Trabb Pardo–Knuth algorithm

From Rosetta Code
Task
Trabb Pardo–Knuth algorithm
You are encouraged to solve this task according to the task description, using any language you may know.

The TPK algorithm is an early example of a programming chrestomathy. It was used in Donald Knuth and Luis Trabb Pardo's Stanford tech report The Early Development of Programming Languages. The report traces the early history of work in developing computer languages in the 1940s and 1950s, giving several translations of the algorithm.

From the wikipedia entry:

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

The task is to implement the algorithm:

  1. Use the function:    
  2. The overflow condition is an answer of greater than 400.
  3. The 'user alert' should not stop processing of other items of the sequence.
  4. Print a prompt before accepting eleven, textual, numeric inputs.
  5. You may optionally print the item as well as its associated result, but the results must be in reverse order of input.
  6. The sequence S may be 'implied' and so not shown explicitly.
  7. Print and show the program in action from a typical run here. (If the output is graphical rather than text then either add a screendump or describe textually what is displayed).



Ada[edit]

with Ada.Text_IO, Ada.Numerics.Generic_Elementary_Functions;
 
procedure Trabb_Pardo_Knuth is
 
type Real is digits 6 range -400.0 .. 400.0;
 
package TIO renames Ada.Text_IO;
package FIO is new TIO.Float_IO(Real);
package Math is new Ada.Numerics.Generic_Elementary_Functions(Real);
 
function F(X: Real) return Real is
begin
return (Math.Sqrt(abs(X)) + 5.0 * X**3);
end F;
 
Values: array(1 .. 11) of Real;
 
begin
TIO.Put("Please enter 11 Numbers:");
for I in Values'Range loop
FIO.Get(Values(I));
end loop;
 
for I in reverse Values'Range loop
TIO.Put("f(");
FIO.Put(Values(I), Fore => 2, Aft => 3, Exp => 0);
TIO.Put(")=");
begin
FIO.Put(F(Values(I)), Fore=> 4, Aft => 3, Exp => 0);
exception
when Constraint_Error => TIO.Put("-->too large<--");
end;
TIO.New_Line;
end loop;
 
end Trabb_Pardo_Knuth;
Output:
> ./trabb_pardo_knuth 
Please enter 11 Numbers:10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
f( 4.301)= 399.886
f( 4.302)=-->too large<--
f( 4.303)=-->too large<--
f( 4.305)=-->too large<--
f( 4.300)= 399.609
f( 4.000)= 322.000
f( 3.000)= 136.732
f( 2.000)=  41.414
f( 1.000)=   6.000
f(-1.000)=  -4.000
f(10.000)=-->too large<--

Agena[edit]

Tested with Agena 2.9.5 Win32

Translation of: ALGOL W
scope   # TPK algorithm in Agena
local y;
local a := [];
local f := proc( t :: number ) is return sqrt(abs(t))+5*t*t*t end;
for i from 0 to 10 do a[i] := tonumber( io.read() ) od;
for i from 10 to 0 by - 1 do
y:=f(a[i]);
if y > 400
then print( "TOO LARGE" )
else printf( "%10.4f\n", y )
fi
od
epocs
Output:
1
2
3
4
5
6
7
8
9
10
11
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
  322.0000
  136.7321
   41.4142
    6.0000

ALGOL 60[edit]

This is as close as possible to Pardo and Knuth's original but works with the GNU MARST ALGOL-to-C compiler. Note Pardo and Knuth did not insist on prompts or textual I/O as their report mostly concerned systems that predated even the idea of keyboard interaction.

begin 
integer i; real y; real array a[0:10];
real procedure f(t); value t; real t;
f:=sqrt(abs(t))+5*t^3;
for i:=0 step 1 until 10 do inreal(0, a[i]);
for i:=10 step -1 until 0 do
begin
y:=f(a[i]);
if y > 400 then outstring(1, "TOO LARGE")
else outreal(1,y);
outchar(1, "\n", 1)
end
end

Compilation and sample run:

bash-3.2$ marst tpk.a60 -o tpk.c
bash-3.2$ gcc tpk.c -lalgol -lm -o tpk
bash-3.2$ ./tpk
1 2 3 4 5 6 7 8 9 10 11
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
322 
136.732050808 
41.4142135624 
6 
bash-3.2$

ALGOL 68[edit]

Translation of: ALGOL W
which was itself a Translation of ALGOL 60.
[ 0 : 10 ]REAL a;
PROC f = ( REAL t )REAL:
sqrt(ABS t)+5*t*t*t;
FOR i FROM LWB a TO UPB a DO read( ( a[ i ] ) ) OD;
FOR i FROM UPB a BY -1 TO LWB a DO
REAL y=f(a[i]);
IF y > 400 THEN print( ( "TOO LARGE", newline ) )
ELSE print( ( fixed( y, -9, 4 ), newline ) )
FI
OD
Output:
1 2 3 4 5 6 7 8 9 10 11
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
 322.0000
 136.7321
  41.4142
   6.0000

ALGOL W[edit]

Translation of: ALGOL 60
begin 
real y; real array a( 0 :: 10 );
real procedure f( real value t );
sqrt(abs(t))+5*t*t*t;
for i:=0 until 10 do read( a(i) );
r_format := "A"; r_w := 9; r_d := 4;
for i:=10 step -1 until 0 do
begin
y:=f(a(i));
if y > 400 then write( "TOO LARGE" )
else write( y );
end
end.
Output:
1 2 3 4 5 6 7 8 9 10 11
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
 322.0000
 136.7320
  41.4142
   6.0000

AutoIt[edit]

; Trabb Pardo–Knuth algorithm
; by James1337 (autoit.de)
; AutoIt Version: 3.3.8.1
 
Local $S, $i, $y
 
Do
$S = InputBox("Trabb Pardo–Knuth algorithm", "Please enter 11 numbers:", "1 2 3 4 5 6 7 8 9 10 11")
If @error Then Exit
$S = StringSplit($S, " ")
Until ($S[0] = 11)
 
For $i = 11 To 1 Step -1
$y = f($S[$i])
If ($y > 400) Then
ConsoleWrite("f(" & $S[$i] & ") = Overflow!" & @CRLF)
Else
ConsoleWrite("f(" & $S[$i] & ") = " & $y & @CRLF)
EndIf
Next
 
Func f($x)
Return Sqrt(Abs($x)) + 5*$x^3
EndFunc
Output:
Input: "1 2 3 4 5 6 7 8 9 10 11"

f(11) = Overflow!
f(10) = Overflow!
f(9) = Overflow!
f(8) = Overflow!
f(7) = Overflow!
f(6) = Overflow!
f(5) = Overflow!
f(4) = 322
f(3) = 136.732050807569
f(2) = 41.4142135623731
f(1) = 6

AWK[edit]

 
# syntax: GAWK -f TRABB_PARDO-KNUTH_ALGORITHM.AWK
BEGIN {
printf("enter 11 numbers: ")
getline S
n = split(S,arr," ")
if (n != 11) {
printf("%d numbers entered; S/B 11\n",n)
exit(1)
}
for (i=n; i>0; i--) {
x = f(arr[i])
printf("f(%s) = %s\n",arr[i],(x>400) ? "too large" : x)
}
exit(0)
}
function abs(x) { if (x >= 0) { return x } else { return -x } }
function f(x) { return sqrt(abs(x)) + 5 * x ^ 3 }
 
Output:
enter 11 numbers: 1 2 3 -4 5 6 -7 8 9 10 11
f(11) = too large
f(10) = too large
f(9) = too large
f(8) = too large
f(-7) = -1712.35
f(6) = too large
f(5) = too large
f(-4) = -318
f(3) = 136.732
f(2) = 41.4142
f(1) = 6

BASIC256[edit]

dim s(11)
print 'enter 11 numbers'
for i = 0 to 10
input i + ">" , s[i]
next i
 
for i = 10 to 0 step -1
print "f(" + s[i] + ")=";
x = f(s[i])
if x > 400 then
print "--- too large ---"
else
print x
endif
next i
end
 
function f(n)
return sqrt(abs(n))+5*n^3
end function
Output:
enter 11 numbers
0>-4
1>-3
2>-4
3>-2
4>-1
5>-
6>1
7>2
8>3
9>4
10>5
f(5)=--- too large ---
f(4)=322
f(3)=136.7320508
f(2)=41.4142136
f(1)=6
f(0)=0
f(-1)=-4
f(-2)=-38.5857864
f(-4)=-318
f(-3)=-133.2679492
f(-4)=-318

C[edit]

 
 
/* Abhishek Ghosh
27th August, 2012 */

 
#include<math.h>
#include<stdio.h>
 
int
main ()
{
double inputs[11], check = 400, result;
int i;
 
printf ("\nPlease enter 11 numbers :");
 
for (i = 0; i < 11; i++)
{
scanf ("%lf", &inputs[i]);
}
 
printf ("\n\n\nEvaluating f(x) = |x|^0.5 + 5x^3 for the given inputs :");
 
for (i = 10; i >= 0; i--)
{
result = sqrt (fabs (inputs[i])) + 5 * pow (inputs[i], 3);
 
printf ("\nf(%lf) = ");
 
if (result > check)
{
printf ("Overflow!");
}
 
else
{
printf ("%lf", result);
}
}
 
return 0;
}
 
Output:
Please enter 11 numbers :10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301



Evaluating f(x) = |x|^0.5 + 5x^3 for the given inputs :
f(3.000000) = 399.886300
f(3.000000) = Overflow!
f(3.000000) = Overflow!
f(3.000000) = Overflow!
f(3.000000) = 399.608644
f(3.000000) = 322.000000
f(3.000000) = 136.732051
f(3.000000) = 41.414214
f(3.000000) = 6.000000
f(6.000000) = -4.000000
f(3.000000) = Overflow!

