moo/stix/lib/bigint.c

/*
 * $Id$
 *
    Copyright (c) 2014-2016 Chung, Hyung-Hwan. All rights reserved.

    Redistribution and use in source and binary forms, with or without
    modification, are permitted provided that the following conditions
    are met:
    1. Redistributions of source code must retain the above copyright
       notice, this list of conditions and the following disclaimer.
    2. Redistributions in binary form must reproduce the above copyright
       notice, this list of conditions and the following disclaimer in the
       documentation and/or other materials provided with the distribution.

    THIS SOFTWARE IS PROVIDED BY THE AUTHOR "AS IS" AND ANY EXPRESS OR
    IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WAfRRANTIES
    OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
    IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
    NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
    THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

/*
 * Copyright (c) 2002 by The XFree86 Project, Inc.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *  
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
 * THE XFREE86 PROJECT BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
 * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 *
 * Except as contained in this notice, the name of the XFree86 Project shall
 * not be used in advertising or otherwise to promote the sale, use or other
 * dealings in this Software without prior written authorization from the
 * XFree86 Project.
 *
 * Author: Paulo César Pereira de Andrade
 */


#include "stix-prv.h"


#define ENABLE_KARATSUBA
#if defined(STIX_DEBUG_BIGINT)
#	define KARATSUBA_CUTOFF 3
#else
#	define KARATSUBA_CUTOFF 32
#endif

#if (STIX_LIW_BITS == STIX_OOW_BITS)
	/* nothing special */
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
#	define MAKE_WORD(hw1,hw2) ((stix_oow_t)(hw1) | (stix_oow_t)(hw2) << STIX_LIW_BITS)
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif

/*#define IS_POWER_OF_2(ui) (((ui) > 0) && (((ui) & (~(ui)+ 1)) == (ui)))*/
#define IS_POWER_OF_2(ui) (((ui) > 0) && ((ui) & ((ui) - 1)) == 0)

#define IS_SIGN_DIFF(x,y) (((x) ^ (y)) < 0)

/* digit character array */
static char* _digitc = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";

/* exponent table */
static stix_uint8_t _exp_tab[] = 
{
	0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 
	0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0
};


#if (STIX_SIZEOF_OOW_T == STIX_SIZEOF_INT) && defined(STIX_HAVE_BUILTIN_UADD_OVERFLOW)
#	define oow_add_overflow(a,b,c)  __builtin_uadd_overflow(a,b,c)
#elif (STIX_SIZEOF_OOW_T == STIX_SIZEOF_LONG) && defined(STIX_HAVE_BUILTIN_UADDL_OVERFLOW)
#	define oow_add_overflow(a,b,c)  __builtin_uaddl_overflow(a,b,c)
#elif (STIX_SIZEOF_OOW_T == STIX_SIZEOF_LONG_LONG) && defined(STIX_HAVE_BUILTIN_UADDLL_OVERFLOW)
#	define oow_add_overflow(a,b,c)  __builtin_uaddll_overflow(a,b,c)
#else
static STIX_INLINE int oow_add_overflow (stix_oow_t a, stix_oow_t b, stix_oow_t* c)
{
	*c = a + b;
	return b > STIX_TYPE_MAX(stix_oow_t) - a;
}
#endif


#if (STIX_SIZEOF_OOW_T == STIX_SIZEOF_INT) && defined(STIX_HAVE_BUILTIN_UMUL_OVERFLOW)
#	define oow_mul_overflow(a,b,c)  __builtin_umul_overflow(a,b,c)
#elif (STIX_SIZEOF_OOW_T == STIX_SIZEOF_LONG) && defined(STIX_HAVE_BUILTIN_UMULL_OVERFLOW)
#	define oow_mul_overflow(a,b,c)  __builtin_umull_overflow(a,b,c)
#elif (STIX_SIZEOF_OOW_T == STIX_SIZEOF_LONG_LONG) && defined(STIX_HAVE_BUILTIN_UMULLL_OVERFLOW)
#	define oow_mul_overflow(a,b,c)  __builtin_umulll_overflow(a,b,c)
#else
static STIX_INLINE int oow_mul_overflow (stix_oow_t a, stix_oow_t b, stix_oow_t* c)
{
#if (STIX_SIZEOF_UINTMAX_T > STIX_SIZEOF_OOW_T)
	stix_uintmax_t k;
	k = (stix_uintmax_t)a * (stix_uintmax_t)b;
	*c = (stix_oow_t)k;
	return (k >> STIX_OOW_BITS) > 0;
	/*return k > STIX_TYPE_MAX(stix_oow_t);*/
#else
	*c = a * b;
	return b != 0 && a > STIX_TYPE_MAX(stix_oow_t) / b; /* works for unsigned types only */
#endif
}
#endif

#if (STIX_SIZEOF_OOI_T == STIX_SIZEOF_INT) && defined(STIX_HAVE_BUILTIN_SMUL_OVERFLOW)
#	define smooi_mul_overflow(stix,a,b,c)  __builtin_smul_overflow(a,b,c)
#elif (STIX_SIZEOF_OOI_T == STIX_SIZEOF_LONG) && defined(STIX_HAVE_BUILTIN_SMULL_OVERFLOW)
#	define smooi_mul_overflow(stix,a,b,c)  __builtin_smull_overflow(a,b,c)
#elif (STIX_SIZEOF_OOI_T == STIX_SIZEOF_LONG_LONG) && defined(STIX_HAVE_BUILTIN_SMULLL_OVERFLOW)
#	define smooi_mul_overflow(stix,a,b,c)  __builtin_smulll_overflow(a,b,c)
#else
static STIX_INLINE int smooi_mul_overflow (stix_t* stix, stix_ooi_t a, stix_ooi_t b, stix_ooi_t* c)
{
	/* take note that this function is not supposed to handle
	 * the whole stix_ooi_t range. it handles the smooi subrange */

#if (STIX_SIZEOF_UINTMAX_T > STIX_SIZEOF_OOI_T)
	stix_intmax_t k;

	STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(a));
	STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(b));

	k = (stix_intmax_t)a * (stix_intmax_t)b;
	*c = (stix_ooi_t)k;

	return k > STIX_TYPE_MAX(stix_ooi_t) || k < STIX_TYPE_MIN(stix_ooi_t);
#else

	stix_ooi_t ua, ub;

	STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(a));
	STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(b));

	*c = a * b;

	ub = (b >= 0)? b: -b;
	ua = (a >= 0)? a: -a;

	/* though this fomula basically works for unsigned types in principle, 
	 * the values used here are all absolute values and they fall in
	 * a safe range to apply this fomula. the safe range is guaranteed because
	 * the sources are supposed to be smoois. */
	return ub != 0 && ua > STIX_TYPE_MAX(stix_ooi_t) / ub; 
#endif
}
#endif

#if (STIX_SIZEOF_LIW_T == STIX_SIZEOF_INT) && defined(STIX_HAVE_BUILTIN_UADD_OVERFLOW)
#	define liw_add_overflow(a,b,c)  __builtin_uadd_overflow(a,b,c)
#elif (STIX_SIZEOF_LIW_T == STIX_SIZEOF_LONG) && defined(STIX_HAVE_BUILTIN_UADDL_OVERFLOW)
#	define liw_add_overflow(a,b,c)  __builtin_uaddl_overflow(a,b,c)
#elif (STIX_SIZEOF_LIW_T == STIX_SIZEOF_LONG_LONG) && defined(STIX_HAVE_BUILTIN_UADDLL_OVERFLOW)
#	define liw_add_overflow(a,b,c)  __builtin_uaddll_overflow(a,b,c)
#else
static STIX_INLINE int liw_add_overflow (stix_liw_t a, stix_liw_t b, stix_liw_t* c)
{
	*c = a + b;
	return b > STIX_TYPE_MAX(stix_liw_t) - a;
}
#endif

#if (STIX_SIZEOF_LIW_T == STIX_SIZEOF_INT) && defined(STIX_HAVE_BUILTIN_UMUL_OVERFLOW)
#	define liw_mul_overflow(a,b,c)  __builtin_umul_overflow(a,b,c)
#elif (STIX_SIZEOF_LIW_T == STIX_SIZEOF_LONG) && defined(STIX_HAVE_BUILTIN_UMULL_OVERFLOW)
#	define liw_mul_overflow(a,b,c)  __builtin_uaddl_overflow(a,b,c)
#elif (STIX_SIZEOF_LIW_T == STIX_SIZEOF_LONG_LONG) && defined(STIX_HAVE_BUILTIN_UMULLL_OVERFLOW)
#	define liw_mul_overflow(a,b,c)  __builtin_uaddll_overflow(a,b,c)
#else
static STIX_INLINE int liw_mul_overflow (stix_liw_t a, stix_liw_t b, stix_liw_t* c)
{
#if (STIX_SIZEOF_UINTMAX_T > STIX_SIZEOF_LIW_T)
	stix_uintmax_t k;
	k = (stix_uintmax_t)a * (stix_uintmax_t)b;
	*c = (stix_liw_t)k;
	return (k >> STIX_LIW_BITS) > 0;
	/*return k > STIX_TYPE_MAX(stix_liw_t);*/
#else
	*c = a * b;
	return b != 0 && a > STIX_TYPE_MAX(stix_liw_t) / b; /* works for unsigned types only */
#endif
}
#endif

static int is_normalized_integer (stix_t* stix, stix_oop_t oop)
{
	if (STIX_OOP_IS_SMOOI(oop)) return 1;
	if (STIX_OOP_IS_POINTER(oop))
	{
		stix_oop_t c;
/* TODO: is it better to introduce a special integer mark into the class itself */
/* TODO: or should it check if it's a subclass, subsubclass, subsubsubclass, etc of a large_integer as well? */
		c = STIX_OBJ_GET_CLASS(oop);

		if (c == stix->_large_positive_integer ||
		    c == stix->_large_negative_integer) 
		{
			stix_oow_t sz;

			sz = STIX_OBJ_GET_SIZE(oop);
			STIX_ASSERT (stix, sz >= 1);

			return ((stix_oop_liword_t)oop)->slot[sz - 1] == 0? 0: 1;
		}
	}

	return 0;
}

STIX_INLINE static int is_bigint (stix_t* stix, stix_oop_t x)
{
	stix_oop_t c;

	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(x));

/* TODO: is it better to introduce a special integer mark into the class itself */
/* TODO: or should it check if it's a subclass, subsubclass, subsubsubclass, etc of a large_integer as well? */
	c = STIX_OBJ_GET_CLASS(x);

	if (c == stix->_large_positive_integer ||
	    c == stix->_large_negative_integer) return 1;

	return 0;
}

STIX_INLINE int stix_isint (stix_t* stix, stix_oop_t x)
{
	if (STIX_OOP_IS_SMOOI(x)) return 1;
	if (STIX_OOP_IS_POINTER(x)) return is_bigint(stix, x);
	return 0;
}

static STIX_INLINE int bigint_to_oow (stix_t* stix, stix_oop_t num, stix_oow_t* w)
{
	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(num));
	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(num) == stix->_large_positive_integer ||
	             STIX_OBJ_GET_CLASS(num) == stix->_large_negative_integer);

#if (STIX_LIW_BITS == STIX_OOW_BITS)
	STIX_ASSERT (stix, STIX_OBJ_GET_SIZE(num) >= 1);
	if (STIX_OBJ_GET_SIZE(num) == 1)
	{
		*w = ((stix_oop_word_t)num)->slot[0];
		return (STIX_OBJ_GET_CLASS(num) == stix->_large_negative_integer)? -1: 1;
	}

#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	/* this function must be called with a real large integer.
	 * a real large integer is at least 2 half-word long.
	 * you must not call this function with an unnormalized
	 * large integer. */

	STIX_ASSERT (stix, STIX_OBJ_GET_SIZE(num) >= 2);
	if (STIX_OBJ_GET_SIZE(num) == 2)
	{
		*w = MAKE_WORD (((stix_oop_halfword_t)num)->slot[0], ((stix_oop_halfword_t)num)->slot[1]);
		return (STIX_OBJ_GET_CLASS(num) == stix->_large_negative_integer)? -1: 1;
	}
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif

	return 0; /* not convertable */
}

static STIX_INLINE int integer_to_oow (stix_t* stix, stix_oop_t x, stix_oow_t* w)
{
	/* return value 
	 *   1 - a positive number including 0 that can fit into stix_oow_t
	 *  -1 - a negative number whose absolute value can fit into stix_oow_t
	 *   0 - number too large or too small
	 */

	if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		v = STIX_OOP_TO_SMOOI(x);
		if (v < 0)
		{
			*w = -v;
			return -1;
		}
		else
		{
			*w = v;
			return 1;
		}
	}

	STIX_ASSERT (stix, is_bigint(stix, x));
	return bigint_to_oow (stix, x, w);
}

int stix_inttooow (stix_t* stix, stix_oop_t x, stix_oow_t* w)
{
	if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		v = STIX_OOP_TO_SMOOI(x);
		if (v < 0)
		{
			*w = -v;
			return -1;
		}
		else
		{
			*w = v;
			return 1;
		}
	}

	if (is_bigint(stix, x)) return bigint_to_oow (stix, x, w);

	return 0; /* not convertable - too big, too small, or not an integer */
}

static STIX_INLINE stix_oop_t make_bigint_with_oow (stix_t* stix, stix_oow_t w)
{
#if (STIX_LIW_BITS == STIX_OOW_BITS)
	STIX_ASSERT (stix, STIX_SIZEOF(stix_oow_t) == STIX_SIZEOF(stix_liw_t));
	return stix_instantiate (stix, stix->_large_positive_integer, &w, 1);
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	stix_liw_t hw[2];
	hw[0] = w /*& STIX_LBMASK(stix_oow_t,STIX_LIW_BITS)*/;
	hw[1] = w >> STIX_LIW_BITS;
	return stix_instantiate (stix, stix->_large_positive_integer, &hw, (hw[1] > 0? 2: 1));
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif
}

static STIX_INLINE stix_oop_t make_bigint_with_ooi (stix_t* stix, stix_ooi_t i)
{
#if (STIX_LIW_BITS == STIX_OOW_BITS)
	stix_oow_t w;

	STIX_ASSERT (stix, STIX_SIZEOF(stix_oow_t) == STIX_SIZEOF(stix_liw_t));
	if (i >= 0)
	{
		w = i;
		return stix_instantiate (stix, stix->_large_positive_integer, &w, 1);
	}
	else
	{
		/* The caller must ensure that i is greater than the smallest value
		 * that stix_ooi_t can represent. otherwise, the absolute value 
		 * cannot be held in stix_ooi_t. */
		STIX_ASSERT (stix, i > STIX_TYPE_MIN(stix_ooi_t));
		w = -i;
		return stix_instantiate (stix, stix->_large_negative_integer, &w, 1);
	}
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	stix_liw_t hw[2];
	stix_oow_t w;

	if (i >= 0)
	{
		w = i;
		hw[0] = w /*& STIX_LBMASK(stix_oow_t,STIX_LIW_BITS)*/;
		hw[1] = w >> STIX_LIW_BITS;
		return stix_instantiate (stix, stix->_large_positive_integer, &hw, (hw[1] > 0? 2: 1));
	}
	else
	{
		STIX_ASSERT (stix, i > STIX_TYPE_MIN(stix_ooi_t));
		w = -i;
		hw[0] = w /*& STIX_LBMASK(stix_oow_t,STIX_LIW_BITS)*/;
		hw[1] = w >> STIX_LIW_BITS;
		return stix_instantiate (stix, stix->_large_negative_integer, &hw, (hw[1] > 0? 2: 1));
	}
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif
}

static STIX_INLINE stix_oop_t make_bloated_bigint_with_ooi (stix_t* stix, stix_ooi_t i, stix_oow_t extra)
{
#if (STIX_LIW_BITS == STIX_OOW_BITS)
	stix_oow_t w;
	stix_oop_t z;

