210 lines
11 KiB
Markdown
210 lines
11 KiB
Markdown
# tenvex
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A header-only C++20 SIMD math library for 4D vector arithmetic.
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tenvex uses **expression templates** — a C++ template metaprogramming technique that allows chained vector operations to be evaluated lazily. A compound expression such as `norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f` is evaluated, at the point of assignment, as a single sequence of SSE4.1 intrinsics without intermediate temporaries.
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## License
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BSD 3-Clause License. Copyright (c) 2026 Artem Zyktin. See [LICENSE.txt](LICENSE.txt).
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## Status
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- **x86-64 / SSE4.1** - implemented and tested.
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- **ARM64 / NEON** - planned, not yet implemented.
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## Features
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- Header-only - just include `tenvex.h`.
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- Expression-template engine: nodes are lazy and evaluated on assignment.
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- C++20 concepts (`expression`, `vec_expr`, `scalar_expr`) enforce type safety at compile time.
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- Storage policy: small trivially-copyable nodes are stored by value, larger ones by `const&`, which also avoids dangling references to temporary sub-expressions.
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- Operations: `+`, `-`, `*` (scalar), `/` (by scalar), `dot3`, `cross3`, `norm3`, `magnitude3`, `==`, `approx_eq`, and component accessors `x()`, `y()`, `z()`, `w()`.
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## Requirements
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- A C++20 compiler (MSVC, GCC, or Clang).
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- An x64 CPU with **SSE4.1** support.
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- Premake for generating the test build (binaries are bundled for Windows, Linux, and macOS).
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## Getting Started
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tenvex is header-only. Copy `src/tenvex/` into your project and include the single public header:
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```cpp
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#include "tenvex.h"
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```
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### Basic Usage
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```cpp
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#include "tenvex.h"
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using namespace tnvx;
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vec4 a = { 1.0f, 2.0f, 3.0f, 0.0f };
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vec4 b = { 4.0f, 5.0f, 6.0f, 0.0f };
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vec4 c = { 1.0f, 0.0f, 1.0f, 0.0f };
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// Arithmetic
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vec4 sum = a + b;
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vec4 diff = a - b;
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vec4 scaled = a * 2.0f; // vector * scalar
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vec4 scaled2 = 3.0f * b; // scalar * vector
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vec4 halved = a / 2.0f; // vector / scalar
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// Vector operations (3-component; the w / homogeneous lane is handled explicitly)
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float d = dot3(a, b); // 3D dot product (ignores w)
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vec4 cr = cross3(a, b); // 3D cross product, result w = 0
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vec4 n = norm3(a); // normalize xyz, w preserved
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float mag = magnitude3(a); // 3D length (ignores w)
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// Compound expression - evaluated lazily, no temporaries, fused on assignment
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vec4 result = norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f;
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```
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`dot3` and `magnitude3` return scalar-expression nodes (`Dot3`, `Magn3`) that are implicitly convertible to `float` (the scalar is taken from lane 0), so `float d = dot3(a, b);` works, and they can also be used as operands inside a larger lazy expression.
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### `vec4`
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`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):
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```cpp
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vec4 zero; // default
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vec4 v = { 1.0f, 2.0f, 3.0f }; // w defaults to 0
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vec4 p = { 1.0f, 2.0f, 3.0f, 1.0f }; // explicit w
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vec4 r = a + b * 2.0f; // built from an expression (evaluates here)
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vf4 raw = v.eval(); // underlying __m128
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```
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Individual components are read on demand from the stored register; `vec4` keeps no separate float copy:
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```cpp
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float cx = v.x(); // lane 0
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float cy = v.y(); // lane 1
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float cz = v.z(); // lane 2
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float cw = v.w(); // lane 3
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```
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### Comparison
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```cpp
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vec4 a = { 1.0f, 2.0f, 3.0f, 4.0f };
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vec4 b = { 1.0f, 2.0f, 3.0f, 4.0f };
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bool exact = (a == b); // exact, all-lane equality
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bool approx1 = approx_eq(a, b); // default epsilon = 1e-6f
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bool approx2 = approx_eq(a, b, 1e-3f); // custom epsilon
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```
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## Architecture
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### Two layers
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- **Eager kernel layer** (`expressions/core.h`, namespace `tnvx::detail`): `TNVX_INLINE` functions over `vf4` (`add`, `sub`, `mul`, `div`, `dot3`, `magnitude3`, `norm3`, `cross3`, `scalar`, `get_lane`, `eq`, `approx_eq`). This is the only place intrinsics live, and the only place the SIMD backend is selected.
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- **Expression layer** (everything else in namespace `tnvx`): lazy nodes that compose and delegate down to the kernels. This layer operates only on `vf4` and contains no intrinsics.
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### Expression templates
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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`.
