static VALUE
bigmul_low_digits(VALUE x, VALUE y, int digits)
{
int xn = RBIGNUM_LEN(x);
if (FIXNUM_P(y)) y = INTVALUE2BIG(y);
int yn = RBIGNUM_LEN(y);
if (digits > xn + yn)
{
digits = xn + yn;
}
VALUE z = rb_big_new(digits, 1);
BDIGIT* xds = RBIGNUM_DIGITS(x);
BDIGIT* yds = RBIGNUM_DIGITS(y);
BDIGIT* zds = RBIGNUM_DIGITS(z);
BDIGIT c0,c1,c2; // carry
int i, j, k, beg, end;
for (k = c0 = c1 = c2 = 0; k < digits; k++)
{
beg = k >= yn - 1 ? k - yn + 1 : 0;
end = k >= xn ? xn - 1 : k;
for (i = beg, j = k - beg; i <= end; ++i, --j)
MULADD(xds[i], yds[j]);
zds[k] = c0;
c0 = c1;
c1 = c2;
c2 = 0;
}
return rb_big_norm(z);
}
VALUE rb_big_barrett_reduce(VALUE x, VALUE m, VALUE mu, int inplace)
{
if (!NEGATIVE_P(x) && MORE(m, x))
{
return x;
}
unsigned long len = RBIGNUM_LEN(m); /* >= 1 */
if (FIXNUM_P(x))
{
return FIX2LONG(x) >= 0 ? x : rb_big_plus(m, x);
}
VALUE q = bigmul_high_digits(x, mu, len - 1, len - 1);
/* q is not normed */
q = rshift_digits_inplace(q, len + 1);
/* [x/m] - 3 <= q <= [x/m] */
q = bigmul_low_digits(q, m, len + 1);
/* q is normed */
VALUE a = inplace ? x : rb_big_clone(x);
if (RBIGNUM_LEN(a) > (long)len + 1)
{
RBIGNUM_SET_LEN(a, len + 1);
}
a = rb_big_minus(a, q);
if (NEGATIVE_P(a))
a = ADD(a, power_of_two((len + 1) * BITSPERDIG));
/* a = (x - q * m) mod (base ** (len + 1)) */
while (!MORE(m, a)) /* that is, m <= a */
a = SUB(a, m);
return rb_big_norm(a);
}
static VALUE
gcd_gmp(VALUE x, VALUE y)
{
return rb_big_norm(rb_gcd_gmp(big(x), big(y)));
}
static VALUE
gcd_normal(VALUE x, VALUE y)
{
return rb_big_norm(rb_gcd_normal(rb_to_int(x), rb_to_int(y)));
}
