# 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 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 ret END ASM END FUNCTION