Jarrett Billingsley wrote:
On Wed, Aug 5, 2009 at 10:16 PM, Don<[email protected]> 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.
Then Q is 0.5*ln(0.5). Dunno what use that is.
