Data update
This commit is contained in:
Ingy döt Net
parent
81fd053722
commit
52a6ef48dd
10248 changed files with 63654 additions and 6775 deletions
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@ -1,72 +1,76 @@
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with Ada.Text_IO;
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with Ada.Integer_Text_IO;
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with Ada.Text_IO; with Ada.Integer_Text_IO;
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with Ada.Strings.Fixed;
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procedure Totient is
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function Totient (N : in Integer) return Integer is
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Tot : Integer := N;
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I : Integer;
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N2 : Integer := N;
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begin
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I := 2;
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while I * I <= N2 loop
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if N2 mod I = 0 then
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while N2 mod I = 0 loop
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N2 := N2 / I;
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end loop;
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Tot := Tot - Tot / I;
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end if;
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function Totient (N : in Integer) return Integer is
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Tot : Integer := N;
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I : Integer;
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N2 : Integer := N;
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begin
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I := 2;
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while I * I <= N2 loop
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if N2 mod I = 0 then
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while N2 mod I = 0 loop
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N2 := N2 / I;
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end loop;
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Tot := Tot - Tot / I;
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end if;
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if I = 2 then
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I := 1;
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end if;
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I := I + 2;
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end loop;
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if I = 2 then
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I := 1;
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end if;
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I := I + 2;
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end loop;
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if N2 > 1 then
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Tot := Tot - Tot / N2;
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end if;
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if N2 > 1 then
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Tot := Tot - Tot / N2;
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end if;
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return Tot;
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end Totient;
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return Tot;
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end Totient;
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Count : Integer := 0;
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Tot : Integer;
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Placeholder : String := " n Phi Is_Prime";
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Image_N : String renames Placeholder ( 1 .. 3);
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Image_Phi : String renames Placeholder ( 6 .. 8);
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Image_Prime : String renames Placeholder (11 .. 17);
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use Ada.Text_IO;
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use Ada.Integer_Text_IO;
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Count : Integer := 0;
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Tot : Integer;
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Placeholder : String := " n Phi Is_Prime";
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Image_N : String renames Placeholder ( 1 .. 3);
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Image_Phi : String renames Placeholder ( 6 .. 8);
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Image_Prime : String renames Placeholder (11 .. Placeholder'Last);
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use Ada.Text_IO;
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use Ada.Integer_Text_IO;
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Last : constant := 25;
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begin
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Put_Line (Placeholder);
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Put_Line (Placeholder);
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for N in 1 .. 25 loop
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Tot := Totient (N);
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for N in 1 .. Last loop
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Tot := Totient (N);
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if N - 1 = Tot then
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Count := Count + 1;
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end if;
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Put (Image_N, N);
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Put (Image_Phi, Tot);
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Image_Prime := (if N - 1 = Tot then " True" else " False");
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Put_Line (Placeholder);
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end loop;
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New_Line;
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if N - 1 = Tot then
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Count := Count + 1;
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end if;
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Put (Image_N, N);
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Put (Image_Phi, Tot);
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Image_Prime := Ada.Strings.Fixed.Tail
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(Source => (if N - 1 = Tot then True'Image else False'Image),
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Count => Image_Prime'Length);
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Put_Line (Placeholder);
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end loop;
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New_Line;
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Put_Line ("Number of primes up to " & Integer'(25)'Image &" =" & Count'Image);
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Put_Line ("Number of primes up to " & Last'Image &" =" & Count'Image);
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for N in 26 .. 100_000 loop
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Tot := Totient (N);
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for N in Last + 1 .. 100_000 loop
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Tot := Totient (N);
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if Tot = N - 1 then
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Count := Count + 1;
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end if;
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if Tot = N - 1 then
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Count := Count + 1;
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end if;
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if N = 100 or N = 1_000 or N mod 10_000 = 0 then
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Put_Line ("Number of primes up to " & N'Image & " =" & Count'Image);
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end if;
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end loop;
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if N = 100 or N = 1_000 or N mod 10_000 = 0 then
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Put_Line ("Number of primes up to " & N'Image & " =" & Count'Image);
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end if;
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end loop;
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end Totient;
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37
Task/Totient-function/Phix/totient-function-1.phix
Normal file
37
Task/Totient-function/Phix/totient-function-1.phix
Normal file
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@ -0,0 +1,37 @@
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with javascript_semantics
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atom t0 = time()
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function totient(integer n)
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integer tot = n, i = 2
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while i*i<=n do
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if mod(n,i)=0 then
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while true do
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n /= i
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if mod(n,i)!=0 then exit end if
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end while
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tot -= tot/i
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end if
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i += iff(i=2?1:2)
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end while
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if n>1 then
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tot -= tot/n
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end if
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return tot
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end function
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printf(1," n phi prime\n")
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printf(1," --------------\n")
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for n=1 to 25 do
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integer tot = totient(n)
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bool prime = (n-1=tot)
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printf(1,"%2d %2d %t\n",{n,tot,prime})
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end for
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printf(1,"\n")
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integer count = 0
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for n=1 to 1e6 do
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-- count += (totient(n)=n-1)
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count += (phi(n)=n-1)
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if find(n,{25,1e2,1e3,1e4,1e5,1e6,1e7}) then
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printf(1,"Number of primes up to %d = %d\n",{n,count})
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end if
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end for
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?elapsed(time()-t0)
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38
Task/Totient-function/Phix/totient-function-2.phix
Normal file
38
Task/Totient-function/Phix/totient-function-2.phix
Normal file
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@ -0,0 +1,38 @@
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with javascript_semantics
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atom t0 = time()
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constant maxphi = 1e7
