A floating-point puzzle

[Jarrett Billingsley]

On Wed, Aug 5, 2009 at 10:16 PM, Don<nospam at nospam.com> wrote:
> Lars T. Kyllingstad 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.
>
> Not quite. They just used exponents which were powers of 10 or 16, rather
> than 2. BTW, T == 1/real.epsilon. I don't know what ALOG does, so I've no
> idea what Q is.

Apparently ALOG is just an old name for LOG.  At least that's what
Google tells me.