try — it takes about two seconds. that's real counting.
the answer
what it's thinking
a calculator that refuses to do math
it adds. it subtracts. it uses zero arithmetic operators to do it.
ok so how
short version: there are no +, -, *,
/, ++, --, += or
-= anywhere in script.js. i grep for them before
every commit. addition and subtraction still come out right. here's the cheat:
-
arrays are secretly counters
push()makes.lengthgo up by exactly one.pop()makes it go down by exactly one. so an array is a counter and.lengthis the value. no operators required, no rules broken (arguably).var n = []; n.push(null); // n.length is 1 n.push(null); // n.length is 2 // look ma, no + -
use it to build two big tables
walk that counter from 0 up to 100000 and write down each step. that's the successor table. do it backwards by popping and you get the predecessor table. 200000 numbers total. it's fine. it's fine.
NEXT[0] = 1 NEXT[1] = 2 NEXT[99999] = 100000 -
then addition is just walking
for
a + b, start ataand askNEXTwhere to go,btimes. subtraction is the same thing but throughPREV. that's it. that's the calculator.result = a repeat b times: result = NEXT[result]
why is it so slow
because it genuinely is doing the work. this isn't a progress bar doing a
little animation while the real answer comes from a hardware
ADD instruction -- there is no hardware instruction. peano
arithmetic really is "keep counting until you get there", so
50000 + 50000 is 50000 separate table lookups and takes about
two seconds. the bar is honest. annoyingly honest.
the bug
there's one wrong number in the successor table, on purpose, and it has
been there since the first version. it only does anything if a walk
lands on 41 and then tries to leave, which means 0+41
is fine and 0+42 is not. add your way through the low forties
and watch it lie to you.
details
- numbers it knows 0 to 100000
- tables 100000 successors, 100000 predecessors
- too big says OVERFLOW and gives up
- too small stops at 0
- to install there is nothing to install. it's three files.
- dependencies none. zero. not even a font.
- arithmetic operators still zero. still checked.