ioccc/1990/theorem

To build:

    make all

Bugs and (Mis)features:

The current status of this entry is:

STATUS: INABIAF - please DO NOT fix

For more detailed information see 1990/theorem in bugs.html.

To use:

    ./theorem expression x1 x2 h y1

where:

    expression - function f(x,y)  (see below)
    x1 - start of interval
    x2 - end of interval
    h - step size
    y1 - initial value  (y(x1) == y1)

Try:

    ./try.sh

Judges' remarks:

The program's source implements four functions, all from the same source file!

When you compile theorem.c as is and run with 5 args, it numerically solves the equation y'=f(x,y), with a step size of h (see above usage), over the interval x=[x1,x2], with the initial condition of y(x1)=y1.

The 'expression' f(x,y) is any function of x and y with the operators:

    +   -       *       /       ^

The symbol ^ is the power operator. Note that it only supports integer powers. Also note that all expressions are evaluated strictly left to right. (i.e., parenthesis aren't supported).

Try running the program with the following args:

    ./theorem y 0 1 0.1 1
    ./theorem 1/x 1 2 0.1 0
    ./theorem 'x^2/y+x' 0 1 0.1 6

But wait, there is more! You also get, free of charge, a reversing filter! Try:

    ./theorem -r 0 0 0 0 < theorem.c > sorter.c

Still not impressed? The author throws in for free, a sort program! Try:

    make sorter
    ls | ./sorter

This program is safe for home use as well. The author has included a safety feature in case you misplace the original program source:

    ./sorter -r 0 0 0 0 < sorter.c > theorem_bkp.c

And finally, as a special offer to users of this entry, the author provides a Fibonacci sequence generator! Try:

    ./sorter 0 0 0 0 < theorem.c > fibonacci.c
    make fibonacci
    ./fibonacci 1 1
    ./fibonacci 2 1

NOTE: if the two args passed to fibonacci and theorem_bkp add to 0 it will print 0 over and over again in an infinite loop. In this case it should not be fixed (another condition where this occurred was fixed in 2023 as it affected usability of the program).

Program available on 9 track and cartridge cassette. Neither Ginsu knife nor Swiss army knife included! :-)

When this program was first shown at the 1990 Summer USENIX conference, it received a standing ovation; a first for a contest entry.

Author's remarks:

Differential equations are solved via the Runge-Kutta method, which guarantees local error proportional to h^5, and total error across a finite interval is at most a constant times h^4.

Sorting is accomplished with a standard shell sort.

Note that the sorting and reversing is limited to files with fewer than 500 lines, each less than 99 characters long.