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The GNU MP Bignum Library

Copyright 2000, 2001 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.




                      AMD K7 MPN SUBROUTINES


This directory contains code optimized for the AMD Athlon CPU.

The mmx subdirectory has routines using MMX instructions.  All Athlons have
MMX, the separate directory is just so that configure can omit it if the
assembler doesn't support MMX.



STATUS

Times for the loops, with all code and data in L1 cache.

                               cycles/limb
	mpn_add/sub_n             1.6

	mpn_copyi                 0.75 or 1.0   \ varying with data alignment
	mpn_copyd                 0.75 or 1.0   /

	mpn_divrem_1             17.0 integer part, 15.0 fractional part
	mpn_mod_1                17.0
	mpn_divexact_by3          8.0

	mpn_l/rshift              1.2

	mpn_mul_1                 3.4
	mpn_addmul/submul_1       3.9

	mpn_mul_basecase          4.42 cycles/crossproduct (approx)
        mpn_sqr_basecase          2.3 cycles/crossproduct (approx)
				  or 4.55 cycles/triangleproduct (approx)

Prefetching of sources hasn't yet been tried.



NOTES

cmov, MMX, 3DNow and some extensions to MMX and 3DNow are available.

Write-allocate L1 data cache means prefetching of destinations is unnecessary.

Floating point multiplications can be done in parallel with integer
multiplications, but there doesn't seem to be any way to make use of this.

Unsigned "mul"s can be issued every 3 cycles.  This suggests 3 is a limit on
the speed of the multiplication routines.  The documentation shows mul
executing in IEU0 (or maybe in IEU0 and IEU1 together), so it might be that,
to get near 3 cycles code has to be arranged so that nothing else is issued
to IEU0.  A busy IEU0 could explain why some code takes 4 cycles and other
apparently equivalent code takes 5.



OPTIMIZATIONS

Unrolled loops are used to reduce looping overhead.  The unrolling is
configurable up to 32 limbs/loop for most routines and up to 64 for some.
The K7 has 64k L1 code cache so quite big unrolling is allowable.

Computed jumps into the unrolling are used to handle sizes not a multiple of
the unrolling.  An attractive feature of this is that times increase
smoothly with operand size, but it may be that some routines should just
have simple loops to finish up, especially when PIC adds between 2 and 16
cycles to get %eip.

Position independent code is implemented using a call to get %eip for the
computed jumps and a ret is always done, rather than an addl $4,%esp or a
popl, so the CPU return address branch prediction stack stays synchronised
with the actual stack in memory.

Branch prediction, in absence of any history, will guess forward jumps are
not taken and backward jumps are taken.  Where possible it's arranged that
the less likely or less important case is under a taken forward jump.



CODING

Instructions in general code have been shown grouped if they can execute
together, which means up to three direct-path instructions which have no
successive dependencies.  K7 always decodes three and has out-of-order
execution, but the groupings show what slots might be available and what
dependency chains exist.

When there's vector-path instructions an effort is made to get triplets of
direct-path instructions in between them, even if there's dependencies,
since this maximizes decoding throughput and might save a cycle or two if
decoding is the limiting factor.



INSTRUCTIONS

adcl       direct
divl       39 cycles back-to-back
lodsl,etc  vector
loop       1 cycle vector (decl/jnz opens up one decode slot)
movd reg   vector
movd mem   direct
mull       issue every 3 cycles, latency 4 cycles low word, 6 cycles high word
popl	   vector (use movl for more than one pop)
pushl	   direct, will pair with a load
shrdl %cl  vector, 3 cycles, seems to be 3 decode too
xorl r,r   false read dependency recognised



REFERENCES

"AMD Athlon Processor X86 Code Optimization Guide", AMD publication number
22007, revision K, February 2002.  Available on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/22007.pdf

"3DNow Technology Manual", AMD publication number 21928G/0-March 2000.
This describes the femms and prefetch instructions.  Available on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/21928.pdf

"AMD Extensions to the 3DNow and MMX Instruction Sets Manual", AMD
publication number 22466, revision D, March 2000.  This describes
instructions added in the Athlon processor, such as pswapd and the extra
prefetch forms.  Available on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/22466.pdf

"3DNow Instruction Porting Guide", AMD publication number 22621, revision B,
August 1999.  This has some notes on general Athlon optimizations as well as
3DNow.  Available on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/22621.pdf




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