2011-07-20 21:49:46 +00:00
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#!/usr/bin/env perl
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#
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# Copyright (c) 2010-2011 Intel Corp.
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# Author: Vinodh.Gopal@intel.com
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# Jim Guilford
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# Erdinc.Ozturk@intel.com
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# Maxim.Perminov@intel.com
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#
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# More information about algorithm used can be found at:
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# http://www.cse.buffalo.edu/srds2009/escs2009_submission_Gopal.pdf
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#
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# ====================================================================
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# Copyright (c) 2011 The OpenSSL Project. All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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#
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# 2. Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in
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# the documentation and/or other materials provided with the
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# distribution.
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#
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# 3. All advertising materials mentioning features or use of this
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# software must display the following acknowledgment:
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# "This product includes software developed by the OpenSSL Project
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# for use in the OpenSSL Toolkit. (http://www.OpenSSL.org/)"
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#
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# 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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# endorse or promote products derived from this software without
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# prior written permission. For written permission, please contact
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# licensing@OpenSSL.org.
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#
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# 5. Products derived from this software may not be called "OpenSSL"
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# nor may "OpenSSL" appear in their names without prior written
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# permission of the OpenSSL Project.
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#
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# 6. Redistributions of any form whatsoever must retain the following
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# acknowledgment:
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# "This product includes software developed by the OpenSSL Project
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# for use in the OpenSSL Toolkit (http://www.OpenSSL.org/)"
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#
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# THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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# EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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# PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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# ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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# NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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# HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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# STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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# OF THE POSSIBILITY OF SUCH DAMAGE.
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# ====================================================================
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$flavour = shift;
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$output = shift;
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if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
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my $win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
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$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
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( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
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( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
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die "can't locate x86_64-xlate.pl";
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open STDOUT,"| $^X $xlate $flavour $output";
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use strict;
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my $code=".text\n\n";
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my $m=0;
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#
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# Define x512 macros
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#
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#MULSTEP_512_ADD MACRO x7, x6, x5, x4, x3, x2, x1, x0, dst, src1, src2, add_src, tmp1, tmp2
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#
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# uses rax, rdx, and args
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sub MULSTEP_512_ADD
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{
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my ($x, $DST, $SRC2, $ASRC, $OP, $TMP)=@_;
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my @X=@$x; # make a copy
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$code.=<<___;
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mov (+8*0)($SRC2), %rax
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mul $OP # rdx:rax = %OP * [0]
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mov ($ASRC), $X[0]
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add %rax, $X[0]
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adc \$0, %rdx
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mov $X[0], $DST
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___
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for(my $i=1;$i<8;$i++) {
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$code.=<<___;
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mov %rdx, $TMP
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mov (+8*$i)($SRC2), %rax
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mul $OP # rdx:rax = %OP * [$i]
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mov (+8*$i)($ASRC), $X[$i]
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add %rax, $X[$i]
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adc \$0, %rdx
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add $TMP, $X[$i]
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adc \$0, %rdx
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___
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}
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$code.=<<___;
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mov %rdx, $X[0]
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___
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}
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#MULSTEP_512 MACRO x7, x6, x5, x4, x3, x2, x1, x0, dst, src2, src1_val, tmp
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#
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# uses rax, rdx, and args
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sub MULSTEP_512
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{
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my ($x, $DST, $SRC2, $OP, $TMP)=@_;
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my @X=@$x; # make a copy
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$code.=<<___;
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mov (+8*0)($SRC2), %rax
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mul $OP # rdx:rax = %OP * [0]
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add %rax, $X[0]
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adc \$0, %rdx
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mov $X[0], $DST
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___
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for(my $i=1;$i<8;$i++) {
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$code.=<<___;
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mov %rdx, $TMP
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mov (+8*$i)($SRC2), %rax
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mul $OP # rdx:rax = %OP * [$i]
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add %rax, $X[$i]
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adc \$0, %rdx
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add $TMP, $X[$i]
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adc \$0, %rdx
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___
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}
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$code.=<<___;
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mov %rdx, $X[0]
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___
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}
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#
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# Swizzle Macros
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#
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# macro to copy data from flat space to swizzled table
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#MACRO swizzle pDst, pSrc, tmp1, tmp2
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# pDst and pSrc are modified
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sub swizzle
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{
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my ($pDst, $pSrc, $cnt, $d0)=@_;
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$code.=<<___;
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mov \$8, $cnt
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loop_$m:
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mov ($pSrc), $d0
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mov $d0#w, ($pDst)
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shr \$16, $d0
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mov $d0#w, (+64*1)($pDst)
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shr \$16, $d0
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mov $d0#w, (+64*2)($pDst)
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shr \$16, $d0
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mov $d0#w, (+64*3)($pDst)
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lea 8($pSrc), $pSrc
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lea 64*4($pDst), $pDst
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dec $cnt
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jnz loop_$m
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___
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$m++;
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}
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# macro to copy data from swizzled table to flat space
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#MACRO unswizzle pDst, pSrc, tmp*3
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sub unswizzle
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{
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my ($pDst, $pSrc, $cnt, $d0, $d1)=@_;
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$code.=<<___;
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mov \$4, $cnt
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loop_$m:
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movzxw (+64*3+256*0)($pSrc), $d0
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movzxw (+64*3+256*1)($pSrc), $d1
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shl \$16, $d0
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shl \$16, $d1
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mov (+64*2+256*0)($pSrc), $d0#w
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mov (+64*2+256*1)($pSrc), $d1#w
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shl \$16, $d0
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shl \$16, $d1
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mov (+64*1+256*0)($pSrc), $d0#w
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mov (+64*1+256*1)($pSrc), $d1#w
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shl \$16, $d0
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shl \$16, $d1
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mov (+64*0+256*0)($pSrc), $d0#w
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mov (+64*0+256*1)($pSrc), $d1#w
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mov $d0, (+8*0)($pDst)
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mov $d1, (+8*1)($pDst)
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lea 256*2($pSrc), $pSrc
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lea 8*2($pDst), $pDst
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sub \$1, $cnt
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jnz loop_$m
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___
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$m++;
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}
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#
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# Data Structures
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#
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# Reduce Data
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#
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#
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# Offset Value
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# 0C0 Carries
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# 0B8 X2[10]
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# 0B0 X2[9]
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# 0A8 X2[8]
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# 0A0 X2[7]
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# 098 X2[6]
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# 090 X2[5]
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# 088 X2[4]
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# 080 X2[3]
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# 078 X2[2]
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# 070 X2[1]
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# 068 X2[0]
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# 060 X1[12] P[10]
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# 058 X1[11] P[9] Z[8]
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# 050 X1[10] P[8] Z[7]
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# 048 X1[9] P[7] Z[6]
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# 040 X1[8] P[6] Z[5]
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# 038 X1[7] P[5] Z[4]
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# 030 X1[6] P[4] Z[3]
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# 028 X1[5] P[3] Z[2]
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# 020 X1[4] P[2] Z[1]
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# 018 X1[3] P[1] Z[0]
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# 010 X1[2] P[0] Y[2]
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# 008 X1[1] Q[1] Y[1]
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# 000 X1[0] Q[0] Y[0]
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my $X1_offset = 0; # 13 qwords
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my $X2_offset = $X1_offset + 13*8; # 11 qwords
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my $Carries_offset = $X2_offset + 11*8; # 1 qword
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my $Q_offset = 0; # 2 qwords
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my $P_offset = $Q_offset + 2*8; # 11 qwords
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my $Y_offset = 0; # 3 qwords
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my $Z_offset = $Y_offset + 3*8; # 9 qwords
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my $Red_Data_Size = $Carries_offset + 1*8; # (25 qwords)
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#
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# Stack Frame
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#
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#
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# offset value
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# ... <old stack contents>
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# ...