C++[edit]

 
#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
#include <iomanip>
 
int main( ) {
std::vector<double> input( 11 ) , results( 11 ) ;
std::cout << "Please enter 11 numbers!\n" ;
for ( int i = 0 ; i < input.size( ) ; i++ )
std::cin >> input[i];
 
std::transform( input.begin( ) , input.end( ) , results.begin( ) ,
[ ]( double n )-> double { return sqrt( abs( n ) ) + 5 * pow( n , 3 ) ; } ) ;
for ( int i = 10 ; i > -1 ; i-- ) {
std::cout << "f( " << std::setw( 3 ) << input[ i ] << " ) : " ;
if ( results[ i ] > 400 )
std::cout << "too large!" ;
else
std::cout << results[ i ] << " !" ;
std::cout << std::endl ;
}
return 0 ;
}
Output:
Please enter 11 numbers!
1
2
3
4
5
6
7
8
9
10
11
f(  11 ) : too large!
f(  10 ) : too large!
f(   9 ) : too large!
f(   8 ) : too large!
f(   7 ) : too large!
f(   6 ) : too large!
f(   5 ) : too large!
f(   4 ) : 322 !
f(   3 ) : 136.732 !
f(   2 ) : 41.4142 !
f(   1 ) : 6 !

Common Lisp[edit]

(defun read-numbers ()
(princ "Enter 11 numbers (space-separated): ")
(let ((numbers '()))
(dotimes (i 11 numbers)
(push (read) numbers))))
 
(defun trabb-pardo-knuth (func overflowp)
(let ((S (read-numbers)))
(format T "~{~a~%~}"
(substitute-if "Overflow!" overflowp (mapcar func S)))))
 
(trabb-pardo-knuth (lambda (x) (+ (expt (abs x) 0.5) (* 5 (expt x 3))))
(lambda (x) (> x 400)))
Output:
Enter 11 numbers (space-separated): 10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
399.88635
Overflow!
Overflow!
Overflow!
399.6087
322.0
136.73206
41.414215
6.0
-4.0
Overflow!

D[edit]

import std.stdio, std.math, std.conv, std.algorithm, std.array;
 
double f(in double x) pure nothrow {
return x.abs.sqrt + 5 * x ^^ 3;
}
 
void main() {
double[] data;
 
while (true) {
"Please enter eleven numbers on a line: ".write;
data = readln.split.map!(to!double).array;
if (data.length == 11)
break;
writeln("Those aren't eleven numbers.");
}
foreach_reverse (immutable x; data) {
immutable y = x.f;
writefln("f(%0.3f) = %s", x, y > 400 ? "Too large" : y.text);
}
}
Output:
Please enter eleven numbers on a line: 1 2 3 -4.55 5.1111 6 -7 8 9 10
Those aren't eleven numbers.
Please enter eleven numbers on a line: 1 2 3 -4.55 5.1111 6 -7 8 9 10 11
f(11.000) = Too large
f(10.000) = Too large
f(9.000) = Too large
f(8.000) = Too large
f(-7.000) = -1712.35
f(6.000) = Too large
f(5.111) = Too large
f(-4.550) = -468.849
f(3.000) = 136.732
f(2.000) = 41.4142
f(1.000) = 6

EchoLisp[edit]

 
(define (trabb-fun n)
(+ (* 5 n n n) (sqrt(abs n))))
 
(define (check-trabb n)
(if (number? n)
(if (<= (trabb-fun n) 400)
(printf "🌱 f(%d) = %d" n (trabb-fun n))
(printf "❌ f(%d) = %d" n (trabb-fun n)))
(error "not a number" n)))
 
(define (trabb (numlist null))
(while (< (length numlist) 11)
(set! numlist (append numlist
(or
(read default: (shuffle (iota 11))
prompt: (format "Please enter %d more numbers" (- 11 (length numlist))))
(error 'incomplete-list numlist))))) ;; users cancel
(for-each check-trabb (reverse (take numlist 11))))
 
Output:
 
(trabb)
;; input : (0 4 1 8 5 9 10 3 6 7 2)
 
🌱 f(2) = 41.41421356237309
f(7) = 1717.6457513110645
f(6) = 1082.4494897427833
🌱 f(3) = 136.73205080756887
f(10) = 5003.162277660168
f(9) = 3648
f(5) = 627.2360679774998
f(8) = 2562.828427124746
🌱 f(1) = 6
🌱 f(4) = 322
🌱 f(0) = 0
 
;; extra credit : let's find the threshold
(lib 'math)
(define (g x) (- (trabb-fun x) 400))
(root g 0 10)
4.301409367213084
 

Ela[edit]

Translation of OCaml version:

open monad io number string
 
:::IO
 
take_numbers 0 xs = do
return $ iter xs
where f x = sqrt (toSingle x) + 5.0 * (x ** 3.0)
p x = x < 400.0
iter [] = return ()
iter (x::xs)
| p res = do
putStrLn (format "f({0}) = {1}" x res)
iter xs
| else = do
putStrLn (format "f({0}) :: Overflow" x)
iter xs
where res = f x
take_numbers n xs = do
x <- readAny
take_numbers (n - 1) (x::xs)
 
do
putStrLn "Please enter 11 numbers:"
take_numbers 11 []
Output:
Please enter 11 numbers:
1
2
3
4
5
6
7
8
9
10
11
f(11) :: Overflow
f(10) :: Overflow
f(9) :: Overflow
f(8) :: Overflow
f(7) :: Overflow
f(6) :: Overflow
f(5) :: Overflow
f(4) = 322
f(3) = 136.732050807569
f(2) = 41.4142135623731
f(1) = 6

Elena[edit]

Translation of: C

ELENA 3.2.1 :

import system'math
import extensions.
 
program =
[
array<real> inputs := real&(11).
console printLine("Please enter 11 numbers :").
0 till:11 do(:i)
[
inputs[i] := console readLine; toReal.
].
 
console printLine("Evaluating f(x) = |x|^0.5 + 5x^3 for the given inputs :").
10 to:0 do(:i)
[
var r1 := inputs[i] absolute; sqrt.
var r2 := inputs[i] power(3).
var r :=inputs[i] /*absolute;*/ sqrt + 5*r2.
 
real result := (inputs[i] absolute; sqrt) + 5 * (inputs[i] power(3)).
 
console print("f(", inputs[i], ")=").
 
if (result > 400)
[
console printLine("Overflow!")
];
[
console printLine(result).
]
]
].
Output:
Please enter 11 numbers :
1
2
3
4
5
6
7
8
9
10
11	
Evaluating f(x) = |x|^0.5 + 5x^3 for the given inputs :
f(11.0)=Overflow!
f(10.0)=Overflow!
f(9.0)=Overflow!
f(8.0)=Overflow!
f(7.0)=Overflow!
f(6.0)=Overflow!
f(5.0)=Overflow!
f(4.0)=322.0
f(3.0)=136.7320508076
f(2.0)=41.41421356237
f(1.0)=6.0

Elixir[edit]

Translation of: Erlang
defmodule Trabb_Pardo_Knuth do
def task do
Enum.reverse( get_11_numbers )
|> Enum.each( fn x -> perform_operation( &function(&1), 400, x ) end )
end
 
defp alert( n ), do: IO.puts "Operation on #{n} overflowed"
 
defp get_11_numbers do
ns = IO.gets( "Input 11 integers. Space delimited, please: " )
|> String.split
|> Enum.map( &String.to_integer &1 )
if 11 == length( ns ), do: ns, else: get_11_numbers
end
 
defp function( x ), do: :math.sqrt( abs(x) ) + 5 * :math.pow( x, 3 )
 
defp perform_operation( fun, overflow, n ), do: perform_operation_check_overflow( n, fun.(n), overflow )
 
defp perform_operation_check_overflow( n, result, overflow ) when result > overflow, do: alert( n )
defp perform_operation_check_overflow( n, result, _overflow ), do: IO.puts "f(#{n}) => #{result}"
end
 
Trabb_Pardo_Knuth.task
Output:
Input 11 integers.  Space delimited, please: 0 1 2 3 4 5 6 7 8 9 10
Operation on 10 overflowed
Operation on 9 overflowed
Operation on 8 overflowed
Operation on 7 overflowed
Operation on 6 overflowed
Operation on 5 overflowed
f(4) => 322.0
f(3) => 136.73205080756887
f(2) => 41.41421356237309
f(1) => 6.0
f(0) => 0.0

Erlang[edit]

 
-module( trabb_pardo_knuth ).
 
