public static IntNum remainder(IntNum x, IntNum y)
{
if (y.isZero())
return x;
IntNum rem = new IntNum ();
divide (x, y, null, rem, TRUNCATE);
return rem.canonicalize ();
}
/** Calculate the integral power of an IntNum.
* @param x the value (base) to exponentiate
* @param y the exponent (must be non-negative)
*/
public static IntNum power(IntNum x, int y)
{
if (y <= 0)
{
if (y == 0)
return one ();
else
throw new Exception ("negative exponent");
}
if (x.isZero ())
return x;
int plen = x.words == null ? 1 : x.ival; // Length of pow2.
int blen = ((x.intLength () * y) >> 5) + 2 * plen;
bool negative = x.isNegative () && (y & 1) != 0;
int[] pow2 = new int [blen];
int[] rwords = new int [blen];
int[] work = new int [blen];
x.getAbsolute (pow2); // pow2 = abs(x);
int rlen = 1;
rwords[0] = 1; // rwords = 1;
for (;;) // for (i = 0; ; i++)
{
// pow2 == x**(2**i)
// prod = x**(sum(j=0..i-1, (y>>j)&1))
if ((y & 1) != 0)
{ // r *= pow2
MPN.mul (work, pow2, plen, rwords, rlen);
int[] tempx = work; work = rwords; rwords = tempx;
rlen += plen;
while (rwords[rlen-1] == 0) rlen--;
}
y >>= 1;
if (y == 0)
break;
// pow2 *= pow2;
MPN.mul (work, pow2, plen, pow2, plen);
int[] temp = work; work = pow2; pow2 = temp; // swap to avoid a copy
plen *= 2;
while (pow2[plen-1] == 0) plen--;
}
if (rwords[rlen-1] < 0)
rlen++;
if (negative)
negate (rwords, rwords, rlen);
return IntNum.make (rwords, rlen);
}
public static IntNum modulo(IntNum x, IntNum y)
{
if (y.isZero())
return x;
IntNum rem = new IntNum ();
divide (x, y, null, rem, FLOOR);
return rem.canonicalize ();
}
public static IntNum lcm(IntNum x, IntNum y)
{
if (x.isZero () || y.isZero ())
return IntNum.zero ();
x = IntNum.abs (x);
y = IntNum.abs (y);
IntNum quotient = new IntNum ();
divide (times (x, y), gcd (x, y), quotient, null, TRUNCATE);
return quotient.canonicalize ();
}
public override double doubleValue()
{
bool neg = num.isNegative ();
if (den.isZero())
return (neg ? Double.NegativeInfinity
: num.isZero() ? Double.NaN
: Double.PositiveInfinity);
IntNum n = num;
if (neg)
n = IntNum.neg (n);
int num_len = n.intLength ();
int den_len = den.intLength ();
int exp = 0;
if (num_len < den_len + 54)
{
exp = den_len + 54 - num_len;
n = IntNum.shift (n, exp);
exp = - exp;
}
// Divide n (which is shifted num) by den, using truncating division,
// and return quot and remainder.
IntNum quot = new IntNum ();
IntNum remainder = new IntNum ();
IntNum.divide (n, den, quot, remainder, TRUNCATE);
quot = quot.canonicalize ();
remainder = remainder.canonicalize ();
return quot.roundToDouble (exp, neg, !remainder.isZero ());
}
/** Return this raised to an integer power.
* Implemented by repeated squaring and multiplication.
* If y < 0, returns div_inv of the result. */
public virtual Numeric power(IntNum y)
{
if (y.isNegative ())
return power(IntNum.neg(y)).div_inv();
Numeric pow2 = this;
Numeric r = null;
for (;;) // for (i = 0; ; i++)
{
// pow2 == x**(2**i)
// prod = x**(sum(j=0..i-1, (y>>j)&1))
if (y.isOdd())
r = r == null ? pow2 : r.mul (pow2); // r *= pow2
y = IntNum.shift (y, -1);
if (y.isZero())
break;
// pow2 *= pow2;
pow2 = pow2.mul (pow2);
}
return r == null ? mul_ident() : r;
}