Data update
This commit is contained in:
Ingy döt Net
parent
5150844a7d
commit
4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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@ -1,6 +0,0 @@
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generic
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type Scalar is digits <>;
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with function A (N : in Natural) return Natural;
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with function B (N : in Positive) return Natural;
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function Continued_Fraction (Steps : in Natural) return Scalar;
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@ -1,11 +0,0 @@
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function Continued_Fraction (Steps : in Natural) return Scalar is
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function A (N : in Natural) return Scalar is (Scalar (Natural'(A (N))));
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function B (N : in Positive) return Scalar is (Scalar (Natural'(B (N))));
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Fraction : Scalar := 0.0;
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begin
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for N in reverse Natural range 1 .. Steps loop
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Fraction := B (N) / (A (N) + Fraction);
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end loop;
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return A (0) + Fraction;
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end Continued_Fraction;
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@ -1,35 +0,0 @@
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with Ada.Text_IO;
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with Continued_Fraction;
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procedure Test_Continued_Fractions is
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type Scalar is digits 15;
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package Square_Root_Of_2 is
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function A (N : in Natural) return Natural is (if N = 0 then 1 else 2);
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function B (N : in Positive) return Natural is (1);
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function Estimate is new Continued_Fraction (Scalar, A, B);
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end Square_Root_Of_2;
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package Napiers_Constant is
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function A (N : in Natural) return Natural is (if N = 0 then 2 else N);
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function B (N : in Positive) return Natural is (if N = 1 then 1 else N-1);
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function Estimate is new Continued_Fraction (Scalar, A, B);
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end Napiers_Constant;
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package Pi is
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function A (N : in Natural) return Natural is (if N = 0 then 3 else 6);
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function B (N : in Positive) return Natural is ((2 * N - 1) ** 2);
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function Estimate is new Continued_Fraction (Scalar, A, B);
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end Pi;
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package Scalar_Text_IO is new Ada.Text_IO.Float_IO (Scalar);
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use Ada.Text_IO, Scalar_Text_IO;
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begin
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Put (Square_Root_Of_2.Estimate (200), Exp => 0); New_Line;
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Put (Napiers_Constant.Estimate (200), Exp => 0); New_Line;
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Put (Pi.Estimate (10000), Exp => 0); New_Line;
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end Test_Continued_Fractions;
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@ -1,6 +0,0 @@
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generic
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type Scalar is digits <>;
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with function A (N : in Natural) return Natural;
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with function B (N : in Positive) return Natural;
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function Continued_Fraction_Ada95 (Steps : in Natural) return Scalar;
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@ -1,18 +0,0 @@
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function Continued_Fraction_Ada95 (Steps : in Natural) return Scalar is
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function A (N : in Natural) return Scalar is
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begin
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return Scalar (Natural'(A (N)));
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end A;
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function B (N : in Positive) return Scalar is
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begin
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return Scalar (Natural'(B (N)));
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end B;
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Fraction : Scalar := 0.0;
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begin
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for N in reverse Natural range 1 .. Steps loop
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Fraction := B (N) / (A (N) + Fraction);
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end loop;
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return A (0) + Fraction;
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end Continued_Fraction_Ada95;
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@ -1,87 +0,0 @@
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with Ada.Text_IO;
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with Continued_Fraction_Ada95;
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procedure Test_Continued_Fractions_Ada95 is
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type Scalar is digits 15;
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package Square_Root_Of_2 is
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function A (N : in Natural) return Natural;
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function B (N : in Positive) return Natural;
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function Estimate is new Continued_Fraction_Ada95 (Scalar, A, B);
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end Square_Root_Of_2;
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package body Square_Root_Of_2 is
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function A (N : in Natural) return Natural is
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begin
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if N = 0 then
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return 1;
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else
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return 2;
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end if;
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end A;
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function B (N : in Positive) return Natural is
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begin
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return 1;
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end B;
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end Square_Root_Of_2;
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package Napiers_Constant is
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function A (N : in Natural) return Natural;
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function B (N : in Positive) return Natural;
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function Estimate is new Continued_Fraction_Ada95 (Scalar, A, B);
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end Napiers_Constant;
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package body Napiers_Constant is
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function A (N : in Natural) return Natural is
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begin
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if N = 0 then
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return 2;
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else
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return N;
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end if;
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end A;
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function B (N : in Positive) return Natural is
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begin
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if N = 1 then
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return 1;
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else
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return N - 1;
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end if;
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end B;
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end Napiers_Constant;
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package Pi is
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function A (N : in Natural) return Natural;
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function B (N : in Positive) return Natural;
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function Estimate is new Continued_Fraction_Ada95 (Scalar, A, B);
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end Pi;
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package body Pi is
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function A (N : in Natural) return Natural is
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begin
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if N = 0 then
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return 3;
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else
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return 6;
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end if;
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end A;
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function B (N : in Positive) return Natural is
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begin
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return (2 * N - 1) ** 2;
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end B;
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end Pi;
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package Scalar_Text_IO is new Ada.Text_IO.Float_IO (Scalar);
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use Ada.Text_IO, Scalar_Text_IO;
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begin
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Put (Square_Root_Of_2.Estimate (200), Exp => 0); New_Line;
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Put (Napiers_Constant.Estimate (200), Exp => 0); New_Line;
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Put (Pi.Estimate (10000), Exp => 0); New_Line;
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end Test_Continued_Fractions_Ada95;
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@ -1,185 +0,0 @@
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identification division.
