--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/symbian-qemu-0.9.1-12/python-2.6.1/Objects/longobject.c Fri Jul 31 15:01:17 2009 +0100
@@ -0,0 +1,3591 @@
+
+
+/* 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 PyLong_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 *);
+
+#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)
+{
+ Py_ssize_t j = ABS(Py_SIZE(v));
+ Py_ssize_t i = j;
+
+ while (i > 0 && v->ob_digit[i-1] == 0)
+ --i;
+ if (i != j)
+ Py_SIZE(v) = (Py_SIZE(v) < 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(Py_ssize_t size)
+{
+ if (size > PY_SSIZE_T_MAX) {
+ PyErr_NoMemory();
+ return NULL;
+ }
+ /* coverity[ampersand_in_size] */
+ /* XXX(nnorwitz): This can overflow --
+ PyObject_NEW_VAR / _PyObject_VAR_SIZE need to detect overflow */
+ return PyObject_NEW_VAR(PyLongObject, &PyLong_Type, size);
+}
+
+PyObject *
+_PyLong_Copy(PyLongObject *src)
+{
+ PyLongObject *result;
+ Py_ssize_t 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 abs_ival;
+ unsigned long t; /* unsigned so >> doesn't propagate sign bit */
+ int ndigits = 0;
+ int negative = 0;
+
+ if (ival < 0) {
+ /* if LONG_MIN == -LONG_MAX-1 (true on most platforms) then
+ ANSI C says that the result of -ival is undefined when ival
+ == LONG_MIN. Hence the following workaround. */
+ abs_ival = (unsigned long)(-1-ival) + 1;
+ negative = 1;
+ }
+ else {
+ abs_ival = (unsigned long)ival;
+ }
+
+ /* 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 = abs_ival;
+ while (t) {
+ ++ndigits;
+ t >>= PyLong_SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ v->ob_size = negative ? -ndigits : ndigits;
+ t = abs_ival;
+ while (t) {
+ *p++ = (digit)(t & PyLong_MASK);
+ t >>= PyLong_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 >>= PyLong_SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ Py_SIZE(v) = ndigits;
+ while (ival) {
+ *p++ = (digit)(ival & PyLong_MASK);
+ ival >>= PyLong_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 integer");
+ return NULL;
+ }
+ if (Py_IS_NAN(dval)) {
+ PyErr_SetString(PyExc_ValueError,
+ "cannot convert float NaN to integer");
+ 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) / PyLong_SHIFT + 1; /* Number of 'digits' in result */
+ v = _PyLong_New(ndig);
+ if (v == NULL)
+ return NULL;
+ frac = ldexp(frac, (expo-1) % PyLong_SHIFT + 1);
+ for (i = ndig; --i >= 0; ) {
+ long bits = (long)frac;
+ v->ob_digit[i] = (digit) bits;
+ frac = frac - (double)bits;
+ frac = ldexp(frac, PyLong_SHIFT);
+ }
+ if (neg)
+ Py_SIZE(v) = -(Py_SIZE(v));
+ return (PyObject *)v;
+}
+
+/* Checking for overflow in PyLong_AsLong is a PITA since C doesn't define
+ * anything about what happens when a signed integer operation overflows,
+ * and some compilers think they're doing you a favor by being "clever"
+ * then. The bit pattern for the largest postive signed long is
+ * (unsigned long)LONG_MAX, and for the smallest negative signed long
+ * it is abs(LONG_MIN), which we could write -(unsigned long)LONG_MIN.
+ * However, some other compilers warn about applying unary minus to an
+ * unsigned operand. Hence the weird "0-".
+ */
+#define PY_ABS_LONG_MIN (0-(unsigned long)LONG_MIN)
+#define PY_ABS_SSIZE_T_MIN (0-(size_t)PY_SSIZE_T_MIN)
+
+/* 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;
+ Py_ssize_t i;
+ int 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 << PyLong_SHIFT) + v->ob_digit[i];
+ if ((x >> PyLong_SHIFT) != prev)
+ goto overflow;
+ }
+ /* Haven't lost any bits, but casting to long requires extra care
+ * (see comment above).
+ */
+ if (x <= (unsigned long)LONG_MAX) {
+ return (long)x * sign;
+ }
+ else if (sign < 0 && x == PY_ABS_LONG_MIN) {
+ return LONG_MIN;
+ }
+ /* else overflow */
+
+ overflow:
+ PyErr_SetString(PyExc_OverflowError,
+ "long int too large to convert to int");
+ return -1;
+}
+
+/* Get a Py_ssize_t from a long int object.
+ Returns -1 and sets an error condition if overflow occurs. */
+
+Py_ssize_t
+PyLong_AsSsize_t(PyObject *vv) {
+ register PyLongObject *v;
+ size_t x, prev;
+ Py_ssize_t i;
+ int sign;
+
+ if (vv == NULL || !PyLong_Check(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 << PyLong_SHIFT) + v->ob_digit[i];
+ if ((x >> PyLong_SHIFT) != prev)
+ goto overflow;
+ }
+ /* Haven't lost any bits, but casting to a signed type requires
+ * extra care (see comment above).
