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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.
tenvex uses **expression templates** - a C++ template metaprogramming technique that enables lazy, zero-overhead evaluation of chained vector operations. A compound expression such as `norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f` collapses, at the point of assignment, into a single fused sequence of SSE4.1 intrinsics with no intermediate temporaries.
## License
BSD 3-Clause License. Copyright (c) 2026 Artem Zyktin. See [LICENSE.txt](https://claude.ai/chat/LICENSE.txt).
## Status
- **x86-64 / SSE4.1** - implemented and tested.
- **ARM64 / NEON** - planned, not yet implemented.
## 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`
- Header-only - just include `tenvex.h`.
- Expression-template engine with zero-cost abstractions: nodes are lazy and fuse on assignment.
- C++20 concepts (`expression`, `vec_expr`, `scalar_expr`) enforce type safety at compile time.
- Storage policy: small trivially-copyable nodes are stored by value, larger ones by `const&`, which also avoids dangling references to temporary sub-expressions.
- Operations: `+`, `-`, `*` (scalar), `/` (by scalar), `dot3`, `cross3`, `norm3`, `magnitude3`, plus `==` and `approx_eq`.
## Requirements
- C++20 compiler (MSVC, GCC, Clang)
- x64 CPU with SSE2 support
- [Premake5](https://premake.github.io/) (binaries included for Windows, Linux, macOS)
- A C++20 compiler (MSVC, GCC, or Clang).
- An x64 CPU with **SSE4.1** support
- Premake for generating the test build (binaries are bundled for Windows, Linux, and macOS).
## Getting Started
@ -38,35 +46,36 @@ 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;
// Arithmetic
vec4 sum = a + b;
vec4 diff = a - b;
vec4 scaled = a * 2.0f; // vector * scalar
vec4 scaled2 = 3.0f * b; // scalar * vector
vec4 halved = a / 2.0f; // vector / scalar
// Vector operations
float d = dot(a, b);
vec4 cr = cross(a, b);
vec4 n = norm(a);
float mag = magnitude(a);
// Vector operations (3-component; the w / homogeneous lane is handled explicitly)
float d = dot3(a, b); // 3D dot product (ignores w)
vec4 cr = cross3(a, b); // 3D cross product, result w = 0
vec4 n = norm3(a); // normalize xyz, w preserved
float mag = magnitude3(a); // 3D length (ignores w)
// Compound expressions — evaluated lazily, no temporaries
vec4 result = norm(a + b * 2.0f) * dot(b, c) + c * 3.0f;
// Compound expression - evaluated lazily, no temporaries, fused on assignment
vec4 result = norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f;
```
### `vec4` Member Functions
`dot3` and `magnitude3` return scalar-expression nodes (`Dot3`, `Magn3`) that are implicitly convertible to `float` (the scalar is extracted from lane 0), so both `float d = dot3(a, b);` and using them inside a larger expression work.
### `vec4`
`vec4` is a 16-byte, `alignas(16)` value type. It can be default-constructed, built from components (with `w` defaulting to `0`), or constructed from any vector expression (which triggers evaluation):
```cpp
vec4 v = { 1.0f, 2.0f, 3.0f, 4.0f };
vec4 zero; // default
vec4 v = { 1.0f, 2.0f, 3.0f }; // w defaults to 0
vec4 p = { 1.0f, 2.0f, 3.0f, 1.0f }; // explicit w
vec4 r = a + b * 2.0f; // built from an expression (evaluates here)
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
vf4 raw = v.eval(); // underlying __m128
```
### Comparison
@ -75,57 +84,72 @@ vec4 n = v.norm(); // unit vector
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
bool exact = (a == b); // exact, all-lane equality
bool approx1 = approx_eq(a, b); // default epsilon = 1e-6f
bool approx2 = approx_eq(a, b, 1e-3f); // custom epsilon
```
## Architecture
### Expression Templates
### Two layers
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`.
- **Eager kernel layer** (`expressions/core.h`, namespace `tnvx::detail`): plain `TNVX_INLINE` functions over `vf4` (`add`, `sub`, `mul`, `div`, `dot3`, `magnitude3`, `norm3`, `cross3`, `scalar`, `eq`, `approx_eq`). This is the only place intrinsics live, and the only place the SIMD backend is selected.
- **Expression layer** (everything else in namespace `tnvx`): lazy nodes that compose and delegate down to the kernels. This layer is architecture-neutral - it only ever sees `vf4`.
### Expression templates
Every operation returns a lazy node rather than evaluating immediately. Nodes inherit from `Expr<Derived>` via CRTP (which provides `self()`) and expose a `vf4 eval() const` method. Evaluation happens only when the result is assigned to a `vec4`, or - for scalar nodes - when converted to `float`.
