Data update
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Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,162 +0,0 @@
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program SquareFree;
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{$IFDEF FPC}
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{$MODE DELPHI}
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{$ELSE}
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{$APPTYPE CONSOLE}
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{$ENDIF}
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const
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//needs 1e10 Byte = 10 Gb maybe someone got 128 Gb :-) nearly linear time
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BigLimit = 10*1000*1000*1000;
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TRILLION = 1000*1000*1000*1000;
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primeLmt = trunc(sqrt(TRILLION+150));
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var
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primes : array of byte;
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sieve : array of byte;
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procedure initPrimes;
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var
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i,lmt,dp :NativeInt;
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Begin
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setlength(primes,80000);
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setlength(sieve,primeLmt);
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sieve[0] := 1;
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sieve[1] := 1;
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i := 2;
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repeat
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IF sieve[i] = 0 then
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Begin
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lmt:= i*i;
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while lmt<primeLmt do
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Begin
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sieve[lmt] := 1;
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inc(lmt,i);
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end;
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end;
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inc(i);
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until i*i>=primeLmt;
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//extract difference of primes
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i := 0;
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lmt := 0;
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dp := 0;
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repeat
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IF sieve[i] = 0 then
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Begin
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primes[lmt] := dp;
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dp := 0;
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inc(lmt);
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end;
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inc(dp);
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inc(i);
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until i >primeLmt;
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setlength(sieve,0);
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setlength(Primes,lmt+1);
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end;
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procedure SieveSquares;
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//mark all powers >=2 of prime => all powers = 2 is sufficient
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var
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pSieve : pByte;
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i,sq,k,prime : NativeInt;
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Begin
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pSieve := @sieve[0];
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prime := 0;
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For i := 0 to High(primes) do
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Begin
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prime := prime+primes[i];
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sq := prime*prime;
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k := sq;
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if sq > BigLimit then
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break;
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repeat
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pSieve[k] := 1;
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inc(k,sq);
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until k> BigLimit;
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end;
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end;
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procedure Count_x10;
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var
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pSieve : pByte;
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i,lmt,cnt: NativeInt;
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begin
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writeln(' square free count');
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writeln('[1 to limit]');
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pSieve := @sieve[0];
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lmt := 10;
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i := 1;
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cnt := 0;
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repeat
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while i <= lmt do
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Begin
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inc(cnt,ORD(pSieve[i] = 0));
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inc(i);
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end;
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writeln(lmt:12,' ',cnt:12);
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IF lmt >= BigLimit then
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BREAK;
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lmt := lmt*10;
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IF lmt >BigLimit then
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lmt := BigLimit;
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until false;
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end;
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function TestSquarefree(N:Uint64):boolean;
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var
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i,prime,sq : NativeUint;
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Begin
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prime := 0;
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result := false;
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For i := 0 to High(primes) do
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Begin
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prime := prime+primes[i];
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sq := sqr(prime);
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IF sq> N then
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BREAK;
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IF N MOD sq = 0 then
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EXIT;
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end;
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result := true;
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end;
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var
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i,k : NativeInt;
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Begin
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InitPrimes;
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setlength(sieve,BigLimit+1);
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SieveSquares;
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writeln('Square free numbers from 1 to 145');
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k := 80 div 4;
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For i := 1 to 145 do
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If sieve[i] = 0 then
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Begin
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write(i:4);
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dec(k);
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IF k = 0 then
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Begin
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writeln;
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k := 80 div 4;
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end;
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end;
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writeln;writeln;
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writeln('Square free numbers from ',TRILLION,' to ',TRILLION+145);
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k := 4;
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For i := TRILLION to TRILLION+145 do
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Begin
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if TestSquarefree(i) then
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Begin
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write(i:20);
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dec(k);
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IF k = 0 then
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Begin
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writeln;
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k := 4;
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end;
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end;
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end;
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writeln;writeln;
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Count_x10;
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end.