-export( [task/0] ).
 
task() ->
Sequence = get_11_numbers(),
S = lists:reverse( Sequence ),
[perform_operation( fun function/1, 400, X) || X <- S].
 
 
alert( N ) -> io:fwrite( "Operation on ~p overflowed~n", [N] ).
 
get_11_numbers() ->
{ok, Ns} = io:fread( "Input 11 integers. Space delimited, please: ", "~d ~d ~d ~d ~d ~d ~d ~d ~d ~d ~d" ),
11 = erlang:length( Ns ),
Ns.
 
function( X ) -> math:sqrt( erlang:abs(X) ) + 5 * math:pow( X, 3 ).
 
perform_operation( Fun, Overflow, N ) -> perform_operation_check_overflow( N, Fun(N), Overflow ).
 
perform_operation_check_overflow( N, Result, Overflow ) when Result > Overflow -> alert( N );
perform_operation_check_overflow( N, Result, _Overflow ) -> io:fwrite( "f(~p) => ~p~n", [N, Result] ).
 
Output:
5> trabb_pardo_knuth:task().
Input 11 integers.  Space delimited, please:  1 2 3 4 5 6 7 8 9 10 11
Operation on 11 overflowed
Operation on 10 overflowed
Operation on 9 overflowed
Operation on 8 overflowed
Operation on 7 overflowed
Operation on 6 overflowed
Operation on 5 overflowed
f(4) => 322.0
f(3) => 136.73205080756887
f(2) => 41.41421356237309
f(1) => 6.0

ERRE[edit]

 
!Trabb Pardo-Knuth algorithm
PROGRAM TPK
!VAR I%,Y
DIM A[10]
 
FUNCTION F(T)
F=SQR(ABS(T))+5*T^3
END FUNCTION
 
BEGIN
DATA(10,-1,1,2,3,4,4.3,4.305,4.303,4.302,4.301)
FOR I%=0 TO 10 DO
READ(A[I%])
END FOR
FOR I%=10 TO 0 STEP -1 DO
Y=F(A[I%])
PRINT("F(";A[I%];")=";)
IF Y>400 THEN PRINT("--->too large<---")
ELSE PRINT(Y)
END IF
END FOR
END PROGRAM
 

Numbers to be elaborated is included in the program with a DATA statement. You can substitute this with an input keyboard like this

   FOR I%=0 TO 10 DO
    PRINT("Number #";I%;)
    INPUT(A[I%])
   END FOR

F#[edit]

 
module ``Trabb Pardo - Knuth``
open System
let f (x: float) = sqrt(abs x) + (5.0 * (x ** 3.0))
 
Console.WriteLine "Enter 11 numbers:"
[for _ in 1..11 -> Convert.ToDouble(Console.ReadLine())]
|> List.rev |> List.map f |> List.iter (function
| n when n <= 400.0 -> Console.WriteLine(n)
| _ -> Console.WriteLine("Overflow"))
 
Output:
fsharpi Program.fsx
[Loading Program.fsx]
Enter 11 numbers:
1
2
3
4
5
6
7
8
9
10
11
Overflow
Overflow
Overflow
Overflow
Overflow
Overflow
Overflow
322
136.732050807569
41.4142135623731
6

Forth[edit]

: f(x)  fdup fsqrt fswap 3e f** 5e f* f+ ;
 
4e2 fconstant f-too-big
 
11 Constant #Elements
 
: float-array ( compile: n -- / run: n -- addr )
create
floats allot
does>
swap floats + ;
 
#Elements float-array vec
 
: get-it ( -- )
." Enter " #Elements . ." numbers:" cr
#Elements 0 DO
." > " pad 25 accept cr
pad swap >float 0= abort" Invalid Number"
i vec F!
LOOP ;
 
: reverse-it ( -- )
#Elements 2/ 0 DO
i vec [email protected] #Elements i - 1- vec [email protected]
i vec F! #Elements i - 1- vec F!
LOOP ;
 
: do-it ( -- )
#Elements 0 DO
i vec [email protected] fdup f. [char] : emit space
f(x) fdup f-too-big f> IF
fdrop ." too large"
ELSE
f.
THEN cr
LOOP ;
 
: tpk ( -- )
get-it reverse-it do-it ;
Output:
Gforth 0.7.2, Copyright (C) 1995-2008 Free Software Foundation, Inc.
Gforth comes with ABSOLUTELY NO WARRANTY; for details type `license'
Type `bye' to exit
tpk Enter 11 numbers:
> 1 
> 2 
> 3 
> 4 
> 5 
> 6 
> 2.71828 
> 3.14159 
> 76 
> 7 
> 8 
8. : too large
7. : too large
76. : too large
3.14159 : 156.80344365595 
2.71828 : 102.07620267347 
6. : too large
5. : too large
4. : 322. 
3. : 136.732050807569 
2. : 41.4142135623731 
1. : 6. 
 ok

Fortran[edit]

Fortran 95[edit]

Works with: Fortran version 95 and later
program tpk
implicit none
 
real, parameter :: overflow = 400.0
real :: a(11), res
integer :: i
 
write(*,*) "Input eleven numbers:"
read(*,*) a
 
a = a(11:1:-1)
do i = 1, 11
res = f(a(i))
write(*, "(a, f0.3, a)", advance = "no") "f(", a(i), ") = "
if(res > overflow) then
write(*, "(a)") "overflow!"
else
write(*, "(f0.3)") res
end if
end do
 
contains
 
real function f(x)
real, intent(in) :: x
 
f = sqrt(abs(x)) + 5.0*x**3
 
end function
end program
Output:
 Input eleven numbers:
10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
f(4.301) = 399.886
f(4.302) = overflow!
f(4.303) = overflow!
f(4.305) = overflow!
f(4.300) = 399.609
f(4.000) = 322.000
f(3.000) = 136.732
f(2.000) = 41.414
f(1.000) = 6.000
f(-1.000) = -4.000
f(10.000) = overflow!

Fortran I[edit]

Written in FORTRAN I (1957), the original language quoted in the 1976 Donald Knuth & Luis Trabb Pardo’s study. Let’ note: no type declarations (INTEGER, REAL), no subprogram FUNCTION (only statement function), no logical IF, no END statement, and only Hollerith strings. The input data are on 2 80-column punched cards, only 1 to 72 columns are used so 6 values are read on the first card and 5 on the second card, so even input data could be numbered in the 73-80 area.

C     THE TPK ALGORITH - FORTRAN I - 1957                               TPK00010
FTPKF(X)=SQRTF(ABSF(X))+5.0*X**3 TPK00020
DIMENSION A(11) TPK00030
READ 100,A TPK00040
100 FORMAT(6F12.4/) TPK00050
DO 3 I=1,11 TPK00060
J=12-I TPK00070
Y=FTPKF(A(J)) TPK00080
IF (Y-400.0)2,2,1 TPK00090
1 PRINT 301,I,A(J) TPK00100
301 FORMAT(I10,F12.7,18H *** TOO LARGE ***) TPK00110
GO TO 10 TPK00120
2 PRINT 302,I,A(J),Y TPK00130
302 FORMAT(I10,2F12.7) TPK00140
3 CONTINUE TPK00150
STOP 0 TPK00160
 

FreeBASIC[edit]

' version 22-07-2017
' compile with: fbc -s console
 
Function f(n As Double) As Double
return Sqr(Abs(n)) + 5 * n ^ 3
End Function
 
' ------=< MAIN >=------
 
Dim As Double x, s(1 To 11)
Dim As Long i
 
For i = 1 To 11
Print Str(i);
Input " => ", s(i)
Next
 
Print
Print String(20,"-")
 
i -= 1
Do
Print "f(" + Str(s(i)) + ") = ";
x = f(s(i))
If x > 400 Then
Print "-=< overflow >=-"
Else
Print x
End If
i -= 1
Loop Until i < 1
 
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
Output:
1 => -5
2 => -3
3 => -2
4 => -1
5 => 0
6 => 1
7 => 2
8 => 3
9 => 4
10 => 5
11 => 6

--------------------
f(6) = -=< overflow >=-
f(5) = -=< overflow >=-
f(4) =  322
f(3) =  136.7320508075689
f(2) =  41.41421356237309
f(1) =  6
f(0) =  0
f(-1) = -4
f(-2) = -38.58578643762691
f(-3) = -133.2679491924311
f(-5) = -622.7639320225002

Go[edit]

Task/Wikipedia[edit]

This solution follows the task description by reversing the sequence. It also rejects non-numeric input until 11 numbers are entered.

package main
 
import (
"fmt"
"log"
"math"
)
 
func main() {
// prompt
fmt.Print("Enter 11 numbers: ")
// accept sequence
var s [11]float64
for i := 0; i < 11; {
if n, _ := fmt.Scan(&s[i]); n > 0 {
i++
}
}
// reverse sequence
for i, item := range s[:5] {
s[i], s[10-i] = s[10-i], item
}
// iterate
for _, item := range s {
if result, overflow := f(item); overflow {
// send alerts to stderr
log.Printf("f(%g) overflow", item)
} else {
// send normal results to stdout
fmt.Printf("f(%g) = %g\n", item, result)
}
}
}
 
func f(x float64) (float64, bool) {
result := math.Sqrt(math.Abs(x)) + 5*x*x*x
return result, result > 400
}
Output:

The input is chosen to show some interesting boundary cases.

