A floating-point puzzle

[Bill Baxter]

On Wed, Aug 5, 2009 at 8:07 AM, Lars T.
Kyllingstad<public at kyllingen.nospamnet> wrote:
> Lars T. Kyllingstad wrote:
>>
>> Here's a puzzle for you floating-point wizards out there. I have to
>> translate the following snippet of FORTRAN code to D:
>>
>>      REAL B,Q,T
>> C     ------------------------------
>> C     |*** COMPUTE MACHINE BASE ***|
>> C     ------------------------------
>>      T = 1.
>> 10    T = T + T
>>      IF ( (1.+T)-T .EQ. 1. ) GOTO 10
>>      B = 0.
>> 20    B = B + 1
>>      IF ( T+B .EQ. T ) GOTO 20
>>      IF ( T+2.*B .GT. T+B ) GOTO 30
>>      B = B + B
>> 30    Q = ALOG(B)
>>      Q = .5/Q
>>
>> Of course I could just do a direct translation, but I have a hunch that T,
>> B, and Q can be expressed in terms of real.epsilon, real.min and so forth. I
>> have no idea how, though. Any ideas?
>>
>> (I am especially puzzled by the line after l.20. How can this test ever be
>> true? Is the fact that the 1 in l.20 is an integer literal significant?)
>>
>> -Lars
>
>
> I finally solved the puzzle by digging through ancient scientific papers, as
> well as some old FORTRAN and ALGOL code, and the solution turned out to be
> an interesting piece of computer history trivia.
>
> After the above code has finished, the variable B contains the radix of the
> computer's numerical system.
>
> Perhaps the comment should have tipped me off, but I had no idea that
> computers had ever been anything but binary. But apparently, back in the 50s
> and 60s there were computers that used the decimal and hexadecimal systems
> as well. Instead of just power on/off, they had 10 or 16 separate voltage
> levels to differentiate between bit values.
>
> I guess I can just drop this part from my code, then. ;)

Very interesting!   Thanks for sharing that.
But I'm not so sure about the 16 separate voltage levels part.  I
think they were probably binary underneath.  Like the BCD (Binary
Coded Decimal) system.

--bb