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Using an informal functional notation, Ackermann's function is defined as follows:
From the point of view of benchmarking, Ackermann's function is interesting because it consists almost entirely of subprogram calls, and nests the calls deeply if required. The number of calls and the degree of nesting is controlled using the two arguments.
We use A(3,6) as the benchmark. This gives us 172233 calls, with a nesting depth of 511.
Example A-3. Source Code for Ackermann's Function
function Ackermann (M, N : in Integer) return Integer is
begin
if M = 0 then
return N + 1;
elsif N = 0 then
return Ackermann (M - 1, 1);
else
return Ackermann (M - 1, Ackermann (M, N - 1));
end if;
end Ackermann;
Ackermann's function provides two opportunities for tail recursion optimization, both of which are taken here. The two parameters are passed in register, and the called procedure saves and restores registers using the register cache mechanism.
The generated code for the default optimization level is given in Example A-4.
Example A-4. Generated Code for Ackermann's Function
1 .file "ackermann.adb" 2 gcc2_compiled.: 3 __gnu_compiled_ada: 4 .text 5 .align 4 6 .global _ada_ackermann 7 .proc 04 8 _ada_ackermann: 9 0000 9DE3BF98 save %sp,-104,%sp 10 0004 A0100018 mov %i0,%l0 11 0008 80A38007 cmp %sp,%g7 12 000c 89D02009 tleu 9 13 .L5: 14 0010 80A42000 cmp %l0,0 15 0014 12800004 bne .L2 16 0018 80A66000 cmp %i1,0 17 001c 1080000C b .L6 18 0020 B0066001 add %i1,1,%i0 19 .L2: 20 0024 12800005 bne .L4 21 0028 90100010 mov %l0,%o0 22 002c A0043FFF add %l0,-1,%l0 23 0030 10BFFFF8 b .L5 24 0034 B2102001 mov 1,%i1 25 .L4: 26 0038 A0023FFF add %o0,-1,%l0 27 003c 7FFFFFF1 call _ada_ackermann,0 28 0040 92067FFF add %i1,-1,%o1 29 0044 10BFFFF3 b .L5 30 0048 B2100008 mov %o0,%i1 31 .L6: 32 004c 81C7E008 ret 33 0050 81E80000 restore