The first program

[PeterCanessa Oh]

I am, in my whimsical way, developing a new programming language/compiler/IDE in which the focus is ease of learning and use rather than, necessarily, efficiency. There are a number of reasons why 'standard' languages are difficult; their syntax, paradigms and concepts, for example. The obvious effects of which are that it takes people a long time to learn to program and even experienced developers make lots of mistakes. As a generalisation the problem is that all these languages were designed by mathematicians and/or engineers and these are not the people who are trying to use them. Examples from LSL, for instance; 'normal' people do not talk about 'integers' and 'floats', let alone radians, angles that start East and increase anti-clockwise or - haha, of course - quaternions.

As well as ditching the prejudices of existing designs I thought I'd abandon the 'traditional' first program as well.  "Hello World" just doesn't do it for me, so I looked-up the first ever program, to re-create it.  Oh the irony; it's very mathematical :-0

 

"In note G of Ada Lovelace's notes on the analytical engine from 1842,
Lovelace describes an algorithm for generating Bernoulli numbers with Babbage's
machine. As a result, the Bernoulli numbers have the distinction of being the
subject of the first computer program."

(http://en.wikipedia.org/wiki/Bernoulli_number)

 

That link gives, amongst all the mathematical details, this code for generating the Bernoulli numbers:

 

Algorithm Akiyama–Tanigawa algorithm for Bn
  Input: Enter integer n.
  Output: Bn.

  for m from 0 by 1 to n do
    A[m] ← 1/(m+1)
    for j from m by -1 to 1 do
      A[j-1] ← j×(A[j-1] - A[j])
  return A[0] (which is Bn)

 

Question 1: What language is that?  I think it's Algol, but I'm not sure.  The '←' for assignment should be quite distinctive.

Question 2: Am I correct in translating "for j from m by -1 to 1 do" as (in LSL) "for(j = m; j > 0; j--){"

Now the biggies:
Question 3: What's wrong with this LSL version? (Apart from not being inlined Rolig and Ela!)

 

float Bernoulli(integer Number){
    if(Number == 0){
        return 1.0;
    }else if(Number == 1){
        return 0.5;
    }else if((Number < 0) || (Number % 2)){
        return 0.0;
    }else{
        list A;
        integer J;
        integer M;
        for(M = 0; M <= Number; M++){
            A += [1.0 / (M + 1.0)];
            for(J = M; J > 0; J--){
                A = llListReplaceList(A, [J * (llList2Float(A, J-1) - llList2Float(A, J))], J-1, J-1);
            }
        }
        return llList2Float(A, 0);
      }
}

default{
    state_entry(){
        integer C;
        for(C = 2; C < 20; C += 2){
            llOwnerSay("B(" + (string) C + ") = " + (string) Bernoulli(C));
            llSleep(0.2);	// Seems to help chat stay in order
        }
    }
}

 

The return paths for < 0, 0, 1 and odd-numbers > 1 are all correct but the even-number results veer-off wildy after B(8) (which is 'close enough', even if it doesn't agree with wikipedia).

 

• B(2) = 0.166667
• B(4) = -0.033333
• B(6) = 0.023818
• B(8) = -0.032196
• B(10) = 0.299849
• B(12) = 29.289020
• B(14) = 5489.975000
• B(16) = 1966391.000000
• B(18) = 2113044000.000000

(Optional bonus) Question 4: Is this PHP a valid translation of the LSL? (Yes, I am playing around with cross-compilers)

 

<?php
	function Bernoulli($Number){
	    if($Number == 0){
	        return 1.0;
	    }elseif($Number == 1){
	        return 0.5;
	    }elseif(($Number < 0) || (($Number % 2) == 1)){
	        return 0.0;
	    }else{
	        for($M = 0; $M <= $Number; $M++){
	            $A[$M] = 1.0 / ($M + 1.0);
	            for($J = $M; $J > 0; $J--){
	                $A[$J-1] = $J * ($A[$J-1] - $A[$J]);
	            }
	        }
	        return $A[0];
	      }
	}

	for($C = 0; $C < 21; $C += 2){
		echo "B(".$C.") = ".Bernoulli($C)."</br>\n"; 
	}
?>

 

Question 5:  Why does it give a different set of (wrong) answers?

 

• B(2) = 0.16666666666667
• B(4) = -0.033333333333334
• B(6) = 0.023809523809568
• B(8) = -0.033333333331542
• B(10) = 0.075757575267314
• B(12) = -0.25311370332041
• B(14) = 1.1666676791536
• B(16) = -7.0685020745223
• B(18) = 69.99698015617

And finally:
Question 6: Good grief! I can't believe the first program was really for something so awkward to calculate. Where is the missing "Felicitous greetings, to Her Majesty, British nationals and citizens of the Empire" program?

[Ela Talaj]

Looks like Python to me