[eigen] Performance question

```Hello all,

My first post on this list... so first of all, a great thank to all
developers (geniuses?) who produced Eigen.

Now my question, which is about a "small" bench I made. I don't use
very big vectors or matrices, just small ones, to performe some
3D geometry algorithms on triangular meshes. The thing is, I have
millions of points and triangles.

The core of the process involves two triangular meshes. One is
transformed (actually translated), then each vertex of the second is
tested against each triangle of the first one. Here, "tested" means
a ray (Eigen::ParametrizedLine) is casted from the vertex, its
intersection with the plane defined by the triangle (Eigen::Hyperplane)
is computed, then a check is made to know if this intersection is
inside the triangle or not (Eigen::Matrix::determinant). This is done
over and over.

I tried using Vector3f, Vector3d, Vector4f and Vector4d as base
point type, the other types being adapted accordingly. And using
(or trying to use) vectorization or not, i.e. giving -msse2 or
-DEIGEN_DONT_VECTORIZE to g++. The test platform is Kubuntu 8.10
(amd64) on AMD Athlon 64X2 5600+ (dual core), with 3GB of RAM.

What I expected: using Vector4f or Vector4d with SSE2 should give
better results (lower times).

The actual results (each test done 3 times and averaged), times
in seconds, lower is better:
+-----+-----+-----+-----+
| 3f  | 3d  | 4f  | 4d  |
-------------+-----+-----+-----+-----+
with sse2    | 213 | 314 | 272 | 397 |
-------------+-----+-----+-----+-----+
without sse2 | 220 | 307 | 272 | 400 |
-------------+-----+-----+-----+-----+

So... no performance gain when using 4x in place of 3x, no
performance gain when using SSE2.

I did my best to avoid creating temporaries, to use lazy eval,
and so on... Any hint about a typical place I could check to
find *why* I don't gain anything would be very appreciated.

If needed, I can provide source code (less than 700 lines).

Best regards,

--
(o< | Yves Bailly                          | -o)
//\ | Linux Dijon  : http://www.coagul.org | //\
\_/ |                                      | \_/`

```

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