	STIX_ASSERT (stix, extra <= STIX_OBJ_SIZE_MAX - 1); 
	STIX_ASSERT (stix, STIX_SIZEOF(stix_oow_t) == STIX_SIZEOF(stix_liw_t));
	if (i >= 0)
	{
		w = i;
		z =stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, 1 + extra);
	}
	else
	{
		STIX_ASSERT (stix, i > STIX_TYPE_MIN(stix_ooi_t));
		w = -i;
		z = stix_instantiate (stix, stix->_large_negative_integer, STIX_NULL, 1 + extra);
	}

	if (!z) return STIX_NULL;
	((stix_oop_liword_t)z)->slot[0] = w;
	return z;

#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	stix_liw_t hw[2];
	stix_oow_t w;
	stix_oop_t z;

	STIX_ASSERT (stix, extra <= STIX_OBJ_SIZE_MAX - 2); 
	if (i >= 0)
	{
		w = i;
		hw[0] = w /*& STIX_LBMASK(stix_oow_t,STIX_LIW_BITS)*/;
		hw[1] = w >> STIX_LIW_BITS;
		z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, (hw[1] > 0? 2: 1) + extra);
	}
	else
	{
		STIX_ASSERT (stix, i > STIX_TYPE_MIN(stix_ooi_t));
		w = -i;
		hw[0] = w /*& STIX_LBMASK(stix_oow_t,STIX_LIW_BITS)*/;
		hw[1] = w >> STIX_LIW_BITS;
		z = stix_instantiate (stix, stix->_large_negative_integer, STIX_NULL, (hw[1] > 0? 2: 1) + extra);
	}

	if (!z) return STIX_NULL;
	((stix_oop_liword_t)z)->slot[0] = hw[0];
	if (hw[1] > 0) ((stix_oop_liword_t)z)->slot[1] = hw[1];
	return z;
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif
}

static STIX_INLINE stix_oop_t make_bigint_with_intmax (stix_t* stix, stix_intmax_t v)
{
	stix_oow_t len;
	stix_liw_t buf[STIX_SIZEOF_INTMAX_T / STIX_SIZEOF_LIW_T];
	stix_uintmax_t ui;

	/* this is not a generic function. it can't handle v 
	 * if it's STIX_TYPE_MIN(stix_intmax_t) */
	STIX_ASSERT (stix, v > STIX_TYPE_MIN(stix_intmax_t));

	ui = (v >= 0)? v: -v;
	len = 0;
	do
	{
		buf[len++] = (stix_liw_t)ui;
		ui = ui >> STIX_LIW_BITS;
	}
	while (ui > 0);

	return stix_instantiate (stix, ((v >= 0)? stix->_large_positive_integer: stix->_large_negative_integer), buf, len);
}

stix_oop_t stix_oowtoint (stix_t* stix, stix_oow_t w)
{
	STIX_ASSERT (stix, STIX_TYPE_IS_UNSIGNED(stix_oow_t));
	/*if (STIX_IN_SMOOI_RANGE(w))*/
	if (w <= STIX_SMOOI_MAX)
	{
		return STIX_SMOOI_TO_OOP(w);
	}
	else
	{
		return make_bigint_with_oow(stix, w);
	}
}

static STIX_INLINE stix_oop_t expand_bigint (stix_t* stix, stix_oop_t oop, stix_oow_t inc)
{
	stix_oop_t z;
	stix_oow_t i;
	stix_oow_t count;

	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(oop));
	count = STIX_OBJ_GET_SIZE(oop);

	if (inc > STIX_OBJ_SIZE_MAX - count)
	{
		stix->errnum = STIX_EOOMEM; /* TODO: is it a soft failure or a hard failure? is this error code proper? */
		return STIX_NULL;
	}

	stix_pushtmp (stix, &oop);
	z = stix_instantiate (stix, STIX_OBJ_GET_CLASS(oop), STIX_NULL, count + inc);
	stix_poptmp (stix);
	if (!z) return STIX_NULL;

	for (i = 0; i < count; i++)
	{
		((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)oop)->slot[i];
	}
	return z;
}


static STIX_INLINE stix_oop_t _clone_bigint (stix_t* stix, stix_oop_t oop, stix_oow_t count, stix_oop_t _class)
{
	stix_oop_t z;
	stix_oow_t i;

	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(oop));
	if (count <= 0) count = STIX_OBJ_GET_SIZE(oop);

	stix_pushtmp (stix, &oop);
	z = stix_instantiate (stix, _class, STIX_NULL, count);
	stix_poptmp (stix);
	if (!z) return STIX_NULL;

	for (i = 0; i < count; i++)
	{
		((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)oop)->slot[i];
	}
	return z;
}

static STIX_INLINE stix_oop_t clone_bigint (stix_t* stix, stix_oop_t oop, stix_oow_t count)
{
	return _clone_bigint (stix, oop, count, STIX_OBJ_GET_CLASS(oop));
}

static STIX_INLINE stix_oop_t clone_bigint_negated (stix_t* stix, stix_oop_t oop, stix_oow_t count)
{
	stix_oop_t c;

	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(oop));
	if (STIX_OBJ_GET_CLASS(oop) == stix->_large_positive_integer)
	{
		c = stix->_large_negative_integer;
	}
	else
	{
		STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(oop) == stix->_large_negative_integer);
		c = stix->_large_positive_integer;
	}

	return _clone_bigint (stix, oop, count, c);
}

static STIX_INLINE stix_oop_t clone_bigint_to_positive (stix_t* stix, stix_oop_t oop, stix_oow_t count)
{
	return _clone_bigint (stix, oop, count, stix->_large_positive_integer);
}

static STIX_INLINE stix_oow_t count_effective (stix_liw_t* x, stix_oow_t xs)
{
#if 0
	while (xs > 1 && x[xs - 1] == 0) xs--;
	return xs;
#else
	while (xs > 1) { if (x[--xs]) return xs + 1; }
	return 1;
#endif
}

static STIX_INLINE stix_oow_t count_effective_digits (stix_oop_t oop)
{
	stix_oow_t i;

	for (i = STIX_OBJ_GET_SIZE(oop); i > 1; )
	{
		--i;
		if (((stix_oop_liword_t)oop)->slot[i]) return i + 1;
	}

	return 1;
}

static stix_oop_t normalize_bigint (stix_t* stix, stix_oop_t oop)
{
	stix_oow_t count;

	STIX_ASSERT (stix, STIX_OOP_IS_POINTER(oop));
	count = count_effective_digits (oop);

#if (STIX_LIW_BITS == STIX_OOW_BITS)
	if (count == 1) /* 1 word */
	{
		stix_oow_t w;

		w = ((stix_oop_liword_t)oop)->slot[0];
		if (STIX_OBJ_GET_CLASS(oop) == stix->_large_positive_integer)
		{
			if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP(w);
		}
		else
		{
			STIX_ASSERT (stix, -STIX_SMOOI_MAX  == STIX_SMOOI_MIN);
			STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(oop) == stix->_large_negative_integer);
			if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP(-(stix_ooi_t)w);
		}
	}
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)

	if (count == 1) /* 1 half-word */
	{
		if (STIX_OBJ_GET_CLASS(oop) == stix->_large_positive_integer)
		{
			return STIX_SMOOI_TO_OOP(((stix_oop_liword_t)oop)->slot[0]);
		}
		else
		{
			STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(oop) == stix->_large_negative_integer);
			return STIX_SMOOI_TO_OOP(-(stix_ooi_t)((stix_oop_liword_t)oop)->slot[0]);
		}
	}
	else if (count == 2) /* 2 half-words */
	{
		stix_oow_t w;

		w = MAKE_WORD (((stix_oop_liword_t)oop)->slot[0], ((stix_oop_liword_t)oop)->slot[1]);
		if (STIX_OBJ_GET_CLASS(oop) == stix->_large_positive_integer)
		{
			if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP(w);
		}
		else
		{
			STIX_ASSERT (stix, -STIX_SMOOI_MAX  == STIX_SMOOI_MIN);
			STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(oop) == stix->_large_negative_integer);
			if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP(-(stix_ooi_t)w);
		}
	}
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif
	if (STIX_OBJ_GET_SIZE(oop) == count)
	{
		/* no compaction is needed. return it as it is */
		return oop;
	}

	return clone_bigint (stix, oop, count);
}

static STIX_INLINE int is_less_unsigned_array (const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys)
{
	stix_oow_t i;

	if (xs != ys) return xs < ys;
	for (i = xs; i > 0; )
	{
		--i;
		if (x[i] != y[i]) return x[i] < y[i];
	}

	return 0;
}

static STIX_INLINE int is_less_unsigned (stix_oop_t x, stix_oop_t y)
{
	return is_less_unsigned_array (
		((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x), 
		((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y));
}

static STIX_INLINE int is_less (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OBJ_GET_CLASS(x) != STIX_OBJ_GET_CLASS(y))
	{
		return STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer;
	}

	if (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)
	{
		return is_less_unsigned (x, y);
	}
	else
	{
		return is_less_unsigned (y, x);
	}
}

static STIX_INLINE int is_greater_unsigned_array (const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys)
{
	stix_oow_t i;

	if (xs != ys) return xs > ys;
	for (i = xs; i > 0; )
	{
		--i;
		if (x[i] != y[i]) return x[i] > y[i];
	}

	return 0;
}

static STIX_INLINE int is_greater_unsigned (stix_oop_t x, stix_oop_t y)
{
	return is_greater_unsigned_array (
		((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x), 
		((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y));
}

static STIX_INLINE int is_greater (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OBJ_GET_CLASS(x) != STIX_OBJ_GET_CLASS(y))
	{
		return STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer;
	}

	if (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)
	{
		return is_greater_unsigned (x, y);
	}
	else
	{
		return is_greater_unsigned (y, x);
	}
}

static STIX_INLINE int is_equal (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	/* check if two large integers are equal to each other */
	return STIX_OBJ_GET_CLASS(x) == STIX_OBJ_GET_CLASS(y) && STIX_OBJ_GET_SIZE(x) == STIX_OBJ_GET_SIZE(y) &&
	       STIX_MEMCMP(((stix_oop_liword_t)x)->slot,  ((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(x) * STIX_SIZEOF(stix_liw_t)) == 0;
}

static void complement2_unsigned_array (stix_t* stix, const stix_liw_t* x, stix_oow_t xs, stix_liw_t* z)
{
	stix_oow_t i;
	stix_lidw_t w;
	stix_lidw_t carry;

	/* get 2's complement (~x + 1) */

	carry = 1; 
	for (i = 0; i < xs; i++)
	{
		w = (stix_lidw_t)(~x[i]) + carry;
		/*w = (stix_lidw_t)(x[i] ^ (~(stix_liw_t)0)) + carry;*/
		carry = w >> STIX_LIW_BITS;
		z[i] = w;
	}

	/* if the array pointed to by x contains all zeros, carry will be
	 * 1 here and it actually requires 1 more slot. Let't take this 8-bit
	 * zero for instance:
	 *    2r00000000  -> 2r11111111 + 1 => 2r0000000100000000
	 * 
	 * this function is not designed to handle such a case.
	 * in fact, 0 is a small integer and it must not stand a change 
	 * to be given to this function */
	STIX_ASSERT (stix, carry == 0);
}

static STIX_INLINE stix_oow_t add_unsigned_array (const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys, stix_liw_t* z)
{
#if 1
	register stix_oow_t i;
	stix_lidw_t w;

	if (xs < ys)
	{
		/* swap x and y */
		i = xs;
		xs = ys;
		ys = i;

		i = (stix_oow_t)x;
		x = y;
		y = (stix_liw_t*)i;
	}

	w = 0;
	i = 0;
	while (i < ys)
	{
		w += (stix_lidw_t)x[i] + (stix_lidw_t)y[i];
		z[i++] = w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS);
		w >>= STIX_LIW_BITS;
	}

	while (w && i < xs)
	{
		w += x[i];
		z[i++] = w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS);
		w >>= STIX_LIW_BITS;
	}

	while (i < xs)
	{
		z[i] = x[i];
		i++;
	}
	if (w) z[i++] = w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS);
	return i;

#else
	register stix_oow_t i;
	stix_lidw_t w;
	stix_liw_t carry = 0;

	if (xs < ys)
	{
		/* swap x and y */
		i = xs;
		xs = ys;
		ys = i;

		i = (stix_oow_t)x;
		x = y;
		y = (stix_liw_t*)i;
	}


	for (i = 0; i < ys; i++)
	{
		w = (stix_lidw_t)x[i] + (stix_lidw_t)y[i] + carry;
		carry = w >> STIX_LIW_BITS;
		z[i] = w /*& STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS) */;
	}

	if (x == z)
	{
		for (; carry && i < xs; i++)
		{
			w = (stix_lidw_t)x[i] + carry;
			carry = w >> STIX_LIW_BITS;
			z[i] = w /*& STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS) */;
		}
		i = xs;
	}
	else
	{
		for (; i < xs; i++)
		{
			w = (stix_lidw_t)x[i] + carry;
			carry = w >> STIX_LIW_BITS;
			z[i] = w /*& STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS)*/;
		}
	}

	if (carry) z[i++] = carry;
	return i; /* the number of effective digits in the result */
#endif
}

static STIX_INLINE stix_oow_t subtract_unsigned_array (stix_t* stix, const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys, stix_liw_t* z)
{
#if 1
	stix_oow_t i;
	stix_lidi_t w = 0;

	if (x == y)
	{
		STIX_ASSERT (stix, xs == ys);
		z[0] = 0;
		return 1;
	}

	STIX_ASSERT (stix, !is_less_unsigned_array(x, xs, y, ys));

	for (i = 0; i < ys; i++)
	{
		w += (stix_lidi_t)x[i] - (stix_lidi_t)y[i];
		z[i] = w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS);
		w >>= STIX_LIW_BITS;
	}

	while (w && i < xs)
	{
		w += x[i];
		z[i++] = w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS);
		w >>= STIX_LIW_BITS;
	}

	while (i < xs)
	{
		z[i] = x[i];
		i++;
	}

	while (i > 1 && z[i - 1] == 0) i--;
	return i;

#else
	stix_oow_t i;
	stix_lidw_t w;
	stix_lidw_t borrow = 0;
	stix_lidw_t borrowed_word;

	if (x == y)
	{
		STIX_ASSERT (stix, xs == ys);
		z[0] = 0;
		return 1;
	}

	STIX_ASSERT (stix, !is_less_unsigned_array(x, xs, y, ys));

	borrowed_word = (stix_lidw_t)1 << STIX_LIW_BITS;
	for (i = 0; i < ys; i++)
	{
		w = (stix_lidw_t)y[i] + borrow;
		if ((stix_lidw_t)x[i] >= w)
		{
			z[i] = x[i] - w;
			borrow = 0;
		}
		else
		{
			z[i] = (borrowed_word + (stix_lidw_t)x[i]) - w; 
			borrow = 1;
		}
	}

	for (; i < xs; i++)
	{
		if (x[i] >= borrow) 
		{
			z[i] = x[i] - (stix_liw_t)borrow;
			borrow = 0;
		}
		else
		{
			z[i] = (borrowed_word + (stix_lidw_t)x[i]) - borrow;
			borrow = 1;
		}
	}