+ */
+ if (x <= (size_t)PY_SSIZE_T_MAX) {
+ return (Py_ssize_t)x * sign;
+ }
+ else if (sign < 0 && x == PY_ABS_SSIZE_T_MIN) {
+ return PY_SSIZE_T_MIN;
+ }
+ /* else overflow */
+
+ 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;
+ Py_ssize_t 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 = Py_SIZE(v);
+ 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 << PyLong_SHIFT) + v->ob_digit[i];
+ if ((x >> PyLong_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;
+ Py_ssize_t i;
+ int 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 << PyLong_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 Py_SIZE(v) == 0 ? 0 : (Py_SIZE(v) < 0 ? -1 : 1);
+}
+
+size_t
+_PyLong_NumBits(PyObject *vv)
+{
+ PyLongObject *v = (PyLongObject *)vv;
+ size_t result = 0;
+ Py_ssize_t ndigits;
+
+ assert(v != NULL);
+ assert(PyLong_Check(v));
+ ndigits = ABS(Py_SIZE(v));
+ assert(ndigits == 0 || v->ob_digit[ndigits - 1] != 0);
+ if (ndigits > 0) {
+ digit msd = v->ob_digit[ndigits - 1];
+
+ result = (ndigits - 1) * PyLong_SHIFT;
+ if (result / PyLong_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 PyLong_SHIFT
+ bits, so it's the ceiling of the quotient. */
+ ndigits = (numsignificantbytes * 8 + PyLong_SHIFT - 1) / PyLong_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 >= PyLong_SHIFT) {
+ /* There's enough to fill a Python digit. */
+ assert(idigit < (int)ndigits);
+ v->ob_digit[idigit] = (digit)(accum & PyLong_MASK);
+ ++idigit;
+ accum >>= PyLong_SHIFT;
+ accumbits -= PyLong_SHIFT;
+ assert(accumbits < PyLong_SHIFT);
+ }
+ }
+ assert(accumbits < PyLong_SHIFT);
+ if (accumbits) {
+ assert(idigit < (int)ndigits);
+ v->ob_digit[idigit] = (digit)accum;
+ ++idigit;
+ }
+ }
+
+ Py_SIZE(v) = 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 */
+ Py_ssize_t 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 (Py_SIZE(v) < 0) {
+ ndigits = -(Py_SIZE(v));
+ if (!is_signed) {
+ PyErr_SetString(PyExc_TypeError,
+ "can't convert negative long to unsigned");
+ return -1;
+ }
+ do_twos_comp = 1;
+ }
+ else {
+ ndigits = Py_SIZE(v);
+ 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 PyLong_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 ^ PyLong_MASK) + carry;
+ carry = thisdigit >> PyLong_SHIFT;
+ thisdigit &= PyLong_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 += PyLong_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) - PyLong_SHIFT));
+ unsigned int nsignbits = 0;
+ while ((s < 0) == do_twos_comp && nsignbits < PyLong_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 << 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. */
+
+double
+PyLong_AsDouble(PyObject *vv)
+{
+ int e = -1;
+ 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;
+ /* 'e' initialized to -1 to silence gcc-4.0.x, but it should be
+ set correctly after a successful _PyLong_AsScaledDouble() call */
+ assert(e >= 0);
+ if (e > INT_MAX / PyLong_SHIFT)
+ goto overflow;
+ errno = 0;
+ x = ldexp(x, e * PyLong_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
+ if ((long)p < 0)
+ return PyLong_FromUnsignedLong((unsigned long)p);
+ 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_FromUnsignedLongLong((unsigned 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 if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
+ x = PyLong_AsLong(vv);
+ else
+ x = PyLong_AsUnsignedLong(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 if (PyLong_Check(vv) && _PyLong_Sign(vv) < 0)
+ x = PyLong_AsLongLong(vv);
+ else
+ x = PyLong_AsUnsignedLongLong(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)
+{
+ PyLongObject *v;
+ unsigned PY_LONG_LONG abs_ival;
+ unsigned PY_LONG_LONG t; /* unsigned so >> doesn't propagate sign bit */
+ int ndigits = 0;
+ int negative = 0;
+
+ if (ival < 0) {
+ /* avoid signed overflow on negation; see comments
+ in PyLong_FromLong above. */
+ abs_ival = (unsigned PY_LONG_LONG)(-1-ival) + 1;
+ negative = 1;
+ }
+ else {
+ abs_ival = (unsigned PY_LONG_LONG)ival;
+ }
+
+ /* 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 = abs_ival;
+ while (t) {
+ ++ndigits;
+ t >>= PyLong_SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ Py_SIZE(v) = negative ? -ndigits : ndigits;
+ t = abs_ival;
+ while (t) {
+ *p++ = (digit)(t & PyLong_MASK);
+ t >>= PyLong_SHIFT;
+ }
+ }
+ return (PyObject *)v;
+}
+
+/* Create a new long int object from a C unsigned PY_LONG_LONG int. */
+
+PyObject *
+PyLong_FromUnsignedLongLong(unsigned PY_LONG_LONG ival)
+{
+ PyLongObject *v;
+ unsigned PY_LONG_LONG t;
+ int ndigits = 0;
+
+ /* Count the number of Python digits. */
+ t = (unsigned PY_LONG_LONG)ival;
+ while (t) {
+ ++ndigits;
+ t >>= PyLong_SHIFT;
+ }
+ v = _PyLong_New(ndigits);
+ if (v != NULL) {
+ digit *p = v->ob_digit;
+ Py_SIZE(v) = ndigits;
+ while (ival) {
+ *p++ = (digit)(ival & PyLong_MASK);
+ ival >>= PyLong_SHIFT;
+ }
+ }
+ return (PyObject *)v;
+}
+
+/* Create a new long int object from a C Py_ssize_t. */
+
+PyObject *
+PyLong_FromSsize_t(Py_ssize_t ival)
+{
+ Py_ssize_t bytes = ival;
+ int one = 1;
+ return _PyLong_FromByteArray(
+ (unsigned char *)&bytes,
+ SIZEOF_SIZE_T, IS_LITTLE_ENDIAN, 1);
+}
+
+/* Create a new long int object from a C size_t. */
+
+PyObject *
+PyLong_FromSize_t(size_t ival)
+{
+ size_t bytes = ival;
+ int one = 1;
+ return _PyLong_FromByteArray(
+ (unsigned char *)&bytes,
+ SIZEOF_SIZE_T, 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 (unsigned PY_LONG_LONG)-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;
+ Py_ssize_t i;
+ int 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 << PyLong_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, Py_ssize_t m, digit *y, Py_ssize_t n)
+{
+ int i;
+ digit carry = 0;
+
+ assert(m >= n);
+ for (i = 0; i < n; ++i) {
+ carry += x[i] + y[i];
+ x[i] = carry & PyLong_MASK;
+ carry >>= PyLong_SHIFT;
+ assert((carry & 1) == carry);
+ }
+ for (; carry && i < m; ++i) {
+ carry += x[i];
+ x[i] = carry & PyLong_MASK;
+ carry >>= PyLong_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, Py_ssize_t m, digit *y, Py_ssize_t n)
+{
+ int i;
+ digit borrow = 0;
+
+ assert(m >= n);
+ for (i = 0; i < n; ++i) {
+ borrow = x[i] - y[i] - borrow;
+ x[i] = borrow & PyLong_MASK;
+ borrow >>= PyLong_SHIFT;
+ borrow &= 1; /* keep only 1 sign bit */
+ }
+ for (; borrow && i < m; ++i) {
+ borrow = x[i] - borrow;
+ x[i] = borrow & PyLong_MASK;
+ borrow >>= PyLong_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)
+{
+ Py_ssize_t size_a = ABS(Py_SIZE(a));
+ PyLongObject *z = _PyLong_New(size_a+1);
+ twodigits carry = extra;
+ Py_ssize_t 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 & PyLong_MASK);
+ carry >>= PyLong_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
+ _PyLong_Format, but that should be done with great care since longs are
+ immutable. */
+
+static digit
+inplace_divrem1(digit *pout, digit *pin, Py_ssize_t size, digit n)
+{
+ twodigits rem = 0;
+
+ assert(n > 0 && n <= PyLong_MASK);
+ pin += size;
+ pout += size;
+ while (--size >= 0) {
+ digit hi;
+ rem = (rem << PyLong_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 Py_ssize_t size = ABS(Py_SIZE(a));
+ PyLongObject *z;
+
+ assert(n > 0 && n <= PyLong_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 the long to a string object with given base,
+ appending a base prefix of 0[box] if base is 2, 8 or 16.
