float, /*nb_float*/
|
|
(unaryfunc) long_oct, /*nb_oct*/
|
|
(unaryfunc) long_hex, /*nb_hex*/
|
|
0, /* nb_inplace_add */
|
|
0, /* nb_inplace_subtract */
|
|
0, /* nb_inplace_multiply */
|
|
0, /* nb_inplace_divide */
|
|
0, /* nb_inplace_remainder */
|
|
0, /* nb_inplace_power */
|
|
0, /* nb_inplace_lshift */
|
|
0, /* nb_inplace_rshift */
|
|
0, /* nb_inplace_and */
|
|
0, /* nb_inplace_xor */
|
|
0, /* nb_inplace_or */
|
|
(binaryfunc)long_div, /* nb_floor_divide */
|
|
long_true_divide, /* nb_true_divide */
|
|
0, /* nb_inplace_floor_divide */
|
|
0, /* nb_inplace_true_divide */
|
|
};
|
|
|
|
PyTypeObject PyLong_Type = {
|
|
PyObject_HEAD_INIT(&PyType_Type)
|
|
0, /* ob_size */
|
|
"long", /* tp_name */
|
|
sizeof(PyLongObject) - sizeof(digit), /* tp_basicsize */
|
|
sizeof(digit), /* tp_itemsize */
|
|
(destructor)long_dealloc, /* tp_dealloc */
|
|
0, /* tp_print */
|
|
0, /* tp_getattr */
|
|
0, /* tp_setattr */
|
|
(cmpfunc)long_compare, /* tp_compare */
|
|
(reprfunc)long_repr, /* tp_repr */
|
|
&long_as_number, /* tp_as_number */
|
|
0, /* tp_as_sequence */
|
|
0, /* tp_as_mapping */
|
|
(hashfunc)long_hash, /* tp_hash */
|
|
0, /* tp_call */
|
|
(reprfunc)long_str, /* tp_str */
|
|
PyObject_GenericGetAttr, /* tp_getattro */
|
|
0, /* tp_setattro */
|
|
0, /* tp_as_buffer */
|
|
Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
|
|
Py_TPFLAGS_BASETYPE, /* tp_flags */
|
|
long_doc, /* tp_doc */
|
|
0, /* tp_traverse */
|
|
0, /* tp_clear */
|
|
0, /* tp_richcompare */
|
|
0, /* tp_weaklistoffset */
|
|
0, /* tp_iter */
|
|
0, /* tp_iternext */
|
|
long_methods, /* tp_methods */
|
|
0, /* tp_members */
|
|
0, /* tp_getset */
|
|
0, /* tp_base */
|
|
0, /* tp_dict */
|
|
0, /* tp_descr_get */
|
|
0, /* tp_descr_set */
|
|
0, /* tp_dictoffset */
|
|
0, /* tp_init */
|
|
0, /* tp_alloc */
|
|
long_new, /* tp_new */
|
|
PyObject_Del, /* tp_free */
|
|
};
|