Enter 11 numbers: 0 1 4.3 4.4 -1 -5 non-number -1e102 -1e103 -Inf Inf NaN 
f(NaN) = NaN
2016/04/15 18:38:29 f(+Inf) overflow
f(-Inf) = NaN
f(-1e+103) = -Inf
f(-1e+102) = -5e+306
f(-5) = -622.7639320225002
f(-1) = -4
2016/04/15 18:38:29 f(4.4) overflow
f(4.3) = 399.6086441353327
f(1) = 6
f(0) = 0

TPK paper[edit]

The original paper had no requirement to reverse the sequence in place, but instead processed the sequence in reverse order.

package main
 
import (
"fmt"
"math"
)
 
func f(t float64) float64 {
return math.Sqrt(math.Abs(t)) + 5*math.Pow(t, 3)
}
 
func main() {
var a [11]float64
for i := range a {
fmt.Scan(&a[i])
}
for i := len(a) - 1; i >= 0; i-- {
if y := f(a[i]); y > 400 {
fmt.Println(i, "TOO LARGE")
} else {
fmt.Println(i, y)
}
}
}

Haskell[edit]

import Control.Monad (replicateM, mapM_)
 
f x = (abs x) ** 0.5 + 5 * x ** 3
 
main = do
putStrLn "Enter 11 numbers for evaluation"
x <- replicateM 11 $ readLn
mapM_ ((\x -> if x > 400
then putStrLn "OVERFLOW"
else print x). f) $ reverse x
 
Output:
Enter 11 numbers for evaluation
1
2
3
4
5
6
7
8
9
10
11
OVERFLOW
OVERFLOW
OVERFLOW
OVERFLOW
OVERFLOW
OVERFLOW
OVERFLOW
322.0
136.73205080756887
41.41421356237309
6.0

Icon and Unicon[edit]

The following Unicon-specific solution can be implemented in Icon by replaces reverse(S) with S[*S to 1 by -1].

procedure main()
S := []
writes("Enter 11 numbers: ")
read() ? every !11 do (tab(many(' \t'))|0,put(S, tab(upto(' \t')|0)))
every item := !reverse(S) do
write(item, " -> ", (400 >= f(item)) | "overflows")
end
 
procedure f(x)
return abs(x)^0.5 + 5*x^3
end

Sample run:

->tpk
Enter 11 numbers: 1 2 3 4 5 6 7 8 9 10 11
11 -> overflows
10 -> overflows
9 -> overflows
8 -> overflows
7 -> overflows
6 -> overflows
5 -> overflows
4 -> 322.0
3 -> 136.7320508075689
2 -> 41.41421356237309
1 -> 6.0
->

Io[edit]

 
// Initialize objects to be used
in_num := File standardInput()
nums := List clone
result := Number
 
// Prompt the user and get numbers from standard input
"Please enter 11 numbers:" println
11 repeat(nums append(in_num readLine() asNumber()))
 
// Reverse the numbers received
nums reverseInPlace
 
// Apply the function and tell the user if the result is above
// our limit. Otherwise, tell them the result.
nums foreach(v,
// v needs parentheses around it for abs to properly convert v to its absolute value
result = (v) abs ** 0.5 + 5 * v ** 3
if (result > 400,
"Overflow!" println
,
result println
)
)
 
Output:
io tpk.io
Please enter 11 numbers:
1
2
3
4
5
6
7
8
9
10
11
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
322
136.7320508075688679
41.4142135623730923
6

J[edit]

Input and output in J is done using "foreigns", in this case it is reading from the keyboard. The calculations are straightforward and applied to the whole set simultaneously. Similarly, overflow detection and changing the value to 'user alert' is also done once for all values.

No checks are done if the input is actually numbers and if there are actually eleven of them. This doesn't affect the algorithm. Additional checks can be done separately.

tpk=: 3 :0
smoutput 'Enter 11 numbers: '
t1=: ((5 * ^&3) + (^&0.5@* *))"0 |. _999&".;._1 ' ' , 1!:1 [ 1
smoutput 'Values of functions of reversed input: ' , ": t1
 ; <@(,&' ')@": ` ((<'user alert ')&[) @. (>&400)"0 t1
)

A possible use scenario:

   tpk ''
Enter 11 numbers:
1 2 3 4 5 6 7 8.8 _9 10.123 0
Values of functions of reversed input: 0 5189.96 _3642 3410.33 1717.65 1082.45 627.236 322 136.732 41.4142 6
0 user alert _3642 user alert user alert user alert user alert 322 136.732 41.4142 6
 

Note that the result of tpk is persisted in t1 and is also its explicit result rather than being an explicit output.

Here's an alternative approach:

get11numbers=: 3 :0
smoutput 'Enter 11 numbers: '
_&". 1!:1]1
)
 
f_x=: %:@| + 5 * ^&3
 
overflow400=: 'user alert'"_`":@.(<:&400)"0
 
tpk=: [email protected][email protected]|[email protected]

And, here's this alternative in action:

   tpk''
Enter 11 numbers:
1 2 3 4 5 6 7 8.8 _9 10.123 0
0
user alert
_3642
user alert
user alert
user alert
user alert
322
136.732
41.4142
6

(clearly, other alternatives are also possible).

Note that no error is reported if something other than 11 numbers are provided, since it's not clear what should be done for that case -- we just process all of them.

Java[edit]

/**
* Alexander Alvonellos
*/

import java.util.*;
import java.io.*;
 
public class TPKA {
public static void main(String... args) {
double[] input = new double[11];
double userInput = 0.0;
Scanner in = new Scanner(System.in);
for(int i = 0; i < 11; i++) {
System.out.print("Please enter a number: ");
String s = in.nextLine();
try {
userInput = Double.parseDouble(s);
} catch (NumberFormatException e) {
System.out.println("You entered invalid input, exiting");
System.exit(1);
}
input[i] = userInput;
}
for(int j = 10; j >= 0; j--) {
double x = input[j]; double y = f(x);
if( y < 400.0) {
System.out.printf("f( %.2f ) = %.2f\n", x, y);
} else {
System.out.printf("f( %.2f ) = %s\n", x, "TOO LARGE");
}
}
}
 
private static double f(double x) {
return Math.pow(Math.abs(x), 0.5) + (5*(Math.pow(x, 3)));
}
}
 
Output:
Please enter a number: 1
Please enter a number: 2
Please enter a number: 3
Please enter a number: 4
Please enter a number: 5
Please enter a number: 6
Please enter a number: 7
Please enter a number: 8
Please enter a number: 9
Please enter a number: 10
Please enter a number: 11
f( 11.00 ) = TOO LARGE
f( 10.00 ) = TOO LARGE
f( 9.00 ) = TOO LARGE
f( 8.00 ) = TOO LARGE
f( 7.00 ) = TOO LARGE
f( 6.00 ) = TOO LARGE
f( 5.00 ) = TOO LARGE
f( 4.00 ) = 322.00
f( 3.00 ) = 136.73
f( 2.00 ) = 41.41
f( 1.00 ) = 6.00

JavaScript[edit]

Spidermonkey[edit]

#!/usr/bin/env js
 
function main() {
var nums = getNumbers(11);
nums.reverse();
for (var i in nums) {
pardoKnuth(nums[i], fn, 400);
}
}
 
function pardoKnuth(n, f, max) {
var res = f(n);
putstr('f(' + String(n) + ')');
if (res > max) {
print(' is too large');
} else {
print(' = ' + String(res));
}
}
 
function fn(x) {
return Math.pow(Math.abs(x), 0.5) + 5 * Math.pow(x, 3);
}
 
function getNumbers(n) {
var nums = [];
print('Enter', n, 'numbers.');
for (var i = 1; i <= n; i++) {
putstr(' ' + i + ': ');
var num = readline();
nums.push(Number(num));
}
return nums;
}
 
main();
 

Results:

Enter 11 numbers.
   1: 1
   2: 2
   3: 3
   4: 4
   5: 5
   6: 6
   7: 7
   8: 8
   9: 9
   10: 10
   11: 11
f(11)  is too large
f(10)  is too large
f(9)  is too large
f(8)  is too large
f(7)  is too large
f(6)  is too large
f(5)  is too large
f(4) = 322
f(3) = 136.73205080756887
f(2) = 41.41421356237309
f(1) = 6

jq[edit]

jq does not currently have an interactive mode allowing a prompt to be issued first, and so the initial prompt is implemented here using "echo", in keeping with the jq approach of dovetailing with other command-line tools.

def f:
def abs: if . < 0 then -. else . end;
def power(x): (x * log) | exp;
. as $x | abs | power(0.5) + (5 * (.*.*. ));
 
