1. L12-Computing Factorial
ECE 2560
L12-Computing Factorial
Department of Electrical and
Computer Engineering
The Ohio State University
ECE Lecture 1

2. HLL to Assembler Pseudo HLL HLL structure Their flow chart HHL code
Corresponding Assembler
ECE Lecture 1

3. Computing n! What is n! ? This can be done recursively
n factorial is n*(n-1)*(n-2)*…(1)
n! = n*(n-1)!
This can be done recursively
Have a subroutine to compute n!
In the computation is n=1 then result is 1
If n>1 then the value is n*(n-1)!
And to compute (n-1)! the routine called again
ECE Lecture 1

4. Pseudocode Factorial – n! function nfact (var n) return z;
if (n=1) then z = 1;
else z = n * nfact(n-1);
end if;
end nfact;
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5. Features of recursive routines
Can have no local data that could be modified in the recursive call
Data needs to be on the stack
Any register used must be restored before the routine returns.
Because there is no local data and no absolute addresses the routine is also “position independent”
Position independent – code that can be run in any location in memory.
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6. Factorial - recursion Arguments will be passed on the stack.
The number n to find n! of is pushed on TOS
Result is returned on the stack.
The value of n! is returned on the TOS
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7. The routine
N is passed on the stack so the stack looks like this when entering routine
So start by saving the state of the processor
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8. The code fact push SR ;save state push R5 push R6 push R7
mov 10(SP),R5 ;get n
cmp #1,R5
jeq rtnval
dec R5 ;R5=n-1
call fact ;compute n-1!
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9. On Recursive call The stack will look like this Now what happens when
you start to return with
values?
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10. Result - on the stack Point size is very small – look at it in word
Result is on the stack and at the top of the stack.
fact push SR ;save state
push R5
push R6
push R7
mov 10(SP),R5 ;get n
cmp #1,R5
jjeq rtnval
dec R5 ;R5=n-1
call fact ;computer n-1!
inc R5 ;R5 now n
pop R6 ;n-1 fact to R6
push R6
call shmult ;stack has null then result
pop R7
jmp cont
rtnval mov #1,R7
cont mov R7,10(SP) ;put value of n! in rtn location
pop R7 ;clean up things
pop R6
pop R5
pop SR
ret
Point size is very small – look at it in word
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11. Performance of code
Code is an extensive use of stack and implementation of good coding practices.
Passing arguments on stack
Routines have no side effects
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12. Extending to 32 bit result
Factorial when result limited to 16 bits does not allow for much range for factorial.
1! = 1
2! = 2
3! = 6
4! = 24
5! = 120
6! = 720
7! = 5040
8! = 40320
9! =
In a 16-bit value 8! Is the largest that can be computed.
Could 32-bits be used?
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13. A look at the math
The math
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