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# tenvex
A header-only C++20 SIMD math library for high-performance 4D vector arithmetic.
tenvex uses **expression templates** — a C++ template metaprogramming technique that enables lazy, zero-overhead evaluation of chained vector operations. Complex expressions like `norm(a + b * 2.0f) * dot(b, c) + c * 3.0f` compile down to a single fused sequence of SSE/AVX intrinsics with no intermediate temporaries.
## Features
- Header-only — just include `tenvex.h`
- Expression template engine with zero-cost abstractions
- All arithmetic backed by SSE/AVX intrinsics (`__m128`)
- C++20 concepts enforce type safety at compile time
- Smart storage policy: small trivial types stored by value, others by `const&`
- Supported operations: `+`, `-`, `*` (scalar), `dot`, `cross`, `norm`, `magnitude`
## Requirements
- C++20 compiler (MSVC, GCC, Clang)
- x64 CPU with SSE2 support
- [Premake5](https://premake.github.io/) (binaries included for Windows, Linux, macOS)
## Getting Started
tenvex is header-only. Copy `src/tenvex/` into your project and include the single public header:
```cpp
#include "tenvex.h"
```
### Basic Usage
```cpp
#include "tenvex.h"
using namespace tnvx;
vec4 a = { 1.0f, 2.0f, 3.0f, 0.0f };
vec4 b = { 4.0f, 5.0f, 6.0f, 0.0f };
vec4 c = { 1.0f, 0.0f, 1.0f, 0.0f };
// Basic arithmetic
vec4 sum = a + b;
vec4 diff = a - b;
vec4 scaled = a * 2.0f;
vec4 scaled2 = 3.0f * b;
// Vector operations
float d = dot(a, b);
vec4 cr = cross(a, b);
vec4 n = norm(a);
float mag = magnitude(a);
// Compound expressions — evaluated lazily, no temporaries
vec4 result = norm(a + b * 2.0f) * dot(b, c) + c * 3.0f;
```
### `vec4` Member Functions
```cpp
vec4 v = { 1.0f, 2.0f, 3.0f, 4.0f };
float x = v.x(); // component accessors
float y = v.y();
float z = v.z();
float w = v.w();
auto arr = v.data(); // std::array<float, 4>
float mag = v.magnitude(); // vector length
vec4 n = v.norm(); // unit vector
```
### Comparison
```cpp
vec4 a = { 1.0f, 2.0f, 3.0f, 4.0f };
vec4 b = { 1.0f, 2.0f, 3.0f, 4.0f };
bool exact = (a == b); // exact equality
bool approx = approx_eq(a, b); // epsilon = 1e-3 (default)
bool approx = approx_eq(a, b, 1e-6f); // custom epsilon
```
## Architecture
### Expression Templates
Every operation returns a lazy expression node rather than evaluating immediately. Nodes inherit from `Expr<Derived>` via CRTP and expose a single `__m128 eval() const` method. Evaluation only happens when the result is assigned to a `vec4`.
```
vec4 result = norm(a + b * 2.0f) * dot(b, c) + c * 3.0f;
// └─ Mul<Norm<Add<vec4, Mul<vec4, Scalar>>>, Mul<Dot<vec4,vec4>, Mul<Scalar,...>>>
// ↑ entire tree collapsed to ~5 SSE instructions at assignment
```
### C++20 Concepts
| Concept | Meaning |
|----------------------|----------------------------------------------|
| `expression<T>` | Any `Expr<T>` subtype with `__m128 eval()` |
| `vector_expression<T>` | An `expression` that is not a `Scalar` |
### Storage Policy
To avoid dangling references to temporary expression nodes, storage is chosen automatically:
```cpp
// trivially copyable & destructible & sizeof <= 16 → stored by value
// otherwise → stored as const T&
template<typename T>
using tnvx_type_storage = std::conditional_t<tnvx_store_by_value<T>, T, const T&>;
```
### Operation Nodes
| Node | Intrinsic(s) | Notes |
|-----------------|-------------------------------------|------------------------------------|
| `Add<L,R>` | `_mm_add_ps` | |
| `Sub<L,R>` | `_mm_sub_ps` | |
| `Mul<E,Scalar>` | `_mm_mul_ps` | Scalar multiplication only |
| `Dot<L,R>` | `_mm_mul_ps` + horizontal shuffle | Result broadcast to all 4 lanes |
| `Cross<L,R>` | `_mm_mul_ps` + `_mm_sub_ps` + shuffles | 3-component; w = 0 |
| `Norm<E>` | `_mm_div_ps` + `_mm_sqrt_ps` | Divide by magnitude |
| `Magnitude<E>` | `_mm_sqrt_ss` | Scalar result |
| `Scalar` | `_mm_set1_ps` | Broadcasts float to all 4 lanes |
## Building
The build system uses [Premake5](https://premake.github.io/). Premake5 binaries are included in `premake/bin/` for all platforms.
### Windows (Visual Studio 2022)
```bat
scripts\config-vs2022.bat
```
Then open the generated solution in `build/` and build the `tenvex_tests` project.
### Other Platforms
Run the appropriate Premake5 binary manually:
```sh
# Linux
./premake/bin/linux/premake5 gmake2
# macOS
./premake/bin/macos/premake5 gmake2
```
Then:
```sh
make config=debug
```
Build output is written to `bin/<system>/x64/<debug|release>/output/`.
## Running Tests
The test suite uses Google Test (vendored in `thirdparty/gtest/`) and covers 18 cases:
| Category | Tests |
|--------------------|-----------------------------------------------------------------------|
| Basic operations | `add`, `sub`, `mult_a`, `mult_b`, `dot`, `cross`, `norm_a/b`, `magnitude_a/b` |
| Compound expressions | `expression_a`, `expression_b`, `expression_c` |
| Math properties | `cross_anticommutative`, `dot_commutative`, `norm_magnitude`, `dot_perpendicular`, `cross_parallel` |
Build and run `tenvex_tests` from the generated project or makefile.
## Project Structure
```
tenvex/
├── src/
│ ├── tenvex/ # Library headers (header-only)
│ │ ├── tenvex.h # Single public include
│ │ ├── vec4.h / vec4_impl.hpp
│ │ └── internal/ # Expression nodes and infrastructure
│ └── tests/
│ └── vec4_tests.cpp # Google Test suite
├── thirdparty/
│ └── gtest/ # Vendored Google Test
├── premake/
│ └── bin/ # Premake5 binaries (Windows, Linux, macOS)
├── scripts/
│ └── config-vs2022.bat # VS2022 project generation
└── premake5.lua # Build configuration
```
## License
BSD 3-Clause License. Copyright (c) 2026 Artem Zyktin. See [LICENSE.txt](LICENSE.txt).