. as $in | split(" ") | map(tonumber)
| if length == 11 then
reverse | map(f | if . > 400 then "TOO LARGE" else . end)
else error("The number of numbers was not 11.")
end
| .[] # print one result per line
Output:
$ echo "Enter 11 numbers on one line; when done, enter the end-of-file character:" ;\
jq -M -s -R -f Trabb_Pardo-Knuth_algorithm.jq
> Enter 11 numbers on one line; when done, enter the end-of-file character:
1 2 3 4 5 6 7 8 9 10 11
"TOO LARGE"
"TOO LARGE"
"TOO LARGE"
"TOO LARGE"
"TOO LARGE"
"TOO LARGE"
"TOO LARGE"
322
136.73205080756887
41.41421356237309
6

Kotlin[edit]

// version 1.1.2
 
fun f(x: Double) = Math.sqrt(Math.abs(x)) + 5.0 * x * x * x
 
fun main(args: Array<String>) {
val da = DoubleArray(11)
println("Please enter 11 numbers:")
var i = 0
while (i < 11) {
print(" ${"%2d".format(i + 1)}: ")
val d = readLine()!!.toDoubleOrNull()
if (d == null)
println("Not a valid number, try again")
else
da[i++] = d
}
println("\nThe sequence you just entered in reverse is:")
da.reverse()
println(da.contentToString())
println("\nProcessing this sequence...")
for (j in 0..10) {
val v = f(da[j])
print(" ${"%2d".format(j + 1)}: ")
if (v > 400.0)
println("Overflow!")
else
println(v)
}
}
Output:

Sample session:

Please enter 11 numbers:
   1: 10
   2: -1
   3: 1
   4: 2
   5: 3
   6: 4
   7: 4.3
   8: 4.305
   9: 4.303
  10: 4.302
  11: 4.301

The sequence you just entered in reverse is:
[4.301, 4.302, 4.303, 4.305, 4.3, 4.0, 3.0, 2.0, 1.0, -1.0, 10.0]

Processing this sequence...
   1: 399.88629974772687
   2: Overflow!
   3: Overflow!
   4: Overflow!
   5: 399.6086441353327
   6: 322.0
   7: 136.73205080756887
   8: 41.41421356237309
   9: 6.0
  10: -4.0
  11: Overflow!

Julia[edit]

f(x) = abs(x)^.5 + 5x^3
for i in map(parseint,reverse(split(readline())))
v = f(i)
println("$i: ", v > 400 ? "TOO LARGE" : v)
end
Output:
1 2 3 4 5 6 7 8 9 10 11
11: TOO LARGE
10: TOO LARGE
9: TOO LARGE
8: TOO LARGE
7: TOO LARGE
6: TOO LARGE
5: TOO LARGE
4: 322.0
3: 136.73205080756887
2: 41.41421356237309
1: 6.0

Lua[edit]

Implementation of task description[edit]

function f (x) return math.abs(x)^0.5 + 5*x^3 end
 
function reverse (t)
local rev = {}
for i, v in ipairs(t) do rev[#t - (i-1)] = v end
return rev
end
 
local sequence, result = {}
print("Enter 11 numbers...")
for n = 1, 11 do
io.write(n .. ": ")
sequence[n] = io.read()
end
for _, x in ipairs(reverse(sequence)) do
result = f(x)
if result > 400 then print("Overflow!") else print(result) end
end
Output:
Enter 11 numbers...
1: 1
2: 2
3: 3
4: 4
5: 5
6: 6
7: 7
8: 8
9: 9
10: 10
11: 11
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
322
136.73205080757
41.414213562373
6

Line-for-line from TPK paper[edit]

local a, y = {}
function f (t)
return math.sqrt(math.abs(t)) + 5*t^3
end
for i = 0, 10 do a[i] = io.read() end
for i = 10, 0, -1 do
y = f(a[i])
if y > 400 then print(i, "TOO LARGE")
else print(i, y) end
end
Output:
1
2
3
4
5
6
7
8
9
10
11
10      TOO LARGE
9       TOO LARGE
8       TOO LARGE
7       TOO LARGE
6       TOO LARGE
5       TOO LARGE
4       TOO LARGE
3       322
2       136.73205080757
1       41.414213562373
0       6

Mathematica[edit]

numbers=RandomReal[{-2,6},11]
tpk[numbers_,overflowVal_]:=Module[{revNumbers},
revNumbers=Reverse[numbers];
f[x_]:=Abs[x]^0.5+5 x^3;
Do[
If[f[i]>overflowVal,
Print["f[",i,"]= Overflow"]
,
Print["f[",i,"]= ",f[i]]
]
,
{i,revNumbers}
]
]
tpk[numbers,400]
Output:
{0.470145,1.18367,2.36984,4.86759,2.40274,5.48793,3.30256,5.34393,4.21944,2.23501,-0.0200707}
f[-0.0200707]= 0.141631
f[2.23501]= 57.3176
f[4.21944]= 377.663
f[5.34393]= Overflow
f[3.30256]= 181.921
f[5.48793]= Overflow
f[2.40274]= 70.9068
f[4.86759]= Overflow
f[2.36984]= 68.0859
f[1.18367]= 9.38004
f[0.470145]= 1.20527

Nim[edit]

Translation of: Python
import math, rdstdin, strutils, algorithm
 
proc f(x): float = x.abs.pow(0.5) + 5 * x.pow(3)
 
proc ask: seq[float] =
readLineFromStdin("\n11 numbers: ").strip.split[0..10].map(parseFloat)
 
var s = ask()
reverse s
for x in s:
let result = f x
stdout.write " ",x,":", if result > 400: "TOO LARGE!" else: $result
echo ""
Output:
11 numbers: 1 2 3 4 5 6 7 8 9 10 11
 11.0:TOO LARGE! 10.0:TOO LARGE! 9.0:TOO LARGE! 8.0:TOO LARGE! 7.0:TOO LARGE! 6.0:TOO LARGE! 5.0:TOO LARGE! 4.0:322.0 3.0:136.7320508075689 2.0:41.41421356237309 1.0:6.0

Objective-C[edit]

Works with: Mac OS X version 10.6+
//
// TPKA.m
// RosettaCode
//
// Created by Alexander Alvonellos on 5/26/12.
// Trabb Pardo-Knuth algorithm
//
 
#import <Foundation/Foundation.h>
double f(double x);
 
double f(double x) {
return pow(abs(x), 0.5) + 5*(pow(x, 3));
}
 
int main (int argc, const char * argv[])
{
@autoreleasepool {
NSMutableArray *input = [[NSMutableArray alloc] initWithCapacity:0];
 
printf("%s", "Instructions: please enter 11 numbers.\n");
for(int i = 0; i < 11; i++) {
double userInput = 0.0;
printf("%s", "Please enter a number: ");
scanf("%lf", &userInput);
[input addObject: @(userInput)];
}
 
for(int i = 10; i >= 0; i--) {
double x = [input[i] doubleValue];
double y = f(x);
printf("f(%.2f) \t=\t", x);
if(y < 400.0) {
printf("%.2f\n", y);
} else {
printf("%s\n", "TOO LARGE");
}
}
}
return 0;
}
 
Output:
Instructions: please enter 11 numbers.
Please enter a number: 1
Please enter a number: 2
Please enter a number: 3
Please enter a number: 4
Please enter a number: 5
Please enter a number: 6
Please enter a number: 7
Please enter a number: 8
Please enter a number: 9
Please enter a number: 10
Please enter a number: 11
f(11.00) 	=	TOO LARGE
f(10.00) 	=	TOO LARGE
f(9.00) 	=	TOO LARGE
f(8.00) 	=	TOO LARGE
f(7.00) 	=	TOO LARGE
f(6.00) 	=	TOO LARGE
f(5.00) 	=	TOO LARGE
f(4.00) 	=	322.00
f(3.00) 	=	136.73
f(2.00) 	=	41.41
f(1.00) 	=	6.00

OCaml[edit]

let f x = sqrt x +. 5.0 *. (x ** 3.0)
let p x = x < 400.0
 
let () =
print_endline "Please enter 11 Numbers:";
let lst = Array.to_list (Array.init 11 (fun _ -> read_float ())) in
List.iter (fun x ->
let res = f x in
if p res
then Printf.printf "f(%g) = %g\n%!" x res
else Printf.eprintf "f(%g) :: Overflow\n%!" x
) (List.rev lst)
Output:
$ ocaml trabb_pardo_knuth.ml
Please enter 11 Numbers:
1
2
3
4
5
6
7
8
9
10
11
f(11) :: Overflow
f(10) :: Overflow
f(9) :: Overflow
f(8) :: Overflow
f(7) :: Overflow
f(6) :: Overflow
f(5) :: Overflow
f(4) = 322
f(3) = 136.732
f(2) = 41.4142
f(1) = 6

We output error messages on stderr. We flush outputs with "%!" so that results and error messages do not appear separated.

