Tupper's self-referential formula: Difference between revisions

=={{header|Lua}}==

Tested with Lua 5.4.5

{{Trans|Algol 68}}

Using Eduardo Bart's lua-bint pure Lua big integer library https://github.com/edubart/lua-bint.<br>

The precision of the big integers must be specified in bits as a parameter of the require.

<syntaxhighlight lang="lua">

do --[[ plot Tupper's self-referential formula

need to find x, y such that:

1/2 < floor( mod( (y/17)*2^ - ( 17x - mod(y,17) ), 2 ) )

where x in 0..106, y in k..k+16

--]]

local bint = require 'bint'(2048) -- need around 600 digits

local k = bint.fromstring( "960939379918958884971672962127852754715004339660129306651505" ..

"519271702802395266424689642842174350718121267153782770623355" ..

"993237280874144307891325963941337723487857735749823926629715" ..

"517173716995165232890538221612403238855866184013235585136048" ..

"828693337902491454229288667081096184496091705183454067827731" ..

"551705405381627380967602565625016981482083418783163849115590" ..

"225610003652351370343874461848378737238198224849863465033159" ..

"410054974700593138339226497249461751545728366702369745461014" ..

"655997933798537483143786841806593422227898388722980000748404" ..

"719" )

local kMod17 = bint.tointeger( k % 17 )

local b17 = bint.frominteger( 17 )

local b2 = bint.frominteger( 2 )

for yDelta = 0, 16 do

for x = 106, 0, -1 do

local powerOf2 = - ( 17 * x ) - ( kMod17 + yDelta ) % 17

-- if powerOf2 = 0, then ( v * 2 ^ powerOf2 ) mod 2 = v mod 2

-- if powerOf2 > 0, then ( v * 2 ^ powerOf2 ) mod 2 = 0

if powerOf2 > 0 then

io.write( " " )

else

local v = ( k + bint.frominteger( yDelta ) ) // b17

if powerOf2 < 0 then

v = v // bint.ipow( b2, bint.frominteger( - powerOf2 ) )

end

v = v % 2

io.write( ( bint.eq( v, 0 ) and " " ) or "#" )

end

end

io.write( "\n" )

end

end

</syntaxhighlight>

{{out}}

Same as Algol 68.