Adding 64 bit numbers using 32 bit arithmetic

Question

How do we add two 64 bit numbers using 32 bit arithmetic??

Answer 1

it looks something like this

/* break up the 64bit number into smaller, 16bit chunks */
struct longint { 
    uint16 word0; 
    uint16 word1;
    uint16 word2;
    uint16 word3;
};

uint16 add(longint *result, longint *a, longint *b)
{
    /* use an intermediate large enough to hold the result
       of adding two 16 bit numbers together. */
    uint32 partial;

    /* add the chunks together, least significant bit first */
    partial = a->word0 + b->word0;

    /* extract thie low 16 bits of the sum and store it */
    result->word0 = partial & 0x0000FFFF;

    /* add the overflow to the next chunk of 16 */
    partial = partial >> 16 + a->word1 + b->word1;
    /* keep doing this for the remaining bits */
    result->word1 = partial & 0x0000FFFF;
    partial = partial >> 16 + a->word2 + b->word2;
    result->word2 = partial & 0x0000FFFF;
    partial = partial >> 16 + a->word3 + b->word3;
    result->word3 = partial & 0x0000FFFF;
    /* if the result overflowed, return nonzero */
    return partial >> 16;
}

Actual hardware doesn't use 32 bits to add 16 bits at a time, only one extra bit of carry is ever needed for addition, and almost all CPU's have a carry status flag for when an addition operation overflowed, so if you are using a 32 bit cpu, you can add 64 bit operands in two, 32 bit operations.