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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 either:
* 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.
or
* the GNU General Public License as published by the Free Software
Foundation; either version 2 of the License, or (at your option) any
later version.
or both in parallel, as here.
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 General Public License
for more details.
You should have received copies of the GNU General Public License and the
GNU Lesser General Public License along with the GNU MP Library. If not,
see https://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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