cpython/Modules/mpzmodule.c

/***********************************************************
Copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam,
The Netherlands.

                        All Rights Reserved

Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice appear in all copies and that
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permission.

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/* MPZ module */

/* This module provides an interface to an alternate Multi-Precision
   library, GNU MP in this case */

/* XXX note: everywhere where mpz_size is called,
   sizeof (limb) == sizeof (long)  has been assumed. */
   

/* MPZ objects */

#include "Python.h"

#include <assert.h>
#include <sys/types.h>		/* For size_t */

/*
**	These are the cpp-flags used in this file...
**
**
** MPZ_MDIV_BUG		works around the mpz_m{div,mod,...} routines.
** 			This bug has been fixed in a later release of
** 			GMP.
** 
** MPZ_GET_STR_BUG	mpz_get_str corrupts memory, seems to be fixed
** 			in a later release
** 
** MPZ_DEBUG		generates a bunch of diagnostic messages
** 
** MPZ_SPARE_MALLOC	if set, results in extra code that tries to
** 			minimize the creation of extra objects.
** 
** MPZ_TEST_DIV		extra diagnostic output on stderr, when division
** 			routines are involved
** 
** MPZ_LIB_DOES_CHECKING	if set, assumes that mpz library doesn't call
** 			alloca with arg < 0 (when casted to a signed
** 			integral type).
** 
** MPZ_CONVERSIONS_AS_METHODS	if set, presents the conversions as
** 			methods. e.g., `mpz(5).long() == 5L'
** 			Later, Guido provided an interface to the
** 			standard functions. So this flag has no been
** 			cleared, and `long(mpz(5)) == 5L'
** 
** MP_TEST_ALLOC	If set, you would discover why MPZ_GET_STR_BUG
**			is needed
** 
** MAKEDUMMYINT		Must be set if dynamic linking will be used
*/


/*
** IMHO, mpz_m{div,mod,divmod}() do the wrong things when the denominator < 0
** This has been fixed with gmp release 2.0
*/
/*#define MPZ_MDIV_BUG fixed the (for me) nexessary parts in libgmp.a */
/*
** IMO, mpz_get_str() assumes a bit too large target space, if he doesn't
** allocate it himself
*/

#include "gmp.h"

#if __GNU_MP__ + 0 == 2
#define GMP2
#define BITS_PER_MP_LIMB mp_bits_per_limb
#else
#define MPZ_GET_STR_BUG
#include "gmp-mparam.h"
#endif

typedef struct {
	PyObject_HEAD
        MP_INT	mpz;		/* the actual number */
} mpzobject;

staticforward PyTypeObject MPZtype;

#define is_mpzobject(v)		((v)->ob_type == &MPZtype)

static const char initialiser_name[] = "mpz";

/* #define MPZ_DEBUG */

static mpzobject *
newmpzobject()
{
	mpzobject *mpzp;


#ifdef MPZ_DEBUG
	fputs( "mpz_object() called...\n", stderr );
#endif /* def MPZ_DEBUG */
	mpzp = PyObject_New(mpzobject, &MPZtype);
	if (mpzp == NULL)
		return NULL;

	mpz_init(&mpzp->mpz);	/* actual initialisation */
	return mpzp;
} /* newmpzobject() */

#ifdef MPZ_GET_STR_BUG
#include "longlong.h"
#endif /* def MPZ_GET_STR_BUG */

static PyObject *
mpz_format(objp, base, withname)
	PyObject *objp;
	int base;
	unsigned char withname;
{
	mpzobject *mpzp = (mpzobject *)objp;
	PyStringObject *strobjp;
	size_t i;
	int cmpres;
	int taglong;
	char *cp;
	char prefix[5], *tcp;


	tcp = &prefix[0];

	if (mpzp == NULL || !is_mpzobject(mpzp)) {
		PyErr_BadInternalCall();
		return NULL;
	}

	assert(base >= 2 && base <= 36);

	if (withname)
		i = strlen(initialiser_name) + 2; /* e.g. 'mpz(' + ')' */
	else
		i = 0;

	if ((cmpres = mpz_cmp_si(&mpzp->mpz, 0L)) == 0)
		base = 10;	/* '0' in every base, right */
	else if (cmpres < 0) {
		*tcp++ = '-';
		i += 1;		/* space to hold '-' */
	}

#ifdef MPZ_DEBUG
	fprintf(stderr, "mpz_format: mpz_sizeinbase %d\n",
		(int)mpz_sizeinbase(&mpzp->mpz, base));
#endif /* def MPZ_DEBUG */
#ifdef MPZ_GET_STR_BUG
#ifdef GMP2
	i += ((size_t) abs(mpzp->mpz._mp_size) * BITS_PER_MP_LIMB
	      * __mp_bases[base].chars_per_bit_exactly) + 1;
#else
	i += ((size_t) abs(mpzp->mpz.size) * BITS_PER_MP_LIMB
	      * __mp_bases[base].chars_per_bit_exactly) + 1;
#endif
#else /* def MPZ_GET_STR_BUG */
	i += (int)mpz_sizeinbase(&mpzp->mpz, base);
#endif /* def MPZ_GET_STR_BUG else */

	if (base == 16) {
		*tcp++ = '0';
		*tcp++ = 'x';
		i += 2;		/* space to hold '0x' */
	}
	else if (base == 8) {
		*tcp++ = '0';
		i += 1;		/* space to hold the extra '0' */
	}
	else if (base > 10) {
		*tcp++ = '0' + base / 10;
		*tcp++ = '0' + base % 10;
		*tcp++ = '#';
		i += 3;		/* space to hold e.g. '12#' */
	}
	else if (base < 10) {
		*tcp++ = '0' + base;
		*tcp++ = '#';
		i += 2;		/* space to hold e.g. '6#' */
	}

	/*
	** the following code looks if we need a 'L' attached to the number
	** it will also attach an 'L' to the value -0x80000000
	*/
	taglong = 0;
	if (mpz_size(&mpzp->mpz) > 1
	    || (long)mpz_get_ui(&mpzp->mpz) < 0L) {
		taglong = 1;
		i += 1;		/* space to hold 'L' */
	}

#ifdef MPZ_DEBUG
	fprintf(stderr, "mpz_format: requesting string size %d\n", i);
#endif /* def MPZ_DEBUG */	
	if ((strobjp =
	     (PyStringObject *)PyString_FromStringAndSize((char *)0, i))
	    == NULL)
		return NULL;

	/* get the beginning of the string memory and start copying things */
	cp = PyString_AS_STRING(strobjp);
	if (withname) {
		strcpy(cp, initialiser_name);
		cp += strlen(initialiser_name);
		*cp++ = '('; /*')'*/
	}

	/* copy the already prepared prefix; e.g. sign and base indicator */
	*tcp = '\0';
	strcpy(cp, prefix);
	cp += tcp - prefix;

	/* since' we have the sign already, let the lib think it's a positive
	   number */
	if (cmpres < 0)
		mpz_neg(&mpzp->mpz,&mpzp->mpz);	/* hack Hack HAck HACk HACK */
	(void)mpz_get_str(cp, base, &mpzp->mpz);
	if (cmpres < 0)
		mpz_neg(&mpzp->mpz,&mpzp->mpz);	/* hack Hack HAck HACk HACK */
#ifdef MPZ_DEBUG
	fprintf(stderr, "mpz_format: base (ultim) %d, mpz_get_str: %s\n",
		base, cp);
#endif /* def MPZ_DEBUG */
	cp += strlen(cp);

	if (taglong)
		*cp++ = 'L';
	if (withname)
		*cp++ = /*'('*/ ')';

