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]);
}
}
}
mpint*
mpfactorial(ulong n)
{
int i;
ulong k;
unsigned cnt;
int max, mmax;
mpdigit p, pp[2];
mpint *r, *s, *stk[31];
cnt = 0;
max = mmax = -1;
p = 1;
r = mpnew(0);
for(k=2; k<=n; k++) {
pp[0] = 0;
pp[1] = 0;
mpvecdigmuladd(&p, 1, (mpdigit)k, pp);
if(pp[1] == 0) /* !overflow */
p = pp[0];
else {
cnt++;
if((cnt & 1) == 0) {
s = stk[max];
mpbits(r, Dbits*(s->top+1+1));
memset(r->p, 0, Dbytes*(s->top+1+1));
mpvecmul(s->p, s->top, &p, 1, r->p);
r->sign = 1;
r->top = s->top+1+1; /* XXX: norm */
mpassign(r, s);
for(i=4; (cnt & (i-1)) == 0; i=i<<1) {
mpmul(stk[max], stk[max-1], r);
mpassign(r, stk[max-1]);
max--;
}
} else {
max++;
if(max > mmax) {
mmax++;
if(max > nelem(stk))
abort();
stk[max] = mpnew(Dbits);
}
stk[max]->top = 1;
stk[max]->p[0] = p;
}
p = (mpdigit)k;
}
}
if(max < 0) {
mpbits(r, Dbits);
r->top = 1;
r->sign = 1;
r->p[0] = p;
} else {
s = stk[max--];
mpbits(r, Dbits*(s->top+1+1));
memset(r->p, 0, Dbytes*(s->top+1+1));
mpvecmul(s->p, s->top, &p, 1, r->p);
r->sign = 1;
r->top = s->top+1+1; /* XXX: norm */
}
while(max >= 0)
mpmul(r, stk[max--], r);
for(max=mmax; max>=0; max--)
mpfree(stk[max]);
mpnorm(r);
return r;
}
void
mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder)
{
int j, s, vn, sign;
mpdigit qd, *up, *vp, *qp;
mpint *u, *v, *t;
// divide bv zero
if(divisor->top == 0)
sysfatal("mpdiv: divide by zero");
// quick check
if(mpmagcmp(dividend, divisor) < 0){
if(remainder != nil)
mpassign(dividend, remainder);
if(quotient != nil)
mpassign(mpzero, quotient);
return;
}
// D1: shift until divisor, v, has hi bit set (needed to make trial
// divisor accurate)
qd = divisor->p[divisor->top-1];
for(s = 0; (qd & mpdighi) == 0; s++)
qd <<= 1;
u = mpnew((dividend->top+2)*Dbits + s);
if(s == 0 && divisor != quotient && divisor != remainder) {
mpassign(dividend, u);
v = divisor;
} else {
mpleft(dividend, s, u);
v = mpnew(divisor->top*Dbits);
mpleft(divisor, s, v);
}
up = u->p+u->top-1;
vp = v->p+v->top-1;
vn = v->top;
// D1a: make sure high digit of dividend is less than high digit of divisor
if(*up >= *vp){
*++up = 0;
u->top++;
}
// storage for multiplies
t = mpnew(4*Dbits);
qp = nil;
if(quotient != nil){
mpbits(quotient, (u->top - v->top)*Dbits);
quotient->top = u->top - v->top;
qp = quotient->p+quotient->top-1;
}
// D2, D7: loop on length of dividend
for(j = u->top; j > vn; j--){
// D3: calculate trial divisor
mpdigdiv(up-1, *vp, &qd);
// D3a: rule out trial divisors 2 greater than real divisor
if(vn > 1) for(;;){
memset(t->p, 0, 3*Dbytes); // mpvecdigmuladd adds to what's there
mpvecdigmuladd(vp-1, 2, qd, t->p);
if(mpveccmp(t->p, 3, up-2, 3) > 0)
qd--;
else
break;
}
// D4: u -= v*qd << j*Dbits
sign = mpvecdigmulsub(v->p, vn, qd, up-vn);
if(sign < 0){
// D6: trial divisor was too high, add back borrowed
// value and decrease divisor
mpvecadd(up-vn, vn+1, v->p, vn, up-vn);
qd--;
}
// D5: save quotient digit
if(qp != nil)
*qp-- = qd;
// push top of u down one
u->top--;
*up-- = 0;
}
if(qp != nil){
mpnorm(quotient);
if(dividend->sign != divisor->sign)
quotient->sign = -1;
}
if(remainder != nil){
mpright(u, s, remainder); // u is the remainder shifted
remainder->sign = dividend->sign;
}
mpfree(t);
mpfree(u);
if(v != divisor)
mpfree(v);
}
