Asp Forum - Fibonacci Benchmark Correction

jzakiya

3/16/2005 1:34:00 PM

The Great Computer Language Shootout Benchmarks
http://shootout.alioth.d...

is using an incorrect fibonacci algorithm benchmark.

Yesterday I sent this comment to correct it.

I (unfortunately) have noticed this incorrect implementation
of the Fiboncacci algorithm permeated in many places now,
one being the book Teach Yourself Ruby in 21 Days.

Hoepfully, the GCLSB will make the correction, and others
will also.

Below is the message I sent the GCLSB.

Jabari Zakiya
jzakiya@mail.com
==============================================================

With regard to the Fibonacci algorithm benchmarks it states:

-------------------------------------------------------------
about the fibonacci benchmark
Each program should calculate the Fibonacci function using the same
naïve recursive-algorithm

F(x)
x = 0 = 1
x = 1 = 1
otherwise = F(x-2) + F(x-1)

Calculate F(N). Correct output N = 32 is:

3524578

For more information see Eric W. Weisstein, "Fibonacci Number." From
MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/FibonacciN...
-----------------------------------------------------------------

This is an incorrect statement of the Fibonacci algotithm.

The Fibonacci series is: 0, 1, 1, 2, 3, 5, 8, 13, 21, .....

The first two terms in the series are: F(0)=0, F(1)=1
from this F(n)= F(n-1)+F(n-2) for n>1

References:
http://goldennumber.net/fi...
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacc...

The reference site: http://mathworld.wolfram.com/FibonacciN...
in fact, states the algorithm correctly, but it was apparently misread.

------------------------------------------
The Fibonacci numbers of the sequence of numbers Fn defined by the Un
in the Lucas sequence, which can be viewed as a particular case of the
Fibonacci polynomials Fn(x) with Fn=Fn(1).
They are companions to the Lucas numbers and satisfy the same
recurrence relation,

Fn = Fn-2 + Fn-1

for n = 3, 4, ..., with F1=F2=1. The first few Fibonacci numbers are 1,
1, 2, 3, 5, 8, 13, 21, ... (Sloane's A000045). As a result of the
definition (1), it is conventional to define F0=0. Fibonacci numbers
are implemented in Mathematica as Fibonacci[n].
-----------------------------------------

As you can see, this does explicitly states F0=0 and NOT F0=1 as the
benchmark states.
It also explicitly defines F1 = F2 = 1. Their description starts the
series as 1, 1, 2,...
to show its relation to the Lucas sequence, from which they derive the
fibonacci sequence.
Thus, the mathworld fibonacci series/algorithm description is
consistent with the other references I provided, and when you account
for F0=0, the sequences are identical.

Thus for N = 32, F(32) = 21708309 and NOT 3524578, which is F(33)
see list of F(N) at http://goldennumber.net/fi...

Thus, all the fibonacci benchmarks produce incorrect answers for each
Fn,
except for F1=1.

Incorrect fibonacci benchmark code examples:

For Ruby:

def fib(n)
if n<2 then
1
else
fib(n-2) + fib(n-1)
end
end

For Forth

: fib (n-m)
dup 2 < if drop 1 else 1- dup recurse swap 1- recurse + then
;

Thus, when n=0 the benchmark algorithms produce Fib(0) = 1,
which is incorrect, and throws off all the correct values for n by 1.

The correct algorithms should account for Fib(0)=0.

Ruby (1.8.2) example:
# Produces correct Fibonacci values and series
def fib(n)
if n<2
n
else
fib(n-2) + fib(n-1)
end
end

or

def fib(n)
if n>1
fib(n-1) + fib(n-2)
else
n
end
end

# or

def fib(n)
if n>1 then fib(n-1)+fib(n-2)
else n
end
end

# or as a oneliners

def fib(n) if n>1: fib(n-1)+fib(n-2) else n end end
def fib(n) if n>1 then fib(n-1)+fib(n-2) else n end end

Forth examples:
\ Produces correct Fibonacci values and series
: fib (n-m)
dup 2 < if exit else 1- dup recurse swap 1- recurse + then
;

\ or better (ANSForth)

: fib (n-m)
dup 1 > if 1- dup recurse swap 1- recurse + then
;

\ or even better (for gforth)

: fib (n-m) recursive
dup 1 > if 1- dup fib swap 1- fib + then
;

To correct all the code examples, just fix the conditional expressions:

if n<2 then fib(n)=1, or equivalent, replace with
if n<2 then fib(n)=n, or equivalent.

