Do bitwise operations on 64-bit integers take time linear in the numbers of bits(64) or constant time ?
1 2 3 4 5 6
x = (1<<59);
y = (1<<60);
x ^= y
Suppose I had the line 6 from the above code inside many nested loops, is it safe to assume it will take a constant number of operations? Or do I need to assume that it takes about 64 operations so that it is something similar(but slightly faster) to looping through all the bits and XORing them?
What about 32-bit integers (int) ?
Modern 64-bit CPUs do bitwise operations in ~1 cycle, including bit shifts and xor. There is no separate unit for shifting 32-bit integers and 64 bit integers. Looping through them manually would be definitely much slower.
modern 32bit processors (x86) support 32bit instructions for 64-bit operations (simd instruction sets like mmx or sse). Compile some code and watch disassembly, then you can read in x86 reference manual timings of instructions used.