	STIX_ASSERT (stix, borrow == 0);

	while (i > 1 && z[i - 1] == 0) i--;
	return i; /* the number of effective digits in the result */
#endif
}

static STIX_INLINE void multiply_unsigned_array (const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys, stix_liw_t* z)
{
	stix_lidw_t v;
	stix_oow_t pa;

	if (xs < ys)
	{
		stix_oow_t i;

		/* swap x and y */
		i = xs;
		xs = ys;
		ys = i;

		i = (stix_oow_t)x;
		x = y;
		y = (stix_liw_t*)i;
	}

	pa = xs;
	if (pa <= ((stix_oow_t)1 << (STIX_LIDW_BITS - (STIX_LIW_BITS * 2))))
	{
		/* Comba(column-array) multiplication */

		/* when the input length is too long, v may overflow. if it
		 * happens, comba's method doesn't work as carry propagation is
		 * affected badly. so we need to use this method only if
		 * the input is short enough. */

		stix_oow_t pa, ix, iy, iz, tx, ty;

		pa = xs + ys;
		v = 0;
		for (ix = 0; ix < pa; ix++)
		{
			ty = (ix < ys - 1)? ix: (ys - 1);
			tx = ix - ty;
			iy = (ty + 1 < xs - tx)? (ty + 1): (xs - tx);

			for (iz = 0; iz < iy; iz++)
			{
				v = v + (stix_lidw_t)x[tx + iz] * (stix_lidw_t)y[ty - iz];
			}

			z[ix] = (stix_liw_t)v;
			v = v >> STIX_LIW_BITS;
		}
	}
	else
	{
		stix_oow_t i, j;
		stix_liw_t carry;

		for (i = 0; i < xs; i++)
		{
			if (x[i] == 0)
			{
				z[i + ys] = 0;
			}
			else
			{
				carry = 0;

				for (j = 0; j < ys; j++)
				{
					v = (stix_lidw_t)x[i] * (stix_lidw_t)y[j] + (stix_lidw_t)carry + (stix_lidw_t)z[i + j];
					z[i + j] = (stix_liw_t)v;
					carry = (stix_liw_t)(v >> STIX_LIW_BITS);
				}

				z[i + j] = carry;
			}
		}
	}
}

/* KARATSUBA MULTIPLICATION
 * 
 * c = |a| * |b|
 *
 * Let B represent the radix(2^DIGIT_BITS)
 * Let n represent half the number of digits
 *
 * a = a1 * B^n + a0
 * b = b1 * B^n + b0
 * a * b => a1b1 * B^2n + ((a1 + a0)(b1 + b0) - (a0b0 + a1b1)) * B^n + a0b0
 *
 * --------------------------------------------------------------------
 * For example, for 2 number 0xFAC2 and 0xABCD => A848635A
 *   DIGIT_BITS = 8 (1 byte, each digit is 1 byte long)
 *   B = 2^8 = 0x100
 *   n = 1 (half the digits of 2 digit numbers)
 *   B^n = 0x100 ^ 1 = 0x100
 *   B^2n = 0x100 ^ 2 = 0x10000
 *   0xFAC2 = 0xFA * 0x100 + 0xC2
 *   0xABCD = 0xAB * 0x100 + 0xCD
 *   a1 = 0xFA, a0 = 0xC2
 *   b1 = 0xAB, b0 = 0xCD
 *   a1b1 = 0xFA * 0xAB = 0xA6FE
 *   a0b0 = 0xC2 * 0xCD = 0x9B5A
 *   a1 + a0 = 0xFA + 0xC2 = 0x1BC
 *   b1 + b0 = 0xAB + 0xCD = 0x178
 * --------------------------------------------------------------------
 *   (A6FE * 10000) + (((1BC * 178) - (985A + A6FE)) * 100) + 9B5A =
 *   (A6FE << (8 * 2)) + (((1BC * 178) - (985A + A6FE)) << (8 * 1)) =
 *   A6FE0000 + 14CC800 + 9B5A = 9848635A 
 * --------------------------------------------------------------------
 *
 * 0xABCD9876 * 0xEFEFABAB => 0xA105C97C9755A8D2
 * B = 2^8 = 0x100
 * n = 2
 * B^n = 0x100 ^ 2 = 0x10000
 * B^2n = 0x100 ^ 4 = 0x100000000
 * 0xABCD9876 = 0xABCD * 0x10000 + 0x9876
 * 0xEFEFABAB = 0xEFEF * 0x10000 + 0xABAB
 * a1 = 0xABCD, a0 = 0x9876
 * b1 - 0xEFEF, b0 = 0xABAB
 * a1b1 = 0xA104C763
 * a0b0 = 0x663CA8D2
 * a1 + a0 = 0x14443
 * b1 + b0 = 0x19B9A
 * --------------------------------------------------------------------
 * (A104C763 * 100000000) + (((14443 * 19B9A) - (663CA8D2 + A104C763)) * 10000) + 663CA8D2 =
 * (A104C763 << (8 * 4)) + (((14443 * 19B9A) - (663CA8D2 + A104C763)) << (8 * 2)) + 663CA8D2 = A105C97C9755A8D2
 * --------------------------------------------------------------------
 *
 *  Multiplying by B is t same as shifting by DIGIT_BITS.
 *  DIGIT_BITS in this implementation is STIX_LIW_BITS
 *  B => 2^STIX_LIW_BITS
 *  X * B^n => X << (STIX_LIW_BITS * n)
 *  X * B^2n => X << (STIX_LIW_BITS * n * 2)
 * --------------------------------------------------------------------
 */
#define CANNOT_KARATSUBA(xs, ys) \
	((xs) < KARATSUBA_CUTOFF || (ys) < KARATSUBA_CUTOFF || \
	((xs) > (ys) && (ys) <= (((xs) + 1) / 2)) || \
	((xs) < (ys) && (xs) <= (((ys) + 1) / 2)))

static STIX_INLINE stix_oow_t multiply_unsigned_array_karatsuba (stix_t* stix, const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys, stix_liw_t* z)
{
#if 1
	stix_lidw_t nshifts;
	stix_lidw_t ndigits_xh, ndigits_xl;
	stix_lidw_t ndigits_yh, ndigits_yl;
	stix_liw_t* tmp[2] = { STIX_NULL, STIX_NULL};
	stix_liw_t* zsp; 
	stix_oow_t tmplen[2];
	stix_oow_t xlen, zcapa;

	zcapa = xs + ys; /* the caller ensures this capacity for z at the minimum*/

	if (xs < ys)
	{
		stix_oow_t i;

		/* swap x and y */
		i = xs;
		xs = ys;
		ys = i;

		i = (stix_oow_t)x;
		x = y;
		y = (stix_liw_t*)i;
	}

	/* calculate value of nshifts, that is 2^(STIX_LIW_BITS*nshifts) */
	nshifts = (xs + 1) / 2;

	ndigits_xl = nshifts; /* ndigits of lower part of x */
	ndigits_xh = xs - nshifts; /* ndigits of upper part of x */
	ndigits_yl = nshifts; /* ndigits of lower part of y */
	ndigits_yh = ys - nshifts; /* ndigits of uppoer part of y */

	STIX_ASSERT (stix, ndigits_xl >= ndigits_xh);
	STIX_ASSERT (stix, ndigits_yl >= ndigits_yh);

	/* make a temporary buffer for (b0 + b1) and (a1 * b1) */
	tmplen[0] = ndigits_xh + ndigits_yh;
	tmplen[1] = ndigits_yl + ndigits_yh + 1; 
	if (tmplen[1] < tmplen[0]) tmplen[1] = tmplen[0];
	tmp[1] = stix_callocmem (stix, STIX_SIZEOF(stix_liw_t) * tmplen[1]); /* TODO: should i use the object memory? */
	if (!tmp[1]) goto oops;

	/* make a temporary for (a0 + a1) and (a0 * b0) */
	tmplen[0] = ndigits_xl + ndigits_yl + 1;
	tmp[0] = stix_callocmem (stix, STIX_SIZEOF(stix_liw_t) * tmplen[0]);
	if (!tmp[0]) goto oops;

	/* tmp[0] = a0 + a1 */
	tmplen[0] = add_unsigned_array (x, ndigits_xl, x + nshifts, ndigits_xh, tmp[0]);

	/* tmp[1] = b0 + b1 */
	tmplen[1] = add_unsigned_array (y, ndigits_yl, y + nshifts, ndigits_yh, tmp[1]);

	/*STIX_DEBUG6 (stix, "karatsuba t %p u %p ndigits_xl %d ndigits_xh %d ndigits_yl %d ndigits_yh %d\n", tmp[0], tmp[1], (int)ndigits_xl, (int)ndigits_xh, (int)ndigits_yl, (int)ndigits_yh);*/
	/*STIX_DEBUG5 (stix, "zcapa %d, tmplen[0] %d tmplen[1] %d nshifts %d total %d\n", (int)zcapa, (int)tmplen[0], (int)tmplen[1], (int)nshifts, (int)(tmplen[0] + tmplen[1] + nshifts));*/

	/* place (a0 + a1) * (b0 + b1) at the shifted position */
	zsp = z + nshifts;
	if (CANNOT_KARATSUBA(tmplen[0], tmplen[1]))
	{
		multiply_unsigned_array (tmp[0], tmplen[0], tmp[1], tmplen[1], zsp);
		xlen = count_effective (zsp, tmplen[0] + tmplen[1]);
	}
	else 
	{
		xlen = multiply_unsigned_array_karatsuba(stix, tmp[0], tmplen[0], tmp[1], tmplen[1], zsp);
		if (xlen == 0) goto oops;
	}

	/* tmp[0] = a0 * b0 */
	tmplen[0] = ndigits_xl + ndigits_yl;
	STIX_MEMSET (tmp[0], 0, sizeof(stix_liw_t) * tmplen[0]);
	if (CANNOT_KARATSUBA(ndigits_xl, ndigits_yl))
	{
		multiply_unsigned_array (x, ndigits_xl, y, ndigits_yl, tmp[0]);
		tmplen[0] = count_effective(tmp[0], tmplen[0]);
	}
	else
	{
		tmplen[0] = multiply_unsigned_array_karatsuba (stix, x, ndigits_xl, y, ndigits_yl, tmp[0]);
		if (tmplen[0] <= 0) goto oops;
	}

	/* tmp[1] = a1 * b1 */
	tmplen[1] = ndigits_xh + ndigits_yh;
	STIX_MEMSET (tmp[1], 0, sizeof(stix_liw_t) * tmplen[1]);
	if (CANNOT_KARATSUBA(ndigits_xh, ndigits_yh))
	{
		multiply_unsigned_array (x + nshifts, ndigits_xh, y + nshifts, ndigits_yh, tmp[1]);
		tmplen[1] = count_effective (tmp[1], tmplen[1]);
	}
	else
	{
		tmplen[1] = multiply_unsigned_array_karatsuba (stix, x + nshifts, ndigits_xh, y + nshifts, ndigits_yh, tmp[1]);
		if (tmplen[1] <= 0) goto oops;
	}

	/* (a0+a1)*(b0+b1) -(a0*b0) */
	xlen = subtract_unsigned_array(stix, zsp, xlen, tmp[0], tmplen[0], zsp);

	/* (a0+a1)*(b0+b1) - (a0*b0) - (a1*b1) */
	xlen = subtract_unsigned_array(stix, zsp, xlen, tmp[1], tmplen[1], zsp);
	/* a1b1 is in tmp[1]. add (a1b1 * B^2n) to the high part of 'z' */
	zsp = z + (nshifts * 2); /* emulate shifting for "* B^2n". */
	xlen = zcapa - (nshifts * 2);
	xlen = add_unsigned_array (zsp, xlen, tmp[1], tmplen[1], zsp);

	/* z = z + a0b0. a0b0 is in tmp[0] */
	xlen = add_unsigned_array(z, zcapa, tmp[0], tmplen[0], z);

	stix_freemem (stix, tmp[1]);
	stix_freemem (stix, tmp[0]);
	return count_effective (z, xlen);

oops:
	if (tmp[1]) stix_freemem (stix, tmp[1]);
	if (tmp[0]) stix_freemem (stix, tmp[0]);
	return 0;

#else
	stix_lidw_t nshifts;
	stix_lidw_t ndigits_xh, ndigits_xl;
	stix_lidw_t ndigits_yh, ndigits_yl;
	stix_liw_t* tmp[3] = { STIX_NULL, STIX_NULL, STIX_NULL };
	stix_liw_t* zsp; 
	stix_oow_t tmplen[3];
	stix_oow_t xlen, zcapa;

	zcapa = xs + ys; /* the caller ensures this capacity for z at the minimum*/

	if (xs < ys)
	{
		stix_oow_t i;

		/* swap x and y */
		i = xs;
		xs = ys;
		ys = i;

		i = (stix_oow_t)x;
		x = y;
		y = (stix_liw_t*)i;
	}

	/* calculate value of nshifts, that is 2^(STIX_LIW_BITS*nshifts) */
	nshifts = (xs + 1) / 2;

	ndigits_xl = nshifts; /* ndigits of lower part of x */
	ndigits_xh = xs - nshifts; /* ndigits of upper part of x */
	ndigits_yl = nshifts; /* ndigits of lower part of y */
	ndigits_yh = ys - nshifts; /* ndigits of uppoer part of y */

	STIX_ASSERT (stix, ndigits_xl >= ndigits_xh);
	STIX_ASSERT (stix, ndigits_yl >= ndigits_yh);

	/* make a temporary buffer for (b0 + b1) and (a1 * b1) */
	tmplen[0] = ndigits_yl + ndigits_yh + 1; 
	tmplen[1] = ndigits_xh + ndigits_yh;
	if (tmplen[1] < tmplen[0]) tmplen[1] = tmplen[0];
	tmp[1] = stix_callocmem (stix, STIX_SIZEOF(stix_liw_t) * tmplen[1]);
	if (!tmp[1]) goto oops;

	/* make a temporary for (a0 + a1) and (a0 * b0) */
	tmplen[0] = ndigits_xl + ndigits_yl;
	tmp[0] = stix_callocmem (stix, STIX_SIZEOF(stix_liw_t) * tmplen[0]);
	if (!tmp[0]) goto oops;

	/* tmp[0] = a0 + a1 */
	tmplen[0] = add_unsigned_array (x, ndigits_xl, x + nshifts, ndigits_xh, tmp[0]);

	/* tmp[1] = b0 + b1 */
	tmplen[1] = add_unsigned_array (y, ndigits_yl, y + nshifts, ndigits_yh, tmp[1]);