I hope this helpfull.

Jabari Zakiya
jzakiya@mail.com

25 Answers

Nikolai Weibull

3/16/2005 1:57:00 PM

* jzakiya@mail.com (Mar 16, 2005 14:40):
> The Great Computer Language Shootout Benchmarks
> http://shootout.alioth.d...
> is using an incorrect fibonacci algorithm benchmark.

I really don't see where you're going with this. The sequence is either

0 1 1 2 3 5 8 13 ...

or

1 1 2 3 5 8 13 ...

Of course, the first makes more sense, but both are almost equally
quoted as the Fibonacci sequence. The first is, as I said, more right,
as you also point out, but it doesn't really matter as far as the
benchmark goes. If everyone implements the algorithm that the benchmark
states, then it really won't matter where the sequence begins,
nikolai

--
::: name: Nikolai Weibull :: aliases: pcp / lone-star / aka :::
::: born: Chicago, IL USA :: loc atm: Gothenburg, Sweden :::
::: page: www.pcppopper.org :: fun atm: gf,lps,ruby,lisp,war3 :::
main(){printf(&linux["\021%six\012\0"],(linux)["have"]+"fun"-97);}

jzakiya

3/17/2005 12:15:00 AM

Nikolai Weibull wrote:
> * jzakiya@mail.com (Mar 16, 2005 14:40):
> > The Great Computer Language Shootout Benchmarks
> > http://shootout.alioth.d...
> > is using an incorrect fibonacci algorithm benchmark.
>
> I really don't see where you're going with this. The sequence is
either
>
> 0 1 1 2 3 5 8 13 ...
>
> or
>
> 1 1 2 3 5 8 13 ...
>
> Of course, the first makes more sense, but both are almost equally
> quoted as the Fibonacci sequence. The first is, as I said, more
right,
> as you also point out, but it doesn't really matter as far as the
> benchmark goes. If everyone implements the algorithm that the
benchmark
> states, then it really won't matter where the sequence begins,
> nikolai
>
> --
> ::: name: Nikolai Weibull :: aliases: pcp / lone-star / aka :::
> ::: born: Chicago, IL USA :: loc atm: Gothenburg, Sweden :::
> ::: page: www.pcppopper.org :: fun atm: gf,lps,ruby,lisp,war3 :::
> main(){printf(&linux["\021%six\012\0"],(linux)["have"]+"fun"-97);}

The point is the stated code for every fibonacci benchmark algorithm
DOES NOT PRODUCE THE CORRECT SERIES!!

Even if you want to start the series using N=1 as the first index
value, the coded algorithms produce the following results:

index N: benchmark F(N) Correct F(N)
1 1 1
2 2 1
3 3 2
4 5 3
5 8 5
6 13 8
7 21 13
etc

Again, THE BENCHMARK CODE PRODUCES INCORRECT RESULTS!
It doesn't even produce the sequence it says it should!

So while the coded algorithm does consistently produce the same
answers, DON'T CALL IT THE FIBONACCI SERIES ALGORITHM!!

Would an algorithm that produces the factorial 0!=0 (and not 0!=1)
be considered to be a correct factorial algorithm? I don't think so.

What is really dangerous is someone using the coded algorithms thinking
that for a given index N the computed fibonacci F(N) value is correct.

This is not about the given code being a valid representation for some
arbitrary benchmark, but about the misrepresentation of that code as
producing the correct results for the fibonacce series, a fundamental
mathematical algorithm that is used in many fields of math and science.