+ Add a trailing "L" if addL is non-zero.
+ If newstyle is zero, then use the pre-2.6 behavior of octal having
+ a leading "0", instead of the prefix "0o" */
+PyAPI_FUNC(PyObject *)
+_PyLong_Format(PyObject *aa, int base, int addL, int newstyle)
+{
+ register PyLongObject *a = (PyLongObject *)aa;
+ PyStringObject *str;
+ Py_ssize_t i, j, sz;
+ Py_ssize_t size_a;
+ char *p;
+ int bits;
+ char sign = '\0';
+
+ if (a == NULL || !PyLong_Check(a)) {
+ PyErr_BadInternalCall();
+ return NULL;
+ }
+ assert(base >= 2 && base <= 36);
+ size_a = ABS(Py_SIZE(a));
+
+ /* 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);
+ j = size_a*PyLong_SHIFT + bits-1;
+ sz = i + j / bits;
+ if (j / PyLong_SHIFT < size_a || sz < i) {
+ PyErr_SetString(PyExc_OverflowError,
+ "long is too large to format");
+ return NULL;
+ }
+ str = (PyStringObject *) PyString_FromStringAndSize((char *)0, sz);
+ if (str == NULL)
+ return NULL;
+ p = PyString_AS_STRING(str) + sz;
+ *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 += PyLong_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. */
+ Py_ssize_t 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 >> PyLong_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 == 2) {
+ *--p = 'b';
+ *--p = '0';
+ }
+ else if (base == 8) {
+ if (newstyle) {
+ *--p = 'o';
+ *--p = '0';
+ }
+ else
+ 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,
+ (Py_ssize_t) (q - PyString_AS_STRING(str)));
+ }
+ return (PyObject *)str;
+}
+
+/* Table of digit values for 8-bit string -> integer conversion.
+ * '0' maps to 0, ..., '9' maps to 9.
+ * 'a' and 'A' map to 10, ..., 'z' and 'Z' map to 35.
+ * All other indices map to 37.
+ * Note that when converting a base B string, a char c is a legitimate
+ * base B digit iff _PyLong_DigitValue[Py_CHARMASK(c)] < B.
+ */
+int _PyLong_DigitValue[256] = {
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 37, 37, 37, 37, 37, 37,
+ 37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
+ 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
+ 37, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
+ 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+ 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37,
+};
+
+/* *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;
+ Py_ssize_t 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;
+ while (_PyLong_DigitValue[Py_CHARMASK(*p)] < base)
+ ++p;
+ *str = p;
+ /* n <- # of Python digits needed, = ceiling(n/PyLong_SHIFT). */
+ n = (p - start) * bits_per_char + PyLong_SHIFT - 1;
+ if (n / bits_per_char < p - start) {
+ PyErr_SetString(PyExc_ValueError,
+ "long string too large to convert");
+ return NULL;
+ }
+ n = n / PyLong_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 = _PyLong_DigitValue[Py_CHARMASK(*p)];
+ assert(k >= 0 && k < base);
+ accum |= (twodigits)(k << bits_in_accum);
+ bits_in_accum += bits_per_char;
+ if (bits_in_accum >= PyLong_SHIFT) {
+ *pdigit++ = (digit)(accum & PyLong_MASK);
+ assert(pdigit - z->ob_digit <= (int)n);
+ accum >>= PyLong_SHIFT;
+ bits_in_accum -= PyLong_SHIFT;
+ assert(bits_in_accum < PyLong_SHIFT);
+ }
+ }
+ if (bits_in_accum) {
+ assert(bits_in_accum <= PyLong_SHIFT);
+ *pdigit++ = (digit)accum;
+ assert(pdigit - z->ob_digit <= (int)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;
+ PyObject *strobj, *strrepr;
+ Py_ssize_t slen;
+
+ 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) {
+ /* No base given. Deduce the base from the contents
+ of the string */
+ if (str[0] != '0')
+ base = 10;
+ else if (str[1] == 'x' || str[1] == 'X')
+ base = 16;
+ else if (str[1] == 'o' || str[1] == 'O')
+ base = 8;
+ else if (str[1] == 'b' || str[1] == 'B')
+ base = 2;
+ else
+ /* "old" (C-style) octal literal, still valid in
+ 2.x, although illegal in 3.x */
+ base = 8;
+ }
+ /* Whether or not we were deducing the base, skip leading chars
+ as needed */
+ if (str[0] == '0' &&
+ ((base == 16 && (str[1] == 'x' || str[1] == 'X')) ||
+ (base == 8 && (str[1] == 'o' || str[1] == 'O')) ||
+ (base == 2 && (str[1] == 'b' || str[1] == 'B'))))
+ str += 2;
+
+ start = str;
+ if ((base & (base - 1)) == 0)
+ z = long_from_binary_base(&str, base);
+ else {
+/***
+Binary bases can be converted in time linear in the number of digits, because
+Python's representation base is binary. Other bases (including decimal!) use
+the simple quadratic-time algorithm below, complicated by some speed tricks.