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# 280 Garray
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# 278 tmp16[15]
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# ... ...
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# 200 tmp16[0]
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# 1F8 tmp[7]
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# ... ...
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# 1C0 tmp[0]
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# 1B8 GT[7]
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# ... ...
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# 180 GT[0]
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# 178 Reduce Data
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# ... ...
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# 0B8 Reduce Data
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# 0B0 reserved
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# 0A8 reserved
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# 0A0 reserved
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# 098 reserved
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# 090 reserved
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# 088 reduce result addr
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# 080 exp[8]
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# ...
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# 048 exp[1]
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# 040 exp[0]
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# 038 reserved
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# 030 loop_idx
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# 028 pg
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# 020 i
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# 018 pData ; arg 4
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# 010 pG ; arg 2
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# 008 pResult ; arg 1
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# 000 rsp ; stack pointer before subtract
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my $rsp_offset = 0;
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my $pResult_offset = 8*1 + $rsp_offset;
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my $pG_offset = 8*1 + $pResult_offset;
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my $pData_offset = 8*1 + $pG_offset;
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my $i_offset = 8*1 + $pData_offset;
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my $pg_offset = 8*1 + $i_offset;
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my $loop_idx_offset = 8*1 + $pg_offset;
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my $reserved1_offset = 8*1 + $loop_idx_offset;
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my $exp_offset = 8*1 + $reserved1_offset;
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my $red_result_addr_offset= 8*9 + $exp_offset;
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my $reserved2_offset = 8*1 + $red_result_addr_offset;
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my $Reduce_Data_offset = 8*5 + $reserved2_offset;
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my $GT_offset = $Red_Data_Size + $Reduce_Data_offset;
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my $tmp_offset = 8*8 + $GT_offset;
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my $tmp16_offset = 8*8 + $tmp_offset;
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my $garray_offset = 8*16 + $tmp16_offset;
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my $mem_size = 8*8*32 + $garray_offset;
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#
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# Offsets within Reduce Data
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#
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#
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# struct MODF_2FOLD_MONT_512_C1_DATA {
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# UINT64 t[8][8];
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# UINT64 m[8];
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# UINT64 m1[8]; /* 2^768 % m */
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# UINT64 m2[8]; /* 2^640 % m */
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# UINT64 k1[2]; /* (- 1/m) % 2^128 */
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# };
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my $T = 0;
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my $M = 512; # = 8 * 8 * 8
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my $M1 = 576; # = 8 * 8 * 9 /* += 8 * 8 */
