So then we move on to what 64-bit is really useful for. Obviously,
there is the arithmetic. If you were previously doing 64-bit
arithmetic through software, you will notice an immediate speed
improvement when doing it through hardware instead. If you have
a program that is scanning memory in any way, it may benefit from
64-bit instructions (for example - copying data 64-bit words at
a time instead of 32-bit words at a time). PostgreSQL might benefit
slightly from either of these, slightly balancing the performance
degradation of using more memory to store the pointers, and more
memory bandwidth the access the pointers.
At least on Sparc processors, v8 and newer, any double precision math (including longs) is performed with a single instruction, just like for a 32 bit datum. Loads and stores of 8 byte datums are also handled via a single instruction. The urban myth that 64bit math is different/better on a 64 bit processor is just that; yes, some lower end processors would emulate/trap those instructions but that an implementation detail, not architecture. I believe that this is all true for other RISC processors as well.

The 64bit API on UltraSparcs does bring along some extra FP registers IIRC.

If, however, you happen to have a very large amount of physical memory
- more memory than is supported by a 32-bit system, but is supported
by your 64-bit system, then the operating system should be able to use
this additional physical memory to cache file system data pages, which
will benefit PostgreSQL if used with tables that are larger than the
memory supported by your 32-bit system, and which have queries which
require more pages than the memory supported by your 32-bit system to
be frequently accessed. If you have a huge database, with many clients
accessing the data, this would be a definate yes. With anything less,
it is a maybe, or a probably not.
Solaris, at least, provided support for far more than 4GB of physical memory on 32 bit kernels. A newer 64 bit kernel might be more efficient, but that's just because the time was taken to support large page sizes and more efficient data structures. It's nothing intrinsic to a 32 vs 64 bit kernel.

-- Alan

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