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Maths (Arithmetic): TIS2

[BBC Micro disc version, Flight]

Name: TIS2 [Show more] Type: Subroutine Category: Maths (Arithmetic) Summary: Calculate A = A / Q Deep dive: Shift-and-subtract division
Context: See this subroutine in context in the source code References: This subroutine is called as follows: * NORM calls TIS2

Calculate the following division, where A is a sign-magnitude number and Q is a positive integer: A = A / Q The value of A is returned as a sign-magnitude number with 96 representing 1, and the maximum value returned is 1 (i.e. 96). This routine is used when normalising vectors, where we represent fractions using integers, so this gives us an approximation to two decimal places.
.TIS2 TAY \ Store the argument A in Y AND #%01111111 \ Strip the sign bit from the argument, so A = |A| CMP Q \ If A >= Q then jump to TI4 to return a 1 with the BCS TI4 \ correct sign LDX #%11111110 \ Set T to have bits 1-7 set, so we can rotate through 7 STX T \ loop iterations, getting a 1 each time, and then \ getting a 0 on the 8th iteration... and we can also \ use T to catch our result bits into bit 0 each time .TIL2 ASL A \ Shift A to the left CMP Q \ If A < Q skip the following subtraction BCC P%+4 SBC Q \ A >= Q, so set A = A - Q \ \ Going into this subtraction we know the C flag is \ set as we passed through the BCC above, and we also \ know that A >= Q, so the C flag will still be set once \ we are done ROL T \ Rotate the counter in T to the left, and catch the \ result bit into bit 0 (which will be a 0 if we didn't \ do the subtraction, or 1 if we did) BCS TIL2 \ If we still have set bits in T, loop back to TIL2 to \ do the next iteration of 7 \ We've done the division and now have a result in the \ range 0-255 here, which we need to reduce to the range \ 0-96. We can do that by multiplying the result by 3/8, \ as 256 * 3/8 = 96 LDA T \ Set T = T / 4 LSR A LSR A STA T LSR A \ Set T = T / 8 + T / 4 ADC T \ = 3T / 8 STA T TYA \ Fetch the sign bit of the original argument A AND #%10000000 ORA T \ Apply the sign bit to T RTS \ Return from the subroutine .TI4 TYA \ Fetch the sign bit of the original argument A AND #%10000000 ORA #96 \ Apply the sign bit to 96 (which represents 1) RTS \ Return from the subroutine