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my $M2 = 640; # = 8 * 8 * 10 /* += 8 * 8 */
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my $K1 = 704; # = 8 * 8 * 11 /* += 8 * 8 */
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#
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# FUNCTIONS
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#
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{{{
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#
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# MULADD_128x512 : Function to multiply 128-bits (2 qwords) by 512-bits (8 qwords)
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# and add 512-bits (8 qwords)
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# to get 640 bits (10 qwords)
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# Input: 128-bit mul source: [rdi+8*1], rbp
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# 512-bit mul source: [rsi+8*n]
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# 512-bit add source: r15, r14, ..., r9, r8
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# Output: r9, r8, r15, r14, r13, r12, r11, r10, [rcx+8*1], [rcx+8*0]
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# Clobbers all regs except: rcx, rsi, rdi
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$code.=<<___;
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.type MULADD_128x512,\@abi-omnipotent
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.align 16
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MULADD_128x512:
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___
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&MULSTEP_512([map("%r$_",(8..15))], "(+8*0)(%rcx)", "%rsi", "%rbp", "%rbx");
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$code.=<<___;
|
|
|
|
mov (+8*1)(%rdi), %rbp
|
|
|
|
___
|
|
|
|
&MULSTEP_512([map("%r$_",(9..15,8))], "(+8*1)(%rcx)", "%rsi", "%rbp", "%rbx");
|
|
|
|
$code.=<<___;
|
|
|
|
ret
|
|
|
|
.size MULADD_128x512,.-MULADD_128x512
|
|
|
|
___
|
|
|
|
}}}
|
|
|
|
|
|
|
|
{{{
|
|
|
|
#MULADD_256x512 MACRO pDst, pA, pB, OP, TMP, X7, X6, X5, X4, X3, X2, X1, X0
|
|
|
|
#
|
|
|
|
# Inputs: pDst: Destination (768 bits, 12 qwords)
|
|
|
|
# pA: Multiplicand (1024 bits, 16 qwords)
|
|
|
|
# pB: Multiplicand (512 bits, 8 qwords)
|
|
|
|
# Dst = Ah * B + Al
|
|
|
|
# where Ah is (in qwords) A[15:12] (256 bits) and Al is A[7:0] (512 bits)
|
|
|
|
# Results in X3 X2 X1 X0 X7 X6 X5 X4 Dst[3:0]
|
|
|
|
# Uses registers: arguments, RAX, RDX
|
|
|
|
sub MULADD_256x512
|
|
|
|
{
|
|
|
|
my ($pDst, $pA, $pB, $OP, $TMP, $X)=@_;
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*12)($pA), $OP
|
|
|
|
___
|
|
|
|
&MULSTEP_512_ADD($X, "(+8*0)($pDst)", $pB, $pA, $OP, $TMP);
|
|
|
|
push(@$X,shift(@$X));
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*13)($pA), $OP
|
|
|
|
___
|
|
|
|
&MULSTEP_512($X, "(+8*1)($pDst)", $pB, $OP, $TMP);
|
|
|
|
push(@$X,shift(@$X));
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*14)($pA), $OP
|
|
|
|
___
|
|
|
|
&MULSTEP_512($X, "(+8*2)($pDst)", $pB, $OP, $TMP);
|
|
|
|
push(@$X,shift(@$X));
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*15)($pA), $OP
|
|
|
|
___
|
|
|
|
&MULSTEP_512($X, "(+8*3)($pDst)", $pB, $OP, $TMP);
|
|
|
|
push(@$X,shift(@$X));
|
|
|
|
}
|
|
|
|
|
|
|
|
#
|
|
|
|
# mont_reduce(UINT64 *x, /* 1024 bits, 16 qwords */
|
|
|
|
# UINT64 *m, /* 512 bits, 8 qwords */
|
|
|
|
# MODF_2FOLD_MONT_512_C1_DATA *data,
|
|
|
|
# UINT64 *r) /* 512 bits, 8 qwords */
|
|
|
|
# Input: x (number to be reduced): tmp16 (Implicit)
|
|
|
|
# m (modulus): [pM] (Implicit)
|
|
|
|
# data (reduce data): [pData] (Implicit)
|
|
|
|
# Output: r (result): Address in [red_res_addr]
|
|
|
|
# result also in: r9, r8, r15, r14, r13, r12, r11, r10
|
|
|
|
|
|
|
|
my @X=map("%r$_",(8..15));
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
.type mont_reduce,\@abi-omnipotent
|
|
|
|
.align 16
|
|
|
|
mont_reduce:
|
|
|
|
___
|
|
|
|
|
|
|
|
my $STACK_DEPTH = 8;
|
|
|
|
#
|
|
|
|
# X1 = Xh * M1 + Xl
|
|
|
|
$code.=<<___;
|
|
|
|
lea (+$Reduce_Data_offset+$X1_offset+$STACK_DEPTH)(%rsp), %rdi # pX1 (Dst) 769 bits, 13 qwords
|
|
|
|
mov (+$pData_offset+$STACK_DEPTH)(%rsp), %rsi # pM1 (Bsrc) 512 bits, 8 qwords
|
|
|
|
add \$$M1, %rsi
|
|
|
|
lea (+$tmp16_offset+$STACK_DEPTH)(%rsp), %rcx # X (Asrc) 1024 bits, 16 qwords
|
|
|
|
|
|
|
|
___
|
|
|
|
|
|
|
|
&MULADD_256x512("%rdi", "%rcx", "%rsi", "%rbp", "%rbx", \@X); # rotates @X 4 times
|
|
|
|
# results in r11, r10, r9, r8, r15, r14, r13, r12, X1[3:0]
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
xor %rax, %rax
|
|
|
|
# X1 += xl
|
|
|
|
add (+8*8)(%rcx), $X[4]
|
|
|
|
adc (+8*9)(%rcx), $X[5]
|
|
|
|
adc (+8*10)(%rcx), $X[6]
|
|
|
|
