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Line 1: {{~~draft~~ task}} ;Introduction Line 17: Make a drawing of the Tupper's formula, either using text, a matrix or creating an image. This task requires arbitrary precision integer operations. If your language does not ~~intrinsecally~~intrinsically support that, you can use a library. ;Epilogue Line 27: :* Wikipedia: [[wp:Tupper's self-referential formula\|Tupper's self-referential formula]] :* [http://www.dgp.toronto.edu/~mooncake/papers/SIGGRAPH2001_Tupper.pdf Tupper, Jeff. "Reliable Two-Dimensional Graphing Methods for Mathematical Formulae with Two Free Variables"] =={{header\|ALGOL 68}}== {{works with\|ALGOL 68G\|Any - tested with release 2.8.3.win32}} Uses Algol 68G's LONG LONG INT which has programmer specifiable precision.<br> Draws the bitmap using ASCII. As only integer arithmetic is used, there's no need for explicit floor operations, and the values of the right-hand side of the inequality can only be 0 or 1. <syntaxhighlight lang="algol68"> BEGIN CO 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 CO PR precision 600 PR LONG LONG INT k = 960 939 379 918 958 884 971 672 962 127 852 754 715 004 339 660 129 306 651 505 519 271 702 802 395 266 424 689 642 842 174 350 718 121 267 153 782 770 623 355 993 237 280 874 144 307 891 325 963 941 337 723 487 857 735 749 823 926 629 715 517 173 716 995 165 232 890 538 221 612 403 238 855 866 184 013 235 585 136 048 828 693 337 902 491 454 229 288 667 081 096 184 496 091 705 183 454 067 827 731 551 705 405 381 627 380 967 602 565 625 016 981 482 083 418 783 163 849 115 590 225 610 003 652 351 370 343 874 461 848 378 737 238 198 224 849 863 465 033 159 410 054 974 700 593 138 339 226 497 249 461 751 545 728 366 702 369 745 461 014 655 997 933 798 537 483 143 786 841 806 593 422 227 898 388 722 980 000 748 404 719; INT k mod 17 = SHORTEN SHORTEN ( k MOD 17 ); FOR y delta FROM 0 TO 16 DO FOR x FROM 106 BY -1 TO 0 DO INT power of 2 = - ( 17 x ) - ( k mod 17 + y delta ) MOD 17; # if power of 2 = 0, then ( v * 2 ^ power of 2 ) MOD 2 = v MOD 2 # # if power of 2 > 0, then ( v * 2 ^ power of 2 ) MOD 2 = 0 # IF power of 2 > 0 THEN print( ( " " ) ) ELSE LONG LONG INT v := ( k + y delta ) OVER 17; IF power of 2 < 0 THEN v OVERAB LONG LONG 2 ^ ABS power of 2 FI; print( ( IF ODD v THEN "#" ELSE " " FI ) ) FI OD; print( ( newline ) ) OD END </syntaxhighlight> {{out}} <pre> # # # ## # # # # # # # ## # # # # # # # # # # # # # # # # # # # # ## # # # # ## # # # # # # ## #### ### ### # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ### ### # # # # # # # # # # # # # # # # ## # # # # # # # # ## # # ### # # # # # # # # # # # # # # # # # # # # # # ## # ## ### # # # # ### ### # ### ### # # # # # ### # # # # # # # # # # # #### # # # # # # # # # # # # # # # # # # # # # ## # # # # # ## ### # # # ## # #### #### # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # ### # # # # # # # # # # # # # # ### # ### ### # ### </pre> =={{header\|C#}}== {{trans\|Java}} <syntaxhighlight lang="C#"> using System; using System.Numerics; class TuppersSelfReferentialFormula { private static readonly BigInteger k = BigInteger.Parse("960939379918958884971672962127852754715" + "004339660129306651505519271702802395266424689642842174350718121267153782" + "770623355993237280874144307891325963941337723487857735749823926629715517" + "173716995165232890538221612403238855866184013235585136048828693337902491" + "454229288667081096184496091705183454067827731551705405381627380967602565" + "625016981482083418783163849115590225610003652351370343874461848378737238" + "198224849863465033159410054974700593138339226497249461751545728366702369" + "745461014655997933798537483143786841806593422227898388722980000748404719"); static void Main(string[] args) { bool[,] matrix = TuppersMatrix(); Console.BackgroundColor = ConsoleColor.Magenta; for (int row = 0; row < 17; row++) { for (int column = 0; column < 106; column++) { Console.Write(matrix[row, column] ? "█" : " "); } Console.WriteLine(); } Console.ResetColor(); // Resets to the default console background and foreground colors } private static bool[,] TuppersMatrix() { bool[,] matrix = new bool[17, 106]; BigInteger seventeen = new BigInteger(17); for (int column = 0; column < 106; column++) { for (int row = 0; row < 17; row++) { BigInteger y = k + row; BigInteger a = y / seventeen; int bb = (int)(y % seventeen) + column * 17; BigInteger b = BigInteger.Pow(2, bb); a /= b; int aa = (int)(a % 2); matrix[row, 105 - column] = (aa == 1); } } return matrix; } } </syntaxhighlight> {{out}} <pre> █ █ █ ██ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ ██ █ █ █ █ █ █ ██ ████ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ ██ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ ██ ███ █ █ █ █ ███ ███ █ ███ ███ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ ██ ███ █ █ █ ██ █ ████ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ ███ ███ █ ███ </pre> =={{header\|C++}}== {{libheader\|Boost}} <syntaxhighlight lang="cpp">#include <iostream> #include <boost/multiprecision/cpp_int.hpp> #include <boost/multiprecision/integer.hpp> int main() { using boost::multiprecision::cpp_int; using boost::multiprecision::pow; const cpp_int k( "9609393799189588849716729621278527547150043396601293066515055192717028" "0239526642468964284217435071812126715378277062335599323728087414430789" "1325963941337723487857735749823926629715517173716995165232890538221612" "4032388558661840132355851360488286933379024914542292886670810961844960" "9170518345406782773155170540538162738096760256562501698148208341878316" "3849115590225610003652351370343874461848378737238198224849863465033159" "4100549747005931383392264972494617515457283667023697454610146559979337" "98537483143786841806593422227898388722980000748404719"); const int rows = 17; const int columns = 106; const cpp_int two(2); for (int row = 0; row < rows; ++row) { for (int column = columns - 1; column >= 0; --column) { cpp_int y = k + row; int b = static_cast<int>(y % 17) + column * 17; cpp_int a = (y / 17) / pow(two, b); std::cout << ((a % 2 == 1) ? u8"\u2588" : u8" "); } std::cout << '\n'; } }</syntaxhighlight> {{out}} <pre style="font-size: .75em;"> █ █ █ ██ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ ██ █ █ █ █ █ █ ██ ████ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ ██ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ ██ ███ █ █ █ █ ███ ███ █ ███ ███ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ ██ ███ █ █ █ ██ █ ████ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ ███ ███ █ ███ </pre> =={{header\|Fōrmulæ}}== Line 46 ⟶ 243: [[File:Fōrmulæ - Tupper's self-referential formula 03.png]] '''Visualization as a matrix.''' The following creates a ~~17×107~~17×106 matrix. Values for which inequality is true are shown as an opaque black color, otherwise they are shown as an transparent color. [[File:Fōrmulæ - Tupper's self-referential formula 04.png]] (image is resized 50% of its original) ~~[[File:Fōrmulæ - Tupper's self-referential formula 05.png]]~~ [[File:Fōrmulæ - Tupper's self-referential formula 05.png\|1070px]] '''Visualization as an image.''' In the following script, a function to draw the Tupper's formula is used to generate the image with different sizes, because the standard 1x1 pixel per unit results to be too small in order to be appreciated: Line 58 ⟶ 257: [[File:Fōrmulæ - Tupper's self-referential formula 07.png]] [[File:Fōrmulæ - Tupper's self-referential formula 08.png]] ~~=={{header\|Julia}}==~~ ~~<syntaxhighlight lang="julia">import Images: colorview, Gray~~ ~~import Plots: plot~~ =={{header\|J}}== ~~setprecision(BigFloat, 8000)~~ '''Tacit Solution''' <syntaxhighlight lang="j">K=. (". (0 ( : 0)) -. LF)"_ 960939379918958884971672962127852754715004339660129306651505 519271702802395266424689642842174350718121267153782770623355 993237280874144307891325963941337723487857735749823926629715 517173716995165232890538221612403238855866184013235585136048 828693337902491454229288667081096184496091705183454067827731 551705405381627380967602565625016981482083418783163849115590 225610003652351370343874461848378737238198224849863465033159 410054974700593138339226497249461751545728366702369745461014 655997933798537483143786841806593422227898388722980000748404 719x ) inequality=. 1r2 < <. o (2 \| (17 %~ ]) * 2 ^ (_17 * <. o [) - 17x \| <.(o=. @:)]) ~~""" get logical inverse of Tupper function values for black on while graphic """~~ ~~function tupper_mat(k)~~ Tupperimage=. ({&' ') o ([ (] inequality K + [)"0/ \|. o ])&:i. f.