Demo or Die #02 31 июля 1999

Программирование

Demo-Building - Generator table of squares.

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   (C) ra! D


       Generator table of squares


   The operation of this generator is based on
very interesting dependence
Mathematically, it looks like this:


      k k-1

     X = X + Nk,


         k k-1

   where X and X - the squares of consecutive
numbers on this and previous iterations duschih;


   k-iteration number, respectively;

   Nk - the number of a number of positive odd
numbers;


   I think that is a small table,
help to understand this algorithm.


                     -

    X 1 2 3 4 ...

                     -

   X ^ 2 1 4 9 16 ...


    N 3 5 7

                     -


   Some comments on this
Example:


   1) This example creates a table
squares of numbers from 0 to 255;

   2) In the table, the squares of numbers
are top-down, ie first
is the square of 255, then the square 254 and so on
(This is due to specific structures
stack).

   The disadvantage of this is difficult to call, say
so it's just a side effect, which
very easily solved by a sufficiently
inverted number whose square
is like this:


             LD A, NUM,

             , Whose square

             ; To find.

             CPL

             LD BC, TABL

             LD H, 0

             LD L, A

             ADD HL, HL

             ADD HL, BC

             LD E, (HL)

             INC HL

             LD D, (HL)


   3) Do not forget at the end of the program
redirect the stack.

;*****************************************
; * GEN_TABL_X ^ 2 *
; * (C) 1999 idea and code by ra! D *
; * Code len: 16b *
;*****************************************


      LD SP, TABL +512

      LD HL, 1

      LD D, H

      LD E, L

      LD B, # FF
LP1 PUSH HL

      INC DE

      INC DE

      ADD HL, DE

      DJNZ LP1

      ; LD SP, nnnn

      ; RET

TABL DEFS 512


   P.S. Incidentally, I have not met any
a mathematical reference, description
this method.
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