	/* tmp[2] = (a0 + a1) * (b0 + b1) */
	tmplen[2] = tmplen[0] + tmplen[1]; 
	tmp[2] = stix_callocmem (stix, STIX_SIZEOF(stix_liw_t) * tmplen[2]);
	if (!tmp[2]) goto oops;
	if (CANNOT_KARATSUBA(tmplen[0], tmplen[1]))
	{
		multiply_unsigned_array (tmp[0], tmplen[0], tmp[1], tmplen[1], tmp[2]);
		xlen = count_effective (tmp[2], tmplen[2]);
	}
	else 
	{
		xlen = multiply_unsigned_array_karatsuba(stix, tmp[0], tmplen[0], tmp[1], tmplen[1], tmp[2]);
		if (xlen == 0) goto oops;
	}

	/* tmp[0] = a0 * b0 */
	tmplen[0] = ndigits_xl + ndigits_yl;
	STIX_MEMSET (tmp[0], 0, sizeof(stix_liw_t) * tmplen[0]);
	if (CANNOT_KARATSUBA(ndigits_xl, ndigits_yl))
	{
		multiply_unsigned_array (x, ndigits_xl, y, ndigits_yl, tmp[0]);
		tmplen[0] = count_effective(tmp[0], tmplen[0]);
	}
	else
	{
		tmplen[0] = multiply_unsigned_array_karatsuba (stix, x, ndigits_xl, y, ndigits_yl, tmp[0]);
		if (tmplen[0] <= 0) goto oops;
	}

	/* tmp[1] = a1 * b1 */
	tmplen[1] = ndigits_xh + ndigits_yh;
	STIX_MEMSET (tmp[1], 0, sizeof(stix_liw_t) * tmplen[1]);
	if (CANNOT_KARATSUBA(ndigits_xh, ndigits_yh))
	{
		multiply_unsigned_array (x + nshifts, ndigits_xh, y + nshifts, ndigits_yh, tmp[1]);
		tmplen[1] = count_effective (tmp[1], tmplen[1]);
	}
	else
	{
		tmplen[1] = multiply_unsigned_array_karatsuba (stix, x + nshifts, ndigits_xh, y + nshifts, ndigits_yh, tmp[1]);
		if (tmplen[1] <= 0) goto oops;
	}

	/* w = w - tmp[0] */
	xlen = subtract_unsigned_array(stix, tmp[2], xlen, tmp[0], tmplen[0], tmp[2]);

	/* r = w - tmp[1] */
	zsp = z + nshifts; /* emulate shifting for "* B^n" */
	xlen = subtract_unsigned_array(stix, tmp[2], xlen, tmp[1], tmplen[1], zsp);

	/* a1b1 is in tmp[1]. add (a1b1 * B^2n) to the high part of 'z' */
	zsp = z + (nshifts * 2); /* emulate shifting for "* B^2n". */
	xlen = zcapa - (nshifts * 2);
	xlen = add_unsigned_array (zsp, xlen, tmp[1], tmplen[1], zsp);

	/* z = z + a0b0. a0b0 is in tmp[0] */
	xlen = add_unsigned_array(z, zcapa, tmp[0], tmplen[0], z);

	stix_freemem (stix, tmp[2]);
	stix_freemem (stix, tmp[1]);
	stix_freemem (stix, tmp[0]);

	return count_effective (z, xlen);

oops:
	if (tmp[2]) stix_freemem (stix, tmp[2]);
	if (tmp[1]) stix_freemem (stix, tmp[1]);
	if (tmp[0]) stix_freemem (stix, tmp[0]);
	return 0;
#endif
}

static STIX_INLINE void lshift_unsigned_array (stix_liw_t* x, stix_oow_t xs, stix_oow_t bits)
{
	/* this function doesn't grow/shrink the array. Shifting is performed
	 * over the given array */

	stix_oow_t word_shifts, bit_shifts, bit_shifts_right;
	stix_oow_t si, di;

	/* get how many words to shift */
	word_shifts = bits / STIX_LIW_BITS;
	if (word_shifts >= xs)
	{
		STIX_MEMSET (x, 0, xs * STIX_SIZEOF(stix_liw_t));
		return;
	}

	/* get how many remaining bits to shift */
	bit_shifts = bits % STIX_LIW_BITS;
	bit_shifts_right = STIX_LIW_BITS - bit_shifts;

	/* shift words and bits */
	di = xs - 1;
	si = di - word_shifts;
	x[di] = x[si] << bit_shifts;
	while (di > word_shifts)
	{
		x[di] = x[di] | (x[--si] >> bit_shifts_right);
		x[--di] = x[si] << bit_shifts;
	}

	/* fill the remaining part with zeros */
	if (word_shifts > 0)
		STIX_MEMSET (x, 0, word_shifts * STIX_SIZEOF(stix_liw_t));
}

static STIX_INLINE void rshift_unsigned_array (stix_liw_t* x, stix_oow_t xs, stix_oow_t bits)
{
	/* this function doesn't grow/shrink the array. Shifting is performed
	 * over the given array */

	stix_oow_t word_shifts, bit_shifts, bit_shifts_left;
	stix_oow_t si, di, bound;

	/* get how many words to shift */
	word_shifts = bits / STIX_LIW_BITS;
	if (word_shifts >= xs)
	{
		STIX_MEMSET (x, 0, xs * STIX_SIZEOF(stix_liw_t));
		return;
	}

	/* get how many remaining bits to shift */
	bit_shifts = bits % STIX_LIW_BITS;
	bit_shifts_left = STIX_LIW_BITS - bit_shifts;

/* TODO: verify this function */
	/* shift words and bits */
	di = 0;
	si = word_shifts;
	x[di] = x[si] >> bit_shifts;
	bound = xs - word_shifts - 1;
	while (di < bound)
	{
		x[di] = x[di] | (x[++si] << bit_shifts_left);
		x[++di] = x[si] >> bit_shifts;
	}

	/* fill the remaining part with zeros */
	if (word_shifts > 0)
		STIX_MEMSET (&x[xs - word_shifts], 0, word_shifts * STIX_SIZEOF(stix_liw_t));
}

static void divide_unsigned_array (stix_t* stix, const stix_liw_t* x, stix_oow_t xs, const stix_liw_t* y, stix_oow_t ys, stix_liw_t* q, stix_liw_t* r)
{
/* TODO: this function needs to be rewritten for performance improvement. 
 *       the binary long division is extremely slow for a big number */

	/* Perform binary long division.
	 * http://en.wikipedia.org/wiki/Division_algorithm
	 * ---------------------------------------------------------------------
	 * Q := 0                 initialize quotient and remainder to zero
	 * R := 0                     
	 * for i = n-1...0 do     where n is number of bits in N
	 *   R := R << 1          left-shift R by 1 bit    
	 *   R(0) := X(i)         set the least-significant bit of R equal to bit i of the numerator
	 *   if R >= Y then
	 *     R = R - Y               
	 *     Q(i) := 1
	 *   end
	 * end 
	 */

	stix_oow_t rs, i , j;

	STIX_ASSERT (stix, xs >= ys);
	STIX_MEMSET (q, 0, STIX_SIZEOF(*q) * xs);
	STIX_MEMSET (r, 0, STIX_SIZEOF(*q) * xs);

	for (i = xs; i > 0; )
	{
		--i;
		for (j = STIX_LIW_BITS; j > 0;)
		{
			--j;

			lshift_unsigned_array (r, xs, 1);
			STIX_SETBITS (stix_liw_t, r[0], 0, 1, STIX_GETBITS(stix_liw_t, x[i], j, 1));

			rs = count_effective (r, xs);
			if (!is_less_unsigned_array (r, rs, y, ys))
			{
				subtract_unsigned_array (stix, r, rs, y, ys, r);
				STIX_SETBITS (stix_liw_t, q[i], j, 1, 1);
			}
		}
	}
}

static stix_oop_t add_unsigned_integers (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oow_t as, bs, zs;
	stix_oop_t z;

	as = STIX_OBJ_GET_SIZE(x);
	bs = STIX_OBJ_GET_SIZE(y);
	zs = (as >= bs? as: bs);

	if (zs >= STIX_OBJ_SIZE_MAX)
	{
		stix->errnum = STIX_EOOMEM; /* TOOD: is it a soft failure or hard failure? */
		return STIX_NULL;
	}
	zs++;

	stix_pushtmp (stix, &x);
	stix_pushtmp (stix, &y);
	z = stix_instantiate (stix, STIX_OBJ_GET_CLASS(x), STIX_NULL, zs);
	stix_poptmps (stix, 2);
	if (!z) return STIX_NULL;

	add_unsigned_array (
		((stix_oop_liword_t)x)->slot, as,
		((stix_oop_liword_t)y)->slot, bs,
		((stix_oop_liword_t)z)->slot
	);

	return z;
}

static stix_oop_t subtract_unsigned_integers (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;

	STIX_ASSERT (stix, !is_less_unsigned(x, y));

	stix_pushtmp (stix, &x);
	stix_pushtmp (stix, &y);
	z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, STIX_OBJ_GET_SIZE(x));
	stix_poptmps (stix, 2);
	if (!z) return STIX_NULL;

	subtract_unsigned_array (stix, 
		((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x),
		((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y),
		((stix_oop_liword_t)z)->slot);
	return z;
}

static stix_oop_t multiply_unsigned_integers (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;
	stix_oow_t xs, ys;

	xs = STIX_OBJ_GET_SIZE(x);
	ys = STIX_OBJ_GET_SIZE(y);

	if (ys > STIX_OBJ_SIZE_MAX - xs)
	{
		stix->errnum = STIX_EOOMEM; /* TOOD: is it a soft failure or hard failure? */
		return STIX_NULL;
	}

	stix_pushtmp (stix, &x);
	stix_pushtmp (stix, &y);
	z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, xs + ys);
	stix_poptmps (stix, 2);
	if (!z) return STIX_NULL;

#if defined(ENABLE_KARATSUBA)
	if (CANNOT_KARATSUBA (xs, ys))
	{
#endif
		multiply_unsigned_array (
			((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x),
			((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y),
			((stix_oop_liword_t)z)->slot);
#if defined(ENABLE_KARATSUBA)
	}
	else
	{
		if (multiply_unsigned_array_karatsuba (
			stix,
			((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x),
			((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y),
			((stix_oop_liword_t)z)->slot) == 0) return STIX_NULL;
	}
#endif
	return z;
}

static stix_oop_t divide_unsigned_integers (stix_t* stix, stix_oop_t x, stix_oop_t y, stix_oop_t* r)
{
	stix_oop_t qq, rr;

	/* the caller must ensure that x >= y */
	STIX_ASSERT (stix, !is_less_unsigned (x, y)); 
	stix_pushtmp (stix, &x);
	stix_pushtmp (stix, &y);
	qq = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, STIX_OBJ_GET_SIZE(x));
	if (!qq) 
	{
		stix_poptmps (stix, 2);
		return STIX_NULL;
	}

	stix_pushtmp (stix, &qq);
	rr = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, STIX_OBJ_GET_SIZE(x));
	stix_poptmps (stix, 3);
	if (!rr) return STIX_NULL;

	divide_unsigned_array (stix,
		((stix_oop_liword_t)x)->slot, STIX_OBJ_GET_SIZE(x),
		((stix_oop_liword_t)y)->slot, STIX_OBJ_GET_SIZE(y),
		((stix_oop_liword_t)qq)->slot, ((stix_oop_liword_t)rr)->slot);

	*r = rr;
	return qq;
}

stix_oop_t stix_addints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t i;

		/* no integer overflow/underflow must occur as the possible integer
		 * range is narrowed by the tag bits used */
		STIX_ASSERT (stix, STIX_SMOOI_MAX + STIX_SMOOI_MAX < STIX_TYPE_MAX(stix_ooi_t));
		STIX_ASSERT (stix, STIX_SMOOI_MIN + STIX_SMOOI_MIN > STIX_TYPE_MIN(stix_ooi_t));

		i = STIX_OOP_TO_SMOOI(x) + STIX_OOP_TO_SMOOI(y);
		if (STIX_IN_SMOOI_RANGE(i)) return STIX_SMOOI_TO_OOP(i);

		return make_bigint_with_ooi (stix, i);
	}
	else
	{
		stix_ooi_t v;

		if (STIX_OOP_IS_SMOOI(x))
		{
			if (!is_bigint(stix,y)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(x);
			if (v == 0) return clone_bigint (stix, y, STIX_OBJ_GET_SIZE(y));

			stix_pushtmp (stix, &y);
			x = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!x) return STIX_NULL;
		}
		else if (STIX_OOP_IS_SMOOI(y))
		{
			if (!is_bigint(stix,x)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(y);
			if (v == 0) return clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));

			stix_pushtmp (stix, &x);
			y = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!y) return STIX_NULL;
		}
		else
		{
			if (!is_bigint(stix,x)) goto oops_einval;
			if (!is_bigint(stix,y)) goto oops_einval;
		}

		if (STIX_OBJ_GET_CLASS(x) != STIX_OBJ_GET_CLASS(y))
		{
			if (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)
			{
				/* x is negative, y is positive */
				if (is_less_unsigned (x, y))
				{
					z = subtract_unsigned_integers (stix, y, x);
					if (!z) return STIX_NULL;
				}
				else
				{
					z = subtract_unsigned_integers (stix, x, y);
					if (!z) return STIX_NULL;
					STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
				}
			}
			else
			{
				/* x is positive, y is negative */
				if (is_less_unsigned (x, y))
				{
					z = subtract_unsigned_integers (stix, y, x);
					if (!z) return STIX_NULL;
					STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
				}
				else
				{
					z = subtract_unsigned_integers (stix, x, y);
					if (!z) return STIX_NULL;
				}
			}
		}
		else
		{
			int neg;
			/* both are positive or negative */
			neg = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer); 
			z = add_unsigned_integers (stix, x, y);
			if (!z) return STIX_NULL;
			if (neg) STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
		}
	}

	return normalize_bigint (stix, z);

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_subints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t i;

		/* no integer overflow/underflow must occur as the possible integer
		 * range is narrowed by the tag bits used */
		STIX_ASSERT (stix, STIX_SMOOI_MAX - STIX_SMOOI_MIN < STIX_TYPE_MAX(stix_ooi_t));
		STIX_ASSERT (stix, STIX_SMOOI_MIN - STIX_SMOOI_MAX > STIX_TYPE_MIN(stix_ooi_t));

		i = STIX_OOP_TO_SMOOI(x) - STIX_OOP_TO_SMOOI(y);
		if (STIX_IN_SMOOI_RANGE(i)) return STIX_SMOOI_TO_OOP(i);

		return make_bigint_with_ooi (stix, i);
	}
	else
	{
		stix_ooi_t v;
		int neg;

		if (STIX_OOP_IS_SMOOI(x))
		{
			if (!is_bigint(stix,y)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(x);
			if (v == 0) 
			{
				/* switch the sign to the opposite and return it */
				return clone_bigint_negated (stix, y, STIX_OBJ_GET_SIZE(y));
			}

			stix_pushtmp (stix, &y);
			x = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!x) return STIX_NULL;
		}
		else if (STIX_OOP_IS_SMOOI(y))
		{
			if (!is_bigint(stix,x)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(y);
			if (v == 0) return clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));

			stix_pushtmp (stix, &x);
			y = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!y) return STIX_NULL;
		}
		else
		{
			if (!is_bigint(stix,x)) goto oops_einval;
			if (!is_bigint(stix,y)) goto oops_einval;
		}

		if (STIX_OBJ_GET_CLASS(x) != STIX_OBJ_GET_CLASS(y))
		{
			neg = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer); 
			z = add_unsigned_integers (stix, x, y);
			if (!z) return STIX_NULL;
			if (neg) STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
		}
		else
		{
			/* both are positive or negative */
			if (is_less_unsigned (x, y))
			{
				neg = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer);
				z = subtract_unsigned_integers (stix, y, x);
				if (!z) return STIX_NULL;
				if (!neg) STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
			}
			else
			{
				neg = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer); 
				z = subtract_unsigned_integers (stix, x, y); /* take x's sign */
				if (!z) return STIX_NULL;
				if (neg) STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
			}
		}
	}

	return normalize_bigint (stix, z);

