mirror of
https://github.com/0intro/conterm
synced 2024-11-25 23:19:36 +03:00
157 lines
3.0 KiB
C
157 lines
3.0 KiB
C
#include "os.h"
|
|
#include <mp.h>
|
|
#include "dat.h"
|
|
|
|
//
|
|
// from knuth's 1969 seminumberical algorithms, pp 233-235 and pp 258-260
|
|
//
|
|
// mpvecmul is an assembly language routine that performs the inner
|
|
// loop.
|
|
//
|
|
// the karatsuba trade off is set empiricly by measuring the algs on
|
|
// a 400 MHz Pentium II.
|
|
//
|
|
|
|
// karatsuba like (see knuth pg 258)
|
|
// prereq: p is already zeroed
|
|
static void
|
|
mpkaratsuba(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p)
|
|
{
|
|
mpdigit *t, *u0, *u1, *v0, *v1, *u0v0, *u1v1, *res, *diffprod;
|
|
int u0len, u1len, v0len, v1len, reslen;
|
|
int sign, n;
|
|
|
|
// divide each piece in half
|
|
n = alen/2;
|
|
if(alen&1)
|
|
n++;
|
|
u0len = n;
|
|
u1len = alen-n;
|
|
if(blen > n){
|
|
v0len = n;
|
|
v1len = blen-n;
|
|
} else {
|
|
v0len = blen;
|
|
v1len = 0;
|
|
}
|
|
u0 = a;
|
|
u1 = a + u0len;
|
|
v0 = b;
|
|
v1 = b + v0len;
|
|
|
|
// room for the partial products
|
|
t = mallocz(Dbytes*5*(2*n+1), 1);
|
|
if(t == nil)
|
|
sysfatal("mpkaratsuba: %r");
|
|
u0v0 = t;
|
|
u1v1 = t + (2*n+1);
|
|
diffprod = t + 2*(2*n+1);
|
|
res = t + 3*(2*n+1);
|
|
reslen = 4*n+1;
|
|
|
|
// t[0] = (u1-u0)
|
|
sign = 1;
|
|
if(mpveccmp(u1, u1len, u0, u0len) < 0){
|
|
sign = -1;
|
|
mpvecsub(u0, u0len, u1, u1len, u0v0);
|
|
} else
|
|
mpvecsub(u1, u1len, u0, u1len, u0v0);
|
|
|
|
// t[1] = (v0-v1)
|
|
if(mpveccmp(v0, v0len, v1, v1len) < 0){
|
|
sign *= -1;
|
|
mpvecsub(v1, v1len, v0, v1len, u1v1);
|
|
} else
|
|
mpvecsub(v0, v0len, v1, v1len, u1v1);
|
|
|
|
// t[4:5] = (u1-u0)*(v0-v1)
|
|
mpvecmul(u0v0, u0len, u1v1, v0len, diffprod);
|
|
|
|
// t[0:1] = u1*v1
|
|
memset(t, 0, 2*(2*n+1)*Dbytes);
|
|
if(v1len > 0)
|
|
mpvecmul(u1, u1len, v1, v1len, u1v1);
|
|
|
|
// t[2:3] = u0v0
|
|
mpvecmul(u0, u0len, v0, v0len, u0v0);
|
|
|
|
// res = u0*v0<<n + u0*v0
|
|
mpvecadd(res, reslen, u0v0, u0len+v0len, res);
|
|
mpvecadd(res+n, reslen-n, u0v0, u0len+v0len, res+n);
|
|
|
|
// res += u1*v1<<n + u1*v1<<2*n
|
|
if(v1len > 0){
|
|
mpvecadd(res+n, reslen-n, u1v1, u1len+v1len, res+n);
|
|
mpvecadd(res+2*n, reslen-2*n, u1v1, u1len+v1len, res+2*n);
|
|
}
|
|
|
|
// res += (u1-u0)*(v0-v1)<<n
|
|
if(sign < 0)
|
|
mpvecsub(res+n, reslen-n, diffprod, u0len+v0len, res+n);
|
|
else
|
|
mpvecadd(res+n, reslen-n, diffprod, u0len+v0len, res+n);
|
|
memmove(p, res, (alen+blen)*Dbytes);
|
|
|
|
free(t);
|
|
}
|
|
|
|
#define KARATSUBAMIN 32
|
|
|
|
void
|
|
mpvecmul(mpdigit *a, int alen, mpdigit *b, int blen, mpdigit *p)
|
|
{
|
|
int i;
|
|
mpdigit d;
|
|
mpdigit *t;
|
|
|
|
// both mpvecdigmuladd and karatsuba are fastest when a is the longer vector
|
|
if(alen < blen){
|
|
i = alen;
|
|
alen = blen;
|
|
blen = i;
|
|
t = a;
|
|
a = b;
|
|
b = t;
|
|
}
|
|
if(blen == 0){
|
|
memset(p, 0, Dbytes*(alen+blen));
|
|
return;
|
|
}
|
|
|
|
if(alen >= KARATSUBAMIN && blen > 1){
|
|
// O(n^1.585)
|
|
mpkaratsuba(a, alen, b, blen, p);
|
|
} else {
|
|
// O(n^2)
|
|
for(i = 0; i < blen; i++){
|
|
d = b[i];
|
|
if(d != 0)
|
|
mpvecdigmuladd(a, alen, d, &p[i]);
|
|
}
|
|
}
|
|
}
|
|
|
|
void
|
|
mpmul(mpint *b1, mpint *b2, mpint *prod)
|
|
{
|
|
mpint *oprod;
|
|
|
|
oprod = nil;
|
|
if(prod == b1 || prod == b2){
|
|
oprod = prod;
|
|
prod = mpnew(0);
|
|
}
|
|
|
|
prod->top = 0;
|
|
mpbits(prod, (b1->top+b2->top+1)*Dbits);
|
|
mpvecmul(b1->p, b1->top, b2->p, b2->top, prod->p);
|
|
prod->top = b1->top+b2->top+1;
|
|
prod->sign = b1->sign*b2->sign;
|
|
mpnorm(prod);
|
|
|
|
if(oprod != nil){
|
|
mpassign(prod, oprod);
|
|
mpfree(prod);
|
|
}
|
|
}
|