high bits of long multiplication in Java?

Question

Is there any way to get the high half of the multiplication of two longs in Java? I.e. the part that vanishes due to overflow. (So the upper 64 bits of the 128-

Answer 1

Let's say you have two longs, x and y, and x = x_hi * 2^32 + x_lo, and y = y_hi * 2^32 + y_lo.

Then x * y == (x_hi * y_hi) * 2^64 + (x_hi * y_lo + x_lo * y_hi) * 2^32 + (x_lo * y_lo).

The high 64 bits of that product can, therefore, be computed as follows:

long x_hi = x >>> 32;
long y_hi = y >>> 32;
long x_lo = x & 0xFFFFFFFFL;
long y_lo = y & 0xFFFFFFFFL;
long prod_hi = (x_hi * y_hi) + ((x_ hi * y_lo) >>> 32) + ((x_lo * y_hi) >>> 32);