Data update
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Ingy döt Net
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2427 changed files with 31826 additions and 3468 deletions
34
Task/Jacobi-symbol/ALGOL-68/jacobi-symbol.alg
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34
Task/Jacobi-symbol/ALGOL-68/jacobi-symbol.alg
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@ -0,0 +1,34 @@
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BEGIN # Jacobi symbol - translation of the Wren sample #
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PROC jacobi = ( INT a in, n in )INT:
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IF n in <= 0 OR NOT ODD n in THEN
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print( ( "The 'n' parameter of jacobi must be an odd positive integer.", newline ) );
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stop
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ELSE
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INT a := a in MOD n in, n := n in;
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INT result := 1;
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WHILE a /= 0 DO
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WHILE NOT ODD a DO
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a OVERAB 2;
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INT nm8 = n MOD 8;
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IF nm8 = 3 OR nm8 = 5 THEN result := - result FI
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OD;
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INT t = a;
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a := n;
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n := t;
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IF a MOD 4 = 3 AND n MOD 4 = 3 THEN result := - result FI;
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a MODAB n
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OD;
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IF n = 1 THEN result ELSE 0 FI
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FI # jacobi # ;
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print( ( "Table of jacobi(a, n):", newline ) );
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print( ( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15", newline ) );
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print( ( "---------------------------------------------------------------", newline ) );
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FOR n BY 2 TO 29 DO
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print( ( whole( n, -3 ) ) );
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FOR a TO 15 DO print( ( whole( jacobi( a, n ), -4 ) ) ) OD;
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print( ( newline ) )
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OD
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END
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33
Task/Jacobi-symbol/ALGOL-W/jacobi-symbol.alg
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33
Task/Jacobi-symbol/ALGOL-W/jacobi-symbol.alg
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@ -0,0 +1,33 @@
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begin % Jacobi symbol %
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integer procedure jacobi( integer value aIn, nIn ) ;
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if nIn <= 0 or not odd( nIn ) then begin
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write( "The 'n' parameter of jacobi must be an odd positive integer." );
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0
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end
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else begin
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integer a, n, js;
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a := aIn rem nIn; n := nIn; js := 1;
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while a not = 0 do begin
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while a rem 2 = 0 do begin
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integer nm8;
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a := a div 2;
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nm8 := n rem 8;
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if nm8 = 3 or nm8 = 5 then js := - js;
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end while_a_rem_2_eq_0 ;
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begin integer t; t := a; a := n; n := t end;
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if a rem 4 = 3 and n rem 4 = 3 then js := - js;
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a := a rem n
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end;
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if n = 1 then js else 0
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end jacobi ;
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write( "Table of jacobi(a, n):" );;
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write( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" );
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write( "---------------------------------------------------------------" );
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for n := 1 step 2 until 29 do begin
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write( i_w := 3, s_w := 0, n );
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for a := 1 until 15 do writeon( i_w := 4, s_w := 0, jacobi( a, n ) );
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end
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end.
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33
Task/Jacobi-symbol/Lua/jacobi-symbol.lua
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33
Task/Jacobi-symbol/Lua/jacobi-symbol.lua
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@ -0,0 +1,33 @@
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do -- Jacobi symbol - translation of the Algol 68 sample
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local function jacobi( aIn, nIn )
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if nIn <= 0 or nIn % 2 == 0 then
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print( "The 'n' parameter of jacobi must be an odd positive integer." )
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return 0
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else
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local a, n, result = aIn % nIn, nIn, 1
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while a ~= 0 do
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while a % 2 == 0 do
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a = math.floor( a / 2 )
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local nm8 = n % 8
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if nm8 == 3 or nm8 == 5 then result = - result end
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end
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a, n = n, a;
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if a % 4 == 3 and n % 4 == 3 then result = - result end
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a = a % n
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end
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return n == 1 and result or 0
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end
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end
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print( "Table of jacobi(a, n):" );
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print( "n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" )
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print( "---------------------------------------------------------------" )
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for n = 1, 29, 2 do
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io.write( string.format( "%3d", n ) )
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for a = 1, 15 do io.write( string.format( "%4d", jacobi( a, n ) ) ) end
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io.write( "\n" )
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end
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end
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69
Task/Jacobi-symbol/PL-M/jacobi-symbol.plm
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69
Task/Jacobi-symbol/PL-M/jacobi-symbol.plm
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@ -0,0 +1,69 @@
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100H: /* JACOBI SYMBOL */
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/* CP/M BDOS SYSTEM CALLS AND I/O ROUTINES */
