cpython/Objects/intobject.c

/* Integer object implementation */

#include "Python.h"
#include <ctype.h>

long
PyInt_GetMax(void)
{
	return LONG_MAX;	/* To initialize sys.maxint */
}

/* Return 1 if exception raised, 0 if caller should retry using longs */
static int
err_ovf(char *msg)
{
	if (PyErr_Warn(PyExc_OverflowWarning, msg) < 0) {
		if (PyErr_ExceptionMatches(PyExc_OverflowWarning))
			PyErr_SetString(PyExc_OverflowError, msg);
		return 1;
	}
	else
		return 0;
}

/* Integers are quite normal objects, to make object handling uniform.
   (Using odd pointers to represent integers would save much space
   but require extra checks for this special case throughout the code.)
   Since a typical Python program spends much of its time allocating
   and deallocating integers, these operations should be very fast.
   Therefore we use a dedicated allocation scheme with a much lower
   overhead (in space and time) than straight malloc(): a simple
   dedicated free list, filled when necessary with memory from malloc().

   block_list is a singly-linked list of all PyIntBlocks ever allocated,
   linked via their next members.  PyIntBlocks are never returned to the
   system before shutdown (PyInt_Fini).

   free_list is a singly-linked list of available PyIntObjects, linked
   via abuse of their ob_type members.
*/

#define BLOCK_SIZE	1000	/* 1K less typical malloc overhead */
#define BHEAD_SIZE	8	/* Enough for a 64-bit pointer */
#define N_INTOBJECTS	((BLOCK_SIZE - BHEAD_SIZE) / sizeof(PyIntObject))

struct _intblock {
	struct _intblock *next;
	PyIntObject objects[N_INTOBJECTS];
};

typedef struct _intblock PyIntBlock;

static PyIntBlock *block_list = NULL;
static PyIntObject *free_list = NULL;

static PyIntObject *
fill_free_list(void)
{
	PyIntObject *p, *q;
	/* Python's object allocator isn't appropriate for large blocks. */
	p = (PyIntObject *) PyMem_MALLOC(sizeof(PyIntBlock));
	if (p == NULL)
		return (PyIntObject *) PyErr_NoMemory();
	((PyIntBlock *)p)->next = block_list;
	block_list = (PyIntBlock *)p;
	/* Link the int objects together, from rear to front, then return
	   the address of the last int object in the block. */
	p = &((PyIntBlock *)p)->objects[0];
	q = p + N_INTOBJECTS;
	while (--q > p)
		q->ob_type = (struct _typeobject *)(q-1);
	q->ob_type = NULL;
	return p + N_INTOBJECTS - 1;
}

#ifndef NSMALLPOSINTS
#define NSMALLPOSINTS		100
#endif
#ifndef NSMALLNEGINTS
#define NSMALLNEGINTS		5
#endif
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
/* References to small integers are saved in this array so that they
   can be shared.
   The integers that are saved are those in the range
   -NSMALLNEGINTS (inclusive) to NSMALLPOSINTS (not inclusive).
*/
static PyIntObject *small_ints[NSMALLNEGINTS + NSMALLPOSINTS];
#endif
#ifdef COUNT_ALLOCS
int quick_int_allocs, quick_neg_int_allocs;
#endif

PyObject *
PyInt_FromLong(long ival)
{
	register PyIntObject *v;
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
	if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) {
		v = small_ints[ival + NSMALLNEGINTS];
		Py_INCREF(v);
#ifdef COUNT_ALLOCS
		if (ival >= 0)
			quick_int_allocs++;
		else
			quick_neg_int_allocs++;
#endif
		return (PyObject *) v;
	}
#endif
	if (free_list == NULL) {
		if ((free_list = fill_free_list()) == NULL)
			return NULL;
	}
	/* Inline PyObject_New */
	v = free_list;
	free_list = (PyIntObject *)v->ob_type;
	PyObject_INIT(v, &PyInt_Type);
	v->ob_ival = ival;
	return (PyObject *) v;
}

static void
int_dealloc(PyIntObject *v)
{
	if (PyInt_CheckExact(v)) {
		v->ob_type = (struct _typeobject *)free_list;
		free_list = v;
	}
	else
		v->ob_type->tp_free((PyObject *)v);
}

