TPK algorithm: Difference between revisions

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Revision as of 16:58, 20 September 2021

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To explain the name "TPK", the authors referred to [[Grimm's law]] (which concerns the consonants 't', 'p', and 'k'), the sounds in the word "typical", and their own initials (Trabb Pardo and Knuth).<ref name="edpl"/> In a talk based on the paper, Knuth said:<ref name="chm"/>

{{quote|You can only appreciate how deep the subject is by seeing how good people struggled with it and how the ideas emerged one at a time. In order to study this—Luis I think was the main instigator of this idea—we take one program—one algorithm—and we write it in every language. And that way from one example we can quickly psych out the flavor of that particular language. We call this the TPK program, and well, the fact that it has the initials of Trabb Pardo and Knuth is just a funny coincidence.}}

In the paper, the authors implement this algorithm in [[Konrad Zuse]]'s [[Plankalkül]], in [[Herman Goldstine|Goldstine]] and [[John von Neumann|von Neumann]]'s [[Flowchart|flow diagrams]], in [[Haskell Curry]]'s proposed notation, in [[Short Code (computer language)|Short Code]] of [[John Mauchly]] and others, in the Intermediate Program Language of [[Arthur Burks]], in the notation of [[Heinz Rutishauser]], in the language and compiler by [[Corrado Böhm]] in 1951–52, in [[Autocode#Glennie's Autocode|Autocode]] of [[Alick Glennie]], in the [[A-0 System|A-2]] system of [[Grace Hopper]], in the [[Laning and Zierler system]], in the earliest proposed [[Fortran]] (1954) of [[John Backus]], in the [[Autocode#Mark 1 Autocode|Autocode]] for [[Manchester Mark 1|Mark 1]] by [[Tony Brooker]], in ПП-2 of [[Andrey Ershov]], in BACAIC of Mandalay Grems and R. E. Porter, in Kompiler 2 of A. Kenton Elsworth and others, in ADES of E. K. Blum, the Internal Translator of [[Alan Perlis]], in [[Fortran]] of John Backus, in [[ARITH-MATIC]] and [[MATH-MATIC]] from [[Grace Hopper]]'s lab, in the system of [[Friedrich L. Bauer|Bauer]] and [[Klaus Samelson|Samelson]], and (in addenda in 2003 and 2009) PACT I and TRANSCODE. They then describe what kind of arithmetic was available, and provide a subjective rating of these languages on parameters of "implementation", "readability", "control structures", "data structures", "machine independence" and "impact", besides mentioning what each was the first to do.

==The algorithm==

Knuth describes it as follows:<ref>Donald Knuth, ''TPK in INTERCAL'', Chapter 7 of ''Selected Papers on Fun and Games'', 2011 (p. 41)</ref>

{{quote|We introduced a simple procedure called the “TPK algorithm,” and gave the flavor of each language by expressing TPK in each particular style. […] The TPK algorithm inputs eleven numbernumbers <math>a_0, a_1, \ldots, a_{10}</math>; then it outputs a sequence of eleven pairs <math>(10, b_{10}), (9, b_9), \ldots, (0, b_0),</math> where

<math>b_i = \begin{cases}

f(a_i), & \text{if }f(a_i) \le 400; \\

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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 ==

==[[ALGOL 60]] implementation==

In the paper, the authors implement this algorithm in [[Konrad Zuse]]'s [[Plankalkül]], in [[Herman Goldstine|Goldstine]] and [[John von Neumann|von Neumann]]'s [[Flowchart|flow diagrams]], in [[Haskell Curry]]'s proposed notation, in [[Short Code (computer language)|Short Code]] of [[John Mauchly]] and others, in the Intermediate Program Language of [[Arthur Burks]], in the notation of [[Heinz Rutishauser]], in the language and compiler by [[Corrado Böhm]] in 1951–52, in [[Autocode#Glennie's Autocode|Autocode]] of [[Alick Glennie]], in the [[A-0 System|A-2]] system of [[Grace Hopper]], in the [[Laning and Zierler system]], in the earliest proposed [[Fortran]] (1954) of [[John Backus]], in the [[Autocode#Mark 1 Autocode|Autocode]] for [[Manchester Mark 1|Mark 1]] by [[Tony Brooker]], in ПП-2 of [[Andrey Ershov]], in BACAIC of Mandalay Grems and R. E. Porter, in Kompiler 2 of A. Kenton Elsworth and others, in ADES of E. K. Blum, the Internal Translator of [[Alan Perlis]], in [[Fortran]] of John Backus, in [[ARITH-MATIC]] and [[MATH-MATIC]] from [[Grace Hopper]]'s lab, in the system of [[Friedrich L. Bauer|Bauer]] and [[Klaus Samelson|Samelson]], and (in addenda in 2003 and 2009) PACT I and TRANSCODE. They then describe what kind of arithmetic was available, and provide a subjective rating of these languages on parameters of "implementation", "readability", "control structures", "data structures", "machine independence" and "impact", besides mentioning what each was the first to do.<ref name="edpl"/>

=== Implementations in more recent languages ===

====[[ALGOL 60]] implementation====

<syntaxhighlight lang="Pascal" line>

begin integer i; real y; real array a[0:10];

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The problem with the usually specified function is that the term <code>5 * t ^ 3</code> gives overflows in almost all languages for very large negative values.

====[[C (programming language)|C]] implementation====

This shows a C implementation equivalent to the above ALGOL 60.

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</syntaxhighlight>

====[[Python (programming language)|Python]] implementation====

This shows a Python implementation.

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</syntaxhighlight>

====[[Rust (programming language)|Rust]] implementation====

This shows a Rust implementation.