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BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END;
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PR$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END;
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PR$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END;
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PR$NL: PROCEDURE; CALL PR$STRING( .( 0DH, 0AH, '$' ) ); END;
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PR$NUMBER: PROCEDURE( N ); /* PRINTS A NUMBER IN THE MINIMUN FIELD WIDTH */
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DECLARE N ADDRESS;
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DECLARE V ADDRESS, N$STR ( 6 )BYTE, W BYTE;
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V = N;
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W = LAST( N$STR );
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N$STR( W ) = '$';
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N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
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DO WHILE( ( V := V / 10 ) > 0 );
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N$STR( W := W - 1 ) = '0' + ( V MOD 10 );
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END;
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CALL PR$STRING( .N$STR( W ) );
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END PR$NUMBER;
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/* TASK */
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JACOBI: PROCEDURE( A$IN, N$IN )BYTE;
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DECLARE ( A$IN, N$IN ) ADDRESS;
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IF N$IN MOD 2 <> 1 THEN DO;
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CALL PR$STRING( .'JACOBI PARAMETER NOT ODD$' );
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RETURN 0;
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END;
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ELSE DO;
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DECLARE ( A, N, NM8, T ) ADDRESS;
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DECLARE JS BYTE;
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A = A$IN MOD N$IN; N = N$IN; JS = 1;
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DO WHILE A <> 0;
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DO WHILE A MOD 2 = 0;
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A = A / 2;
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NM8 = N MOD 8;
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IF NM8 = 3 OR NM8 = 5 THEN JS = - JS;
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END;
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T = A; A = N; N = T;
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IF A MOD 4 = 3 AND N MOD 4 = 3 THEN JS = - JS;
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A = A MOD N;
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END;
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IF N = 1 THEN RETURN JS;
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ELSE RETURN 0;
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END;
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END JACOBI ;
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DECLARE ( A, N )ADDRESS;
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DECLARE JS BYTE;
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CALL PR$STRING( .'TABLE OF JACOBI(A, N):$' );CALL PR$NL;
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CALL PR$STRING( .'N/A 1 2 3 4 5 6 7$' );
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CALL PR$STRING( .' 8 9 10 11 12 13 14 15$' );CALL PR$NL;
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CALL PR$STRING( .'-------------------------------$' );
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CALL PR$STRING( .'--------------------------------$' );CALL PR$NL;
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DO N = 1 TO 29 BY 2;
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CALL PR$CHAR( ' ' );
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IF N < 10 THEN CALL PR$CHAR( ' ' );
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CALL PR$NUMBER( N );
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DO A = 1 TO 15;
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JS = JACOBI( A, N );
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IF JS = 0 THEN CALL PR$STRING( .' 0$' );
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ELSE IF JS = 1 THEN CALL PR$STRING( .' 1$' );
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ELSE CALL PR$STRING( .' -1$' );
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END;
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CALL PR$NL;
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END;
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EOF
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@ -1,20 +1,22 @@
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func jacobi(n, k) {
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func jacobi(a, n) {
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assert(k > 0, "#{k} must be positive")
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assert(k.is_odd, "#{k} must be odd")
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assert(n > 0, "#{n} must be positive")
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assert(n.is_odd, "#{n} must be odd")
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var t = 1
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while (n %= k) {
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var v = n.valuation(2)
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t *= (-1)**v if (k%8 ~~ [3,5])
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n >>= v
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(n,k) = (k,n)
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t = -t if ([n%4, k%4] == [3,3])
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while (a %= n) {
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if (a.is_even) {
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var v = a.valuation(2)
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t *= (-1)**v if (n%8 ~~ [3,5])
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a >>= v
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}
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(a,n) = (n,a)
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t = -t if ([a%4, n%4] == [3,3])
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}
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k==1 ? t : 0
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n==1 ? t : 0
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}
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for n in (0..50), k in (0..50) {
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assert_eq(jacobi(n, 2*k + 1), kronecker(n, 2*k + 1))
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for a in (0..50), n in (0..50) {
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assert_eq(jacobi(a, 2*n + 1), kronecker(a, 2*n + 1))
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}
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@ -1,4 +1,4 @@
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import "/fmt" for Fmt
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import "./fmt" for Fmt
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var jacobi = Fn.new { |a, n|
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if (!n.isInteger || n <= 0 || n%2 == 0) {
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@ -26,8 +26,8 @@ System.print("n/a 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15")
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System.print("---------------------------------------------------------------")
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var n = 1
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while (n < 31) {
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System.write(Fmt.d(3, n))
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for (a in 1..15) System.write(Fmt.d(4, jacobi.call(a, n)))
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Fmt.write("$3d", n)
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for (a in 1..15) Fmt.write("$4d", jacobi.call(a, n))
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System.print()
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n = n + 2
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}
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