adc (+8*11)(%rcx), $X[7]
|
|
|
|
adc \$0, %rax
|
|
|
|
# X1 is now rax, r11-r8, r15-r12, tmp16[3:0]
|
|
|
|
|
|
|
|
#
|
|
|
|
# check for carry ;; carry stored in rax
|
|
|
|
mov $X[4], (+8*8)(%rdi) # rdi points to X1
|
|
|
|
mov $X[5], (+8*9)(%rdi)
|
|
|
|
mov $X[6], %rbp
|
|
|
|
mov $X[7], (+8*11)(%rdi)
|
|
|
|
|
|
|
|
mov %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp)
|
|
|
|
|
|
|
|
mov (+8*0)(%rdi), $X[4]
|
|
|
|
mov (+8*1)(%rdi), $X[5]
|
|
|
|
mov (+8*2)(%rdi), $X[6]
|
|
|
|
mov (+8*3)(%rdi), $X[7]
|
|
|
|
|
|
|
|
# X1 is now stored in: X1[11], rbp, X1[9:8], r15-r8
|
|
|
|
# rdi -> X1
|
|
|
|
# rsi -> M1
|
|
|
|
|
|
|
|
#
|
|
|
|
# X2 = Xh * M2 + Xl
|
|
|
|
# do first part (X2 = Xh * M2)
|
|
|
|
add \$8*10, %rdi # rdi -> pXh ; 128 bits, 2 qwords
|
|
|
|
# Xh is actually { [rdi+8*1], rbp }
|
|
|
|
add \$($M2-$M1), %rsi # rsi -> M2
|
|
|
|
lea (+$Reduce_Data_offset+$X2_offset+$STACK_DEPTH)(%rsp), %rcx # rcx -> pX2 ; 641 bits, 11 qwords
|
|
|
|
___
|
|
|
|
unshift(@X,pop(@X)); unshift(@X,pop(@X));
|
|
|
|
$code.=<<___;
|
|
|
|
|
|
|
|
call MULADD_128x512 # args in rcx, rdi / rbp, rsi, r15-r8
|
|
|
|
# result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0]
|
|
|
|
mov (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rax
|
|
|
|
|
|
|
|
# X2 += Xl
|
|
|
|
add (+8*8-8*10)(%rdi), $X[6] # (-8*10) is to adjust rdi -> Xh to Xl
|
|
|
|
adc (+8*9-8*10)(%rdi), $X[7]
|
|
|
|
mov $X[6], (+8*8)(%rcx)
|
|
|
|
mov $X[7], (+8*9)(%rcx)
|
|
|
|
|
|
|
|
adc %rax, %rax
|
|
|
|
mov %rax, (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp)
|
|
|
|
|
|
|
|
lea (+$Reduce_Data_offset+$Q_offset+$STACK_DEPTH)(%rsp), %rdi # rdi -> pQ ; 128 bits, 2 qwords
|
|
|
|
add \$($K1-$M2), %rsi # rsi -> pK1 ; 128 bits, 2 qwords
|
|
|
|
|
|
|
|
# MUL_128x128t128 rdi, rcx, rsi ; Q = X2 * K1 (bottom half)
|
|
|
|
# B1:B0 = rsi[1:0] = K1[1:0]
|
|
|
|
# A1:A0 = rcx[1:0] = X2[1:0]
|
|
|
|
# Result = rdi[1],rbp = Q[1],rbp
|
|
|
|
mov (%rsi), %r8 # B0
|
|
|
|
mov (+8*1)(%rsi), %rbx # B1
|
|
|
|
|
|
|
|
mov (%rcx), %rax # A0
|
|
|
|
mul %r8 # B0
|
|
|
|
mov %rax, %rbp
|
|
|
|
mov %rdx, %r9
|
|
|
|
|
|
|
|
mov (+8*1)(%rcx), %rax # A1
|
|
|
|
mul %r8 # B0
|
|
|
|
add %rax, %r9
|
|
|
|
|
|
|
|
mov (%rcx), %rax # A0
|
|
|
|
mul %rbx # B1
|
|
|
|
add %rax, %r9
|
|
|
|
|
|
|
|
mov %r9, (+8*1)(%rdi)
|
|
|
|
# end MUL_128x128t128
|
|
|
|
|
|
|
|
sub \$($K1-$M), %rsi
|
|
|
|
|
|
|
|
mov (%rcx), $X[6]
|
|
|
|
mov (+8*1)(%rcx), $X[7] # r9:r8 = X2[1:0]
|
|
|
|
|
|
|
|
call MULADD_128x512 # args in rcx, rdi / rbp, rsi, r15-r8
|
|
|
|
# result in r9, r8, r15, r14, r13, r12, r11, r10, X2[1:0]
|
|
|
|
|
|
|
|
# load first half of m to rdx, rdi, rbx, rax
|
|
|
|
# moved this here for efficiency
|
|
|
|
mov (+8*0)(%rsi), %rax
|
|
|
|
mov (+8*1)(%rsi), %rbx
|
|
|
|
mov (+8*2)(%rsi), %rdi
|
|
|
|
mov (+8*3)(%rsi), %rdx
|
|
|
|
|
|
|
|
# continue with reduction
|
|
|
|
mov (+$Reduce_Data_offset+$Carries_offset+$STACK_DEPTH)(%rsp), %rbp
|
|
|
|
|
|
|
|
add (+8*8)(%rcx), $X[6]
|
|
|
|
adc (+8*9)(%rcx), $X[7]
|
|
|
|
|
|
|
|
#accumulate the final carry to rbp
|
|
|
|
adc %rbp, %rbp
|
|
|
|
|
|
|
|
# Add in overflow corrections: R = (X2>>128) += T[overflow]
|
|
|
|
# R = {r9, r8, r15, r14, ..., r10}
|
|
|
|
shl \$3, %rbp
|
|
|
|
mov (+$pData_offset+$STACK_DEPTH)(%rsp), %rcx # rsi -> Data (and points to T)
|
|
|
|
add %rcx, %rbp # pT ; 512 bits, 8 qwords, spread out
|
|
|
|
|
|
|
|
# rsi will be used to generate a mask after the addition
|
|
|
|
xor %rsi, %rsi
|
|
|
|
|
|
|
|
add (+8*8*0)(%rbp), $X[0]
|
|
|
|
adc (+8*8*1)(%rbp), $X[1]
|
|
|
|
adc (+8*8*2)(%rbp), $X[2]
|
|
|
|
adc (+8*8*3)(%rbp), $X[3]
|
|
|
|
adc (+8*8*4)(%rbp), $X[4]
|
|
|
|
adc (+8*8*5)(%rbp), $X[5]
|
|
|
|
adc (+8*8*6)(%rbp), $X[6]
|
|
|
|
adc (+8*8*7)(%rbp), $X[7]
|
|
|
|
|
|
|
|
# if there is a carry: rsi = 0xFFFFFFFFFFFFFFFF
|
|
|
|
# if carry is clear: rsi = 0x0000000000000000
|
|
|
|
sbb \$0, %rsi
|
|
|
|
|
|
|
|
# if carry is clear, subtract 0. Otherwise, subtract 256 bits of m
|
|
|
|
and %rsi, %rax
|
|
|
|
and %rsi, %rbx
|
|
|
|
and %rsi, %rdi
|
|
|
|
and %rsi, %rdx
|
|
|
|
|
|
|
|
mov \$1, %rbp
|
|
|
|
sub %rax, $X[0]
|
|
|
|
sbb %rbx, $X[1]
|
|
|
|
sbb %rdi, $X[2]
|
|
|
|
sbb %rdx, $X[3]
|
|
|
|
|
|
|
|
# if there is a borrow: rbp = 0
|
|
|
|
# if there is no borrow: rbp = 1
|
|
|
|
# this is used to save the borrows in between the first half and the 2nd half of the subtraction of m
|
|
|
|
sbb \$0, %rbp
|
|
|
|
|
|
|
|
#load second half of m to rdx, rdi, rbx, rax
|
|
|
|
|
|
|
|
add \$$M, %rcx
|
|
|
|
mov (+8*4)(%rcx), %rax
|
|
|
|
mov (+8*5)(%rcx), %rbx
|
|
|
|
mov (+8*6)(%rcx), %rdi
|
|
|
|
mov (+8*7)(%rcx), %rdx
|
|
|
|
|
|
|
|
# use the rsi mask as before
|
|
|
|
# if carry is clear, subtract 0. Otherwise, subtract 256 bits of m
|
|