	*cp = '\0';

#ifdef MPZ_DEBUG
	fprintf(stderr,
		"mpz_format: cp (str end) %p, begin %p, diff %d, i %d\n",
		cp, PyString_AS_STRING(strobjp),
		cp - PyString_AS_STRING(strobjp), i);
#endif /* def MPZ_DEBUG */	
	assert(cp - PyString_AS_STRING(strobjp) <= i);

	if (cp - PyString_AS_STRING(strobjp) != i) {
		strobjp->ob_size -= i - (cp - PyString_AS_STRING(strobjp));
	}

	return (PyObject *)strobjp;
} /* mpz_format() */

/* MPZ methods */

static void
mpz_dealloc(mpzp)
	mpzobject *mpzp;
{
#ifdef MPZ_DEBUG
	fputs( "mpz_dealloc() called...\n", stderr );
#endif /* def MPZ_DEBUG */
	mpz_clear(&mpzp->mpz);
	PyObject_Del(mpzp);
} /* mpz_dealloc() */


/* pointers to frequently used values 0, 1 and -1 */
static mpzobject *mpz_value_zero, *mpz_value_one, *mpz_value_mone;

static int
mpz_compare(a, b)
	mpzobject *a, *b;
{
	int cmpres;


	/* guido sez it's better to return -1, 0 or 1 */
	return (cmpres = mpz_cmp( &a->mpz, &b->mpz )) == 0 ? 0
		: cmpres > 0 ? 1 : -1;
} /* mpz_compare() */

static PyObject *
mpz_addition(a, b)
	mpzobject *a;
	mpzobject *b;
{
	mpzobject *z;

	
#ifdef MPZ_SPARE_MALLOC
	if (mpz_cmp_ui(&a->mpz, (unsigned long int)0) == 0) {
		Py_INCREF(b);
		return (PyObject *)b;
	}

	if (mpz_cmp_ui(&b->mpz, (unsigned long int)0) == 0) {
		Py_INCREF(a);
		return (PyObject *)a;
	}
#endif /* def MPZ_SPARE_MALLOC */

	if ((z = newmpzobject()) == NULL)
		return NULL;
	
	mpz_add(&z->mpz, &a->mpz, &b->mpz);
	return (PyObject *)z;
} /* mpz_addition() */

static PyObject *
mpz_substract(a, b)
	mpzobject *a;
	mpzobject *b;
{
	mpzobject *z;

	
#ifdef MPZ_SPARE_MALLOC
	if (mpz_cmp_ui(&b->mpz, (unsigned long int)0) == 0) {
		Py_INCREF(a);
		return (PyObject *)a;
	}
#endif /* MPZ_SPARE_MALLOC */	

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_sub(&z->mpz, &a->mpz, &b->mpz);
	return (PyObject *)z;
} /* mpz_substract() */

static PyObject *
mpz_multiply(a, b)
	mpzobject *a;
	mpzobject *b;
{
#ifdef MPZ_SPARE_MALLOC
	int cmpres;
#endif /* def MPZ_SPARE_MALLOC */
	mpzobject *z;


#ifdef MPZ_SPARE_MALLOC
	if ((cmpres = mpz_cmp_ui(&a->mpz, (unsigned long int)0)) == 0) {
		Py_INCREF(mpz_value_zero);
		return (PyObject *)mpz_value_zero;
	}
	if (cmpres > 0 && mpz_cmp_ui(&a->mpz, (unsigned long int)1) == 0) {
		Py_INCREF(b);
		return (PyObject *)b;
	}

	if ((cmpres = mpz_cmp_ui(&b->mpz, (unsigned long_int)0)) == 0) {
		Py_INCREF(mpz_value_zero);
		return (PyObject *)mpz_value_zero;
	}
	if (cmpres > 0 && mpz_cmp_ui(&b->mpz, (unsigned long int)1) == 0) {
		Py_INCREF(a);
		return (PyObject *)a;
	}
#endif /* MPZ_SPARE_MALLOC */

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_mul( &z->mpz, &a->mpz, &b->mpz );
	return (PyObject *)z;
	
} /* mpz_multiply() */

static PyObject *
mpz_divide(a, b)
	mpzobject *a;
	mpzobject *b;
{
#ifdef MPZ_SPARE_MALLOC
	int cmpres;
#endif /* def MPZ_SPARE_MALLOC */
	mpzobject *z;


	if ((
#ifdef MPZ_SPARE_MALLOC
	     cmpres =
#endif /* def MPZ_SPARE_MALLOC */
	     mpz_cmp_ui(&b->mpz, (unsigned long int)0)) == 0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "mpz./ by zero");
		return NULL;
	}
#ifdef MPZ_SPARE_MALLOC
	if (cmpres > 0 && mpz_cmp_ui(&b->mpz(unsigned long int)1) == 0) {
		Py_INCREF(a);
		return (PyObject *)a;
	}
#endif /* def MPZ_SPARE_MALLOC */

	if ((z = newmpzobject()) == NULL)
		return NULL;

#ifdef MPZ_TEST_DIV
	fputs("mpz_divide:  div result", stderr);
	mpz_div(&z->mpz, &a->mpz, &b->mpz);
	mpz_out_str(stderr, 10, &z->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */
#ifdef MPZ_MDIV_BUG
	if ((mpz_cmp_ui(&a->mpz, (unsigned long int)0) < 0)
	    != (mpz_cmp_ui(&b->mpz, (unsigned long int)0) < 0)) {
		/*
		** numerator has other sign than denominator: we have
		** to look at the remainder for a correction, since mpz_mdiv
		** also calls mpz_divmod, I can as well do it myself
		*/
		MP_INT tmpmpz;


		mpz_init(&tmpmpz);
		mpz_divmod(&z->mpz, &tmpmpz, &a->mpz, &b->mpz);

		if (mpz_cmp_ui(&tmpmpz, (unsigned long int)0) != 0)
			mpz_sub_ui(&z->mpz, &z->mpz, (unsigned long int)1);

		mpz_clear(&tmpmpz);
	}
	else
		mpz_div(&z->mpz, &a->mpz, &b->mpz);
		/* the ``naive'' implementation does it right for operands
		   having the same sign */

#else /* def MPZ_MDIV_BUG */
	mpz_mdiv(&z->mpz, &a->mpz, &b->mpz);
#endif /* def MPZ_MDIV_BUG else */
#ifdef MPZ_TEST_DIV
	fputs("mpz_divide: mdiv result", stderr);
	mpz_out_str(stderr, 10, &z->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */
	return (PyObject *)z;
	
