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⌂ ∞ ▽ Elite on the BBC Micro and NES

Maths (Arithmetic): ROOT

[6502 Second Processor version, Loader 1]

       Name: ROOT                                                    [Show more]
       Type: Subroutine
   Category: Maths (Arithmetic)
    Summary: Calculate ZP = SQRT(ZP(1 0))

    Context: See this subroutine in context in the source code
 References: This subroutine is called as follows:
             * PLL1 (Part 1 of 3) calls ROOT




 Calculate the following square root:

   ZP = SQRT(ZP(1 0))

 This routine is identical to LL5 in the main game code - it even has the same
 label names. The only difference is that LL5 calculates Q = SQRT(R Q), but
 apart from the variables used, the instructions are identical, so see the LL5
 routine in the main game code for more details on the algorithm used here.



.ROOT

 LDY ZP+1               \ Set (Y Q) = ZP(1 0)
 LDA ZP
 STA Q

                        \ So now to calculate ZP = SQRT(Y Q)

 LDX #0                 \ Set X = 0, to hold the remainder

 STX ZP                 \ Set ZP = 0, to hold the result

 LDA #8                 \ Set P = 8, to use as a loop counter
 STA P

.LL6

 CPX ZP                 \ If X < ZP, jump to LL7
 BCC LL7

 BNE LL8                \ If X > ZP, jump to LL8

 CPY #64                \ If Y < 64, jump to LL7 with the C flag clear,
 BCC LL7                \ otherwise fall through into LL8 with the C flag set

.LL8

 TYA                    \ Set Y = Y - 64
 SBC #64                \
 TAY                    \ This subtraction will work as we know C is set from
                        \ the BCC above, and the result will not underflow as we
                        \ already checked that Y >= 64, so the C flag is also
                        \ set for the next subtraction

 TXA                    \ Set X = X - ZP
 SBC ZP
 TAX

.LL7

 ROL ZP                 \ Shift the result in Q to the left, shifting the C flag
                        \ into bit 0 and bit 7 into the C flag

 ASL Q                  \ Shift the dividend in (Y S) to the left, inserting
 TYA                    \ bit 7 from above into bit 0
 ROL A
 TAY

 TXA                    \ Shift the remainder in X to the left
 ROL A
 TAX

 ASL Q                  \ Shift the dividend in (Y S) to the left
 TYA
 ROL A
 TAY

 TXA                    \ Shift the remainder in X to the left
 ROL A
 TAX

 DEC P                  \ Decrement the loop counter

 BNE LL6                \ Loop back to LL6 until we have done 8 loops

 RTS                    \ Return from the subroutine