static void
int_free(PyIntObject *v)
{
	v->ob_type = (struct _typeobject *)free_list;
	free_list = v;
}

long
PyInt_AsLong(register PyObject *op)
{
	PyNumberMethods *nb;
	PyIntObject *io;
	long val;

	if (op && PyInt_Check(op))
		return PyInt_AS_LONG((PyIntObject*) op);

	if (op == NULL || (nb = op->ob_type->tp_as_number) == NULL ||
	    nb->nb_int == NULL) {
		PyErr_SetString(PyExc_TypeError, "an integer is required");
		return -1;
	}

	io = (PyIntObject*) (*nb->nb_int) (op);
	if (io == NULL)
		return -1;
	if (!PyInt_Check(io)) {
		if (PyLong_Check(io)) {
			/* got a long? => retry int conversion */
			val = PyLong_AsLong((PyObject *)io);
			if (PyErr_Occurred()) {
				Py_DECREF(io);
				return -1;
			}
		}
		else
		{
			PyErr_SetString(PyExc_TypeError,
					"nb_int should return int object");
			return -1;
		}
	}

	val = PyInt_AS_LONG(io);
	Py_DECREF(io);

	return val;
}

PyObject *
PyInt_FromString(char *s, char **pend, int base)
{
	char *end;
	long x;
	char buffer[256]; /* For errors */

	if ((base != 0 && base < 2) || base > 36) {
		PyErr_SetString(PyExc_ValueError, "int() base must be >= 2 and <= 36");
		return NULL;
	}

	while (*s && isspace(Py_CHARMASK(*s)))
		s++;
	errno = 0;
	if (base == 0 && s[0] == '0')
		x = (long) PyOS_strtoul(s, &end, base);
	else
		x = PyOS_strtol(s, &end, base);
	if (end == s || !isalnum(Py_CHARMASK(end[-1])))
		goto bad;
	while (*end && isspace(Py_CHARMASK(*end)))
		end++;
	if (*end != '\0') {
  bad:
		PyOS_snprintf(buffer, sizeof(buffer),
			      "invalid literal for int(): %.200s", s);
		PyErr_SetString(PyExc_ValueError, buffer);
		return NULL;
	}
	else if (errno != 0) {
		if (err_ovf("string/unicode conversion"))
			return NULL;
		return PyLong_FromString(s, pend, base);
	}
	if (pend)
		*pend = end;
	return PyInt_FromLong(x);
}

#ifdef Py_USING_UNICODE
PyObject *
PyInt_FromUnicode(Py_UNICODE *s, int length, int base)
{
	PyObject *result;
	char *buffer = PyMem_MALLOC(length+1);

	if (buffer == NULL)
		return NULL;

	if (PyUnicode_EncodeDecimal(s, length, buffer, NULL)) {
		PyMem_FREE(buffer);
		return NULL;
	}
	result = PyInt_FromString(buffer, NULL, base);
	PyMem_FREE(buffer);
	return result;
}
#endif

/* Methods */

/* Integers are seen as the "smallest" of all numeric types and thus
   don't have any knowledge about conversion of other types to
   integers. */

#define CONVERT_TO_LONG(obj, lng)		\
	if (PyInt_Check(obj)) {			\
		lng = PyInt_AS_LONG(obj);	\
	}					\
	else {					\
		Py_INCREF(Py_NotImplemented);	\
		return Py_NotImplemented;	\
	}

/* ARGSUSED */
static int
int_print(PyIntObject *v, FILE *fp, int flags)
     /* flags -- not used but required by interface */
{
	fprintf(fp, "%ld", v->ob_ival);
	return 0;
}

static PyObject *
int_repr(PyIntObject *v)
{
	char buf[64];
	PyOS_snprintf(buf, sizeof(buf), "%ld", v->ob_ival);
	return PyString_FromString(buf);
}

static int
int_compare(PyIntObject *v, PyIntObject *w)
{
	register long i = v->ob_ival;
	register long j = w->ob_ival;
	return (i < j) ? -1 : (i > j) ? 1 : 0;
}

static long
int_hash(PyIntObject *v)
{
	/* XXX If this is changed, you also need to change the way
	   Python's long, float and complex types are hashed. */
	long x = v -> ob_ival;
	if (x == -1)
		x = -2;
	return x;
}

static PyObject *
int_add(PyIntObject *v, PyIntObject *w)
{
	register long a, b, x;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	x = a + b;
	if ((x^a) >= 0 || (x^b) >= 0)
		return PyInt_FromLong(x);
	if (err_ovf("integer addition"))
		return NULL;
	return PyLong_Type.tp_as_number->nb_add((PyObject *)v, (PyObject *)w);
}

static PyObject *
int_sub(PyIntObject *v, PyIntObject *w)
{
	register long a, b, x;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	x = a - b;
	if ((x^a) >= 0 || (x^~b) >= 0)
		return PyInt_FromLong(x);
	if (err_ovf("integer subtraction"))
		return NULL;
	return PyLong_Type.tp_as_number->nb_subtract((PyObject *)v,
						     (PyObject *)w);
}

/*
Integer overflow checking for * is painful:  Python tried a couple ways, but
they didn't work on all platforms, or failed in endcases (a product of
-sys.maxint-1 has been a particular pain).

Here's another way:

The native long product x*y is either exactly right or *way* off, being
just the last n bits of the true product, where n is the number of bits
in a long (the delivered product is the true product plus i*2**n for
some integer i).

The native double product (double)x * (double)y is subject to three
rounding errors:  on a sizeof(long)==8 box, each cast to double can lose
info, and even on a sizeof(long)==4 box, the multiplication can lose info.
But, unlike the native long product, it's not in *range* trouble:  even
if sizeof(long)==32 (256-bit longs), the product easily fits in the
dynamic range of a double.  So the leading 50 (or so) bits of the double
product are correct.

We check these two ways against each other, and declare victory if they're
approximately the same.  Else, because the native long product is the only
one that can lose catastrophic amounts of information, it's the native long
product that must have overflowed.
*/

static PyObject *
int_mul(PyObject *v, PyObject *w)
{
	long a, b;
	long longprod;			/* a*b in native long arithmetic */
	double doubled_longprod;	/* (double)longprod */
	double doubleprod;		/* (double)a * (double)b */

	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	longprod = a * b;
	doubleprod = (double)a * (double)b;
	doubled_longprod = (double)longprod;

	/* Fast path for normal case:  small multiplicands, and no info
	   is lost in either method. */
	if (doubled_longprod == doubleprod)
		return PyInt_FromLong(longprod);

	/* Somebody somewhere lost info.  Close enough, or way off?  Note
	   that a != 0 and b != 0 (else doubled_longprod == doubleprod == 0).
	   The difference either is or isn't significant compared to the
	   true value (of which doubleprod is a good approximation).
	*/
	{
		const double diff = doubled_longprod - doubleprod;
		const double absdiff = diff >= 0.0 ? diff : -diff;
		const double absprod = doubleprod >= 0.0 ? doubleprod :
							  -doubleprod;
		/* absdiff/absprod <= 1/32 iff
		   32 * absdiff <= absprod -- 5 good bits is "close enough" */
		if (32.0 * absdiff <= absprod)
			return PyInt_FromLong(longprod);
		else if (err_ovf("integer multiplication"))
			return NULL;
		else
			return PyLong_Type.tp_as_number->nb_multiply(v, w);
	}
}

/* Return type of i_divmod */
enum divmod_result {
	DIVMOD_OK,		/* Correct result */
	DIVMOD_OVERFLOW,	/* Overflow, try again using longs */
	DIVMOD_ERROR		/* Exception raised */
};

static enum divmod_result
i_divmod(register long x, register long y,
         long *p_xdivy, long *p_xmody)
{
	long xdivy, xmody;