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_mulints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
	#if STIX_SIZEOF_INTMAX_T > STIX_SIZEOF_OOI_T
		stix_intmax_t i;
		i = (stix_intmax_t)STIX_OOP_TO_SMOOI(x) * (stix_intmax_t)STIX_OOP_TO_SMOOI(y);
		if (STIX_IN_SMOOI_RANGE(i)) return STIX_SMOOI_TO_OOP((stix_ooi_t)i);
		return make_bigint_with_intmax (stix, i);
	#else
		stix_ooi_t i;
		stix_ooi_t xv, yv;

		xv = STIX_OOP_TO_SMOOI(x);
		yv = STIX_OOP_TO_SMOOI(y);
		if (smooi_mul_overflow (stix, xv, yv, &i))
		{
			/* overflowed - convert x and y normal objects and carry on */

			/* no need to call stix_pushtmp before creating x because
			 * xv and yv contains actual values needed */
			x = make_bigint_with_ooi (stix, xv);
			if (!x) return STIX_NULL;

			stix_pushtmp (stix, &x); /* protect x made above */
			y = make_bigint_with_ooi (stix, yv);
			stix_poptmp (stix);
			if (!y) return STIX_NULL;

			goto normal;
		}
		else
		{
			if (STIX_IN_SMOOI_RANGE(i)) return STIX_SMOOI_TO_OOP(i);
			return make_bigint_with_ooi (stix, i);
		}
	#endif
	}
	else
	{
		stix_ooi_t v;

		if (STIX_OOP_IS_SMOOI(x))
		{
			if (!is_bigint(stix,y)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(x);
			switch (v)
			{
				case 0:
					return STIX_SMOOI_TO_OOP(0);
				case 1:
					return clone_bigint (stix, y, STIX_OBJ_GET_SIZE(y));
				case -1:
					return clone_bigint_negated (stix, y, STIX_OBJ_GET_SIZE(y));
			}

			stix_pushtmp (stix, &y);
			x = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!x) return STIX_NULL;
		}
		else if (STIX_OOP_IS_SMOOI(y))
		{
			if (!is_bigint(stix,x)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(y);
			switch (v)
			{
				case 0:
					return STIX_SMOOI_TO_OOP(0);
				case 1:
					return clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));
				case -1:
					return clone_bigint_negated (stix, x, STIX_OBJ_GET_SIZE(x));
			}

			stix_pushtmp (stix, &x);
			y = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!y) return STIX_NULL;
		}
		else
		{
			if (!is_bigint(stix,x)) goto oops_einval;
			if (!is_bigint(stix,y)) goto oops_einval;
		}

	normal:
		z = multiply_unsigned_integers (stix, x, y);
		if (!z) return STIX_NULL;
		if (STIX_OBJ_GET_CLASS(x) != STIX_OBJ_GET_CLASS(y))
			STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);
	}

	return normalize_bigint (stix, z);

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_divints (stix_t* stix, stix_oop_t x, stix_oop_t y, int modulo, stix_oop_t* rem)
{
	stix_oop_t z, r;
	int x_neg, y_neg;

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t xv, yv, q, r;

		xv = STIX_OOP_TO_SMOOI(x);
		yv = STIX_OOP_TO_SMOOI(y);

		if (yv == 0)
		{
			stix->errnum = STIX_EDIVBY0;
			return STIX_NULL;
		}

		if (xv == 0)
		{
			if (rem) *rem = STIX_SMOOI_TO_OOP(0);
			return STIX_SMOOI_TO_OOP(0);
		}

		/* In C89, integer division with a negative number  is
		 * implementation dependent. In C99, it truncates towards zero.
		 * 
		 * http://python-history.blogspot.kr/2010/08/why-pythons-integer-division-floors.html
		 *   The integer division operation (//) and its sibling, 
		 *   the modulo operation (%), go together and satisfy a nice
		 *   mathematical relationship (all variables are integers):
		 *      a/b = q with remainder r
		 *   such that
		 *      b*q + r = a and 0 <= r < b (assuming- a and b are >= 0).
		 * 
		 *   If you want the relationship to extend for negative a
		 *   (keeping b positive), you have two choices: if you truncate q
		 *   towards zero, r will become negative, so that the invariant
		 *   changes to 0 <= abs(r) < abs(b). otherwise, you can floor q
		 *   towards negative infinity, and the invariant remains 0 <= r < b. 
		 */

		q = xv / yv;
		STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(q));

		r = xv - yv * q; /* xv % yv; */
		if (r)
		{
			if (modulo)
			{
				/* modulo */
				/*
					xv      yv      q       r
					-------------------------
					 7       3      2       1
					-7       3     -3       2
					 7      -3     -3      -2
					-7      -3      2      -1
				 */

				/* r must be floored. that is, it rounds away from zero 
				 * and towards negative infinity */
				if (IS_SIGN_DIFF(yv, r))
				{
					/* if the divisor has a different sign from r,
					 * change the sign of r to the divisor's sign */
					r += yv;
					--q;
					STIX_ASSERT (stix, r && !IS_SIGN_DIFF(yv, r));
				}
			}
			else
			{
				/* remainder */
				/*
					xv      yv      q       r
					-------------------------
					 7       3      2       1
					-7       3     -2      -1
					 7      -3     -2       1
					-7      -3      2      -1
				 */
				if (xv && IS_SIGN_DIFF(xv, r)) 
				{
					/* if the dividend has a different sign from r,
					 * change the sign of r to the dividend's sign.
					 * all the compilers i've worked with produced
					 * the quotient and the remainder that don't need
					 * any adjustment. however, there may be an esoteric
					 * architecture. */
					r -= yv;
					++q;
					STIX_ASSERT (stix, xv && !IS_SIGN_DIFF(xv, r));
				}
			}
		}

		if (rem)
		{
			STIX_ASSERT (stix, STIX_IN_SMOOI_RANGE(r));
			*rem = STIX_SMOOI_TO_OOP(r);
		}

		return STIX_SMOOI_TO_OOP((stix_ooi_t)q);
	}
	else 
	{
		if (STIX_OOP_IS_SMOOI(x))
		{
			stix_ooi_t v;

			if (!is_bigint(stix,y)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(x);
			if (v == 0)
			{
				if (rem) *rem = STIX_SMOOI_TO_OOP(0);
				return STIX_SMOOI_TO_OOP(0);
			}

			stix_pushtmp (stix, &y);
			x = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!x) return STIX_NULL;
		}
		else if (STIX_OOP_IS_SMOOI(y))
		{
			stix_ooi_t v;

			if (!is_bigint(stix,x)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(y);
			switch (v)
			{
				case 0:
					stix->errnum = STIX_EDIVBY0;
					return STIX_NULL;

				case 1:
					z = clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));
					if (!z) return STIX_NULL;
					if (rem) *rem = STIX_SMOOI_TO_OOP(0);
					return z;


				case -1:
					z = clone_bigint_negated (stix, x, STIX_OBJ_GET_SIZE(x));
					if (!z) return STIX_NULL;
					if (rem) *rem = STIX_SMOOI_TO_OOP(0);
					return z;

	/*
				default:
					if (IS_POWER_OF_2(v))
					{
	TODO:
	DO SHIFTING. how to get remainder..
	if v is powerof2, do shifting???

						z = clone_bigint_negated (stix, x, STIX_OBJ_GET_SIZE(x));
						rshift_unsigned_array (z, STIX_OBJ_GET_SIZE(z), 10);
					}
	*/
			}

			stix_pushtmp (stix, &x);
			y = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!y) return STIX_NULL;
		}
		else
		{
			if (!is_bigint(stix,x)) goto oops_einval;
			if (!is_bigint(stix,y)) goto oops_einval;
		}
	}

	x_neg = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer);
	y_neg = (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer);

	stix_pushtmp (stix, &x);
	stix_pushtmp (stix, &y);
	z = divide_unsigned_integers (stix, x, y, &r);
	stix_poptmps (stix, 2);
	if (!z) return STIX_NULL;

	if (x_neg) 
	{
		/* the class on r must be set before normalize_bigint() 
		 * because it can get changed to a small integer */
		STIX_OBJ_SET_CLASS(r, stix->_large_negative_integer);
	}

	if (x_neg != y_neg)
	{
		STIX_OBJ_SET_CLASS(z, stix->_large_negative_integer);

		stix_pushtmp (stix, &z);
		stix_pushtmp (stix, &y);
		r = normalize_bigint (stix, r);
		stix_poptmps (stix, 2);
		if (!r) return STIX_NULL;

		if (r != STIX_SMOOI_TO_OOP(0) && modulo)
		{
			if (rem)
			{
				stix_pushtmp (stix, &z);
				stix_pushtmp (stix, &y);
				r = stix_addints (stix, r, y);
				stix_poptmps (stix, 2);
				if (!r) return STIX_NULL;

				stix_pushtmp (stix, &r);
				z = normalize_bigint (stix, z);
				stix_poptmp (stix);
				if (!z) return STIX_NULL;

				stix_pushtmp (stix, &r);
				z = stix_subints (stix, z, STIX_SMOOI_TO_OOP(1));
				stix_poptmp (stix);
				if (!z) return STIX_NULL;

				*rem = r;
				return z;
			}
			else
			{
				/* remainder is not needed at all */
/* TODO: subtract 1 without normalization??? */
				z = normalize_bigint (stix, z);
				if (!z) return STIX_NULL;
				return stix_subints (stix, z, STIX_SMOOI_TO_OOP(1));
			}
		}
	}
	else
	{
		stix_pushtmp (stix, &z);
		r = normalize_bigint (stix, r);
		stix_poptmp (stix);
		if (!r) return STIX_NULL;
	}

	if (rem) *rem = r;
	return normalize_bigint (stix, z);

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}


stix_oop_t stix_negateint (stix_t* stix, stix_oop_t x)
{
	if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;
		v = STIX_OOP_TO_SMOOI(x);
		return STIX_SMOOI_TO_OOP(-v);
	}
	else
	{
		if (!is_bigint(stix, x)) goto oops_einval;
		return clone_bigint_negated (stix, x, STIX_OBJ_GET_SIZE(x));
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_bitatint (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	/* y is 0-based */

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v1, v2, v3;

		v1 = STIX_OOP_TO_SMOOI(x);
		v2 = STIX_OOP_TO_SMOOI(y);

		if (v2 < 0) return STIX_SMOOI_TO_OOP(0);
		if (v1 >= 0)
		{
			/* the absolute value may be composed of up to 
			 * STIX_SMOOI_BITS - 1 bits as there is a sign bit.*/
			if (v2 >= STIX_SMOOI_BITS - 1) return STIX_SMOOI_TO_OOP(0);
			v3 = ((stix_oow_t)v1 >> v2) & 1;
		}
		else
		{
			if (v2 >= STIX_SMOOI_BITS - 1) return STIX_SMOOI_TO_OOP(1);
			v3 = ((~(stix_oow_t)-v1 + 1) >> v2) & 1;
		}
		return STIX_SMOOI_TO_OOP(v3);
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		if (!is_bigint(stix, y)) goto oops_einval;

		if (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer) return STIX_SMOOI_TO_OOP(0);

		/* y is definitely >= STIX_SMOOI_BITS */
		if (STIX_OOP_TO_SMOOI(x) >= 0) 
			return STIX_SMOOI_TO_OOP(0);
		else 
			return STIX_SMOOI_TO_OOP(1);
	}
	else if (STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v;
		stix_oow_t wp, bp, xs;

		if (!is_bigint(stix, x)) goto oops_einval;
		v = STIX_OOP_TO_SMOOI(y);

		if (v < 0) return STIX_SMOOI_TO_OOP(0);
		wp = v / STIX_LIW_BITS;
		bp = v - (wp * STIX_LIW_BITS);

		xs = STIX_OBJ_GET_SIZE(x);
		if (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)
		{
			if (wp >= xs) return STIX_SMOOI_TO_OOP(0);
			v = (((stix_oop_liword_t)x)->slot[wp] >> bp) & 1;
		}
		else
		{
			stix_lidw_t w, carry;
			stix_oow_t i;

			if (wp >= xs) return STIX_SMOOI_TO_OOP(1);

			carry = 1;
			for (i = 0; i <= wp; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
			}
			v = ((stix_oow_t)w >> bp) & 1;
		}

		return STIX_SMOOI_TO_OOP(v);
	}
	else
	{
	#if defined(STIX_LIMIT_OBJ_SIZE)
		/* nothing */
	#else
		stix_oow_t w, wp, bp, xs;
		stix_ooi_t v;
		int sign;
	#endif

		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;

	#if defined(STIX_LIMIT_OBJ_SIZE)
		if (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer) return STIX_SMOOI_TO_OOP(0);

		STIX_ASSERT (stix, STIX_OBJ_SIZE_BITS_MAX <= STIX_TYPE_MAX(stix_oow_t));
		if (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)
		{
			return STIX_SMOOI_TO_OOP (0);
		}
		else
		{
			return STIX_SMOOI_TO_OOP (1);
		}
	#else
		xs = STIX_OBJ_GET_SIZE(x);

		if (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer) return STIX_SMOOI_TO_OOP(0);

		sign = bigint_to_oow (stix, y, &w);
		STIX_ASSERT (stix, sign >= 0);
		if (sign >= 1)
		{
			wp = w / STIX_LIW_BITS;
			bp = w - (wp * STIX_LIW_BITS);
		}
		else
		{
			stix_oop_t quo, rem;

			STIX_ASSERT (stix, sign == 0);

			stix_pushtmp (stix, &x);
			quo = stix_divints (stix, y, STIX_SMOOI_TO_OOP(STIX_LIW_BITS), 0, &rem);
			stix_poptmp (stix);
			if (!quo) return STIX_NULL;

			sign = integer_to_oow (stix, quo, &wp);
			STIX_ASSERT (stix, sign >= 0);
			if (sign == 0)
			{
				/* too large. set it to xs so that it gets out of
				 * the valid range */
				wp = xs;
			}

