bit manipulation - Signed extension from 24 bit to 32 bit in C++

Question

I have 3 unsigned bytes that are coming over the wire separately.

[byte1, byte2, byte3]

I need to convert these to a signed 32-bit value but I am not quite sure how to handle the sign of the negative values.

I thought of copying the bytes to the upper 3 bytes in the int32 and then shifting everything to the right but I read this may have unexpected behavior.

Is there an easier way to handle this?

The representation is using two's complement.

Answer 1

You could use:

uint32_t sign_extend_24_32(uint32_t x) {
    const int bits = 24;
    uint32_t m = 1u << (bits - 1);
    return (x ^ m) - m;
}

This works because:

• if the old sign was 1, then the XOR makes it zero and the subtraction will set it and borrow through all higher bits, setting them as well.
• if the old sign was 0, the XOR will set it, the subtract resets it again and doesn't borrow so the upper bits stay 0.

Templated version

template<class T>
T sign_extend(T x, const int bits) {
    T m = 1;
    m <<= bits - 1;
    return (x ^ m) - m;
}