Intel and AMD have expanded the x64 instruction sets over time. In particular, the SIMD (Single instruction, multiple data) instructions have become progressively wider and more general: from 64 bits to 128 bits (SSE2), to 256 bits (AVX/AVX2) to 512 bits (AVX-512). Interestingly, many instructions defined on 256 bits registers through AVX/AVX2 are not available on 512 bits registers.

With SSSE3, Intel introduced sign instructions, with the corresponding intrinsic functions (e.g., _mm_sign_epi8). There are 8-bit, 16-bit and 32-bit versions.  It was extended to 256-bit registers in AVX2.

What these instructions do is to apply the sign of one parameter to the other parameter. It is most easily explained as pseucode code:

```function sign(a, b): # a and b are integers
if b == 0 : return 0
if b < 0 : return -a
if b > 0 : return a
```

The SIMD equivalent does the same operation but with many values at once. Thus, with SSSE3 and psignb, you can generate sixteen signed 8-bit integers at once.

You can view it as a generalization of the absolute function: abs(a) = sign(a,a). The sign instructions are very fast. They are used in numerical analysis and machine learning: e.g., it is used in llama.cpp, the open source LLM project.

When Intel designed AVX-512 they decided to omit the sign instructions. So while we have the intrinsic function  _mm256_sign_epi8, we don’t have _mm512_sign_epi8. The same instructions are missing for 16 bits and 32 bits integers (e.g., no _m512_sign_epi16 is found).

You may implement it for AVX-512 with a several instructions. I found this one approach:

```#include <x86intrin.h>

__m512i _mm512_sign_epi8(__m512i a, __m512i b) {
__m512i zero = _mm512_setzero_si512();
__m512i a_blt0 = _mm512_mask_mov_epi8(zero, blt0, a);
}
```

It is disappointingly expensive. It might compile to four or five instructions:

```vpmovb2m k2, zmm1
vpxor xmm2, xmm2, xmm2
vpcmpb k1, zmm1, zmm2, 2
vpblendmb zmm1{k2}, zmm2, zmm0
vpsubb zmm0{k1}, zmm2, zmm1
```

In practice, you may not need to pay such a high price. The reason the problem is difficult is that we have three cases to handle (three signs b=0, b>0, b<0).  If you do not care about the case ‘b = 0’, then you can do it in two instruction, not counting the zero (one xor):

```#include <x86intrin.h>

__m512i _mm512_sign_epi8_cheated(__m512i a, __m512i b) {
__m512i zero = _mm512_setzero_si512();
}
```

E.g., we implemented…

```function sign_cheated(a, b): # a and b are integers
if b < 0 : return -a
if b ≥ 0 : return a
```

Daniel Lemire

A computer science professor at the University of Quebec (TELUQ).

1. -.- says:

you can do it in two instruction

Three if you include the xor (though I think it’s fair to ignore it).

Alternative `_mm512_sign_epi8` which is one byte shorter due to avoiding `vpcmpb` =P

```// zero elements __mmask64 bne0 = _mm512_test_epi8_mask(b, b); a = _mm512_maskz_mov_epi8(bne0, a); // negate elements __mmask64 blt0 = _mm512_movepi8_mask(b); return _mm512_mask_sub_epi8(a, blt0, _mm512_setzero_si512(), a);; ```

2. -.- says:

if b ≤ 0

Nit: it’s actually `b<0` (you’ll need to fix the other condition too).

3. David Gonzales says:

generalization of the absolution function: abs(a) = sign(a,b)
should be abs(a) = sign(a,a)

4. Geert Bosch says:

What about the case when either value is NaN? Got to return something

5. Julien says:

A couple of typos here?

You can view is as a generalization of the absolution function: abs(a)
= sign(a,b).

Should be “…view it as a…” and “…abs(a) = sign(a, a)…”, isn’t it?

6. Bob Bobson says:

Is there a reason not to use _mm256_sign_epi8 twice?

1. You could try but it definitively generates more instructions and several of these instructions have long latencies.

```__m512i _mm512_sign_epi8_alt(__m512i a, __m512i b) {
__m256i a1 = _mm512_extracti64x4_epi64(a,0);
__m256i a2 = _mm512_extracti64x4_epi64(a,1);
__m256i b1 = _mm512_castsi512_si256 (b);
__m256i b2 = _mm512_extracti64x4_epi64(b,1);
a1 = _mm256_sign_epi8(a1,b1);
a2 = _mm256_sign_epi8(a2,b2);
__m512i r = _mm512_castsi256_si512(a1);
r = _mm512_inserti64x4(r,a2, 1);
return r;
}

```
1. Ray Fannucia says:

The following 2 extract intrinsics:

__m256i a1 = _mm512_extracti64x4_epi64(a,0);
__m256i b1 = _mm512_extracti64x4_epi64(b,0);

can be replaced with cast intrinsics:

__m256i a1 = _mm512_castsi512_si256 (a);
__m256i b1 = _mm512_castsi512_si256 (b);

which do not generate any instructions.

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