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program-id. show-continued-fractions.
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environment division.
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configuration section.
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repository.
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function continued-fractions
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function all intrinsic.
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procedure division.
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fractions-main.
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display "Square root 2 approximately : "
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continued-fractions("sqrt-2-alpha", "sqrt-2-beta", 100)
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display "Napier constant approximately : "
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continued-fractions("napier-alpha", "napier-beta", 40)
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display "Pi approximately : "
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continued-fractions("pi-alpha", "pi-beta", 10000)
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goback.
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end program show-continued-fractions.
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*> **************************************************************
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identification division.
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function-id. continued-fractions.
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data division.
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working-storage section.
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01 alpha-function usage program-pointer.
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01 beta-function usage program-pointer.
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01 alpha usage float-long.
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01 beta usage float-long.
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01 running usage float-long.
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01 i usage binary-long.
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linkage section.
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01 alpha-name pic x any length.
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01 beta-name pic x any length.
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01 iterations pic 9 any length.
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01 approximation usage float-long.
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procedure division using
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alpha-name beta-name iterations
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returning approximation.
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set alpha-function to entry alpha-name
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if alpha-function = null then
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display "error: no " alpha-name " function" upon syserr
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goback
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end-if
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set beta-function to entry beta-name
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if beta-function = null then
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display "error: no " beta-name " function" upon syserr
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goback
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end-if
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move 0 to alpha beta running
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perform varying i from iterations by -1 until i = 0
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call alpha-function using i returning alpha
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call beta-function using i returning beta
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compute running = beta / (alpha + running)
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end-perform
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call alpha-function using 0 returning alpha
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compute approximation = alpha + running
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goback.
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end function continued-fractions.
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*> ******************************
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identification division.
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program-id. sqrt-2-alpha.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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if iteration equal 0 then
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move 1.0 to result
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else
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move 2.0 to result
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end-if
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goback.
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end program sqrt-2-alpha.
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*> ******************************
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identification division.
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program-id. sqrt-2-beta.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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move 1.0 to result
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goback.
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end program sqrt-2-beta.
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*> ******************************
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identification division.
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program-id. napier-alpha.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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if iteration equal 0 then
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move 2.0 to result
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else
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move iteration to result
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end-if
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goback.
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end program napier-alpha.
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*> ******************************
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identification division.
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program-id. napier-beta.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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if iteration = 1 then
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move 1.0 to result
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else
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compute result = iteration - 1.0
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end-if
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goback.
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end program napier-beta.
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*> ******************************
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identification division.
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program-id. pi-alpha.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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if iteration equal 0 then
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move 3.0 to result
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else
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move 6.0 to result
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end-if
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goback.
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end program pi-alpha.
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*> ******************************
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identification division.
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program-id. pi-beta.
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data division.
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working-storage section.
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01 result usage float-long.
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linkage section.
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01 iteration usage binary-long unsigned.
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procedure division using iteration returning result.
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compute result = (2 * iteration - 1) ** 2
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goback.
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end program pi-beta.
