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Import gmp 3.1

                   INTEL PENTIUM P5 MPN SUBROUTINES


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


STATUS

                                cycles/limb

	mpn_add_n/sub_n            2.375

	mpn_copyi/copyd            1.0

	mpn_divrem_1              44.0
	mpn_mod_1                 44.0
	mpn_divexact_by3          15.0

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

	mpn_mul_1                 13.0
	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)

Pentium MMX gets the following improvements

	mpn_l/rshift               1.75


1. 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.

2. 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.

3. 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 with it as 9.



RELEVANT OPTIMIZATION ISSUES

1. 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.

2. Pairing of memory operations requires that the two issued operations refer
to different cache banks.  The simplest way to insure 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.



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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