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#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "cputime.h"
#define DIVREM(qp,np,dp,nn) \
(nn < DIV_DC_THRESHOLD) \
? mpn_sb_divrem_mn (qp, np, nn + nn, dp, nn) \
: mpn_dc_divrem_n_new (qp, np, dp, nn)
static mp_limb_t
mpn_dc_divrem_n_new (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n)
{
mp_size_t l, m;
mp_limb_t qh, cc, ql;
mp_ptr tmp;
MPFR_TMP_DECL (marker);
l = n / 2;
m = n - l; /* m >= l */
MPFR_TMP_MARK (marker);
qh = DIVREM (qp + l, np + 2 * l, dp + l, m);
/* partial remainder is in {np, 2l+m} = {np, n+l} */
/* subtract Q1 * D0, where Q1 = {qp + l, m}, D0 = {d, l} */
tmp = MPFR_TMP_ALLOC_LIMBS (n);
mpn_mul (tmp, qp + l, m, dp, l);
cc = mpn_sub_n (np + l, np + l, tmp, n);
if (qh) cc += mpn_sub_n (np + n, np + n, dp, l);
/* have to subtract cc at np[n+l] */
while (cc)
{
qh -= mpn_sub_1 (qp + l, qp + l, m, (mp_limb_t) 1);
cc -= mpn_add_n (np + l, np + l, dp, n);
}
ql = DIVREM (qp, np + m, dp + m, l);
/* partial remainder is in {np, m+l} = {np, n} */
/* subtract Q0 * D0', where Q0 = {qp, l}, D0' = {d, m} */
mpn_mul (tmp, dp, m, qp, l);
cc = mpn_sub_n (np, np, tmp, n);
MPFR_TMP_FREE (marker);
if (ql) cc += mpn_sub_n (np + l, np + l, dp, m);
while (cc)
{
ql -= mpn_sub_1 (qp, qp, l, (mp_limb_t) 1);
cc -= mpn_add_n (np, np, dp, n);
}
/* propagate ql */
qh += mpn_add_1 (qp + l, qp + l, m, ql);
return qh;
}
#define DIVREM_HIGH(qp,np,dp,nn) \
(nn < DIV_DC_THRESHOLD) \
? mpn_sb_divrem_mn (qp, np, nn + nn, dp, nn) \
: mpn_dc_divrem_n_high (qp, np, dp, nn)
static mp_limb_t
mpn_dc_divrem_n_high (mp_ptr qp, mp_ptr np, mp_srcptr dp, mp_size_t n)
{
mp_size_t l, m;
mp_limb_t qh, cc, ql;
mp_ptr tmp;
MPFR_TMP_DECL (marker);
l = (n-1) / 2 ;
m = n - l; /* m >= l */
MPFR_TMP_MARK (marker);
qh = DIVREM (qp + l, np + 2 * l, dp + l, m);
/* partial remainder is in {np, 2l+m} = {np, n+l} */
/* subtract Q1 * D0, where Q1 = {qp + l, m}, D0 = {d, l} */
tmp = MPFR_TMP_ALLOC_LIMBS (n);
mpn_mul (tmp, qp + l, m, dp, l); /* FIXME: use a short product */
/* mpfr_mulhigh_n (tmp+m+l-2*l, qp+l+m-l, dp, l); */
cc = mpn_sub_n (np + l, np + l, tmp, n);
MPFR_TMP_FREE (marker);
if (qh) cc += mpn_sub_n (np + n, np + n, dp, l);
/* have to subtract cc at np[n+l] */
while (cc)
{
qh -= mpn_sub_1 (qp + l, qp + l, m, (mp_limb_t) 1);
cc -= mpn_add_n (np + l, np + l, dp, n);
}
ql = DIVREM_HIGH (qp, np + m, dp + m, l);
/* propagate ql */
qh += mpn_add_1 (qp + l, qp + l, m, ql);
return qh;
}
void bench (int argc, const char *argv[])
{
int n = (argc > 1) ? atoi (argv[1]) : 10000;
int k = (argc > 2) ? atoi (argv[2]) : 1;
mp_limb_t *n0p, *np, *n2p, *qp, *q2p, *dp;
int st;
int i;
n0p = malloc (2 * n * sizeof (mp_limb_t));
np = malloc (2 * n * sizeof (mp_limb_t));
n2p = malloc (2 * n * sizeof (mp_limb_t));
dp = malloc (n * sizeof (mp_limb_t));
qp = malloc (n * sizeof (mp_limb_t));
