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#include "os.h"
#include <mp.h>
#include "dat.h"
// division ala knuth, seminumerical algorithms, pp 237-238
// the numbers are stored backwards to what knuth expects so j
// counts down rather than up.
void
mpdiv(mpint *dividend, mpint *divisor, mpint *quotient, mpint *remainder)
{
int j, s, vn, sign, qsign, rsign;
mpdigit qd, *up, *vp, *qp;
mpint *u, *v, *t;
assert(quotient != remainder);
assert(divisor->flags & MPnorm);
// divide bv zero
if(divisor->top == 0)
abort();
// division by one or small powers of two
if(divisor->top == 1 && (divisor->p[0] & divisor->p[0]-1) == 0){
vlong r = 0;
if(dividend->top > 0)
r = (vlong)dividend->sign * (dividend->p[0] & divisor->p[0]-1);
if(quotient != nil){
sign = divisor->sign;
for(s = 0; ((divisor->p[0] >> s) & 1) == 0; s++)
;
mpright(dividend, s, quotient);
if(sign < 0)
quotient->sign ^= (-mpmagcmp(quotient, mpzero) >> 31) << 1;
}
if(remainder != nil){
remainder->flags |= dividend->flags & MPtimesafe;
vtomp(r, remainder);
}
return;
}
assert((dividend->flags & MPtimesafe) == 0);
// quick check
if(mpmagcmp(dividend, divisor) < 0){
if(remainder != nil)
mpassign(dividend, remainder);
if(quotient != nil)
mpassign(mpzero, quotient);
return;
}
qsign = divisor->sign * dividend->sign;
rsign = dividend->sign;
if(quotient != nil)
quotient->sign = qsign;
if(remainder != nil)
remainder->sign = rsign;
// 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){
assert((quotient->flags & MPtimesafe) == 0);
mpnorm(quotient);
}
if(remainder != nil){
assert((remainder->flags & MPtimesafe) == 0);
mpright(u, s, remainder); // u is the remainder shifted
}
mpfree(t);
mpfree(u);
if(v != divisor)
mpfree(v);
}
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