			STIX_ASSERT (stix, STIX_OOP_IS_SMOOI(rem));
			bp = STIX_OOP_TO_SMOOI(rem);
			STIX_ASSERT (stix, bp >= 0 && bp < STIX_LIW_BITS);
		}

		if (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)
		{
			if (wp >= xs) return STIX_SMOOI_TO_OOP(0);
			v = (((stix_oop_liword_t)x)->slot[wp] >> bp) & 1;
		}
		else
		{
			stix_lidw_t w, carry;
			stix_oow_t i;

			if (wp >= xs) return STIX_SMOOI_TO_OOP(1);

			carry = 1;
			for (i = 0; i <= wp; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
			}
			v = ((stix_oow_t)w >> bp) & 1;
		}

		return STIX_SMOOI_TO_OOP(v);
	#endif
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_bitandints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v1, v2, v3;

		v1 = STIX_OOP_TO_SMOOI(x);
		v2 = STIX_OOP_TO_SMOOI(y);
		v3 = v1 & v2;

		if (STIX_IN_SMOOI_RANGE(v3)) return STIX_SMOOI_TO_OOP(v3);
		return make_bigint_with_ooi (stix, v3);
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, y)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(x);
		if (v == 0) return STIX_SMOOI_TO_OOP(0);

		stix_pushtmp (stix, &y);
		x = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else if (STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, x)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(y);
		if (v == 0) return STIX_SMOOI_TO_OOP(0);

		stix_pushtmp (stix, &x);
		y = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else
	{
		stix_oop_t z;
		stix_oow_t i, xs, ys, zs, zalloc;
		int negx, negy;

		if (!is_bigint(stix,x) || !is_bigint(stix, y)) goto oops_einval;

	bigint_and_bigint:
		xs = STIX_OBJ_GET_SIZE(x);
		ys = STIX_OBJ_GET_SIZE(y);

		if (xs < ys)
		{
			/* make sure that x is greater than or equal to y */
			z = x;
			x = y;
			y = z;
			zs = ys;
			ys = xs;
			xs = zs;
		}

		negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;
		negy = (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? 1: 0;

		if (negx && negy)
		{
			zalloc = xs + 1;
			zs = xs;
		}
		else if (negx)
		{
			zalloc = ys;
			zs = ys;
		}
		else if (negy)
		{
			zalloc = xs;
			zs = xs;
		}
		else
		{
			zalloc = ys;
			zs = ys;
		}

		stix_pushtmp (stix, &x);
		stix_pushtmp (stix, &y);
		z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, zalloc);
		stix_poptmps (stix, 2);
		if (!z) return STIX_NULL;

		if (negx && negy)
		{
			/* both are negative */
			stix_lidw_t w[2];
			stix_lidw_t carry[2];

			carry[0] = 1;
			carry[1] = 1;
			/* 2's complement on both x and y and perform bitwise-and */
			for (i = 0; i < ys; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;

				w[1] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry[1];
				carry[1] = w[1] >> STIX_LIW_BITS;

				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0] & (stix_liw_t)w[1];
			}
			STIX_ASSERT (stix, carry[1] == 0);

			/* 2's complement on the remaining part of x. the lacking part
			 * in y is treated as if they are all 1s. */
			for (; i < xs; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0];
			}
			STIX_ASSERT (stix, carry[0] == 0);

			/* 2's complement on the final result */
			((stix_oop_liword_t)z)->slot[zs] = ~(stix_liw_t)0;
			carry[0] = 1;
			for (i = 0; i <= zs; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)z)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0];
			}
			STIX_ASSERT (stix, carry[0] == 0);

			STIX_OBJ_SET_CLASS (z, stix->_large_negative_integer);
		}
		else if (negx)
		{
			/* x is negative, y is positive */
			stix_lidw_t w, carry;

			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w & ((stix_oop_liword_t)y)->slot[i];
			}

			/* the lacking part in y is all 0's. the remaining part in x is
			 * just masked out when bitwise-anded with 0. so nothing is done
			 * to handle the remaining part in x */
		}
		else if (negy)
		{
			/* x is positive, y is negative  */
			stix_lidw_t w, carry;

			/* x & 2's complement on y up to ys */
			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] & (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);

			/* handle the longer part in x than y
			 * 
			 * For example,
			 *  x => + 1010 1100
			 *  y => -      0011
			 * 
			 * If y is extended to the same length as x, 
			 * it is a negative 0000 0001. 
			 * 2's complement is performed on this imaginary extension.
			 * the result is '1111 1101' (1111 1100 + 1).
			 * 
			 * when y is shorter and negative, the lacking part can be
			 * treated as all 1s in the 2's complement format.
			 * 
			 * the remaining part in x can be just copied to the 
			 * final result 'z'.
			 */
			for (; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i];
			}
		}
		else
		{
			/* both are positive */
			for (i = 0; i < ys; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] & ((stix_oop_liword_t)y)->slot[i];
			}
		}

		return normalize_bigint(stix, z);
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_bitorints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v1, v2, v3;

		v1 = STIX_OOP_TO_SMOOI(x);
		v2 = STIX_OOP_TO_SMOOI(y);
		v3 = v1 | v2;

		if (STIX_IN_SMOOI_RANGE(v3)) return STIX_SMOOI_TO_OOP(v3);
		return make_bigint_with_ooi (stix, v3);
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, y)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(x);
		if (v == 0) return clone_bigint(stix, y, STIX_OBJ_GET_SIZE(y));

		stix_pushtmp (stix, &y);
		x = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else if (STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, x)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(y);
		if (v == 0) return clone_bigint(stix, x, STIX_OBJ_GET_SIZE(x));

		stix_pushtmp (stix, &x);
		y = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else
	{
		stix_oop_t z;
		stix_oow_t i, xs, ys, zs, zalloc;
		int negx, negy;

		if (!is_bigint(stix,x) || !is_bigint(stix, y)) goto oops_einval;

	bigint_and_bigint:
		xs = STIX_OBJ_GET_SIZE(x);
		ys = STIX_OBJ_GET_SIZE(y);

		if (xs < ys)
		{
			/* make sure that x is greater than or equal to y */
			z = x;
			x = y;
			y = z;
			zs = ys;
			ys = xs;
			xs = zs;
		}

		negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;
		negy = (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? 1: 0;

		if (negx && negy)
		{
			zalloc = ys + 1;
			zs = ys;
		}
		else if (negx)
		{
			zalloc = xs + 1;
			zs = xs;
		}
		else if (negy)
		{
			zalloc = ys + 1;
			zs = ys;
		}
		else
		{
			zalloc = xs;
			zs = xs;
		}

		if (zalloc < zs)
		{
			/* overflow in zalloc calculation above */
			stix->errnum = STIX_EOOMEM; /* TODO: is it a soft failure or hard failure? */
			return STIX_NULL;
		}

		stix_pushtmp (stix, &x);
		stix_pushtmp (stix, &y);
		z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, zalloc);
		stix_poptmps (stix, 2);
		if (!z) return STIX_NULL;

		if (negx && negy)
		{
			/* both are negative */
			stix_lidw_t w[2];
			stix_lidw_t carry[2];

			carry[0] = 1;
			carry[1] = 1;
			/* 2's complement on both x and y and perform bitwise-and */
			for (i = 0; i < ys; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;

				w[1] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry[1];
				carry[1] = w[1] >> STIX_LIW_BITS;

				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0] | (stix_liw_t)w[1];
			}
			STIX_ASSERT (stix, carry[1] == 0);

			/* do nothing about the extra part in x and the lacking part
			 * in y for the reason shown in [NOTE] in the 'else if' block
			 * further down. */

		adjust_to_negative:
			/* 2's complement on the final result */
			((stix_oop_liword_t)z)->slot[zs] = ~(stix_liw_t)0;
			carry[0] = 1;
			for (i = 0; i <= zs; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)z)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0];
			}
			STIX_ASSERT (stix, carry[0] == 0);

			STIX_OBJ_SET_CLASS (z, stix->_large_negative_integer);
		}
		else if (negx)
		{
			/* x is negative, y is positive */
			stix_lidw_t w, carry;

			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w | ((stix_oop_liword_t)y)->slot[i];
			}

			for (; i < xs; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
			}

			STIX_ASSERT (stix, carry == 0);
			goto adjust_to_negative;
		}
		else if (negy)
		{
			/* x is positive, y is negative  */
			stix_lidw_t w, carry;

			/* x & 2's complement on y up to ys */
			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] | (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);

			/* [NOTE]
			 *  in theory, the lacking part in ys is all 1s when y is
			 *  extended to the width of x. but those 1s are inverted to
			 *  0s when another 2's complement is performed over the final
			 *  result after the jump to 'adjust_to_negative'.
			 *  setting zs to 'xs + 1' and performing the following loop is 
			 *  redundant.
			for (; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ~(stix_liw_t)0;
			}
			*/
			goto adjust_to_negative;
		}
		else
		{
			/* both are positive */
			for (i = 0; i < ys; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] | ((stix_oop_liword_t)y)->slot[i];
			}

			for (; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i];
			}
		}

		return normalize_bigint(stix, z);
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_bitxorints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v1, v2, v3;

		v1 = STIX_OOP_TO_SMOOI(x);
		v2 = STIX_OOP_TO_SMOOI(y);
		v3 = v1 ^ v2;

		if (STIX_IN_SMOOI_RANGE(v3)) return STIX_SMOOI_TO_OOP(v3);
		return make_bigint_with_ooi (stix, v3);
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, y)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(x);
		if (v == 0) return clone_bigint(stix, y, STIX_OBJ_GET_SIZE(y));

		stix_pushtmp (stix, &y);
		x = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else if (STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v;

		if (!is_bigint(stix, x)) goto oops_einval;

		v = STIX_OOP_TO_SMOOI(y);
		if (v == 0) return clone_bigint(stix, x, STIX_OBJ_GET_SIZE(x));

		stix_pushtmp (stix, &x);
		y = make_bigint_with_ooi (stix, v);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		goto bigint_and_bigint;
	}
	else
	{
		stix_oop_t z;
		stix_oow_t i, xs, ys, zs, zalloc;
		int negx, negy;

		if (!is_bigint(stix,x) || !is_bigint(stix, y)) goto oops_einval;

	bigint_and_bigint:
		xs = STIX_OBJ_GET_SIZE(x);
		ys = STIX_OBJ_GET_SIZE(y);

		if (xs < ys)
		{
			/* make sure that x is greater than or equal to y */
			z = x;
			x = y;
			y = z;
			zs = ys;
			ys = xs;
			xs = zs;
		}

		negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;
		negy = (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? 1: 0;

		if (negx && negy)
		{
			zalloc = xs;
			zs = xs;
		}
		else if (negx)
		{
			zalloc = xs + 1;
			zs = xs;
		}
		else if (negy)
		{
			zalloc = xs + 1;
			zs = xs;
		}
		else
		{
			zalloc = xs;
			zs = xs;
		}

		if (zalloc < zs)
		{
			/* overflow in zalloc calculation above */
			stix->errnum = STIX_EOOMEM; /* TODO: is it a soft failure or hard failure? */
			return STIX_NULL;
		}

		stix_pushtmp (stix, &x);
		stix_pushtmp (stix, &y);
		z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, zalloc);
		stix_poptmps (stix, 2);
		if (!z) return STIX_NULL;

		if (negx && negy)
		{
			/* both are negative */
			stix_lidw_t w[2];
			stix_lidw_t carry[2];

			carry[0] = 1;
			carry[1] = 1;
			/* 2's complement on both x and y and perform bitwise-and */
			for (i = 0; i < ys; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;

				w[1] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry[1];
				carry[1] = w[1] >> STIX_LIW_BITS;

				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0] ^ (stix_liw_t)w[1];
			}
			STIX_ASSERT (stix, carry[1] == 0);

			/* treat the lacking part in y as all 1s */
			for (; i < xs; i++)
			{
				w[0] = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry[0];
				carry[0] = w[0] >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w[0] ^ (~(stix_liw_t)0);
			}
			STIX_ASSERT (stix, carry[0] == 0);
		}
		else if (negx)
		{
			/* x is negative, y is positive */
			stix_lidw_t w, carry;

			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w ^ ((stix_oop_liword_t)y)->slot[i];
			}

			/* treat the lacking part in y as all 0s */
			for (; i < xs; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);

		adjust_to_negative:
			/* 2's complement on the final result */
			((stix_oop_liword_t)z)->slot[zs] = ~(stix_liw_t)0;
			carry = 1;
			for (i = 0; i <= zs; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)z)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);

			STIX_OBJ_SET_CLASS (z, stix->_large_negative_integer);
		}
		else if (negy)
		{
			/* x is positive, y is negative  */
			stix_lidw_t w, carry;

			/* x & 2's complement on y up to ys */
			carry = 1;
			for (i = 0; i < ys; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)y)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] ^ (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);

			/* treat the lacking part in y as all 1s */
			for (; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] ^ (~(stix_liw_t)0);
			}

			goto adjust_to_negative;
		}
		else
		{
			/* both are positive */
			for (i = 0; i < ys; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i] ^ ((stix_oop_liword_t)y)->slot[i];
			}

			/* treat the lacking part in y as all 0s */
			for (; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ((stix_oop_liword_t)x)->slot[i];
			}
		}

		return normalize_bigint(stix, z);
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_bitinvint (stix_t* stix, stix_oop_t x)
{
	if (STIX_OOP_IS_SMOOI(x))
	{
		stix_ooi_t v;

		v = STIX_OOP_TO_SMOOI(x);
		v = ~v;

		if (STIX_IN_SMOOI_RANGE(v)) return STIX_SMOOI_TO_OOP(v);
		return make_bigint_with_ooi (stix, v);
	}
	else
	{
		stix_oop_t z;
		stix_oow_t i, xs, zs, zalloc;
		int negx;

		if (!is_bigint(stix,x)) goto oops_einval;

		xs = STIX_OBJ_GET_SIZE(x);
		negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;

		if (negx)
		{
			zalloc = xs;
			zs = xs;
		}
		else
		{
			zalloc = xs + 1;
			zs = xs;
		}

		if (zalloc < zs)
		{
			/* overflow in zalloc calculation above */
			stix->errnum = STIX_EOOMEM; /* TODO: is it a soft failure or hard failure? */
			return STIX_NULL;
		}

		stix_pushtmp (stix, &x);
		z = stix_instantiate (stix, stix->_large_positive_integer, STIX_NULL, zalloc);
		stix_poptmp (stix);
		if (!z) return STIX_NULL;

		if (negx)
		{
			stix_lidw_t w, carry;

			carry = 1;
			for (i = 0; i < xs; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = ~(stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);
		}
		else
		{
			stix_lidw_t w, carry;

		#if 0
			for (i = 0; i < xs; i++)
			{
				((stix_oop_liword_t)z)->slot[i] = ~((stix_oop_liword_t)x)->slot[i];
			}

			((stix_oop_liword_t)z)->slot[zs] = ~(stix_liw_t)0;
			carry = 1;
			for (i = 0; i <= zs; i++)
			{
				w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)z)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
			}
			STIX_ASSERT (stix, carry == 0);
		#else
			carry = 1;
			for (i = 0; i < xs; i++)
			{
				w = (stix_lidw_t)(((stix_oop_liword_t)x)->slot[i]) + carry;
				carry = w >> STIX_LIW_BITS;
				((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
			}
			STIX_ASSERT (stix, i == zs);
			((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)carry;
			STIX_ASSERT (stix, (carry >> STIX_LIW_BITS) == 0);
		#endif

			STIX_OBJ_SET_CLASS (z, stix->_large_negative_integer);
		}

		return normalize_bigint(stix, z);
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

static STIX_INLINE stix_oop_t rshift_negative_bigint (stix_t* stix, stix_oop_t x, stix_oow_t shift)
{
	stix_oop_t z;
	stix_lidw_t w;
	stix_lidw_t carry;
	stix_oow_t i, xs;

