Elite on the BBC Micro and NES

# Version analysis of LOIN (Part 2 of 7)

This code appears in the following versions (click to see it in the source code):

Code variations between these versions are shown below.

```       Name: LOIN (Part 2 of 7)
Type: Subroutine
Category: Drawing lines
Summary: Draw a line: Line has a shallow gradient, step right along x-axis
Deep dive: Bresenham's line algorithm

This routine draws a line from (X1, Y1) to (X2, Y2). It has multiple stages.
If we get here, then:

* |delta_y| < |delta_x|

* The line is closer to being horizontal than vertical

* We are going to step right along the x-axis

* We potentially swap coordinates to make sure X1 < X2

.STPX

LDX X1                 \ Set X = X1

CPX X2                 \ If X1 < X2, jump down to LI3, as the coordinates are
BCC LI3                \ already in the order that we want

DEC SWAP               \ Otherwise decrement SWAP from 0 to &FF, to denote that
\ we are swapping the coordinates around

LDA X2                 \ Swap the values of X1 and X2
STA X1
STX X2

TAX                    \ Set X = X1

LDA Y2                 \ Swap the values of Y1 and Y2
LDY Y1
STA Y1
STY Y2

.LI3

\ By this point we know the line is horizontal-ish and
\ X1 < X2, so we're going from left to right as we go
\ from X1 to X2

```

Code variation 1 of 9Related to the screen mode

Tap on a block to expand it, and tap it again to revert.

```Cassette, Flight, Docked6502SP, MasterElectron LDA Y1                 \ Set A = Y1 / 8, so A now contains the character row
LSR A                  \ that will contain our horizontal line
LSR A
LSR A

ORA #&60               \ As A < 32, this effectively adds &60 to A, which gives
\ us the screen address of the character row (as each
\ character row takes up 256 bytes, and the first
\ character row is at screen address &6000, or page &60)

STA SCH                \ Store the page number of the character row in SCH, so
\ the high byte of SC is set correctly for drawing the
\ start of our line
LDY Y1                 \ Look up the page number of the character row that
LDA ylookup,Y          \ contains the pixel with the y-coordinate in Y1, and
STA SC+1               \ store it in SC+1, so the high byte of SC is set
\ correctly for drawing our line
\ We now calculate the address of the character block
\ containing the pixel (X1, Y1) and put it in SC(1 0),
\ as follows:
\
\   SC = &5800 + (Y1 div 8 * 256) + (Y1 div 8 * 64) + 32
\
\ See the deep dive on "Drawing pixels in the Electron
\ version" for details

LDA Y1                 \ Set A = Y1 / 8, so A now contains the character row
LSR A                  \ that will contain our horizontal line
LSR A
LSR A

STA SC+1               \ Set SC+1 = A, so (SC+1 0) = A * 256
\                           = char row * 256

LSR A                  \ Set (A SC) = (A SC) / 4
ROR SC                 \            = (4 * ((char row * 64) + 32)) / 4
LSR A                  \            = char row * 64 + 32
ROR SC

ADC SC+1               \ Set SC(1 0) = (A SC) + (SC+1 0) + &5800
ADC #&58               \             = (char row * 64 + 32)
STA SC+1               \               + char row * 256
\               + &5800
\
\ which is what we want, so SC(1 0) contains the address
\ of the first visible pixel on the character row
\ containing the point (X1, Y1)

TXA                    \ Each character block contains 8 pixel rows, so to get
AND #%11111000         \ the address of the first byte in the character block
\ that we need to draw into, as an offset from the start
\ of the row, we clear bits 0-2

ADC SC                 \ And add the result to SC(1 0) to get the character
STA SC                 \ block on the row we want

BCC P%+4               \ If the addition of the low bytes overflowed, increment
INC SC+1               \ the high byte

\ So SC(1 0) now contains the address of the first pixel
\ in the character block containing the (X1, Y1), taking
\ the screen borders into consideration
```
``` LDA Y1                 \ Set Y = Y1 mod 8, which is the pixel row within the
AND #7                 \ character block at which we want to draw the start of
TAY                    \ our line (as each character block has 8 rows)

```

Code variation 2 of 9Related to the screen mode

This variation is blank in the Electron version.

