Bitwise packing/unpacking – generalized solution for arbitrary values

I’m trying to adapt this answer to arbitrary numeric values.

Let’s say we have 3 (unsigned) numbers:

v1, v2, v3

and we know the respective max values they may have:

max1, max2, max3.

max1 * max2 * max3 < 2^32,

so the result (packed value) is to be within 32 bits.

How to pack/unpack them without “magic” hardcoding?

Answer

Here is a slightly different way to do it.

int max1 = 1000;
int max2 = 500;
int max3 = 500;

shift values determined based on most significant set bit of maximums.

int size1 = 32-Integer.numberOfLeadingZeros(max1);
int size2 = 32-Integer.numberOfLeadingZeros(max2);
int size3 = 32-Integer.numberOfLeadingZeros(max3);

mask values determined by complementing -1 shifted size bits.

int mask1 = ~(-1<<size1);
int mask2 = ~(-1<<size2);
int mask3 = ~(-1<<size3);

int v1 = 934;
int v2 = 293;
int v3 = 349;

Nothing really new here. Second shift shifts both first and second values.

int packed = (((v3<<size2)|v2)<<size1)|v1;

Now reverse it

v1 = packed&mask1;
// this saves the shifted packed version for the next step
v2 = (packed = packed>>>size1)&mask2;
v3 = (packed>>>size2)&mask3;
        
System.out.println(v1);
System.out.println(v2);
System.out.println(v3);

Prints

934
293
349