|
|
and %rsi, %rax
|
|
|
|
and %rsi, %rbx
|
|
|
|
and %rsi, %rdi
|
|
|
|
and %rsi, %rdx
|
|
|
|
|
|
|
|
# if rbp = 0, there was a borrow before, it is moved to the carry flag
|
|
|
|
# if rbp = 1, there was not a borrow before, carry flag is cleared
|
|
|
|
sub \$1, %rbp
|
|
|
|
|
|
|
|
sbb %rax, $X[4]
|
|
|
|
sbb %rbx, $X[5]
|
|
|
|
sbb %rdi, $X[6]
|
|
|
|
sbb %rdx, $X[7]
|
|
|
|
|
|
|
|
# write R back to memory
|
|
|
|
|
|
|
|
mov (+$red_result_addr_offset+$STACK_DEPTH)(%rsp), %rsi
|
|
|
|
mov $X[0], (+8*0)(%rsi)
|
|
|
|
mov $X[1], (+8*1)(%rsi)
|
|
|
|
mov $X[2], (+8*2)(%rsi)
|
|
|
|
mov $X[3], (+8*3)(%rsi)
|
|
|
|
mov $X[4], (+8*4)(%rsi)
|
|
|
|
mov $X[5], (+8*5)(%rsi)
|
|
|
|
mov $X[6], (+8*6)(%rsi)
|
|
|
|
mov $X[7], (+8*7)(%rsi)
|
|
|
|
|
|
|
|
ret
|
|
|
|
.size mont_reduce,.-mont_reduce
|
|
|
|
___
|
|
|
|
}}}
|
|
|
|
|
|
|
|
{{{
|
|
|
|
#MUL_512x512 MACRO pDst, pA, pB, x7, x6, x5, x4, x3, x2, x1, x0, tmp*2
|
|
|
|
#
|
|
|
|
# Inputs: pDst: Destination (1024 bits, 16 qwords)
|
|
|
|
# pA: Multiplicand (512 bits, 8 qwords)
|
|
|
|
# pB: Multiplicand (512 bits, 8 qwords)
|
|
|
|
# Uses registers rax, rdx, args
|
|
|
|
# B operand in [pB] and also in x7...x0
|
|
|
|
sub MUL_512x512
|
|
|
|
{
|
|
|
|
my ($pDst, $pA, $pB, $x, $OP, $TMP, $pDst_o)=@_;
|
|
|
|
my ($pDst, $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/);
|
|
|
|
my @X=@$x; # make a copy
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*0)($pA), $OP
|
|
|
|
|
|
|
|
mov $X[0], %rax
|
|
|
|
mul $OP # rdx:rax = %OP * [0]
|
|
|
|
mov %rax, (+$pDst_o+8*0)($pDst)
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
___
|
|
|
|
for(my $i=1;$i<8;$i++) {
|
|
|
|
$code.=<<___;
|
|
|
|
mov $X[$i], %rax
|
|
|
|
mul $OP # rdx:rax = %OP * [$i]
|
|
|
|
add %rax, $X[$i-1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov %rdx, $X[$i]
|
|
|
|
___
|
|
|
|
}
|
|
|
|
|
|
|
|
for(my $i=1;$i<8;$i++) {
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+8*$i)($pA), $OP
|
|
|
|
___
|
|
|
|
|
|
|
|
&MULSTEP_512(\@X, "(+$pDst_o+8*$i)($pDst)", $pB, $OP, $TMP);
|
|
|
|
push(@X,shift(@X));
|
|
|
|
}
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
mov $X[0], (+$pDst_o+8*8)($pDst)
|
|
|
|
mov $X[1], (+$pDst_o+8*9)($pDst)
|
|
|
|
mov $X[2], (+$pDst_o+8*10)($pDst)
|
|
|
|
mov $X[3], (+$pDst_o+8*11)($pDst)
|
|
|
|
mov $X[4], (+$pDst_o+8*12)($pDst)
|
|
|
|
mov $X[5], (+$pDst_o+8*13)($pDst)
|
|
|
|
mov $X[6], (+$pDst_o+8*14)($pDst)
|
|
|
|
mov $X[7], (+$pDst_o+8*15)($pDst)
|
|
|
|
___
|
|
|
|
}
|
|
|
|
|
|
|
|
#
|
|
|
|
# mont_mul_a3b : subroutine to compute (Src1 * Src2) % M (all 512-bits)
|
|
|
|
# Input: src1: Address of source 1: rdi
|
|
|
|
# src2: Address of source 2: rsi
|
|
|
|
# Output: dst: Address of destination: [red_res_addr]
|
|
|
|
# src2 and result also in: r9, r8, r15, r14, r13, r12, r11, r10
|
|
|
|
# Temp: Clobbers [tmp16], all registers
|
|
|
|
$code.=<<___;
|
|
|
|
.type mont_mul_a3b,\@abi-omnipotent
|
|
|
|
.align 16
|
|
|
|
mont_mul_a3b:
|
|
|
|
#
|
|
|
|
# multiply tmp = src1 * src2
|
|
|
|
# For multiply: dst = rcx, src1 = rdi, src2 = rsi
|
|
|
|
# stack depth is extra 8 from call
|
|
|
|
___
|
|
|
|
&MUL_512x512("%rsp+$tmp16_offset+8", "%rdi", "%rsi", [map("%r$_",(10..15,8..9))], "%rbp", "%rbx");
|
|
|
|
$code.=<<___;
|
|
|
|
#
|
|
|
|
# Dst = tmp % m
|
|
|
|
# Call reduce(tmp, m, data, dst)
|
|
|
|
|
|
|
|
# tail recursion optimization: jmp to mont_reduce and return from there
|
|
|
|
jmp mont_reduce
|
|
|
|
# call mont_reduce
|
|
|
|
# ret
|
|
|
|
.size mont_mul_a3b,.-mont_mul_a3b
|
|
|
|
___
|
|
|
|
}}}
|
|
|
|
|
|
|
|
{{{
|
|
|
|
#SQR_512 MACRO pDest, pA, x7, x6, x5, x4, x3, x2, x1, x0, tmp*4
|
|
|
|
#
|
|
|
|
# Input in memory [pA] and also in x7...x0
|
|
|
|
# Uses all argument registers plus rax and rdx
|
|
|
|
#
|
|
|
|
# This version computes all of the off-diagonal terms into memory,
|
|
|
|
# and then it adds in the diagonal terms
|
|
|
|
|
|
|
|
sub SQR_512
|
|
|
|
{
|
|
|
|
my ($pDst, $pA, $x, $A, $tmp, $x7, $x6, $pDst_o)=@_;
|
|
|
|
my ($pDst, $pDst_o) = ($pDst =~ m/([^+]*)\+?(.*)?/);
|
|
|
|
my @X=@$x; # make a copy
|
|
|
|
$code.=<<___;
|
|
|
|
# ------------------
|
|
|
|
# first pass 01...07
|
|
|
|
# ------------------
|
|
|
|
mov $X[0], $A
|
|
|
|
|
|
|
|
mov $X[1],%rax
|
|
|
|
mul $A
|
|
|
|
mov %rax, (+$pDst_o+8*1)($pDst)
|
|
|
|
___
|
|
|
|
for(my $i=2;$i<8;$i++) {
|
|
|
|
$code.=<<___;
|
|
|
|
mov %rdx, $X[$i-2]
|
|
|
|
mov $X[$i],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[$i-2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
___
|
|
|
|
}
|
|
|
|
$code.=<<___;
|
|
|
|
mov %rdx, $x7
|
|
|
|
|
|
|
|
mov $X[0], (+$pDst_o+8*2)($pDst)
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# second pass 12...17
|
|
|
|
# ------------------
|
|
|
|
|
|
|