	if (y == 0) {
		PyErr_SetString(PyExc_ZeroDivisionError,
				"integer division or modulo by zero");
		return DIVMOD_ERROR;
	}
	/* (-sys.maxint-1)/-1 is the only overflow case. */
	if (y == -1 && x < 0 && x == -x) {
		if (err_ovf("integer division"))
			return DIVMOD_ERROR;
		return DIVMOD_OVERFLOW;
	}
	xdivy = x / y;
	xmody = x - xdivy * y;
	/* If the signs of x and y differ, and the remainder is non-0,
	 * C89 doesn't define whether xdivy is now the floor or the
	 * ceiling of the infinitely precise quotient.  We want the floor,
	 * and we have it iff the remainder's sign matches y's.
	 */
	if (xmody && ((y ^ xmody) < 0) /* i.e. and signs differ */) {
		xmody += y;
		--xdivy;
		assert(xmody && ((y ^ xmody) >= 0));
	}
	*p_xdivy = xdivy;
	*p_xmody = xmody;
	return DIVMOD_OK;
}

static PyObject *
int_div(PyIntObject *x, PyIntObject *y)
{
	long xi, yi;
	long d, m;
	CONVERT_TO_LONG(x, xi);
	CONVERT_TO_LONG(y, yi);
	switch (i_divmod(xi, yi, &d, &m)) {
	case DIVMOD_OK:
		return PyInt_FromLong(d);
	case DIVMOD_OVERFLOW:
		return PyLong_Type.tp_as_number->nb_divide((PyObject *)x,
							   (PyObject *)y);
	default:
		return NULL;
	}
}

static PyObject *
int_classic_div(PyIntObject *x, PyIntObject *y)
{
	long xi, yi;
	long d, m;
	CONVERT_TO_LONG(x, xi);
	CONVERT_TO_LONG(y, yi);
	if (Py_DivisionWarningFlag &&
	    PyErr_Warn(PyExc_DeprecationWarning, "classic int division") < 0)
		return NULL;
	switch (i_divmod(xi, yi, &d, &m)) {
	case DIVMOD_OK:
		return PyInt_FromLong(d);
	case DIVMOD_OVERFLOW:
		return PyLong_Type.tp_as_number->nb_divide((PyObject *)x,
							   (PyObject *)y);
	default:
		return NULL;
	}
}

static PyObject *
int_true_divide(PyObject *v, PyObject *w)
{
	/* If they aren't both ints, give someone else a chance.  In
	   particular, this lets int/long get handled by longs, which
	   underflows to 0 gracefully if the long is too big to convert
	   to float. */
	if (PyInt_Check(v) && PyInt_Check(w))
		return PyFloat_Type.tp_as_number->nb_true_divide(v, w);
	Py_INCREF(Py_NotImplemented);
	return Py_NotImplemented;
}

static PyObject *
int_mod(PyIntObject *x, PyIntObject *y)
{
	long xi, yi;
	long d, m;
	CONVERT_TO_LONG(x, xi);
	CONVERT_TO_LONG(y, yi);
	switch (i_divmod(xi, yi, &d, &m)) {
	case DIVMOD_OK:
		return PyInt_FromLong(m);
	case DIVMOD_OVERFLOW:
		return PyLong_Type.tp_as_number->nb_remainder((PyObject *)x,
							      (PyObject *)y);
	default:
		return NULL;
	}
}

static PyObject *
int_divmod(PyIntObject *x, PyIntObject *y)
{
	long xi, yi;
	long d, m;
	CONVERT_TO_LONG(x, xi);
	CONVERT_TO_LONG(y, yi);
	switch (i_divmod(xi, yi, &d, &m)) {
	case DIVMOD_OK:
		return Py_BuildValue("(ll)", d, m);
	case DIVMOD_OVERFLOW:
		return PyLong_Type.tp_as_number->nb_divmod((PyObject *)x,
							   (PyObject *)y);
	default:
		return NULL;
	}
}

