Split Multiplication of integers

Question

I need an algorithm that uses two 32-bit integers as parameters, and returns the multiplication of these parameters split into two other 32-bit integers: 32-highest-bits par

Answer 1

Just use 16 bits digits.

void multiply(uint32_t a, uint32_t b, uint32_t* h, uint32_t* l) {
    uint32_t const base = 0x10000;
    uint32_t al = a%base, ah = a/base, bl = b%base, bh = b/base;
    *l = al*bl;
    *h = ah*bh;
    uint32_t rlh = *l/base + al*bh;
    *h += rlh/base;
    rlh = rlh%base + ah*bl;
    *h += rlh/base;
    *l = (rlh%base)*base + *l%base;
}

Answer 2

This is the explanation and an implementation of the Karatsubas-Algorithm. I have downloaded the code and ran it several times. It seems that it's doing well. You can modify the code according to your need.

Answer 3

As I commented, you can treat each number as a binary string of length 32.

Just multiply these numbers using school arithmetic. You will get a 64 character long string.

Then just partition it.

If you want fast multiplication, then you can look into Karatsuba multiplication algorithm.

Answer 4

If the unsigned long type are supported, this should work:

void umult32(uint32 a, uint32 b, uint32* c, uint32* d)
{
  unsigned long long x = ((unsigned long long)a)* ((unsigned long long)b); //Thanks to @Толя
  *c = x&0xffffffff;
  *d = (x >> 32) & 0xffffffff;
}

Logic borrowed from here.