|
mov (+8*1)($pA), $A
|
|
|
|
|
|
|
|
mov (+8*2)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[1], (+$pDst_o+8*3)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*3)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[2], (+$pDst_o+8*4)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*4)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[3]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[3]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*5)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[4]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[4]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[6],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[1]
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# third pass 23...27
|
|
|
|
# ------------------
|
|
|
|
mov (+8*2)($pA), $A
|
|
|
|
|
|
|
|
mov (+8*3)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[3]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[3], (+$pDst_o+8*5)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*4)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[4]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[4]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[4], (+$pDst_o+8*6)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*5)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[6],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[2]
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# fourth pass 34...37
|
|
|
|
# ------------------
|
|
|
|
|
|
|
|
mov (+8*3)($pA), $A
|
|
|
|
|
|
|
|
mov (+8*4)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[5], (+$pDst_o+8*7)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov (+8*5)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $x7
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $x7, (+$pDst_o+8*8)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[6],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[5]
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# fifth pass 45...47
|
|
|
|
# ------------------
|
|
|
|
mov (+8*4)($pA), $A
|
|
|
|
|
|
|
|
mov (+8*5)($pA),%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[1], (+$pDst_o+8*9)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[6],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[2], (+$pDst_o+8*10)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $X[1]
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# sixth pass 56...57
|
|
|
|
# ------------------
|
|
|
|
mov (+8*5)($pA), $A
|
|
|
|
|
|
|
|
mov $X[6],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[5], (+$pDst_o+8*11)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[0]
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
add $X[0], $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[1], (+$pDst_o+8*12)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, $X[2]
|
|
|
|
|
|
|
|
# ------------------
|
|
|
|
# seventh pass 67
|
|
|
|
# ------------------
|
|
|
|
mov $X[6], $A
|
|
|
|
|
|
|
|
mov $X[7],%rax
|
|
|
|
mul $A
|
|
|
|
add %rax, $X[2]
|
|
|
|
adc \$0, %rdx
|
|
|
|
mov $X[2], (+$pDst_o+8*13)($pDst)
|
|
|
|
|
|
|
|
mov %rdx, (+$pDst_o+8*14)($pDst)
|
|
|
|
|
|
|
|
# start finalize (add in squares, and double off-terms)
|
|
|
|
mov (+$pDst_o+8*1)($pDst), $X[0]
|
|
|
|
mov (+$pDst_o+8*2)($pDst), $X[1]
|
|
|
|
mov (+$pDst_o+8*3)($pDst), $X[2]
|
|
|
|
mov (+$pDst_o+8*4)($pDst), $X[3]
|
|
|
|
mov (+$pDst_o+8*5)($pDst), $X[4]
|
|
|
|
mov (+$pDst_o+8*6)($pDst), $X[5]
|
|
|
|
|
|
|
|
mov (+8*3)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
mov %rax, $x6
|
|
|
|
mov %rdx, $X[6]
|
|
|
|
|
|
|
|
add $X[0], $X[0]
|
|
|
|
adc $X[1], $X[1]
|
|
|
|
adc $X[2], $X[2]
|
|
|
|
adc $X[3], $X[3]
|
|
|
|
adc $X[4], $X[4]
|
|
|
|
adc $X[5], $X[5]
|
|
|
|
adc \$0, $X[6]
|
|
|
|
|
|
|
|
mov (+8*0)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
mov %rax, (+$pDst_o+8*0)($pDst)
|
|
|
|
mov %rdx, $A
|
|
|
|
|
|
|
|
mov (+8*1)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
|
|
|
|
add $A, $X[0]
|
|
|
|
adc %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $A
|
|
|
|
mov $X[0], (+$pDst_o+8*1)($pDst)
|
|
|
|
mov $X[1], (+$pDst_o+8*2)($pDst)
|
|
|
|
|
|
|
|
mov (+8*2)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
|
|
|
|
add $A, $X[2]
|
|
|
|
adc %rax, $X[3]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $A
|
|
|
|
|
|
|
|
mov $X[2], (+$pDst_o+8*3)($pDst)
|
|
|
|
mov $X[3], (+$pDst_o+8*4)($pDst)
|
|
|
|
|
|
|
|
xor $tmp, $tmp
|
|
|
|
add $A, $X[4]
|
|
|
|
adc $x6, $X[5]
|
|
|
|
adc \$0, $tmp
|
|
|
|
|
|
|
|
mov $X[4], (+$pDst_o+8*5)($pDst)
|
|
|
|
mov $X[5], (+$pDst_o+8*6)($pDst)
|
|
|
|
|
|
|
|
# %%tmp has 0/1 in column 7
|
|
|
|
# %%A6 has a full value in column 7
|
|
|
|
|
|
|
|
mov (+$pDst_o+8*7)($pDst), $X[0]
|
|
|
|
