Maths (Arithmetic): LL5

       Name: LL5                                                     [Show more]
       Type: Subroutine
   Category: Maths (Arithmetic)
    Summary: Calculate Q = SQRT(R Q)
  Deep dive: Calculating square roots
    Context: See this subroutine in context in the source code
 References: This subroutine is called as follows:
             * Main flight loop (Part 15 of 16) calls LL5
             * NORM calls LL5
             * SUN (Part 3 of 4) calls LL5
             * TT111 calls LL5


 Calculate the following square root:

   Q = SQRT(R Q)


.LL5

 LDY R                  ; Set (Y S) = (R Q)
 LDA Q
 STA S

                        ; So now to calculate Q = SQRT(Y S)

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

 STX Q                  ; Set Q = 0, to hold the result

 LDA #8                 ; Set T = 8, to use as a loop counter
 STA T

.LL6

 CPX Q                  ; If X < Q, jump to LL7
 BCC LL7

 BNE P%+6               ; If X > Q, skip the next two instructions

 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

 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 - Q
 SBC Q
 TAX

.LL7

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

 ASL S                  ; 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 S                  ; 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 T                  ; Decrement the loop counter

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

 RTS                    ; Return from the subroutine