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02110-1301, USA.





                   INTEL PENTIUM P5 MPN SUBROUTINES


This directory contains mpn functions optimized for Intel Pentium (P5,P54)
processors.  The mmx subdirectory has additional code for Pentium with MMX
(P55).


STATUS

                                cycles/limb

	mpn_add_n/sub_n            2.375

	mpn_mul_1                 12.0
	mpn_add/submul_1          14.0

	mpn_mul_basecase          14.2 cycles/crossproduct (approx)

	mpn_sqr_basecase           8 cycles/crossproduct (approx)
                                   or 15.5 cycles/triangleproduct (approx)

	mpn_l/rshift               5.375 normal (6.0 on P54)
				   1.875 special shift by 1 bit

	mpn_divrem_1              44.0
	mpn_mod_1                 28.0
	mpn_divexact_by3          15.0

	mpn_copyi/copyd            1.0

Pentium MMX gets the following improvements

	mpn_l/rshift               1.75

	mpn_mul_1                 12.0 normal, 7.0 for 16-bit multiplier


mpn_add_n and mpn_sub_n run at asymptotically 2 cycles/limb.  Due to loop
overhead and other delays (cache refill?), they run at or near 2.5
cycles/limb.

mpn_mul_1, mpn_addmul_1, mpn_submul_1 all run 1 cycle faster than they
should.  Intel documentation says a mul instruction is 10 cycles, but it
measures 9 and the routines using it run as 9.



P55 MMX AND X87

The cost of switching between MMX and x87 floating point on P55 is about 100
cycles (fld1/por/emms for instance).  In order to avoid that the two aren't
mixed and currently that means using MMX and not x87.

MMX offers a big speedup for lshift and rshift, and a nice speedup for
16-bit multipliers in mpn_mul_1.  If fast code using x87 is found then
perhaps the preference for MMX will be reversed.




P54 SHLDL

mpn_lshift and mpn_rshift run at about 6 cycles/limb on P5 and P54, but the
documentation indicates that they should take only 43/8 = 5.375 cycles/limb,
or 5 cycles/limb asymptotically.  The P55 runs them at the expected speed.

It seems that on P54 a shldl or shrdl allows pairing in one following cycle,
but not two.  For example, back to back repetitions of the following

	shldl(	%cl, %eax, %ebx)
	xorl	%edx, %edx
	xorl	%esi, %esi

run at 5 cycles, as expected, but repetitions of the following run at 7
cycles, whereas 6 would be expected (and is achieved on P55),

	shldl(	%cl, %eax, %ebx)
	xorl	%edx, %edx
	xorl	%esi, %esi
	xorl	%edi, %edi
	xorl	%ebp, %ebp

Three xorls run at 7 cycles too, so it doesn't seem to be just that pairing
inhibited is only in the second following cycle (or something like that).

Avoiding this problem would bring P54 shifts down from 6.0 c/l to 5.5 with a
pattern of shift, 2 loads, shift, 2 stores, shift, etc.  A start has been
made on something like that, but it's not yet complete.




OTHER NOTES

Prefetching Destinations

    Pentium doesn't allocate cache lines on writes, unlike most other modern
    processors.  Since the functions in the mpn class do array writes, we
    have to handle allocating the destination cache lines by reading a word
    from it in the loops, to achieve the best performance.

Prefetching Sources

    Prefetching of sources is pointless since there's no out-of-order loads.
    Any load instruction blocks until the line is brought to L1, so it may
    as well be the load that wants the data which blocks.

Data Cache Bank Clashes

    Pairing of memory operations requires that the two issued operations
    refer to different cache banks (ie. different addresses modulo 32
    bytes).  The simplest way to ensure this is to read/write two words from
    the same object.  If we make operations on different objects, they might
    or might not be to the same cache bank.

PIC %eip Fetching

    A simple call $+5 and popl can be used to get %eip, there's no need to
    balance calls and returns since P5 doesn't have any return stack branch
    prediction.

Float Multiplies

    fmul is pairable and can be issued every 2 cycles (with a 4 cycle
    latency for data ready to use).  This is a lot better than integer mull
    or imull at 9 cycles non-pairing.  Unfortunately the advantage is
    quickly eaten away by needing to throw data through memory back to the
    integer registers to adjust for fild and fist being signed, and to do
    things like propagating carry bits.





REFERENCES

"Intel Architecture Optimization Manual", 1997, order number 242816.  This
is mostly about P5, the parts about P6 aren't relevant.  Available on-line:

        http://download.intel.com/design/PentiumII/manuals/242816.htm



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