mov (+$pDst_o+8*8)($pDst), $X[1]
|
|
|
|
mov (+$pDst_o+8*9)($pDst), $X[2]
|
|
|
|
mov (+$pDst_o+8*10)($pDst), $X[3]
|
|
|
|
mov (+$pDst_o+8*11)($pDst), $X[4]
|
|
|
|
mov (+$pDst_o+8*12)($pDst), $X[5]
|
|
|
|
mov (+$pDst_o+8*13)($pDst), $x6
|
|
|
|
mov (+$pDst_o+8*14)($pDst), $x7
|
|
|
|
|
|
|
|
mov $X[7], %rax
|
|
|
|
mul %rax
|
|
|
|
mov %rax, $X[7]
|
|
|
|
mov %rdx, $A
|
|
|
|
|
|
|
|
add $X[0], $X[0]
|
|
|
|
adc $X[1], $X[1]
|
|
|
|
adc $X[2], $X[2]
|
|
|
|
adc $X[3], $X[3]
|
|
|
|
adc $X[4], $X[4]
|
|
|
|
adc $X[5], $X[5]
|
|
|
|
adc $x6, $x6
|
|
|
|
adc $x7, $x7
|
|
|
|
adc \$0, $A
|
|
|
|
|
|
|
|
add $tmp, $X[0]
|
|
|
|
|
|
|
|
mov (+8*4)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
|
|
|
|
add $X[6], $X[0]
|
|
|
|
adc %rax, $X[1]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $tmp
|
|
|
|
|
|
|
|
mov $X[0], (+$pDst_o+8*7)($pDst)
|
|
|
|
mov $X[1], (+$pDst_o+8*8)($pDst)
|
|
|
|
|
|
|
|
mov (+8*5)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
|
|
|
|
add $tmp, $X[2]
|
|
|
|
adc %rax, $X[3]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov %rdx, $tmp
|
|
|
|
|
|
|
|
mov $X[2], (+$pDst_o+8*9)($pDst)
|
|
|
|
mov $X[3], (+$pDst_o+8*10)($pDst)
|
|
|
|
|
|
|
|
mov (+8*6)($pA), %rax
|
|
|
|
mul %rax
|
|
|
|
|
|
|
|
add $tmp, $X[4]
|
|
|
|
adc %rax, $X[5]
|
|
|
|
adc \$0, %rdx
|
|
|
|
|
|
|
|
mov $X[4], (+$pDst_o+8*11)($pDst)
|
|
|
|
mov $X[5], (+$pDst_o+8*12)($pDst)
|
|
|
|
|
|
|
|
add %rdx, $x6
|
|
|
|
adc $X[7], $x7
|
|
|
|
adc \$0, $A
|
|
|
|
|
|
|
|
mov $x6, (+$pDst_o+8*13)($pDst)
|
|
|
|
mov $x7, (+$pDst_o+8*14)($pDst)
|
|
|
|
mov $A, (+$pDst_o+8*15)($pDst)
|
|
|
|
___
|
|
|
|
}
|
|
|
|
|
|
|
|
#
|
|
|
|
# sqr_reduce: subroutine to compute Result = reduce(Result * Result)
|
|
|
|
#
|
|
|
|
# input and result also in: r9, r8, r15, r14, r13, r12, r11, r10
|
|
|
|
#
|
|
|
|
$code.=<<___;
|
|
|
|
.type sqr_reduce,\@abi-omnipotent
|
|
|
|
.align 16
|
|
|
|
sqr_reduce:
|
|
|
|
mov (+$pResult_offset+8)(%rsp), %rcx
|
|
|
|
___
|
|
|
|
&SQR_512("%rsp+$tmp16_offset+8", "%rcx", [map("%r$_",(10..15,8..9))], "%rbx", "%rbp", "%rsi", "%rdi");
|
|
|
|
$code.=<<___;
|
|
|
|
# tail recursion optimization: jmp to mont_reduce and return from there
|
|
|
|
jmp mont_reduce
|
|
|
|
# call mont_reduce
|
|
|
|
# ret
|
|
|
|
.size sqr_reduce,.-sqr_reduce
|
|
|
|
___
|
|
|
|
}}}
|
|
|
|
|
|
|
|
#
|
|
|
|
# MAIN FUNCTION
|
|
|
|
#
|
|
|
|
|
|
|
|
#mod_exp_512(UINT64 *result, /* 512 bits, 8 qwords */
|
|
|
|
# UINT64 *g, /* 512 bits, 8 qwords */
|
|
|
|
# UINT64 *exp, /* 512 bits, 8 qwords */
|
|
|
|
# struct mod_ctx_512 *data)
|
|
|
|
|
|
|
|
# window size = 5
|
|
|
|
# table size = 2^5 = 32
|
|
|
|
#table_entries equ 32
|
|
|
|
#table_size equ table_entries * 8
|
|
|
|
$code.=<<___;
|
|
|
|
.globl mod_exp_512
|
|
|
|
.type mod_exp_512,\@function,4
|
|
|
|
mod_exp_512:
|
|
|
|
push %rbp
|
|
|
|
push %rbx
|
|
|
|
push %r12
|
|
|
|
push %r13
|
|
|
|
push %r14
|
|
|
|
push %r15
|
|
|
|
|
|
|
|
# adjust stack down and then align it with cache boundary
|
|
|
|
mov %rsp, %r8
|
|
|
|
sub \$($mem_size), %rsp
|
2011-08-19 06:30:32 +00:00
|
|
|
and \$-64, %rsp
|
2011-07-20 21:49:46 +00:00
|
|
|
|
|
|
|
# store previous stack pointer and arguments
|
|
|
|
mov %r8, (+$rsp_offset)(%rsp)
|
|
|
|
mov %rdi, (+$pResult_offset)(%rsp)
|
|
|
|
mov %rsi, (+$pG_offset)(%rsp)
|
|
|
|
mov %rcx, (+$pData_offset)(%rsp)
|
|
|
|
.Lbody:
|
|
|
|
# transform g into montgomery space
|
|
|
|
# GT = reduce(g * C2) = reduce(g * (2^256))
|
|
|
|
# reduce expects to have the input in [tmp16]
|
|
|
|
pxor %xmm4, %xmm4
|
|
|
|
movdqu (+16*0)(%rsi), %xmm0
|
|
|
|
movdqu (+16*1)(%rsi), %xmm1
|
|
|
|
movdqu (+16*2)(%rsi), %xmm2
|
|
|
|
movdqu (+16*3)(%rsi), %xmm3
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*0)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*1)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp)
|
|
|
|
movdqa %xmm0, (+$tmp16_offset+16*2)(%rsp)
|
|
|
|
movdqa %xmm1, (+$tmp16_offset+16*3)(%rsp)
|
|
|
|
movdqa %xmm2, (+$tmp16_offset+16*4)(%rsp)
|
|
|
|
movdqa %xmm3, (+$tmp16_offset+16*5)(%rsp)
|
|
|
|
|
|
|
|
# load pExp before rdx gets blown away
|
|
|
|
movdqu (+16*0)(%rdx), %xmm0
|
|
|
|
movdqu (+16*1)(%rdx), %xmm1
|
|
|
|
movdqu (+16*2)(%rdx), %xmm2
|
|
|
|
movdqu (+16*3)(%rdx), %xmm3
|
|
|
|
|
|
|
|
lea (+$GT_offset)(%rsp), %rbx
|
|
|
|
mov %rbx, (+$red_result_addr_offset)(%rsp)
|
|
|
|
call mont_reduce
|
|
|
|
|
|
|
|
# Initialize tmp = C
|
|
|
|
lea (+$tmp_offset)(%rsp), %rcx
|
|
|
|
xor %rax, %rax
|
|
|
|
mov %rax, (+8*0)(%rcx)
|
|
|
|
mov %rax, (+8*1)(%rcx)
|
|
|
|
mov %rax, (+8*3)(%rcx)
|
|
|
|
mov %rax, (+8*4)(%rcx)
|
|
|
|
mov %rax, (+8*5)(%rcx)
|
|
|
|
mov %rax, (+8*6)(%rcx)
|
|
|
|
mov %rax, (+8*7)(%rcx)
|
|
|
|
mov %rax, (+$exp_offset+8*8)(%rsp)
|
|
|
|