PARI/GP[edit]

{
print("11 numbers: ");
v=vector(11, n, eval(input()));
v=apply(x->x=sqrt(abs(x))+5*x^3;if(x>400,"overflow",x), v);
vector(11, i, v[12-i])
}
Output:
11 numbers:
1
2
3
4
5
6
7
8
9
10
11
%1 = ["overflow", "overflow", "overflow", "overflow", "overflow", "overflow",
"overflow", 322.0000000000000000000000000, 136.7320508075688772935274463, 41.414
21356237309504880168872, 6.000000000000000000000000000]

Perl[edit]

#!/usr/bin/perl
use strict ;
use warnings ;
 
my $number ;
my @sequence ;
print "Please enter 11 numbers!\n" ;
for my $i ( 0..10 ) {
$number = <STDIN> ;
chomp $number ;
push @sequence , $number ;
}
map { my $result = sqrt( abs ( $_ ) ) + 5 * $_** 3 ; print "f( $_ ) " ; $result > 400 ? print "too large!\n" : print ": $result\n" ; }
reverse @sequence ;
 
Output:
Please enter 11 numbers!
2
1.2
3
3.4
4
4.5
5 
7.8
2.7
13
11.2
f( 11.2 ) too large!
f( 13 ) too large!
f( 2.7 ) : 100.058167672516
f( 7.8 ) too large!
f( 5 ) too large!
f( 4.5 ) too large!
f( 4 ) : 322
f( 3.4 ) : 198.363908891459
f( 3 ) : 136.732050807569
f( 1.2 ) : 9.73544511501033
f( 2 ) : 41.4142135623731

Perl 6[edit]

my @nums = prompt("Please type 11 space-separated numbers: ").words
until @nums == 11;
for @nums.reverse -> $n {
my $r = $n.abs.sqrt + 5 * $n ** 3;
say "$n\t{ $r > 400 ?? 'Urk!' !! $r }";
}
Output:
Please type 11 space-separated numbers: 10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
4.301	399.88629974772681
4.302	Urk!
4.303	Urk!
4.305	Urk!
4.3	399.60864413533278
4	322
3	136.73205080756887
2	41.414213562373092
1	6
-1	-4
10	Urk!

Phix[edit]

function f(atom x)
return sqrt(abs(x))+5*power(x,3)
end function
 
string s = substitute(prompt_string("Enter 11 numbers:"),","," ")
sequence S = scanf(s,"%f %f %f %f %f %f %f %f %f %f %f")
if length(S)!=1 then puts(1,"not 11 numbers") abort(0) end if
S = reverse(S[1])
for i=1 to length(S) do
atom result = f(S[i])
if result>400 then
printf(1,"f(%g):overflow\n",{S[i]})
else
printf(1,"f(%g):%g\n",{S[i],result})
end if
end for
Output:
Enter 11 numbers:10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
f(4.301):399.886
f(4.302):overflow
f(4.303):overflow
f(4.305):overflow
f(4.3):399.609
f(4):322
f(3):136.732
f(2):41.4142
f(1):6
f(-1):-4
f(10):overflow

Enter 11 numbers:1,2,3,4,5,6,7,8,9,10,11
f(11):overflow
f(10):overflow
f(9):overflow
f(8):overflow
f(7):overflow
f(6):overflow
f(5):overflow
f(4):322
f(3):136.732
f(2):41.4142
f(1):6

Enter 11 numbers:0.470145,1.18367,2.36984,4.86759,2.40274,5.48793,3.30256,5.34393,4.21944,2.23501,-0.0200707
f(-0.0200707):0.141631
f(2.23501):57.3174
f(4.21944):377.662
f(5.34393):overflow
f(3.30256):181.921
f(5.48793):overflow
f(2.40274):70.9071
f(4.86759):overflow
f(2.36984):68.0862
f(1.18367):9.38002
f(0.470145):1.20527

PicoLisp[edit]

(de f (X)
(+ (sqrt (abs X)) (* 5 X X X)) )
 
(trace 'f)
 
(in NIL
(prin "Input 11 numbers: ")
(for X (reverse (make (do 11 (link (read)))))
(when (> (f X) 400)
(prinl "TOO LARGE") ) ) )

Test:

Input 11 numbers: 1 2 3 4 5 6 7 8 9 10 11
f : 11
f = 6658
TOO LARGE
f : 10
f = 5003
TOO LARGE
f : 9
f = 3648
TOO LARGE
f : 8
f = 2562
TOO LARGE
f : 7
f = 1717
TOO LARGE
f : 6
f = 1082
TOO LARGE
f : 5
f = 627
TOO LARGE
f : 4
f = 322
f : 3
f = 136
f : 2
f = 41
f : 1
f = 6

PL/I[edit]

 
Trabb: Procedure options (main); /* 11 November 2013 */
 
declare (i, n) fixed binary;
declare s fixed (5,1) controlled;
declare g fixed (15,5);
 
put ('Please type 11 values:');
do i = 1 to 11;
allocate s;
get (s);
put (s);
end;
put skip(2) ('Results:');
do i = 1 to 11;
g = f(s); put skip list (s);
if g > 400 then put ('Too large'); else put (g);
free s;
end;
 
f: procedure (x) returns (fixed(15,5));
declare x fixed (5,1);
return (sqrt(abs(x)) + 5*x**3);
end f;
 
end Trabb;
 
Output:
Please type 11 values: 
     1.0 
     3.0 
     2.0 
    -4.0 
    -5.0 
     6.0 
     7.0 
     9.0 
    11.0 
     1.5 
     2.4 

Results: 
     2.4                          70.66920 
     1.5                          18.09974 
    11.0                Too large 
     9.0                Too large 
     7.0                Too large 
     6.0                Too large 
    -5.0                        -622.76391 
    -4.0                        -318.00000 
     2.0                          41.41421 
     3.0                         136.73205 
     1.0                           6.00000 

PL/M[edit]

Assuming the existence of suitable external library routines.

TPK: DO;
/* external I/O and real mathematical routines */
WRITE$STRING: PROCEDURE( S ) EXTERNAL; DECLARE S POINTER; END;
WRITE$REAL: PROCEDURE( R ) EXTERNAL; DECLARE R REAL; END;
WRITE$NL: PROCEDURE EXTERNAL; END;
READ$REAL: PROCEDURE( R ) REAL EXTERNAL; DECLARE R POINTER; END;
REAL$ABS: PROCEDURE( R ) REAL EXTERNAL; DECLARE R REAL; END;
REAL$SQRT: PROCEDURE( R ) REAL EXTERNAL; DECLARE R REAL; END;
/* end external routines */
 
F: PROCEDURE( T ) REAL;
DECLARE T REAL;
RETURN REAL$SQRT(REAL$ABS(T))+5*T*T*T;
END F;
MAIN: PROCEDURE;
DECLARE Y REAL, A( 11 ) REAL, I INTEGER;
DO I = 0 TO 10;
CALL READ$REAL( @A( I ) );
END;
DO I = 10 TO 0 BY -1;
Y = F( A( I ) );
IF Y > 400.0 THEN CALL WRITE$STRING( @( 'TOO LARGE', 0 ) );
ELSE CALL WRITE$REAL( Y );
CALL WRITE$NL();
END;
END MAIN;
 
END TPK;
Output:
1 2 3 4 5 6 7 8 9 10 11
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
TOO LARGE
322.0000
136.7321
 41.4142
  6.0000

PowerShell[edit]

 
function Get-Tpk
{
[CmdletBinding()]
[OutputType([PSCustomObject])]
Param
(
[Parameter(Mandatory=$true,
ValueFromPipeline=$true,
ValueFromPipelineByPropertyName=$true,
Position=0)]
[double]
$Number
)
 
Begin
{
function Get-TpkFunction ([double]$Number)
{
[Math]::Pow([Math]::Abs($Number),(0.5)) + 5 * [Math]::Pow($Number,3)
}
 
[object[]]$output = @()
}
Process
{
$Number | ForEach-Object {
$n = Get-TpkFunction $_
 
if ($n -le 400)
{
$result = $n
}
else
{
$result = "Overflow"
}
}
 
$output += [PSCustomObject]@{
Number = $Number
Result = $result
}
}
End
{
[Array]::Reverse($output)
$output
}
}
 
 
$tpk = 1..11 | Get-Tpk
$tpk
 
Output:
Number Result          
------ ------          
    11 Overflow        
    10 Overflow        
     9 Overflow        
     8 Overflow        
     7 Overflow        
     6 Overflow        
     5 Overflow        
     4 322             
     3 136.732050807569
     2 41.4142135623731
     1 6               

Sort back to ascending order ignoring Overflow results:

 
$tpk | where result -ne overflow | sort number
 
Output:
Number           Result
------           ------
     1                6
     2 41.4142135623731
     3 136.732050807569
     4              322

PureBasic[edit]

Procedure.d f(x.d)
ProcedureReturn Pow(Abs(x), 0.5) + 5 * x * x * x
EndProcedure
 
Procedure split(i.s, delimeter.s, List o.d())
Protected index = CountString(i, delimeter) + 1 ;add 1 because last entry will not have a delimeter
 
While index > 0
AddElement(o())
o() = ValD(Trim(StringField(i, index, delimeter)))
index - 1
Wend
 
ProcedureReturn ListSize(o())
EndProcedure
 
Define i$, entriesAreValid = 0, result.d, output$
NewList numbers.d()
 
