Landon Curt Noll
4ee4c731f7
While not strictly necessary, replacing the two ASCII tab characters in the markdown copyright comment makes it easier to detect problematic TAB indentation within markdown files. After this commit, only 90 markdown files have leading ASCII TAB characters. And again, while not strictly necessary, we can consider running expand on those 90 markdown files to see what effect that might have on the HTML files they produce. Replace leading ASCII TAB characters with multiples of 8 ASCII SPACE characters (the default action of the `expand(1)` tool) might have an negative effect on some HTML formatting where **hack-a-round** formatting was attempted to fix broken indentation caused by problematic ASCII TAB characters. Think of this as a baseline for evaluating leading TAB characters within markdown files. TODO: Consider either using `expand(1)` to replace leading ASCII TAB characters with multiples of 8 ASCII SPACE characters AND/OR modifying the appropriate `bin` tool to convert leading ASCII TAB characters into multiples of 8 ASCII SPACE characters.
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.