Ternary functions for SSE and AVX2
Introduction
AVX512F introduced instruction vpternlog (intrinsic
_mm512_ternarylogic_epi{32,64}), which evaluates a three-argument
boolean function for each bit of operands. The function is given as
an integer number from 0 to 255.
This repository contains a kind of library which allows a programmer to use ternary functions in SSE, XOP, AVX2 and x86 in similar manner, by choosing the function by its number.
In native AVX512F code you would write:
// 0x96 = A xor B xor C const __m512i res = _mm512_ternarylogic_epi32(A, B, C, 0x96);
With help of the library you can write an AVX2 program:
const __m256i res = ternarylogic::avx2::ternary<0x96>(A, B, C);
or a SSE program:
const __m128i res = ternarylogic::sse::ternary<0x96>(A, B, C);
Details
The function number comes from the result column of the function's truth table. The number is formed from bits a, b, ... h. You can find more details and examples in my article.
| A | B | C | function |
| 0 | 0 | 0 | a |
| 0 | 0 | 1 | b |
| 0 | 1 | 0 | c |
| 0 | 1 | 1 | d |
| 1 | 0 | 0 | e |
| 1 | 0 | 1 | f |
| 1 | 1 | 0 | g |
| 1 | 1 | 1 | h |
Intel has published list of all functions in form of logical expression in their monumental document "Intel® 64 and IA-32 Architectures Software Developer’s Manual Volume 2 (2A, 2B, 2C & 2D): Instruction Set Reference, A-Z".
I extracted these functions and created application which generates SSE
and AVX2 code. List of function is in the file py/data/intel.txt,
I also put there more details. Later I manually optimized some of these
function. And in the end I developed a program which found many better
representations of functions for both Intel and AMD flavours of SIMD
ISA.
Usage
You need python and make.
Type make, then following files will be generated:
ternary_sse.cpp,ternary_avx2.cpp,ternary_avx512.cpp(use only two-argument logic instructions),ternary_xop.cpp,ternary_x86_32.cpp,ternary_x86_64.cpp.
You can include them directly into your application.
Programs validate_sse, validate_avx2 and validate_xop
test if all generated functions are correct.
See also
- Samuel Neves (@sneves) published cool C++ library for dealing with function numbers using constexpr. Check it out. https://github.com/sneves/avx512-utils