If OpenConsole()
Repeat
PrintN(#crlf$ + "Enter eleven numbers that are each separated by spaces or commas:")
 
i$ = Input(
i$ = Trim(i$)
If split(i$, ",", numbers.d()) < 11
ClearList(numbers())
If split(i$, " ", numbers.d()) < 11
PrintN("Not enough numbers were supplied.")
ClearList(numbers())
Else
entriesAreValid = 1
EndIf
Else
entriesAreValid = 1
EndIf
Until entriesAreValid = 1
 
ForEach numbers()
output$ = "f(" + RTrim(RTrim(StrD(numbers(), 3), "0"), ".") + ") = "
result.d = f(numbers())
If result > 400
output$ + "Too Large"
Else
output$ + RTrim(RTrim(StrD(result, 3), "0"), ".")
EndIf
PrintN(output$)
Next
 
Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf
Output:
Enter eleven numbers that are each separated by spaces or commas:
10, -1, 1, 2, 3, 4, 4.3, 4.305, 4.303, 4.302, 4.301
f(4.301) = 399.886
f(4.302) = Too Large
f(4.303) = Too Large
f(4.305) = Too Large
f(4.3) = 399.609
f(4) = 322
f(3) = 136.732
f(2) = 41.414
f(1) = 6
f(-1) = -4
f(10) = Too Large

Python[edit]

Functional[edit]

Python 3.2.2 (default, Sep  4 2011, 09:51:08) [MSC v.1500 32 bit (Intel)] on win32
Type "copyright", "credits" or "license()" for more information.
>>> def f(x): return abs(x) ** 0.5 + 5 * x**3
 
>>> print(', '.join('%s:%s' % (x, v if v<=400 else "TOO LARGE!")
for x,v in ((y, f(float(y))) for y in input('\nnumbers: ').strip().split()[:11][::-1])))
 
11 numbers: 1 2 3 4 5 6 7 8 9 10 11
11:TOO LARGE!, 10:TOO LARGE!, 9:TOO LARGE!, 8:TOO LARGE!, 7:TOO LARGE!, 6:TOO LARGE!, 5:TOO LARGE!, 4:322.0, 3:136.73205080756887, 2:41.41421356237309, 1:6.0
>>>

Procedural[edit]

def f(x):
return abs(x) ** 0.5 + 5 * x**3
 
def ask():
return [float(y)
for y in input('\n11 numbers: ').strip().split()[:11]]
 
if __name__ == '__main__':
s = ask()
s.reverse()
for x in s:
result = f(x)
if result > 400:
print(' %s:%s' % (x, "TOO LARGE!"), end='')
else:
print(' %s:%s' % (x, result), end='')
print('')
Sample output:
11 numbers: 1 2 3 4 5 6 7 8 9 10 11
 11.0:TOO LARGE! 10.0:TOO LARGE! 9.0:TOO LARGE! 8.0:TOO LARGE! 7.0:TOO LARGE! 6.0:TOO LARGE! 5.0:TOO LARGE! 4.0:322.0 3.0:136.73205080756887 2.0:41.41421356237309 1.0:6.0

R[edit]

S <- scan(n=11)
 
f <- function(x) sqrt(abs(x)) + 5*x^3
 
for (i in rev(S)) {
res <- f(i)
if (res > 400)
print("Too large!")
else
print(res)
}
Sample output:
> source("~/tpk.R")
1: 1 2 3 4 5
6: 6 7 8 9 10
11: 11
Read 11 items
[1] "Too large!"
[1] "Too large!"
[1] "Too large!"
[1] "Too large!"
[1] "Too large!"
[1] "Too large!"
[1] "Too large!"
[1] 322
[1] 136.7321
[1] 41.41421
[1] 6

Racket[edit]

 
#lang racket
 
(define input
(for/list ([i 11])
(printf "Enter a number (~a of 11): " (+ 1 i))
(read)))
 
(for ([x (reverse input)])
(define res (+ (sqrt (abs x)) (* 5 (expt x 3))))
(if (> res 400)
(displayln "Overflow!")
(printf "f(~a) = ~a\n" x res)))
 
Output:
Enter a number (1 of 11): 1
Enter a number (2 of 11): 2
Enter a number (3 of 11): 3
Enter a number (4 of 11): 4
Enter a number (5 of 11): 5
Enter a number (6 of 11): 6
Enter a number (7 of 11): 7
Enter a number (8 of 11): 8
Enter a number (9 of 11): 9
Enter a number (10 of 11): 10
Enter a number (11 of 11): 11
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
Overflow!
f(4) = 322
f(3) = 136.73205080756887
f(2) = 41.41421356237309
f(1) = 6

REXX[edit]

The REXX language doesn't have a   sqrt   function, so a RYO version is included here.     [RYO   =   Roll Your Own.]

It could be noted that almost half of this program is devoted to prompting, parsing and validating of the (input) numbers,
not to mention some hefty code to support right-justified numbers such that they are aligned when displayed.

/*REXX program implements the Trabb─Pardo-Knuth algorithm for N numbers (default is 11).*/
numeric digits 200 /*the number of digits precision to use*/
parse arg N .; if N=='' | N=="," then N=11 /*Not specified? Then use the default.*/
maxValue= 400 /*the maximum value f(x) can have. */
wid= 20 /* ··· but only show this many digits.*/
frac= 5 /* ··· show this # of fractional digs.*/
say ' _____ ' /* ◄───── display a vinculum.*/
say 'function: ƒ(x) ≡ √ │x│ + (5 * x^3)'
prompt= 'enter ' N " numbers for the Trabb─Pardo─Knuth algorithm: (or Quit)"
 
do ask=0; say; /*░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░*/
say prompt; say; pull $; say /*░*/
if abbrev('QUIT',$,1) then do; say 'quitting.'; exit 1; end /*░*/
ok=0 /*░*/
select /*validate there're N numbers.*/ /*░*/
when $='' then say "no numbers entered" /*░*/
when words($)<N then say "not enough numbers entered" /*░*/
when words($)>N then say "too many numbers entered" /*░*/
otherwise ok=1 /*░*/
end /*select*/ /*░*/
if \ok then iterate /* [↓] W=max width. */ /*░*/
w=0; do v=1 for N; _=word($, v); w=max(w, length(_) ) /*░*/
if datatype(_, 'N') then iterate /*numeric ?*/ /*░*/
say _ "isn't numeric"; iterate ask /*░*/
end /*v*/ /*░*/
leave /*░*/
end /*ask*/ /*░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░░*/
 
say 'numbers entered: ' $
say
do i=N by -1 for N; #=word($, i) / 1 /*process the numbers in reverse. */
g = fmt( f( # ) ) /*invoke function ƒ with arg number.*/
gw=right( 'ƒ('#") ", w+7) /*nicely formatted ƒ(number). */
if g>maxValue then say gw "is > " maxValue ' ['space(g)"]"
else say gw " = " g
end /*i*/ /* [↑] display the result to terminal.*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
f: procedure; parse arg x; return sqrt( abs(x) ) + 5 * x**3
/*──────────────────────────────────────────────────────────────────────────────────────*/
fmt: z=right(translate(format(arg(1), wid, frac), 'e', "E"), wid) /*right adjust; use e*/
if pos(.,z)\==0 then z=left(strip(strip(z,'T',0),"T",.),wid) /*strip trailing 0 &.*/
return right(z, wid - 4*(pos('e', z)==0) ) /*adjust: no exponent*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g *.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h % 2 + 1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g
output   when prompted, using the input of:     5   3.3   3   2e-1   1   0   -1   -222   -33   4.0004   +5
                           _____
function:        ƒ(x)  ≡  √ │x│   +   (5 * x^3)

enter  11  numbers for the Trabb─Pardo─Knuth algorithm:     (or Quit)

5   3.3   3   2e-1   1   0   -1   -222   -33   4.0004   +5   ◄■■■■■■■■■■■ this is what the user entered.

numbers entered:  5   3.3   3   2E-1   1   0   -1   -222   -33   4.0004   +5

        ƒ(5)  is >   400  [627.23607]
   ƒ(4.0004)     =         322.09611
      ƒ(-33)     =     -179679.25544
     ƒ(-222)     =   -54705225.10034
       ƒ(-1)     =          -4
        ƒ(0)     =           0
        ƒ(1)     =           6
      ƒ(0.2)     =           0.48721
        ƒ(3)     =         136.73205
      ƒ(3.3)     =         181.50159
        ƒ(5)  is >   400  [627.23607]

Ring[edit]

 
# Project : Trabb Pardo–Knuth algorithm
# Date  : 2017/10/06
# Author : Gal Zsolt (~ CalmoSoft ~)
# Email  : <[email protected]>
 
decimals(3)
x = list(11)
for n=1 to 11
x[n] = n
next
 
s = [-5, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6]
for i = 1 to 11
see string(i) + " => " + s[i] + nl
next
see copy("-", 20) + nl
i = i - 1
 
while i > 0
see "f(" + string(s[i]) + ") = "
x = f(s[i])
if x > 400
see "-=< overflow >=-" + nl
else
see x + nl
ok
i = i - 1
end
 
func f(n)
return sqrt(fabs(n)) + 5 * pow(n, 3)
 

Output:

