[PATCH] Optimize TestRayAASquare in Geometry.cpp

[Stan]

There is a todo line 244 of Geometry.cpp that says :

// Exactly like TestRaySquare with u=(1,0), v=(0,1)
// Assume the compiler is clever enough to inline and simplify all this
// (TODO: stop assuming that)

[Stan]

Fix the Todo.

[Stan]

Documented Version of Above Patch

[Stan]

Replace some scalar computations by the value to save some computations, add doxygen documentation, and rename some variables to make the code more readable.

[elexis]

Yeah, that's the right direction in my understanding.

• It would be better though to not rename variables, as they have the same name in the other code as well and the patch will be easier to review.

• Remove the au, av, bu, bv variables, as you can just reference u.X etc..

• The goal is to completely remove the constants u, v. So the u.Multiply(hw) things also need to be simplified / consolidated.

Those vector functions are defined in FixedVector2D.h and reflect the usual vector operations known from linear algebra.

[Stan]

Assert the previous comments, though we cannot remove u and v for now.

[Stan]

Here are the maths behind the changes as you can see there is not much to be done for s1,s3

S0
(1;0) * X + (0;1) * Y - (B;C)
= (X;Y) - (B;C)
= (X-B;Y-C)
= (Halfsize - a)

S1
(1;0) * X - (0;1) * Y - (B;C)
= (X; - Y) - (B;C)
= (X-B;-Y-C)

S2
- (1;0) * X - (0;1) * Y - (B;C)
= -(X;Y) - (B;C)
= (-X-B;-Y-C)
= (-Halfsize - a)

S3
- (1;0) * X + (0;1) * Y - (B;C)
= (-X;Y) - (B;C)
= (-X-B;Y-C)


(X;Y)-(0,2Y)
(X;Y) = (X;-Y) 

[Stan]

A proposal to simplify further the code.

[elexis]

An alpha 19 replay and it's profiling data showing the performance details. The match was a 40min 3v3 with 200 pop capacity and too many trees.

[elexis]

In 17500:

Pathfinder optimization, fixes #3541.
Simplify the math of Geometry::TestRayAASquare.

[elexis]

The patch removes two constants (0 and 1) and useless compuation (for example 1*x + 0*y).

Notice the last two peaks show 10% performance improvement. Otherwise not too much gain.