9.1.2 Memory Management Tactics

One way KAP enhances performance on cache-memory machines is to use a combination of loop blocking, loop interchanging, and loop unrolling to optimize the cache hit ratios of operands in loops. Memory management in KAP is enabled when /scalaropt=3 and /roundoff=3 have been specified. These are the default settings for these qualifiers.

When arrays are being processed in loops, KAP improves memory access patterns by restructuring the code to work on small sections of the arrays that fit in the cache and thereby giving large cache hit ratios. The sizes of these sections are controlled by using the memory management command qualifiers /cacheline , /cachesize , /fpregisters , /dpregisters , and /setassociativity .

The default settings for these are the standard machine characteristics for which the code is being targeted. These default settings will give the best results for most programs. For some special cases, you may want to modify these settings to adjust the sizes of the array sections that are meant to reside in the cache. The algorithm that KAP uses keeps square blocks of data in the cache.

The following matrix multiplication example shows how loop interchanging, loop blocking, scalar temporary variables, and strip mining can be used. Because these techniques introduce some additional overhead, they are not used with small, simple loops.

DIMENSION A2(N,N),B2(N,N),C2(N,N),D2(N,N)

  DO I = 1, N
    DO J = 1, N
      DO K = 1, N
             C2(I,J) = C2(I,J) + A2(I,K) * B2(K,J)
      ENDDO
    ENDDO
 ENDDO

Becomes:

DIMENSION A2(N,N), B2(N,N), C2(N,N), D2(N,N)
INTEGER II1, II2, II3, II4, II7, II8, II9, II10, II13, II14, II15
X, II16, II19, II20, II21, II22, II23, II24, II25, II26, II27,
X    II28
REAL RR1, RR2, RR3, RR4, RR5, RR6, RR7, RR8, RR9, RR10, RR11,
X    RR12, RR13, RR14, RR15, RR16, RR17, RR18, RR19
  II3 = 1
  II1 = MOD (N - 1, 21) + 1
  II2 = II1
  II7 = MOD (N - 1, 21) + 1
  II13 = MOD (N - 1, 21) + 1
    DO 12 II4=1,N,21
     II9 = 1
     II8 = II7
     II27 = II3 + II2 - 3
     II28 = II3 + II2 - 1
     DO  II10=1,N,21
         II15 = 1
         II14 = II13
          II19 = II9 + II8 - 1
          II20 = II9 + II8 - 1
          II24 = II9 + II8 - 1
          II23 = II9 + II8 - 1
          DO 10 II16=1,N,21
          II21 = II15 + II14 - 3
          II22 = II15 + II14 -1
                   DO 5 J=II3,II27,3

              DO 3 I=II15,II21,3
                RR1 = C2(I,J)
                RR2 = C2(I+1,J)
                RR3 = C2(I,J+1)
                RR4 = C2(I+1,J+1)
                RR5 = C2(I,J+2)
                RR6 = C2(I+1,J+2)
                RR7 = C2(I+2,J)
                RR8 = C2(I+2,J+1)
                RR9 = C2(I+2,J+2)
                    DO 2 K=II9,II19,1
                    RR17 = A2(I,K) * B2(K,J)
                    RR1 = RR1 + RR17
                   RR17 = A2(I+1,K) * B2(K,J)
                   RR2 = RR2 + RR17
                   RR17 = A2(I,K) * B2(K,J+1)
                   RR3 = RR3 + RR17
                   RR17 = A2(I+1,K) * B2(K,J+1)
                   RR4 = RR4 + RR17
                   RR17 = A2(I,K) * B2(K,J+2)
                   RR5 = RR5 + RR17
                    RR17 = A2(I+1,K) * B2(K,J+2)
                   RR6 = RR6 + RR17
                   RR17 = A2(I+2,K) * B2(K,J)
                   RR7 = RR7 + RR17
                  RR17 = A2(I+2,K) * B2(K,J+1)
                  RR8 = RR8 + RR17
                  RR17 = A2(I+2,K) * B2(K,J+2)
                  RR9 = RR9 + RR17
         2   CONTINUE
               C2(I,J) = RR1
               C2(I+1,J) = RR2
                C2(I,J+1) = RR3
                 C2(I+1,J+1) = RR4
                 C2(I,J+2) = RR5
                 C2(I+1,J+2) = RR6
                 C2(I+2,J) = RR7
                 C2(I+2,J+1) = RR8
                 C2(I+2,J+2) = RR9
             3   CONTINUE
                  DO 5 I=I,II22,1
                    RR10 = C2(I,J)
                    RR11 = C2(I,J+1)
                    RR12 = C2(I,J+2)
                     DO 4 K=II9,II20,1
                     RR18 = A2(I,K) * B2(K,J)
                     RR10 = RR10 + RR18
                     RR18 = A2(I,K) * B2(K,J+1)
                     RR11 = RR11 + RR18
                     RR18 = A2(I,K) * B2(K,J+2)
                    RR12 = RR12 + RR18
             4   CONTINUE
                   C2(I,J) = RR10
                     C2(I,J+1) = RR11
                  C2(I,J+2) = RR12
              5  CONTINUE
                  II25 = II15 + II14 - 3
                  II26 = II15 + II14 - 1
                    DO 9 J=J,II28,1
                        DO 7 I=II15,II25,3
                     RR13 = C2(I,J)
                    RR14 = C2(I+1,J)
                   RR15 = C2(I+2,J)
                     DO 6 K=II9,II23,1
                      RR19 = A2(I,K) * B2(K,J)
                      RR13 = RR13 + RR19
                      RR19 = A2(I+1,K) * B2(K,J)
                      RR14 = RR14 + RR19
                       RR19 = A2(I+2,K) * B2(K,J)
                     RR15 = RR15 + RR19
              6  CONTINUE
                    C2(I,J) = RR13
                    C2(I+1,J) = RR14
                    C2(I+2,J) = RR15
                 7 CONTINUE

                     DO 9 I=I,II26,1
                     RR16 = C2(I,J)
                      DO 8 K=II9,II24,1
                       RR16 = RR16 + A2(I,K) * B2(K,J)
            8  CONTINUE
                C2(I,J) = RR16
                  9  CONTINUE
                    II15 = II15 + II14
                    II14 = 21
            10  CONTINUE
                II9 = II9 + II8
                II8 = 21
               11  CONTINUE
                  II3 = II3 + II2
                    II2 = 21
        12  CONTINUE


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