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Ingy döt Net 2023-10-02 18:11:16 -07:00
parent 796d366b97
commit 35bcdeebf8
504 changed files with 7045 additions and 610 deletions
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Task/Square-form-factorization/ALGOL-68/square-form-factorization.alg Normal file
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BEGIN # Daniel Shanks's Square Form Factorization (SquFoF) - based on the Wren sample #
MODE INTEGER = LONG INT; # large enough INT type #
PROC(LONG REAL)LONG REAL size sqrt = long sqrt; # sqrt for INTEGER values #
[]INTEGER multipliers = ( 1, 3, 5, 7, 11, 3 * 5, 3 * 7, 3 * 11
, 5 * 7, 5 * 11, 7 * 11, 3 * 5 * 7, 3 * 5 * 11
, 3 * 7 * 11, 5 * 7 * 11, 3 * 5 * 7 * 11
);
PROC gcd = ( INTEGER x, y )INTEGER: # iterative gcd #
BEGIN
INTEGER a := x, b := y;
WHILE b /= 0 DO
INTEGER next a = b;
b := a MOD b;
a := next a
OD;
ABS a
END # gcd # ;
PROC squfof = ( INTEGER n )INTEGER:
IF INTEGER s = ENTIER ( size sqrt( n ) + 0.5 );
s * s = n
THEN s
ELSE INTEGER result := 0;
FOR multiplier FROM LWB multipliers TO UPB multipliers WHILE result = 0 DO
INTEGER d = n * multipliers[ multiplier ];
INTEGER pp := ENTIER size sqrt( d );
INTEGER p prev := pp;
INTEGER po = p prev;
INTEGER q prev := 1;
INTEGER qq := d - ( po * po );
INTEGER l = ENTIER size sqrt( s * 8 );
INTEGER bb = 3 * l;
INTEGER i := 2;
INTEGER b := 0;
INTEGER q := 0;
INTEGER r := 0;
BOOL again := TRUE;
WHILE i < bb AND again DO
b := ( po + pp ) OVER qq;
pp := ( b * qq ) - pp;
q := qq;
qq := q prev + ( b * ( p prev - pp ) );
r := ENTIER ( size sqrt( qq ) + 0.5 );
IF i MOD 2 = 0 THEN again := r * r /= qq FI;
IF again THEN
q prev := q;
p prev := pp;
i +:= 1
FI
OD;
IF i < bb THEN
b := ( po - pp ) OVER r;
p prev := pp := ( b * r ) + pp;
q prev := r;
qq := ( d - ( p prev * p prev ) ) OVER q prev;
i := 0;
WHILE
b := ( po + pp ) OVER qq;
p prev := pp;
pp := ( b * qq ) - pp;
q := qq;
qq := q prev + ( b * ( p prev - pp ) );
q prev := q;
i +:= 1;
pp /= p prev
DO SKIP OD
FI;
r := gcd( n, q prev );
IF r /= 1 AND r /=n THEN result := r FI
OD;
result
FI # squfof # ;
[]INTEGER examples = ( 2501, 12851
, 13289, 75301
, 120787, 967009
, 997417, 7091569
, 13290059, 42854447
, 223553581, 2027651281
, 11111111111, 100895598169
, 1002742628021, 60012462237239
, 287129523414791, 9007199254740931
, 11111111111111111, 314159265358979323
, 384307168202281507, 419244183493398773
, 658812288346769681, 922337203685477563
, 1000000000000000127, 1152921505680588799
, 1537228672809128917, 4611686018427387877
);
print( ( "Integer Factor Quotient", newline ) );
print( ( "----------------------------------------", newline ) );
FOR example FROM LWB examples TO UPB examples DO
INTEGER n = examples[ example ];
INTEGER fact = squfof( n );
STRING quot = IF fact = 0 THEN "fail" ELSE whole( n OVER fact, 0 ) FI;
print( ( whole( n, -20 ), " ", whole( fact, -10 ), " ", quot, newline ) )
OD
END