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/* Test mpn_hgcd_appr.
Copyright 1991, 1993, 1994, 1996, 1997, 2000-2004, 2011 Free Software
Foundation, Inc.
This file is part of the GNU MP Library test suite.
The GNU MP Library test suite is free software; you can redistribute it
and/or modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 3 of the License,
or (at your option) any later version.
The GNU MP Library test suite 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 General
Public License for more details.
You should have received a copy of the GNU General Public License along with
the GNU MP Library test suite. If not, see https://www.gnu.org/licenses/. */
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "gmp-impl.h"
#include "tests.h"
static mp_size_t one_test (mpz_t, mpz_t, int);
static void debug_mp (mpz_t, int);
#define MIN_OPERAND_SIZE 2
struct hgcd_ref
{
mpz_t m[2][2];
};
static void hgcd_ref_init (struct hgcd_ref *hgcd);
static void hgcd_ref_clear (struct hgcd_ref *hgcd);
static int hgcd_ref (struct hgcd_ref *hgcd, mpz_t a, mpz_t b);
static int hgcd_ref_equal (const struct hgcd_ref *, const struct hgcd_ref *);
static int hgcd_appr_valid_p (mpz_t, mpz_t, mp_size_t, struct hgcd_ref *,
mpz_t, mpz_t, mp_size_t, struct hgcd_matrix *);
static int verbose_flag = 0;
int
main (int argc, char **argv)
{
mpz_t op1, op2, temp1, temp2;
int i, j, chain_len;
gmp_randstate_ptr rands;
mpz_t bs;
unsigned long size_range;
if (argc > 1)
{
if (strcmp (argv[1], "-v") == 0)
verbose_flag = 1;
else
{
fprintf (stderr, "Invalid argument.\n");
return 1;
}
}
tests_start ();
rands = RANDS;
mpz_init (bs);
mpz_init (op1);
mpz_init (op2);
mpz_init (temp1);
mpz_init (temp2);
for (i = 0; i < 15; i++)
{
/* Generate plain operands with unknown gcd. These types of operands
have proven to trigger certain bugs in development versions of the
gcd code. */
mpz_urandomb (bs, rands, 32);
size_range = mpz_get_ui (bs) % 13 + 2;
mpz_urandomb (bs, rands, size_range);
mpz_urandomb (op1, rands, mpz_get_ui (bs) + MIN_OPERAND_SIZE);
mpz_urandomb (bs, rands, size_range);
mpz_urandomb (op2, rands, mpz_get_ui (bs) + MIN_OPERAND_SIZE);
if (mpz_cmp (op1, op2) < 0)
mpz_swap (op1, op2);
if (mpz_size (op1) > 0)
one_test (op1, op2, i);
/* Generate a division chain backwards, allowing otherwise
unlikely huge quotients. */
mpz_set_ui (op1, 0);
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 16 + 1);
mpz_rrandomb (op2, rands, mpz_get_ui (bs));
mpz_add_ui (op2, op2, 1);
#if 0
chain_len = 1000000;
#else
mpz_urandomb (bs, rands, 32);
chain_len = mpz_get_ui (bs) % (GMP_NUMB_BITS * GCD_DC_THRESHOLD / 256);
#endif
for (j = 0; j < chain_len; j++)
{
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 12 + 1);
mpz_rrandomb (temp2, rands, mpz_get_ui (bs) + 1);
mpz_add_ui (temp2, temp2, 1);
mpz_mul (temp1, op2, temp2);
mpz_add (op1, op1, temp1);
/* Don't generate overly huge operands. */
if (SIZ (op1) > 3 * GCD_DC_THRESHOLD)
break;