} /* mpz_divide() */

static PyObject *
mpz_remainder(a, b)
	mpzobject *a;
	mpzobject *b;
{
#ifdef MPZ_SPARE_MALLOC
	int cmpres;
#endif /* def MPZ_SPARE_MALLOC */	
	mpzobject *z;

	
	if ((
#ifdef MPZ_SPARE_MALLOC	     
	     cmpres =
#endif /* def MPZ_SPARE_MALLOC */	
	     mpz_cmp_ui(&b->mpz, (unsigned long int)0)) == 0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "mpz.% by zero");
		return NULL;
	}
#ifdef MPZ_SPARE_MALLOC
	if (cmpres > 0) {
		if ((cmpres = mpz_cmp_ui(&b->mpz, (unsigned long int)2)) == 0)
		{
			Py_INCREF(mpz_value_one);
			return (PyObject *)mpz_value_one;
		}
		if (cmpres < 0) {
			/* b must be 1 now */
			Py_INCREF(mpz_value_zero);
			return (PyObject *)mpz_value_zero;
		}
	}
#endif /* def MPZ_SPARE_MALLOC */	

	if ((z = newmpzobject()) == NULL)
		return NULL;

#ifdef MPZ_TEST_DIV
	fputs("mpz_remain:  mod result", stderr);
	mpz_mod(&z->mpz, &a->mpz, &b->mpz);
	mpz_out_str(stderr, 10, &z->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */
#ifdef MPZ_MDIV_BUG

	/* the ``naive'' implementation does it right for operands
	   having the same sign */
	mpz_mod(&z->mpz, &a->mpz, &b->mpz);

	/* assumption: z, a and b all point to different locations */
	if ((mpz_cmp_ui(&a->mpz, (unsigned long int)0) < 0)
	    != (mpz_cmp_ui(&b->mpz, (unsigned long int)0) < 0)
	    && mpz_cmp_ui(&z->mpz, (unsigned long int)0) != 0)
		mpz_add(&z->mpz, &z->mpz, &b->mpz);
		/*
		** numerator has other sign than denominator: we have
		** to look at the remainder for a correction, since mpz_mdiv
		** also calls mpz_divmod, I can as well do it myself
		*/
#else /* def MPZ_MDIV_BUG */
	mpz_mmod(&z->mpz, &a->mpz, &b->mpz);
#endif /* def MPZ_MDIV_BUG else */
#ifdef MPZ_TEST_DIV
	fputs("mpz_remain: mmod result", stderr);
	mpz_out_str(stderr, 10, &z->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */
	return (PyObject *)z;
	
} /* mpz_remainder() */

static PyObject *
mpz_div_and_mod(a, b)
	mpzobject *a;
	mpzobject *b;
{
	PyObject *z = NULL;
	mpzobject *x = NULL, *y = NULL;


	if (mpz_cmp_ui(&b->mpz, (unsigned long int)0) == 0) {
		PyErr_SetString(PyExc_ZeroDivisionError, "mpz.divmod by zero");
		return NULL;
	}

	if ((z = PyTuple_New(2)) == NULL
	    || (x = newmpzobject()) == NULL
	    || (y = newmpzobject()) == NULL) {
		Py_XDECREF(z);
		Py_XDECREF(x);
		Py_XDECREF(y);
		return NULL;
	}

#ifdef MPZ_TEST_DIV
	fputs("mpz_divmod:  dm  result", stderr);
	mpz_divmod(&x->mpz, &y->mpz, &a->mpz, &b->mpz);
	mpz_out_str(stderr, 10, &x->mpz);
	putc('\n', stderr);
	mpz_out_str(stderr, 10, &y->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */
#ifdef MPZ_MDIV_BUG
	mpz_divmod(&x->mpz, &y->mpz, &a->mpz, &b->mpz);
	if ((mpz_cmp_ui(&a->mpz, (unsigned long int)0) < 0)
	    != (mpz_cmp_ui(&b->mpz, (unsigned long int)0) < 0)
	    && mpz_cmp_ui(&y->mpz, (unsigned long int)0) != 0) {
		/*
		** numerator has other sign than denominator: we have
		** to look at the remainder for a correction.
		*/
		mpz_add(&y->mpz, &y->mpz, &b->mpz);
		mpz_sub_ui(&x->mpz, &x->mpz, (unsigned long int)1);
	}
#else /* def MPZ_MDIV_BUG */
	mpz_mdivmod( &x->mpz, &y->mpz, &a->mpz, &b->mpz );
#endif /* def MPZ_MDIV_BUG else */
#ifdef MPZ_TEST_DIV
	fputs("mpz_divmod: mdm  result", stderr);
	mpz_out_str(stderr, 10, &x->mpz);
	putc('\n', stderr);
	mpz_out_str(stderr, 10, &y->mpz);
	putc('\n', stderr);
#endif /* def MPZ_TEST_DIV */

	(void)PyTuple_SetItem(z, 0, (PyObject *)x);
	(void)PyTuple_SetItem(z, 1, (PyObject *)y);
	
	return z;
} /* mpz_div_and_mod() */

static PyObject *
mpz_power(a, b, m)
	mpzobject *a;
	mpzobject *b;
        mpzobject *m;
{
	mpzobject *z;
	int cmpres;

 	if ((PyObject *)m != Py_None) {
		mpzobject *z2;
		Py_INCREF(Py_None);
		z=(mpzobject *)mpz_power(a, b, (mpzobject *)Py_None);
		Py_DECREF(Py_None);
		if (z==NULL) return((PyObject *)z);
		z2=(mpzobject *)mpz_remainder(z, m);
		Py_DECREF(z);
		return((PyObject *)z2);
	}	    

	if ((cmpres = mpz_cmp_ui(&b->mpz, (unsigned long int)0)) == 0) {
		/* the gnu-mp lib sets pow(0,0) to 0, we to 1 */

		Py_INCREF(mpz_value_one);
		return (PyObject *)mpz_value_one;
	}
		
	if (cmpres < 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.pow to negative exponent");
		return NULL;
	}

	if ((cmpres = mpz_cmp_ui(&a->mpz, (unsigned long int)0)) == 0) {
		/* the base is 0 */

		Py_INCREF(mpz_value_zero);
		return (PyObject *)mpz_value_zero;
	}
	else if (cmpres > 0
		 && mpz_cmp_ui(&a->mpz, (unsigned long int)1) == 0) {
		/* the base is 1 */

		Py_INCREF(mpz_value_one);
		return (PyObject *)mpz_value_one;
	}
	else if (cmpres < 0
		 && mpz_cmp_si(&a->mpz, (long int)-1) == 0) {

		MP_INT tmpmpz;
		/* the base is -1: pow(-1, any) == 1,-1 for even,uneven b */
		/* XXX this code needs to be optimized: what's better?
		   mpz_mmod_ui or mpz_mod_2exp, I choose for the latter
		   for *un*obvious reasons */

		/* is the exponent even? */
		mpz_init(&tmpmpz);

		/* look to the remainder after a division by (1 << 1) */
		mpz_mod_2exp(&tmpmpz, &b->mpz, (unsigned long int)1);

		if (mpz_cmp_ui(&tmpmpz, (unsigned int)0) == 0) {
			mpz_clear(&tmpmpz);
			Py_INCREF(mpz_value_one);
			return (PyObject *)mpz_value_one;
		}
		mpz_clear(&tmpmpz);
		Py_INCREF(mpz_value_mone);
		return (PyObject *)mpz_value_mone;
	}

