cpython/Objects/intobject.c

/* Integer object implementation */

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

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

/* Standard Booleans */

PyIntObject _Py_ZeroStruct = {
	PyObject_HEAD_INIT(&PyInt_Type)
	0
};

PyIntObject _Py_TrueStruct = {
	PyObject_HEAD_INIT(&PyInt_Type)
	1
};

/* 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().
*/

#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;
	/* XXX Int blocks escape the object heap. Use PyObject_MALLOC ??? */
	p = (PyIntObject *) PyMem_MALLOC(sizeof(PyIntBlock));
	if (p == NULL)
		return (PyIntObject *) PyErr_NoMemory();
	((PyIntBlock *)p)->next = block_list;
	block_list = (PyIntBlock *)p;
	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		1
#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]) != NULL) {
		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;
	}
	/* PyObject_New is inlined */
	v = free_list;
	free_list = (PyIntObject *)v->ob_type;
	PyObject_INIT(v, &PyInt_Type);
	v->ob_ival = ival;
#if NSMALLNEGINTS + NSMALLPOSINTS > 0
	if (-NSMALLNEGINTS <= ival && ival < NSMALLPOSINTS) {
		/* save this one for a following allocation */
		Py_INCREF(v);
		small_ints[ival + NSMALLNEGINTS] = v;
	}
#endif
	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);
}

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)) {
		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:
		sprintf(buffer, "invalid literal for int(): %.200s", s);
		PyErr_SetString(PyExc_ValueError, buffer);
		return NULL;
	}
	else if (errno != 0) {
		sprintf(buffer, "int() literal too large: %.200s", s);
		PyErr_SetString(PyExc_ValueError, buffer);
		return NULL;
	}
	if (pend)
		*pend = end;
	return PyInt_FromLong(x);
}

#ifdef Py_USING_UNICODE
PyObject *
PyInt_FromUnicode(Py_UNICODE *s, int length, int base)
{
	char buffer[256];
	
	if (length >= sizeof(buffer)) {
		PyErr_SetString(PyExc_ValueError,
				"int() literal too large to convert");
		return NULL;
	}
	if (PyUnicode_EncodeDecimal(s, length, buffer, NULL))
		return NULL;
	return PyInt_FromString(buffer, NULL, base);
}
#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[20];
	sprintf(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 used to be done using a double, but on 64
bit machines (where both long and double are 64 bit) this fails
because the double doesn't have enough precision.  John Tromp suggests
the following algorithm:

Suppose again we normalize a and b to be nonnegative.
Let ah and al (bh and bl) be the high and low 32 bits of a (b, resp.).
Now we test ah and bh against zero and get essentially 3 possible outcomes.

1) both ah and bh > 0 : then report overflow

2) both ah and bh = 0 : then compute a*b and report overflow if it comes out
                        negative

3) ah > 0 and bh = 0  : compute ah*bl and report overflow if it's >= 2^31
                        compute al*bl and report overflow if it's negative
                        add (ah*bl)<<32 to al*bl and report overflow if
                        it's negative

In case of no overflow the result is then negated if necessary.

The majority of cases will be 2), in which case this method is the same as
what I suggested before. If multiplication is expensive enough, then the
other method is faster on case 3), but also more work to program, so I
guess the above is the preferred solution.

*/

static PyObject *
int_mul(PyObject *v, PyObject *w)
{
	long a, b, ah, bh, x, y;
	int s = 1;

	if (v->ob_type->tp_as_sequence &&
			v->ob_type->tp_as_sequence->sq_repeat) {
		/* sequence * int */
		a = PyInt_AsLong(w);
		return (*v->ob_type->tp_as_sequence->sq_repeat)(v, a);
	}
	else if (w->ob_type->tp_as_sequence &&
			w->ob_type->tp_as_sequence->sq_repeat) {
		/* int * sequence */
		a = PyInt_AsLong(v);
		return (*w->ob_type->tp_as_sequence->sq_repeat)(w, a);
	}

	CONVERT_TO_LONG(v, a);
	CONVERT_TO_LONG(w, b);
	ah = a >> (LONG_BIT/2);
	bh = b >> (LONG_BIT/2);

	/* Quick test for common case: two small positive ints */

	if (ah == 0 && bh == 0) {
		x = a*b;
		if (x < 0)
			goto bad;
		return PyInt_FromLong(x);
	}

	/* Arrange that a >= b >= 0 */

	if (a < 0) {
		a = -a;
		if (a < 0) {
			/* Largest negative */
			if (b == 0 || b == 1) {
				x = a*b;
				goto ok;
			}
			else
				goto bad;
		}
		s = -s;
		ah = a >> (LONG_BIT/2);
	}
	if (b < 0) {
		b = -b;
		if (b < 0) {
			/* Largest negative */
			if (a == 0 || (a == 1 && s == 1)) {
				x = a*b;
				goto ok;
			}
			else
				goto bad;
		}
		s = -s;
		bh = b >> (LONG_BIT/2);
	}

	/* 1) both ah and bh > 0 : then report overflow */

	if (ah != 0 && bh != 0)
		goto bad;

	/* 2) both ah and bh = 0 : then compute a*b and report
				   overflow if it comes out negative */

	if (ah == 0 && bh == 0) {
		x = a*b;
		if (x < 0)
			goto bad;
		return PyInt_FromLong(x*s);
	}

	if (a < b) {
		/* Swap */
		x = a;
		a = b;
		b = x;
		ah = bh;
		/* bh not used beyond this point */
	}

	/* 3) ah > 0 and bh = 0  : compute ah*bl and report overflow if
				   it's >= 2^31
                        compute al*bl and report overflow if it's negative
                        add (ah*bl)<<32 to al*bl and report overflow if
                        it's negative
			(NB b == bl in this case, and we make a = al) */

	y = ah*b;
	if (y >= (1L << (LONG_BIT/2 - 1)))
		goto bad;
	a &= (1L << (LONG_BIT/2)) - 1;
	x = a*b;
	if (x < 0)
		goto bad;
	x += y << (LONG_BIT/2);
	if (x < 0)
		goto bad;
 ok:
	return PyInt_FromLong(x * s);

 bad:
	if (err_ovf("integer multiplication"))
		return NULL;
	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) {
		if (err_ovf("integer negation"))
			return NULL;
		return PyNumber_Negative(PyLong_FromLong(a));
	}
	return PyInt_FromLong(x);
}

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

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)
{
	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) {
		Py_INCREF(v);
		return (PyObject *) v;
	}
	if (b >= LONG_BIT) {
		return PyInt_FromLong(0L);
	}
	a = (long)((unsigned long)a << b);
	return PyInt_FromLong(a);
}

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) {
		Py_INCREF(v);
		return (PyObject *) 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 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)
		strcpy(buf, "0");
	else
		sprintf(buf, "0%lo", x);
	return PyString_FromString(buf);
}

static PyObject *
int_hex(PyIntObject *v)
{
	char buf[100];
	long x = v -> ob_ival;
	sprintf(buf, "0x%lx", x);
	return PyString_FromString(buf);
}

staticforward 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 char 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.";

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*/
	0,			/*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 */
        0,					/* 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 */
	0,					/* 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 */
};

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); /* XXX PyObject_FREE ??? */
			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;
		}
	}
}