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Recursive Karatsuba Pseudocode

Jul 4th, 2017
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  1. This is pseudocode for a space-optimized recursive implementation of the Karatsuba multiplication algorithm.
  2.  
  3. MUL(X,Y,N):
  4. ;X points to the first multiplicand of N digits
  5. ;Y points to the second multiplicand of N digits
  6. ;N is an integer power of 2
  7. ;Assumes yucky big endian
  8. X.loc = scrap-6+4N ;\
  9. Y.loc = X.loc+N ; |The location of the local X,Y, and Z vars
  10. Z.loc = Y.loc+N ; |M is the location of the results of sub multiplies
  11. M.loc = X.loc-N ;/
  12. IF N==1: ;\
  13. X*Y->Z[0:2] ; |Base Case
  14. RETURN ;/
  15. COPY(X,inputX,N) ;Copy the input X to the local X variable
  16. COPY(Y,inputY,N) ;Copy the input Y to the local Y variable
  17. MUL(X[N/2:N],Y[N/2:N],N/2) ;Multiply the bottom half of the digits of X and Y
  18. COPY(Z[N:2N],M,N) ;Copy the result of the previous multiply to the bottom half of Z
  19. MUL(X[0:N/2],Y[0:N/2],N/2) ;Multiply the top half of the digits of X and Y
  20. COPY(Z[0:N],M,N) ;Copy the result of the previous multiply to the top half of Z
  21. sign=0
  22. SUB(X[0:N/2],X[N/2:N],N/2) ;Subtract the bottom half of X from the top half, returning flags
  23. IF underflow
  24. NEG(X[0:N/2],N/2)
  25. sign=1
  26. SUB(Y[0:N/2],Y[N/2:N],N/2) ;Subtract the bottom half of Y from the top half, returning flags
  27. IF underflow
  28. NEG(Y[0:N/2],N/2)
  29. sign=~sign
  30. MUL(X[0:N/2],Y[0:N/2],N/2)
  31. SUB(M[0:N],Z[0:N],N)
  32. SUB(M[0:N],Z[N:2N],N)
  33. IF sign==1
  34. ADDir(Z[0:3N/2],M[0:N],N) ;ADD N digits, then continue as long as there is overflow
  35. RETURN
  36. ELSE
  37. SUBir(Z[0:3N/2],M[0:N]) ;SUB N digits, then continue as long as there is underflow
  38. RETURN
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