Math Function Vectorization

Feature Design Document

Background

Current Code Base

TiFlash currently has an relatively old math function vectorization mechanism inheritated from ClickHouse's old code base:
https://github.com/pingcap/tiflash/blob/34d7570a34c0daec5ca9c705296470b31d743d91/dbms/src/Functions/FunctionsMath.h#L30

However, when distributing the products, we never tried to enable it. Actually, at ClickHouse's master, this library has already been removed:
https://github.com/ClickHouse/ClickHouse/blob/d0e6f8ebc120a682bb09231fbbba1a904c8c29bb/src/Functions/FunctionMathUnary.h#L171

It seems that vectorclass has already become somehow inactive since 2021. Clickhouse quit using vectorized math functions anymore.

Vectorization Solution

Besides vectorclass, there are several alternatives providing math function vectorization:

• SLEEF is a promising candidate. However, there is no new release since 2020.
• SVML is the most famous one. However, it is designed for Intel CPU and it is a proprietary product.
• LIBMVEC is a part of glibc licenced under LGPL. TiFlash is now mostly used on GNU/Linux envrionment. This can be considered as a suitable choice.

For aarch64 platform, tiflash has already introduced optimized-routines as one of its contrib library; which can provide vectorized variants for log, cos, sin, exp.

Proposed Solution

libmvec is generally available in environment with glibc 2.22+. However, as we still need to support some ancient platform like CentOS 7, it is possible that the deployed env does not have libmvec.

Therefore, we can use dlopen with dlsym to dynamically detect whether libmvec is available.

Another consideration is that vectorized math function will have a lower precision. Therefore, there are potential changes in behavior when vectorization is enabled. To avoid trouble, we should provide a switch for the user and disable vectorization on default.

Summary

• remove dbms/cmake/find_vectorclass.cmake and related macros in source.
• add unary_math_vectorization = false to tiflash's configuration.
• add unit tests for unary math functions.
• vectorized the following functions on x86-64 using libmvec(libmvec's exp performs slower, so we do not use it):
  • cos
  • sin
  • tan
  • acos
  • asin
  • atan
  • log
  • log2
  • cbrt
• vectorize the following functions on aarch64 using optimized-routines:
  • cos
  • sin
  • log
  • exp
  • log10
  • atan
• update doc?

Auxiliary

How to check libmvec is available?

Vector ABI

more details

Start with dbms/src/Functions/FunctionsMath.h and dbms/cmake/find_vectorclass.cmake, then compare the linked ClickHouse implementation and existing source macros. Done means removing the vectorclass machinery, adding the configuration switch and architecture-specific vectorization described here, and adding unary math unit tests; documentation is updated if required.