## Predicated AVX-512 Byte & Word Operations

This article presents common patterns that can be used to workaround the limitation of some AVX-512 instructions that can only operate on 32-bit and 64-bit elements. For example, logical instructions including `VPANDx`, `VPANDNx`, `VPORx`, `VPXORx`, and `VPTERNLOGx` only work with 32-bit or 64-bit elements. Even `AVX512_BW` extension doesn't add complementary versions of these instructions that would operate on 8-bit and 16-bit elements. However, it's possible to use different instructions that operate on 8-bit and 16-bit elements to perform common operations like predicated zeroing or filling with ones.

## Missing Operations

The following instructions can only be used with 32-bit and 64-bit elements:

• `VPANDD`, `VPANDQ`
• `VPANDND`, `VPANDNQ`
• `VPORD`, `VPORQ`
• `VPXORD`, `VPXORQ`
• `VPTERNLOGD`, `VPTERNLOGQ`

• Set 8-bit or 16-bit elements to zero
• Set 8-bit or 16-bit elements to -1 (all bits set to one)
• Complement bits in 8-bit or 16-bit elements (bitwise not)

## Clearing 8-bit or 16-bit Elements to Zero

It's possible to replace the VPXORx instruction with instruction that would do the exact same thing when called with the same inputs. The simplest and the most straightforward approach is to subtract them as `x - x == 0`. The following code implements an efficient element zeroing for all element sizes:

``````// AVX-512: Clear 8-bit elements depending on the predicate `k`
}

// AVX-512: Clear 16-bit elements depending on the predicate `k`
}

// AVX-512: Clear 32-bit elements depending on the predicate `k`
}

// AVX-512: Clear 64-bit elements depending on the predicate `k`
}
``````

## Filling or Complementing Bits of 8-bit & 16-bit Elements

Filling all bits to ones is trivial with `VPTERNLOGx` instruction with`0xFF` predicate, which means to ignore all inputs and set all outputs to `1` (bitwise). However, since there are no ternary logic instruction for 8-bit and 16-bit elements we have to get a little more creative.

To help with our approach we would need an additional vector register, which would have all bits set to ones (of all elements). Such vector register can be used as an input to implement both bitwise fill and negation operations. Bitwise fills can be implemented by using saturated additions (which are supported for 8-bit and 16-bit elements) and bitwise negation can be implemented as subtraction from `~0`.

First, let's introduce the all ones constant:

``````static inline __m512i avx512_ones() {
__m512i u = _mm512_undefined_epi32();
return _mm512_ternarylogic_epi32(u, u, u, 0xFF);
}
``````

This constant would be used in some places, but to make sure that the C/C++ compiler is not emitting this sequence multiple times it could be better to just pass it to all the functions, which is not done here to keep things simple.

The bitwise 8-bit and 16-bit element fill implemented via unsigned saturating addition is below:

``````// AVX-512: Fill 8-bit elements depending on the predicate `k`
}

// AVX-512: Fill 16-bit elements depending on the predicate `k`
}
``````

Alternatively, instead of saturated addition it's possible to use unsigned maximum as well, which could be cheaper on some hardware:

``````// AVX-512: Fill 8-bit elements depending on the predicate `k`
}

// AVX-512: Fill 16-bit elements depending on the predicate `k`
}
``````

The same trick can be used to implement bit negation, as `~x == ~0 - x`:

``````// AVX-512: Complement 8-bit elements with ones depending on the predicate `k`
}

// AVX-512: Complement 16-bit elements with ones depending on the predicate `k`
}
``````

## Combining Filling and Zeroing

With the implementations presented above and a static mask it's possible to go further and to implement a logic to set particular bytes in a vector to zero, ones, or keep them untouched, and to do this with a single instruction. To make this possible we would need a register that would contain a mask of all bytes to be filled, and a predicate `k` that would be used together with zeroing `{k}{z}` to zero bytes, see below:

``````// AVX-512: Example of an approach to set bytes to all ones, all zeros, or to keep them untouched.
__m512i example(__m512i x) {
// Vector of bytes to be filled with ones, unprocessed bytes must be zero.
__m512i ones = _mm512_set1_epi32(0xFF000000);

// Mask of bytes to be processed - zero bits indicate bytes in the input to be zeroed.

// A single instruction to fill, clear, or keep bytes untouched depending on `ones` and k`.
}
``````

In the example above every MSB byte in all 32-bit elements of `x` is set to all ones and fhe first and third LSB bytes are cleared. The operation can be written as `(x | 0xFF000000) & 0xFF00FF00` and it's performed with a single instruction. Of course it can do any 64-byte pattern, bits can be complemented instead of filled, it all depends on use-case.

## Other Uses of -1 Constant

If the constant -1 is already in a register, it can be used to implement the following operations:

• Adding one by using subtraction - `x - (-1) == x + 1`
• Subtracting one by using addition - `x + (-1) == x - 1`
• Comparing whether a value is greater than or equal to zero, replacing 0 constant - `x >= 0 == x > -1`
• Comparing whether a value is lesser than zero, replacing 0 constant - `x < 0 == x <= -1`
• Implementing `(x + (0x1 << ELEMENT_SIZE)) >> 1` with `VPAVGx` instruction, could be also rewritten as `(x >> 1) | 0x80` with `VPAVGB` and `(x >> 1) | 0x8000` with `VPAVGW`

Additionally, with zero instead of -1 `VPAVGx` can be used as a rounding shift right by 1 bit, although I have never used this instruction for such purpose.

## Conclusion

This article only aimed at using byte/word instructions to implement some special cases of bitwise operations that are used often in SIMD programming. If anyone needs regular and predicated bitwise operations that work with 8-bit and 16-bit element sizes the best way is to use 32-bit or 64-bit versions without a predicate and to merge the result with predicated `VMOVDQU8` or `VMOVDQU16` later.