Data update
This commit is contained in:
Ingy döt Net
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7735 changed files with 38060 additions and 199180 deletions
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@ -1,112 +0,0 @@
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with Ada.Command_Line;
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with Ada.Text_IO;
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with GNU_Multiple_Precision.Big_Integers;
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with GNU_Multiple_Precision.Big_Rationals;
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use GNU_Multiple_Precision;
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procedure Pi_Digits is
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type Int is mod 2 ** 64;
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package Int_To_Big is new Big_Integers.Modular_Conversions (Int);
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-- constants
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Zero : constant Big_Integer := Int_To_Big.To_Big_Integer (0);
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One : constant Big_Integer := Int_To_Big.To_Big_Integer (1);
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Two : constant Big_Integer := Int_To_Big.To_Big_Integer (2);
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Three : constant Big_Integer := Int_To_Big.To_Big_Integer (3);
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Four : constant Big_Integer := Int_To_Big.To_Big_Integer (4);
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Ten : constant Big_Integer := Int_To_Big.To_Big_Integer (10);
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-- type LFT = (Integer, Integer, Integer, Integer
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type LFT is record
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Q, R, S, T : Big_Integer;
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end record;
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-- extr :: LFT -> Integer -> Rational
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function Extr (T : LFT; X : Big_Integer) return Big_Rational is
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use Big_Integers;
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Result : Big_Rational;
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begin
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-- extr (q,r,s,t) x = ((fromInteger q) * x + (fromInteger r)) /
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-- ((fromInteger s) * x + (fromInteger t))
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Big_Rationals.Set_Numerator (Item => Result,
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New_Value => T.Q * X + T.R,
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Canonicalize => False);
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Big_Rationals.Set_Denominator (Item => Result,
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New_Value => T.S * X + T.T);
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return Result;
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end Extr;
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-- unit :: LFT
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function Unit return LFT is
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begin
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-- unit = (1,0,0,1)
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return LFT'(Q => One, R => Zero, S => Zero, T => One);
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end Unit;
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-- comp :: LFT -> LFT -> LFT
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function Comp (T1, T2 : LFT) return LFT is
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use Big_Integers;
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begin
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-- comp (q,r,s,t) (u,v,w,x) = (q*u+r*w,q*v+r*x,s*u+t*w,s*v+t*x)
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return LFT'(Q => T1.Q * T2.Q + T1.R * T2.S,
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R => T1.Q * T2.R + T1.R * T2.T,
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S => T1.S * T2.Q + T1.T * T2.S,
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T => T1.S * T2.R + T1.T * T2.T);
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end Comp;
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-- lfts = [(k, 4*k+2, 0, 2*k+1) | k<-[1..]
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K : Big_Integer := Zero;
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function LFTS return LFT is
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use Big_Integers;
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begin
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K := K + One;
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return LFT'(Q => K,
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R => Four * K + Two,
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S => Zero,
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T => Two * K + One);
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end LFTS;
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-- next z = floor (extr z 3)
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function Next (T : LFT) return Big_Integer is
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begin
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return Big_Rationals.To_Big_Integer (Extr (T, Three));
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end Next;
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-- safe z n = (n == floor (extr z 4)
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function Safe (T : LFT; N : Big_Integer) return Boolean is
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begin
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return N = Big_Rationals.To_Big_Integer (Extr (T, Four));
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end Safe;
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-- prod z n = comp (10, -10*n, 0, 1)
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function Prod (T : LFT; N : Big_Integer) return LFT is
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use Big_Integers;
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begin
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return Comp (LFT'(Q => Ten, R => -Ten * N, S => Zero, T => One), T);
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end Prod;
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procedure Print_Pi (Digit_Count : Positive) is
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Z : LFT := Unit;
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Y : Big_Integer;
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Count : Natural := 0;
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begin
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loop
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Y := Next (Z);
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if Safe (Z, Y) then
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Count := Count + 1;
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Ada.Text_IO.Put (Big_Integers.Image (Y));
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exit when Count >= Digit_Count;
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Z := Prod (Z, Y);
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else
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Z := Comp (Z, LFTS);
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end if;
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end loop;
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end Print_Pi;
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N : Positive := 250;
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begin
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if Ada.Command_Line.Argument_Count = 1 then
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N := Positive'Value (Ada.Command_Line.Argument (1));
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end if;
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Print_Pi (N);