Tap on a block to expand it, and tap it again to revert.

```Cassette, Flight, Docked6502SP, Master TXA                    \ Set A = bits 3-7 of X1
AND #%11111000
TXA                    \ Set A = 2 * bits 2-6 of X1
AND #%11111100         \
ASL A                  \ and shift bit 7 of X1 into the C flag
```

Code variation 3 of 9Related to the screen mode

This variation is blank in the Electron version.

```Cassette, Flight, Docked, 6502SP, Master STA SC                 \ Store this value in SC, so SC(1 0) now contains the
\ screen address of the far left end (x-coordinate = 0)
\ of the horizontal pixel row that we want to draw the
\ start of our line on
```

Code variation 4 of 9Related to the screen mode

Tap on a block to expand it, and tap it again to revert.

```Cassette, Flight, Docked, Electron6502SP, Master TXA                    \ Set X = X1 mod 8, which is the horizontal pixel number
AND #7                 \ within the character block where the line starts (as
TAX                    \ each pixel line in the character block is 8 pixels
\ wide)

LDA TWOS,X             \ Fetch a 1-pixel byte from TWOS where pixel X is set,
STA R                  \ and store it in R
BCC P%+4               \ If bit 7 of X1 was set, so X1 > 127, increment the
INC SC+1               \ high byte of SC(1 0) to point to the second page on
\ of the row

TXA                    \ Set R = X1 mod 4, which is the horizontal pixel number
AND #3                 \ within the character block where the line starts (as
STA R                  \ each pixel line in the character block is 4 pixels
\ wide)
```

Code variation 5 of 9Other (e.g. bug fix, optimisation)

Part 2 of the LOIN routine in the advanced versions uses logarithms to speed up the multiplication.

Tap on a block to expand it, and tap it again to revert.

```Cassette, Flight, Docked, Electron6502SP, Master                        \ The following calculates:
\
\   Q = Q / P
\     = |delta_y| / |delta_x|
\
\ using the same shift-and-subtract algorithm that's
\ documented in TIS2

LDA Q                  \ Set A = |delta_y|

LDX #%11111110         \ Set Q to have bits 1-7 set, so we can rotate through 7
STX Q                  \ loop iterations, getting a 1 each time, and then
\ getting a 0 on the 8th iteration... and we can also
\ use Q to catch our result bits into bit 0 each time

.LIL1

ASL A                  \ Shift A to the left

BCS LI4                \ If bit 7 of A was set, then jump straight to the
\ subtraction

CMP P                  \ If A < P, skip the following subtraction
BCC LI5

.LI4

SBC P                  \ A >= P, so set A = A - P

SEC                    \ Set the C flag to rotate into the result in Q

.LI5

ROL Q                  \ Rotate the counter in Q 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 LIL1               \ If we still have set bits in Q, loop back to TIL2 to
\ do the next iteration of 7

\ We now have:
\
\   Q = A / P
\     = |delta_y| / |delta_x|
\
\ and the C flag is clear

LDX P                  \ Set X = P + 1
INX                    \       = |delta_x| + 1
\
\ We add 1 so we can skip the first pixel plot if the
\ line is being drawn with swapped coordinates

LDA Y2                 \ Set A = Y2 - Y1 - 1 (as the C flag is clear following
SBC Y1                 \ the above division)

BCS DOWN               \ If Y2 >= Y1 - 1 then jump to DOWN, as we need to draw
\ the line to the right and down
\ The following section calculates:
\
\   Q = Q / P
\     = |delta_y| / |delta_x|
\
\ using the log tables at logL and log to calculate:
\
\   A = log(Q) - log(P)
\     = log(|delta_y|) - log(|delta_x|)
\
\ by first subtracting the low bytes of the logarithms
\ from the table at LogL, and then subtracting the high
\ bytes from the table at log, before applying the
\ antilog to get the result of the division and putting
\ it in Q

LDX Q                  \ Set X = |delta_y|

BEQ LIlog7             \ If |delta_y| = 0, jump to LIlog7 to return 0 as the
\ result of the division

LDA logL,X             \ Set A = log(Q) - log(P)
LDX P                  \       = log(|delta_y|) - log(|delta_x|)
SEC                    \
SBC logL,X             \ by first subtracting the low bytes of log(Q) - log(P)
```

Code variation 6 of 9Other (e.g. bug fix, optimisation)

The Master version omits half of the logarithm algorithm when compared to the 6502SP version.