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@ -1,35 +0,0 @@
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proc calc(f, n) {
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var r = 0.0;
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for k in 1..n by -1 {
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var v = f.pair(k);
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r = v(2) / (v(1) + r);
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}
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return f.pair(0)(1) + r;
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}
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record Sqrt2 {
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proc pair(n) {
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return (if n == 0 then 1 else 2,
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1);
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}
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}
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record Napier {
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proc pair(n) {
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return (if n == 0 then 2 else n,
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if n == 1 then 1 else n - 1);
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}
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}
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record Pi {
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proc pair(n) {
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return (if n == 0 then 3 else 6,
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(2*n - 1)**2);
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}
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}
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config const n = 200;
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writeln(calc(new Sqrt2(), n));
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writeln(calc(new Napier(), n));
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writeln(calc(new Pi(), n));
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@ -1,25 +1,23 @@
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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;">constant</span> <span style="color: #000000;">precision</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">10000</span>
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with javascript_semantics
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constant precision = 10000
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<span style="color: #008080;">function</span> <span style="color: #000000;">continued_fraction</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">steps</span><span style="color: #0000FF;">=</span><span style="color: #000000;">precision</span><span style="color: #0000FF;">)</span>
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<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">res</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;">steps</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
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<span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</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;">res</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">b</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">a</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">res</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: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">+</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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function continued_fraction(integer f, steps=precision)
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atom a, b, res = 0
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for n=steps to 1 by -1 do
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{a, b} = f(n)
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res := b / (a + res)
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end for
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{a} = f(0)
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return a + res
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end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">sqr2</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</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;">1</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function sqr2(integer n) return {iff(n=0?1:2),1} end function
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<span style="color: #008080;">function</span> <span style="color: #000000;">nap</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">2</span><span style="color: #0000FF;">:</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #008080;">iff</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;">1</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: #008080;">end</span> <span style="color: #008080;">function</span>
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function nap(integer n) return {iff(n=0?2:n),iff(n=1?1:n-1)} end function
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|
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<span style="color: #008080;">function</span> <span style="color: #000000;">pi</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">3</span><span style="color: #0000FF;">:</span><span style="color: #000000;">6</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</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;">2</span><span style="color: #0000FF;">)}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
|
||||
function pi(integer n) return {iff(n=0?3:6),power(2*n-1,2)} end function
|
||||
|
||||
<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;">"Precision: %d\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">precision</span><span style="color: #0000FF;">})</span>
|
||||
<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;">"Sqr(2): %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">continued_fraction</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sqr2</span><span style="color: #0000FF;">)})</span>
|
||||
<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;">"Napier: %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">continued_fraction</span><span style="color: #0000FF;">(</span><span style="color: #000000;">nap</span><span style="color: #0000FF;">)})</span>
|
||||
<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;">"Pi: %.10g\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">continued_fraction</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pi</span><span style="color: #0000FF;">)})</span>
|
||||
<!--
|
||||
printf(1,"Precision: %d\n", {precision})
|
||||
printf(1,"Sqr(2): %.10g\n", {continued_fraction(sqr2)})
|
||||
printf(1,"Napier: %.10g\n", {continued_fraction(nap)})
|
||||
printf(1,"Pi: %.10g\n", {continued_fraction(pi)})
|
||||
|
|
|
|||
|
|
@ -1,3 +1,6 @@
|
|||
#Only print to 17 digits due to floating-point imprecision
|
||||
options(digits=17)
|
||||
|
||||
a_sqrt2 <- function(n) ifelse(n==1, 1, 2)
|
||||
b_sqrt2 <- function(n) return(1)
|
||||
|
||||
|
|
@ -9,16 +12,15 @@ b_pi <- function(n) (2*n-1)^2
|
|||
|
||||
continued_fraction <- function(a, b, n){
|
||||
frac <- function(x, d) a(x)+b(x)/d
|
||||
#Only print to 17 digits due to floating-point imprecision
|
||||
print(Reduce(frac, c(1:n,1), right=TRUE), digits=17)
|
||||
Reduce(frac, 1:n, 1, right=TRUE)
|
||||
}
|
||||
|
||||
print(sqrt(2), digits=17)
|
||||
sqrt(2)
|
||||
continued_fraction(a_sqrt2, b_sqrt2, 100)
|
||||
|
||||
print(exp(1), digits=17)
|
||||
exp(1)
|
||||
continued_fraction(a_e, b_e, 100)
|
||||
|
||||
print(pi, digits=17)
|
||||
pi_ests <- sapply(cumprod(c(100, rep(10,3))),
|
||||
function(n) continued_fraction(a_pi, b_pi, n))
|
||||
pi
|
||||
sapply(cumprod(c(100, rep(10,3))),
|
||||
function(n) continued_fraction(a_pi, b_pi, n))
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
-- 28 Jul 2025
|
||||
include Settings
|
||||
-- 23 Aug 2025
|
||||
include Setting
|
||||
numeric digits 30
|
||||
|
||||
say 'CONTINUED FRACTION'
|
||||
|
|
|
|||
|
|
@ -1,9 +1,6 @@
|
|||
# Evaluates some interesting continued fractions.
|
||||
|
||||
Cfrac! ← +⊢^!0∧(÷:⊙+:°⊟)⊙0≡^!^.+1⇌⇡
|
||||
Fsqrt₂ ← [⊃(+1>0)⋅1]
|
||||
Fe ← [⊃(⨬⋅2∘>0.|⨬⋅1-1>1.)]
|
||||
Fpi ← [⊃(×3+1>0|ⁿ2-1×2)]
|
||||
&p$"√2 = _"Cfrac!Fsqrt₂ 200
|
||||
&p$"e = _"Cfrac!Fe 200
|
||||
&p$"π = _"Cfrac!Fpi 200
|
||||
F‼ ← +^0 0⊙◌⍢(⊙-₁÷+⊙⊸⊃^0^1|⋅±) 0
|
||||
&p$"√2 = _" F‼(+1>₀|⋅1) 10
|
||||
&p$"e = _" F‼(⨬⋅2∘⊸>₀|⨬⋅1-₁⊸>₁) 10
|
||||
&p$"π = _" F‼(×3+1>₀|ⁿ2-1×2) 100
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue