Geomancy

Linear is nice, but slow. Those are naughty, but a bit faster.

• All data types are monomorphic, unpacked and specialized.
• Mat4 and Vec4 are ByteArray#.
• Mat4xMat4 and Mat4xVec4 is done with SIMD.

Matrix layout

CPU-side matrices compose in MVP order, optimized for mconcat (local1 : local2 : ... : root) operation.

GPU-side, in GLSL, it is PVM * v.

The Numbers

Storing a list of 1000 transformations (e.g. rendering instance data):

benchmarking 4x4 poke/1000/geomancy
time                 11.76 μs   (11.66 μs .. 11.92 μs)
                     0.999 R²   (0.998 R² .. 1.000 R²)
mean                 11.75 μs   (11.69 μs .. 11.86 μs)
std dev              283.4 ns   (199.0 ns .. 399.0 ns)
variance introduced by outliers: 26% (moderately inflated)

If you're willing to adjust your shaders, it's only 2.4 times slower.

benchmarking 4x4 poke/1000/linear
time                 28.29 μs   (28.21 μs .. 28.38 μs)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 28.40 μs   (28.34 μs .. 28.50 μs)
std dev              267.4 ns   (145.5 ns .. 419.9 ns)

Keeping your shaders straight make the affair 6.1x slower.

benchmarking 4x4 poke/1000/linear/T
time                 73.70 μs   (73.06 μs .. 74.49 μs)
                     1.000 R²   (0.999 R² .. 1.000 R²)
mean                 72.77 μs   (72.50 μs .. 73.22 μs)
std dev              1.129 μs   (793.5 ns .. 1.580 μs)

Folding down a gloss-style scene graph is where it is all started:

benchmarking 4x4 multiply/1000/geomancy
time                 20.79 μs   (20.77 μs .. 20.83 μs)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 20.80 μs   (20.78 μs .. 20.83 μs)
std dev              76.71 ns   (60.01 ns .. 99.06 ns)

benchmarking 4x4 multiply/1000/linear
time                 173.9 μs   (173.6 μs .. 174.4 μs)
                     1.000 R²   (1.000 R² .. 1.000 R²)
mean                 173.5 μs   (173.2 μs .. 174.4 μs)
std dev              1.733 μs   (727.8 ns .. 3.422 μs)

Add that time to the poking that'll follow.

Sure, it is in the lower microseconds range, but this budget can be used elsewhere.