[u/mdw/catacomb] / mpx-ksqr.c

/* -*-c-*-
 *
 * $Id: mpx-ksqr.c,v 1.1 1999/12/11 10:57:43 mdw Exp $
 *
 * Karatsuba-based squaring algorithm
 *
 * (c) 1999 Straylight/Edgeware
 */

/*----- Licensing notice --------------------------------------------------* 
 *
 * This file is part of Catacomb.
 *
 * Catacomb is free software; you can redistribute it and/or modify
 * it under the terms of the GNU Library General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or (at your option) any later version.
 * 
 * Catacomb is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU Library General Public License for more details.
 * 
 * You should have received a copy of the GNU Library General Public
 * License along with Catacomb; if not, write to the Free
 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA 02111-1307, USA.
 */

/*----- Revision history --------------------------------------------------* 
 *
 * $Log: mpx-ksqr.c,v $
 * Revision 1.1  1999/12/11 10:57:43  mdw
 * Karatsuba squaring algorithm.
 *
 */

/*----- Header files ------------------------------------------------------*/

#include <stdio.h>

#include "mpx.h"

/*----- Tweakables --------------------------------------------------------*/

#ifdef TEST_RIG
#  undef KARATSUBA_CUTOFF
#  define KARATSUBA_CUTOFF 2
#endif

/*----- Addition macros ---------------------------------------------------*/

#define ULSL1(dv, av, avl) do {						\
  mpw *_dv = (dv);							\
  const mpw *_av = (av), *_avl = (avl);					\
  mpw _c = 0;								\
									\
  while (_av < _avl) {							\
    mpw _x = *_av++;							\
    *_dv++ = MPW(_c | (_x << 1));					\
    _c = MPW(_x >> (MPW_BITS - 1));					\
  }									\
  *_dv++ = _c;								\
} while (0)

#define UADD(dv, av, avl) do {						\
  mpw *_dv = (dv);							\
  const mpw *_av = (av), *_avl = (avl);					\
  mpw _c = 0;								\
									\
  while (_av < _avl) {							\
    mpw _a, _b;								\
    mpd _x;								\
    _a = *_av++;							\
    _b = *_dv;								\
    _x = (mpd)_a + (mpd)_b + _c;					\
    *_dv++ = MPW(_x);							\
    _c = _x >> MPW_BITS;						\
  }									\
  while (_c) {								\
    mpd _x = (mpd)*_dv + (mpd)_c;					\
    *_dv++ = MPW(_x);							\
    _c = _x >> MPW_BITS;						\
  }									\
} while (0)

/*----- Main code ---------------------------------------------------------*/

/* --- @mpx_ksqr@ --- *
 *
 * Arguments:	@mpw *dv, *dvl@ = pointer to destination buffer
 *		@const mpw *av, *avl@ = pointer to first argument
 *		@mpw *sv, *svl@ = pointer to scratch workspace
 *
 * Returns:	---
 *
 * Use:		Squares a multiprecision integers using something similar to
 *		Karatsuba's multiplication algorithm.  This is rather faster
 *		than traditional long multiplication (e.g., @mpx_umul@) on
 *		large numbers, although more expensive on small ones, and
 *		rather simpler than full-blown Karatsuba multiplication.
 *
 *		The destination must be twice as large as the argument.  The
 *		scratch space must be twice as large as the argument, plus
 *		the magic number @KARATSUBA_SLOP@.
 */

void mpx_ksqr(mpw *dv, mpw *dvl,
	      const mpw *av, const mpw *avl,
	      mpw *sv, mpw *svl)
{
  const mpw *avm;
  size_t m;

  /* --- Dispose of easy cases to @mpx_usqr@ --- *
   *
   * Karatsuba is only a win on large numbers, because of all the
   * recursiveness and bookkeeping.  The recursive calls make a quick check
   * to see whether to bottom out to @mpx_usqr@ which should help quite a
   * lot, but sometimes the only way to know is to make sure...
   */

  MPX_SHRINK(av, avl);

  if (avl - av <= KARATSUBA_CUTOFF) {
    mpx_usqr(dv, dvl, av, avl);
    return;
  }

  /* --- How the algorithm works --- *
   *
   * Unlike Karatsuba's identity for multiplication which isn't particularly
   * obvious, the identity for multiplication is known to all schoolchildren.
   * Let %$A = xb + y$%.  Then %$A^2 = x^2 b^x + 2 x y b + y^2$%.  So now I
   * have three multiplications, each four times easier, and that's a win.
   */