#ifdef MPZ_LIB_DOES_CHECKING
	/* check if it's doable: sizeof(exp) > sizeof(long) &&
	   abs(base) > 1 ?? --> No Way */
	if (mpz_size(&b->mpz) > 1)
		return (PyObject *)PyErr_NoMemory();
#else /* def MPZ_LIB_DOES_CHECKING */
	/* wet finger method */
	if (mpz_cmp_ui(&b->mpz, (unsigned long int)0x10000) >= 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.pow outrageous exponent");
		return NULL;
	}
#endif /* def MPZ_LIB_DOES_CHECKING else */

	if ((z = newmpzobject()) == NULL)
		return NULL;
	
	mpz_pow_ui(&z->mpz, &a->mpz, mpz_get_ui(&b->mpz));
	
	return (PyObject *)z;
} /* mpz_power() */


static PyObject *
mpz_negative(v)
	mpzobject *v;
{
	mpzobject *z;

	
#ifdef MPZ_SPARE_MALLOC
	if (mpz_cmp_ui(&v->mpz, (unsigned long int)0) == 0) {
		/* -0 == 0 */
		Py_INCREF(v);
		return (PyObject *)v;
	}
#endif /* def MPZ_SPARE_MALLOC */

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_neg(&z->mpz, &v->mpz);
	return (PyObject *)z;
} /* mpz_negative() */


static PyObject *
mpz_positive(v)
	mpzobject *v;
{
	Py_INCREF(v);
	return (PyObject *)v;
} /* mpz_positive() */


static PyObject *
mpz_absolute(v)
	mpzobject *v;
{
	mpzobject *z;

	
	if (mpz_cmp_ui(&v->mpz, (unsigned long int)0) >= 0) {
		Py_INCREF(v);
		return (PyObject *)v;
	}

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_neg(&z->mpz, &v->mpz);
	return (PyObject *)z;
} /* mpz_absolute() */

static int
mpz_nonzero(v)
	mpzobject *v;
{
	return mpz_cmp_ui(&v->mpz, (unsigned long int)0) != 0;
} /* mpz_nonzero() */
		
static PyObject *
py_mpz_invert(v)
	mpzobject *v;
{
	mpzobject *z;


	/* I think mpz_com does exactly what needed */
	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_com(&z->mpz, &v->mpz);
	return (PyObject *)z;
} /* py_mpz_invert() */

static PyObject *
mpz_lshift(a, b)
	mpzobject *a;
	mpzobject *b;
{
	int cmpres;
	mpzobject *z;


	if ((cmpres = mpz_cmp_ui(&b->mpz, (unsigned long int)0)) == 0) {
		/* a << 0 == a */
		Py_INCREF(a);
		return (PyObject *)a;
	}

	if (cmpres < 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.<< negative shift count");
		return NULL;
	}

#ifdef MPZ_LIB_DOES_CHECKING
	if (mpz_size(&b->mpz) > 1)
		return (PyObject *)PyErr_NoMemory();
#else /* def MPZ_LIB_DOES_CHECKING */
	/* wet finger method */
	if (mpz_cmp_ui(&b->mpz, (unsigned long int)0x10000) >= 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.<< outrageous shift count");
		return NULL;
	}
#endif /* def MPZ_LIB_DOES_CHECKING else */

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_mul_2exp(&z->mpz, &a->mpz, mpz_get_ui(&b->mpz));
	return (PyObject *)z;
} /* mpz_lshift() */

static PyObject *
mpz_rshift(a, b)
	mpzobject *a;
	mpzobject *b;
{
	int cmpres;
	mpzobject *z;


	if ((cmpres = mpz_cmp_ui(&b->mpz, (unsigned long int)0)) == 0) {
		/* a >> 0 == a */
		Py_INCREF(a);
		return (PyObject *)a;
	}

	if (cmpres < 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.>> negative shift count");
		return NULL;
	}

	if (mpz_size(&b->mpz) > 1)
		return (PyObject *)PyErr_NoMemory();

	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_div_2exp(&z->mpz, &a->mpz, mpz_get_ui(&b->mpz));
	return (PyObject *)z;
} /* mpz_rshift() */

static PyObject *
mpz_andfunc(a, b)
	mpzobject *a;
	mpzobject *b;
{
	mpzobject *z;


	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_and(&z->mpz, &a->mpz, &b->mpz);
	return (PyObject *)z;
} /* mpz_andfunc() */

/* hack Hack HAck HACk HACK, XXX this code is dead slow */
void
mpz_xor(res, op1, op2)
	MP_INT *res;
	const MP_INT *op1;
	const MP_INT *op2;
{
	MP_INT tmpmpz;
	
	mpz_init(&tmpmpz);

	mpz_and(res, op1, op2);
	mpz_com(&tmpmpz, res);
	mpz_ior(res, op1, op2);
	mpz_and(res, res, &tmpmpz);

	mpz_clear(&tmpmpz);
} /* mpz_xor() HACK */

static PyObject *
mpz_xorfunc(a, b)
	mpzobject *a;
	mpzobject *b;
{
	mpzobject *z;


	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_xor(&z->mpz, &a->mpz, &b->mpz);
	return (PyObject *)z;
} /* mpz_xorfunc() */

static PyObject *
mpz_orfunc(a, b)
	mpzobject *a;
	mpzobject *b;
{
	mpzobject *z;


	if ((z = newmpzobject()) == NULL)
		return NULL;

	mpz_ior(&z->mpz, &a->mpz, &b->mpz);
	return (PyObject *)z;
} /* mpz_orfunc() */

/* MPZ initialisation */

#include "longintrepr.h"

static PyObject *
MPZ_mpz(self, args)
	PyObject *self;
	PyObject *args;
{
	mpzobject *mpzp;
	PyObject *objp;


#ifdef MPZ_DEBUG
	fputs("MPZ_mpz() called...\n", stderr);
#endif /* def MPZ_DEBUG */

	if (!PyArg_Parse(args, "O", &objp))
		return NULL;

	/* at least we know it's some object */
	/* note DON't Py_DECREF args NEITHER objp */

	if (PyInt_Check(objp)) {
		long lval;

		if (!PyArg_Parse(objp, "l", &lval))
			return NULL;
		
		if (lval == (long)0) {
			Py_INCREF(mpz_value_zero);
			mpzp = mpz_value_zero;
		}
		else if (lval == (long)1) {
			Py_INCREF(mpz_value_one);
			mpzp = mpz_value_one;
		}			
		else if ((mpzp = newmpzobject()) == NULL)
			return NULL;
		else mpz_set_si(&mpzp->mpz, lval);
	}
	else if (PyLong_Check(objp)) {
		MP_INT mplongdigit;
		int i;
		unsigned char isnegative;
		

		if ((mpzp = newmpzobject()) == NULL)
			return NULL;

		mpz_set_si(&mpzp->mpz, 0L);
		mpz_init(&mplongdigit);
		
		/* how we're gonna handle this? */
		if ((isnegative =
		     ((i = ((PyLongObject *)objp)->ob_size) < 0) ))
			i = -i;

		while (i--) {
			mpz_set_ui(&mplongdigit,
				   (unsigned long)
				   ((PyLongObject *)objp)->ob_digit[i]);
			mpz_mul_2exp(&mplongdigit,&mplongdigit,
				     (unsigned long int)i * SHIFT);
			mpz_ior(&mpzp->mpz, &mpzp->mpz, &mplongdigit);
		}

		if (isnegative)
			mpz_neg(&mpzp->mpz, &mpzp->mpz);

		/* get rid of allocation for tmp variable */
		mpz_clear(&mplongdigit);
	}
	else if (PyString_Check(objp)) {
		unsigned char *cp = (unsigned char *)PyString_AS_STRING(objp);
		int len = PyString_GET_SIZE(objp);
		MP_INT mplongdigit;

		if ((mpzp = newmpzobject()) == NULL)
			return NULL;

		mpz_set_si(&mpzp->mpz, 0L);
		mpz_init(&mplongdigit);
		
