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Calculator Example

The following is a lic script file that generates the code templates to perform a matrix transpose on a 2D blocked matrix. The matrix size is U1xU2 and the block size is B1xB2. Before executing the script file, variables U1, U2, B1 and B2 should be set to the appropriate integer values. This script file is available in the examples/lic directory in the SUIF distribution.

// Need to set U1, U2, B1 and B2 to appropriate integer values before
// calling this script file.
// Size of the matrix = U1xU2
// Size of the blocks that is assigned to each processor = B1xB2

//  The column assignments
//          p1  p2  p1x p2x i1  i2  b1  b2  a1  a2
//           1   2   3   4   5   6   7   8   9  10

// iteration space
// 1 <= i1 <= U1 and 1 <= i2 <= U2 
# iter = { !1 <= @5 <= U1!
           !1 <= @6 <= U1!}

// Data decompositions of array A
// B1*p1 <= a1-1 < B1 + B1*p1 and B2*p2 <= a2-1 < B2 + B2*p2
# dda  = { !B1@1 <=  @9  - 1 < B1 + B1@1!
           !B2@2 <=  @10 - 1 < B2 + B2@2! }

// Data decompositions of array B
// B1*p1 <= b1-1 < B1 + B1*p1 and B2*p2 <= b2-1 < B2 + B2*p2
# ddb  = { !B1@3 <=  @7 - 1 < B1 + B1@3!
           !B2@4 <=  @8 - 1 < B2 + B2@4! }

// Left hand side A[i1][i2] = ...
// i1 = a1 and i2 = a2
# lhs  = { !@5 = @9!
           !@6 = @10! }

// Right hand side  ... = B[i2][i1]
// i2 = b1 and i1 = b2
# rhs  = { !@6 = @7!
           !@5 = @8! }

# res  = { iter
           dda
           ddb
           lhs
           rhs }

// No communication
# prc  = { res 
           !@1 = @3!
           !@2 = @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)

// Communication
# prc  = { res 
           !@1 > @3! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)

# prc  = { res 
           !@1 < @3! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)

# prc  = { res 
           !@1 = @3!
           !@2 > @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)

# prc  = { res 
           !@1 = @3!
           !@2 < @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)

end

The results of running this example for a 1000x1000 matrix with square blocks of 32 in lic is:

csh> lic
 > U1 = 1000
1000
 > U2 = 1000
1000
 > B1 = 32
32
 > B2 = 32
32
 > < tst1
# iter = { !1 <= @5 <= U1!
           !1 <= @6 <= U1!}

# dda  = { !B1@1 <=  @9  - 1 < B1 + B1@1!
           !B2@2 <=  @10 - 1 < B2 + B2@2! }

# ddb  = { !B1@3 <=  @7 - 1 < B1 + B1@3!
           !B2@4 <=  @8 - 1 < B2 + B2@4! }

# lhs  = { !@5 = @9!
           !@6 = @10! }

# rhs  = { !@6 = @7!
           !@5 = @8! }

# res  = { iter
           dda
           ddb
           lhs
           rhs }

# prc  = { res
           !@1 = @3!
           !@2 = @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)
if((proc1 >= 0)&&(proc1 <= 31))
   if(proc2 == proc1);
      p1x = proc1;
      p2x = proc1;
      for(i1 = 1+32*proc1; i1 <= MIN( 32+32*proc1, 1000); i1++)
         for(i2 = 1+32*proc1; i2 <= MIN( 32+32*proc1, 1000); i2++)
            b1 = i2;
            b2 = i1;
            a1 = i1;
            a2 = i2;

# prc  = { res
           !@1 > @3! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)
if((proc1 >= 1)&&(proc1 <= 31))
   if((proc2 >= 0)&&(proc2 <= -1+proc1))
      p1x = proc2;
      p2x = proc1;
      for(i1 = 1+32*proc1; i1 <= MIN( 32+32*proc1, 1000); i1++)
         for(i2 = 1+32*proc2; i2 <= 32+32*proc2; i2++)
            b1 = i2;
            b2 = i1;
            a1 = i1;
            a2 = i2;

# prc  = { res
           !@1 < @3! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)
if((proc1 >= 0)&&(proc1 <= 30))
   if((proc2 >= 1+proc1)&&(proc2 <= 31))
      p1x = proc2;
      p2x = proc1;
      for(i1 = 1+32*proc1; i1 <= 32+32*proc1; i1++)
         for(i2 = 1+32*proc2; i2 <= MIN( 32+32*proc2, 1000); i2++)
            b1 = i2;
            b2 = i1;
            a1 = i1;
            a2 = i2;

# prc  = { res
           !@1 = @3!
           !@2 > @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)
cannot create code

# prc  = { res
           !@1 = @3!
           !@2 < @4! }
prc.code(proc1  proc2  p1x p2x i1  i2  b1  b2  a1  a2)
cannot create code

end
 > quit
csh>

When the blocks are not square but rectangles, the above script file will generate the necessary code which is much more complicated. For example, try using the following parameters.

U1 = 1000
U2 = 1000
B1 = 32
B2 = 80

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