Math Magic

Lesson 15 – Math Magic

You’ve been writing formulas inline; now collect them into functions. DEF FN gives each formula a name so your code reads like intent instead of algebra.

[📷 suggested: screenshot showing PRINT lines calling several functions]

The One-Minute Tour

• DEF FNNAME(X)=expression defines a numeric function.
• Commodore BASIC V2 supports one argument, one line, one numeric result.
• Use uppercase names without spaces (e.g., FNSCORE).

Basic Function Toolkit

NEW
10 DEF FNSQ(X)=X*X
20 DEF FNDB(N)=N*2
30 PRINT FNSQ(5)
40 PRINT FNDB(7)

Output:

25
14

Functions drop inline: PRINT 20+FNSQ(3) works just fine.

Percentages, Scaling, and Rounding

NEW
10 DEF FNPERCENT(S)=INT(S*100/MAX)
20 MAX=500
30 SCORE=275
40 PRINT "SCORE:";SCORE;"(";FNPERCENT(SCORE);"%)"

Use globals (MAX) to supply extra context. Commodore BASIC functions only accept one argument, so globals keep them useful.

Gravity Helper for Your Loop

NEW
10 DEF FNFALL(T)=VY*T-4.9*T*T
20 VY=8
30 FOR T=0 TO 3 STEP .2
40 Y=FNFALL(T)
50 IF Y<0 THEN EXIT
60 PRINT T;Y
70 NEXT T

FNFALL encapsulates a physics formula so the main loop stays readable. With a screen POKE you could bring back the trajectory from Lesson 10.

Pattern Functions for Generators

NEW
10 DEF FNCHESS(X)= (X AND 1)=0
20 FOR R=0 TO 7
30 FOR C=0 TO 7
40 IF FNCHESS(R+C) THEN PRINT "#"; ELSE PRINT " ";
50 NEXT C
60 PRINT
70 NEXT R

FNCHESS returns true/false, letting you alternate characters elegantly inside nested loops.

Random Helpers

NEW
10 DEF FNROLL(N)=INT(RND(1)*N)+1
20 FOR I=1 TO 5
30 PRINT "D6:";FNROLL(6)," D20:";FNROLL(20)
40 NEXT I

Random dice, percentages, scaling—they all benefit from a named function you can drop into scoring logic.

Combining Globals with Dummy Arguments

Need more than one input? Store extra values globally, use a dummy parameter to satisfy BASIC’s single-argument rule.

NEW
10 X1=4:Y1=5:X2=18:Y2=9
20 DEF FNDIST(Q)=SQR((X2-X1)^2+(Y2-Y1)^2)
30 PRINT "DIST:";INT(FNDIST(0))

Not elegant, but effective—and common practice in 1980s code.

Experiment Section

• Add DEF FNFX(S)=INT(SPEED*S) to convert player speed to animation frames.
• Use DEF FNHP(V)=MINHP+INT((MAXHP-MINHP)*V) to scale hit points.
• Integrate Lesson 14’s generators: call a function inside nested loops to pick tiles.
• Combine with Lesson 13 logic: IF FNHIT(NX,NY)=1 THEN ... wraps collision math in a friendly wrapper.
• Precompute tables: fill an array with FOR I=0 TO 15:LOOKUP(I)=FNFX(I/15).

[📷 suggested: screenshot showing a HUD that uses function output]

Concept Expansion

Functions are the maths sibling of subroutines: they only return a value, but that value can express physics, scoring, or procedural rules concisely. Later you’ll embed similar logic in machine code, but the interfaces will look familiar.

Game Integration

• Scoring: SCORE=SCORE+FNCOMBO(HITS) to reward streaks.
• Projectile motion: call FNFALL to update bullet arcs each frame.
• Damage curves: HP=HP-FNDAMAGE(WEAPON) to centralise balancing.
• Enemy AI: ANGLE=FNTRACK(PX,PY,EX,EY) returns chase direction (store positions in globals first).

From the Vault

• Paradroid — read design diaries referencing control formulas.
• Commodore 64 — understand how floating-point arithmetic behaves on the 6510.

Quick Reference

DEF FNSQ(X)=X*X               : REM define
PRINT FNSQ(5)                 : REM call
DEF FNROLL(N)=INT(RND(1)*N)+1 : REM random range helper

• Functions must appear before you call them.
• Names must be FN followed by letters (no spaces).
• Use globals for extra context; reset them before each call if needed.

What You’ve Learnt

• Defined reusable formulas with DEF FN.
• Balanced the single-argument limitation using globals.
• Dropped functions into loops, scoring, and physics for cleaner code.
• Built a toolbox of random, pattern, and physics helpers ready for the Week 2 mini-game.

Next lesson: Mini-Game: Maze Craze — stitch the whole week together into a procedural maze run.