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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@ -1,12 +1,3 @@
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F commatize(number, step = 3, sep = ‘,’)
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V s = reversed(String(number))
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String r = s[0]
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L(i) 1 .< s.len
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I i % step == 0
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r ‘’= sep
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r ‘’= s[i]
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R reversed(r)
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F isqrt(BigInt x)
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assert(x >= 0)
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@ -27,7 +18,7 @@ F isqrt(BigInt x)
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R r
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print(‘The integer square root of integers from 0 to 65 are:’)
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L(i) 66
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L(i) 0.<66
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print(isqrt(BigInt(i)), end' ‘ ’)
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print()
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@ -1,87 +0,0 @@
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with Ada.Text_Io;
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with Ada.Numerics.Big_Numbers.Big_Integers;
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with Ada.Strings.Fixed;
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procedure Integer_Square_Root is
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use Ada.Numerics.Big_Numbers.Big_Integers;
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use Ada.Text_Io;
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function Isqrt (X : Big_Integer) return Big_Integer is
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Q : Big_Integer := 1;
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Z, T, R : Big_Integer;
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begin
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while Q <= X loop
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Q := Q * 4;
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end loop;
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Z := X;
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R := 0;
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while Q > 1 loop
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Q := Q / 4;
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T := Z - R - Q;
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R := R / 2;
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if T >= 0 then
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Z := T;
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R := R + Q;
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end if;
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end loop;
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return R;
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end Isqrt;
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function Commatize (N : Big_Integer; Width : Positive) return String is
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S : constant String := To_String (N, Width);
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Image : String (1 .. Width + Width / 3) := (others => ' ');
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Pos : Natural := Image'Last;
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begin
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for I in S'Range loop
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Image (Pos) := S (S'Last - I + S'First);
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exit when Image (Pos) = ' ';
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Pos := Pos - 1;
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if I mod 3 = 0 and S (S'Last - I + S'First - 1) /= ' ' then
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Image (Pos) := ''';
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Pos := Pos - 1;
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end if;
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end loop;
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return Image;
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end Commatize;
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type Mode_Kind is (Tens, Ones, Spacer, Result);
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begin
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Put_Line ("Integer square roots of integers 0 .. 65:");
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for Mode in Mode_Kind loop
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for N in 0 .. 65 loop
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case Mode is
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when Tens => Put ((if N / 10 = 0
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then " "
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else Natural'Image (N / 10)));
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when Ones => Put (Natural'Image (N mod 10));
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when Spacer => Put ("--");
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when Result => Put (To_String (Isqrt (To_Big_Integer (N))));
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end case;
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end loop;
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New_Line;
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end loop;
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New_Line;
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declare
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package Integer_Io is new Ada.Text_Io.Integer_Io (Natural);
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use Ada.Strings.Fixed;
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N : Integer := 1;
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P, R : Big_Integer;
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begin
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Put_Line ("| N|" & 80 * " " & "7**N|" & 30 * " " & "isqrt (7**N)|");
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Put_Line (133 * "=");
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loop
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P := 7**N;
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R := Isqrt (P);
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Put ("|"); Integer_Io.Put (N, Width => 3);
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Put ("|"); Put (Commatize (P, Width => 63));
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Put ("|"); Put (Commatize (R, Width => 32));
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Put ("|"); New_Line;
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exit when N >= 73;
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N := N + 2;
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end loop;
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Put_Line (133 * "=");
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end;
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end Integer_Square_Root;
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@ -4,8 +4,8 @@ commatize: function [x][
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isqrt: function [x][
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num: new x
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q: new 1
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r: new 0
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q: 1
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r: 0
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while [q =< num]-> shl.safe 'q 2
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while [q > 1][
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@ -14,7 +14,7 @@ isqrt: function [x][
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shr 'r 1
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if t >= 0 [
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num: t
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r: new r+q
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r: r+q
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]
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]
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return r
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@ -1,74 +0,0 @@
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IDENTIFICATION DIVISION.
