linmath.hpp

linmath.hpp is a freestanding, header-only linear algebra library for C++ designed with a strong emphasis on:

• predictable performance
• minimal dependencies
• SIMD acceleration
• freestanding compatibility

The project started as a modern C++ reinterpretation of linmath.h, aiming to preserve its simplicity and transparency while introducing:

• C++ ergonomics
• runtime SIMD dispatch
• optimized matrix/vector operations

The goal is a small, portable math library suitable for engines, tools, and freestanding environments.

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Key Features

• Freestanding friendly
• Header-only
• Runtime SIMD dispatch
• SSE2 / AVX / AVX2 / NEON support
• Scalar fallback
• No dynamic allocation
• No exceptions
• No RTTI
• Deterministic instruction cost
• Predictable memory layout

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SIMD Support

SIMD acceleration is optional and detected at runtime.

Supported execution paths:

Mode	Architecture
Scalar	baseline
SSE2	x86
AVX / AVX2	x86
NEON	ARM

SIMD can be disabled at compile time (define once before any include):

#define LMATH_FORCE_NO_SIMD

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Benchmark Methodology

All benchmarks were executed with:

• 200,000,000 iterations
• 40,000,000 warm‑up iterations (not included in measured time)

Environment:

CPU: Intel Core i5‑9300H
OS: Windows 10
Compiler: MSVC

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Benchmark Results

x64 — AVX2

Function	Time
lm::sqrtf SIMD	896.94 ms
lm::rsqrtf SIMD	637.34 ms
lm::vec3 dot SIMD	51.87 ms
glm::vec3 dot SIMD	50.41 ms
lm::mat4 mul SIMD	1389.33 ms
glm::mat4 mul SIMD	4107.18 ms
lm::mat4 * vec4 SIMD	627.09 ms
glm::mat4 * vec4 SIMD	834.72 ms
lm::mat4 look_at SIMD	5142.53 ms
glm::mat4 lookAt SIMD	3739.55 ms

x64 — SSE2

Function	Time
lm::sqrtf SIMD	697.68 ms
lm::rsqrtf SIMD	465.08 ms
lm::vec3 dot SIMD	52.39 ms
glm::vec3 dot SIMD	50.56 ms
lm::mat4 mul SIMD	3644.14 ms
glm::mat4 mul SIMD	4573.58 ms
lm::mat4 * vec4 SIMD	986.78 ms
glm::mat4 * vec4 SIMD	1017.16 ms
lm::mat4 look_at SIMD	5473.76 ms
glm::mat4 lookAt SIMD	4131.30 ms

x64 — Scalar (No SIMD)

Function	lm	glm	linmath
sqrtf	879.26 ms	—	—
rsqrtf	438.53 ms	—	—
vec3 dot	52.45 ms	50.48 ms	51.18 ms
vec3 norm	1627.12 ms	1163.73 ms	102.05 ms
vec3 cross	529.61 ms	1138.32 ms	252.55 ms
mat4 translate	40.95 ms	1745.55 ms	1350.19 ms
mat4 rotate_x	1926.75 ms	8458.00 ms	9467.67 ms
mat4 mul	3410.49 ms	4580.78 ms	5408.38 ms
mat4 * vec4	833.22 ms	1014.19 ms	1412.46 ms
mat4 look_at	5450.31 ms	4574.57 ms	5866.87 ms

x86 — Scalar (No SIMD)

Function	lm	glm	linmath
sqrtf	2133.10 ms	—	—
rsqrtf	1421.35 ms	—	—
vec3 dot	50.63 ms	51.20 ms	50.62 ms
vec3 norm	2484.36 ms	2416.90 ms	2175.95 ms
vec3 cross	940.44 ms	822.28 ms	922.33 ms
mat4 translate	1829.01 ms	8256.54 ms	2650.63 ms
mat4 rotate_x	4825.54 ms	20466.82 ms	16719.11 ms
mat4 mul	5777.06 ms	13695.82 ms	9128.60 ms
mat4 * vec4	1142.84 ms	3165.83 ms	2201.41 ms
mat4 look_at	13845.12 ms	13605.16 ms	14764.14 ms

x86 — SSE2

Function	Time
lm::sqrtf SIMD	826.78 ms
lm::rsqrtf SIMD	580.39 ms
lm::vec3 dot SIMD	50.68 ms
glm::vec3 dot SIMD	53.31 ms
lm::mat4 mul SIMD	4102.49 ms
glm::mat4 mul SIMD	4582.56 ms
lm::mat4 * vec4 SIMD	1925.10 ms
glm::mat4 * vec4 SIMD	1922.73 ms
lm::mat4 look_at SIMD	5945.23 ms
glm::mat4 lookAt SIMD	6156.01 ms

x86 — AVX2

Function	Time
lm::sqrtf SIMD	741.63 ms
lm::rsqrtf SIMD	489.42 ms
lm::vec3 dot SIMD	50.91 ms
glm::vec3 dot SIMD	53.05 ms
lm::mat4 mul SIMD	2846.12 ms
glm::mat4 mul SIMD	4065.42 ms
lm::mat4 * vec4 SIMD	1039.83 ms
glm::mat4 * vec4 SIMD	1787.38 ms
lm::mat4 look_at SIMD	5749.46 ms
glm::mat4 lookAt SIMD	6254.61 ms

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Acknowledgements

This project would not exist without the original linmath.h.

Special thanks to its author for creating a minimal and elegant C math library that inspired this C++ implementation.

License

See LICENSE file for details.