Jabari Zakiya

ES

3/17/2005 12:24:00 AM

jzakiya@mail.com wrote:
> Nikolai Weibull wrote:
>
>>* jzakiya@mail.com (Mar 16, 2005 14:40):
>>
>>>The Great Computer Language Shootout Benchmarks
>>>http://shootout.alioth.d...
>>>is using an incorrect fibonacci algorithm benchmark.
>>
>>I really don't see where you're going with this. The sequence is
>
> either
>
>> 0 1 1 2 3 5 8 13 ...
>>
>>or
>>
>> 1 1 2 3 5 8 13 ...
>>
>>Of course, the first makes more sense, but both are almost equally
>>quoted as the Fibonacci sequence. The first is, as I said, more
>
> right,
>
>>as you also point out, but it doesn't really matter as far as the
>>benchmark goes. If everyone implements the algorithm that the
>
> benchmark
>
>>states, then it really won't matter where the sequence begins,
>> nikolai
>>
>>--
>>::: name: Nikolai Weibull :: aliases: pcp / lone-star / aka :::
>>::: born: Chicago, IL USA :: loc atm: Gothenburg, Sweden :::
>>::: page: www.pcppopper.org :: fun atm: gf,lps,ruby,lisp,war3 :::
>>main(){printf(&linux["\021%six\012\0"],(linux)["have"]+"fun"-97);}
>
>
>
> The point is the stated code for every fibonacci benchmark algorithm
> DOES NOT PRODUCE THE CORRECT SERIES!!
>
> Even if you want to start the series using N=1 as the first index
> value, the coded algorithms produce the following results:
>
> index N: benchmark F(N) Correct F(N)
> 1 1 1
> 2 2 1
> 3 3 2
> 4 5 3
> 5 8 5
> 6 13 8
> 7 21 13
> etc
>
> Again, THE BENCHMARK CODE PRODUCES INCORRECT RESULTS!
> It doesn't even produce the sequence it says it should!
>
> So while the coded algorithm does consistently produce the same
> answers, DON'T CALL IT THE FIBONACCI SERIES ALGORITHM!!
>
> Would an algorithm that produces the factorial 0!=0 (and not 0!=1)
> be considered to be a correct factorial algorithm? I don't think so.
>
> What is really dangerous is someone using the coded algorithms thinking
> that for a given index N the computed fibonacci F(N) value is correct.
>
> This is not about the given code being a valid representation for some
> arbitrary benchmark, but about the misrepresentation of that code as
> producing the correct results for the fibonacce series, a fundamental
> mathematical algorithm that is used in many fields of math and science.

OK, OK, the world will come to an end. It'll be fixed, I'm sure.
Geez.

> Jabari Zakiya

E

Michael Campbell

3/17/2005 12:44:00 AM

On Thu, 17 Mar 2005 09:19:46 +0900, jzakiya@mail.com <jzakiya@mail.com> wrote:

> The point is the stated code for every fibonacci benchmark algorithm
> DOES NOT PRODUCE THE CORRECT SERIES!!

Consider it the fibonacci series with an (added/missing) element.

The point of the exercise is to benchmark HOW it's done, and how
various languages compare. The output is a side-effect, and long as
it's consistent across languages.

Joel VanderWerf

3/17/2005 12:53:00 AM

jzakiya@mail.com wrote:
> The point is the stated code for every fibonacci benchmark algorithm
> DOES NOT PRODUCE THE CORRECT SERIES!!
>
> Even if you want to start the series using N=1 as the first index
> value, the coded algorithms produce the following results:
>
> index N: benchmark F(N) Correct F(N)
> 1 1 1
> 2 2 1
> 3 3 2
> 4 5 3
> 5 8 5
> 6 13 8
> 7 21 13
> etc
>
> Again, THE BENCHMARK CODE PRODUCES INCORRECT RESULTS!
> It doesn't even produce the sequence it says it should!
>
> So while the coded algorithm does consistently produce the same
> answers, DON'T CALL IT THE FIBONACCI SERIES ALGORITHM!!
>
> Would an algorithm that produces the factorial 0!=0 (and not 0!=1)
> be considered to be a correct factorial algorithm? I don't think so.
>
> What is really dangerous is someone using the coded algorithms thinking
> that for a given index N the computed fibonacci F(N) value is correct.
>
> This is not about the given code being a valid representation for some
> arbitrary benchmark, but about the misrepresentation of that code as
> producing the correct results for the fibonacce series, a fundamental
> mathematical algorithm that is used in many fields of math and science.

