I know this is a rather old post but I wanted simplify the answer since I stumbled upon it while looking for something else. XOR (eXclusive OR/either or), can be translated simply as toggle on/off. Which will either exclude (if exists) or include (if nonexistent) the specified bits. Using 4 bits (1111) we get 16 … Read more
For 32-bit integers, this is a simple and straightforward route: unsigned int n; n–; n |= n >> 1; // Divide by 2^k for consecutive doublings of k up to 32, n |= n >> 2; // and then or the results. n |= n >> 4; n |= n >> 8; n |= n … Read more
What’s wrong with return ((x<0) == (y<0)); ?
If you have a CPU with efficient SIMD instructions, SSE/MMX paddb (_mm_add_epi8) is also viable. Peter Cordes’ answer also describes GNU C (gcc/clang) vector syntax, and safety for strict-aliasing UB. I strongly encourage reviewing that answer as well. Doing it yourself with uint64_t is fully portable, but still requires care to avoid alignment problems and … Read more
Just fill the non mask bits with ones so that they propagate carry: // increments x on bits belonging to mask x = ((x | ~mask) + 1) & mask;
int getMax(int a, int b) { int c = a – b; int k = (c >> 31) & 0x1; int max = a – k * c; return max; } Let’s dissect this. This first line appears to be straightforward – it stores the difference of a and b. This value is negative if … Read more
I still write code for systems that do not have floating point support in hardware. In these systems you need bit-shifting for nearly all your arithmetic. Also you need shifts to generate hashes. Polynomial arithmetic (CRC, Reed-Solomon Codes are the mainstream applications) or uses shifts as well. However, shifts are just used because they are … Read more
You can see how it works by doing the substitution: x1 = x0 xor y0 y2 = x1 xor y0 x2 = x1 xor y2 Substituting, x1 = x0 xor y0 y2 = (x0 xor y0) xor y0 x2 = (x0 xor y0) xor ((x0 xor y0) xor y0) Because xor is fully associative and … Read more
Question: What do we know about the Hamming distance d(x,y)? Answer: It is non-negative: d(x,y) ≥ 0 It is only zero for identical inputs: d(x,y) = 0 ⇔ x = y It is symmetric: d(x,y) = d(y,x) It obeys the triangle inequality, d(x,z) ≤ d(x,y) + d(y,z) Question: Why do we care? Answer: Because it … Read more
Endianness only matters for layout of data in memory. As soon as data is loaded by the processor to be operated on, endianness is completely irrelevent. Shifts, bitwise operations, and so on perform as you would expect (data logically laid out as low-order bit to high) regardless of endianness.