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```
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vec4 result = norm3(a + b * 2.0f) * dot3(b, c) + c * 3.0f;
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// Add< Mul< Norm3< Add<vec4, Mul<vec4, Scalar>> >, Scalar >, Mul<vec4, Scalar> >
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// evaluated as one SSE4.1 sequence at assignment
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```
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### C++20 concepts
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| Concept | Meaning |
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| ---------------- | ----------------------------------------------------------------------- |
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| `expression<T>` | Derives from `Expr<T>` and has `eval() -> vf4` and `self() -> const T&` |
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| `vec_expr<T>` | An `expression` marked as a vector expression (`is_vec_expr<T>`) |
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| `scalar_expr<T>` | An `expression` marked as a scalar expression (`is_scalar_expr<T>`) |
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### Storage policy
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Each node's operands are stored by value or by `const&` depending on size and triviality. This avoids dangling references to temporary sub-expressions:
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```cpp
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// trivially copyable && trivially destructible && sizeof(T) <= 16 -> stored by value
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// otherwise -> stored as const T&
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template<typename T>
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using tnvx_ref_or_value_t =
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std::conditional_t<is_stored_by_value_v<T>, T, const T&>;
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```
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### Operation nodes
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| Node | Concept | Intrinsics | Notes |
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| ------------- | ------------- | ----------------------------------------------------------- | --------------------------------------------------------------------------- |
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| `Scalar` | `scalar_expr` | `_mm_set_ps1` | Broadcasts a `float` to all 4 lanes |
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| `Add<L,R>` | `vec_expr` | `_mm_add_ps` | |
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| `Sub<L,R>` | `vec_expr` | `_mm_sub_ps` | |
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| `Mul<L,R>` | vec / scalar | `_mm_mul_ps` | Scalar multiply only (no component-wise `vec * vec`). Operands may be vector×scalar, scalar×vector, or scalar×scalar; a scalar operand is a `float` or a scalar expression |
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| `Div<L,R>` | `vec_expr` | `_mm_div_ps` | Vector divided by a scalar (`float`) |
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| `Dot3<L,R>` | `scalar_expr` | `_mm_dp_ps` (mask `0x7F`) | 3-component dot (ignores w), broadcast to all lanes; convertible to `float` |
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| `Cross3<L,R>` | `vec_expr` | `_mm_shuffle_ps` + `_mm_mul_ps` + `_mm_sub_ps` | 3-component cross product; result `w = 0` |
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| `Norm3<E>` | `vec_expr` | `_mm_dp_ps` + `_mm_sqrt_ps` + `_mm_div_ps` + `_mm_blend_ps` | Normalizes xyz by the 3D magnitude; preserves w |
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| `Magn3<E>` | `scalar_expr` | `_mm_sqrt_ps(_mm_dp_ps(..., 0x7F))` | 3-component length (ignores w), broadcast; convertible to `float` |
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Comparison helpers (free functions in `tnvx`, backed by `tnvx::detail`):
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| Function | Intrinsics | Notes |
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| ---------------------------- | --------------------------------------- | ------------------------------ |
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| `operator==` | `_mm_cmpeq_ps` + `_mm_movemask_ps` | Exact, all-lane equality |
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| `approx_eq(a, b, eps=1e-6f)` | `_mm_andnot_ps` + `_mm_cmple_ps` + mask | Per-lane abs difference <= eps |
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## Building
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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. On GCC/Clang the `tenvex_tests` project is built with `-msse4.1`; projects that consume the headers must enable SSE4.1 in their own build.
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### Windows (Visual Studio 2022)
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```bat
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scripts\config-vs2022.bat
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```
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Then open the generated solution under `build/` and build the `tenvex_tests` project.
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### Linux / macOS
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```sh
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# Linux
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./premake/bin/linux/premake5 gmake2
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# macOS
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./premake/bin/macos/premake5 gmake2
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# then
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make config=debug # or: make config=release
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```
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Build output is written to `bin/<system>/x64/<debug|release>/output/`.
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## Running Tests
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The test suite uses Google Test (vendored in `thirdparty/gtest/`) and currently covers 27 cases:
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| Category | Tests |
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| -------------------- | ---------------------------------------------------------------------------------------------------------- |
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| Basic operations | `add`, `sub`, `mult_a`, `mult_b`, `div`, `dot3`, `cross`, `norm_a`, `norm_b`, `magnitude_a`, `magnitude_b` |
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| Compound expressions | `mixed_type_add`, `expression_a`, `expression_b`, `expression_c`, `expression_d`, `expression_from_temporaries` |
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| Math properties | `cross_anticommutative`, `dot_commutative`, `norm_magnitude`, `dot_perpendicular`, `cross_parallel`, `w_is_zero_with_nonzero_input_w`, `preserves_nontrivial_w`, `zero_vector_is_nan` |
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| Type system | `dot3_times_literal_collapses`, `magnitude3_times_literal_collapses` |
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Build and run `tenvex_tests` from the generated project or makefile.
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## Benchmarks
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A [Google Benchmark](https://github.com/google/benchmark) suite (vendored in `thirdparty/benchmark/`) lives in `src/benchmarks/` and is built as the `tenvex_bench` project. Build in **release** and run the resulting executable; on GCC/Clang it is built with `-msse4.1`. A subset can be selected at runtime, e.g. `tenvex_bench --benchmark_filter=Compound`.
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A naive scalar reference implementation - `naive::vec4` in `src/naive/naive_vec4.h` - mirrors the tenvex API and semantics with plain `float` math (everything `inline`, by-value, reciprocal-multiply for division/normalization). It is benchmarked side by side (the `BM_Naive_*` cases) and has its own mirrored test suite (`src/tests/naive_tests.cpp`), so the SIMD path can be compared against a straightforward baseline.
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### Findings (per-vec4, release, single machine)
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- tenvex matches hand-written intrinsics on the same expression - the expression-template abstraction is zero-cost.
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- Arithmetic-heavy compound expressions: tenvex ~1.8x faster than the scalar baseline.
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- Isolated `dot3` / `norm3`: the scalar baseline is competitive or faster - `_mm_dp_ps` is high-latency and a 3-component reduction gains little from SIMD.
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- These are latency-bound, per-vec4 figures. Bulk / SoA throughput is out of scope. |