The >>> operator lets you treat int and long as 32- and 64-bit unsigned integral types, which are missing from the Java language. This is useful when you shift something that does not represent a numeric value. For example, you could represent a black and white bit map image using 32-bit ints, where each int … Read more
Here’s a solution with only 4 main steps: const uint64_t column_mask = 0x8080808080808080ull; const uint64_t magic = 0x2040810204081ull; int get_col(uint64_t board, int col) { uint64_t column = (board << col) & column_mask; column *= magic; return (column >> 56) & 0xff; } It works like this: the board is shifted to align the column with … Read more
In every case (including divisible by 2): if (number % n == 0) do(); Anding with a mask of low order bits is just obfuscation, and with a modern compiler will not be any faster than writing the code in a readable fashion. If you have to test all of the cases, you might improve … Read more
Yep. The timeit module in the standard library is how you check on those things. E.g: $ python -m timeit -s ‘def isodd(x): x & 1’ ‘isodd(9)’ 1000000 loops, best of 3: 0.446 usec per loop $ python -m timeit -s ‘def isodd(x): x & 1’ ‘isodd(10)’ 1000000 loops, best of 3: 0.443 usec per … Read more
Well, the answer is pretty simple. If you have an int value: int log2(int value) { return Integer.SIZE – Integer.numberOfLeadingZeros(value); } The same exists for Long… [Edit] If shaving milliseconds is an issue here, Integer.numberOfLeadingZeros(int) is reasonably efficient, but still does 15 operations… Expanding a reasonable amount of memory (300 bytes, static) you could shave … Read more
Let’s use 16 bits for our example. In that case, ~0 is equal to 1111111111111111 When we left-shift this n bits (3 in your case), we get: 1111111111111000 because the 1s at the left are discarded and 0s are fed in at the right. Then re-complementing it gives: 0000000000000111 so it’s just a clever way … Read more
The next draft (hybi-07) of the WebSockets specification is being implemented in most browsers and it will add built-in binary support to the protocol and API. However, until then, WebSockets payload is encoded as UTF-8. In order to send binary data you must use some way of encoding the binary data as UTF-8. There are … Read more
First, if this variable is to be updated after (nearly) every instruction, the obvious piece of advice is this: don’t Only update it when the subsequent instructions need its value. At any other time, there’s no point in updating it. But anyway, when we update it, what we want is this behavior: R < 0 … Read more
C compiler performs integer promotions before executing the shift. Rule 6.3.1.1 of the standard says: If an int can represent all values of the original type, the value is converted to an int; otherwise, it is converted to an unsigned int. These are called the integer promotions. Since all values of unsigned char can be … Read more
There exist algorithms more efficient than O(N^2) to multiply two numbers (see Karatsuba, Pollard, Schönhage–Strassen, etc.) The two problems “multiply two arbitrary N-bit numbers” and “Square an arbitrary N-bit number” have the same complexity. We have 4*x*y = (x+y)^2 – (x-y)^2 So if squaring N-bit integers takes O(f(N)) time, then the product of two arbitrary … Read more