	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer);
	xs = STIX_OBJ_GET_SIZE(x);

	stix_pushtmp (stix, &x);
	/* +1 for the second inversion below */
	z = stix_instantiate (stix, stix->_large_negative_integer, STIX_NULL, xs + 1);
	stix_poptmp (stix);
	if (!z) return STIX_NULL;

	/* the following lines roughly for 'z = stix_bitinv (stix, x)' */
	carry = 1;
	for (i = 0; i < xs; i++)
	{
		w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)x)->slot[i]) + carry;
		carry = w >> STIX_LIW_BITS;
		((stix_oop_liword_t)z)->slot[i] = ~(stix_liw_t)w;
	}
	STIX_ASSERT (stix, carry == 0);

	/* shift to the right */
	rshift_unsigned_array (((stix_oop_liword_t)z)->slot, xs, shift);

	/* the following lines roughly for 'z = stix_bitinv (stix, z)' */
#if 0
	for (i = 0; i < xs; i++)
	{
		((stix_oop_liword_t)z)->slot[i] = ~((stix_oop_liword_t)z)->slot[i];
	}
	((stix_oop_liword_t)z)->slot[xs] = ~(stix_liw_t)0;

	carry = 1;
	for (i = 0; i <= xs; i++)
	{
		w = (stix_lidw_t)((stix_liw_t)~((stix_oop_liword_t)z)->slot[i]) + carry;
		carry = w >> STIX_LIW_BITS;
		((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
	}
	STIX_ASSERT (stix, carry == 0);
#else
	carry = 1;
	for (i = 0; i < xs; i++)
	{
		w = (stix_lidw_t)(((stix_oop_liword_t)z)->slot[i]) + carry;
		carry = w >> STIX_LIW_BITS;
		((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)w;
	}
	((stix_oop_liword_t)z)->slot[i] = (stix_liw_t)carry;
	STIX_ASSERT (stix, (carry >> STIX_LIW_BITS) == 0);
#endif

	return z; /* z is not normalized */
}

#if defined(STIX_LIMIT_OBJ_SIZE)
	/* nothing */
#else

static STIX_INLINE stix_oop_t rshift_negative_bigint_and_normalize (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;
	stix_oow_t shift;
	int sign;

	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer);
	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer);

	/* for convenience in subtraction below. 
	 * it could be STIX_TYPE_MAX(stix_oow_t) 
	 * if make_bigint_with_intmax() or something
	 * similar were used instead of STIX_SMOOI_TO_OOP().*/
	shift = STIX_SMOOI_MAX;
	do
	{
		stix_pushtmp (stix, &y);
		z = rshift_negative_bigint (stix, x, shift);
		stix_poptmp (stix);
		if (!z) return STIX_NULL;

		/* y is a negative number. use stix_addints() until it becomes 0 */
		stix_pushtmp (stix, &z);
		y = stix_addints (stix, y, STIX_SMOOI_TO_OOP(shift));
		stix_poptmp (stix);
		if (!y) return STIX_NULL;

		sign = integer_to_oow (stix, y, &shift);
		if (sign == 0) shift = STIX_SMOOI_MAX;
		else 
		{
			if (shift == 0)
			{
				/* no more shift */
				return normalize_bigint (stix, z);
			}
			STIX_ASSERT (stix, sign <= -1);
		}

		stix_pushtmp (stix, &y);
		x = normalize_bigint (stix, z);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		if (STIX_OOP_IS_SMOOI(x))
		{
			/* for normaization above, x can become a small integer */
			stix_ooi_t v;

			v = STIX_OOP_TO_SMOOI(x);
			STIX_ASSERT (stix, v < 0);

			/* normal right shift of a small negative integer */
			if (shift >= STIX_OOI_BITS - 1) 
			{
				/* when y is still a large integer, this condition is met
				 * met as STIX_SMOOI_MAX > STIX_OOI_BITS. so i can simly 
				 * terminate the loop after this */
				return STIX_SMOOI_TO_OOP(-1);
			}
			else 
			{
				v = (stix_ooi_t)(((stix_oow_t)v >> shift) | STIX_HBMASK(stix_oow_t, shift));
				if (STIX_IN_SMOOI_RANGE(v)) 
					return STIX_SMOOI_TO_OOP(v);
				else 
					return make_bigint_with_ooi (stix, v);
			}
		}
	}
	while (1);

	/* this part must not be reached */
	STIX_ASSERT (stix, !"internal error - must not happen");
	stix->errnum = STIX_EINTERN;
	return STIX_NULL;
}

static STIX_INLINE stix_oop_t rshift_positive_bigint_and_normalize (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;
	stix_oow_t zs, shift;
	int sign;

	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer);
	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer);

	zs = STIX_OBJ_GET_SIZE(x);

	stix_pushtmp (stix, &y);
	z = clone_bigint (stix, x, zs);
	stix_poptmp (stix);
	if (!z) return STIX_NULL;

	/* for convenience in subtraction below. 
	 * it could be STIX_TYPE_MAX(stix_oow_t) 
	 * if make_bigint_with_intmax() or something
	 * similar were used instead of STIX_SMOOI_TO_OOP().*/
	shift = STIX_SMOOI_MAX;
	do
	{
		rshift_unsigned_array (((stix_oop_liword_t)z)->slot, zs, shift);
		if (count_effective (((stix_oop_liword_t)z)->slot, zs) == 1 &&
		    ((stix_oop_liword_t)z)->slot[0] == 0) 
		{
			/* if z is 0, i don't have to go on */
			break;
		}

		/* y is a negative number. use stix_addints() until it becomes 0 */
		stix_pushtmp (stix, &z);
		y = stix_addints (stix, y, STIX_SMOOI_TO_OOP(shift));
		stix_poptmp (stix);
		if (!y) return STIX_NULL;

		sign = integer_to_oow (stix, y, &shift);
		if (sign == 0) shift = STIX_SMOOI_MAX;
		else 
		{
			if (shift == 0) break;
			STIX_ASSERT (stix, sign <= -1);
		}
	}
	while (1);

	return normalize_bigint(stix, z);
}

static STIX_INLINE stix_oop_t lshift_bigint_and_normalize (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	stix_oop_t z;
	stix_oow_t wshift, shift;
	int sign;

	STIX_ASSERT (stix, STIX_OBJ_GET_CLASS(y) == stix->_large_positive_integer);

	/* this loop is very inefficient as shifting is repeated
	 * with lshift_unsigned_array(). however, this part of the
	 * code is not likey to be useful because the amount of
	 * memory available is certainly not enough to support 
	 * huge shifts greater than STIX_TYPE_MAX(stix_oow_t) */
	shift = STIX_SMOOI_MAX;
	do
	{
		/* for convenience only in subtraction below. 
		 * should it be between STIX_SMOOI_MAX and STIX_TYPE_MAX(stix_oow_t),
		 * the second parameter to stix_subints() can't be composed
		 * using STIX_SMOOI_TO_OOP() */
		wshift = shift / STIX_LIW_BITS;
		if (shift > wshift * STIX_LIW_BITS) wshift++;

		stix_pushtmp (stix, &y);
		z = expand_bigint (stix, x, wshift);
		stix_poptmp (stix);
		if (!z) return STIX_NULL;

		lshift_unsigned_array (((stix_oop_liword_t)z)->slot, STIX_OBJ_GET_SIZE(z), shift);

		stix_pushtmp (stix, &y);
		x = normalize_bigint (stix, z);
		stix_poptmp (stix);
		if (!x) return STIX_NULL;

		stix_pushtmp (stix, &x);
		y = stix_subints (stix, y, STIX_SMOOI_TO_OOP(shift));
		stix_poptmp (stix);
		if (!y) return STIX_NULL;

		sign = integer_to_oow (stix, y, &shift);
		if (sign == 0) shift = STIX_SMOOI_MAX;
		else
		{
			if (shift == 0) 
			{
				STIX_ASSERT (stix, is_normalized_integer (stix, x));
				return x;
			}
			STIX_ASSERT (stix, sign >= 1);
		}
	}
	while (1);

	/* this part must not be reached */
	STIX_ASSERT (stix, !"internal error - must not happen");
	stix->errnum = STIX_EINTERN;
	return STIX_NULL;
}

#endif

stix_oop_t stix_bitshiftint (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	/* left shift if y is positive,
	 * right shift if y is negative */

	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		stix_ooi_t v1, v2;

		v1 = STIX_OOP_TO_SMOOI(x);
		v2 = STIX_OOP_TO_SMOOI(y);
		if (v1 == 0 || v2 == 0) 
		{
			/* return without cloning as x is a small integer */
			return x; 
		}

		if (v2 > 0)
		{
			/* left shift */
			stix_oop_t z;
			stix_oow_t wshift;

			wshift = v2 / STIX_LIW_BITS;
			if (v2 > wshift * STIX_LIW_BITS) wshift++;

			z = make_bloated_bigint_with_ooi (stix, v1, wshift);
			if (!z) return STIX_NULL;

			lshift_unsigned_array (((stix_oop_liword_t)z)->slot, STIX_OBJ_GET_SIZE(z), v2);
			return normalize_bigint (stix, z);
		}
		else
		{
			/* right shift */
			stix_ooi_t v;

			v2 = -v2;
			if (v1 < 0)
			{
				/* guarantee arithmetic shift preserving the sign bit
				 * regardless of compiler implementation.
				 *
				 *    binary    decimal   shifted by
				 *   -------------------------------
				 *   10000011    (-125)    0
				 *   11000001    (-63)     1
				 *   11100000    (-32)     2
				 *   11110000    (-16)     3
				 *   11111000    (-8)      4
				 *   11111100    (-4)      5
				 *   11111110    (-2)      6
				 *   11111111    (-1)      7
				 *   11111111    (-1)      8
				 */
				
				if (v2 >= STIX_OOI_BITS - 1) v = -1;
				else 
				{
					/* STIX_HBMASK_SAFE(stix_oow_t, v2 + 1) could also be
					 * used as a mask. but the sign bit is shifted in. 
					 * so, masking up to 'v2' bits is sufficient */
					v = (stix_ooi_t)(((stix_oow_t)v1 >> v2) | STIX_HBMASK(stix_oow_t, v2));
				}
			}
			else
			{
				if (v2 >= STIX_OOI_BITS) v = 0;
				else v = v1 >> v2;
			}
			if (STIX_IN_SMOOI_RANGE(v)) return STIX_SMOOI_TO_OOP(v);
			return make_bigint_with_ooi (stix, v);
		}
	}
	else
	{
		int sign, negx, negy;
		stix_oow_t shift;

		if (STIX_OOP_IS_SMOOI(x))
		{
			stix_ooi_t v;

			if (!is_bigint(stix,y)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(x);
			if (v == 0) return STIX_SMOOI_TO_OOP(0);

			if (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)
			{
				/* right shift - special case.
				 * x is a small integer. it is just a few bytes long.
				 * y is a large negative integer. its smallest absolute value
				 * is STIX_SMOOI_MAX. i know the final answer. */
				return (v < 0)? STIX_SMOOI_TO_OOP(-1): STIX_SMOOI_TO_OOP(0);
			}

			stix_pushtmp (stix, &y);
			x = make_bigint_with_ooi (stix, v);
			stix_poptmp (stix);
			if (!x) return STIX_NULL;

			goto bigint_and_bigint;
		}
		else if (STIX_OOP_IS_SMOOI(y))
		{
			stix_ooi_t v;

			if (!is_bigint(stix,x)) goto oops_einval;

			v = STIX_OOP_TO_SMOOI(y);
			if (v == 0) return clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));

			negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;
			if (v > 0)
			{
				sign = 1;
				negy = 0;
				shift = v;
				goto bigint_and_positive_oow;
			}
			else 
			{
				sign = -1;
				negy = 1;
				shift = -v;
				goto bigint_and_negative_oow;
			}
		}
		else
		{
			stix_oop_t z;

			if (!is_bigint(stix,x) || !is_bigint(stix, y)) goto oops_einval;

		bigint_and_bigint:
			negx = (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? 1: 0;
			negy = (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? 1: 0;

			sign = bigint_to_oow (stix, y, &shift);
			if (sign == 0)
			{
				/* y is too big or too small */
				if (negy)
				{
					/* right shift */
				#if defined(STIX_LIMIT_OBJ_SIZE)
					/* the maximum number of bit shifts are guaranteed to be
					 * small enough to fit into the stix_oow_t type. so i can 
					 * easily assume that all bits are shifted out */
					STIX_ASSERT (stix, STIX_OBJ_SIZE_BITS_MAX <= STIX_TYPE_MAX(stix_oow_t));
					return (negx)? STIX_SMOOI_TO_OOP(-1): STIX_SMOOI_TO_OOP(0);
				#else
					if (negx)
						return rshift_negative_bigint_and_normalize (stix, x, y);
					else
						return rshift_positive_bigint_and_normalize (stix, x, y);
				#endif
				}
				else
				{
					/* left shift */
				#if defined(STIX_LIMIT_OBJ_SIZE)
					/* the maximum number of bit shifts are guaranteed to be
					 * small enough to fit into the stix_oow_t type. so i can 
					 * simply return a failure here becuase it's surely too 
					 * large after shifting */
					STIX_ASSERT (stix, STIX_TYPE_MAX(stix_oow_t) >= STIX_OBJ_SIZE_BITS_MAX);
					stix->errnum = STIX_EOOMEM; /* is it a soft failure or a hard failure? is this error code proper? */
					return STIX_NULL;
				#else
					return lshift_bigint_and_normalize (stix, x, y);
				#endif
				}
			}
			else if (sign >= 1)
			{
				/* left shift */
				stix_oow_t wshift;

			bigint_and_positive_oow:
				wshift = shift / STIX_LIW_BITS;
				if (shift > wshift * STIX_LIW_BITS) wshift++;

				z = expand_bigint (stix, x, wshift);
				if (!z) return STIX_NULL;

				lshift_unsigned_array (((stix_oop_liword_t)z)->slot, STIX_OBJ_GET_SIZE(z), shift);
			}
			else 
			{
				/* right shift */
			bigint_and_negative_oow:

				STIX_ASSERT (stix, sign <= -1);

				if (negx)
				{
					z = rshift_negative_bigint (stix, x, shift);
					if (!z) return STIX_NULL;
				}
				else
				{
					z = clone_bigint (stix, x, STIX_OBJ_GET_SIZE(x));
					if (!z) return STIX_NULL;
					rshift_unsigned_array (((stix_oop_liword_t)z)->slot, STIX_OBJ_GET_SIZE(z), shift);
				}
			}

			return normalize_bigint(stix, z);
		}
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

static stix_uint8_t ooch_val_tab[] =
{
	99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
	99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
	99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99,
	 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 99, 99, 99, 99, 99, 99,
	99, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
	25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 99, 99, 99, 99, 99,
	99, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24,
	25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 99, 99, 99, 99, 99
};

stix_oop_t stix_strtoint (stix_t* stix, const stix_ooch_t* str, stix_oow_t len, int radix)
{
	int sign = 1;
	const stix_ooch_t* ptr, * start, * end;
	stix_lidw_t w, v;
	stix_liw_t hw[16], * hwp = STIX_NULL;
	stix_oow_t hwlen, outlen;
	stix_oop_t res;

	if (radix < 0) 
	{
		/* when radix is less than 0, it treats it as if '-' is preceeding */
		sign = -1;
		radix = -radix;
	}

