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Maths (Arithmetic): MULT1

[BBC Master version]

Name: MULT1 [Show more] Type: Subroutine Category: Maths (Arithmetic) Summary: Calculate (A P) = Q * A Deep dive: Shift-and-add multiplication
Context: See this subroutine in context in the source code Variations: See code variations for this subroutine in the different versions References: This subroutine is called as follows: * MAD calls MULT1 * MULT12 calls MULT1

Do the following multiplication of two 8-bit sign-magnitude numbers: (A P) = Q * A
.MULT1 TAX \ Store A in X AND #%01111111 \ Set P = |A| >> 1 LSR A \ and C flag = bit 0 of A STA P TXA \ Restore argument A EOR Q \ Set bit 7 of A and T if Q and A have different signs, AND #%10000000 \ clear bit 7 if they have the same signs, 0 all other STA T \ bits, i.e. T contains the sign bit of Q * A LDA Q \ Set A = |Q| AND #%01111111 BEQ mu10 \ If |Q| = 0 jump to mu10 (with A set to 0) TAX \ Set T1 = |Q| - 1 DEX \ STX T1 \ We subtract 1 as the C flag will be set when we want \ to do an addition in the loop below \ We are now going to work our way through the bits of \ P, and do a shift-add for any bits that are set, \ keeping the running total in A. We already set up \ the first shift at the start of this routine, as \ P = |A| >> 1 and C = bit 0 of A, so we now need to set \ up a loop to sift through the other 7 bits in P LDA #0 \ Set A = 0 so we can start building the answer in A TAX \ Copy A into X. There is a comment in the original \ source here that says "just in case", which refers to \ the MULT1 routine in the cassette and disc versions, \ which set X to 0 (as they use X as a loop counter). \ The version here doesn't use a loop, but this \ instruction makes sure the unrolled version returns \ the same results as the loop versions, just in case \ something out there relies on MULT1 returning X = 0 \.MUL4 \ These instructions are commented out in the original \ \ source. They contain the original loop version of the \BCC P%+4 \ code that's used in the disc and cassette versions \ADC T1 \ROR A \ROR P \DEX \BNE MUL4 \LSR A \ROR P \ORA T \RTS \ \.mu10 \STA P \RTS \ We now repeat the following four instruction block \ seven times, one for each remaining bit in P. In the \ cassette and disc versions of Elite the following is \ done with a loop, but it is marginally faster to \ unroll the loop and have seven copies of the code, \ though it does take up a bit more memory BCC P%+4 \ If C (i.e. the next bit from P) is set, do the ADC T1 \ addition for this bit of P: \ \ A = A + T1 + C \ = A + |Q| - 1 + 1 \ = A + |Q| ROR A \ As mentioned above, this ROR shifts A right and \ catches bit 0 in C - giving another digit for our \ result - and the next ROR sticks that bit into the \ left end of P while also extracting the next bit of P \ for the next addition ROR P \ Add the overspill from shifting A to the right onto \ the start of P, and shift P right to fetch the next \ bit for the calculation BCC P%+4 \ Repeat for the second time ADC T1 ROR A ROR P BCC P%+4 \ Repeat for the third time ADC T1 ROR A ROR P BCC P%+4 \ Repeat for the fourth time ADC T1 ROR A ROR P BCC P%+4 \ Repeat for the fifth time ADC T1 ROR A ROR P BCC P%+4 \ Repeat for the sixth time ADC T1 ROR A ROR P BCC P%+4 \ Repeat for the seventh time ADC T1 ROR A ROR P LSR A \ Rotate (A P) once more to get the final result, as ROR P \ we only pushed 7 bits through the above process ORA T \ Set the sign bit of the result that we stored in T RTS \ Return from the subroutine .mu10 STA P \ If we get here, the result is 0 and A = 0, so set \ P = 0 so (A P) = 0 RTS \ Return from the subroutine