static PyObject *
int_pow(PyIntObject *v, PyIntObject *w, PyIntObject *z)
{
	register long iv, iw, iz=0, ix, temp, prev;
	CONVERT_TO_LONG(v, iv);
	CONVERT_TO_LONG(w, iw);
	if (iw < 0) {
		if ((PyObject *)z != Py_None) {
			PyErr_SetString(PyExc_TypeError, "pow() 2nd argument "
			     "cannot be negative when 3rd argument specified");
			return NULL;
		}
		/* Return a float.  This works because we know that
		   this calls float_pow() which converts its
		   arguments to double. */
		return PyFloat_Type.tp_as_number->nb_power(
			(PyObject *)v, (PyObject *)w, (PyObject *)z);
	}
 	if ((PyObject *)z != Py_None) {
		CONVERT_TO_LONG(z, iz);
		if (iz == 0) {
			PyErr_SetString(PyExc_ValueError,
					"pow() 3rd argument cannot be 0");
			return NULL;
		}
	}
	/*
	 * XXX: The original exponentiation code stopped looping
	 * when temp hit zero; this code will continue onwards
	 * unnecessarily, but at least it won't cause any errors.
	 * Hopefully the speed improvement from the fast exponentiation
	 * will compensate for the slight inefficiency.
	 * XXX: Better handling of overflows is desperately needed.
	 */
 	temp = iv;
	ix = 1;
	while (iw > 0) {
	 	prev = ix;	/* Save value for overflow check */
	 	if (iw & 1) {
		 	ix = ix*temp;
			if (temp == 0)
				break; /* Avoid ix / 0 */
			if (ix / temp != prev) {
				if (err_ovf("integer exponentiation"))
					return NULL;
				return PyLong_Type.tp_as_number->nb_power(
					(PyObject *)v,
					(PyObject *)w,
					(PyObject *)z);
			}
		}
	 	iw >>= 1;	/* Shift exponent down by 1 bit */
	        if (iw==0) break;
	 	prev = temp;
	 	temp *= temp;	/* Square the value of temp */
	 	if (prev!=0 && temp/prev!=prev) {
			if (err_ovf("integer exponentiation"))
				return NULL;
			return PyLong_Type.tp_as_number->nb_power(
				(PyObject *)v, (PyObject *)w, (PyObject *)z);
		}
	 	if (iz) {
			/* If we did a multiplication, perform a modulo */
		 	ix = ix % iz;
		 	temp = temp % iz;
		}
	}
	if (iz) {
	 	long div, mod;
		switch (i_divmod(ix, iz, &div, &mod)) {
		case DIVMOD_OK:
			ix = mod;
			break;
		case DIVMOD_OVERFLOW:
			return PyLong_Type.tp_as_number->nb_power(
				(PyObject *)v, (PyObject *)w, (PyObject *)z);
		default:
			return NULL;
		}
	}
	return PyInt_FromLong(ix);
}

static PyObject *
int_neg(PyIntObject *v)
{
	register long a, x;
	a = v->ob_ival;
	x = -a;
	if (a < 0 && x < 0) {
		PyObject *o;
		if (err_ovf("integer negation"))
			return NULL;
		o = PyLong_FromLong(a);
		if (o != NULL) {
			PyObject *result = PyNumber_Negative(o);
			Py_DECREF(o);
			return result;
		}
		return NULL;
	}
	return PyInt_FromLong(x);
}

static PyObject *
int_pos(PyIntObject *v)
{
	if (PyInt_CheckExact(v)) {
		Py_INCREF(v);
		return (PyObject *)v;
	}
	else
		return PyInt_FromLong(v->ob_ival);
}

static PyObject *
int_abs(PyIntObject *v)
{
	if (v->ob_ival >= 0)
		return int_pos(v);
	else
		return int_neg(v);
}

static int
int_nonzero(PyIntObject *v)
{
	return v->ob_ival != 0;
}

static PyObject *
int_invert(PyIntObject *v)
{
	return PyInt_FromLong(~v->ob_ival);
}

static PyObject *
int_lshift(PyIntObject *v, PyIntObject *w)
{
	long a, b, c;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	if (b < 0) {
		PyErr_SetString(PyExc_ValueError, "negative shift count");
		return NULL;
	}
	if (a == 0 || b == 0)
		return int_pos(v);
	if (b >= LONG_BIT) {
		if (PyErr_Warn(PyExc_FutureWarning,
			       "x<<y losing bits or changing sign "
			       "will return a long in Python 2.4 and up") < 0)
			return NULL;
		return PyInt_FromLong(0L);
	}
	c = a << b;
	if (a != Py_ARITHMETIC_RIGHT_SHIFT(long, c, b)) {
		if (PyErr_Warn(PyExc_FutureWarning,
			       "x<<y losing bits or changing sign "
			       "will return a long in Python 2.4 and up") < 0)
			return NULL;
	}
	return PyInt_FromLong(c);
}

