bit-manipulation

Multiplying two binary numbers takes n^2 time, yet squaring a number can be done more efficiently somehow. (with n being the number of bits) How could that be? Or is it not possible? This is insanity! 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 N-bit integers can be obtained in O

Example. 123456, and we want the third from the right ('4') out. The idea in practise is to access each digit seperately (ie. 6 5 4 3 2 1). C/C++/C# preferred. A more efficient implementation might be something like this: char nthdigit(int x, int n) { while (n--) { x /= 10; } return (x % 10) + '0'; } This saves the effort of converting all digits to string format if you only want one of them. And, you don't have to allocate space for the converted string. If speed is a concern, you could precalculate an array of powers of 10 and use n to index into this array: char nthdigit(int x, int n) {

How do I expand the hexadecimal number 0x1234 to 0x11223344 in a high-performance way? unsigned int c = 0x1234, b; b = (c & 0xff) << 4 | c & 0xf | (c & 0xff0) << 8 | (c & 0xff00) << 12 | (c & 0xf000) << 16; printf("%p -> %p\n", c, b); Output: 0x1234 -> 0x11223344 I need this for color conversion. Users provide their data in the form 0xARGB, and I need to convert it to 0xAARRGGBB . And yes, there could be millions, because each could be a pixel. 1000x1000 pixels equals to one million. The actual case is even more complicated, because a single 32-bit value contains both foreground and background

Given a matrix of size n x m filled with 0's and 1's e.g.: 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 if the matrix has 1 at (i,j), fill the column j and row i with 1's i.e., we get: 1 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 Required complexity: O(n*m) time and O(1) space NOTE: you are not allowed to store anything except '0' or '1' in the matrix entries Above is a Microsoft Interview Question. I thought for two hours now. I have some clues but can't proceed any more. Ok. The first important part of this question is that Even using a straight forward brute-force way , it can't be easily solved. If

What is the best way to construct a bit mask in C with m set bits preceded by k unset bits, and followed by n unset bits: 00..0 11..1 00..0 k m n For example, k=1, m=4, n=3 would result in the bit mask: 01111000 ~(~0 << m) << n So, you are asking for m set bits prefixed by k reset bits and followed by n reset bits? We can ignore k since it will largely be constrained by the choice of integer type. mask = ((1 << m) - 1) << n; quinmars I like both solutions. Here is another way that comes to my mind (probably not better). ((~((unsigned int)0) << k) >> (k + n)) << n EDIT: There was a bug in my