asciilifeform: yes, that's what a keyboard is

asciilifeform: ben_vulpes: http://btcbase.org/log/2017-09-12#1712731 ☝︎

asciilifeform: lol!

asciilifeform: ?

asciilifeform: so that it can get stuck in the piston when humidity goes up 5%

asciilifeform: ben_vulpes: so why wood then

asciilifeform: ewwww

asciilifeform: how would you make the meniscus ?

asciilifeform: ( and 'redefine the shape' is not an answer )

asciilifeform: ben_vulpes: how do you propose to make 200+ identical wooden keys with the proper shape ?

asciilifeform: 95% of the academitards dun even bother with any attempt other than 'how do i montgomery slightly faster'

asciilifeform: srsly, couplea kg worth by nao

asciilifeform currently surrounded by tall pile of -- mostly worthless -- literature re mod mult

asciilifeform: good enough for tokamak, good enough for kbd...

asciilifeform: that's quite ok, make whole thing from it

asciilifeform: lol chrome not zinc

asciilifeform: monel ( and more recent inconel ) is spiffy unreactive nickel alloy, used in aggressive envir (e.g. molten na reactor tubing)

asciilifeform: no moar than steel 'is' carbon

asciilifeform: nickel is prolly the least biocompatible metal

asciilifeform: ugh ever wore a nickel watchband ?

asciilifeform: dunno if anything'd beat monel.

asciilifeform: so i'd go for, say, monel.

asciilifeform: well thread was re a hypothetical nothing-spared kbd.

asciilifeform: why not ?

asciilifeform: i was thinking of machining but yes

asciilifeform: it would be if stainless

asciilifeform: certainly not shiny like scalpel, no.

asciilifeform: sure

asciilifeform: it will tarnish when full enough of acidic finger oil.

asciilifeform: no 'speshul rsa forms' in ffa.

asciilifeform: a*b mod m MUST WORK FOR ALL INTEGERS .

asciilifeform: ( the thing is widely used in rsatrons which agree to constrain themselves thusly, but is entirely irrelevant in ffa )

asciilifeform: if either condition is false, it will silently shit out garbage.

asciilifeform: specifically demands that the modulus be odd, and that it must be greater than either multiplicand.

asciilifeform: reason is that it demands special forms and therefor is not a general-purpose modexp

asciilifeform: incidentally i dun think i've put into the logs why montgomery's modular mult algo is unusable

asciilifeform: everything you've seen in ffa to date, is unrollable into iron circuit.

asciilifeform: re 'mechanism', also can restate : if something cannot be expressed as a boolean circuit, it is not constantspacetimeizable.

asciilifeform: ( in heathen world, if the upper bit of one comparand is set, and the other's corresponding bit is not, you stop right there )

asciilifeform: this was probably obvious to everybody tuned in, but bears restating.

asciilifeform: comparing (or subtracting) 0 and 0 takes same time as maxint and maxint or maxint and 0 etc

asciilifeform: http://btcbase.org/log/2017-09-12#1713184 << in ffaworld, a < or > or == comparison is not only a subtraction (O(N)) but another O(N) test for nullity (xor all the words together) ☝︎☟︎

asciilifeform: hiya mod6

asciilifeform: ( and http://btcbase.org/log/2017-08-10#1696834 probably being canonical statement thereof ) ☝︎

asciilifeform: http://btcbase.org/log/2017-09-12#1713185 << the 'mechanism' is... algebra ( see also http://btcbase.org/log/2017-08-10#1696309 etc ) ☝︎☝︎

asciilifeform: mircea_popescu: silver tarnishes and has abysmal mechanical properties and why

asciilifeform brb

asciilifeform: it requires a constant-time gcd, however, to be constant-time. ( and has a problem same as above in that it takes much MORE time than naive algo if you don't reuse modulus forever )

asciilifeform: incidentally there are other algos where you pre-bake a thing for a given modulus and save some cycles. montgomery's, for example.

asciilifeform: possib

asciilifeform: it is ~greater~ number of cycles, by far, if you count the 'tooling' cost of preparing the table for each new modulus.

asciilifeform: but actually congrats to mircea_popescu for reinventing 2 separate knuth algos.

asciilifeform: but useless for ptronic.

asciilifeform: it is ok for rsa where you sink it to the bottom of the sea and never intend to change the modulus

asciilifeform: called 'addition chains'

asciilifeform: this btw is also in vol2 of knuth ☟︎

asciilifeform: which takes ages

asciilifeform: and for every new modulus, you gotta cook up a list

asciilifeform: because we're muxing over the entire list every single time

asciilifeform: except it does exactly as many cycles as the classical method.

asciilifeform: 9266137

asciilifeform: i dun get from where you got the 1s

asciilifeform: and you're stuck adding a+b... again

asciilifeform: then a mod m == a, b mod m == b, etc

asciilifeform: ( all bits set )

asciilifeform: let's take the case where modulus is maxint

asciilifeform: ( additions produce B+W-bit ints, and these get out of hand very quickly)

asciilifeform: but with moar space overhead.

asciilifeform: as far as i can see it is exactly same

asciilifeform: i dun see what this gives you tho

asciilifeform: you do if you want to get anything out of having a table

asciilifeform: which is an instant cache death.

asciilifeform: it is bad for being indexed by a secret

asciilifeform: whole point of ffa, is this notdoing

asciilifeform: which is somethign we specifically aint doing

asciilifeform: mircea_popescu: that's the kochian table approach

asciilifeform: except we dun get to use 'where there are 1s'

asciilifeform: all bitnesses -- same.

asciilifeform: modulus bitness == operand bitness. this is ffa after all.

asciilifeform: only if we did not then have to sum'em ( the 30 in the example )

asciilifeform: the modulus is same bitness as the operands, and is not small.

asciilifeform: but aside from this , it isn't clear to me that it saves any cycles

asciilifeform: i'ma need to find a proof that this holds for all integers. ☟︎

asciilifeform: now what happens if the inputs are not coprime ?

asciilifeform: but sure

asciilifeform: ( i thought we were doing a+b )

asciilifeform: last one was supposed to be mod

asciilifeform: 1433293, 7926803, 9266137

asciilifeform: ok:

asciilifeform: a=5, b=7, m=11

asciilifeform: ok:

asciilifeform: so as to avoid this.

asciilifeform: tkae 4 primez plox

asciilifeform: ahahahahahaha

asciilifeform: plz carry on

asciilifeform: lolk

asciilifeform: waaait why bad

asciilifeform: ok...

asciilifeform: if you allow a+b+c addition to take place, you have exactly same proggy i have now.

asciilifeform: karatsuba terms a+b+c ( k. squaring, for simplicity. mult. has four of'em ). we want a+b+c mod m.