  /* --- First things --- *
   *
   * Sort out where to break the factor in half.
   */

  m = (avl - av + 1) >> 1;
  avm = av + m;

  /* --- Sort out everything --- */

  {
    mpw *ssv = sv + 2 * m;
    mpw *tdv = dv + m;
    mpw *rdv = tdv + m;

    /* --- The cross term in the middle needs a multiply --- *
     *
     * This isn't actually true, since %$x y = ((x + y)^2 - (x - y)^2)/4%.
     * But that's two squarings, versus one multiplication.
     */

    if (m > KARATSUBA_CUTOFF)
      mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl);
    else
      mpx_umul(sv, ssv, av, avm, avm, avl);
    ULSL1(tdv, sv, ssv);
    MPX_ZERO(dv, tdv);
    MPX_ZERO(rdv + m + 1, dvl);

    if (m > KARATSUBA_CUTOFF)
      mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
    else
      mpx_usqr(sv, ssv, avm, avl);
    UADD(rdv, sv, ssv);
    
    if (m > KARATSUBA_CUTOFF)
      mpx_ksqr(sv, ssv, av, avm, ssv, svl);
    else
      mpx_usqr(sv, ssv, av, avm);
    UADD(dv, sv, ssv);
  }
}

/*----- Test rig ----------------------------------------------------------*/

#ifdef TEST_RIG

#include <mLib/alloc.h>
#include <mLib/testrig.h>

#include "mpscan.h"

#define ALLOC(v, vl, sz) do {                                           \
  size_t _sz = (sz);                                                    \
  mpw *_vv = xmalloc(MPWS(_sz));                                        \
  mpw *_vvl = _vv + _sz;                                                \
  (v) = _vv;                                                            \
  (vl) = _vvl;                                                          \
} while (0)

#define LOAD(v, vl, d) do {                                             \
  const dstr *_d = (d);                                                 \
  mpw *_v, *_vl;                                                        \
  ALLOC(_v, _vl, MPW_RQ(_d->len));                                      \
  mpx_loadb(_v, _vl, _d->buf, _d->len);                                 \
  (v) = _v;                                                             \
  (vl) = _vl;                                                           \
} while (0)

#define MAX(x, y) ((x) > (y) ? (x) : (y))

static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
{
  fputs(msg, stderr);
  MPX_SHRINK(v, vl);
  while (v < vl)
    fprintf(stderr, " %08lx", (unsigned long)*--vl);
  fputc('\n', stderr);
}

static int usqr(dstr *v)
{
  mpw *a, *al;
  mpw *c, *cl;
  mpw *d, *dl;
  mpw *s, *sl;
  size_t m;
  int ok = 1;

  LOAD(a, al, &v[0]);
  LOAD(c, cl, &v[1]);
  m = al - a + 1;
  ALLOC(d, dl, 2 * m);
  ALLOC(s, sl, 2 * m + 32);

  mpx_ksqr(d, dl, a, al, s, sl);
  if (MPX_UCMP(d, dl, !=, c, cl)) {
    fprintf(stderr, "\n*** usqr failed\n");
    dumpmp("       a", a, al);
    dumpmp("expected", c, cl);
    dumpmp("  result", d, dl);
    ok = 0;
  }

  free(a); free(c); free(d); free(s);
  return (ok);
}

static test_chunk defs[] = {
  { "usqr", usqr, { &type_hex, &type_hex, 0 } },
  { 0, 0, { 0 } }
};

int main(int argc, char *argv[])
{
  test_run(argc, argv, defs, SRCDIR"/tests/mpx");
  return (0);
}