mpz_urandomb (bs, rands, 32);
mpz_urandomb (bs, rands, mpz_get_ui (bs) % 12 + 1);
mpz_rrandomb (temp2, rands, mpz_get_ui (bs) + 1);
mpz_add_ui (temp2, temp2, 1);
mpz_mul (temp1, op1, temp2);
mpz_add (op2, op2, temp1);
/* Don't generate overly huge operands. */
if (SIZ (op2) > 3 * GCD_DC_THRESHOLD)
break;
}
if (mpz_cmp (op1, op2) < 0)
mpz_swap (op1, op2);
if (mpz_size (op1) > 0)
one_test (op1, op2, i);
}
mpz_clear (bs);
mpz_clear (op1);
mpz_clear (op2);
mpz_clear (temp1);
mpz_clear (temp2);
tests_end ();
exit (0);
}
static void
debug_mp (mpz_t x, int base)
{
mpz_out_str (stderr, base, x); fputc ('\n', stderr);
}
static mp_size_t
one_test (mpz_t a, mpz_t b, int i)
{
struct hgcd_matrix hgcd;
struct hgcd_ref ref;
mpz_t ref_r0;
mpz_t ref_r1;
mpz_t hgcd_r0;
mpz_t hgcd_r1;
int res[2];
mp_size_t asize;
mp_size_t bsize;
mp_size_t hgcd_init_scratch;
mp_size_t hgcd_scratch;
mp_ptr hgcd_init_tp;
mp_ptr hgcd_tp;
mp_limb_t marker[4];
asize = a->_mp_size;
bsize = b->_mp_size;
ASSERT (asize >= bsize);
hgcd_init_scratch = MPN_HGCD_MATRIX_INIT_ITCH (asize);
hgcd_init_tp = refmpn_malloc_limbs (hgcd_init_scratch + 2) + 1;
mpn_hgcd_matrix_init (&hgcd, asize, hgcd_init_tp);
hgcd_scratch = mpn_hgcd_appr_itch (asize);
hgcd_tp = refmpn_malloc_limbs (hgcd_scratch + 2) + 1;
mpn_random (marker, 4);
hgcd_init_tp[-1] = marker[0];
hgcd_init_tp[hgcd_init_scratch] = marker[1];
hgcd_tp[-1] = marker[2];
hgcd_tp[hgcd_scratch] = marker[3];
#if 0
fprintf (stderr,
"one_test: i = %d asize = %d, bsize = %d\n",
i, a->_mp_size, b->_mp_size);
gmp_fprintf (stderr,
"one_test: i = %d\n"
" a = %Zx\n"
" b = %Zx\n",
i, a, b);
#endif
hgcd_ref_init (&ref);
mpz_init_set (ref_r0, a);
mpz_init_set (ref_r1, b);
res[0] = hgcd_ref (&ref, ref_r0, ref_r1);
mpz_init_set (hgcd_r0, a);
mpz_init_set (hgcd_r1, b);
if (bsize < asize)
{
_mpz_realloc (hgcd_r1, asize);
MPN_ZERO (hgcd_r1->_mp_d + bsize, asize - bsize);
}
res[1] = mpn_hgcd_appr (hgcd_r0->_mp_d,
hgcd_r1->_mp_d,
asize,
&hgcd, hgcd_tp);
if (hgcd_init_tp[-1] != marker[0]
|| hgcd_init_tp[hgcd_init_scratch] != marker[1]
|| hgcd_tp[-1] != marker[2]
|| hgcd_tp[hgcd_scratch] != marker[3])
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "scratch space overwritten!\n");
if (hgcd_init_tp[-1] != marker[0])
gmp_fprintf (stderr,
"before init_tp: %Mx\n"
"expected: %Mx\n",
hgcd_init_tp[-1], marker[0]);
if (hgcd_init_tp[hgcd_init_scratch] != marker[1])
gmp_fprintf (stderr,
"after init_tp: %Mx\n"
"expected: %Mx\n",
hgcd_init_tp[hgcd_init_scratch], marker[1]);
if (hgcd_tp[-1] != marker[2])
gmp_fprintf (stderr,
"before tp: %Mx\n"
"expected: %Mx\n",
hgcd_tp[-1], marker[2]);
if (hgcd_tp[hgcd_scratch] != marker[3])
gmp_fprintf (stderr,
"after tp: %Mx\n"
"expected: %Mx\n",
hgcd_tp[hgcd_scratch], marker[3]);
abort ();
}
if (!hgcd_appr_valid_p (a, b, res[0], &ref, ref_r0, ref_r1,
res[1], &hgcd))
{
fprintf (stderr, "ERROR in test %d\n", i);
fprintf (stderr, "Invalid results for hgcd and hgcd_ref\n");
fprintf (stderr, "op1="); debug_mp (a, -16);