+
+First some math: the largest integer that can be expressed in N base-B digits
+is B**N-1. Consequently, if we have an N-digit input in base B, the worst-
+case number of Python digits needed to hold it is the smallest integer n s.t.
+
+ PyLong_BASE**n-1 >= B**N-1 [or, adding 1 to both sides]
+ PyLong_BASE**n >= B**N [taking logs to base PyLong_BASE]
+ n >= log(B**N)/log(PyLong_BASE) = N * log(B)/log(PyLong_BASE)
+
+The static array log_base_PyLong_BASE[base] == log(base)/log(PyLong_BASE) so we can compute
+this quickly. A Python long with that much space is reserved near the start,
+and the result is computed into it.
+
+The input string is actually treated as being in base base**i (i.e., i digits
+are processed at a time), where two more static arrays hold:
+
+ convwidth_base[base] = the largest integer i such that base**i <= PyLong_BASE
+ convmultmax_base[base] = base ** convwidth_base[base]
+
+The first of these is the largest i such that i consecutive input digits
+must fit in a single Python digit. The second is effectively the input
+base we're really using.
+
+Viewing the input as a sequence <c0, c1, ..., c_n-1> of digits in base
+convmultmax_base[base], the result is "simply"
+
+ (((c0*B + c1)*B + c2)*B + c3)*B + ... ))) + c_n-1
+
+where B = convmultmax_base[base].
+
+Error analysis: as above, the number of Python digits `n` needed is worst-
+case
+
+ n >= N * log(B)/log(PyLong_BASE)
+
+where `N` is the number of input digits in base `B`. This is computed via
+
+ size_z = (Py_ssize_t)((scan - str) * log_base_PyLong_BASE[base]) + 1;
+
+below. Two numeric concerns are how much space this can waste, and whether
+the computed result can be too small. To be concrete, assume PyLong_BASE = 2**15,
+which is the default (and it's unlikely anyone changes that).
+
+Waste isn't a problem: provided the first input digit isn't 0, the difference
+between the worst-case input with N digits and the smallest input with N
+digits is about a factor of B, but B is small compared to PyLong_BASE so at most
+one allocated Python digit can remain unused on that count. If
+N*log(B)/log(PyLong_BASE) is mathematically an exact integer, then truncating that
+and adding 1 returns a result 1 larger than necessary. However, that can't
+happen: whenever B is a power of 2, long_from_binary_base() is called
+instead, and it's impossible for B**i to be an integer power of 2**15 when
+B is not a power of 2 (i.e., it's impossible for N*log(B)/log(PyLong_BASE) to be
+an exact integer when B is not a power of 2, since B**i has a prime factor
+other than 2 in that case, but (2**15)**j's only prime factor is 2).
+
+The computed result can be too small if the true value of N*log(B)/log(PyLong_BASE)
+is a little bit larger than an exact integer, but due to roundoff errors (in
+computing log(B), log(PyLong_BASE), their quotient, and/or multiplying that by N)
+yields a numeric result a little less than that integer. Unfortunately, "how
+close can a transcendental function get to an integer over some range?"
+questions are generally theoretically intractable. Computer analysis via
+continued fractions is practical: expand log(B)/log(PyLong_BASE) via continued
+fractions, giving a sequence i/j of "the best" rational approximations. Then
+j*log(B)/log(PyLong_BASE) is approximately equal to (the integer) i. This shows that
+we can get very close to being in trouble, but very rarely. For example,
+76573 is a denominator in one of the continued-fraction approximations to
+log(10)/log(2**15), and indeed:
+
+ >>> log(10)/log(2**15)*76573
+ 16958.000000654003
+
+is very close to an integer. If we were working with IEEE single-precision,
+rounding errors could kill us. Finding worst cases in IEEE double-precision
+requires better-than-double-precision log() functions, and Tim didn't bother.
+Instead the code checks to see whether the allocated space is enough as each
+new Python digit is added, and copies the whole thing to a larger long if not.
+This should happen extremely rarely, and in fact I don't have a test case
+that triggers it(!). Instead the code was tested by artificially allocating
+just 1 digit at the start, so that the copying code was exercised for every
+digit beyond the first.
+***/
+ register twodigits c; /* current input character */
+ Py_ssize_t size_z;
+ int i;
+ int convwidth;
+ twodigits convmultmax, convmult;
+ digit *pz, *pzstop;
+ char* scan;
+
+ static double log_base_PyLong_BASE[37] = {0.0e0,};
+ static int convwidth_base[37] = {0,};
+ static twodigits convmultmax_base[37] = {0,};
+
+ if (log_base_PyLong_BASE[base] == 0.0) {
+ twodigits convmax = base;
+ int i = 1;
+
+ log_base_PyLong_BASE[base] = log((double)base) /
+ log((double)PyLong_BASE);
+ for (;;) {
+ twodigits next = convmax * base;
+ if (next > PyLong_BASE)
+ break;
+ convmax = next;
+ ++i;
+ }
+ convmultmax_base[base] = convmax;
+ assert(i > 0);
+ convwidth_base[base] = i;
+ }
+
+ /* Find length of the string of numeric characters. */
+ scan = str;
+ while (_PyLong_DigitValue[Py_CHARMASK(*scan)] < base)
+ ++scan;
+
+ /* Create a long object that can contain the largest possible
+ * integer with this base and length. Note that there's no
+ * need to initialize z->ob_digit -- no slot is read up before
+ * being stored into.
+ */
+ size_z = (Py_ssize_t)((scan - str) * log_base_PyLong_BASE[base]) + 1;
+ /* Uncomment next line to test exceedingly rare copy code */
+ /* size_z = 1; */
+ assert(size_z > 0);
+ z = _PyLong_New(size_z);
+ if (z == NULL)
+ return NULL;
+ Py_SIZE(z) = 0;
+
+ /* `convwidth` consecutive input digits are treated as a single
+ * digit in base `convmultmax`.