#endif

/*----- That's all, folks -------------------------------------------------*/
Commit	Line	Data
5bf74dea	1	/* --c--
	2	*
	3	* $Id: mpx-ksqr.c,v 1.1 1999/12/11 10:57:43 mdw Exp $
	4	*
	5	* Karatsuba-based squaring algorithm
	6	*
	7	* (c) 1999 Straylight/Edgeware
	8	*/
	9
	10	/----- Licensing notice --------------------------------------------------
	11	*
	12	* This file is part of Catacomb.
	13	*
	14	* Catacomb is free software; you can redistribute it and/or modify
	15	* it under the terms of the GNU Library General Public License as
	16	* published by the Free Software Foundation; either version 2 of the
	17	* License, or (at your option) any later version.
	18	*
	19	* Catacomb is distributed in the hope that it will be useful,
	20	* but WITHOUT ANY WARRANTY; without even the implied warranty of
	21	* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
	22	* GNU Library General Public License for more details.
	23	*
	24	* You should have received a copy of the GNU Library General Public
	25	* License along with Catacomb; if not, write to the Free
	26	* Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
	27	* MA 02111-1307, USA.
	28	*/
	29
	30	/----- Revision history --------------------------------------------------
	31	*
	32	* $Log: mpx-ksqr.c,v $
	33	* Revision 1.1 1999/12/11 10:57:43 mdw
	34	* Karatsuba squaring algorithm.
	35	*
	36	*/
	37
	38	/----- Header files ------------------------------------------------------/
	39
	40	#include <stdio.h>
	41
	42	#include "mpx.h"
	43
	44	/----- Tweakables --------------------------------------------------------/
	45
	46	#ifdef TEST_RIG
	47	# undef KARATSUBA_CUTOFF
	48	# define KARATSUBA_CUTOFF 2
	49	#endif
	50
	51	/----- Addition macros ---------------------------------------------------/
	52
	53	#define ULSL1(dv, av, avl) do { \
	54	mpw *_dv = (dv); \
	55	const mpw _av = (av), _avl = (avl); \
	56	mpw _c = 0; \
	57	\
	58	while (_av < _avl) { \
	59	mpw _x = *_av++; \
	60	*_dv++ = MPW(_c \| (_x << 1)); \
	61	_c = MPW(_x >> (MPW_BITS - 1)); \
	62	} \
	63	*_dv++ = _c; \
	64	} while (0)
65
66	#define UADD(dv, av, avl) do { \
67	mpw *_dv = (dv); \
68	const mpw _av = (av), _avl = (avl); \
69	mpw _c = 0; \
70	\
71	while (_av < _avl) { \
72	mpw _a, _b; \
73	mpd _x; \
74	_a = *_av++; \
75	_b = *_dv; \
76	_x = (mpd)_a + (mpd)_b + _c; \
77	*_dv++ = MPW(_x); \
78	_c = _x >> MPW_BITS; \
79	} \
80	while (_c) { \
81	mpd _x = (mpd)*_dv + (mpd)_c; \
82	*_dv++ = MPW(_x); \
83	_c = _x >> MPW_BITS; \
84	} \
85	} while (0)
86
87	/----- Main code ---------------------------------------------------------/
88
89	/* --- @mpx_ksqr@ --- *
90	*
91	* Arguments: @mpw dv, dvl@ = pointer to destination buffer
92	* @const mpw av, avl@ = pointer to first argument
93	* @mpw sv, svl@ = pointer to scratch workspace
94	*
95	* Returns: ---
96	*
97	* Use: Squares a multiprecision integers using something similar to
98	* Karatsuba's multiplication algorithm. This is rather faster
99	* than traditional long multiplication (e.g., @mpx_umul@) on
100	* large numbers, although more expensive on small ones, and
101	* rather simpler than full-blown Karatsuba multiplication.
102	*
103	* The destination must be twice as large as the argument. The
104	* scratch space must be twice as large as the argument, plus
105	* the magic number @KARATSUBA_SLOP@.
106	*/
107
108	void mpx_ksqr(mpw dv, mpw dvl,
109	const mpw av, const mpw avl,
110	mpw sv, mpw svl)
111	{
112	const mpw *avm;
113	size_t m;
114
115	/* --- Dispose of easy cases to @mpx_usqr@ --- *
116	*
