QBASIC is the BASIC interpreter which has been shipped
as part of MS-DOS since version 5.0 (circa 1991). This
includes MS-DOS running on machines running Windows.
QBASIC extends the usual BASIC language in several ways, but
the only extension we will use is that of long integer.
Those new to QBASIC can find information on the language
Although QBASIC is no longer distributed with some newer
versions of Windows, it can be gotten from Microsoft as part of a
package of utilities in the file
currently available at
QBASIC supports two types of integers:
x&. The long integer is an extension to the BASIC language.
The basic arithmetic operations,
+, -, are
available from the keyboard. Integer division (dropping any
remainder) is represented by the
The modular reduction operator is represented with the
print 8 + 7 mod 13
print 5 * 4 mod 13
print 7 \ 2
The Russian Peasant method for modular exponentiation is implemented in the simple program found in POWMOD1.BAS. A more flexible implementation of the algorithm for long integers can be found in the file POWMOD2.BAS. Here the algorithm is in the form of a function call.
The program located in the file ORDER.BAS computes the order of a number modulo a specified modulus (if it has an order) by a simple exhaustive method.
The program in the file FACTORPR.BAS will extract a single prime factor from a composite number using Pollard's Rho algorithm. This algorithm uses long integers and is implemented as a function call so it is usable as part of larger programs.
The 32 bit (about 10 digit) machine word length of QBASIC can be exceeded by using either a multiple precision library or a BASIC interpreter which includes multiple precision arithmetic.
The package BIGNUM.BAS is a simple multiple precision package
written for QBASIC. BIGNUM.BAS was written by Marc Kummel of
Dunn Middle School, Santa Barbara, CA, and can be found at
UBASIC, a BASIC interpreter with built in multiple precision was
written by Yuji Kida of Rikkyo Univ and is available from