Distance.bas
This calculates an approximation for the distance formula r=SQR
(x2 + y2),
based on two parameters, x
and y
. The return value is not guaranteed to be accurate -
and indeed can be as high as 10% inaccurate as x and y approach 255 (the upper limit for input).
The return value is an integer - chosen because screen is 256 pixels wide, and the diagonal across the screen
is bigger than 1 byte can hold.
If you need accurate results, you should go with iSqrt
or fSqrt
from this library.
For speed, this can't be beaten, however.
Comparing -
answer = distance(i, j)
against
answer = iSqrt(i * i + j * j)
shows over a range of i
and j
1..250
:
- distance 8.98 seconds
iSqrt 50.1 seconds
Distance is definitely faster, if you're willing to accept the greater inaccuracy (you probably are).
By the by - standard floating point square root:
fSqrt
function: 44 minutes (2625.14 seconds)SQR
(ROM) - 122 minutes. (7336.86 seconds)
Shows how awful that ROM SQR routine really is...
Formula is: in a right angle triangle with sides A and B, and hypotenuse H, as an estimate of length of H, it returns (A + B) - (half the smallest of A and B) - (1/4 the smallest of A and B) + (1/16 the smallest of A and B)
FUNCTION fastcall distance (a as ubyte, b as ubyte) as uInteger
REM returns a fast approximation of SQRT (a^2 + b^2) - the distance formula, generated from taylor series expansion.
REM This version fundamentally by Alcoholics Anonymous, improving on Britlion's earlier version - which itself
REM was suggested, with thanks, by NA_TH_AN.
asm
POP HL ;' return address
;' First parameter in A
POP BC ;' second parameter -> B
PUSH HL ;' put return back
;' First find out which is bigger - A or B.
cp b
ld c,b
jr nc, distance_AisMAX
ld c,a
distance_AisMAX:
;' c = MIN(a,b)
srl c ;' c = MIN/2
sub c ;' a = A - MIN/2
srl c ;' c = MIN/4
sub c ;' a = A - MIN/2 - MIN/4
srl c
srl c ;' c = MIN/16
add a,c ;' a = A - MIN/2 - MIN/4 + MIN/16
add a,b ;' a = A + B - MIN/2 - MIN/4 + MIN/16
ld l,a
ld h,0 ;' hl = result
ret nc
inc h ;' catch 9th bit
END ASM
END FUNCTION