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PROGRAM-ID. I-SQRT.
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DATA DIVISION.
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WORKING-STORAGE SECTION.
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01 QUAD-RET-VARS.
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03 X PIC 9(18).
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03 Q PIC 9(18).
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03 Z PIC 9(18).
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03 T PIC S9(18).
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03 R PIC 9(18).
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01 TO-65-VARS.
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03 ISQRT-N PIC 99.
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03 DISP-LN PIC X(22) VALUE SPACES.
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03 DISP-FMT PIC Z9.
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03 PTR PIC 99 VALUE 1.
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01 BIG-SQRT-VARS.
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03 POW-7 PIC 9(18) VALUE 7.
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03 POW-N PIC 99 VALUE 1.
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03 POW-N-OUT PIC Z9.
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03 POW-7-OUT PIC Z(10).
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PROCEDURE DIVISION.
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BEGIN.
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PERFORM SQRTS-TO-65.
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PERFORM BIG-SQRTS.
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STOP RUN.
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SQRTS-TO-65.
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PERFORM DISP-SMALL-SQRT
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VARYING ISQRT-N FROM 0 BY 1
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UNTIL ISQRT-N IS GREATER THAN 65.
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DISP-SMALL-SQRT.
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MOVE ISQRT-N TO X.
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PERFORM ISQRT.
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MOVE R TO DISP-FMT.
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STRING DISP-FMT DELIMITED BY SIZE INTO DISP-LN
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WITH POINTER PTR.
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IF PTR IS GREATER THAN 22,
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DISPLAY DISP-LN,
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MOVE 1 TO PTR.
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BIG-SQRTS.
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PERFORM BIG-SQRT 10 TIMES.
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BIG-SQRT.
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MOVE POW-7 TO X.
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PERFORM ISQRT.
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MOVE POW-N TO POW-N-OUT.
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MOVE R TO POW-7-OUT.
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DISPLAY "ISQRT(7^" POW-N-OUT ") = " POW-7-OUT.
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ADD 2 TO POW-N.
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MULTIPLY 49 BY POW-7.
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ISQRT.
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MOVE 1 TO Q.
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PERFORM MUL-Q-BY-4 UNTIL Q IS GREATER THAN X.
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MOVE X TO Z.
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MOVE ZERO TO R.
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PERFORM ISQRT-STEP UNTIL Q IS NOT GREATER THAN 1.
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MUL-Q-BY-4.
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MULTIPLY 4 BY Q.
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ISQRT-STEP.
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DIVIDE 4 INTO Q.
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COMPUTE T = Z - R - Q.
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DIVIDE 2 INTO R.
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IF T IS NOT LESS THAN ZERO,
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MOVE T TO Z,
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ADD Q TO R.
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@ -1,8 +1,6 @@
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func isqrt x .
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q = 1
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while q <= x
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q *= 4
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.
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while q <= x : q *= 4
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while q > 1
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q = q div 4
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t = x - r - q
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@ -1,46 +1,44 @@
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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;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
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with javascript_semantics
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include mpfr.e
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<span style="color: #008080;">function</span> <span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">if</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</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: #7060A8;">crash</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"Argument cannot be negative."</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: #004080;">mpz</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">),</span>
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<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(),</span>
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<span style="color: #000000;">z</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">while</span> <span style="color: #7060A8;">mpz_cmp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)<=</span> <span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</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;">while</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)></span><span style="color: #000000;">0</span> <span style="color: #008080;">do</span>
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<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_fdiv_q_ui</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</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;">if</span> <span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</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: #7060A8;">mpz_set</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
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<span style="color: #7060A8;">mpz_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</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;">while</span>
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<span style="color: #004080;">string</span> <span style="color: #000000;">star</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_cmp_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #008000;">"*"</span><span style="color: #0000FF;">:</span><span style="color: #008000;">" "</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">return</span> <span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">))&</span><span style="color: #000000;">star</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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function isqrt(mpz x)
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if mpz_cmp_si(x,0)<0 then
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crash("Argument cannot be negative.")