It's somewhat arbitrary how you index the sequence. IMHO the essence
(the "Fibonacci nature", if you will) of the sequence is the recurrence
relation, not the initial conditions. If you start at 5, 8, ... you
still get the golden section (the limit of the ratio of successive
terms), after all. And it is possible to define generalized Fib. seq.
that start with two given values.

In any case, the algorithms are computationally equivalent in a very
strong sense (you can obtain one from the other by incrementing or
decrementing the input), and so for the purposes of benchmarking they
can both be called "the Fibonacci algorithm".

What's _really_ dangerous is thinking that F(n) must have some absolute
significance, like e or pi. There's probably _some_ author out there who
wrote a paper defining F(0) and F(1) differently, possibly for a good
reason. If I were writing a paper using F, I would feel compelled to
define F(0) and F(1) to avoid ambiguity, but I'd feel silly defining pi.

Nikolai Weibull

3/17/2005 1:00:00 AM

* jzakiya@mail.com (Mar 17, 2005 01:30):
> Would an algorithm that produces the factorial 0!=0 (and not 0!=1) be
> considered to be a correct factorial algorithm? I don't think so.

Well, it's only "by convention" really. You could define 0! = 0 if you
so wished. It wouldn't make much sense, but you could.

> What is really dangerous is someone using the coded algorithms
> thinking that for a given index N the computed fibonacci F(N) value is
> correct.

Eh, since when did the GLS become authoritative on algorithm
implementation?

> This is not about the given code being a valid representation for some
> arbitrary benchmark, but about the misrepresentation of that code as
> producing the correct results for the fibonacce series, a fundamental
> mathematical algorithm that is used in many fields of math and
> science.

Worthy of a crusade?,
nikolai

--
::: name: Nikolai Weibull :: aliases: pcp / lone-star / aka :::
::: born: Chicago, IL USA :: loc atm: Gothenburg, Sweden :::
::: page: www.pcppopper.org :: fun atm: gf,lps,ruby,lisp,war3 :::
main(){printf(&linux["\021%six\012\0"],(linux)["have"]+"fun"-97);}

Douglas Livingstone

3/17/2005 1:18:00 AM

On Thu, 17 Mar 2005 09:59:57 +0900, Nikolai Weibull
<mailing-lists.ruby-talk@rawuncut.elitemail.org> wrote:

> > What is really dangerous is someone using the coded algorithms
> > thinking that for a given index N the computed fibonacci F(N) value is
> > correct.
>
> Eh, since when did the GLS become authoritative on algorithm
> implementation?
>

It is a high visibility set of code samples which don't do what is
written on the box. Through a combination of lazyness and "I'm right
you're wrong" it probably won't get fixed... but that doen't make it
right ;)

Just tack "These are implementations of a modified fibonacci series,
don't steal them if you want a real fibonacci series" at the top and
all will be fine. Except for the guy who wrote the first sample code.
He'll look quite silly. Shame he's probably the guy who would have to
put up the message...

Douglas

Michael Walter

3/17/2005 1:41:00 AM

Hello Jabari,

On Wed, 16 Mar 2005 22:34:50 +0900, jzakiya@mail.com <jzakiya@mail.com> wrote:
> Each program should calculate the Fibonacci function using the same
> naïve recursive-algorithm
>
> F(x)
> x = 0 = 1
> x = 1 = 1
> otherwise = F(x-2) + F(x-1)
>
> Calculate F(N). Correct output N = 32 is:
>
> 3524578

Nowhere in this text F(x) is defined as the x-th Fibonacci number. [*]

I'm sure the author would be glad to add a small note stating that
"F(x) is the (x+1)-th Fibonacci number", though. Did you notice that
the choice of defining F(x) to be the (x+1)-th Fibonacci number is
similar to choosing a[n] to be the (n+1)-th element of the array a?

Hope that helps,
Michael

[*] Note that I'm talking about Fibonacci numbers.