```
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
vec4 result = norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f;
// Add< Mul< Norm3< Add<vec4, Mul<vec4, Scalar>> >, Scalar >, Mul<vec4, Scalar> >
// ^ the whole tree collapses to a short fused SSE4.1 sequence at assignment
```
### C++20 Concepts
### C++20 concepts
| Concept | Meaning |
|----------------------|----------------------------------------------|
| `expression<T>` | Any `Expr<T>` subtype with `__m128 eval()` |
| `vector_expression<T>` | An `expression` that is not a `Scalar` |
| Concept | Meaning |
| ---------------- | ----------------------------------------------------------------------- |
| `expression<T>` | Derives from `Expr<T>` and has `eval() -> vf4` and `self() -> const T&` |
| `vec_expr<T>` | An `expression` marked as a vector expression (`is_vec_expr<T>`) |
| `scalar_expr<T>` | An `expression` marked as a scalar expression (`is_scalar_expr<T>`) |
### Storage Policy
### Storage policy
To avoid dangling references to temporary expression nodes, storage is chosen automatically:
To keep small nodes register-friendly and to avoid dangling references to temporary sub-expressions, each node's operands are stored by value or by `const&` automatically:
```cpp
// trivially copyable & destructible & sizeof <= 16 → stored by value
// otherwise → stored as const T&
// trivially copyable && trivially destructible && sizeof(T) <= 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&>;
using tnvx_ref_or_value_t =
std::conditional_t<is_stored_by_value_v<T>, T, const T&>;
```
### Operation Nodes
### 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 |
| Node | Concept | Intrinsics | Notes |
| ------------- | ------------- | ----------------------------------------------------------- | --------------------------------------------------------------------------- |
| `Scalar` | `scalar_expr` | `_mm_set_ps1` | Broadcasts a `float` to all 4 lanes |
| `Add<L,R>` | `vec_expr` | `_mm_add_ps` | |
| `Sub<L,R>` | `vec_expr` | `_mm_sub_ps` | |
| `Mul<L,R>` | vec / scalar | `_mm_mul_ps` | Scalar multiply: `vec * float`, `float * vec`, `scalar * scalar` |
| `Div<L,R>` | `vec_expr` | `_mm_div_ps` | Vector divided by a scalar (`float`) |
| `Dot3<L,R>` | `scalar_expr` | `_mm_dp_ps` (mask `0x7F`) | 3-component dot (ignores w), broadcast to all lanes; convertible to `float` |
| `Cross3<L,R>` | `vec_expr` | `_mm_shuffle_ps` + `_mm_mul_ps` + `_mm_sub_ps` | 3-component cross product; result `w = 0` |
| `Norm3<E>` | `vec_expr` | `_mm_dp_ps` + `_mm_sqrt_ps` + `_mm_div_ps` + `_mm_blend_ps` | Normalizes xyz by the 3D magnitude; preserves w |
| `Magn3<E>` | `scalar_expr` | `_mm_sqrt_ps(_mm_dp_ps(..., 0x7F))` | 3-component length (ignores w), broadcast; convertible to `float` |
Comparison helpers (free functions in `tnvx`, backed by `tnvx::detail`):
| Function | Intrinsics | Notes |
| ---------------------------- | --------------------------------------- | ------------------------------ |
| `operator==` | `_mm_cmpeq_ps` + `_mm_movemask_ps` | Exact, all-lane equality |
| `approx_eq(a, b, eps=1e-6f)` | `_mm_andnot_ps` + `_mm_cmple_ps` + mask | Per-lane abs difference <= eps |
## Building
The build system uses [Premake5](https://premake.github.io/). Premake5 binaries are included in `premake/bin/` for all platforms.
The build uses [Premake5](https://premake.github.io/); binaries are bundled in `premake/bin/` for all platforms. The workspace is x64-only and uses C++20, with `debug` and `release` configurations and `tenvex_tests` as the start project.
### Windows (Visual Studio 2022)
@ -133,11 +157,9 @@ The build system uses [Premake5](https://premake.github.io/). Premake5 binaries
scripts\config-vs2022.bat
```
Then open the generated solution in `build/` and build the `tenvex_tests` project.
Then open the generated solution under `build/` and build the `tenvex_tests` project.
### Other Platforms
Run the appropriate Premake5 binary manually:
### Linux / macOS
```sh
# Linux
@ -145,48 +167,21 @@ Run the appropriate Premake5 binary manually:
# macOS
./premake/bin/macos/premake5 gmake2
```
Then:
```sh
make config=debug
# then
make config=debug # or: make config=release
```
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:
The test suite uses Google Test (vendored in `thirdparty/gtest/`) and currently covers 19 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` |
| Category | Tests |
| -------------------- | ---------------------------------------------------------------------------------------------------------- |
| Basic operations | `add`, `sub`, `mult_a`, `mult_b`, `div`, `dot3`, `cross`, `norm_a`, `norm_b`, `magnitude_a`, `magnitude_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).