/* FIXME: Document storage need. */
mp_size_t
mpn_hgcd_reduce (struct hgcd_matrix *M,
mp_ptr ap, mp_ptr bp, mp_size_t n, mp_size_t p,
mp_ptr tp)
{
mp_size_t nn;
if (BELOW_THRESHOLD (n, HGCD_REDUCE_THRESHOLD))
{
nn = mpn_hgcd (ap + p, bp + p, n - p, M, tp);
if (nn > 0)
/* Needs 2*(p + M->n) <= 2*(floor(n/2) + ceil(n/2) - 1)
= 2 (n - 1) */
return mpn_hgcd_matrix_adjust (M, p + nn, ap, bp, p, tp);
}
else
{
MPN_COPY (tp, ap + p, n - p);
MPN_COPY (tp + n - p, bp + p, n - p);
if (mpn_hgcd_appr (tp, tp + n - p, n - p, M, tp + 2*(n-p)))
return hgcd_matrix_apply (M, ap, bp, n);
}
return 0;
}
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];
}
/* Destroys inputs. */
int
mpn_hgcd_appr (mp_ptr ap, mp_ptr bp, mp_size_t n,
struct hgcd_matrix *M, mp_ptr tp)
{
mp_size_t s;
int success = 0;
ASSERT (n > 0);
ASSERT ((ap[n-1] | bp[n-1]) != 0);
if (n <= 2)
/* Implies s = n. A fairly uninteresting case but exercised by the
random inputs of the testsuite. */
return 0;
ASSERT ((n+1)/2 - 1 < M->alloc);
/* We aim for reduction of to GMP_NUMB_BITS * s bits. But each time
we discard some of the least significant limbs, we must keep one
additional bit to account for the truncation error. We maintain
the GMP_NUMB_BITS * s - extra_bits as the current target size. */
s = n/2 + 1;
if (BELOW_THRESHOLD (n, HGCD_APPR_THRESHOLD))
{
unsigned extra_bits = 0;
while (n > 2)
{
mp_size_t nn;
ASSERT (n > s);
ASSERT (n <= 2*s);
nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
if (!nn)
break;
n = nn;
success = 1;
/* We can truncate and discard the lower p bits whenever nbits <=
2*sbits - p. To account for the truncation error, we must
adjust
sbits <-- sbits + 1 - p,
rather than just sbits <-- sbits - p. This adjustment makes
the produced matrix sligthly smaller than it could be. */
if (GMP_NUMB_BITS * (n + 1) + 2 * extra_bits <= 2*GMP_NUMB_BITS * s)
{
mp_size_t p = (GMP_NUMB_BITS * (2*s - n) - 2*extra_bits) / GMP_NUMB_BITS;
if (extra_bits == 0)
{
/* We cross a limb boundary and bump s. We can't do that
if the result is that it makes makes min(U, V)
smaller than 2^{GMP_NUMB_BITS} s. */
if (s + 1 == n
|| mpn_zero_p (ap + s + 1, n - s - 1)
|| mpn_zero_p (bp + s + 1, n - s - 1))
continue;
extra_bits = GMP_NUMB_BITS - 1;
s++;
}
else
{
extra_bits--;
}
/* Drop the p least significant limbs */
ap += p; bp += p; n -= p; s -= p;
}
}
ASSERT (s > 0);
if (extra_bits > 0)
{
/* We can get here only of we have dropped at least one of the
least significant bits, so we can decrement ap and bp. We can
then shift left extra bits using mpn_shiftr. */
/* NOTE: In the unlikely case that n is large, it would be
preferable to do an initial subdiv step to reduce the size
before shifting, but that would mean daplicating
mpn_gcd_subdiv_step with a bit count rather than a limb
count. */
ap--; bp--;
ap[0] = mpn_rshift (ap+1, ap+1, n, GMP_NUMB_BITS - extra_bits);
bp[0] = mpn_rshift (bp+1, bp+1, n, GMP_NUMB_BITS - extra_bits);
n += (ap[n] | bp[n]) > 0;
ASSERT (success);
while (n > 2)
{
mp_size_t nn;
ASSERT (n > s);
ASSERT (n <= 2*s);
nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
if (!nn)
return 1;
n = nn;
}
}
if (n == 2)
{
struct hgcd_matrix1 M1;
ASSERT (s == 1);
if (mpn_hgcd2 (ap[1], ap[0], bp[1], bp[0], &M1))
{
/* Multiply M <- M * M1 */
mpn_hgcd_matrix_mul_1 (M, &M1, tp);
success = 1;
}
}
return success;
}
else
{
mp_size_t n2 = (3*n)/4 + 1;
mp_size_t p = n/2;
mp_size_t nn;
nn = mpn_hgcd_reduce (M, ap, bp, n, p, tp);
if (nn)
{
n = nn;
/* FIXME: Discard some of the low limbs immediately? */
success = 1;
}
while (n > n2)
{
mp_size_t nn;
/* Needs n + 1 storage */
nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
if (!nn)
return success;
n = nn;
success = 1;
}
if (n > s + 2)
{
struct hgcd_matrix M1;
mp_size_t scratch;
p = 2*s - n + 1;
scratch = MPN_HGCD_MATRIX_INIT_ITCH (n-p);
mpn_hgcd_matrix_init(&M1, n - p, tp);
if (mpn_hgcd_appr (ap + p, bp + p, n - p, &M1, tp + scratch))
{
/* We always have max(M) > 2^{-(GMP_NUMB_BITS + 1)} max(M1) */
ASSERT (M->n + 2 >= M1.n);
/* Furthermore, assume M ends with a quotient (1, q; 0, 1),
then either q or q + 1 is a correct quotient, and M1 will
start with either (1, 0; 1, 1) or (2, 1; 1, 1). This
rules out the case that the size of M * M1 is much
smaller than the expected M->n + M1->n. */
ASSERT (M->n + M1.n < M->alloc);
/* We need a bound for of M->n + M1.n. Let n be the original
input size. Then
ceil(n/2) - 1 >= size of product >= M.n + M1.n - 2
and it follows that
M.n + M1.n <= ceil(n/2) + 1
Then 3*(M.n + M1.n) + 5 <= 3 * ceil(n/2) + 8 is the
amount of needed scratch space. */
mpn_hgcd_matrix_mul (M, &M1, tp + scratch);
return 1;
}
}
for(;;)
{
mp_size_t nn;
ASSERT (n > s);
ASSERT (n <= 2*s);
nn = mpn_hgcd_step (n, ap, bp, s, M, tp);
if (!nn)
return success;
n = nn;
success = 1;
}
}
}
