100H: /* LONG MULTIPLICATION OF LARGE INTEGERS */ /* LARGE INTEGERS ARE REPRESENTED BY ARRAYS OF BYTES WHOSE VALUES ARE */ /* A SINGLE DECIMAL DIGIT OF THE NUMBER */ /* THE LEAST SIGNIFICANT DIGIT OF THE LARGE INTEGER IS IN ELEMENT 1 */ /* ELEMENT 0 CONTAINS THE NUMBER OF DIGITS THE NUMBER HAS */ BDOS: PROCEDURE( FN, ARG ); /* CP/M BDOS SYSTEM CALL */ DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END BDOS; PRINT$CHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END; PRINT$STRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; DECLARE PRINT$NL LITERALLY 'PRINT$STRING( .( 0DH, 0AH, ''$'' ) )'; DECLARE LONG$INTEGER LITERALLY '(201)BYTE'; DECLARE DIGIT$BASE LITERALLY '10'; /* PRINTS A LONG INTEGER */ PRINT$LONG$INTEGER: PROCEDURE( N$PTR ); DECLARE N$PTR ADDRESS; DECLARE N BASED N$PTR LONG$INTEGER; DECLARE ( D, F ) BYTE; F = N( 0 ); DO D = 1 TO N( 0 ); CALL PRINT$CHAR( N( F ) + '0' ); F = F - 1; END; END PRINT$LONG$INTEGER; /* IMPLEMENTS LONG MULTIPLICATION, C IS SET TO A * B */ /* C CAN BE THE SAME LONG$INTEGER AS A OR B */ LONG$MULTIPLY: PROCEDURE( A$PTR, B$PTR, C$PTR ); DECLARE ( A$PTR, B$PTR, C$PTR ) ADDRESS; DECLARE ( A BASED A$PTR, B BASED B$PTR, C BASED C$PTR ) LONG$INTEGER; DECLARE MRESULT LONG$INTEGER; DECLARE RPOS BYTE; /* MULTIPLIES THE LONG INTEGER IN B BY THE INTEGER A, THE RESULT */ /* IS ADDED TO C, STARTING FROM DIGIT START */ /* OVERFLOW IS IGNORED */ MULTIPLY$ELEMENT: PROCEDURE( A, B$PTR, C$PTR, START ); DECLARE ( B$PTR, C$PTR ) ADDRESS; DECLARE ( A, START ) BYTE; DECLARE ( B BASED B$PTR, C BASED C$PTR ) LONG$INTEGER; DECLARE ( CDIGIT, D$CARRY, BPOS, CPOS ) BYTE; D$CARRY = 0; CPOS = START; DO BPOS = 1 TO B( 0 ); CDIGIT = C( CPOS ) + ( A * B( BPOS ) ) + D$CARRY; IF CDIGIT < DIGIT$BASE THEN D$CARRY = 0; ELSE DO; /* HAVE DIGITS TO CARRY */ D$CARRY = CDIGIT / DIGIT$BASE; CDIGIT = CDIGIT MOD DIGIT$BASE; END; C( CPOS ) = CDIGIT; CPOS = CPOS + 1; END; C( CPOS ) = D$CARRY; /* REMOVE LEADING ZEROS BUT IF THE NUMBER IS 0, KEEP THE FINAL 0 */ DO WHILE( CPOS > 1 AND C( CPOS ) = 0 ); CPOS = CPOS - 1; END; C( 0 ) = CPOS; END MULTIPLY$ELEMENT ; /* THE RESULT WILL BE COMPUTED IN MRESULT, ALLOWING A OR B TO BE C */ DO RPOS = 1 TO LAST( MRESULT ); MRESULT( RPOS ) = 0; END; /* MULTIPLY BY EACH DIGIT AND ADD TO THE RESULT */ DO RPOS = 1 TO A( 0 ); IF A( RPOS ) <> 0 THEN DO; CALL MULTIPLY$ELEMENT( A( RPOS ), B$PTR, .MRESULT, RPOS ); END; END; /* RETURN THE RESULT IN C */ DO RPOS = 0 TO MRESULT( 0 ); C( RPOS ) = MRESULT( RPOS ); END; END; /* CALCULATE AND OUTPUT 2^128 */ DECLARE ( TWO$TO$64, TWO$TO$128 ) LONG$INTEGER; DECLARE ( PWR, TPOS ) BYTE; /* CONSTRUCT 2^64 IN TWO$TO$64 */ DO TPOS = 0 TO LAST( TWO$TO$64 ); TWO$TO$64( TPOS ) = 0; END; TWO$TO$64( 0 ) = 1; TWO$TO$64( 1 ) = 2; PWR = 1; DO WHILE PWR < 64; CALL LONG$MULTIPLY( .TWO$TO$64, .TWO$TO$64, .TWO$TO$64 ); PWR = PWR + PWR; END; /* CONSTRUCT 2^128 */ TWO$TO$128( 0 ) = 1; TWO$TO$128( 1 ) = 0; CALL LONG$MULTIPLY( .TWO$TO$64, .TWO$TO$64, .TWO$TO$128 ); CALL PRINT$STRING( .( '2', 05EH, '128: $' ) ); /* 05EH = "^" IN ASCII */ CALL PRINT$LONG$INTEGER( .TWO$TO$128 ); CALL PRINT$NL; EOF