Bitwise shift operation on a 128-bit number

Question

Lets say that I have an array of 4 32-bit integers which I use to store the 128-bit number

How can I perform left and right shift on this 128-bit number?

Thanks!

Answer 1

Working with uint128? If you can, use the x86 SSE instructions, which were designed for exactly that. (Then, when you've bitshifted your value, you're ready to do other 128-bit operations...)

SSE2 bit shifts take ~4 instructions on average, with one branch (a case statement). No issues with shifting more than 32 bits, either. The full code for doing this is, using gcc intrinsics rather than raw assembler, is in sseutil.c (github: "Unusual uses of SSE2") -- and it's a bit bigger than makes sense to paste here.

The hurdle for many people in using SSE2 is that shift ops take immediate (constant) shift counts. You can solve that with a bit of C preprocessor twiddling (wordpress: C preprocessor tricks). After that, you have op sequences like:

LeftShift(uint128 x, int n) = _mm_slli_epi64(_mm_slli_si128(x, n/8), n%8)

for n = 65..71, 73..79, … 121..127 ... doing the whole shift in two instructions.

Answer 2

void shiftl128 (
    unsigned int& a,
    unsigned int& b,
    unsigned int& c,
    unsigned int& d,
    size_t k)
{
    assert (k <= 128);
    if (k >= 32) // shifting a 32-bit integer by more than 31 bits is "undefined"
    {
        a=b;
        b=c;
        c=d;
        d=0;
        shiftl128(a,b,c,d,k-32);
    }
    else
    {
        a = (a << k) | (b >> (32-k));
        b = (b << k) | (c >> (32-k));
        c = (c << k) | (d >> (32-k));
        d = (d << k);
    }
}

void shiftr128 (
    unsigned int& a,
    unsigned int& b,
    unsigned int& c,
    unsigned int& d,
    size_t k)
{
    assert (k <= 128);
    if (k >= 32) // shifting a 32-bit integer by more than 31 bits is "undefined"
    {
        d=c;
        c=b;
        b=a;
        a=0;
        shiftr128(a,b,c,d,k-32);
    }
    else
    {
        d = (c << (32-k)) | (d >> k); \
        c = (b << (32-k)) | (c >> k); \
        b = (a << (32-k)) | (b >> k); \
        a = (a >> k);
    }
}

Answer 3

Instead of using a 128 bit number why not use a bitset? Using a bitset, you can adjust how big you want it to be. Plus you can perform quite a few operations on it.

You can find more information on these here:

http://www.cppreference.com/wiki/utility/bitset/start?do=backlink

Answer 4

First, if you're shifting by n bits and n is greater than or equal to 32, divide by 32 and shift whole integers. This should be trivial. Now you're left with a remaining shift count from 0 to 31. If it's zero, return early, you're done.

For each integer you'll need to shift by the remaining n, then shift the adjacent integer by the same amount and combine the valid bits from each.

Answer 5

Since you mentioned you're storing your 128-bit value in an array of 4 integers, you could do the following:

void left_shift(unsigned int* array)
{   
    for (int i=3; i >= 0; i--)
    {
        array[i] = array[i] << 1;

        if (i > 0)
        {
            unsigned int top_bit = (array[i-1] >> 31) & 0x1;
            array[i] = array[i] | top_bit;
        }
    }
}

void right_shift(unsigned int* array)
{   
    for (int i=0; i < 4; i++)
    {
        array[i] = array[i] >> 1;

        if (i < 3)
        {
            unsigned int bottom_bit = (array[i+1] & 0x1) << 31;
            array[i] = array[i] | bottom_bit;
        }
    }
}