</syntaxhighlight> Example use: <syntaxhighlight lang="j"> 17 Tupperimage 106</syntaxhighlight> Produces the following text-based image, {{out}} <pre> * * ** * * * * * * * ** * * * * * * * * * * * * * * * * * * * * ** * * * * ** * * * * * * * *** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * ** * * *** * * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * *** * * * * * * * * * * * **** * * * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * ** * ** ** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *** * * * * * * * * * * * * * * *** * * * * *** </pre> The code is tacit and fixed (in other words, it is point-free): <syntaxhighlight lang="j"> _80 [\ (5!:5) <'Tupperimage' {&' '@:([ (] (1r2 < <.@:(2 \| (17 %~ ]) 2 ^ (_17 * <.@:[) - 17x \| <.@:])) 9609 39379918958884971672962127852754715004339660129306651505519271702802395266424689 64284217435071812126715378277062335599323728087414430789132596394133772348785773 57498239266297155171737169951652328905382216124032388558661840132355851360488286 93337902491454229288667081096184496091705183454067827731551705405381627380967602 56562501698148208341878316384911559022561000365235137034387446184837873723819822 48498634650331594100549747005931383392264972494617515457283667023697454610146559 97933798537483143786841806593422227898388722980000748404719x"_ + [)"0/ \|.@:])&:i .</syntaxhighlight> Alternatively, <syntaxhighlight lang="j">Tuppergraph=. viewmat o ([ load o ('viewmat'"_)) o ([ (] inequality K + [)"0/ \|. o ])&:i. 17 Tuppergraph 106</syntaxhighlight> produces the following graph, [[File:J Tupper graph.png]] =={{header\|Java}}== <syntaxhighlight lang="java"> import java.io.IOException; import java.io.PrintStream; import java.math.BigInteger; import java.util.Arrays; public final class TuppersSelfReferentialFormula { public static void main(String[] args) throws IOException { boolean[][] matrix = tuppersMatrix(); PrintStream writer = new PrintStream(System.out, true, "UTF-8"); writer.println("\033[45m"); // Magenta background for ( int row = 0; row < 17; row++ ) { for ( int column = 0; column < 106; column++ ) { String character = matrix[row][column] ? "\u2588" : " "; writer.print(character); } writer.println(); } writer.close(); } private static boolean[][] tuppersMatrix() { boolean[][] matrix = new boolean[17][106]; Arrays.stream(matrix).forEach( row -> Arrays.fill(row, true) ); final BigInteger seventeen = BigInteger.valueOf(17); for ( int column = 0; column < 106; column++ ) { for ( int row = 0; row < 17; row++ ) { BigInteger y = k.add(BigInteger.valueOf(row)); BigInteger a = y.divideAndRemainder(seventeen)[0]; int bb = y.mod(seventeen).intValueExact(); bb += column * 17; BigInteger b = BigInteger.TWO.pow(bb); a = a.divideAndRemainder(b)[0]; int aa = a.mod(BigInteger.TWO).intValueExact(); matrix[row][105 - column] = ( aa == 1 ); } } return matrix; } private static final BigInteger k = new BigInteger("960939379918958884971672962127852754715" + "004339660129306651505519271702802395266424689642842174350718121267153782" + "770623355993237280874144307891325963941337723487857735749823926629715517" + "173716995165232890538221612403238855866184013235585136048828693337902491" + "454229288667081096184496091705183454067827731551705405381627380967602565" + "625016981482083418783163849115590225610003652351370343874461848378737238" + "198224849863465033159410054974700593138339226497249461751545728366702369" + "745461014655997933798537483143786841806593422227898388722980000748404719"); } </syntaxhighlight> {{ out }} [[Media:TuppersJava.png]] =={{header\|Julia}}== <syntaxhighlight lang="julia">import Plots: heatmap, savefig """ get logical inverse of Tupper function values for black on background graphic """ function tupper_mat(k::BigInt) tmatrix = trues(17, 106) for (i, x) in enumerate(0.0:1:105), (j, y) in enumerate(k:k+16) tmatrix[18 - j, 107 - i] = 1/2 >!= ~~floor~~(~~mod(floor~~(y /÷ 17) ÷ 2^(~~-17~~17x + ~~floor~~(x)y ~~- mod(floor(y),~~% 17)),) % 2)) end return tmatrix Line 85 ⟶ 409: function test_tupper() bmap = tupper_mat(k) display(~~plot~~heatmap(~~colorview(Gray~~bmap, ~~bmap)~~legend = :none, aspect_ratio = 1, ylims = [1,17])) savefig("tupper.png") end Line 92 ⟶ 416: </syntaxhighlight>{{out}} [[File:~~Tupper~~Tupper2.png\|center]] =={{header\|Lua}}== Tested with Lua 5.4.6 {{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 'lua-bint-master\\bint'(2048) -- need around 600 digits local k = bint.fromstring( "960939379918958884971672962127852754715004339660129306651505" .. "519271702802395266424689642842174350718121267153782770623355" .. "993237280874144307891325963941337723487857735749823926629715" .. "517173716995165232890538221612403238855866184013235585136048" .. "828693337902491454229288667081096184496091705183454067827731" .. "551705405381627380967602565625016981482083418783163849115590" .. "225610003652351370343874461848378737238198224849863465033159" .. "410054974700593138339226497249461751545728366702369745461014" .. "655997933798537483143786841806593422227898388722980000748404" .. "719" ) local b2 = bint.frominteger( 2 ) local b17 = bint.frominteger( 17 ) local kMod17 = bint.tointeger( k % b17 ) 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. =={{header\|Mathematica}}/{{header\|Wolfram Language}}== {{trans\|Julia}} <syntaxhighlight lang="Mathematica"> (Define the Tupper's self-referential formula function) tupperMat[k_] := Table[1 - Mod[Floor[Mod[Floor[y/17] 2^(-17 Floor[x] - Mod[y, 17]), 2]], 2], {y, k, k + 16}, {x, 0, 105}] (Define the constant k) k = 960939379918958884971672962127852754715004339660129306651505519271\ 7028023952664246896428421743507181212671537827706233559932372808741443\ 0789132596394133772348785773574982392662971551717371699516523289053822\ 1612403238855866184013235585136048828693337902491454229288667081096184\ 4960917051834540678277315517054053816273809676025656250169814820834187\ 8316384911559022561000365235137034387446184837873723819822484986346503\ 3159410054974700593138339226497249461751545728366702369745461014655997\ 933798537483143786841806593422227898388722980000748404719; (Display the heatmap) ArrayPlot[Map[Reverse, tupperMat[k]], AspectRatio -> 1/6, Frame -> False, ImageSize -> Large, ColorRules -> {0 -> Black, 1 -> White}] </syntaxhighlight> {{out}} [[File:Tupper's self-referential formula.png\|thumb]] =={{header\|Nim}}== {{trans\|python}} {{libheader\|integers}} <syntaxhighlight lang="Nim">import std/[algorithm, sugar] import integers let k = newInteger("960939379918958884971672962127852754715004339660129306651505519" & "271702802395266424689642842174350718121267153782770623355993237" & "280874144307891325963941337723487857735749823926629715517173716" & "995165232890538221612403238855866184013235585136048828693337902" & "491454229288667081096184496091705183454067827731551705405381627" & "380967602565625016981482083418783163849115590225610003652351370" & "343874461848378737238198224849863465033159410054974700593138339" & "226497249461751545728366702369745461014655997933798537483143786" & "841806593422227898388722980000748404719") proc tuppersFormula(x, y: Integer): bool = ## Return true if point at (x, y) (x and y both start at 0) ## is to be drawn black, False otherwise result = (k + y) div 17 div 2^(17 * x + y mod 17) mod 2 != 0 let values = collect: for y in 0..16: collect: for x in 0..105: tuppersFormula(x, y) let f = open("tupper.txt", fmWrite) for row in values: for value in reversed(row): # x = 0 starts at the left so reverse the whole row. f.write if value: "\u2588" else: " " f.write '\n' f.close() </syntaxhighlight> {{out}} Same as Python. =={{header\|Phix}}== {{libheader\|Phix/pGUI}} You can run this online [http://phix.x10.mx/p2js/tupper.htm here]. The pixel/canvas/window sizes are a little off compared to desktop/Phix both initially and when resizing, the latter also goes quite a bit smaller, hopefully all that'll be fixed in js when the new gui that I'm working on right now finally gets shipped. You can run this online [http://phix.x10.mx/p2js/tupper.htm here]. The pixel/canvas/window sizes are a little off compared to desktop/Phix both initially and when resizing, the latter also goes quite a bit smaller (see below), hopefully all that'll be fixed in js when the new gui that I'm working on right now finally gets shipped. <!--<syntaxhighlight lang="phix">(phixonline)--> <span style="color: #000080;font-style:italic;">-- demo\rosetta\Tupper.exw</span> Line 113 ⟶ 555: 655_997_933_798_537_483_143_786_841_806_593_422_227_898_388_722_980_000_748_404_719"""</span> <span style="color: #004080;">mpz</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #000000;">kstr</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"out"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"_\n"</span><span style="color: #0000FF;">)),</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span> <span style="color: #004080;">mpfr</span> <span style="color: #000000;">half</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">two</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> ~~<span style="color: #0000FF;">{</span>~~<span style="color: #000000;">t3~~</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">}~~</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">~~mpfr_inits~~mpfr_init</span><span style="color: #0000FF;">(~~</span><span style="color: #000000;">2</span><span style="color: #0000FF;">~~)</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">bitmap</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">' '</span><span style="color: #0000FF;">,</span><span style="color: #000000;">106</span><span style="color: #0000FF;">),</span><span style="color: #000000;">17</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">17</span> <span style="color: #008080;">do</span> <span style="color: #7060A8;">mpz_add_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">t2r17</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">106</span> <span style="color: #008080;">do</span> <span style="color: #7060A8;">mpfr_si_pow_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t4t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">17</span><span style="color: #0000FF;"></span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">j</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">t2r17</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">~~mpfr_set_z~~mpfr_mul_z</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">mpfr_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t4</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">mpfr_fmod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">two</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">mpfr_floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t3</span><span style="color: #0000FF;">)</span> Line 139 ⟶ 580: <span style="color: #008080;">function</span> <span style="color: #000000;">redraw_cb</span><span style="color: #0000FF;">(</span><span style="color: #004080;">Ihandle</span> <span style="color: #000080;font-style:italic;">/canvas/</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">width</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">height</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupGetIntInt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"RASTERSIZE"</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">ms</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">max</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">width</span><span style="color: #0000FF;">-</span><span style="color: #000000;">109</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">107</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">((</span><span style="color: #000000;">height</span><span style="color: #0000FF;">-</span><span style="color: #000000;">19</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">18</span><span style="color: #0000FF;">))),</span> <span style="color: #000000;">mm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ms</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cx</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">width</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">cy</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">height</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> Line 159 ⟶ 600: <span style="color: #000000;">canvas</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupCanvas</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">Icallback</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"redraw_cb"</span><span style="color: #0000FF;">))</span> <span style="color: #000000;">dlg</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">IupDialog</span><span style="color: #0000FF;">(</span><span style="color: #000000;">canvas</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"RASTERSIZE=553x130, MINSIZE=231x76"</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">IupSetAttribute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dlg</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"TITLE"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"Tupper's self-referential formula"</span><span style="color: #0000FF;">)</span> Line 171 ⟶ 612: <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <!--</syntaxhighlight>--> {{out}} At its smallest size on desktop/Phix: [[File:PhixTupper.png\|center]] And the largest worth posting here, but it will go larger: [[File:PhixTupperLarge.png\|center]] =={{header\|Python}}== Original code programmed by the user halex [https://stackoverflow.com/questions/29805197/imprecise-floats-in-tuppers-self-referential-formula] <syntaxhighlight lang="python">#!/usr/bin/python import codecs import os def tuppers_formula(x, y): """Return True if point (x, y) (x and y both start at 0) is to be drawn black, False otherwise """ k = 960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995165232890538221612403238855866184013235585136048828693337902491454229288667081096184496091705183454067827731551705405381627380967602565625016981482083418783163849115590225610003652351370343874461848378737238198224849863465033159410054974700593138339226497249461751545728366702369745461014655997933798537483143786841806593422227898388722980000748404719 return ((k + y)//17//2(17int(x) + int(y)%17))%2 > 0.5 with codecs.open("tupper.txt", "w", "utf-8") as f: values = [[tuppers_formula(x, y) for x in range(106)] for y in range(17)] for row in values: for value in row[::-1]: # x = 0 starts at the left so reverse the whole row if value: f.write("\u2588") # Write a block else: f.write(" ") f.write(os.linesep)</syntaxhighlight> {{out}} The result is the file tupper.txt with the content: <pre style="font-size: .75em;"> █ █ █ ██ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ ██ █ █ █ █ █ █ ██ ████ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ ██ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ ██ ███ █ █ █ █ ███ ███ █ ███ ███ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ ██ ███ █ █ █ ██ █ ████ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ ███ ███ █ ███ </pre> =={{header\|Rust}}== <syntaxhighlight lang="rust">use num::bigint::BigInt; use num::{FromPrimitive, pow}; use std::primitive::bool; /// Tupper function value maxtrix for graphic fn tuppermat(kconst: BigInt) -> Vec<[bool; 106]> { let mut tmatrix = vec![[true; 106]; 17]; let bigone: BigInt = BigInt::from_u32(1).unwrap(); let bigtwo: BigInt = BigInt::from_u32(2).unwrap(); for i in 0..106 { for j in 0..17 { let y: BigInt = kconst.clone() + j; let mut a: BigInt = y.clone() / 17; let mut b: BigInt = y.clone() % 17; b += i * 17; b = pow(bigtwo.clone(), b.try_into().unwrap()); a /= b; a %= 2; tmatrix[j][105 - i] = a == bigone; } } return tmatrix } fn main() { let k: BigInt = BigInt::parse_bytes(b"960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995165232890538221612403238855866184013235585136048828693337902491454229288667081096184496091705183454067827731551705405381627380967602565625016981482083418783163849115590225610003652351370343874461848378737238198224849863465033159410054974700593138339226497249461751545728366702369745461014655997933798537483143786841806593422227898388722980000748404719", 10).unwrap(); let bmap = tuppermat(k); for line in bmap.iter() { for c in line.iter() { if *c { print!("\u{2588}"); } else { print!(" "); } } println!() } } </syntaxhighlight>{{out}} <pre> █ █ █ ██ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ ██ █ █ █ █ █ █ ██ ████ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ █ █ █ ██ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ ██ ███ █ █ █ █ ███ ███ █ ███ ███ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ██ █ █ █ █ █ ██ ███ █ █ █ ██ █ ████ ████ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ █ █ █ █ █ █ █ █ █ █ █ █ █ ███ █ ███ ███ █ ███ </pre> =={{header\|Wren}}== Line 177 ⟶ 731: {{libheader\|Wren-big}} {{libheader\|Wren-iterate}} {{libheader\|Go-fonts}} This works albeit rather slowly, taking almost 1.5 minutes to calculate the points to be plotted. The culprit here is BigRat which is written entirely in Wren and always uses maximum precision. Unfortunately, we can't use GMP in a DOME application which would be much faster than this. <syntaxhighlight lang="~~ecmascript~~wren">import "dome" for Window import "graphics" for Canvas, Color, Font import "./plot" for Axes import "./big" for BigRat Line 222 ⟶ 777: Window.resize(840, 260) Canvas.cls(Color.white) Font.load("Go-Regular9", "Go-Regular.ttf", 9) Canvas.font = "Go-Regular9" var axes = Axes.new(100, 200, 660, 180, -10..110, -1..17) axes.draw(Color.black, 2) Line 228 ⟶ 785: axes.mark(xMarks, yMarks, Color.black, 2) axes.label(xMarks, yMarks, Color.black, 2, Color.black) axes.plot(Pts, Color.black, "■█") // uses character ~~0x25A0~~0x2588 }