	STIX_ASSERT (stix, radix >= 2 && radix <= 36);

	ptr = str;
	end = str + len;

	if (ptr < end)
	{
		if (*ptr == '+') ptr++;
		else if (*ptr == '-') 
		{
			ptr++; 
			sign = -1;
		}
	}

	if (ptr >= end) goto oops_einval; /* no digits */

	while (ptr < end && *ptr == '0') 
	{
		/* skip leading zeros */
		ptr++;
	}
	if (ptr >= end)
	{
		/* all zeros */
		return STIX_SMOOI_TO_OOP(0);
	}

	hwlen = 0;
	start = ptr; /* this is the real start */

	if (IS_POWER_OF_2(radix))
	{
		unsigned int exp;
		unsigned int bitcnt;

		/* get log2(radix) in a fast way under the fact that
		 * radix is a power of 2. the exponent acquired is
		 * the number of bits that a digit of the given radix takes up */
	#if defined(STIX_HAVE_BUILTIN_CTZ)
		exp = __builtin_ctz(radix);

	#elif defined(__GNUC__) && (defined(__x86_64) || defined(__amd64) || defined(__i386) || defined(i386))
		/* use the Bit Scan Forward instruction */
		__asm__ volatile (
			"bsf %1,%0\n\t"
			: "=r"(exp) /* output */
			: "r"(radix) /* input */
		);

	#elif defined(USE_UGLY_CODE) && defined(__GNUC__) && defined(__arm__) && (defined(__ARM_ARCH_5__) || defined(__ARM_ARCH_6__) || defined(__ARM_ARCH_7__) || defined(__ARM_ARCH_8__))

		/* CLZ is available in ARMv5T and above. there is no instruction to
		 * count trailing zeros or something similar. using RBIT with CLZ
		 * would be good in ARMv6T2 and above to avoid further calculation
		 * afte CLZ */
		__asm__ volatile (
			"clz %0,%1\n\t"
			: "=r"(exp) /* output */
			: "r"(radix) /* input */
		);
		exp = (STIX_SIZEOF(exp) * 8) - exp - 1; 

		/* TODO: PPC - use cntlz, cntlzw, cntlzd, SPARC - use lzcnt, MIPS clz */
	#else
		exp = _exp_tab[radix];
	#endif

		/* bytes */
		outlen = ((stix_oow_t)(end - str) * exp + 7) / 8; 
		/* number of stix_liw_t */
		outlen = (outlen + STIX_SIZEOF(hw[0]) - 1) / STIX_SIZEOF(hw[0]);

		if (outlen > STIX_COUNTOF(hw)) 
		{
			hwp = stix_allocmem (stix, outlen * STIX_SIZEOF(hw[0]));
			if (!hwp) return STIX_NULL;
		}
		else
		{
			hwp = hw;
		}

		w = 0;
		bitcnt = 0;
		ptr = end - 1;

		while (ptr >= start)
		{
			if (*ptr < 0 || *ptr >= STIX_COUNTOF(ooch_val_tab)) goto oops_einval;
			v = ooch_val_tab[*ptr];
			if (v >= radix) goto oops_einval;

			w |= (v << bitcnt);
			bitcnt += exp;
			if (bitcnt >= STIX_LIW_BITS)
			{
				bitcnt -= STIX_LIW_BITS;
				hwp[hwlen++] = w; /*(stix_liw_t)(w & STIX_LBMASK(stix_lidw_t, STIX_LIW_BITS));*/
				w >>= STIX_LIW_BITS;
			}

			ptr--;
		}

		STIX_ASSERT (stix, w <= STIX_TYPE_MAX(stix_liw_t));
		if (hwlen == 0 || w > 0) hwp[hwlen++] = w;
	}
	else
	{
		stix_lidw_t r1, r2;
		stix_liw_t multiplier;
		int dg, i, safe_ndigits;

		w = 0;
		ptr = start;

		safe_ndigits = stix->bigint[radix].safe_ndigits;
		multiplier = (stix_liw_t)stix->bigint[radix].multiplier;

		outlen = (end - str) / safe_ndigits + 1;
		if (outlen > STIX_COUNTOF(hw)) 
		{
			hwp = stix_allocmem (stix, outlen * STIX_SIZEOF(stix_liw_t));
			if (!hwp) return STIX_NULL;
		}
		else
		{
			hwp = hw;
		}

		STIX_ASSERT (stix, ptr < end);
		do
		{
			r1 = 0;
			for (dg = 0; dg < safe_ndigits; dg++)
			{
				if (ptr >= end) 
				{
					multiplier = 1;
					for (i = 0; i < dg; i++) multiplier *= radix;
					break;
				}

				if (*ptr < 0 || *ptr >= STIX_COUNTOF(ooch_val_tab)) goto oops_einval;
				v = ooch_val_tab[*ptr];
				if (v >= radix) goto oops_einval;

				r1 = r1 * radix + (stix_liw_t)v;
				ptr++;
			}


			r2 = r1;
			for (i = 0; i < hwlen; i++)
			{
				stix_liw_t high, low;

				v = (stix_lidw_t)hwp[i] * multiplier;
				high = (stix_liw_t)(v >> STIX_LIW_BITS);
				low = (stix_liw_t)(v /*& STIX_LBMASK(stix_oow_t, STIX_LIW_BITS)*/);

			#if defined(liw_add_overflow)
				/* use liw_add_overflow() only if it's compiler-builtin. */
				r2 = high + liw_add_overflow(low, r2, &low);
			#else
				/* don't use the fall-back version of liw_add_overflow() */
				low += r2;
				r2 = (stix_lidw_t)high + (low < r2);
			#endif

				hwp[i] = low;
			}
			if (r2) hwp[hwlen++] = (stix_liw_t)r2;
		}
		while (ptr < end);
	}

	STIX_ASSERT (stix, hwlen >= 1);

#if (STIX_LIW_BITS == STIX_OOW_BITS)
	if (hwlen == 1) 
	{
		w = hwp[0];
		STIX_ASSERT (stix, -STIX_SMOOI_MAX == STIX_SMOOI_MIN);
		if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP((stix_ooi_t)w * sign);
	}
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	if (hwlen == 1) 
	{
		STIX_ASSERT (stix, hwp[0] <= STIX_SMOOI_MAX);
		return STIX_SMOOI_TO_OOP((stix_ooi_t)hwp[0] * sign);
	}
	else if (hwlen == 2)
	{
		w = MAKE_WORD(hwp[0], hwp[1]);
		STIX_ASSERT (stix, -STIX_SMOOI_MAX == STIX_SMOOI_MIN);
		if (w <= STIX_SMOOI_MAX) return STIX_SMOOI_TO_OOP((stix_ooi_t)w * sign);
	}
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif

	res = stix_instantiate (stix, (sign < 0? stix->_large_negative_integer: stix->_large_positive_integer), hwp, hwlen);
	if (hwp && hw != hwp) stix_freemem (stix, hwp);

	return res;

oops_einval:
	if (hwp && hw != hwp) stix_freemem (stix, hwp);
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

static stix_oow_t oow_to_text (stix_t* stix, stix_oow_t w, int radix, stix_ooch_t* buf)
{
	stix_ooch_t* ptr;
	STIX_ASSERT (stix, radix >= 2 && radix <= 36);

	ptr = buf;
	do
	{
		*ptr++ = _digitc[w % radix];
		w /= radix;
	}
	while (w > 0);

	return ptr - buf;
}

static void reverse_string (stix_ooch_t* str, stix_oow_t len)
{
	stix_ooch_t ch;
	stix_ooch_t* start = str;
	stix_ooch_t* end = str + len - 1;

	while (start < end)
	{
		ch = *start;
		*start++ = *end;
		*end-- = ch;
	}
}

stix_oop_t stix_eqints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) == STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x) || STIX_OOP_IS_SMOOI(y)) 
	{
		return stix->_false;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return is_equal(stix, x, y)? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_neints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) != STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x) || STIX_OOP_IS_SMOOI(y)) 
	{
		return stix->_true;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return !is_equal(stix, x, y)? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_gtints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) > STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		if (!is_bigint(stix, y)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(y)) 
	{
		if (!is_bigint(stix, x)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)? stix->_true: stix->_false;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return is_greater(stix, x, y)? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_geints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) >= STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		if (!is_bigint(stix, y)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(y) == stix->_large_negative_integer)? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(y)) 
	{
		if (!is_bigint(stix, x)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(x) == stix->_large_positive_integer)? stix->_true: stix->_false;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return (is_greater(stix, x, y) || is_equal(stix, x, y))? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_ltints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) < STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		if (!is_bigint(stix, y)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(y) == stix->_large_positive_integer)? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(y)) 
	{
		if (!is_bigint(stix, x)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? stix->_true: stix->_false;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return is_less(stix, x, y)? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_leints (stix_t* stix, stix_oop_t x, stix_oop_t y)
{
	if (STIX_OOP_IS_SMOOI(x) && STIX_OOP_IS_SMOOI(y))
	{
		return (STIX_OOP_TO_SMOOI(x) <= STIX_OOP_TO_SMOOI(y))? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(x))
	{
		if (!is_bigint(stix, y)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(y) == stix->_large_positive_integer)? stix->_true: stix->_false;
	}
	else if (STIX_OOP_IS_SMOOI(y)) 
	{
		if (!is_bigint(stix, x)) goto oops_einval;
		return (STIX_OBJ_GET_CLASS(x) == stix->_large_negative_integer)? stix->_true: stix->_false;
	}
	else 
	{
		if (!is_bigint(stix, x) || !is_bigint(stix, y)) goto oops_einval;
		return (is_less(stix, x, y) || is_equal(stix, x, y))? stix->_true: stix->_false;
	}

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}

stix_oop_t stix_inttostr (stix_t* stix, stix_oop_t num, int radix)
{
	stix_ooi_t v = 0;
	stix_oow_t w;
	stix_oow_t as, bs, rs;
#if (STIX_LIW_BITS == STIX_OOW_BITS)
	stix_liw_t b[1];
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	stix_liw_t b[2];
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif
	stix_liw_t* a, * q, * r;
	stix_liw_t* t = STIX_NULL;
	stix_ooch_t* xbuf = STIX_NULL;
	stix_oow_t xlen = 0, seglen;
	stix_oop_t s;

	STIX_ASSERT (stix, radix >= 2 && radix <= 36);

	if (!stix_isint(stix,num)) goto oops_einval;
	v = integer_to_oow (stix, num, &w);

	if (v)
	{
		/* Use a static buffer for simple conversion as the largest
		 * size is known. The largest buffer is required for radix 2.
		 * For a binary conversion(radix 2), the number of bits is
		 * the maximum number of digits that can be produced. +1 is
		 * needed for the sign. */
		stix_ooch_t buf[STIX_OOW_BITS + 1];
		stix_oow_t len;

		len = oow_to_text (stix, w, radix, buf);
		if (v < 0) buf[len++] = '-';

		reverse_string (buf, len);
		return stix_makestring (stix, buf, len);
	}

	as = STIX_OBJ_GET_SIZE(num);

	if (IS_POWER_OF_2(radix))
	{
		unsigned int exp, accbits;
		stix_lidw_t acc;
		stix_oow_t xpos;

		exp = _exp_tab[radix];
		xlen = as * ((STIX_LIW_BITS + exp) / exp) + 1;
		xpos = xlen;

		xbuf = (stix_ooch_t*)stix_allocmem (stix, STIX_SIZEOF(*xbuf) * xlen);
		if (!xbuf) return STIX_NULL;

		acc = 0;
		accbits = 0;

		w = 0;
		while (w < as)
		{
			acc |= (stix_lidw_t)((stix_oop_liword_t)num)->slot[w] << accbits;
			accbits += STIX_LIW_BITS;

			w++;
			do
			{
				xbuf[--xpos] = _digitc[acc & (radix - 1)]; /* acc % radix */
				accbits -= exp;
				acc >>= exp;
				if (w < as)
				{
					if (accbits < exp) break;
				}
				else
				{
					if (acc <= 0) break;
				}
			}
			while (1);
		}

		STIX_ASSERT (stix, xpos >= 1);
		if (STIX_OBJ_GET_CLASS(num) == stix->_large_negative_integer) xbuf[--xpos] = '-';

		s = stix_makestring (stix, &xbuf[xpos], xlen - xpos);
		stix_freemem (stix, xbuf);
		return s;
	}

	/* Do it in a hard way for other cases */
/* TODO: migrate these buffers into stix_t? */
/* TODO: find an optimial buffer size */
	xbuf = (stix_ooch_t*)stix_allocmem (stix, STIX_SIZEOF(*xbuf) * (as * STIX_LIW_BITS + 1));
	if (!xbuf) return STIX_NULL;

	t = (stix_liw_t*)stix_callocmem (stix, STIX_SIZEOF(*t) * as * 3);
	if (!t) 
	{
		stix_freemem (stix, xbuf);
		return STIX_NULL;
	}

#if (STIX_LIW_BITS == STIX_OOW_BITS)
	b[0] = stix->bigint[radix].multiplier; /* block divisor */
	bs = 1;
#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
	b[0] = stix->bigint[radix].multiplier /*& STIX_LBMASK(stix_oow_t, STIX_LIW_BITS)*/;
	b[1] = stix->bigint[radix].multiplier >> STIX_LIW_BITS;
	bs = (b[1] > 0)? 2: 1;
#else
#	error UNSUPPORTED LIW BIT SIZE
#endif

	a = &t[0];
	q = &t[as];
	r = &t[as * 2];

	STIX_MEMCPY (a, ((stix_oop_liword_t)num)->slot, STIX_SIZEOF(*a) * as);

	do
	{
		if (is_less_unsigned_array (b, bs, a, as))
		{
			stix_liw_t* tmp;

			divide_unsigned_array (stix, a, as, b, bs, q, r);

			/* get 'rs' before 'as' gets changed */
			rs = count_effective (r, as); 
 
			/* swap a and q for later division */
			tmp = a;
			a = q;
			q = tmp;

			as = count_effective (a, as);
		}
		else
		{
			/* it is the last block */
			r = a;
			rs = as;
		}

	#if (STIX_LIW_BITS == STIX_OOW_BITS)
		STIX_ASSERT (stix, rs == 1);
		w = r[0];
	#elif (STIX_LIW_BITS == STIX_OOHW_BITS)
		if (rs == 1) w = r[0];
		else 
		{
			STIX_ASSERT (stix, rs == 2);
			w = MAKE_WORD (r[0], r[1]);
		}
	#else
	#	error UNSUPPORTED LIW BIT SIZE
	#endif
		seglen = oow_to_text (stix, w, radix, &xbuf[xlen]);
		xlen += seglen;
		if (r == a) break; /* reached the last block */

		/* fill unfilled leading digits with zeros as it's not 
		 * the last block */
		while (seglen < stix->bigint[radix].safe_ndigits)
		{
			xbuf[xlen++] = '0';
			seglen++;
		}
	}
	while (1);

	if (STIX_OBJ_GET_CLASS(num) == stix->_large_negative_integer) xbuf[xlen++] = '-';
	reverse_string (xbuf, xlen);
	s = stix_makestring (stix, xbuf, xlen);

	stix_freemem (stix, t);
	stix_freemem (stix, xbuf);
	return s;

oops_einval:
	stix->errnum = STIX_EINVAL;
	return STIX_NULL;
}