FCL/interim/QEMU: comparison symbian-qemu-0.9.1-12/python-2.6.1/Objects/longobject.c

equal deleted inserted replaced

-:ffa851df0825
+:2fb8b9db1c86
+/* 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 */
+};