A floating-point puzzle

[Lars T. Kyllingstad]

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. ;)

-Lars