Editing Strength reduction (section)

=== Outer loop ===

Back to the whole picture:

<syntaxhighlight lang="nasm">
0010  ; for (i = 0, i < n; i++)
0020    {
0030      r1 = #0                        ; i = 0
0050      load r2, n
0220      fr3 = #0.0
0340      fr4 = #1.0
0040  G0000:
0060      cmp r1, r2                     ; i < n
0070      bge G0001
0080
0190      r8   = r1 * r2                 ; calculate subscript i * n
0117      r20  = r8 + r2                 ; limit
0118      r10  = r8 * #8                 ; initial value of r10
0119      r22  = r20 * #8                ; new limit
0090      ; for (j = 0; j < n; j++)
0100        {
0120  G0002:
0147           cmp r10, r22              ; r10 = 8*(r8 + j) < 8*(r8 + n) = r22
0150           bge G0003
0160
0170           ; A[i,j] = 0.0;
0230           fstore fr3, A[r10]
0240
0245           r10 = r10 + #8            ; strength reduced multiply
0260           br G0002
0270        }
0280  G0003:
0290      ; A[i,i] = 1.0;
0320      r14 = r8  + r1                 ; calculate subscript i * n + i
0330      r15 = r14 * #8                 ; calculate byte address
0350      fstore fr4, A[r15]
0360
0370      ;i++
0380      r1 = r1 + #1
0390      br G0000
0400    }
0410  G0001:
</syntaxhighlight>

There are now four multiplications within the outer loop that increments r1. Register r8 = r1*r2 at 0190 can be strength reduced by setting it before entering the loop (0055) and incrementing it by r2 at the bottom of the loop (0385).

The value r8*8 (at 0118) can be strength reduced by initializing it (0056) and adding 8*r2 to it when r8 gets incremented (0386).

Register r20 is being incremented by the invariant/constant r2 each time through the loop at 0117. After being incremented, it is multiplied by 8 to create r22 at 0119. That multiplication can be strength reduced by adding 8*r2 each time through the loop.

<syntaxhighlight lang="nasm">
0010  ; for (i = 0, i < n; i++)
0020    {
0030      r1 = #0                        ; i = 0
0050      load r2, n
0220      fr3 = #0.0
0340      fr4 = #1.0
0055      r8  = r1 * r2                  ; set initial value for r8
0056      r40 = r8 * #8                  ; initial value for r8 * 8
0057      r30 = r2 * #8                  ; increment for r40
0058      r20 = r8 + r2                  ; copied from 0117
0058      r22 = r20 * #8                 ; initial value of r22
0040  G0000:
0060      cmp r1, r2                     ; i < n
0070      bge G0001
0080
0190  ;  r8   = r1 * r2    killed        ; calculate subscript i * n
0117  ;  r20  = r8 + r2    killed - dead code
0118      r10  = r40                     ; strength reduced expression to r40
0119  ;  r22  = r20 * #8   killed        ; strength reduced
0090      ; for (j = 0; j < n; j++)
0100        {
0120  G0002:
0147           cmp r10, r22              ; r10 = 8*(r8 + j) < 8*(r8 + n) = r22
0150           bge G0003
0160
0170           ; A[i,j] = 0.0;
0230           fstore fr3, A[r10]
0240
0245           r10 = r10 + #8            ; strength reduced multiply
0260           br G0002
0270        }
0280  G0003:
0290      ; A[i,i] = 1.0;
0320      r14 = r8  + r1                 ; calculate subscript i * n + i
0330      r15 = r14 * #8                 ; calculate byte address
0350      fstore fr4, A[r15]
0360
0370      ;i++
0380      r1  = r1 + #1
0385      r8  = r8 + r2                  ; strength reduce r8 = r1 * r2
0386      r40 = r40 + r30                ; strength reduce expression r8 * 8
0388      r22 = r22 + r30                ; strength reduce r22 = r20 * 8
0390      br G0000
0400    }
0410  G0001:
</syntaxhighlight>