Re: integer representation in pari

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

On Thu, May 27, 2010 at 05:27:00PM -0400, Sam Steingold wrote:
> Hi,
> It appears that integers are represented differently on different platforms.
> Specifically, the "byte" order is different.
> I have two machines, both little-endian:
> 32bit AMD with "GP/PARI CALCULATOR Version 2.3.4 (released)"
> 64bit Intel Pentium D with "GP/PARI CALCULATOR Version 2.3.5 (released)"

Unfortunately this is the next line which is of importance here.
Specifically, it depends whether you use the GMP kernel or the PARI kernel.

> (gdb) p readseq("7906420317433764459701366445")
> $1 = 11282736

Instead of using the debugger, you could just \x in gp:
7906420317433764459701366445
\x
[&=00000000010b6940] INT(lg=4,CLONE):0300000000000004 (+,lgefint=4):4000000000000004 3cbd223800046ead 00000000198c09a0

> so we can see that the number is represented as 3 "32-bit bytes" in
> positions 2,3,4,
> ***LOW*** bytes first

So you use the GMP kernel on 32bit.

> 64-bit machine:
> (+ (ash 428607904 64) 4376692036787793581)
> => 7906420317433764459701366445
> 
> so we can see that the number is represented as 2 "64-bit bytes" in
> positions 2,3,
> ***HIGH*** bytes first.

So you use the PARI kernel on 64bit.

> Where is this documented?

In the documentation. Try
??libpari
and look up the definition of t_INT page 21.

> Where is this behavior defined?

You can use 
./Configure --with-gmp
or
./Configure --without-gmp
to force one kernel to be used. (--without-gmp is the default
for PARI 2.3, --with-gmp is the default for PARI 2.4.3)

> How do I know what byte order is used on which platform?

Looks at the name of the libpari library: if it is named
libpari-gmp.so.2 then it is using the GMP kernel.

You can also check whether the C macro PARI_KERNEL_GMP is defined,
but usually it is better to use int_W() to acces the mantissa.

Cheers,
Bill.