Maths (Arithmetic): FMLTU

       Name: FMLTU                                                   [Show more]
       Type: Subroutine
   Category: Maths (Arithmetic)
    Summary: Calculate A = A * Q / 256
  Deep dive: Multiplication and division using logarithms
    Context: See this subroutine in context in the source code
 References: This subroutine is called as follows:
             * DOEXP calls FMLTU
             * LL51 calls FMLTU
             * LL9 (Part 5 of 12) calls FMLTU
             * MVEIT (Part 3 of 9) calls FMLTU
             * PLS22 calls FMLTU


 Do the following multiplication of two unsigned 8-bit numbers, returning only
 the high byte of the result:

   (A ?) = A * Q

 or, to put it another way:

   A = A * Q / 256

 The advanced versions of Elite use logarithms to speed up the multiplication
 process. See the deep dive on "Multiplication using logarithms" for more
 details.


 Returns:

   C flag               The C flag is clear if A = 0, or set if we return a
                        result from one of the log tables


.FMLTU

 STX P                  ; Store X in P so we can preserve it through the call to
                        ; FMULTU

 STA widget             ; Store A in widget, so now widget = argument A

 TAX                    ; Transfer A into X, so now X = argument A

 BEQ MU3                ; If A = 0, jump to MU3 to return a result of 0, as
                        ; 0 * Q / 256 is always 0

                        ; We now want to calculate La + Lq, first adding the low
                        ; bytes (from the logL table), and then the high bytes
                        ; (from the log table)

 LDA logL,X             ; Set A = low byte of La
                        ;       = low byte of La (as we set X to A above)

 LDX Q                  ; Set X = Q

 BEQ MU3again           ; If X = 0, jump to MU3again to return a result of 0, as
                        ; A * 0 / 256 is always 0

 CLC                    ; Set A = A + low byte of Lq
 ADC logL,X             ;       = low byte of La + low byte of Lq

 BMI oddlog             ; If A > 127, jump to oddlog

 LDA log,X              ; Set A = high byte of Lq

 LDX widget             ; Set A = A + C + high byte of La
 ADC log,X              ;       = high byte of Lq + high byte of La + C
                        ;
                        ; so we now have:
                        ;
                        ;   A = high byte of (La + Lq)

 BCC MU3again           ; If the addition fitted into one byte and didn't carry,
                        ; then La + Lq < 256, so we jump to MU3again to return a
                        ; result of 0 and the C flag clear

                        ; If we get here then the C flag is set, ready for when
                        ; we return from the subroutine below

 TAX                    ; Otherwise La + Lq >= 256, so we return the A-th entry
 LDA antilog,X          ; from the antilog table

 LDX P                  ; Restore X from P so it is preserved

 RTS                    ; Return from the subroutine

.oddlog

 LDA log,X              ; Set A = high byte of Lq

 LDX widget             ; Set A = A + C + high byte of La
 ADC log,X              ;       = high byte of Lq + high byte of La + C
                        ;
                        ; so we now have:
                        ;
                        ;   A = high byte of (La + Lq)

 BCC MU3again           ; If the addition fitted into one byte and didn't carry,
                        ; then La + Lq < 256, so we jump to MU3again to return a
                        ; result of 0 and the C flag clear

                        ; If we get here then the C flag is set, ready for when
                        ; we return from the subroutine below

 TAX                    ; Otherwise La + Lq >= 256, so we return the A-th entry
 LDA antilogODD,X       ; from the antilogODD table

.MU3

                        ; If we get here then A (our result) is already 0

 LDX P                  ; Restore X from P so it is preserved

 RTS                    ; Return from the subroutine

.MU3again

 LDA #0                 ; Set A = 0

 LDX P                  ; Restore X from P so it is preserved

 RTS                    ; Return from the subroutine