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sequence s_phi
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procedure computePhi()
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s_phi = tagset(maxphi)
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for i=2 to maxphi do
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if s_phi[i]=i then
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for j=i to maxphi by i do
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s_phi[j] -= s_phi[j] / i;
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end for
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end if
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end for
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end procedure
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function countPrimes(int lo, hi)
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int count = 0;
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for i=lo to hi do
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if s_phi[i] == i-1 then
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count += 1
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end if
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end for
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return count;
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end function
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computePhi()
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printf(1," n phi prime\n")
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printf(1," --------------\n")
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for n=1 to 25 do
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integer tot = s_phi[n]
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bool prime = (n-1=tot)
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printf(1,"%2d %2d %t\n",{n,tot,prime})
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end for
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printf(1,"\n")
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for n in {25,1e2,1e3,1e4,1e5,1e6,1e7} do
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printf(1,"Number of primes up to %d = %d\n",{n,countPrimes(1,n)})
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end for
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?elapsed(time()-t0)
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@ -1,37 +0,0 @@
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(phixonline)-->
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<span style="color: #008080;">function</span> <span style="color: #000000;">totient</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">2</span>
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<span style="color: #008080;">while</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">*</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
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<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">n</span> <span style="color: #0000FF;">/=</span> <span style="color: #000000;">i</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #000000;">tot</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">tot</span><span style="color: #0000FF;">/</span><span style="color: #000000;">i</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;">i</span> <span style="color: #0000FF;">+=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</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>
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<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
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<span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
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<span style="color: #000000;">tot</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">tot</span><span style="color: #0000FF;">/</span><span style="color: #000000;">n</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">tot</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</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;">" n phi prime\n"</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;">" --------------\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">25</span> <span style="color: #008080;">do</span>
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<span style="color: #004080;">integer</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">totient</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">prime</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">=</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">)</span>
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">prime</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">isp</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prime</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"true"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">"false"</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;">"%2d %2d %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">tot</span><span style="color: #0000FF;">,</span><span style="color: #000000;">isp</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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<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 primes up to 25 = %d\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">26</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100000</span> <span style="color: #008080;">do</span>
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<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">totient</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10000</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100000</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</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;">"Number of primes up to %-6d = %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">})</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">if</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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136
Task/Totient-function/REXX/totient-function-3.rexx
Normal file
136
Task/Totient-function/REXX/totient-function-3.rexx
Normal file
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@ -0,0 +1,136 @@
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include Settings
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say version; say 'Totient function (Phi)'; say
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call Time('r')
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numeric digits 10; cycl. = 0; m = 7
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call First25A
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call PrimeCountA m
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say Format(Time('e'),,3) 'seconds'; say
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call Time('r')
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call Totients 10**m
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call First25B
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call PrimeCountB m
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say Format(Time('e'),,3) 'seconds'
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exit
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First25A:
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procedure
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say 'A: using calls to an optimized Totient()'; say
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = Totient(i)
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16); say
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say 'Found' Right(n,6) 'primes <' Right(25,8)
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return
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PrimeCountA:
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procedure
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arg x
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n = 0; d = 1
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do i = 1
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p = Totient(i)
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'primes <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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First25B:
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procedure expose toti.
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say 'B: generate and save all Totients, and use the stored values'; say
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say ' N Phi(N) Prime?'
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say Copies('-',16)
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n = 0
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do i = 1 to 25
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p = toti.totient.i
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if p = i-1 then do
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n = n+1; pr = 'Yes'
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end
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else
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pr = ''
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say Right(i,2) Right(p,6) pr
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end
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say Copies('-',16)
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say
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say 'Found' Right(n,6) 'primes <' Right(25,8)
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return
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PrimeCountB:
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procedure expose toti.
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arg x
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n = 0; d = 1
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do i = 1
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p = toti.totient.i
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if p = i-1 then
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n = n+1
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e = Xpon(i)
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if e > d then do
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say 'Found' Right(n,6) 'primes <' Right(10**e,8)
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if e > x-1 then
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leave i
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d = e
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end
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end
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say
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return
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Totient:
|
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/* Euler's totient function */
|
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procedure expose toti.
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arg x
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/* Fast values */
|
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if x < 3 then
|
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return 1
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||||
if x < 5 then
|
||||
return 2
|
||||
/* Multiplicative property using Factors */
|
||||
f = Factors(x)+1; fact.factor.f = 0
|
||||
y = 1; v = fact.factor.1; n = 1
|
||||
do i = 2 to f
|
||||
a = fact.factor.i
|
||||
if a = v then
|
||||
n = n+1
|
||||
else do
|
||||
y = y*v**(n-1)*(v-1)
|
||||
v = a; n = 1
|
||||
end
|
||||
end
|
||||
return y
|
||||
|
||||
Totients:
|
||||
/* Euler's totient numbers */
|
||||
procedure expose toti.
|
||||
arg x
|
||||
/* Recurring sequence */
|
||||
do i = 1 to x
|
||||
toti.totient.i = i
|
||||
end
|
||||
do i = 2 to x
|
||||
if toti.totient.i < i then
|
||||
iterate i
|
||||
do j = i by i to x
|
||||
toti.totient.j = toti.totient.j-toti.totient.j/i
|
||||
end
|
||||
end
|
||||
toti.0 = x
|
||||
return x
|
||||
|
||||
include Functions
|
||||
include Numbers
|
||||
include Abend
|
||||
Loading…
Add table
Add a link
Reference in a new issue