TPK algorithm
The Trabb Pardo-Knuth algorithm is a program introduced by Donald Knuth and Luis Trabb Pardo to illustrate the evolution of computer programming languages.
In their 1980 work "The Early Development of Programming Languages", Trabb Pardo and Knuth introduced a trivial program which involved arrays, indexing, mathematical functions, subroutines, I/O, conditionals and iteration. They then wrote implementations of the algorithm in several early programming languages to show how such concepts were expressed.
The simpler Hello world program has been used for much the same purpose.
The algorithm
ask for 11 numbers into set S
reverse set S
for each item in set S
do an operation
if result overflows
alert user
else
print result
The algorithm reads eleven numbers from an input device, stores them in an array, and then processes them in reverse order, applying a user-defined function to each value and reporting either the value of the function or a message to the effect that the value has exceeded some threshold.
Implementations
begin integer i; real y; real array a[0:10];
real procedure f(t); real t; value t;
f := sqrt(abs(t))+5*t^3;
for i := 0 step 1 until 10 do read(a[i]);
for i := 10 step -1 until 0 do
begin y := f(a[i]);
if y > 400 then write(i, "TOO LARGE")
else write(i,y);
end
end
The problem with the usually specified function is that the term 5*t^3 gives overflows in almost all languages for very large negative values.
The following Perl implementation is 79 bytes.
map print(($_>400?"TOO LARGE":$_).$/),reverse map 5*($x=<>)**3+sqrt abs$x,1..11
Python version
The following Python version of the algorithm uses the common Python idiom of using a list instead of an array:
from math import sqrt
def f(t):
return sqrt(abs(t))+5*t**3
a = [int(raw_input()) for i in range(11)]
for i in reversed(a):
print i,
y = f(i)
print "TOO LARGE" if if y > 400 else y
Ruby version
The Ruby version takes advantage of some of its features:
Array.new(11) { gets.to_i }.reverse.each do |x|
y = Math.sqrt(x.abs) + 5*x ** 3
puts "#{x} #{(y>400) ? 'TOO LARGE' : y}"
end
Ruby handles numerical overflow by returning Infinity, which is greater than 400.
References
- "The Early Development of Programming Languages" in A History of Computing in the Twentieth Century, New York, Academic Press, 1980. ISBN 0-12-491650-3 (Reprinted in Knuth, Donald E., et al, Selected Papers on Computer Languages, Stanford, CA, CSLI, 2003. ISBN 1-57586-382-0)