		/* let's do it the same way as with the long conversion:
		   without thinking how it can be faster (-: :-) */

		cp += len;
		while (len--) {
			mpz_set_ui(&mplongdigit, (unsigned long)*--cp );
			mpz_mul_2exp(&mplongdigit,&mplongdigit,
				     (unsigned long int)len * 8);
			mpz_ior(&mpzp->mpz, &mpzp->mpz, &mplongdigit);
		}

		/* get rid of allocation for tmp variable */
		mpz_clear(&mplongdigit);
	}
	else if (is_mpzobject(objp)) {
		Py_INCREF(objp);
		mpzp = (mpzobject *)objp;
	}
	else {
		PyErr_SetString(PyExc_TypeError,
"mpz.mpz() expects integer, long, string or mpz object argument");
		return NULL;
	}


#ifdef MPZ_DEBUG
	fputs("MPZ_mpz: created mpz=", stderr);
	mpz_out_str(stderr, 10, &mpzp->mpz);
	putc('\n', stderr);
#endif /* def MPZ_DEBUG */
	return (PyObject *)mpzp;
} /* MPZ_mpz() */

static mpzobject *
mpz_mpzcoerce(z)
	PyObject *z;
{
	/* shortcut: 9 out of 10 times the type is already ok */
	if (is_mpzobject(z)) {
		Py_INCREF(z);
		return (mpzobject *)z;	/* coercion succeeded */
	}

	/* what types do we accept?: intobjects and longobjects */
	if (PyInt_Check(z) || PyLong_Check(z))
		return (mpzobject *)MPZ_mpz((PyObject *)NULL, z);

	PyErr_SetString(PyExc_TypeError,
			"number coercion (to mpzobject) failed");
	return NULL;
} /* mpz_mpzcoerce() */
	
/* Forward */
static void mpz_divm Py_PROTO((MP_INT *res, const MP_INT *num,
			       const MP_INT *den, const MP_INT *mod));

static PyObject *
MPZ_powm(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *base, *exp, *mod;
	mpzobject *mpzbase = NULL, *mpzexp = NULL, *mpzmod = NULL;
	mpzobject *z;
	int tstres;

	
	if (!PyArg_Parse(args, "(OOO)", &base, &exp, &mod))
		return NULL;

	if ((mpzbase = mpz_mpzcoerce(base)) == NULL
	    || (mpzexp = mpz_mpzcoerce(exp)) == NULL
	    || (mpzmod = mpz_mpzcoerce(mod)) == NULL
	    || (z = newmpzobject()) == NULL) {
		Py_XDECREF(mpzbase);
		Py_XDECREF(mpzexp);
		Py_XDECREF(mpzmod);
		return NULL;
	}

	if ((tstres=mpz_cmp_ui(&mpzexp->mpz, (unsigned long int)0)) == 0) {
		Py_INCREF(mpz_value_one);
		return (PyObject *)mpz_value_one;
	}

	if (tstres < 0) {
		MP_INT absexp;
		/* negative exp */

		mpz_init_set(&absexp, &mpzexp->mpz);
		mpz_abs(&absexp, &absexp);
		mpz_powm(&z->mpz, &mpzbase->mpz, &absexp, &mpzmod->mpz);

		mpz_divm(&z->mpz, &mpz_value_one->mpz, &z->mpz, &mpzmod->mpz);
		
		mpz_clear(&absexp);
	}
	else {
		mpz_powm(&z->mpz, &mpzbase->mpz, &mpzexp->mpz, &mpzmod->mpz);
	}
		
	Py_DECREF(mpzbase);
	Py_DECREF(mpzexp);
	Py_DECREF(mpzmod);

	return (PyObject *)z;
} /* MPZ_powm() */


static PyObject *
MPZ_gcd(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *op1, *op2;
	mpzobject *mpzop1 = NULL, *mpzop2 = NULL;
	mpzobject *z;

	
	if (!PyArg_Parse(args, "(OO)", &op1, &op2))
		return NULL;

	if ((mpzop1 = mpz_mpzcoerce(op1)) == NULL
	    || (mpzop2 = mpz_mpzcoerce(op2)) == NULL
	    || (z = newmpzobject()) == NULL) {
		Py_XDECREF(mpzop1);
		Py_XDECREF(mpzop2);
		return NULL;
	}

	/* ok, we have three mpzobjects, and an initialised result holder */
	mpz_gcd(&z->mpz, &mpzop1->mpz, &mpzop2->mpz);

	Py_DECREF(mpzop1);
	Py_DECREF(mpzop2);

	return (PyObject *)z;
} /* MPZ_gcd() */


static PyObject *
MPZ_gcdext(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *op1, *op2, *z = NULL;
	mpzobject *mpzop1 = NULL, *mpzop2 = NULL;
	mpzobject *g = NULL, *s = NULL, *t = NULL;

	
	if (!PyArg_Parse(args, "(OO)", &op1, &op2))
		return NULL;

	if ((mpzop1 = mpz_mpzcoerce(op1)) == NULL
	    || (mpzop2 = mpz_mpzcoerce(op2)) == NULL
	    || (z = PyTuple_New(3)) == NULL
	    || (g = newmpzobject()) == NULL
	    || (s = newmpzobject()) == NULL
	    || (t = newmpzobject()) == NULL) {
		Py_XDECREF(mpzop1);
		Py_XDECREF(mpzop2);
		Py_XDECREF(z);
		Py_XDECREF(g);
		Py_XDECREF(s);
		/*Py_XDECREF(t);*/
		return NULL;
	}

	mpz_gcdext(&g->mpz, &s->mpz, &t->mpz, &mpzop1->mpz, &mpzop2->mpz);

	Py_DECREF(mpzop1);
	Py_DECREF(mpzop2);

	(void)PyTuple_SetItem(z, 0, (PyObject *)g);
	(void)PyTuple_SetItem(z, 1, (PyObject *)s);
	(void)PyTuple_SetItem(z, 2, (PyObject *)t);

	return (PyObject *)z;
} /* MPZ_gcdext() */


static PyObject *
MPZ_sqrt(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *op;
	mpzobject *mpzop = NULL;
	mpzobject *z;

	
	if (!PyArg_Parse(args, "O", &op))
		return NULL;

	if ((mpzop = mpz_mpzcoerce(op)) == NULL
	    || (z = newmpzobject()) == NULL) {
		Py_XDECREF(mpzop);
		return NULL;
	}

	mpz_sqrt(&z->mpz, &mpzop->mpz);

	Py_DECREF(mpzop);

	return (PyObject *)z;
} /* MPZ_sqrt() */


static PyObject *
MPZ_sqrtrem(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *op, *z = NULL;
	mpzobject *mpzop = NULL;
	mpzobject *root = NULL, *rem = NULL;

	
	if (!PyArg_Parse(args, "O", &op))
		return NULL;

	if ((mpzop = mpz_mpzcoerce(op)) == NULL
	    || (z = PyTuple_New(2)) == NULL
	    || (root = newmpzobject()) == NULL
	    || (rem = newmpzobject()) == NULL) {
		Py_XDECREF(mpzop);
		Py_XDECREF(z);
		Py_XDECREF(root);
		/*Py_XDECREF(rem);*/
		return NULL;
	}

	mpz_sqrtrem(&root->mpz, &rem->mpz, &mpzop->mpz);