+ */
+ convwidth = convwidth_base[base];
+ convmultmax = convmultmax_base[base];
+
+ /* Work ;-) */
+ while (str < scan) {
+ /* grab up to convwidth digits from the input string */
+ c = (digit)_PyLong_DigitValue[Py_CHARMASK(*str++)];
+ for (i = 1; i < convwidth && str != scan; ++i, ++str) {
+ c = (twodigits)(c * base +
+ _PyLong_DigitValue[Py_CHARMASK(*str)]);
+ assert(c < PyLong_BASE);
+ }
+
+ convmult = convmultmax;
+ /* Calculate the shift only if we couldn't get
+ * convwidth digits.
+ */
+ if (i != convwidth) {
+ convmult = base;
+ for ( ; i > 1; --i)
+ convmult *= base;
+ }
+
+ /* Multiply z by convmult, and add c. */
+ pz = z->ob_digit;
+ pzstop = pz + Py_SIZE(z);
+ for (; pz < pzstop; ++pz) {
+ c += (twodigits)*pz * convmult;
+ *pz = (digit)(c & PyLong_MASK);
+ c >>= PyLong_SHIFT;
+ }
+ /* carry off the current end? */
+ if (c) {
+ assert(c < PyLong_BASE);
+ if (Py_SIZE(z) < size_z) {
+ *pz = (digit)c;
+ ++Py_SIZE(z);
+ }
+ else {
+ PyLongObject *tmp;
+ /* Extremely rare. Get more space. */
+ assert(Py_SIZE(z) == size_z);
+ tmp = _PyLong_New(size_z + 1);
+ if (tmp == NULL) {
+ Py_DECREF(z);
+ return NULL;
+ }
+ memcpy(tmp->ob_digit,
+ z->ob_digit,
+ sizeof(digit) * size_z);
+ Py_DECREF(z);
+ z = tmp;
+ z->ob_digit[size_z] = (digit)c;
+ ++size_z;
+ }
+ }
+ }
+ }
+ if (z == NULL)
+ return NULL;
+ if (str == start)
+ goto onError;
+ if (sign < 0)
+ Py_SIZE(z) = -(Py_SIZE(z));
+ 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:
+ Py_XDECREF(z);
+ slen = strlen(orig_str) < 200 ? strlen(orig_str) : 200;
+ strobj = PyString_FromStringAndSize(orig_str, slen);
+ if (strobj == NULL)
+ return NULL;
+ strrepr = PyObject_Repr(strobj);
+ Py_DECREF(strobj);
+ if (strrepr == NULL)
+ return NULL;
+ PyErr_Format(PyExc_ValueError,
+ "invalid literal for long() with base %d: %s",
+ base, PyString_AS_STRING(strrepr));
+ Py_DECREF(strrepr);
+ return NULL;
+}
+
+#ifdef Py_USING_UNICODE
+PyObject *
+PyLong_FromUnicode(Py_UNICODE *u, Py_ssize_t length, int base)
+{
+ PyObject *result;
+ char *buffer = (char *)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_long(PyObject *v);
+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)
+{
+ Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+ 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);
+ if (*pdiv == NULL)
+ return -1;
+ 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);
+ if (*prem == NULL) {
+ Py_DECREF(z);
+ return -1;
+ }
+ }
+ 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)
+{
+ Py_ssize_t size_v = ABS(Py_SIZE(v1)), size_w = ABS(Py_SIZE(w1));
+ digit d = (digit) ((twodigits)PyLong_BASE / (w1->ob_digit[size_w-1] + 1));
+ PyLongObject *v = mul1(v1, d);
+ PyLongObject *w = mul1(w1, d);
+ PyLongObject *a;
+ Py_ssize_t 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(Py_REFCNT(v) == 1); /* Since v will be used as accumulator! */
+ assert(size_w == ABS(Py_SIZE(w))); /* That's how d was calculated */
+
+ size_v = ABS(Py_SIZE(v));
+ k = size_v - size_w;
+ a = _PyLong_New(k + 1);
+
+ for (j = size_v; 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 = PyLong_MASK;
+ else
+ q = (((twodigits)vj << PyLong_SHIFT) + v->ob_digit[j-1]) /
+ w->ob_digit[size_w-1];
+
+ while (w->ob_digit[size_w-2]*q >
+ ((
+ ((twodigits)vj << PyLong_SHIFT)
+ + v->ob_digit[j-1]
+ - q*w->ob_digit[size_w-1]
+ ) << PyLong_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 >> PyLong_SHIFT);
+ carry += v->ob_digit[i+k] - z
+ + ((twodigits)zz << PyLong_SHIFT);
+ v->ob_digit[i+k] = (digit)(carry & PyLong_MASK);
+ carry = Py_ARITHMETIC_RIGHT_SHIFT(PyLong_BASE_TWODIGITS_TYPE,
+ carry, PyLong_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 & PyLong_MASK);
+ carry = Py_ARITHMETIC_RIGHT_SHIFT(
+ PyLong_BASE_TWODIGITS_TYPE,
+ carry, PyLong_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)
+{
+ Py_TYPE(v)->tp_free(v);
+}
+
+static PyObject *
+long_repr(PyObject *v)
+{
+ return _PyLong_Format(v, 10, 1, 0);
+}
+
+static PyObject *
+long_str(PyObject *v)
+{
+ return _PyLong_Format(v, 10, 0, 0);
+}
+
+static int
+long_compare(PyLongObject *a, PyLongObject *b)
+{
+ Py_ssize_t sign;
+
+ if (Py_SIZE(a) != Py_SIZE(b)) {
+ if (ABS(Py_SIZE(a)) == 0 && ABS(Py_SIZE(b)) == 0)
+ sign = 0;
+ else
+ sign = Py_SIZE(a) - Py_SIZE(b);
+ }
+ else {
+ Py_ssize_t i = ABS(Py_SIZE(a));
+ 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 (Py_SIZE(a) < 0)
+ sign = -sign;
+ }
+ }
+ return sign < 0 ? -1 : sign > 0 ? 1 : 0;
+}
+
+static long
+long_hash(PyLongObject *v)
+{
+ long x;
+ Py_ssize_t i;
+ int 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_PyLong_SHIFT (8*sizeof(long) - PyLong_SHIFT)
+ /* The following loop produces a C long x such that (unsigned long)x
+ is congruent to the absolute value of v modulo ULONG_MAX. The
+ resulting x is nonzero if and only if v is. */
+ while (--i >= 0) {
+ /* Force a native long #-bits (32 or 64) circular shift */
+ x = ((x << PyLong_SHIFT) & ~PyLong_MASK) | ((x >> LONG_BIT_PyLong_SHIFT) & PyLong_MASK);
