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    later version.

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			AMD K6 MPN SUBROUTINES



This directory contains code optimized for AMD K6 CPUs, meaning K6, K6-2 and
K6-3.

The mmx subdirectory has MMX code suiting plain K6, the k62mmx subdirectory
has MMX code suiting K6-2 and K6-3.  All chips in the K6 family have MMX,
the separate directories are just so that ./configure can omit them if the
assembler doesn't support MMX.




STATUS

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

                                 cycles/limb

	mpn_add_n/sub_n            3.25 normal, 2.75 in-place

	mpn_mul_1                  6.25
	mpn_add/submul_1           7.65-8.4  (varying with data values)

	mpn_mul_basecase           9.25 cycles/crossproduct (approx)
	mpn_sqr_basecase           4.7  cycles/crossproduct (approx)
                                   or 9.2 cycles/triangleproduct (approx)

	mpn_l/rshift               3.0

	mpn_divrem_1              20.0
	mpn_mod_1                 20.0
	mpn_divexact_by3          11.0

	mpn_copyi                  1.0
	mpn_copyd                  1.0


K6-2 and K6-3 have dual-issue MMX and get the following improvements.

	mpn_l/rshift               1.75


Prefetching of sources hasn't yet given any joy.  With the 3DNow "prefetch"
instruction, code seems to run slower, and with just "mov" loads it doesn't
seem faster.  Results so far are inconsistent.  The K6 does a hardware
prefetch of the second cache line in a sector, so the penalty for not
prefetching in software is reduced.




NOTES

All K6 family chips have MMX, but only K6-2 and K6-3 have 3DNow.

Plain K6 executes MMX instructions only in the X pipe, but K6-2 and K6-3 can
execute them in both X and Y (and in both together).

Branch misprediction penalty is 1 to 4 cycles (Optimization Manual
chapter 6 table 12).

Write-allocate L1 data cache means prefetching of destinations is unnecessary.
Store queue is 7 entries of 64 bits each.

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.



OPTIMIZATIONS

Unrolled loops are used to reduce looping overhead.  The unrolling is
configurable up to 32 limbs/loop for most routines, up to 64 for some.

Sometimes computed jumps into the unrolling are used to handle sizes not a
multiple of the unrolling.  An attractive feature of this is that times
smoothly increase with operand size, but an indirect jump is about 6 cycles
and the setups about another 6, so it depends on how much the unrolled code
is faster than a simple loop as to whether a computed jump ought to be used.

Position independent code is implemented using a call to get eip for
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.  Such a call however still costs 4 to 7
cycles.

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.



MMX

Putting emms or femms as late as possible in a routine seems to be fastest.
Perhaps an emms or femms stalls until all outstanding MMX instructions have
completed, so putting it later gives them a chance to complete on their own,
in parallel with other operations (like register popping).

The Optimization Manual chapter 5 recommends using a femms on K6-2 and K6-3
at the start of a routine, in case it's been preceded by x87 floating point
operations.  This isn't done because in gmp programs it's expected that x87
floating point won't be much used and that chances are an mpn routine won't
have been preceded by any x87 code.



CODING

Instructions in general code are shown paired if they can decode and execute
together, meaning two short decode instructions with the second not
depending on the first, only the first using the shifter, no more than one
load, and no more than one store.

K6 does some out of order execution so the pairings aren't essential, they
just show what slots might be available.  When decoding is the limiting
factor things can be scheduled that might not execute until later.



NOTES

Code alignment

- if an opcode/modrm or 0Fh/opcode/modrm crosses a cache line boundary,
  short decode is inhibited.  The cross.pl script detects this.

- loops and branch targets should be aligned to 16 bytes, or ensure at least
  2 instructions before a 32 byte boundary.  This makes use of the 16 byte
  cache in the BTB.

Addressing modes

- (%esi) degrades decoding from short to vector.  0(%esi) doesn't have this
  problem, and can be used as an equivalent, or easier is just to use a
  different register, like %ebx.

- K6 and pre-CXT core K6-2 have the following problem.  (K6-2 CXT and K6-3
  have it fixed, these being cpuid function 1 signatures 0x588 to 0x58F).

  If more than 3 bytes are needed to determine instruction length then
  decoding degrades from direct to long, or from long to vector.  This
  happens with forms like "0F opcode mod/rm" with mod/rm=00-xxx-100 since
  with mod=00 the sib determines whether there's a displacement.

  This affects all MMX and 3DNow instructions, and others with an 0F prefix,
  like movzbl.  The modes affected are anything with an index and no
  displacement, or an index but no base, and this includes (%esp) which is
  really (,%esp,1).

  The cross.pl script detects problem cases.  The workaround is to always
  use a displacement, and to do this with Zdisp if it's zero so the
  assembler doesn't discard it.

  See Optimization Manual rev D page 67 and 3DNow Porting Guide rev B pages
  13-14 and 36-37.

Calls

- indirect jumps and calls are not branch predicted, they measure about 6
  cycles.

Various

- adcl      2 cycles of decode, maybe 2 cycles executing in the X pipe
- bsf       12-27 cycles
- emms      5 cycles
- femms     3 cycles
- jecxz     2 cycles taken, 13 not taken (optimization manual says 7 not taken)
- divl      20 cycles back-to-back
- imull     2 decode, 3 execute
- mull      2 decode, 3 execute (optimization manual decoding sample)
- prefetch  2 cycles
- rcll/rcrl implicit by one bit: 2 cycles
            immediate or %cl count: 11 + 2 per bit for dword
                                    13 + 4 per bit for byte
- setCC	    2 cycles
- xchgl	%eax,reg  1.5 cycles, back-to-back (strange)
        reg,reg   2 cycles, back-to-back




REFERENCES

"AMD-K6 Processor Code Optimization Application Note", AMD publication
number 21924, revision D amendment 0, January 2000.  This describes K6-2 and
K6-3.  Available on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/21924.pdf

"AMD-K6 MMX Enhanced Processor x86 Code Optimization Application Note", AMD
publication number 21828, revision A amendment 0, August 1997.  This is an
older edition of the above document, describing plain K6.  Available
on-line,

http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/21828.pdf

"3DNow Technology Manual", AMD publication number 21928G/0-March 2000.
This describes the femms and prefetch instructions, but nothing else from
3DNow has been used.  Available on-line,

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

"3DNow Instruction Porting Guide", AMD publication number 22621, revision B,
August 1999.  This has some notes on general K6 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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