A floating-point puzzle

[Don]

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.

> I guess I can just drop this part from my code, then. ;)

> 
> -Lars