amx.hpp File Reference

The matrix coprocessor of Apple's M-series chips (AMX), for the double matrix product. More...

#include <algorithm>
#include <array>
#include <cstring>
#include <atomic>
#include <cmath>
#include <cstddef>
#include <cstdint>
#include <initializer_list>
#include "simd.hpp"

Include dependency graph for amx.hpp:

Go to the source code of this file.

Namespaces
namespace	numerical
	The NumericAL public API.
namespace	numerical::detail

Functions
bool	numerical::detail::amx_usable () noexcept
	Whether this chip's AMX can be used: known family and a passing self-test, decided once.

Detailed Description

The matrix coprocessor of Apple's M-series chips (AMX), for the double matrix product.

Apple documents no instruction for it; the encodings used here are the ones the AMX has kept from the M1 to the M4 for loads, stores and the 64-bit fused multiply-add. Each core reaches it through instructions the assembler emits as raw words, so no compiler support is needed and the library stays header-only.

Because the instructions are not documented, the path is used only where it is known to work:

• it is compiled only for arm64 macOS, and not at all under NUMERICAL_NO_AMX;
• it is used only on a chip whose CPU family is one of the M1 to M4 families (which the A14 and A15 share), so no other chip can meet an instruction it lacks, and not in a virtual machine;
• on first use a product computed through it must equal, to the bit, the same product computed by std::fma in ascending order of the depth; else the path stays off for the process;
• numerical::limit_gemm_path keeps products off it at run time, and the Python package reads NUMERICAL_AMX=0: under such a cap, not even the self-test runs.

Every element of C is a chain of fused multiply-adds in ascending order of the depth, so a product through the AMX is the same on any number of threads; it differs from the vector path's separately rounded products in the last bits, as any fused product does.

Definition in file amx.hpp.