ZIT: Zig Tensor Library

A high-performance numerical computing library for the Zig programming language, focused on tensor operations and linear algebra.

Goals

• Provide a clean, efficient tensor library for scientific computing in Zig
• Support multiple backends (CPU SIMD, GPU via Metal/WebGPU)
• Deliver best-in-class performance for numerical operations
• Serve as a foundation for machine learning and data processing applications
• Maintain Zig-native design principles: explicit, reusable, comprehensible

Implementation Plan

Phase 1: Core Tensor Implementation

• Set up basic project structure
• Define initial Tensor type
• Implement tensor creation functions
  • Zeros, ones, eye, random initialization
  • From slice/array
  • Implement proper memory management with allocator pattern
• Add shape manipulation capabilities
  • Reshape, transpose, concat, stack
  • Slicing and indexing
• Build comprehensive test suite
• Implement basic data loading/saving

Expected outcome: A usable basic tensor library with proper memory management.

Phase 2: Element-wise Operations

• Basic element-wise operations
  • add, subtract, multiply, divide
  • pow, exp, log, sqrt, etc.
  • Function mapping and transformation
• Broadcasting implementation
  • Auto-expandable dimensions
  • Efficient memory handling during broadcasts
• Optimized vectorized versions of operations
  • SIMD acceleration
  • Parallel implementations for large tensors
• Add benchmarking suite

Expected outcome: A library capable of performing efficient element-wise operations with SIMD acceleration.

Phase 3: Linear Algebra

• Matrix multiplication
  • Various multiplication algorithms
  • Cache-friendly implementations
• Decompositions
  • LU, QR, SVD, Eigendecomposition
• System solving
  • Linear systems
  • Least squares
• Additional operations
  • Determinant, trace, norm
  • Inverse, pseudo-inverse

Expected outcome: A comprehensive linear algebra library capable of handling most scientific computing needs.

Phase 4: Multi-threading and Optimization

• Thread pool implementation
• Parallel algorithms for large tensor operations
• Block-based processing for cache optimization
• Memory usage optimization
  • Buffer manager for memory reuse
  • In-place operations
• Performance profiling and optimization

Expected outcome: Highly performant implementations that scale with available hardware.

Phase 5: GPU Acceleration

• Metal backend (macOS/iOS)
  • Kernel implementations for common operations
  • Memory management between CPU/GPU
• WebGPU backend (cross-platform)
• Automatic backend selection
• Benchmark comparison between CPU and GPU implementations

Expected outcome: GPU acceleration for tensor operations with significant performance improvements for large workloads.

Phase 6: Advanced Features

• Automatic differentiation
• Statistical functions
• Signal processing capabilities
• Integration with visualization tools
• Special function support

Expected outcome: A feature-rich library suitable for advanced scientific computing applications.

Performance Considerations

• Memory layout: Use contiguous layouts for better cache performance
• SIMD vectorization: Leverage Zig's SIMD capabilities for element-wise operations
• Parallelization: Use thread pools for large tensor operations
• Backend switching: Automatically select the fastest backend for each operation
• Buffer reuse: Minimize allocations through buffer management
• Algorithm selection: Different algorithms based on tensor size and shape