# ZX BASIC:Distance.bas

This calculates an approximation for the distance formula r=SQR(x^2 + y^2), 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

' returns a fast approximation of SQRT (a^2 + b^2) - the distance formula, generated from taylor series expansion.
' This version fundamentally by Alcoholics Anonymous, improving on Britlion's earlier version - which itself was suggested, with thanks, by NA_TH_AN.

ASM
;' 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
ret
END ASM
END FUNCTION
```