static PyObject *
int_rshift(PyIntObject *v, PyIntObject *w)
{
	register long a, b;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	if (b < 0) {
		PyErr_SetString(PyExc_ValueError, "negative shift count");
		return NULL;
	}
	if (a == 0 || b == 0)
		return int_pos(v);
	if (b >= LONG_BIT) {
		if (a < 0)
			a = -1;
		else
			a = 0;
	}
	else {
		a = Py_ARITHMETIC_RIGHT_SHIFT(long, a, b);
	}
	return PyInt_FromLong(a);
}

static PyObject *
int_and(PyIntObject *v, PyIntObject *w)
{
	register long a, b;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	return PyInt_FromLong(a & b);
}

static PyObject *
int_xor(PyIntObject *v, PyIntObject *w)
{
	register long a, b;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	return PyInt_FromLong(a ^ b);
}

static PyObject *
int_or(PyIntObject *v, PyIntObject *w)
{
	register long a, b;
	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	return PyInt_FromLong(a | b);
}

static int
int_coerce(PyObject **pv, PyObject **pw)
{
	if (PyInt_Check(*pw)) {
		Py_INCREF(*pv);
		Py_INCREF(*pw);
		return 0;
	}
	return 1; /* Can't do it */
}

static PyObject *
int_int(PyIntObject *v)
{
	Py_INCREF(v);
	return (PyObject *)v;
}

static PyObject *
int_long(PyIntObject *v)
{
	return PyLong_FromLong((v -> ob_ival));
}

static PyObject *
int_float(PyIntObject *v)
{
	return PyFloat_FromDouble((double)(v -> ob_ival));
}

static PyObject *
int_oct(PyIntObject *v)
{
	char buf[100];
	long x = v -> ob_ival;
	if (x < 0) {
		if (PyErr_Warn(PyExc_FutureWarning,
			       "hex()/oct() of negative int will return "
			       "a signed string in Python 2.4 and up") < 0)
			return NULL;
	}
	if (x == 0)
		strcpy(buf, "0");
	else
		PyOS_snprintf(buf, sizeof(buf), "0%lo", x);
	return PyString_FromString(buf);
}

static PyObject *
int_hex(PyIntObject *v)
{
	char buf[100];
	long x = v -> ob_ival;
	if (x < 0) {
		if (PyErr_Warn(PyExc_FutureWarning,
			       "hex()/oct() of negative int will return "
			       "a signed string in Python 2.4 and up") < 0)
			return NULL;
	}
	PyOS_snprintf(buf, sizeof(buf), "0x%lx", x);
	return PyString_FromString(buf);
}

static PyObject *
int_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds);

static PyObject *
int_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
	PyObject *x = NULL;
	int base = -909;
	static char *kwlist[] = {"x", "base", 0};

	if (type != &PyInt_Type)
		return int_subtype_new(type, args, kwds); /* Wimp out */
	if (!PyArg_ParseTupleAndKeywords(args, kwds, "|Oi:int", kwlist,
					 &x, &base))
		return NULL;
	if (x == NULL)
		return PyInt_FromLong(0L);
	if (base == -909)
		return PyNumber_Int(x);
	if (PyString_Check(x))
		return PyInt_FromString(PyString_AS_STRING(x), NULL, base);
#ifdef Py_USING_UNICODE
	if (PyUnicode_Check(x))
		return PyInt_FromUnicode(PyUnicode_AS_UNICODE(x),
					 PyUnicode_GET_SIZE(x),
					 base);
#endif
	PyErr_SetString(PyExc_TypeError,
			"int() can't convert non-string with explicit base");
	return NULL;
}