	Py_DECREF(mpzop);

	(void)PyTuple_SetItem(z, 0, (PyObject *)root);
	(void)PyTuple_SetItem(z, 1, (PyObject *)rem);

	return (PyObject *)z;
} /* MPZ_sqrtrem() */


static void
#if __STDC__
mpz_divm(MP_INT *res, const MP_INT *num, const MP_INT *den, const MP_INT *mod)
#else
mpz_divm(res, num, den, mod)
	MP_INT *res;
	const MP_INT *num;
	const MP_INT *den;
	const MP_INT *mod;
#endif
{
	MP_INT s0, s1, q, r, x, d0, d1;

	mpz_init_set(&s0, num);
	mpz_init_set_ui(&s1, 0);
	mpz_init(&q);
	mpz_init(&r);
	mpz_init(&x);
	mpz_init_set(&d0, den);
	mpz_init_set(&d1, mod);

#ifdef GMP2
	while (d1._mp_size != 0) {
#else
	while (d1.size != 0) {
#endif
		mpz_divmod(&q, &r, &d0, &d1);
		mpz_set(&d0, &d1);
		mpz_set(&d1, &r);

		mpz_mul(&x, &s1, &q);
		mpz_sub(&x, &s0, &x);
		mpz_set(&s0, &s1);
		mpz_set(&s1, &x);
	}

#ifdef GMP2
	if (d0._mp_size != 1 || d0._mp_d[0] != 1)
		res->_mp_size = 0; /* trouble: the gcd != 1; set s to zero */
#else
	if (d0.size != 1 || d0.d[0] != 1)
		res->size = 0;	/* trouble: the gcd != 1; set s to zero */
#endif
	else {
#ifdef MPZ_MDIV_BUG
		/* watch out here! first check the signs, and then perform
		   the mpz_mod() since mod could point to res */
		if ((s0.size < 0) != (mod->size < 0)) {
			mpz_mod(res, &s0, mod);

			if (res->size)
				mpz_add(res, res, mod);
		}
		else
			mpz_mod(res, &s0, mod);
		
#else /* def MPZ_MDIV_BUG */
		mpz_mmod(res, &s0, mod);
#endif /* def MPZ_MDIV_BUG else */
	}

	mpz_clear(&s0);
	mpz_clear(&s1);
	mpz_clear(&q);
	mpz_clear(&r);
	mpz_clear(&x);
	mpz_clear(&d0);
	mpz_clear(&d1);
} /* mpz_divm() */


static PyObject *
MPZ_divm(self, args)
	PyObject *self;
	PyObject *args;
{
	PyObject *num, *den, *mod;
	mpzobject *mpznum, *mpzden, *mpzmod = NULL;
	mpzobject *z = NULL;

	
	if (!PyArg_Parse(args, "(OOO)", &num, &den, &mod))
		return NULL;

	if ((mpznum = mpz_mpzcoerce(num)) == NULL
	    || (mpzden = mpz_mpzcoerce(den)) == NULL
	    || (mpzmod = mpz_mpzcoerce(mod)) == NULL
	    || (z = newmpzobject()) == NULL ) {
		Py_XDECREF(mpznum);
		Py_XDECREF(mpzden);
		Py_XDECREF(mpzmod);
		return NULL;
	}
	
	mpz_divm(&z->mpz, &mpznum->mpz, &mpzden->mpz, &mpzmod->mpz);

	Py_DECREF(mpznum);
	Py_DECREF(mpzden);
	Py_DECREF(mpzmod);

	if (mpz_cmp_ui(&z->mpz, (unsigned long int)0) == 0) {
		Py_DECREF(z);
		PyErr_SetString(PyExc_ValueError,
				"gcd(den, mod) != 1 or num == 0");
		return NULL;
	}

	return (PyObject *)z;
} /* MPZ_divm() */


/* MPZ methods-as-attributes */
#ifdef MPZ_CONVERSIONS_AS_METHODS
static PyObject *
mpz_int(self, args)
	mpzobject *self;
	PyObject *args;
#else /* def MPZ_CONVERSIONS_AS_METHODS */
static PyObject *
mpz_int(self)
	mpzobject *self;
#endif /* def MPZ_CONVERSIONS_AS_METHODS else */
{
	long sli;


#ifdef MPZ_CONVERSIONS_AS_METHODS
	if (!PyArg_NoArgs(args))
		return NULL;
#endif /* def MPZ_CONVERSIONS_AS_METHODS */

	if (mpz_size(&self->mpz) > 1
	    || (sli = (long)mpz_get_ui(&self->mpz)) < (long)0 ) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.int() arg too long to convert");
		return NULL;
	}

	if (mpz_cmp_ui(&self->mpz, (unsigned long)0) < 0)
		sli = -sli;

	return PyInt_FromLong(sli);
} /* mpz_int() */
	
static PyObject *
#ifdef MPZ_CONVERSIONS_AS_METHODS
mpz_long(self, args)
	mpzobject *self;
	PyObject *args;
#else /* def MPZ_CONVERSIONS_AS_METHODS */
mpz_long(self)
	mpzobject *self;
#endif /* def MPZ_CONVERSIONS_AS_METHODS else */
{
	int i, isnegative;
	unsigned long int uli;
	PyLongObject *longobjp;
	int ldcount;
	int bitpointer, newbitpointer;
	MP_INT mpzscratch;


#ifdef MPZ_CONVERSIONS_AS_METHODS
	if (!PyArg_NoArgs(args))
		return NULL;
#endif /* def MPZ_CONVERSIONS_AS_METHODS */

	/* determine length of python-long to be allocated */
	if ((longobjp = _PyLong_New(i = (int)
			    ((mpz_size(&self->mpz) * BITS_PER_MP_LIMB
			      + SHIFT - 1) /
			     SHIFT))) == NULL)
		return NULL;

	/* determine sign, and copy self to scratch var */
	mpz_init_set(&mpzscratch, &self->mpz);
	if ((isnegative = (mpz_cmp_ui(&self->mpz, (unsigned long int)0) < 0)))
		mpz_neg(&mpzscratch, &mpzscratch);

	/* let those bits come, let those bits go,
	   e.g. dismantle mpzscratch, build PyLongObject */

	bitpointer = 0;		/* the number of valid bits in stock */
	newbitpointer = 0;
	ldcount = 0;		/* the python-long limb counter */
	uli = (unsigned long int)0;
	while (i--) {
		longobjp->ob_digit[ldcount] = uli & MASK;

		/* check if we've had enough bits for this digit */
		if (bitpointer < SHIFT) {
			uli = mpz_get_ui(&mpzscratch);
			longobjp->ob_digit[ldcount] |=
				(uli << bitpointer) & MASK;
			uli >>= SHIFT-bitpointer;
			bitpointer += BITS_PER_MP_LIMB;
			mpz_div_2exp(&mpzscratch, &mpzscratch,
				     BITS_PER_MP_LIMB);
		}
		else
			uli >>= SHIFT;
		bitpointer -= SHIFT;
		ldcount++;
	}

	assert(mpz_cmp_ui(&mpzscratch, (unsigned long int)0) == 0);
	mpz_clear(&mpzscratch);
	assert(ldcount <= longobjp->ob_size);

	/* long_normalize() is file-static */
	/* longobjp = long_normalize(longobjp); */
	while (ldcount > 0 && longobjp->ob_digit[ldcount-1] == 0)
		ldcount--;
	longobjp->ob_size = ldcount;
	

	if (isnegative)
		longobjp->ob_size = -longobjp->ob_size;

	return (PyObject *)longobjp;
	
} /* mpz_long() */


/* I would have avoided pow() anyways, so ... */
static const double multiplier = 256.0 * 256.0 * 256.0 * 256.0;
	
#ifdef MPZ_CONVERSIONS_AS_METHODS
static PyObject *
mpz_float(self, args)
	mpzobject *self;
	PyObject *args;
#else /* def MPZ_CONVERSIONS_AS_METHODS */
static PyObject *
mpz_float(self)
	mpzobject *self;
#endif /* def MPZ_CONVERSIONS_AS_METHODS else */
{
	int i, isnegative;
	double x;
	double mulstate;
	MP_INT mpzscratch;


#ifdef MPZ_CONVERSIONS_AS_METHODS
	if (!PyArg_NoArgs(args))
		return NULL;
#endif /* def MPZ_CONVERSIONS_AS_METHODS */

	i = (int)mpz_size(&self->mpz);
	
	/* determine sign, and copy abs(self) to scratch var */
	if ((isnegative = (mpz_cmp_ui(&self->mpz, (unsigned long int)0) < 0)))
	{
		mpz_init(&mpzscratch);
		mpz_neg(&mpzscratch, &self->mpz);
	}
	else
		mpz_init_set(&mpzscratch, &self->mpz);

	/* let those bits come, let those bits go,
	   e.g. dismantle mpzscratch, build PyFloatObject */

	/* Can this overflow?  Dunno, protect against that possibility. */
	PyFPE_START_PROTECT("mpz_float", return 0)
	x = 0.0;
	mulstate = 1.0;
	while (i--) {
		x += mulstate * mpz_get_ui(&mpzscratch);
		mulstate *= multiplier;
		mpz_div_2exp(&mpzscratch, &mpzscratch, BITS_PER_MP_LIMB);
	}
	PyFPE_END_PROTECT(mulstate)

	assert(mpz_cmp_ui(&mpzscratch, (unsigned long int)0) == 0);
	mpz_clear(&mpzscratch);

	if (isnegative)
		x = -x;

	return PyFloat_FromDouble(x);
	
} /* mpz_float() */

#ifdef MPZ_CONVERSIONS_AS_METHODS
static PyObject *
mpz_hex(self, args)
	mpzobject *self;
	PyObject *args;
#else /* def MPZ_CONVERSIONS_AS_METHODS */
static PyObject *
mpz_hex(self)
	mpzobject *self;
#endif /* def MPZ_CONVERSIONS_AS_METHODS else */
{
#ifdef MPZ_CONVERSIONS_AS_METHODS
	if (!PyArg_NoArgs(args))
		return NULL;
#endif /* def MPZ_CONVERSIONS_AS_METHODS */
	
	return mpz_format(self, 16, (unsigned char)1);
} /* mpz_hex() */
	
#ifdef MPZ_CONVERSIONS_AS_METHODS
static PyObject *
mpz_oct(self, args)
	mpzobject *self;
	PyObject *args;
#else /* def MPZ_CONVERSIONS_AS_METHODS */
static PyObject *
mpz_oct(self)
	mpzobject *self;
#endif /* def MPZ_CONVERSIONS_AS_METHODS else */
{
#ifdef MPZ_CONVERSIONS_AS_METHODS
	if (!PyArg_NoArgs(args))
		return NULL;
#endif /* def MPZ_CONVERSIONS_AS_METHODS */
	
	return mpz_format(self, 8, (unsigned char)1);
} /* mpz_oct() */
	
static PyObject *
mpz_binary(self, args)
	mpzobject *self;
	PyObject *args;
{
	int size;
	PyStringObject *strobjp;
	char *cp;
	MP_INT mp;
	unsigned long ldigit;
	
	if (!PyArg_NoArgs(args))
		return NULL;

	if (mpz_cmp_ui(&self->mpz, (unsigned long int)0) < 0) {
		PyErr_SetString(PyExc_ValueError,
				"mpz.binary() arg must be >= 0");
		return NULL;
	}

	mpz_init_set(&mp, &self->mpz);
	size = (int)mpz_size(&mp);

	if ((strobjp = (PyStringObject *)
	     PyString_FromStringAndSize(
		     (char *)0, size * sizeof (unsigned long int))) == NULL)
		return NULL;

	/* get the beginning of the string memory and start copying things */
	cp = PyString_AS_STRING(strobjp);

	/* this has been programmed using a (fairly) decent lib-i/f it could
	   be must faster if we looked into the GMP lib */
	while (size--) {
		ldigit = mpz_get_ui(&mp);
		mpz_div_2exp(&mp, &mp, BITS_PER_MP_LIMB);
		*cp++ = (unsigned char)(ldigit & 0xFF);
		*cp++ = (unsigned char)((ldigit >>= 8) & 0xFF);
		*cp++ = (unsigned char)((ldigit >>= 8) & 0xFF);
		*cp++ = (unsigned char)((ldigit >>= 8) & 0xFF);
	}

	while (strobjp->ob_size && !*--cp)
		strobjp->ob_size--;

	return (PyObject *)strobjp;
} /* mpz_binary() */
	

static PyMethodDef mpz_methods[] = {
#ifdef MPZ_CONVERSIONS_AS_METHODS
	{"int",			mpz_int},
	{"long",		mpz_long},
	{"float",		mpz_float},
	{"hex",			mpz_hex},
	{"oct",			mpz_oct},
#endif /* def MPZ_CONVERSIONS_AS_METHODS */
	{"binary",		(PyCFunction)mpz_binary},
	{NULL,			NULL}		/* sentinel */
};

static PyObject *
mpz_getattr(self, name)
	mpzobject *self;
	char *name;
{
	return Py_FindMethod(mpz_methods, (PyObject *)self, name);
} /* mpz_getattr() */


static int
mpz_coerce(pv, pw)
	PyObject **pv;
	PyObject **pw;
{
	PyObject *z;

#ifdef MPZ_DEBUG
	fputs("mpz_coerce() called...\n", stderr);
#endif /* def MPZ_DEBUG */

	assert(is_mpzobject(*pv));

	/* always convert other arg to mpz value, except for floats */
	if (!PyFloat_Check(*pw)) {
		if ((z = (PyObject *)mpz_mpzcoerce(*pw)) == NULL)
			return -1;	/* -1: an error always has been set */
		
		Py_INCREF(*pv);
		*pw = z;
	}
	else {
		if ((z = mpz_float(*pv, NULL)) == NULL)
			return -1;

		Py_INCREF(*pw);
		*pv = z;
	}
	return 0;		/* coercion succeeded */

} /* mpz_coerce() */


static PyObject *
mpz_repr(v)
	PyObject *v;
{
	return mpz_format(v, 10, (unsigned char)1);
} /* mpz_repr() */



