Explanation

Contents

Explanation#

The ideas behind aether, grouped by topic and ordered from first use to advanced. Each page answers one question; new words are in the Glossary.

Arrays and memory#

What a view is, who owns a buffer, and why an expression does not allocate.

Views and items: What a View is, and why an Item lives in registers.
Expression templates: Why a + b*s does not allocate.
Memory ownership: Who owns a buffer, host or device, and how to copy it.

Run kernels#

Code that runs on both machines, with several devices, and on the CPU’s vector units.

Host vs device code: What AETHER_DEVICEHOST means, and when you need a GPU kernel entry point.
CPU SIMD backend: How aether vectorizes on the CPU, with no GPU involved.
Why the numerics stay domain-independent: What aether knows, what it does not, and where mathematics earns its place.
Multi-device residency: Keep a replica per GPU, or partition data across several.

Numerics and precision#

The fold order, division, compensated sums and non-finite rules every target computes against, and how to get more than float or double.

Numerics contract: The rules every target computes against.
Accumulation: Adding many producers’ contributions into one per-sample slot without a data race.
Banded/emulated real arithmetic: BandedReal: double precision from three float limbs, and when to use it.

Interoperability#

Interoperability: How a NumPy, CuPy or PyTorch array becomes an aether View without a copy. The contract the family shares is on raptor’s interoperability page.

Large matrices#

Linear algebra for large matrices: LU, Cholesky, eigenvalues, QR and ordered block sums by a team of threads on one matrix, up to 4096 by 4096, with the scratch each routine needs.

Embedded C#

Plain-C reference core: Standalone C99 functions that reproduce aether’s arithmetic bit for bit.