L12-Computing Factorial

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L12-Computing Factorial
ECE 2560

• Department of Electrical and
• Computer Engineering
• The Ohio State University

2
HLL to Assembler

• Pseudo HLL
• HLL structure
• Their flow chart
• HHL code
• Corresponding Assembler

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Computing n!

• What is n! ?
• 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 n1 then result is 1
• If ngt1 then the value is n(n-1)!
• And to compute (n-1)! the routine called again

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Pseudocode

• Factorial n!
• function nfact (var n) return z
• if (n1) then z 1
• else z n nfact(n-1)
• end if
• end nfact

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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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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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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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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 R5n-1
• push R5
• call fact compute n-1!

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On Recursive call

• The stack will look like this
• Now what happens when
• you start to return with
• values?

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Result - on the stack

• 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 R5n-1
• push R5
• call fact computer n-1!
• inc R5 R5 now n
• pop R6 n-1 fact to R6
• push R5
• push R6
• call shmult stack has null then result
• pop R7
• pop R7
• jmp cont

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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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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! 362880
• In a 16-bit value 8! Is the largest that can be
  computed.
• Could 32-bits be used?

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A look at the math

• The math