/** 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);
}
public static RatNum make(IntNum num, IntNum den)
{
IntNum g = IntNum.gcd(num, den);
if (den.isNegative())
{
g = IntNum.neg(g);
}
if (!g.isOne())
{
num = IntNum.quotient(num, g);
den = IntNum.quotient(den, g);
}
return(den.isOne() ? (RatNum)num : (RatNum)(new IntFraction(num, den)));
}
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()));
}
public static IntFraction neg(IntFraction x)
{
// If x is normalized, we do not need to call RatNum.make to normalize.
return(new IntFraction(IntNum.neg(x.numerator()), x.denominator()));
}