Bit Twiddling Hacks Summary

Wed, 27 May 2026 22:40:00 +0800

Bit Twiddling Hacks Summary

This note summarizes practical techniques from Bit Twiddling Hacks.
It follows the same style as common-algorithm-patterns.md: each topic has Explanation + C++ Framework.

0) Preconditions and Portability

Explanation

Bit hacks are highly sensitive to integer representation and shift semantics:

Prefer unsigned fixed-width types like uint32_t / uint64_t.
Right-shifting negative signed values is implementation-defined.
Be careful with overflow-prone expressions such as x - y.

Code Framework

#include <bit>
#include <cstdint>
#include <limits>

using u32 = uint32_t;
using u64 = uint64_t;
using i32 = int32_t;

1) Sign and Opposite-Sign Detection

Explanation

Sign extraction is often normalized to -1 / 0 / 1.
Two values have opposite signs when their sign bits differ.

Code Framework

int sign3(int x) {
    return (x > 0) - (x < 0); // -1 / 0 / 1
}

bool oppositeSigns(int x, int y) {
    return (x ^ y) < 0;
}

2) Branchless abs / min / max

Explanation

Useful when branch misprediction is expensive, but always benchmark against normal standard-library versions first.

Bit-Hacks on H&W

Bit Twiddling Hacks Summary

Bit Twiddling Hacks Summary

0) Preconditions and Portability

Explanation

Code Framework

1) Sign and Opposite-Sign Detection

Explanation

Code Framework

2) Branchless abs / min / max

Explanation