+ x += v->ob_digit[i];
+ /* If the addition above overflowed (thinking of x as
+ unsigned), we compensate by incrementing. This preserves
+ the value modulo ULONG_MAX. */
+ if ((unsigned long)x < v->ob_digit[i])
+ x++;
+ }
+#undef LONG_BIT_PyLong_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)
+{
+ Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+ 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; }
+ { Py_ssize_t 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 & PyLong_MASK;
+ carry >>= PyLong_SHIFT;
+ }
+ for (; i < size_a; ++i) {
+ carry += a->ob_digit[i];
+ z->ob_digit[i] = carry & PyLong_MASK;
+ carry >>= PyLong_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)
+{
+ Py_ssize_t size_a = ABS(Py_SIZE(a)), size_b = ABS(Py_SIZE(b));
+ PyLongObject *z;
+ Py_ssize_t 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; }
+ { Py_ssize_t 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>PyLong_SHIFT. */
+ borrow = a->ob_digit[i] - b->ob_digit[i] - borrow;
+ z->ob_digit[i] = borrow & PyLong_MASK;
+ borrow >>= PyLong_SHIFT;
+ borrow &= 1; /* Keep only one sign bit */
+ }
+ for (; i < size_a; ++i) {
+ borrow = a->ob_digit[i] - borrow;
+ z->ob_digit[i] = borrow & PyLong_MASK;
+ borrow >>= PyLong_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;
+ Py_ssize_t size_a = ABS(Py_SIZE(a));
+ Py_ssize_t size_b = ABS(Py_SIZE(b));
+ Py_ssize_t i;
+
+ z = _PyLong_New(size_a + size_b);
+ if (z == NULL)
+ return NULL;
+
+ memset(z->ob_digit, 0, Py_SIZE(z) * 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 & PyLong_MASK);
+ carry >>= PyLong_SHIFT;
+ assert(carry <= PyLong_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 & PyLong_MASK);
+ carry >>= PyLong_SHIFT;
+ assert(carry <= (PyLong_MASK << 1));
+ }
+ if (carry) {
+ carry += *pz;
+ *pz++ = (digit)(carry & PyLong_MASK);
+ carry >>= PyLong_SHIFT;
+ }
+ if (carry)
+ *pz += (digit)(carry & PyLong_MASK);
+ assert((carry >> PyLong_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 & PyLong_MASK);
+ carry >>= PyLong_SHIFT;
+ assert(carry <= PyLong_MASK);
+ }
+ if (carry)
+ *pz += (digit)(carry & PyLong_MASK);
+ assert((carry >> PyLong_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, Py_ssize_t size, PyLongObject **high, PyLongObject **low)
+{
+ PyLongObject *hi, *lo;
+ Py_ssize_t size_lo, size_hi;
+ const Py_ssize_t size_n = ABS(Py_SIZE(n));
+
+ 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)
+{
+ Py_ssize_t asize = ABS(Py_SIZE(a));
+ Py_ssize_t bsize = ABS(Py_SIZE(b));
+ PyLongObject *ah = NULL;
+ PyLongObject *al = NULL;
+ PyLongObject *bh = NULL;
+ PyLongObject *bl = NULL;
+ PyLongObject *ret = NULL;
+ PyLongObject *t1, *t2, *t3;
+ Py_ssize_t shift; /* the number of digits we split off */
+ Py_ssize_t 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(Py_SIZE(ah) > 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
+ * PyLong_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, Py_SIZE(ret) * sizeof(digit));
+#endif
+
+ /* 2. t1 <- ah*bh, and copy into high digits of result. */
+ if ((t1 = k_mul(ah, bh)) == NULL) goto fail;
+ assert(Py_SIZE(t1) >= 0);
+ assert(2*shift + Py_SIZE(t1) <= Py_SIZE(ret));
+ memcpy(ret->ob_digit + 2*shift, t1->ob_digit,
+ Py_SIZE(t1) * sizeof(digit));
+
+ /* Zero-out the digits higher than the ah*bh copy. */
+ i = Py_SIZE(ret) - 2*shift - Py_SIZE(t1);
+ if (i)
+ memset(ret->ob_digit + 2*shift + Py_SIZE(t1), 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(Py_SIZE(t2) >= 0);
+ assert(Py_SIZE(t2) <= 2*shift); /* no overlap with high digits */
+ memcpy(ret->ob_digit, t2->ob_digit, Py_SIZE(t2) * sizeof(digit));
+
+ /* Zero out remaining digits. */
+ i = 2*shift - Py_SIZE(t2); /* number of uninitialized digits */
+ if (i)
+ memset(ret->ob_digit + Py_SIZE(t2), 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 = Py_SIZE(ret) - shift; /* # digits after shift */
+ (void)v_isub(ret->ob_digit + shift, i, t2->ob_digit, Py_SIZE(t2));
+ Py_DECREF(t2);
+
+ (void)v_isub(ret->ob_digit + shift, i, t1->ob_digit, Py_SIZE(t1));
+ 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(Py_SIZE(t3) >= 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, Py_SIZE(t3));
+ 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 PyLong_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 Py_ssize_t asize = ABS(Py_SIZE(a));
+ Py_ssize_t bsize = ABS(Py_SIZE(b));
+ Py_ssize_t 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, Py_SIZE(ret) * 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 Py_ssize_t nbtouse = MIN(bsize, asize);
+
+ /* Multiply the next slice of b by a. */
+ memcpy(bslice->ob_digit, b->ob_digit + nbdone,
+ nbtouse * sizeof(digit));
+ Py_SIZE(bslice) = nbtouse;
+ product = k_mul(a, bslice);
+ if (product == NULL)
+ goto fail;
+
+ /* Add into result. */
+ (void)v_iadd(ret->ob_digit + nbdone, Py_SIZE(ret) - nbdone,
+ product->ob_digit, Py_SIZE(product));
+ 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 ((Py_SIZE(mod) < 0 && Py_SIZE(w) > 0) ||
