Question

I want to extract the n most significant bits from an integer in C++ and convert those n bits to an integer.

For example

int a=1200;
// its binary representation within 32 bit word-size is
// 00000000000000000000010010110000

Now I want to extract the 4 most significant digits from that representation, i.e. 1111

00000000000000000000010010110000
                     ^^^^

and convert them again to an integer (1001 in decimal = 9).

How is possible with a simple c++ function without loops?

Answer 1

Some processors have an instruction to count the leading binary zeros of an integer, and some compilers have instrinsics to allow you to use that instruction. For example, using GCC:

uint32_t significant_bits(uint32_t value, unsigned bits) {
    unsigned leading_zeros = __builtin_clz(value);
    unsigned highest_bit = 32 - leading_zeros;
    unsigned lowest_bit = highest_bit - bits;

    return value >> lowest_bit;
}

For simplicity, I left out checks that the requested number of bits are available. For Microsoft’s compiler, the intrinsic is called __lzcnt.

If your compiler doesn’t provide that intrinsic, and you processor doesn’t have a suitable instruction, then one way to count the zeros quickly is with a binary search:

unsigned leading_zeros(int32_t value) {
    unsigned count = 0;
    if ((value & 0xffff0000u) == 0) {
        count += 16;
        value <<= 16;
    }
    if ((value & 0xff000000u) == 0) {
        count += 8;
        value <<= 8;
    }
    if ((value & 0xf0000000u) == 0) {
        count += 4;
        value <<= 4;
    }
    if ((value & 0xc0000000u) == 0) {
        count += 2;
        value <<= 2;
    }
    if ((value & 0x80000000u) == 0) {
        count += 1;
    }
    return count;
}