117	* Karatsuba is only a win on large numbers, because of all the
118	* recursiveness and bookkeeping. The recursive calls make a quick check
119	* to see whether to bottom out to @mpx_usqr@ which should help quite a
120	* lot, but sometimes the only way to know is to make sure...
121	*/
122
123	MPX_SHRINK(av, avl);
124
125	if (avl - av <= KARATSUBA_CUTOFF) {
126	mpx_usqr(dv, dvl, av, avl);
127	return;
128	}
129
130	/* --- How the algorithm works --- *
131	*
132	* Unlike Karatsuba's identity for multiplication which isn't particularly
133	* obvious, the identity for multiplication is known to all schoolchildren.
134	* Let %$A = xb + y$%. Then %$A^2 = x^2 b^x + 2 x y b + y^2$%. So now I
135	* have three multiplications, each four times easier, and that's a win.
136	*/
137
138	/* --- First things --- *
139	*
140	* Sort out where to break the factor in half.
141	*/
142
143	m = (avl - av + 1) >> 1;
144	avm = av + m;
145
146	/* --- Sort out everything --- */
147
148	{
149	mpw ssv = sv + 2 m;
150	mpw *tdv = dv + m;
151	mpw *rdv = tdv + m;
152
153	/* --- The cross term in the middle needs a multiply --- *
154	*
155	* This isn't actually true, since %$x y = ((x + y)^2 - (x - y)^2)/4%.
156	* But that's two squarings, versus one multiplication.
157	*/
158
159	if (m > KARATSUBA_CUTOFF)
160	mpx_kmul(sv, ssv, av, avm, avm, avl, ssv, svl);
161	else
162	mpx_umul(sv, ssv, av, avm, avm, avl);
163	ULSL1(tdv, sv, ssv);
164	MPX_ZERO(dv, tdv);
165	MPX_ZERO(rdv + m + 1, dvl);
166
167	if (m > KARATSUBA_CUTOFF)
168	mpx_ksqr(sv, ssv, avm, avl, ssv, svl);
169	else
170	mpx_usqr(sv, ssv, avm, avl);
171	UADD(rdv, sv, ssv);
172
173	if (m > KARATSUBA_CUTOFF)
174	mpx_ksqr(sv, ssv, av, avm, ssv, svl);
175	else
176	mpx_usqr(sv, ssv, av, avm);
177	UADD(dv, sv, ssv);
178	}
179	}
180
181	/----- Test rig ----------------------------------------------------------/
182
183	#ifdef TEST_RIG
184
185	#include <mLib/alloc.h>
186	#include <mLib/testrig.h>
187
188	#include "mpscan.h"
189
190	#define ALLOC(v, vl, sz) do { \
191	size_t _sz = (sz); \
192	mpw *_vv = xmalloc(MPWS(_sz)); \
193	mpw *_vvl = _vv + _sz; \
194	(v) = _vv; \
195	(vl) = _vvl; \
196	} while (0)
197
198	#define LOAD(v, vl, d) do { \
199	const dstr *_d = (d); \
200	mpw _v, _vl; \
201	ALLOC(_v, _vl, MPW_RQ(_d->len)); \
202	mpx_loadb(_v, _vl, _d->buf, _d->len); \
203	(v) = _v; \
204	(vl) = _vl; \
205	} while (0)
206
207	#define MAX(x, y) ((x) > (y) ? (x) : (y))
208
209	static void dumpmp(const char msg, const mpw v, const mpw *vl)
210	{
211	fputs(msg, stderr);
212	MPX_SHRINK(v, vl);
213	while (v < vl)
214	fprintf(stderr, " %08lx", (unsigned long)*--vl);
215	fputc('\n', stderr);
216	}
217
218	static int usqr(dstr *v)
219	{
220	mpw a, al;
221	mpw c, cl;
222	mpw d, dl;
223	mpw s, sl;
224	size_t m;
225	int ok = 1;
226
227	LOAD(a, al, &v[0]);
228	LOAD(c, cl, &v[1]);
229	m = al - a + 1;
230	ALLOC(d, dl, 2 * m);
231	ALLOC(s, sl, 2 * m + 32);
232
233	mpx_ksqr(d, dl, a, al, s, sl);
234	if (MPX_UCMP(d, dl, !=, c, cl)) {
235	fprintf(stderr, "\n*** usqr failed\n");
236	dumpmp(" a", a, al);
237	dumpmp("expected", c, cl);
238	dumpmp(" result", d, dl);
239	ok = 0;
240	}
241
242	free(a); free(c); free(d); free(s);
243	return (ok);
244	}
245
246	static test_chunk defs[] = {
247	{ "usqr", usqr, { &type_hex, &type_hex, 0 } },
248	{ 0, 0, { 0 } }
249	};
250
251	int main(int argc, char *argv[])
252	{
253	test_run(argc, argv, defs, SRCDIR"/tests/mpx");
254	return (0);
255	}
256
257	#endif
258
259	/----- That's all, folks -------------------------------------------------/