Silicon Array

Numerical Computing Library for Apple Silicon

• Header-only C++23 library -- just #include <silarray.h>
• Switchable CPU/GPU backend via sil::use_cpu() / sil::use_mps() (default: GPU)
• CPU: Accelerate framework (vDSP, CBLAS, NEON)
• GPU: Metal Shading Language (MSL) — STEEL SGEMM, K-unrolled GEMV, online-softmax, right-sized reductions, and conv2d that dispatches to Apple's MPSGraph for medium/large-channel shapes
• MLX-style lazy evaluation: operations build a computation graph; sil::eval() evaluates multiple arrays in a single topological pass
• Affine fusion for chained scalar operations
• Zero-copy slicing via array::slice(start, count) for efficient batched data access
• Data types: float, int, bool

Requirements

• macOS with Apple Silicon
• Xcode Command Line Tools (clang++ with C++23 support)
• Frameworks: Metal, Accelerate, MetalPerformanceShaders, MetalPerformanceShadersGraph, Foundation

Example

#include <silarray.h>

auto a = sil::ones<float>({1000, 1000});
auto b = sil::ones<float>({1000, 1000});

auto c = a + b;       // builds a lazy graph node (no compute yet)
auto d = a.dot(b);    // also lazy

sil::eval(c, d);       // evaluates both in a single topological pass

sil::use_cpu();        // switch to CPU backend
auto e = a + b;        // CPU-side eager

For training loops, prefer batch evaluation:

W1 = W1 - dW1 * lr;
b1 = b1 - db1 * lr;
W2 = W2 - dW2 * lr;
b2 = b2 - db2 * lr;
sil::eval(W1, b1, W2, b2);   // single eval evaluates the whole graph

Operations

CPU/GPU switchable

Category	Operations
Arithmetic	+ - * / pow (elementwise, with broadcasting)
In-place	+= -= *= /=
Linear algebra	dot (STEEL SGEMM on GPU, CBLAS on CPU)
Activations	sigmoid relu softmax layer_norm
Fused ops	linear (dot + bias), linear_sigmoid (dot + bias + sigmoid)
Reduction	sum sum(axis) min max argmax
Convolution	conv2d (NHWC; smallch3 kernel for C_in=3, MPSGraph for C_in ≥ 16, JIT implicit-GEMM fallback)

CPU/GPU switchable (continued)

Category	Operations
NN utilities	sigmoid_backward
Slicing	slice(start, count) (zero-copy view)
Evaluation	eval(), free function sil::eval(arrays...), sil::synchronize()

CPU only

Category	Operations
Comparison	== != > < >= <=
Shape	clone transpose reshape broadcast
Creation	empty zeros ones random constants
Reduction	mean mean(axis) count all
NN utilities	mean_square_error one_hot
Selection	where(condition, x, y)
Testing	array_equal allclose

Performance

Competitive with MLX across most operations on Apple M1 Pro, measured with eval+sync per iteration.

Category	vs MLX
SGEMM (square, 1024–8192)	Same speed
GEMV (1x4096x4096, single-vector inference)	Same speed
Small-batch SGEMM (32x4096x768)	3.4x faster
Elementwise (add, mul, div, pow)	Same speed
Reduction (sum, min, max)	1.1–1.2x faster
Argmax	1.3–1.9x faster
Softmax	Same to 1.1x faster (incl. cols > 4096)
Layer norm	1.5–3.6x faster
Conv2d (ResNet mid, 16×64×56×56, k=3)	1.5x faster (via MPSGraph)
Conv2d (ResNet deep, 16×128×28×28, k=3)	Tied to 1.1x faster (via MPSGraph)
Conv2d (ImageNet first, 1×3×224×224, k=3)	1.1x faster (smallch3 kernel)
BMM attention	Same speed
Transformer block	Same to 1.1x faster
MLP inference	Noisy (±5–20%, shape-dependent)

See bench/README.md for detailed results.

Build and Run

Unit tests

cd test
make

Tests can be run in different device modes:

./test          # GPU mode (default)
./test --gpu    # explicit GPU
./test --cpu    # CPU mode

MNIST

cd test
make mnist
./mnist

Benchmarks

Benchmarks compare against Eigen, MLX, libtorch, and ggml.

just bench-all          # all benchmarks
just bench-micro        # micro only

# or manually:
cd bench
make run                # all benchmarks
make table              # Markdown table output

See bench/README.md for setup instructions and full results.

Architecture

include/
  silarray.h          Main header (includes all below)
  array.h             Core array class with expression templates
  cpu.h               CPU backend (Accelerate: vDSP, CBLAS, NEON)
  gpu.h               GPU backend (Metal/MSL kernels, MPSMatrixMultiplication, MPSGraph)
  device.h            Device selection (CPU/MPS switch)
  types.h             Type concepts (float, int, bool)
  objc.h              Objective-C bridge for Metal API
  unified_memory.h    GPU shared memory management

License

MIT license (c) 2026 Yuji Hirose