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end if
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mpz q = mpz_init(1),
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r = mpz_init(0),
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t = mpz_init(),
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z = mpz_init_set(x)
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while mpz_cmp(q,x)<= 0 do
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mpz_mul_si(q,q,4)
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end while
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while mpz_cmp_si(q,1)>0 do
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assert(mpz_fdiv_q_ui(q, q, 4)=0)
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mpz_sub(t,z,r)
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mpz_sub(t,t,q)
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assert(mpz_fdiv_q_ui(r, r, 2)=0)
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if mpz_cmp_si(t,0) >= 0 then
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mpz_set(z,t)
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mpz_add(r,r,q)
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end if
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end while
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string star = iff(mpz_cmp_si(z,0)=0?"*":" ")
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return shorten(mpz_get_str(r,10,true))&star
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end function
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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;">"The integer square roots of integers from 0 to 65 are:\n"</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">65</span> <span style="color: #008080;">do</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;">"%s "</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">trim</span><span style="color: #0000FF;">(</span><span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</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;">"\n\npower 7 ^ power integer square root\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;">mpz</span> <span style="color: #000000;">pow7</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">(</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)</span>
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<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">9000</span> <span style="color: #008080;">do</span>
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<span style="color: #008080;">if</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">73</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</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>
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<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">100</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span>
|
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<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;"><</span><span style="color: #000000;">1000</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">or</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</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;">"%4d %58s %61s\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">isqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">)})</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
|
||||
<span style="color: #7060A8;">mpz_mul_si</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">pow7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
|
||||
<!--
|
||||
printf(1,"The integer square roots of integers from 0 to 65 are:\n")
|
||||
for i=0 to 65 do
|
||||
printf(1,"%s ", {trim(isqrt(mpz_init(i)))})
|
||||
end for
|
||||
printf(1,"\n\npower %24s 7 ^ power %45s integer square root\n",{" "," "})
|
||||
printf(1,"----- %s %s\n",{repeat('-',57),repeat('-',58)})
|
||||
mpz pow7 = mpz_init(7)
|
||||
for i=1 to 9000 do
|
||||
if (i<=73 and remainder(i,2)=1)
|
||||
or (i<100 and remainder(i,10)=5)
|
||||
or (i<1000 and remainder(i,100)=0)
|
||||
or remainder(i,1000)=0 then
|
||||
printf(1,"%4d %58s %61s\n", {i, shorten(mpz_get_str(pow7,10,true)),isqrt(pow7)})
|
||||
end if
|
||||
mpz_mul_si(pow7,pow7,7)
|
||||
end for
|
||||
|
|
|
|||
|
|
@ -1,5 +1,5 @@
|
|||
-- 28 Jul 2025
|
||||
include Settings
|
||||
-- 23 Aug 2025
|
||||
include Setting
|
||||
|
||||
say 'ISQRT (INTEGER SQUARE ROOT)'
|
||||
say version
|
||||
|
|
@ -18,9 +18,9 @@ call Task2 12345,1,12345,'F'
|
|||
exit
|
||||
|
||||
Task1:
|
||||
procedure
|
||||
procedure expose glob.
|
||||
arg xx
|
||||
call time('r')
|
||||
call Timer 'x'
|
||||
say 'Integer square root for n = 0...'xx
|
||||
do n = 0 to xx
|
||||
call Charout ,QuadraticResidue(n)' '
|
||||
|
|
@ -30,9 +30,9 @@ call Timer
|
|||
return
|
||||
|
||||
Task2:
|
||||
procedure expose Memo.
|
||||
procedure expose Memo. glob.
|
||||
arg xx,yy,zz,mm
|
||||
call Time('r')
|
||||
call Timer 'x'
|
||||
select
|
||||
when mm = 'Q' then
|
||||
t = 'Quadratic residue'
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue