Scalar Optimizations
J. (Ram) Ramanujam
Slides adapted from Aiken (2006), Bodik (2001)
Brief Comment
"Optimization" isn't!
We can do optimization on functions &
variables, game-theory scenarios, graph
theory problems, . but not programs!
What would an
FOURIER-MOTZKIN ELIMINATION
Elimination of variables for solving linear inequalities
Solve:
2x1
11x2
3
3 x1
+
2 x2
5
x1
+
3 x2
4
3
2x1
Let us eliminate variable x2 .
Rearrange the set of inequalities into 3 groups
3 x1
2 x2
5
x1
Group 1:
+
+
3 x2
4
Grou
Dependences in loop nests
Loops of the form:
for i1 = L1 to U1 do
for i2 = L2 to U2 do
.
for in = Ln to Un do
BODY(i1, i2, , in)
endfor
.
endfor
endfor
Lj and Uj are afne functions of i1, i2, , ij1
There is a dependence in a loop nest if there are iterati
INTRODUCTION
DEPENDENCE DEFINITIONS
J. (RAM) RAMANUJAM
LOUISIANA STATE UNIVERSITY
J. (Ram) Ramanujam
Overview
Programming multicore architectures (parallel computers)
Main steps in compiling for parallel computers
High performance systems and programmi