Question

I would like to cast unsigned int (32bit) A to unsigned short int (16bit) B in a following way:

• if A <= 2^16-1 then B=A
• if A > 2^16-1 then B=2^16-1

In other words to cast A but if it is > of maximum allowed value for 16bit to set it as max value.

How can this be achieved with bit operations or other non branching method?

Answer 1

Find minimum of two integers without branching:

http://graphics.stanford.edu/~seander/bithacks.html#IntegerMinOrMax

On some rare machines where branching
is very expensive and no condition
move instructions exist, the above
expression might be faster than the
obvious approach, r = (x < y) ? x : y,
even though it involves two more
instructions. (Typically, the obvious
approach is best, though.)

Just to kick things off, here’s a brain-dead benchmark. I’m trying to get a 50/50 mix of large and small values “at random”:

#include <iostream>
#include <stdint.h>

int main() {
    uint32_t total = 0;
    uint32_t n = 27465;
    for (int i = 0; i < 1000*1000*500; ++i) {
        n *= 30029; // worst PRNG in the world
        uint32_t a = n & 0x1ffff;
        #ifdef EMPTY
            uint16_t b = a; // gives the wrong total, of course.
        #endif
        #ifdef NORMAL
            uint16_t b = (a > 0xffff) ? 0xffff : a;
        #endif
        #ifdef RUSLIK
            uint16_t b = (-(a >> 16) >> 16) | a;
        #endif
        #ifdef BITHACK
            uint16_t b = a ^ ((0xffff ^ a) & -(0xffff < a));
        #endif
        total += b;
    }
    std::cout << total << "\n";
}

On my compiler (gcc 4.3.4 on cygwin with -O3), NORMAL wins, followed by RUSLIK, then BITHACK, respectively 0.3, 0.5 and 0.9 seconds slower than the empty loop. Really this benchmark means nothing, I haven’t even checked the emitted code to see whether the compiler’s smart enough to outwit me somewhere. But I like ruslik’s anyway.