fprintf (stderr, "op2="); debug_mp (b, -16);
fprintf (stderr, "hgcd_ref: %ld\n", (long) res[0]);
fprintf (stderr, "mpn_hgcd_appr: %ld\n", (long) res[1]);
abort ();
}
refmpn_free_limbs (hgcd_init_tp - 1);
refmpn_free_limbs (hgcd_tp - 1);
hgcd_ref_clear (&ref);
mpz_clear (ref_r0);
mpz_clear (ref_r1);
mpz_clear (hgcd_r0);
mpz_clear (hgcd_r1);
return res[0];
}
static void
hgcd_ref_init (struct hgcd_ref *hgcd)
{
unsigned i;
for (i = 0; i<2; i++)
{
unsigned j;
for (j = 0; j<2; j++)
mpz_init (hgcd->m[i][j]);
}
}
static void
hgcd_ref_clear (struct hgcd_ref *hgcd)
{
unsigned i;
for (i = 0; i<2; i++)
{
unsigned j;
for (j = 0; j<2; j++)
mpz_clear (hgcd->m[i][j]);
}
}
static int
sdiv_qr (mpz_t q, mpz_t r, mp_size_t s, const mpz_t a, const mpz_t b)
{
mpz_fdiv_qr (q, r, a, b);
if (mpz_size (r) <= s)
{
mpz_add (r, r, b);
mpz_sub_ui (q, q, 1);
}
return (mpz_sgn (q) > 0);
}
static int
hgcd_ref (struct hgcd_ref *hgcd, mpz_t a, mpz_t b)
{
mp_size_t n = MAX (mpz_size (a), mpz_size (b));
mp_size_t s = n/2 + 1;
mpz_t q;
int res;
if (mpz_size (a) <= s || mpz_size (b) <= s)
return 0;
res = mpz_cmp (a, b);
if (res < 0)
{
mpz_sub (b, b, a);
if (mpz_size (b) <= s)
return 0;
mpz_set_ui (hgcd->m[0][0], 1); mpz_set_ui (hgcd->m[0][1], 0);
mpz_set_ui (hgcd->m[1][0], 1); mpz_set_ui (hgcd->m[1][1], 1);
}
else if (res > 0)
{
mpz_sub (a, a, b);
if (mpz_size (a) <= s)
return 0;
mpz_set_ui (hgcd->m[0][0], 1); mpz_set_ui (hgcd->m[0][1], 1);
mpz_set_ui (hgcd->m[1][0], 0); mpz_set_ui (hgcd->m[1][1], 1);
}
else
return 0;
mpz_init (q);
for (;;)
{
ASSERT (mpz_size (a) > s);
ASSERT (mpz_size (b) > s);
if (mpz_cmp (a, b) > 0)
{
if (!sdiv_qr (q, a, s, a, b))
break;
mpz_addmul (hgcd->m[0][1], q, hgcd->m[0][0]);
mpz_addmul (hgcd->m[1][1], q, hgcd->m[1][0]);
}
else
{
if (!sdiv_qr (q, b, s, b, a))
break;
mpz_addmul (hgcd->m[0][0], q, hgcd->m[0][1]);
mpz_addmul (hgcd->m[1][0], q, hgcd->m[1][1]);
}
}
mpz_clear (q);
return 1;
}
static int
hgcd_ref_equal (const struct hgcd_ref *A, const struct hgcd_ref *B)
{
unsigned i;
for (i = 0; i<2; i++)
{
unsigned j;
for (j = 0; j<2; j++)
if (mpz_cmp (A->m[i][j], B->m[i][j]) != 0)
return 0;
}
return 1;
}
static int
hgcd_appr_valid_p (mpz_t a, mpz_t b, mp_size_t res0,
struct hgcd_ref *ref, mpz_t ref_r0, mpz_t ref_r1,
mp_size_t res1, struct hgcd_matrix *hgcd)
{
mp_size_t n = MAX (mpz_size (a), mpz_size (b));
mp_size_t s = n/2 + 1;
mp_bitcnt_t dbits, abits, margin;
mpz_t appr_r0, appr_r1, t, q;
struct hgcd_ref appr;
if (!res0)
{
if (!res1)
return 1;
fprintf (stderr, "mpn_hgcd_appr returned 1 when no reduction possible.\n");
return 0;
}
/* NOTE: No *_clear calls on error return, since we're going to
abort anyway. */
mpz_init (t);
mpz_init (q);
hgcd_ref_init (&appr);
mpz_init (appr_r0);
mpz_init (appr_r1);
if (mpz_size (ref_r0) <= s)
{
fprintf (stderr, "ref_r0 too small!!!: "); debug_mp (ref_r0, 16);
return 0;
}
if (mpz_size (ref_r1) <= s)
{
fprintf (stderr, "ref_r1 too small!!!: "); debug_mp (ref_r1, 16);
return 0;
}