1 => -5
2 => -3
3 => -2
4 => -1
5 => 0
6 => 1
7 => 2
8 => 3
9 => 4
10 => 5
11 => 6
--------------------
f(6) = -=< overflow >=-
f(5) = -=< overflow >=-
f(4) = 322
f(3) = 136.732
f(2) = 41.414
f(1) = 6
f(0) = 0
f(-1) = -4
f(-2) = -38.586
f(-3) = -133.268
f(-5) = -622.764

Ruby[edit]

def f(x) x.abs ** 0.5 + 5 * x ** 3 end
 
puts "Please enter 11 numbers:"
nums = 11.times.map{ gets.to_f }
 
nums.reverse_each do |n|
print "f(#{n}) = "
res = f(n)
puts res > 400 ? "Overflow!" : res
end
Output:
ruby tpk.rb
Please enter 11 numbers:
1
2
3
4
5
6
7
8
9
-1
-4
f(-4.0) = -318.0
f(-1.0) = -4.0
f(9.0) = Overflow!
f(8.0) = Overflow!
f(7.0) = Overflow!
f(6.0) = Overflow!
f(5.0) = Overflow!
f(4.0) = 322.0
f(3.0) = 136.73205080756887
f(2.0) = 41.41421356237309
f(1.0) = 6.0

Scala[edit]

object TPKa extends App {
final val numbers = scala.collection.mutable.MutableList[Double]()
final val in = new java.util.Scanner(System.in)
while (numbers.length < CAPACITY) {
print("enter a number: ")
try {
numbers += in.nextDouble()
}
catch {
case _: Exception =>
in.next()
println("invalid input, try again")
}
}
 
numbers reverseMap { x =>
val fx = Math.pow(Math.abs(x), .5D) + 5D * (Math.pow(x, 3))
if (fx < THRESHOLD)
print("%8.3f -> %8.3f\n".format(x, fx))
else
print("%8.3f -> %s\n".format(x, Double.PositiveInfinity.toString))
}
 
private final val THRESHOLD = 400D
private final val CAPACITY = 11
}

Sidef[edit]

Translation of: Perl 6
var nums; do {
nums = Sys.readln("Please type 11 space-separated numbers: ").nums
} while(nums.len != 11)
 
nums.reverse.each { |n|
var r = (n.abs.sqrt + (5 * n**3));
say "#{n}\t#{ r > 400 ? 'Urk!' : r }";
}
Output:
Please type 11 space-separated numbers: 10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
4.301	399.886299747726800445468371077898575778355
4.302	Urk!
4.303	Urk!
4.305	Urk!
4.3	399.608644135332772087455898679984992632401
4	322
3	136.732050807568877293527446341505872366943
2	41.41421356237309504880168872420969807857
1	6
-1	-4
10	Urk!

Sinclair ZX81 BASIC[edit]

Works with the unexpanded (1k RAM) ZX81

 10 DIM A(11)
20 PRINT "ENTER ELEVEN NUMBERS:"
30 FOR I=1 TO 11
40 INPUT A(I)
50 NEXT I
60 FOR I=11 TO 1 STEP -1
70 LET Y=SQR ABS A(I)+5*A(I)**3
80 IF Y<=400 THEN GOTO 110
90 PRINT A(I),"TOO LARGE"
100 GOTO 120
110 PRINT A(I),Y
120 NEXT I
Output:
ENTER ELEVEN NUMBERS:
2.8             111.43332
3.333           186.95529
1.01            6.1564926
2.55            84.503747
11              TOO LARGE
6               TOO LARGE
5               TOO LARGE
4               322
3               136.73205
2               41.414214
1               6

Swift[edit]

Works with: Swift 2.0
import Foundation
 
print("Enter 11 numbers for the Trabb─Pardo─Knuth algorithm:")
 
let f: (Double) -> Double = { sqrt(fabs($0)) + 5 * pow($0, 3) }
 
(1...11)
.generate()
.map { i -> Double in
print("\(i): ", terminator: "")
guard let s = readLine(), let n = Double(s) else { return 0 }
return n
}
.reverse()
.forEach {
let result = f($0)
print("f(\($0))", result > 400.0 ? "OVERFLOW" : result, separator: "\t")
}
 
Output:
Enter 11 numbers for the Trabb─Pardo─Knuth algorithm:
1: 1
2: 2
3: 3
4: 4
5: 5
6: 6
7: 7
8: 8
9: 9
10: 10
11: 11
f(11.0)	OVERFLOW
f(10.0)	OVERFLOW
f(9.0)	OVERFLOW
f(8.0)	OVERFLOW
f(7.0)	OVERFLOW
f(6.0)	OVERFLOW
f(5.0)	OVERFLOW
f(4.0)	322.0
f(3.0)	136.732050807569
f(2.0)	41.4142135623731
f(1.0)	6.0

Symsyn[edit]

 
|Trabb Pardo–Knuth algorithm
 
a : 11 0
 
i
if i LE 10
[] $s
~ $s w
w a.i
+ i
goif
endif
10 i
if i GE 0
call f
if x GT 400
'too large' $s
else
~ x $s
endif
~ i $r
+ ' ' $r
+ $r $s.1
$s []
- i
goif
endif
stop
 
f a.i t
* t t x
* x t x
* 5 x
abs t
sqrt t y
+ y x
return
 

Tcl[edit]

# Helper procedures
proc f {x} {expr {abs($x)**0.5 + 5*$x**3}}
proc overflow {y} {expr {$y > 400}}
 
# Read in 11 numbers, with nice prompting
fconfigure stdout -buffering none
for {set n 1} {$n <= 11} {incr n} {
puts -nonewline "number ${n}: "
lappend S [scan [gets stdin] "%f"]
}
 
# Process and print results in reverse order
foreach x [lreverse $S] {
set result [f $x]
if {[overflow $result]} {
puts "${x}: TOO LARGE!"
} else {
puts "${x}: $result"
}
}
Sample run:
number 1: 0
number 2: 1
number 3: 2
number 4: 3
number 5: 4
number 6: 5
number 7: 6
number 8: 7
number 9: 8
number 10: 9
number 11: 10
10.0: TOO LARGE!
9.0: TOO LARGE!
8.0: TOO LARGE!
7.0: TOO LARGE!
6.0: TOO LARGE!
5.0: TOO LARGE!
4.0: 322.0
3.0: 136.73205080756887
2.0: 41.41421356237309
1.0: 6.0
0.0: 0.0

VBScript[edit]

 
Function tpk(s)
arr = Split(s," ")
For i = UBound(arr) To 0 Step -1
n = fx(CDbl(arr(i)))
If n > 400 Then
WScript.StdOut.WriteLine arr(i) & " = OVERFLOW"
Else
WScript.StdOut.WriteLine arr(i) & " = " & n
End If
Next
End Function
 
Function fx(x)
fx = Sqr(Abs(x))+5*x^3
End Function
 
'testing the function
WScript.StdOut.Write "Please enter a series of numbers:"
list = WScript.StdIn.ReadLine
tpk(list)
 
Output:

The number series was derived from the example of C.

C:\>cscript /nologo tpk.vbs
Please enter 10 numbers:10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
4.301 = 399.886299747727
4.302 = OVERFLOW
4.303 = OVERFLOW
4.305 = OVERFLOW
4.3 = 399.608644135333
4 = 322
3 = 136.732050807569
2 = 41.4142135623731
1 = 6
-1 = -4
10 = OVERFLOW

XPL0[edit]

include c:\cxpl\codes;
 
func real F(X);
real X;
return sqrt(abs(X)) + 5.0*X*X*X;
 
real Result, S(11); int I;
[Text(0, "Please enter 11 numbers: ");
for I:= 0 to 11-1 do S(I):= RlIn(0);
 
for I:= 11-1 downto 0 do
[RlOut(0, S(I));
Result:= F(S(I));
if Result > 400.0 then
Text(0, " overflows")
else RlOut(0, Result);
CrLf(0)];
]
Output:
Please enter 11 numbers: 10 -1 1 2 3 4 4.3 4.305 4.303 4.302 4.301
    4.30100  399.88630
    4.30200  overflows
    4.30300  overflows
    4.30500  overflows
    4.30000  399.60864
    4.00000  322.00000
    3.00000  136.73205
    2.00000   41.41421
    1.00000    6.00000
   -1.00000   -4.00000
   10.00000  overflows

zkl[edit]

fcn f(x) { x.abs().pow(0.5) + x.pow(3)*5 }
reg ns; do{
ns=ask("11 numbers seperated by spaces: ");
try{ ns=ns.split(" ").filter().apply("toFloat") } catch{}
}while(not ns.isType(List) or ns.len()!=11);
ns.reverse().apply(fcn(x){
fx:=f(x); "f(%7.3f)-->%s".fmt(x, if(fx>400)"Overflow" else fx) })
.pump(Console.println);
Output:
11 numbers seperated by spaces: 10 -1 1     2 3 4 4.3 4.305 4.303 4.302 4.301
f(  4.301)-->399.886
f(  4.302)-->Overflow
f(  4.303)-->Overflow
f(  4.305)-->Overflow
f(  4.300)-->399.609
f(  4.000)-->322
f(  3.000)-->136.732
f(  2.000)-->41.4142
f(  1.000)-->6
f( -1.000)-->-4
f( 10.000)-->Overflow