+ (Py_SIZE(mod) > 0 && Py_SIZE(w) < 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 failed, aexp = -1, bexp = -1;
+
+ 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;
+ /* 'aexp' and 'bexp' were initialized to -1 to silence gcc-4.0.x,
+ but should really be set correctly after sucessful calls to
+ _PyLong_AsScaledDouble() */
+ assert(aexp >= 0 && bexp >= 0);
+
+ 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**(PyLong_SHIFT*(aexp-bexp)) */
+ ad /= bd; /* overflow/underflow impossible here */
+ aexp -= bexp;
+ if (aexp > INT_MAX / PyLong_SHIFT)
+ goto overflow;
+ else if (aexp < -(INT_MAX / PyLong_SHIFT))
+ return PyFloat_FromDouble(0.0); /* underflow to 0 */
+ errno = 0;
+ ad = ldexp(ad, aexp * PyLong_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 */
+ Py_ssize_t 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));
+ if (c == NULL)
+ goto Error;
+ }
+ else if (x == Py_None)
+ c = NULL;
+ else {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_INCREF(Py_NotImplemented);
+ return Py_NotImplemented;
+ }
+
+ if (Py_SIZE(b) < 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 (Py_SIZE(c) == 0) {
+ PyErr_SetString(PyExc_ValueError,
+ "pow() 3rd argument cannot be 0");
+ goto Error;
+ }
+
+ /* if modulus < 0:
+ negativeOutput = True
+ modulus = -modulus */
+ if (Py_SIZE(c) < 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 ((Py_SIZE(c) == 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 (Py_SIZE(a) < 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 (Py_SIZE(b) <= FIVEARY_CUTOFF) {
+ /* Left-to-right binary exponentiation (HAC Algorithm 14.79) */
+ /* http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf */
+ for (i = Py_SIZE(b) - 1; i >= 0; --i) {
+ digit bi = b->ob_digit[i];
+
+ for (j = 1 << (PyLong_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 = Py_SIZE(b) - 1; i >= 0; --i) {
+ const digit bi = b->ob_digit[i];
+
+ for (j = PyLong_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 && (Py_SIZE(z) != 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:
+ if (Py_SIZE(b) > FIVEARY_CUTOFF) {
+ for (i = 0; i < 32; ++i)
+ Py_XDECREF(table[i]);
+ }
+ Py_DECREF(a);
+ Py_DECREF(b);
+ Py_XDECREF(c);
+ Py_XDECREF(temp);
+ 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;
+ Py_SIZE(x) = -(Py_SIZE(x));
+ return (PyObject *)x;
+}
+
+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_long((PyObject *)v);
+}
+
+static int
+long_nonzero(PyLongObject *v)
+{
+ return ABS(Py_SIZE(v)) != 0;
+}
+
+static PyObject *
+long_rshift(PyLongObject *v, PyLongObject *w)
+{
+ PyLongObject *a, *b;
+ PyLongObject *z = NULL;
+ long shiftby;
+ Py_ssize_t newsize, wordshift, loshift, hishift, i, j;
+ digit lomask, himask;
+
+ CONVERT_BINOP((PyObject *)v, (PyObject *)w, &a, &b);
+
+ if (Py_SIZE(a) < 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 / PyLong_SHIFT;
+ newsize = ABS(Py_SIZE(a)) - wordshift;
+ if (newsize <= 0) {
+ z = _PyLong_New(0);
+ Py_DECREF(a);
+ Py_DECREF(b);
+ return (PyObject *)z;
+ }
+ loshift = shiftby % PyLong_SHIFT;
+ hishift = PyLong_SHIFT - loshift;
+ lomask = ((digit)1 << hishift) - 1;
+ himask = PyLong_MASK ^ lomask;
+ z = _PyLong_New(newsize);
+ if (z == NULL)
+ goto rshift_error;
+ if (Py_SIZE(a) < 0)
+ Py_SIZE(z) = -(Py_SIZE(z));
+ 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;
+ Py_ssize_t 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, PyLong_SHIFT) */
+ wordshift = (int)shiftby / PyLong_SHIFT;
+ remshift = (int)shiftby - wordshift * PyLong_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 & PyLong_MASK);
+ accum >>= PyLong_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 PyLong_MASK */
+ int negz;
+ Py_ssize_t size_a, size_b, size_z;
+ PyLongObject *z;
+ int i;
+ digit diga, digb;
+ PyObject *v;
+
+ if (Py_SIZE(a) < 0) {
+ a = (PyLongObject *) long_invert(a);
+ if (a == NULL)
+ return NULL;
+ maska = PyLong_MASK;
+ }
+ else {
+ Py_INCREF(a);
+ maska = 0;
+ }
+ if (Py_SIZE(b) < 0) {
+ b = (PyLongObject *) long_invert(b);
+ if (b == NULL) {
+ Py_DECREF(a);
+ return NULL;
+ }
+ maskb = PyLong_MASK;
+ }
+ else {
+ Py_INCREF(b);
+ maskb = 0;
+ }
+
+ negz = 0;
+ switch (op) {
+ case '^':
+ if (maska != maskb) {
+ maska ^= PyLong_MASK;
+ negz = -1;
+ }
+ break;
+ case '&':
+ if (maska && maskb) {
+ op = '|';
+ maska ^= PyLong_MASK;
+ maskb ^= PyLong_MASK;
+ negz = -1;
+ }
+ break;
+ case '|':
+ if (maska || maskb) {
+ op = '&';
+ maska ^= PyLong_MASK;
+ maskb ^= PyLong_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 = Py_SIZE(a);
+ size_b = Py_SIZE(b);
+ 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 (z == NULL) {
+ Py_DECREF(a);
+ Py_DECREF(b);
+ 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));
+ if (*pw == NULL)
+ return -1;
+ 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 _PyLong_Format(v, 8, 1, 0);
+}
+
+static PyObject *
+long_hex(PyObject *v)
+{
+ return _PyLong_Format(v, 16, 1, 0);
+}
+
+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)) {