/* Wimpy, slow approach to tp_new calls for subtypes of int:
   first create a regular int from whatever arguments we got,
   then allocate a subtype instance and initialize its ob_ival
   from the regular int.  The regular int is then thrown away.
*/
static PyObject *
int_subtype_new(PyTypeObject *type, PyObject *args, PyObject *kwds)
{
	PyObject *tmp, *new;

	assert(PyType_IsSubtype(type, &PyInt_Type));
	tmp = int_new(&PyInt_Type, args, kwds);
	if (tmp == NULL)
		return NULL;
	assert(PyInt_Check(tmp));
	new = type->tp_alloc(type, 0);
	if (new == NULL)
		return NULL;
	((PyIntObject *)new)->ob_ival = ((PyIntObject *)tmp)->ob_ival;
	Py_DECREF(tmp);
	return new;
}

static PyObject *
int_getnewargs(PyIntObject *v)
{
	return Py_BuildValue("(l)", v->ob_ival);
}

static PyMethodDef int_methods[] = {
	{"__getnewargs__",	(PyCFunction)int_getnewargs,	METH_NOARGS},
	{NULL,		NULL}		/* sentinel */
};

PyDoc_STRVAR(int_doc,
"int(x[, base]) -> integer\n\
\n\
Convert a string or number to an integer, if possible.  A floating point\n\
argument will be truncated towards zero (this does not include a string\n\
representation of a floating point number!)  When converting a string, use\n\
the optional base.  It is an error to supply a base when converting a\n\
non-string. If the argument is outside the integer range a long object\n\
will be returned instead.");

static PyNumberMethods int_as_number = {
	(binaryfunc)int_add,	/*nb_add*/
	(binaryfunc)int_sub,	/*nb_subtract*/
	(binaryfunc)int_mul,	/*nb_multiply*/
	(binaryfunc)int_classic_div, /*nb_divide*/
	(binaryfunc)int_mod,	/*nb_remainder*/
	(binaryfunc)int_divmod,	/*nb_divmod*/
	(ternaryfunc)int_pow,	/*nb_power*/
	(unaryfunc)int_neg,	/*nb_negative*/
	(unaryfunc)int_pos,	/*nb_positive*/
	(unaryfunc)int_abs,	/*nb_absolute*/
	(inquiry)int_nonzero,	/*nb_nonzero*/
	(unaryfunc)int_invert,	/*nb_invert*/
	(binaryfunc)int_lshift,	/*nb_lshift*/
	(binaryfunc)int_rshift,	/*nb_rshift*/
	(binaryfunc)int_and,	/*nb_and*/
	(binaryfunc)int_xor,	/*nb_xor*/
	(binaryfunc)int_or,	/*nb_or*/
	int_coerce,		/*nb_coerce*/
	(unaryfunc)int_int,	/*nb_int*/
	(unaryfunc)int_long,	/*nb_long*/
	(unaryfunc)int_float,	/*nb_float*/
	(unaryfunc)int_oct,	/*nb_oct*/
	(unaryfunc)int_hex, 	/*nb_hex*/
	0,			/*nb_inplace_add*/
	0,			/*nb_inplace_subtract*/
	0,			/*nb_inplace_multiply*/
	0,			/*nb_inplace_divide*/
	0,			/*nb_inplace_remainder*/
	0,			/*nb_inplace_power*/
	0,			/*nb_inplace_lshift*/
	0,			/*nb_inplace_rshift*/
	0,			/*nb_inplace_and*/
	0,			/*nb_inplace_xor*/
	0,			/*nb_inplace_or*/
	(binaryfunc)int_div,	/* nb_floor_divide */
	int_true_divide,	/* nb_true_divide */
	0,			/* nb_inplace_floor_divide */
	0,			/* nb_inplace_true_divide */
};

