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#include <stdio.h>
#include <stdlib.h>
#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"
#include "timming.h"
#define MAX_BASECASE_THREEHOLD 500
#define TOLERANCE 102/100
/*
<----------- un ----------->
___________________________
/ . / ^
/ . . / |
/ . . / |
/ . . / vn
/ . . / |
/ . . / |
/ . . / |
/__________________________/ v
<----- vn ----><-- un-vn --> <---- vn--- ->
rn ------> ignore low part of v and u for all partial products
rn ---------------> ignore low part of u for all partial products
rn -----------------------------> ignore low part of u for some partial products
Algorithm:
1. Use common mpn_mul_1/mpn_addmul_1 loops, but exclude results more than one
limbs under result part.
2. If (lowest limb) > (number of rows of first ignored column), compute
another column, propagate carry.
*/
#if 0
void
mpn_mulhigh_n_basecase (mp_ptr rp, mp_ptr up, mp_ptr vp, mp_size_t n)
{
mp_size_t i;
{
mp_limb_t tmp1, tmp2, tmp3;
umul_ppmm (tmp1, rp[0], up[n-2], vp[0]);
umul_ppmm (tmp3, tmp2, up[n-1], vp[0]);
add_ssaaaa (rp[2], rp[1], tmp3, tmp2, 0, tmp1);
}
for (i = 3 ; i <= n ; i++)
rp[i] = mpn_addmul_1 (rp, up + n - i, i, vp[i - 2]);
rp[n+1] = mpn_addmul_1 (rp + 1, up, n, vp[n - 1]);
}
#endif
/* Put in rp[n-1..2n-1] an approximation of the n+1 high limbs
of {mp, n} * {np, n}.
The error is at worst of ln(n) for rp[n] and rp[n-1] is totally wrong */
void
mpn_mulhigh_n_basecase (mp_ptr rp, mp_srcptr up, mp_srcptr vp, mp_size_t n)
{
mp_size_t i;
rp += n-1;
umul_ppmm (rp[1], rp[0], up[n-1], vp[0]);
for (i = 1 ; i < n ; i++)
rp[i+1] = mpn_addmul_1 (rp, up + (n - i - 1), i+1, vp[i]);
}
mp_size_t mpn_mulhigh_ktab[1024];
void
mpn_mulhigh_n (mp_ptr rp, mp_srcptr np, mp_srcptr mp, mp_size_t n)
{
mp_size_t k;
if (n >= 1024)
abort ();
k = mpn_mulhigh_ktab[n];
if (k < 0)
mpn_mul_basecase (rp, np, n, mp, n);
else if (k == 0)
mpn_mulhigh_n_basecase (rp, np, mp, n);
else
{
mp_size_t l = n - k;
mp_limb_t cy;
mpn_mul_n (rp + 2 * l, np + l, mp + l, k); /* fills rp[2l..2n-1] */
mpn_mulhigh_n (rp, np + k, mp, l); /* fills rp[l-1..2l-1] */
cy = mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
mpn_mulhigh_n (rp, np, mp + k, l); /* fills rp[l-1..2l-1] */
cy += mpn_add_n (rp + n - 1, rp + n - 1, rp + l - 1, l + 1);
mpn_add_1 (rp + n + l, rp + n + l, k, cy); /* propagate carry */
}
}
mp_size_t
find_best_k (mp_size_t n)
{
mp_limb_t a[n], b[n], c[2*n];
mp_size_t k, kbest;
unsigned long long t, tbest;
if (n == 0)
return -1;
CALCUL_OVERHEAD;
mpn_random (a, n);
mpn_random (b, n);
/* Check k == -1, mpn_mul_base_basecase */
mpn_mulhigh_ktab[n] = -1;
kbest = -1;
tbest = MEASURE (mpn_mulhigh_n (c, a, b, n) );
/* Check k == 0, mpn_mulhigh_basecase */
mpn_mulhigh_ktab[n] = 0;
t = MEASURE (mpn_mulhigh_n (c, a, b, n) );
if (t * TOLERANCE < tbest)
kbest = 0, tbest = t;
/* Check Mulder */
for (k = (n+1)/2 ; k < n ; k++) {
mpn_mulhigh_ktab[n] = k;
t = MEASURE (mpn_mulhigh_n (c, a, b, n));
if (t *TOLERANCE < tbest)
kbest = k, tbest = t;
}
return kbest;
}
void
tune (mp_size_t n)
{
/* Find ThreeHold */
mp_size_t k;
for (k = 0 ; k <= n ; k++) {
mpn_mulhigh_ktab[k] = find_best_k (k);
printf ("%d, ", mpn_mulhigh_ktab[k]);
fflush (stdout);
}
putchar ('\n');
}
#ifndef SIZE
#define SIZE 15
#endif
int
main (int argc, const char *argv[])
{
mp_limb_t *a, *b, *c, *r;
mp_size_t an, bn, cn, size, size_end, size_step;
int i;
unsigned long long t1, t2, t3;
printf ("%s [SIZE_START [SIZE_END [SIZE_STEP]]]\n", argv[0]);
size = SIZE;
if (argc >= 2)
size = atol (argv[1]);
size_end = size;
if (argc >= 3)
size_end = atol (argv[2]);
size_step = 1;
if (argc >= 4)
size_step = atol (argv[3]);
printf ("Tune in progress...\n");
tune (size_end);
for ( ; size <= size_end ; size += size_step) {
printf ("Size= %4u ", size);
a = malloc (sizeof(mp_limb_t)*size);
b = malloc (sizeof(mp_limb_t)*size);
c = malloc (sizeof(mp_limb_t)*size*3);
r = malloc (sizeof(mp_limb_t)*size*3);
CALCUL_OVERHEAD;
mpn_random (a, size);
mpn_random (b, size);
t1 = MEASURE (mpn_mulhigh_n (c, a, b, size));
printf ("mulhigh_n: %7Lu ", t1);
t2 = MEASURE (mpn_mul_n (r, a, b, size));
printf ("mpn_mul_n: %7Lu ", t2);
t3 = MEASURE (mpn_mulhigh_n_basecase (c, a, b, size));
printf ("mulhigh_bc: %7Lu ", t3);
printf ("Ratio: %f %c %c\n", (double) t2 / t1,
t1 < t2 ? '*' : ' ',
t1 < t3 ? '$' : ' ' );
if (size < 50 && size == size_end)
{
printf ("High: ");
for (i = 2*size-1 ; i>=size-1 ; i--)
printf ("%08X ", c[i]);
printf("\nmuln: ");
for (i = 2*size-1 ; i>=size-1 ; i--)
printf ("%08X ", r[i]);
printf("\n");
}
free (a);
free (b);
free (c);
free (r);
}
return 0;
}
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