q2p = malloc (n * sizeof (mp_limb_t));
mpn_random (n0p, 2 * n);
mpn_random (dp, n);
dp[n - 1] |= GMP_LIMB_HIGHBIT;
printf ("DIV_DC_THRESHOLD=%u\n", DIV_DC_THRESHOLD);
st = cputime ();
for (i = 0; i < k; i++)
{
MPN_COPY (np, n0p, 2 * n);
mpn_divrem (qp, 0, np, 2 * n, dp, n);
}
printf ("mpn_divrem took %dms\n", cputime () - st);
st = cputime ();
for (i = 0; i < k; i++)
{
MPN_COPY (n2p, n0p, 2 * n);
mpn_dc_divrem_n_new (q2p, n2p, dp, n);
}
printf ("mpn_dc_divrem_n_new took %dms\n", cputime () - st);
if (mpn_cmp (np, n2p, n) || mpn_cmp (qp, q2p, n))
abort ();
st = cputime ();
for (i = 0; i < k; i++)
{
MPN_COPY (n2p, n0p, 2 * n);
mpn_dc_divrem_n_high (q2p, n2p, dp, n);
}
printf ("mpn_dc_divrem_n_high took %dms\n", cputime () - st);
for (i = n - 1; i >= 0 && q2p[i] == qp[i]; i--);
if (i >= 0)
printf ("limbs %d differ: %lu %lu %ld\n", i, qp[i], q2p[i],
(long) q2p[i]-qp[i]);
}
void
check (int argc, const char *argv[])
{
int n = (argc > 1) ? atoi (argv[1]) : 1000;
int k = (argc > 2) ? atoi (argv[2]) : 10000000;
mp_limb_t *n0p, *np, *n2p, *qp, *q2p, *dp;
mp_limb_t max, qqh1, qqh2;
int st;
int i;
int j;
mp_limb_t max_error;
count_leading_zeros (max_error, n);
max_error = 2*(BITS_PER_MP_LIMB-max_error);
printf ("For N=%lu estimated max_error=%lu ulps\n",
(unsigned long) n, (unsigned long) max_error);
n0p = malloc (2 * n * sizeof (mp_limb_t));
np = malloc (2 * n * sizeof (mp_limb_t));
n2p = malloc (2 * n * sizeof (mp_limb_t));
dp = malloc (n * sizeof (mp_limb_t));
qp = malloc (n * sizeof (mp_limb_t));
q2p = malloc (n * sizeof (mp_limb_t));
max = 0;
for (j = 0 ; j < k ; j++)
{
mpn_random2 (n0p, 2 * n);
mpn_random2 (dp, n);
dp[n - 1] |= GMP_LIMB_HIGHBIT;
MPN_COPY (np, n0p, 2 * n);
mpn_divrem (qp, 0, np, 2 * n, dp, n);
MPN_COPY (n2p, n0p, 2 * n);
qqh2 = mpn_dc_divrem_n_high (q2p, n2p, dp, n);
if (mpn_cmp (qp, q2p, n) > 0)
{
printf ("QP > QP_high\n");
if (n <= 10)
{
printf ("dp=");
for (i = n-1 ; i >= 0 ; i--)
printf (" %016Lx", (unsigned long) dp[i]);
printf ("\nn0p=");
for (i = 2*n-1 ; i >= 0 ; i--)
printf (" %016Lx", (unsigned long) n0p[i]);
printf ("\nqp=");
for (i = n-1 ; i >= 0 ; i--)
printf (" %016Lx", (unsigned long) qp[i]);
printf ("\nq2p=");
for (i = n-1 ; i >= 0 ; i--)
printf (" %016Lx", (unsigned long) q2p[i]);
printf ("\nQcarry=%lu\n", qqh2);
}
return;
}
mpn_sub_n (q2p, q2p, qp, n);
for (i = n-1 ; i >= 0 && q2p[i] == 0 ; i--);
if (i > 0)
{
printf ("Error for i=%d\n", i);
return;
}
if (q2p[0] >= max_error)
{
printf ("Too many wrong ulps: %lu\n",
(unsigned long) q2p[0]);
return;
}
if (max < q2p[0])
max = q2p[0];
}
printf ("Done. Max error=%lu ulps\n", max);
return;
}
int
main (int argc, const char *argv[])
{
if (argc > 1 && strcmp (argv[1], "-check") == 0)
check (argc-1, argv+1);
else
bench (argc, argv);
return 0;
}
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