Optimizing Compiler for Engineering Problems

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Optimizing Compiler for Engineering Problems
Petr R. Ivankov
August 22, 2008
Abstract
New information technologies provide a lot of prospects for perfor-
mance improvement. One of them is ”Dynamic Source Code Generation
and Compilation”. This article shows how this way provides high perfor-
mance for engineering problems.
1 Introduction
Present day engineering problems require multidisciplinary usage of computer.
For example engineers use following IT branches: math calculations, 3D graph-
ics, real time control, databases. Software devoted for every single branch is
not effective. This circumstance reflects common integration strategy of IT.
There exists a myth that performance requires specialization and contradicts
universality and/or integration strategy. This article shows that very universal
software can provide very high performance. Section 2 is devoted to universal
software. Section 3 describes runtime optimizing for it.
2 Universal Framework for Science and Engi-
neering
Information about universal engineering software is contained at following web
cites.
• Universal Framework for Science and Engineering homepage
http://www.mathframe.com/;
• CodeProject articles devoted to framework applications
http://www.codeproject.com/script/articles/list articles.asp?userid=3080377;
• Arxiv articles [1], [2] devoted to framework applications.
• SourceForge projects
AstroFrame https://sourceforge.net/projects/astrohalaxy;
CategoryTheory https://sourceforge.net/projects/categorytheory/;
1

Runtime Optimizing Compiler for Engineering Problems 2
Described framework is based on three principles. First one is component
approach. Second principle is insertion of math formulas. Third principle is
openness of framework. So let us consider them.
2.1 Component approach
The best method of complicated phenomenon grasping is a decomposition of
the phenomenon. The phenomenon contains objects (components) and there
exist links between objects. Any object may belong to a set of domains. For
example a source of physical field [8] has a geometrical position. Hence it is
a subject of positioning domain. This object may be linked to other object of
positioning domain by positioning links. If source of physical field receives and
then transmits information then it is a consumer of information. So it is also
a subject of information domain and may be linked to sources of information.
And at last it is a subject of physical field domain. Typical picture of objects
(components) of virtual reality simulation is presented on Figure 1. This picture
Figure 1: Typical example of virtual reality
shows motion of 3D shape. We have ordinary differential equations of the shape
motion
x¨ = f(x, x˙).
The component at left bottom is a solver of these equations. It is a source
of information. In this situation we should perform some transformation of this
information. To do this we use “Transformation of variables”. Later component

Runtime Optimizing Compiler for Engineering Problems 3
is a consumer of information of the solver. So it is connected to solver by
information link. We also have a “Frame of shape”. It is a moved reference
frame that uses information form the solver and from the “Transformation of
variables”. So it is a consumer of information and it is connected to its providers
of information. The “3D Shape” is rigidly connected to this frame. The shape
is connected to the frame by geometrical positioning link. Also we have a
virtual camera and its reference frame. They are also connected by geometrical
positioning link. And at last the camera is connected to the shape by visibility
link.
2.2 Formula editor
We need rich formula editor for interdisciplinary software. Insertion of formulas
enables us use them in different tasks of virtual reality. These formulas may be
used for definition of signals, transformation of 3D figures, definition of right
parts of differential equations, and definition of size and color of figures, etc. The
formulas may contain real, integer, boolean, vector variables etc. In the Cat-
egoryTheory project https://sourceforge.net/projects/categorytheory/
formula, the editor operates even with Galois fields. Implemented in related
projects formula editor formula editor is case sensitive and operates with a lots
of types. Result of calculation depends on types of variables. Let sin(a) be a
formula of formula editor. What is its meaning? If a is a real variable then
result of formula is a real value. However if a is an array then sin(a) is also an
array of componentwise calculation of sin. If a is a real array and b is a real
variable then a + b means an array of sums of components of a with b. Any
function of formula editor may be a variable or result of calculation. A function
as result is not a value of function but it is the whole function. This fact seems
unusual for people who do not know functional analysis. For example if a is a
real variable then f(a) means result of calculation of f . If a is a function then
f(a) is a composition of functions. Formula editor supports matrix and vector
operations. Examples of usage of vector and matrix operations are presented
below:
f taf,
(q−1 + h)−1,
a × b.
These examples contains transposition of matrixes, products of matrixes, in-
version of matrixes and vector product of 3D vectors. A very good sample of
these operations’ applications is Kalman filter [9]. In particular this filter is used
in motion control systems. You can download and evaluate example of this filter
from: http://www.codeproject.com/cs/library/UniversalEnggFrmwork6.asp
The formula editor supports Dirac delta function. The presence of the delta
function at the right part of the ordinary differential equation shows that the
result function is not continuous. Following picture shows presence of delta
function in formula editor
f(t)δ(t)

Runtime Optimizing Compiler for Engineering Problems 4
2.3 Openness of the software
Usually, every developer or company has its own projects of those object do-
main. This software does not require discarding of existing projects. Any object
domain project may be included to this software. If you wish to include your
project or its part, then you should develop an adapter, compile the class library,
and link it to this software. The adapter should contain one or more classes that
implement one or more interfaces of this software. A more profound description
of these interfaces is contained in the developer’s guide. You can download the
guide from AstroFrame homepage https://sourceforge.net/projects/astrohalaxy.
3 Optimizing Compiler
Optimizing compiler transforms formula editor expressions to C# code. Then
CodeDom
http://msdn.microsoft.com/en-us/library/650ax5cx.aspx
performs compilation. Generated code do not contain cycles or unnecessary
assignments. Let us consider some examples of generated code.
3.1 Matrix Product
Formula editor indicates matrix product as ab where a and b are first and second
factor respectively. Dimension of a and b depends on framework project. Gener-
ated code looks like:
var 2[0, 0] = var 0[0, 0] * var 1[0, 0] + var 0[0, 1] * var 1[1, 0] +
var 0[0, 2] * var 1[2, 0] + var 0[0, 3] * var 1[3, 0];
var 2[0, 1] = var 0[0, 0] * var 1[0, 1] + var 0[0, 1] * var 1[1, 1] +
var 0[0, 2] * var 1[2, 1] + var 0[0, 3] * var 1[3, 1];
...
where var 0, var 1 and var 2 corresponds to a, b and ab respectively So we
have code without cycles and unnecessary assignments. It is possible code gen-
eration even without arrays.
3.2 Vector Calculation
Formula editor is context sensitive. It has high level of abstraction. For example
if a and b are vectors then a+b is vector sum. But if a is a scalar then a+b means
componentwise sum to scalar. Following code shows this situation: var 2[0] =
var 0 + var 1[0];
var 2[1] = var 0 + var 1[1];
var 2[2] = var 0 + var 1[2];
...
where var 0, var 1 and var 2 corresponds to a, b and result of calculation
respectively.

REFERENCES 5
3.3 Sum
If a is number array then formula editor can represent sum of its elements by
the following way
∑
a; (1)
var 1 = var 0[0] + var 0[1] + var 0[2] + var 0[3] + ...;
where var 0, var 1 corresponds to a and
∑
a respectively. Generated code
is presented below:
3.4 Symbolic Differentiation
Framework contains symbolic differentiation. Expression ddt sin t
2 match to the
following code. var 1 = 2 * var 0 * Math.Sin(var 0);
where var 0, var 1 corresponds to t and result of differentiation.
3.5 Conclusion
There exists opinion that .NET does not match to scientific and engineering
problems. One reason that .NET requires garbage collection. However the
framework construct new objects during project loading only. Main calculations
do not contain construction and therefore they do not require garbage collec-
tion. Second reason is that .NET has slow performance. This article shows
that runtime compilation enables us reach very high performance. Besides this
circumstances .NET have a lot of other properties that are useful for scientific
and engineering problems. Thank you very much.
References
[1] Petr R. Ivankov, Nikolay P. Ivankov. The framework for simulation of dy-
namics of mechanical aggregates. arXiv:cs/0701119.
[2] Petr R. Ivankov, Nikolay P. Ivankov. The virtual reality framework for
engineering objects. arXiv:cs/0612126.
[3] A new approach to magnetic angular momentum manage-
ment for large scientific satellites. Iida H. (1), Ninomya K.
http://cat.inist.fr/?aModele=afficheN&cpsidt=3049179
[4] Spin-stabilisation, Wikipedia http://en.wikipedia.org/wiki/Spin-stabilisation
[5] Elasticity (physics), Wikipedia http://en.wikipedia.org/wiki/Elasticity %28physics%29
[6] Finite field, Wikipedia http://en.wikipedia.org/wiki/Galois field
[7] Category theory, Wikipedia http://en.wikipedia.org/wiki/Category Theory
[8] Field (physics), Wikipedia http://en.wikipedia.org/wiki/Field %28physics%29