Reverse LUT for LOP3.LUT

Accelerated Computing CUDA CUDA Programming and Performance
1

Is there a reference table anywhere, where one can take the LUT value from a SASS dumped LOP3.LUT instruction and see what the actual logic ops are?

Thanks,

2

Any number of different sequences of logic operations can map to the same truth table, i.e. this is a many-to-one mapping, not a bijection. Therefore one cannot unambiguously map a truth-table value back to a particular sequence of logic operations.

But one can certainly set up a logic equation corresponding to a LOP3.LUT truth table (see code below) and then transform that into any particular form (e.g. DNF, CNF, NAND) desired.

/* emulate GPU's LOP3.LUT (three-input logic op with 8-bit truth table) */
uint32_t lop3_fast (uint32_t a, uint32_t b, uint32_t c, uint8_t ttbl)
{
    uint32_t r = 0;
    if (ttbl & 0x01) r |= ~a & ~b & ~c;
    if (ttbl & 0x02) r |= ~a & ~b &  c;
    if (ttbl & 0x04) r |= ~a &  b & ~c;
    if (ttbl & 0x08) r |= ~a &  b &  c;
    if (ttbl & 0x10) r |=  a & ~b & ~c;
    if (ttbl & 0x20) r |=  a & ~b &  c;
    if (ttbl & 0x40) r |=  a &  b & ~c;
    if (ttbl & 0x80) r |=  a &  b &  c;
    return r;
}
3

Thanks, I should have seen that, (the many to one).

I’m trying to optimise and the LOP3’s are making things somewhat opaque.

4

For the record: Intel offer an AVX512 instruction “vpternlog” performing the same function as LOP3. They publish a couple of tables showing all 256 logic op combinations.

Currently it is at the beginning of “Intel® 64 and IA-32 Architectures Software Developer’s Manual
Volume 2C: Instruction Set Reference, V-Z” available here.

5

@rs277 The canonicalization rules used to generate tables 5-1 and 5-2 in the Intel manual are not clear. Other than for the simplest cases using OR and AND, I am not sure how these tables are particularly useful? I do not usually think in terms of NAND, NOR, XNOR.

For the forward direction (3-input logic formula to 8-bit truth table) there is this, of course:

    a = 0xf0;
    b = 0xcc;
    c = 0xaa;
    printf ("%02x\n", <logic-formula-using-inputs-a-b-c>);

No dark secrets here, and this is also documented in the PTX manual.

After spending some more time looking into this, mapping arbitrary logic (of, say, 5 variables) in an optimal fashion to LOP3 instructions is a very hard problem indeed.

6

No, and I’ve refered to that PTX manual formula before.
For me, it’s more been a case, when examining SASS with a view to optimising, knowing what the boolean function being used is handy to know.

I found a more readable version of the same thing here.