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--- base:approximation_to_distance [2020-02-09 14:39] – created djmips
+++ base:approximation_to_distance [2020-02-11 01:45] (current) – djmips
@@ Line 7: / Line 7: @@
+The formula is d = max(|xd|, |yd|) + 1/2 × min(|xd|, |yd|) where xd = (x1-x2) and yd = (y1-y2)
-Note that for 6502 we can take the approximation even further by noting the coefficient for max is close to one and the coefficient for min is close enough to 1/2 to use that as a faster calculation that's acceptable for a lot of game use.
+Note that for 6502 we will use a shift right to calculate the multiply by 1/2.
 <code>
@@ Line 16: / Line 17: @@
 ; than (9/8) + one bit uncertainty.
- lda x1          ; x1 - x2
+; input: x1,y1  x2,y2
+; uses: A xd,yd
+; output: approximate distance between x1,y1 and x2,y2 in A + ninth bit in C
+; If the actual distance is 228 or less the result estimate will fit in 8 bits
+Dist:
+ lda x1
  sec
  sbc x2
  sta xd
- bpl .posxdiff   ; abs()
+ bcs posxdiff
- lda #00         ;
+ eor #$FF
- sec
+ adc #1
- sbc xd
+posxdiff:
-.posxdiff:
  sta xd
- lda y1          ; y1 - y2
+ lda y1
  sec
  sbc y2
- sta yd
+ bcs posydiff
- bpl .posydiff   ; abs()
+ eor #$FF
- lda #00
+ adc #1
- sec
+posydiff:
- sbc yd
-.posydiff:
  cmp xd
- bcs .ygreater
+ bcs ygreater
- lsr              ; ydelta / 2
+ lsr
- adc xd           ; + xdelta
+ clc
+ adc xd
+ rts
+ygreater:
+ lsr xd
+ clc
+ adc xd
  rts
-.ygreater:
- sta yd
- lda xd
- lsr              ; xdelta / 2
- cls
- adc yd           ; + ydelta
- rts
 </code>