+ /* Since PyLong_FromString doesn't have a length parameter,
+ * check here for possible NULs in the string. */
+ char *string = PyString_AS_STRING(x);
+ if (strlen(string) != PyString_Size(x)) {
+ /* create a repr() of the input string,
+ * just like PyLong_FromString does. */
+ PyObject *srepr;
+ srepr = PyObject_Repr(x);
+ if (srepr == NULL)
+ return NULL;
+ PyErr_Format(PyExc_ValueError,
+ "invalid literal for long() with base %d: %s",
+ base, PyString_AS_STRING(srepr));
+ Py_DECREF(srepr);
+ return NULL;
+ }
+ 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, *newobj;
+ Py_ssize_t 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 = Py_SIZE(tmp);
+ if (n < 0)
+ n = -n;
+ newobj = (PyLongObject *)type->tp_alloc(type, n);
+ if (newobj == NULL) {
+ Py_DECREF(tmp);
+ return NULL;
+ }
+ assert(PyLong_Check(newobj));
+ Py_SIZE(newobj) = Py_SIZE(tmp);
+ for (i = 0; i < n; i++)
+ newobj->ob_digit[i] = tmp->ob_digit[i];
+ Py_DECREF(tmp);
+ return (PyObject *)newobj;
+}
+
+static PyObject *
+long_getnewargs(PyLongObject *v)
+{
+ return Py_BuildValue("(N)", _PyLong_Copy(v));
+}
+
+static PyObject *
+long_getN(PyLongObject *v, void *context) {
+ return PyLong_FromLong((Py_intptr_t)context);
+}
+
+static PyObject *
+long__format__(PyObject *self, PyObject *args)
+{
+ PyObject *format_spec;
+
+ if (!PyArg_ParseTuple(args, "O:__format__", &format_spec))
+ return NULL;
+ if (PyBytes_Check(format_spec))
+ return _PyLong_FormatAdvanced(self,
+ PyBytes_AS_STRING(format_spec),
+ PyBytes_GET_SIZE(format_spec));
+ if (PyUnicode_Check(format_spec)) {
+ /* Convert format_spec to a str */
+ PyObject *result;
+ PyObject *str_spec = PyObject_Str(format_spec);
+
+ if (str_spec == NULL)
+ return NULL;
+
+ result = _PyLong_FormatAdvanced(self,
+ PyBytes_AS_STRING(str_spec),
+ PyBytes_GET_SIZE(str_spec));
+
+ Py_DECREF(str_spec);
+ return result;
+ }
+ PyErr_SetString(PyExc_TypeError, "__format__ requires str or unicode");
+ return NULL;
+}
+
+static PyObject *
+long_sizeof(PyLongObject *v)
+{
+ Py_ssize_t res;
+
+ res = v->ob_type->tp_basicsize;
+ if (v->ob_size != 0)
+ res += abs(v->ob_size) * sizeof(digit);
+ return PyInt_FromSsize_t(res);
+}
+
+#if 0
+static PyObject *
+long_is_finite(PyObject *v)
+{
+ Py_RETURN_TRUE;
+}
+#endif
+
+static PyMethodDef long_methods[] = {
+ {"conjugate", (PyCFunction)long_long, METH_NOARGS,
+ "Returns self, the complex conjugate of any long."},
+#if 0
+ {"is_finite", (PyCFunction)long_is_finite, METH_NOARGS,
+ "Returns always True."},
+#endif
+ {"__trunc__", (PyCFunction)long_long, METH_NOARGS,
+ "Truncating an Integral returns itself."},
+ {"__getnewargs__", (PyCFunction)long_getnewargs, METH_NOARGS},
+ {"__format__", (PyCFunction)long__format__, METH_VARARGS},
+ {"__sizeof__", (PyCFunction)long_sizeof, METH_NOARGS,
+ "Returns size in memory, in bytes"},
+ {NULL, NULL} /* sentinel */
+};
+
+static PyGetSetDef long_getset[] = {
+ {"real",
+ (getter)long_long, (setter)NULL,
+ "the real part of a complex number",
+ NULL},
+ {"imag",
+ (getter)long_getN, (setter)NULL,
+ "the imaginary part of a complex number",
+ (void*)0},
+ {"numerator",
+ (getter)long_long, (setter)NULL,
+ "the numerator of a rational number in lowest terms",
+ NULL},
+ {"denominator",
+ (getter)long_getN, (setter)NULL,
+ "the denominator of a rational number in lowest terms",
+ (void*)1},
+ {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*/
+ long_classic_div, /*nb_divide*/
+ long_mod, /*nb_remainder*/
+ long_divmod, /*nb_divmod*/
+ long_pow, /*nb_power*/
+ (unaryfunc) long_neg, /*nb_negative*/
+ (unaryfunc) long_long, /*tp_positive*/
+ (unaryfunc) long_abs, /*tp_absolute*/
+ (inquiry) long_nonzero, /*tp_nonzero*/
+ (unaryfunc) long_invert, /*nb_invert*/
+ long_lshift, /*nb_lshift*/
+ (binaryfunc) long_rshift, /*nb_rshift*/
+ long_and, /*nb_and*/
+ long_xor, /*nb_xor*/
+ long_or, /*nb_or*/
+ long_coerce, /*nb_coerce*/
+ long_int, /*nb_int*/
+ long_long, /*nb_long*/
+ long_float, /*nb_float*/
+ long_oct, /*nb_oct*/
+ 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 */
+ long_div, /* nb_floor_divide */
+ long_true_divide, /* nb_true_divide */
+ 0, /* nb_inplace_floor_divide */
+ 0, /* nb_inplace_true_divide */
+ long_long, /* nb_index */
+};
+
+PyTypeObject PyLong_Type = {
+ PyObject_HEAD_INIT(&PyType_Type)
+ 0, /* ob_size */
+ "long", /* tp_name */
+ sizeof(PyLongObject) - sizeof(digit), /* tp_basicsize */
+ sizeof(digit), /* tp_itemsize */
+ long_dealloc, /* tp_dealloc */
+ 0, /* tp_print */
+ 0, /* tp_getattr */
+ 0, /* tp_setattr */
+ (cmpfunc)long_compare, /* tp_compare */
+ 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 */
+ long_str, /* tp_str */
+ PyObject_GenericGetAttr, /* tp_getattro */
+ 0, /* tp_setattro */
+ 0, /* tp_as_buffer */
+ Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
+ Py_TPFLAGS_BASETYPE | Py_TPFLAGS_LONG_SUBCLASS, /* 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 */
+ long_getset, /* 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 */
+};