#define UF (unaryfunc)
#define BF (binaryfunc)
#define TF (ternaryfunc)
#define IF (inquiry)
#define CF (coercion)

static PyNumberMethods mpz_as_number = {
	BF mpz_addition,	/*nb_add*/
	BF mpz_substract,	/*nb_subtract*/
	BF mpz_multiply,	/*nb_multiply*/
	BF mpz_divide,		/*nb_divide*/
	BF mpz_remainder,	/*nb_remainder*/
	BF mpz_div_and_mod,	/*nb_divmod*/
	TF mpz_power,		/*nb_power*/
	UF mpz_negative,	/*nb_negative*/
	UF mpz_positive,	/*tp_positive*/
	UF mpz_absolute,	/*tp_absolute*/
	IF mpz_nonzero,		/*tp_nonzero*/
	UF py_mpz_invert,	/*nb_invert*/
	BF mpz_lshift,		/*nb_lshift*/
	BF mpz_rshift,		/*nb_rshift*/
	BF mpz_andfunc,		/*nb_and*/
	BF mpz_xorfunc,		/*nb_xor*/
	BF mpz_orfunc,		/*nb_or*/
	CF mpz_coerce,		/*nb_coerce*/
#ifndef MPZ_CONVERSIONS_AS_METHODS
	UF mpz_int,		/*nb_int*/
	UF mpz_long,		/*nb_long*/
	UF mpz_float,		/*nb_float*/
	UF mpz_oct,		/*nb_oct*/
	UF mpz_hex,		/*nb_hex*/
#endif /* ndef MPZ_CONVERSIONS_AS_METHODS */
};

static PyTypeObject MPZtype = {
	PyObject_HEAD_INIT(&PyType_Type)
	0,			/*ob_size*/
	"mpz",			/*tp_name*/
	sizeof(mpzobject),	/*tp_size*/
	0,			/*tp_itemsize*/
	/* methods */
	(destructor)mpz_dealloc, /*tp_dealloc*/
	0,			/*tp_print*/
	(getattrfunc)mpz_getattr, /*tp_getattr*/
	0,			/*tp_setattr*/
	(cmpfunc)mpz_compare,	/*tp_compare*/
	(reprfunc)mpz_repr,	/*tp_repr*/
        &mpz_as_number, 	/*tp_as_number*/
};

/* List of functions exported by this module */

static PyMethodDef mpz_functions[] = {
#if 0
	{initialiser_name,	MPZ_mpz},
#else /* 0 */
	/* until guido ``fixes'' struct PyMethodDef */
	{(char *)initialiser_name,	MPZ_mpz},
#endif /* 0 else */	
	{"powm",		MPZ_powm},
	{"gcd",			MPZ_gcd},
	{"gcdext",		MPZ_gcdext},
	{"sqrt",		MPZ_sqrt},
	{"sqrtrem",		MPZ_sqrtrem},
	{"divm",		MPZ_divm},
	{NULL,			NULL}		 /* Sentinel */
};


/* #define MP_TEST_ALLOC */

#ifdef MP_TEST_ALLOC
#define MP_TEST_SIZE		4
static const char mp_test_magic[MP_TEST_SIZE] = {'\xAA','\xAA','\xAA','\xAA'};
static mp_test_error( location )
	int *location;
{
	/* assumptions: *alloc returns address dividable by 4,
	mpz_* routines allocate in chunks dividable by four */
	fprintf(stderr, "MP_TEST_ERROR: location holds 0x%08d\n", *location );
	Py_FatalError("MP_TEST_ERROR");
} /* static mp_test_error() */
#define MP_EXTRA_ALLOC(size)	((size) + MP_TEST_SIZE)
#define MP_SET_TEST(basep,size)	(void)memcpy( ((char *)(basep))+(size), mp_test_magic, MP_TEST_SIZE)
#define MP_DO_TEST(basep,size)	if ( !memcmp( ((char *)(basep))+(size), mp_test_magic, MP_TEST_SIZE ) ) \
					; \
				else \
					mp_test_error((int *)((char *)(basep) + size))
#else /* def MP_TEST_ALLOC */
#define MP_EXTRA_ALLOC(size)	(size)
#define MP_SET_TEST(basep,size)
#define MP_DO_TEST(basep,size)
#endif /* def MP_TEST_ALLOC else */

void *mp_allocate( alloc_size )
	size_t	alloc_size;
{
	void *res;

#ifdef MPZ_DEBUG
	fprintf(stderr, "mp_allocate  :                             size %ld\n",
		alloc_size);
#endif /* def MPZ_DEBUG */	

	if ( (res = malloc(MP_EXTRA_ALLOC(alloc_size))) == NULL )
		Py_FatalError("mp_allocate failure");

#ifdef MPZ_DEBUG
	fprintf(stderr, "mp_allocate  :     address %08p\n", res);
#endif /* def MPZ_DEBUG */	

	MP_SET_TEST(res,alloc_size);
	
	return res;
} /* mp_allocate() */


void *mp_reallocate( ptr, old_size, new_size )
	void *ptr;
	size_t old_size;
	size_t new_size;
{
	void *res;

#ifdef MPZ_DEBUG
	fprintf(stderr, "mp_reallocate: old address %08p, old size %ld\n",
		ptr, old_size);
#endif /* def MPZ_DEBUG */	

	MP_DO_TEST(ptr, old_size);
	
	if ( (res = realloc(ptr, MP_EXTRA_ALLOC(new_size))) == NULL )
		Py_FatalError("mp_reallocate failure");

#ifdef MPZ_DEBUG
	fprintf(stderr, "mp_reallocate: new address %08p, new size %ld\n",
		res, new_size);
#endif /* def MPZ_DEBUG */	

	MP_SET_TEST(res, new_size);

	return res;
} /* mp_reallocate() */


void mp_free( ptr, size )
	void *ptr;
	size_t size;
{

#ifdef MPZ_DEBUG
	fprintf(stderr, "mp_free      : old address %08p, old size %ld\n",
		ptr, size);
#endif /* def MPZ_DEBUG */	

	MP_DO_TEST(ptr, size);
	free(ptr);
} /* mp_free() */



/* Initialize this module. */

DL_EXPORT(void)
initmpz()
{
	PyObject *module;
	PyObject *dict;

#ifdef MPZ_DEBUG
	fputs( "initmpz() called...\n", stderr );
#endif /* def MPZ_DEBUG */

	mp_set_memory_functions( mp_allocate, mp_reallocate, mp_free );
	module = Py_InitModule("mpz", mpz_functions);

	/* create some frequently used constants */
	if ((mpz_value_zero = newmpzobject()) == NULL)
		Py_FatalError("initmpz: can't initialize mpz constants");
	mpz_set_ui(&mpz_value_zero->mpz, (unsigned long int)0);

	if ((mpz_value_one = newmpzobject()) == NULL)
		Py_FatalError("initmpz: can't initialize mpz constants");
	mpz_set_ui(&mpz_value_one->mpz, (unsigned long int)1);

	if ((mpz_value_mone = newmpzobject()) == NULL)
		Py_FatalError("initmpz: can't initialize mpz constants");
	mpz_set_si(&mpz_value_mone->mpz, (long)-1);

	dict = PyModule_GetDict(module);
	if (dict != NULL) {
		PyDict_SetItemString(dict, "MPZType", (PyObject*)&MPZtype);
	}

} /* initmpz() */
#ifdef MAKEDUMMYINT
int _mpz_dummy_int;	/* XXX otherwise, we're .bss-less (DYNLOAD->Jack?) */
#endif /* def MAKEDUMMYINT */