FORTRAN 77 on PDP-11

[Paul Koning]

>>>>> "Jerome" == Jerome H Fine <jhfinexgs2 at compsys.to> writes:

 Jerome> What I am complaining about is not the internal operations,
 Jerome> but the conversion routines.  I went to the trouble of
 Jerome> printing out the values in OCTAL so that I could figure out
 Jerome> the problem.  A 56 bit mantissa should allow a value of
 Jerome> 36,028,797,018,963,968 when the leading (invisible) bit is
 Jerome> one with the remaining bits zero.  The displayed value is
 Jerome> 36,028,797,018,963,965 instead or less by 3. ...

That would be a bug.  Not surprising.  Floating point arithmetic
should be, and can be, accurate to the last bit.  But very often it is
not, because it's *hard* to do that.  DEC had a team of specialists
who worked on the numeric algorithms for VAX.  The PDP-11 libraries
didn't get the benefit of that work, so it is not surprising to find
errors in the last few bits.

As I said, if you want exact answers, DO NOT use float.

 >> There the GNU MP library, and others like it.  Long integer
 >> arithmetic libraries are commonly found in crypto library
 >> packages.  Come to think of it, you'll find functions that are
 >> helpful in stuff relating to prime numbers -- since prime numbers
 >> also figure prominently in cryptography.
 >> 
 >> So you could use MP (which is in C) directly, given a suitable
 >> compiler.  Or you could port it to Fortran...
 >> 
 Jerome> Any idea where I could download the source code?  Given that
 Jerome> FORTRAN is not really suitable for shifting and using carry
 Jerome> bits, I would port to MACRO-11.

It's right in the GNU software library listing:
http://directory.fsf.org/GNU/gnump.html

 Jerome> In general, sieve methods for prime numbers don't ever need
 Jerome> division and rarely need multiplication.  Addition and
 Jerome> comparing are the primary operations.  Increment is also
 Jerome> needed (with increment by 2 and 4 being a big time saver).
 Jerome> So the only other thing needed are accurate conversion
 Jerome> routines to allow output in decimal instead of octal.  I
 Jerome> presume that the latter is best done using subtraction of
 Jerome> multiple powers of TEN which are stored in a table unless
 Jerome> there are better methods of converting the output?  Any
 Jerome> suggestions?

I'm sure I/O is part of GnuMP.  Decimal?  Probably, I haven't looked.
Multiplication is very definitely in there, it has to be, that's a
critical function for crypto.  Division I don't know about either.
It certainly should be there if GnuMP was aiming to be a general
arithmetic package.  If all else fails, it certainly has modular
arithmetic (again, because of crypto) from which you can synthesize
division if it isn't already there.

Oh yes, I'm quite sure it also includes primality tests --
presumably the Miller-Rabin test.

	   paul