Isaac Gouy

3/18/2005 6:06:00 PM

Douglas Livingstone wrote:
> On Thu, 17 Mar 2005 09:59:57 +0900, Nikolai Weibull
> <mailing-lists.ruby-talk@rawuncut.elitemail.org> wrote:
>
> > > What is really dangerous is someone using the coded algorithms
> > > thinking that for a given index N the computed fibonacci F(N)
value is
> > > correct.
> >
> > Eh, since when did the GLS become authoritative on algorithm
> > implementation?
> >
>
> It is a high visibility set of code samples which don't do what is
> written on the box. Through a combination of lazyness and "I'm right
> you're wrong" it probably won't get fixed... but that doen't make it
> right ;)

Are you offering to fix all the programs and submit new versions?

> Just tack "These are implementations of a modified fibonacci series,
> don't steal them if you want a real fibonacci series" at the top and
> all will be fine. Except for the guy who wrote the first sample code.
> He'll look quite silly. Shame he's probably the guy who would have
to
> put up the message...

Actually we inherited this particular set of programs from the original
Shootout. The author of the original Shootout noted that he'd seen both
referred to as the Fibonacci sequence.

Josef 'Jupp' Schugt

3/18/2005 7:57:00 PM

Hi!

Jabari Zakiya wrote:

> This is an incorrect statement of the Fibonacci algotithm.
>
> The Fibonacci series is: 0, 1, 1, 2, 3, 5, 8, 13, 21, .....
>
> The first two terms in the series are: F(0)=0, F(1)=1
> from this F(n)= F(n-1)+F(n-2) for n>1

The above is an incorrect statement about the nature of mathematics.

Here we have one definition for the Fibonacci series:

.........................................................................
Definition A: Fibonacci series
Let F(0) = 1, F(1) = 1. For any natural number n > 1 define
F(n) = F(n-1) + F(n-2). The series F defined in such a way is called
"Fibonacci series".
.........................................................................

Here we have another one:

.........................................................................
Definition B: Fibonacci series
Let F(0) = 0, F(1) = 1. For any natural number n > 1 define
F(n) = F(n-1) + F(n-2). The series F defined in such a way is called
"Fibonacci series".
.........................................................................

From a mathematical point of view it simply makes no sense to say that
one of these definitions is 'correct' and the other one is 'incorrect'.

All one can say that one of these sequences is more commonly termed as
'Fibonacci series' then the other.

Addition 1:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 2

Addition 2:

0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0

Both kinds of additions are used. Addition 1 for natural numbers and the
like and Addition 2 for the commutative associative division algebra
where multiplication can be seen as logical AND and addition can be seen
as logical XOR:

0 * 0 = 0 <-> false AND false = false
0 * 1 = 0 <-> false AND true = false
1 * 0 = 0 <-> true AND false = false
1 * 1 = 1 <-> true AND true = true

0 + 0 = 0 <-> false XOR false = false
0 + 1 = 1 <-> false XOR true = true
1 + 0 = 1 <-> true XOR false = true
1 + 1 = 0 <-> true XOR true = false

Robert Sedgewick, Algorithms in C++ has

1, 1, 2, 3, 5, 8, 13, 21, ...

Cormen, Leiserson, Rives, Algorithms has

0, 1, 1, 2, 3, 5, 8, 13, ...

Ottmann, Widmeyer, Algorithmen und Datenstrukturen again has

1, 1, 2, 3, 5, 8, 13, 21, ...

If I were to propose the definition I would use F(0) = 0. The reason is
the golden ratio f and its conjugate F:

f = (1.0 + sqrt(5.0)) / 2.0
F = (1.0 - sqrt(5.0)) / 2.0

With the definition F(0) = 0 the following holds:

F(i) == (f**i - F**i) / sqrt(5.0)

The whole issue is not worth a holy cursade. One should keep in mind
that a benchmark exists for one and only one reason: Benchmarking.

The true reason to give the test a name like 'Fibonacci series' is that
this is more mnemonic than "benchmarking series Nr. 4711".

Just my two Euro Cent,

Josef 'Jupp' Schugt
--
Dear President George Walker Bush,
the way in which it is tried to install a software patent directive
clearly shows that the EU not democratic. We urgently need brothers in
arms who help us establish democratic structures.

comp.lang.ruby

Fibonacci Benchmark Correction

jzakiya

Nikolai Weibull

jzakiya

ES

Michael Campbell

Joel VanderWerf

Nikolai Weibull

Douglas Livingstone

Michael Walter

Isaac Gouy

Josef 'Jupp' Schugt

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