mpz_sub (t, ref_r0, ref_r1);
dbits = mpz_sizeinbase (t, 2);
if (dbits > s*GMP_NUMB_BITS)
{
fprintf (stderr, "ref |r0 - r1| too large!!!: "); debug_mp (t, 16);
return 0;
}
if (!res1)
{
mpz_set (appr_r0, a);
mpz_set (appr_r1, b);
}
else
{
unsigned i;
for (i = 0; i<2; i++)
{
unsigned j;
for (j = 0; j<2; j++)
{
mp_size_t mn = hgcd->n;
MPN_NORMALIZE (hgcd->p[i][j], mn);
mpz_realloc (appr.m[i][j], mn);
MPN_COPY (PTR (appr.m[i][j]), hgcd->p[i][j], mn);
SIZ (appr.m[i][j]) = mn;
}
}
mpz_mul (appr_r0, appr.m[1][1], a);
mpz_mul (t, appr.m[0][1], b);
mpz_sub (appr_r0, appr_r0, t);
if (mpz_sgn (appr_r0) <= 0
|| mpz_size (appr_r0) <= s)
{
fprintf (stderr, "appr_r0 too small: "); debug_mp (appr_r0, 16);
return 0;
}
mpz_mul (appr_r1, appr.m[1][0], a);
mpz_mul (t, appr.m[0][0], b);
mpz_sub (appr_r1, t, appr_r1);
if (mpz_sgn (appr_r1) <= 0
|| mpz_size (appr_r1) <= s)
{
fprintf (stderr, "appr_r1 too small: "); debug_mp (appr_r1, 16);
return 0;
}
}
mpz_sub (t, appr_r0, appr_r1);
abits = mpz_sizeinbase (t, 2);
if (abits < dbits)
{
fprintf (stderr, "|r0 - r1| too small: "); debug_mp (t, 16);
return 0;
}
/* We lose one bit each time we discard the least significant limbs.
For the lehmer code, that can happen at most s * (GMP_NUMB_BITS)
/ (GMP_NUMB_BITS - 1) times. For the dc code, we lose an entire
limb (or more?) for each level of recursion. */
margin = (n/2+1) * GMP_NUMB_BITS / (GMP_NUMB_BITS - 1);
{
mp_size_t rn;
for (rn = n; ABOVE_THRESHOLD (rn, HGCD_APPR_THRESHOLD); rn = (rn + 1)/2)
margin += GMP_NUMB_BITS;
}
if (verbose_flag && abits > dbits)
fprintf (stderr, "n = %u: sbits = %u: ref #(r0-r1): %u, appr #(r0-r1): %u excess: %d, margin: %u\n",
(unsigned) n, (unsigned) s*GMP_NUMB_BITS,
(unsigned) dbits, (unsigned) abits,
(int) (abits - s * GMP_NUMB_BITS), (unsigned) margin);
if (abits > s*GMP_NUMB_BITS + margin)
{
fprintf (stderr, "appr |r0 - r1| much larger than minimal (by %u bits, margin = %u bits)\n",
(unsigned) (abits - s*GMP_NUMB_BITS), (unsigned) margin);
return 0;
}
while (mpz_cmp (appr_r0, ref_r0) > 0 || mpz_cmp (appr_r1, ref_r1) > 0)
{
ASSERT (mpz_size (appr_r0) > s);
ASSERT (mpz_size (appr_r1) > s);
if (mpz_cmp (appr_r0, appr_r1) > 0)
{
if (!sdiv_qr (q, appr_r0, s, appr_r0, appr_r1))
break;
mpz_addmul (appr.m[0][1], q, appr.m[0][0]);
mpz_addmul (appr.m[1][1], q, appr.m[1][0]);
}
else
{
if (!sdiv_qr (q, appr_r1, s, appr_r1, appr_r0))
break;
mpz_addmul (appr.m[0][0], q, appr.m[0][1]);
mpz_addmul (appr.m[1][0], q, appr.m[1][1]);
}
}
if (mpz_cmp (appr_r0, ref_r0) != 0
|| mpz_cmp (appr_r1, ref_r1) != 0
|| !hgcd_ref_equal (ref, &appr))
{
fprintf (stderr, "appr_r0: "); debug_mp (appr_r0, 16);
fprintf (stderr, "ref_r0: "); debug_mp (ref_r0, 16);
fprintf (stderr, "appr_r1: "); debug_mp (appr_r1, 16);
fprintf (stderr, "ref_r1: "); debug_mp (ref_r1, 16);
return 0;
}
mpz_clear (t);
mpz_clear (q);
hgcd_ref_clear (&appr);
mpz_clear (appr_r0);
mpz_clear (appr_r1);
return 1;
}
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