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@ -1,29 +1,27 @@
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(phixonline)-->
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<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
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<span style="color: #008080;">function</span> <span style="color: #000000;">square_frees</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">finish</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">maxprime</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">get_maxprime</span><span style="color: #0000FF;">(</span><span style="color: #000000;">finish</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">start</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">finish</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">square_free</span><span style="color: #0000FF;">(</span><span style="color: #000000;">start</span><span style="color: #0000FF;">,</span><span style="color: #000000;">maxprime</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">res</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">start</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #000000;">start</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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with javascript_semantics
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function square_frees(atom start, finish)
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sequence res = {}
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integer maxprime = get_maxprime(finish)
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while start<=finish do
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if square_free(start,maxprime) then
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res &= start
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end if
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start += 1
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end while
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return res
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end function
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<span style="color: #008080;">procedure</span> <span style="color: #000000;">show_range</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">finish</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">jb</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">fmt</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">square_frees</span><span style="color: #0000FF;">(</span><span style="color: #000000;">start</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">finish</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"There are %d square-free integers from %,d to %,d:\n%s\n"</span><span style="color: #0000FF;">,</span>
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<span style="color: #0000FF;">{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #000000;">start</span><span style="color: #0000FF;">,</span><span style="color: #000000;">finish</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join_by</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">jb</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">fmt</span><span style="color: #0000FF;">)})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
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<span style="color: #000000;">show_range</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">145</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%4d"</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">show_range</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1e12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1e12</span><span style="color: #0000FF;">+</span><span style="color: #000000;">145</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%14d"</span><span style="color: #0000FF;">)</span>
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procedure show_range(atom start, finish, integer jb, string fmt)
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sequence res = square_frees(start, finish)
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printf(1,"There are %d square-free integers from %,d to %,d:\n%s\n",
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{length(res),start,finish,join_by(res,1,jb,"","\n",fmt)})
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end procedure
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show_range(1,145,20,"%4d")
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show_range(1e12,1e12+145,5,"%14d")
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nNumber of square-free integers:\n"</span><span style="color: #0000FF;">);</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">6</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">lim</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">len</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">square_frees</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">))</span>
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<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" from %,d to %,d = %,d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">lim</span><span style="color: #0000FF;">,</span><span style="color: #000000;">len</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
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<!--
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printf(1,"\nNumber of square-free integers:\n");
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for i=2 to 6 do
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integer lim = power(10,i),
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len = length(square_frees(1,lim))
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printf(1," from %,d to %,d = %,d\n", {1,lim,len})
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end for
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@ -1,6 +1,7 @@
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include Settings
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-- 24 Aug 2025
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include Setting
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say 'SQUARE-FREE INTEGERS - 6 Mar 2025'
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say 'SQUARE-FREE INTEGERS'
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say version
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say
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numeric digits 5
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@ -74,7 +75,4 @@ say '--------------'
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say Format(Time('e'),,3) 'seconds'
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return
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include Numbers
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include Sequences
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include Functions
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include Abend
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include Math
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@ -1,6 +1,7 @@
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Sqf ← ≠0/↧◿⊸(×.↘2⇡+1⌊√)
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⟜⧻▽⊸≡Sqf +1⇡145
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⟜⧻▽⊸≡Sqf +1e12+1⇡145
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# Find all squares and their multiples, and mask them out.
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▽:⇡⟜(¬±°⊚/◇⊂≡(□×⇡+1)⌊÷:⟜(.×.↘2⇡√.))1000000
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⊙◌≡(/+<)⇌[⍥(×10.)4 100]¤
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Sqf ← ≠0/↧◿⊸(˙×↘2⇡+1⌊√)
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⧻⟜▽⊸≡Sqf +1⇡145
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⧻⟜▽⊸≡Sqf +1e12+1⇡145
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# Find all squares and their multiples, mask them out.
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⍉▽>0/↧⊸⊞◿⊃(˙ט▽⟜=⟜(⊣°/×)↘2⇡⌊+1√|↘1⇡)2000000
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# Count them.
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≡(⧻▽⊸≤)⊢[⍥⊸×₁₀ 5 100]¤
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