PyTypeObject PyInt_Type = {
	PyObject_HEAD_INIT(&PyType_Type)
	0,
	"int",
	sizeof(PyIntObject),
	0,
	(destructor)int_dealloc,		/* tp_dealloc */
	(printfunc)int_print,			/* tp_print */
	0,					/* tp_getattr */
	0,					/* tp_setattr */
	(cmpfunc)int_compare,			/* tp_compare */
	(reprfunc)int_repr,			/* tp_repr */
	&int_as_number,				/* tp_as_number */
	0,					/* tp_as_sequence */
	0,					/* tp_as_mapping */
	(hashfunc)int_hash,			/* tp_hash */
        0,					/* tp_call */
        (reprfunc)int_repr,			/* tp_str */
	PyObject_GenericGetAttr,		/* tp_getattro */
	0,					/* tp_setattro */
	0,					/* tp_as_buffer */
	Py_TPFLAGS_DEFAULT | Py_TPFLAGS_CHECKTYPES |
		Py_TPFLAGS_BASETYPE,		/* tp_flags */
	int_doc,				/* tp_doc */
	0,					/* tp_traverse */
	0,					/* tp_clear */
	0,					/* tp_richcompare */
	0,					/* tp_weaklistoffset */
	0,					/* tp_iter */
	0,					/* tp_iternext */
	int_methods,				/* tp_methods */
	0,					/* tp_members */
	0,					/* tp_getset */
	0,					/* tp_base */
	0,					/* tp_dict */
	0,					/* tp_descr_get */
	0,					/* tp_descr_set */
	0,					/* tp_dictoffset */
	0,					/* tp_init */
	0,					/* tp_alloc */
	int_new,				/* tp_new */
	(freefunc)int_free,           		/* tp_free */
};

int
_PyInt_Init(void)
{
	PyIntObject *v;
	int ival;
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
	for (ival = -NSMALLNEGINTS; ival < NSMALLPOSINTS; ival++) {
		if ((free_list = fill_free_list()) == NULL)
			return 0;
		/* PyObject_New is inlined */
		v = free_list;
		free_list = (PyIntObject *)v->ob_type;
		PyObject_INIT(v, &PyInt_Type);
		v->ob_ival = ival;
		small_ints[ival + NSMALLNEGINTS] = v;
	}
#endif
	return 1;
}

void
PyInt_Fini(void)
{
	PyIntObject *p;
	PyIntBlock *list, *next;
	int i;
	int bc, bf;	/* block count, number of freed blocks */
	int irem, isum;	/* remaining unfreed ints per block, total */

#if NSMALLNEGINTS + NSMALLPOSINTS > 0
        PyIntObject **q;

        i = NSMALLNEGINTS + NSMALLPOSINTS;
        q = small_ints;
        while (--i >= 0) {
                Py_XDECREF(*q);
                *q++ = NULL;
        }
#endif
	bc = 0;
	bf = 0;
	isum = 0;
	list = block_list;
	block_list = NULL;
	free_list = NULL;
	while (list != NULL) {
		bc++;
		irem = 0;
		for (i = 0, p = &list->objects[0];
		     i < N_INTOBJECTS;
		     i++, p++) {
			if (PyInt_CheckExact(p) && p->ob_refcnt != 0)
				irem++;
		}
		next = list->next;
		if (irem) {
			list->next = block_list;
			block_list = list;
			for (i = 0, p = &list->objects[0];
			     i < N_INTOBJECTS;
			     i++, p++) {
				if (!PyInt_CheckExact(p) ||
				    p->ob_refcnt == 0) {
					p->ob_type = (struct _typeobject *)
						free_list;
					free_list = p;
				}
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
				else if (-NSMALLNEGINTS <= p->ob_ival &&
					 p->ob_ival < NSMALLPOSINTS &&
					 small_ints[p->ob_ival +
						    NSMALLNEGINTS] == NULL) {
					Py_INCREF(p);
					small_ints[p->ob_ival +
						   NSMALLNEGINTS] = p;
				}
#endif
			}
		}
		else {
			PyMem_FREE(list);
			bf++;
		}
		isum += irem;
		list = next;
	}
	if (!Py_VerboseFlag)
		return;
	fprintf(stderr, "# cleanup ints");
	if (!isum) {
		fprintf(stderr, "\n");
	}
	else {
		fprintf(stderr,
			": %d unfreed int%s in %d out of %d block%s\n",
			isum, isum == 1 ? "" : "s",
			bc - bf, bc, bc == 1 ? "" : "s");
	}
	if (Py_VerboseFlag > 1) {
		list = block_list;
		while (list != NULL) {
			for (i = 0, p = &list->objects[0];
			     i < N_INTOBJECTS;
			     i++, p++) {
				if (PyInt_CheckExact(p) && p->ob_refcnt != 0)
					fprintf(stderr,
				"#   <int at %p, refcnt=%d, val=%ld>\n",
						p, p->ob_refcnt, p->ob_ival);
			}
			list = list->next;
		}
	}
}