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end Pi_Digits;
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@ -9,7 +9,7 @@ d: 0
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dotWritten: false
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while [true][
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if? (n*t) > (4*q)+r-t [
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switch (n*t) > (4*q)+r-t [
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d: d+1
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prints n
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unless dotWritten [
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@ -23,8 +23,7 @@ while [true][
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n: ((10*(r + 3*q)) / t) - 10*n
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q: q*10
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r: nr
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]
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else [
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][
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nr: (r + 2*q) * l
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nn: ((q*(2 + 7*k)) + r*l) / (t*l)
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q: q*k
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@ -1,57 +0,0 @@
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Function Get-Pi ( $Digits )
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{
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$Big = [bigint[]](0..10)
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$ndigits = 0
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$Output = ""
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$q = $t = $k = $Big[1]
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$r = $Big[0]
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$l = $n = $Big[3]
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# Calculate first digit
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$nr = ( $Big[2] * $q + $r ) * $l
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$nn = ( $q * ( $Big[7] * $k + $Big[2] ) + $r * $l ) / ( $t * $l )
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$q *= $k
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$t *= $l
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$l += $Big[2]
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$k = $k + $Big[1]
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$n = $nn
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$r = $nr
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$Output += [string]$n + '.'
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$ndigits++
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$nr = $Big[10] * ( $r - $n * $t )
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$n = ( ( $Big[10] * ( 3 * $q + $r ) ) / $t ) - 10 * $n
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$q *= $Big[10]
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$r = $nr
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While ( $ndigits -lt $Digits )
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{
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While ( $ndigits % 100 -ne 0 -or -not $Output )
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{
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If ( $Big[4] * $q + $r - $t -lt $n * $t )
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{
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$Output += [string]$n
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$ndigits++
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$nr = $Big[10] * ( $r - $n * $t )
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$n = ( ( $Big[10] * ( 3 * $q + $r ) ) / $t ) - 10 * $n
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$q *= $Big[10]
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$r = $nr
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}
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Else
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{
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$nr = ( $Big[2] * $q + $r ) * $l
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$nn = ( $q * ( $Big[7] * $k + $Big[2] ) + $r * $l ) / ( $t * $l )
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$q *= $k
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$t *= $l
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$l += $Big[2]
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$k = $k + $Big[1]
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$n = $nn
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$r = $nr
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}
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}
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$Output
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$Output = ""
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}
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}
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@ -1 +0,0 @@
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[math]::pi
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@ -1,2 +0,0 @@
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.Net digits of pi
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3.14159265358979
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@ -1,29 +1,36 @@
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/*REXX program spits out decimal digits of pi (one digit at a time) until Ctrl─Break.*/
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parse arg digs oFID . /*obtain optional argument from the CL.*/
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if digs=='' | digs=="," then digs= 1e6 /*Not specified? Then use the default.*/
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if oFID=='' | oFID=="," then oFID='PI_SPIT.OUT' /* " " " " " " */
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write= digs<0 /*if ODIGS is <0, also spit pi to file.*/
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numeric digits abs(digs) + 4 /*with bigger digs, spitting is slower.*/
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call time 'Reset' /*reset the wall─clock (elapsed) timer.*/
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signal on halt /*───► HALT when Ctrl─Break is pressed.*/
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spit= 0 /*the index of the spitted pi dec. digs*/
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pi=0; v=5; vv=v*v; g=239; gg=g*g; s= 16 /*assign some values to some variables.*/
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r= 4 /*calculate π with increasing accuracy */
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do n=1 by 2 until old=pi; old= pi /*just calculate pi with odd integers*/
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pi= pi + s / (n*v) - r / (n*g) /* ··· using John Machin's formula.*/
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s= -s; r= -r; v= v * vv; g= g * gg /*compute some variables for shortcuts.*/
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if n>3 then spit= spit + 1 /*maintain a lag for pi digits rounding*/
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if spit<4 then iterate /*Not enough digs yet? Then don't show*/
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$= substr(pi, spit-3, 1) /*lag behind the true pi calculation. */
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call charout , $ /*write the spitted digits to the term.*/
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if write then call charout oFID, $ /* " " " " " a file?*/
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end /*n*/
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-- 12 Sep 2025
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include Setting
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signal on halt
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arg digs
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if digs = '' then
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digs=1000
