Trabb Pardo Knuth Algorithm

April 27, 2012

In their 1973 paper “The Early Development of Programming Languages,” Luis Trabb Pardo and Donald Knuth give the following algorithm as a means of assessing programming languages:

ask for 11 numbers to be read into a sequence S reverse sequence S for each item in sequence S call a function to do an operation if result overflows alert user else print result

Though it is trivial, the algorithm involves arrays, indexing, mathematical functions, subroutines, I/O, conditionals and iteration, and thus exposes many basic operations of a programming language.

Your task is to write a program that implements the Trabb Pardo Knuth algorithm. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

Posted by programmingpraxis

Filed in Exercises

12 Comments »

12 Responses to “Trabb Pardo Knuth Algorithm”

Programming Praxis – Trabb Pardo Knuth Algorithm « Bonsai Code said
April 27, 2012 at 10:04 AM
[…] today’s Programming Praxis exercise, our goal is to implement a simple algorithm that could serve as an […]

Remco Niemeijer said

April 27, 2012 at 10:04 AM

My Haskell solution (see http://bonsaicode.wordpress.com/2012/04/27/programming-praxis-trabb-pardo-knuth-algorithm/ for a version with comments):

import Control.Monad

f :: Double -> Double
f x = sqrt (abs x) + 5 * x^3

main :: IO ()
main = mapM_ (putStrLn . (\x -> if x > 400 then "TOO LARGE" else show x) . f) .
       reverse =<< replicateM 11 readLn

ardnew said

April 27, 2012 at 5:01 PM

Implementation in C. The algorithm doesn’t check if overflow occurred when reading input from the user

#include <stdio.h>
#include <stdint.h>

#define NUM_ELEMENTS 11

// Performs multiplication on 2 32-bit integers
uint32_t mult_uint32(uint32_t a, uint32_t b, uint8_t *o)
{
  uint64_t p = (uint64_t)a * b;
  *o = p > UINT32_MAX;
  return p;  
}

int main(void)
{
  uint32_t sequence[NUM_ELEMENTS];
  uint32_t product;
  uint8_t  overflow;  
  size_t   i;
  
  printf("Please enter %u numbers:\n", NUM_ELEMENTS);

  // Read numbers into the sequence
  for (i = 0; i < NUM_ELEMENTS; ++i)
    scanf("%u", &sequence[i]);
    
  // Reverse sequence
  for (i = 0; i < NUM_ELEMENTS / 2; ++i)
  {
    sequence[i] ^= sequence[NUM_ELEMENTS - i - 1];
    sequence[NUM_ELEMENTS - i - 1] ^= sequence[i];
    sequence[i] ^= sequence[NUM_ELEMENTS - i - 1];
  }

  // Call a function to perform an arithmetic operation on
  // each element of the sequence
  for (i = 0; i < NUM_ELEMENTS; ++i)
  {
    product = mult_uint32(sequence[i], sequence[i], &overflow);
    
    // Alert user if overflow occurred
    if (overflow)
      printf("%u * %u = %s\n", sequence[i], sequence[i], "overflow");
    // Otherwise print result
    else
      printf("%u * %u = %u\n", sequence[i], sequence[i], product);
  }
  
  return 0;
}

Mike said

April 27, 2012 at 5:07 PM

Here’s a fairly literal implementation in Python 2.7:

def tpk():
    print "Enter 11 numbers:"
    S = [input("{:2}: ".format(n)) for n in range(1,12)]

    S.reverse()

    for item in S:
        try:
            x = pow(9.9, item)

        except OverflowError:
            print "OverflowError for {}".format(item)

        else:
            print x

Note: “input()” is generally not safe, because it actually executes the user input.

The Trabb Pardo Knuth Algorithm in Elisp | Irreal said
April 27, 2012 at 6:49 PM
[…] latest Programming Praxis Exercise is interesting. Back in 1973, Luis Trabb Pardo and Don Knuth published an algorithm that was meant […]
tartley said
April 28, 2012 at 12:09 PM
Almost the same as Mike’s, here as Python3. My personal preference is with fewer intermediate variables in this case.
```
from sys import stderr
from math import sqrt

def main():
    for number in reversed([input('> ') for _ in range(11)]):
        try:
            print(sqrt(float(number)))
        except (ValueError, OverflowError) as e:
            print('{} {} for {}'.format(
                type(e).__name__, str(e), number), file=stderr)
```
‘input’ in Python3 is the same as ‘raw_input’ in Python2, i.e. it doesn’t eval the input, but just returns it as a string. This means I cast to float before passing to my function ‘sqrt’. I broaden the scope of error catching from OverflowError to all ValueErrors, which includes failure to convert the entered string into a float.
treeowl said
April 29, 2012 at 7:41 AM
Remco, I think a Haskell solution truer to the spirit of the exercise would probably use something like GHC’s exception system to handle numeric overflow. Yours forbids it, rather than actually dealing with it.

David said

May 13, 2012 at 7:47 PM

Forth version, just don’t enter a double precision number.

11 Constant #Elements

: int-array ( compile: n -- / run: n -- addr )
    create 
        cells allot
    does>
        swap cells + ;

#Elements int-array vec

: get-input  ( -- )
    ." Enter " #Elements . ." numbers:" cr
    11 0 DO
        ." > " pad 25 accept cr
        pad swap number  i vec !
    LOOP ;

: reverse-it ( -- )
    #Elements 2/  0 DO
        i vec @  #Elements i - 1- vec @
        i vec !  #Elements i - 1- vec !
    LOOP ;

: 2^24*   ( n -- n ? )  \ multiply by 2^24,
          \ result TRUE is success, FALSE is overflow
    $1000000 m* 0= ;

: show-output  ( -- )
    #Elements 0 DO
        i vec @ 2^24* IF
            .
        ELSE
            ." Overflow"
        THEN cr
    LOOP ;

: tbk  ( -- )
    get-input
    reverse-it
    show-output ;

Execution

tbk Enter 11 numbers:
> 372
> 11
> 42
> 1
> 7
> 0
> 3772
> 2991
> 44
> 2
> 1
16777216
33554432
738197504
Overflow
Overflow
0
117440512
16777216
704643072
184549376
Overflow
 ok

Benjamin Samson said
May 14, 2012 at 6:03 AM
my implementation in Python:

def tbk():
s = raw_input("Enter 11 numbers separated by space: ")
s = s.split(‘ ‘)
s.reverse()

for i in s:
try:
result = pow(9.9, int(i))
except OverflowError:
print "Overflow error for {}".format(i)
else:
print result
tartley said
May 14, 2012 at 10:05 AM
Benjamin, see the link “Howto: posting source code” in the blog titlebar for how to post source code in your comments. Personally I found the third of the three described methods simplest.
Benjamin Samson said
May 14, 2012 at 10:12 AM
I saw that one after asking here. Should have search around before asking. Haha! Thanks anyway!
Rick Bhowmick said
May 1, 2014 at 7:09 AM
In Scala:
`
Seq.fill(11){Console.readInt}.reverse.map(i => Try(sqrt(i)).foreach {
case Success(root) => println(root)
case Failure(_) => println(“Could not compute sqrt”)
}
`

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