See below for more variations related to this code.

This variation is blank in the Cassette, Disc (flight), Disc (docked), Master and Electron versions.

```6502SP BMI LIlog4             \ If A > 127, jump to LIlog4
```

Code variation 7 of 9Other (e.g. bug fix, optimisation)

See variation 6 above for details.

This variation is blank in the Cassette, Disc (flight), Disc (docked) and Electron versions.

Tap on a block to expand it, and tap it again to revert.

```Master6502SP LDX Q                  \ And then subtracting the high bytes of log(Q) - log(P)
LDA log,X              \ so now A contains the high byte of log(Q) - log(P)
LDX P
SBC log,X

BCS LIlog5             \ If the subtraction fitted into one byte and didn't
\ underflow, then log(Q) - log(P) < 256, so we jump to
\ LIlog5 to return a result of 255

TAX                    \ Otherwise we set A to the A-th entry from the antilog
LDA alogh,X            \ table so the result of the division is now in A

.LIlog5

LDA #255               \ The division is very close to 1, so set A to the
\ LIlog6 to return the result (this BNE is effectively a
\ JMP as A is never zero)

.LIlog7
LDX Q                  \ And then subtracting the high bytes of log(Q) - log(P)
LDA log,X              \ so now A contains the high byte of log(Q) - log(P)
LDX P
SBC log,X

BCS LIlog5             \ If the subtraction fitted into one byte and didn't
\ underflow, then log(Q) - log(P) < 256, so we jump to
\ LIlog5 to return a result of 255

TAX                    \ Otherwise we set A to the A-th entry from the antilog
LDA antilog,X          \ table so the result of the division is now in A

.LIlog5

LDA #255               \ The division is very close to 1, so set A to the
\ LIlog6 to return the result (this BNE is effectively a
\ JMP as A is never zero)

.LIlog7
```

Code variation 8 of 9Other (e.g. bug fix, optimisation)

See variation 6 above for details.

This variation is blank in the Cassette, Disc (flight), Disc (docked) and Electron versions.

Tap on a block to expand it, and tap it again to revert.

```Master6502SP LDA #0                 \ The numerator in the division is 0, so set A to 0
LDA #0                 \ The numerator in the division is 0, so set A to 0 and
BEQ LIlog6             \ jump to LIlog6 to return the result (this BEQ is
\ effectively a JMP as A is always zero)

.LIlog4

LDX Q                  \ Subtract the high bytes of log(Q) - log(P) so now A
LDA log,X              \ contains the high byte of log(Q) - log(P)
LDX P
SBC log,X

BCS LIlog5             \ If the subtraction fitted into one byte and didn't
\ underflow, then log(Q) - log(P) < 256, so we jump to
\ LIlog5 to return a result of 255

TAX                    \ Otherwise we set A to the A-th entry from the
LDA antilogODD,X       \ antilogODD so the result of the division is now in A
```

Code variation 9 of 9Other (e.g. bug fix, optimisation)

See variation 6 above for details.

This variation is blank in the Cassette, Disc (flight), Disc (docked) and Electron versions.

```6502SP, Master.LIlog6

STA Q                  \ Store the result of the division in Q, so we have:
\
\   Q = |delta_y| / |delta_x|

LDX P                  \ Set X = P
\       = |delta_x|

BEQ LIEXS              \ If |delta_x| = 0, return from the subroutine, as LIEXS
\ contains a BEQ LIEX instruction, and LIEX contains an
\ RTS

INX                    \ Set X = P + 1
\       = |delta_x| + 1
\
\ We add 1 so we can skip the first pixel plot if the
\ line is being drawn with swapped coordinates

LDA Y2                 \ If Y2 < Y1 then skip the following instruction
CMP Y1
BCC P%+5

JMP DOWN               \ Y2 >= Y1, so jump to DOWN, as we need to draw the line
\ to the right and down
```