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$= substr(pi, spit - 2); L= length($) - 4 /*handle any residual decimal digits. */
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if L>0 then do /*if any residual digits, then show 'em*/
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call charout , substr($, 1, L) /*write to term. */
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if write then call charout oFID, substr($, 1, L) /* " " file? */
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end
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say /*stick a fork in it, we're all done. */
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exit: say; say n%2+1 'iterations took' format(time("Elapsed"),,2) 'seconds.'; exit 0
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halt: say; say 'PI_SPIT halted via use of Ctrl─Break.'; signal exit /*show iterations.*/
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say 'PI - Machin formula'
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say version
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say
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numeric digits digs+4
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spit=0; pie=0; v=5; vv=v*v; g=239; gg=g*g; s=16; r=4
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do n = 1 by 2 until old = pie
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old=pie; pie=pie+s/(n*v)-r/(n*g)
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s=-s; r=-r; v=v*vv; g=g*gg
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if n > 3 then
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spit=spit+1
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if spit < 4 then
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iterate
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dd=SubStr(pie,spit-3,1); call CharOut ,dd
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end
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dd=SubStr(pie,spit-2); l=Length(dd)-4
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if l>0 then
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call CharOut ,SubStr(dd,1,l)
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say
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say 'Specified' digs 'digits exhausted.'
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call Timer
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exit
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Halt:
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say
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say 'Halted because of Ctrl-Break.'
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call Timer
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exit
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include Math
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@ -1,32 +1,40 @@
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/*REXX program spits out decimal digits of pi (one digit at a time) until Ctrl-Break.*/
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signal on halt /*───► HALT when Ctrl─Break is pressed.*/
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parse arg digs oFID . /*obtain optional argument from the CL.*/
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if digs=='' | digs=="," then digs= 300 /*Not specified? Then use the default.*/
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if oFID=='' | oFID=="," then oFID='PI_SPIT2.OUT' /* " " " " " " */
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numeric digits digs /*with bigger digs, spitting is slower.*/
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q=1; r=0; t=1; k=1; n=3; L=3; z=0 /*define some REXX variables. */
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dot=1 /*DOT≡a flag when a dot in pi is shown.*/
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do until z==digs; qq= q+q /* qq is a fast version of: q*2 */
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tn= t*n /* t*n is used twice (below). */
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if qq+qq+r-t < tn then do; z= z+1 /* qq+qq is faster than qq*2 */
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call charout , n
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call charout oFID, n
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if dot then do; dot=0; call charout , .
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call charout oFID, .
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end
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nr= (r - tn) * 10
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n = ((( (qq+q+r) * 10) / t) - n*10) %1
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q = q*10
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end
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else do; nr= (qq+r) * L
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tL= t*L
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n = (q * (k*7 + 2) + r*L) / tL %1
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q = q*k
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t = tL
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L = L+2
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k = k+1
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end /* %1≡fast way doing TRUNC of a number.*/
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r=nr
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end /*forever*/
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exit /*stick a fork in it, we're all done. */
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halt: say; say 'PI_SPIT2 halted via use of Ctrl-Break.'; exit
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-- 12 Sep 2025
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include Setting
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signal on halt
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arg digs
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if digs = '' then
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digs=1000
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say 'PI - Gibbons Spigot'
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say version
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say
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numeric digits digs+4
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q=1; r=0; t=1; k=1; n=3; l=3; z=0; dot=1
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do until z = digs
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qq=q+q; tn=t*n
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if qq+qq+r-t < tn then do
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z=z+1; call CharOut ,n
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if dot then do
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dot=0; call CharOut ,.
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end
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nr=(r-tn)*10; n=((((qq+q+r)*10)/t)-n*10)%1
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q=q*10
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end
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else do
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nr=(qq+r)*l; tl=t*l; n=(q*(k*7+2)+r*l)/tl%1
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q=q*k; t=tl; l=l+2; k=k+1
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end
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r=nr
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end
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say
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say 'Specified' digs 'digits exhausted.'
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call Timer
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exit
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Halt:
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say
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say 'Halted because of Ctrl-Break.'
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call Timer
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exit
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include Math
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