/**
* Computes the value of this number raised to an integral power. Follows semantics of Java
* Math.pow as closely as possible.
*
* @param exp the integer exponent
* @return x raised to the integral power exp
*/
public WB_DoubleDouble pow(final int exp) {
if (exp == 0.0) {
return valueOf(1.0);
}
WB_DoubleDouble r = new WB_DoubleDouble(this);
WB_DoubleDouble s = valueOf(1.0);
int n = Math.abs(exp);
if (n > 1) {
/* Use binary exponentiation */
while (n > 0) {
if ((n % 2) == 1) {
s.selfMultiply(r);
}
n /= 2;
if (n > 0) {
r = r.sqr();
}
}
} else {
s = r;
}
/* Compute the reciprocal if n is negative. */
if (exp < 0) {
return s.reciprocal();
}
return s;
}
/**
* Computes the positive square root of this value. If the number is NaN or negative, NaN is
* returned.
*
* @return the positive square root of this number. If the argument is NaN or less than zero, the
* result is NaN.
*/
public WB_DoubleDouble sqrt() {
/*
* Strategy: Use Karp's trick: if x is an approximation to sqrt(a), then
*
* sqrt(a) = a*x + [a - (a*x)^2] * x / 2 (approx)
*
* The approximation is accurate to twice the accuracy of x. Also, the
* multiplication (a*x) and [-]*x can be done with only half the
* precision.
*/
if (isZero()) {
return valueOf(0.0);
}
if (isNegative()) {
return NaN;
}
final double x = 1.0 / Math.sqrt(hi);
final double ax = hi * x;
final WB_DoubleDouble axdd = valueOf(ax);
final WB_DoubleDouble diffSq = this.subtract(axdd.sqr());
final double d2 = diffSq.hi * (x * 0.5);
return axdd.add(d2);
}