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Jan 21st, 2017
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  1. function f( n : Z ) : Z
  2. precondition n > 0
  3. var x : Z
  4. y : Z
  5. u : Z
  6. v : Z
  7. r : Z
  8. begin
  9. x:=1
  10. {n>0 /\ x=1}
  11. y:=1
  12. {n>0 /\ x=1 /\ y=1}
  13. r:=0
  14. {n>0 /\ x=1 /\ y=1 /\ r=0}
  15. while r<>n do
  16. invariant r =
  17. { }
  18. begin
  19. if r<n then
  20. { n>0 /\ x>=1 /\ y>=1 /\ r >=0 /\ x mod 2 = 1 /\ y mod 2 = /\ r > x-1)}
  21. begin
  22. r:=r+x
  23. { }
  24. x:=x+2
  25. end
  26. else
  27. begin
  28. r:=r-y
  29. { }
  30. y:=y+2
  31. end
  32. end
  33. { }
  34. { }
  35. u:=(x-y) / 2
  36. { }
  37. v:=((x+y)/ 2)-1
  38. { }
  39. { }
  40. f := n
  41. end
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