movq \$1, (+8*2)(%rcx)
|
|
|
|
|
|
|
|
lea (+$garray_offset)(%rsp), %rbp
|
|
|
|
mov %rcx, %rsi # pTmp
|
|
|
|
mov %rbp, %rdi # Garray[][0]
|
|
|
|
___
|
|
|
|
|
|
|
|
&swizzle("%rdi", "%rcx", "%rax", "%rbx");
|
|
|
|
|
|
|
|
# for (rax = 31; rax != 0; rax--) {
|
|
|
|
# tmp = reduce(tmp * G)
|
|
|
|
# swizzle(pg, tmp);
|
|
|
|
# pg += 2; }
|
|
|
|
$code.=<<___;
|
|
|
|
mov \$31, %rax
|
|
|
|
mov %rax, (+$i_offset)(%rsp)
|
|
|
|
mov %rbp, (+$pg_offset)(%rsp)
|
|
|
|
# rsi -> pTmp
|
|
|
|
mov %rsi, (+$red_result_addr_offset)(%rsp)
|
|
|
|
mov (+8*0)(%rsi), %r10
|
|
|
|
mov (+8*1)(%rsi), %r11
|
|
|
|
mov (+8*2)(%rsi), %r12
|
|
|
|
mov (+8*3)(%rsi), %r13
|
|
|
|
mov (+8*4)(%rsi), %r14
|
|
|
|
mov (+8*5)(%rsi), %r15
|
|
|
|
mov (+8*6)(%rsi), %r8
|
|
|
|
mov (+8*7)(%rsi), %r9
|
|
|
|
init_loop:
|
|
|
|
lea (+$GT_offset)(%rsp), %rdi
|
|
|
|
call mont_mul_a3b
|
|
|
|
lea (+$tmp_offset)(%rsp), %rsi
|
|
|
|
mov (+$pg_offset)(%rsp), %rbp
|
|
|
|
add \$2, %rbp
|
|
|
|
mov %rbp, (+$pg_offset)(%rsp)
|
|
|
|
mov %rsi, %rcx # rcx = rsi = addr of tmp
|
|
|
|
___
|
|
|
|
|
|
|
|
&swizzle("%rbp", "%rcx", "%rax", "%rbx");
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+$i_offset)(%rsp), %rax
|
|
|
|
sub \$1, %rax
|
|
|
|
mov %rax, (+$i_offset)(%rsp)
|
|
|
|
jne init_loop
|
|
|
|
|
|
|
|
#
|
|
|
|
# Copy exponent onto stack
|
|
|
|
movdqa %xmm0, (+$exp_offset+16*0)(%rsp)
|
|
|
|
movdqa %xmm1, (+$exp_offset+16*1)(%rsp)
|
|
|
|
movdqa %xmm2, (+$exp_offset+16*2)(%rsp)
|
|
|
|
movdqa %xmm3, (+$exp_offset+16*3)(%rsp)
|
|
|
|
|
|
|
|
|
|
|
|
#
|
|
|
|
# Do exponentiation
|
|
|
|
# Initialize result to G[exp{511:507}]
|
|
|
|
mov (+$exp_offset+62)(%rsp), %eax
|
|
|
|
mov %rax, %rdx
|
|
|
|
shr \$11, %rax
|
|
|
|
and \$0x07FF, %edx
|
|
|
|
mov %edx, (+$exp_offset+62)(%rsp)
|
|
|
|
lea (+$garray_offset)(%rsp,%rax,2), %rsi
|
|
|
|
mov (+$pResult_offset)(%rsp), %rdx
|
|
|
|
___
|
|
|
|
|
|
|
|
&unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax");
|
|
|
|
|
|
|
|
#
|
|
|
|
# Loop variables
|
|
|
|
# rcx = [loop_idx] = index: 510-5 to 0 by 5
|
|
|
|
$code.=<<___;
|
|
|
|
movq \$505, (+$loop_idx_offset)(%rsp)
|
|
|
|
|
|
|
|
mov (+$pResult_offset)(%rsp), %rcx
|
|
|
|
mov %rcx, (+$red_result_addr_offset)(%rsp)
|
|
|
|
mov (+8*0)(%rcx), %r10
|
|
|
|
mov (+8*1)(%rcx), %r11
|
|
|
|
mov (+8*2)(%rcx), %r12
|
|
|
|
mov (+8*3)(%rcx), %r13
|
|
|
|
mov (+8*4)(%rcx), %r14
|
|
|
|
mov (+8*5)(%rcx), %r15
|
|
|
|
mov (+8*6)(%rcx), %r8
|
|
|
|
mov (+8*7)(%rcx), %r9
|
|
|
|
jmp sqr_2
|
|
|
|
|
|
|
|
main_loop_a3b:
|
|
|
|
call sqr_reduce
|
|
|
|
call sqr_reduce
|
|
|
|
call sqr_reduce
|
|
|
|
sqr_2:
|
|
|
|
call sqr_reduce
|
|
|
|
call sqr_reduce
|
|
|
|
|
|
|
|
#
|
|
|
|
# Do multiply, first look up proper value in Garray
|
|
|
|
mov (+$loop_idx_offset)(%rsp), %rcx # bit index
|
|
|
|
mov %rcx, %rax
|
|
|
|
shr \$4, %rax # rax is word pointer
|
|
|
|
mov (+$exp_offset)(%rsp,%rax,2), %edx
|
|
|
|
and \$15, %rcx
|
|
|
|
shrq %cl, %rdx
|
|
|
|
and \$0x1F, %rdx
|
|
|
|
|
|
|
|
lea (+$garray_offset)(%rsp,%rdx,2), %rsi
|
|
|
|
lea (+$tmp_offset)(%rsp), %rdx
|
|
|
|
mov %rdx, %rdi
|
|
|
|
___
|
|
|
|
|
|
|
|
&unswizzle("%rdx", "%rsi", "%rbp", "%rbx", "%rax");
|
|
|
|
# rdi = tmp = pG
|
|
|
|
|
|
|
|
#
|
|
|
|
# Call mod_mul_a1(pDst, pSrc1, pSrc2, pM, pData)
|
|
|
|
# result result pG M Data
|
|
|
|
$code.=<<___;
|
|
|
|
mov (+$pResult_offset)(%rsp), %rsi
|
|
|
|
call mont_mul_a3b
|
|
|
|
|
|
|
|
#
|
|
|
|
# finish loop
|
|
|
|
mov (+$loop_idx_offset)(%rsp), %rcx
|
|
|
|
sub \$5, %rcx
|
|
|
|
mov %rcx, (+$loop_idx_offset)(%rsp)
|
|
|
|
jge main_loop_a3b
|
|
|
|
|
|
|
|
#
|
|
|
|
|
|
|
|
end_main_loop_a3b:
|
|
|
|
# transform result out of Montgomery space
|
|
|
|
# result = reduce(result)
|
|
|
|
mov (+$pResult_offset)(%rsp), %rdx
|
|
|
|
pxor %xmm4, %xmm4
|
|
|
|
movdqu (+16*0)(%rdx), %xmm0
|
|
|
|
movdqu (+16*1)(%rdx), %xmm1
|
|
|
|
movdqu (+16*2)(%rdx), %xmm2
|
|
|
|
movdqu (+16*3)(%rdx), %xmm3
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*4)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*5)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*6)(%rsp)
|
|
|
|
movdqa %xmm4, (+$tmp16_offset+16*7)(%rsp)
|
|
|
|
movdqa %xmm0, (+$tmp16_offset+16*0)(%rsp)
|
|
|
|
movdqa %xmm1, (+$tmp16_offset+16*1)(%rsp)
|
|
|
|
movdqa %xmm2, (+$tmp16_offset+16*2)(%rsp)
|
|
|
|
movdqa %xmm3, (+$tmp16_offset+16*3)(%rsp)
|
|
|
|
call mont_reduce
|
|
|
|
|
|
|
|
# If result > m, subract m
|
|
|
|
# load result into r15:r8
|
|
|
|
mov (+$pResult_offset)(%rsp), %rax
|
|
|
|
mov (+8*0)(%rax), %r8
|
|
|
|
mov (+8*1)(%rax), %r9
|
|
|
|
mov (+8*2)(%rax), %r10
|
|
|
|
mov (+8*3)(%rax), %r11
|
|
|
|
mov (+8*4)(%rax), %r12
|
|
|
|
mov (+8*5)(%rax), %r13
|
|
|
|
mov (+8*6)(%rax), %r14
|
|
|
|
mov (+8*7)(%rax), %r15
|
|
|
|
|
|
|
|
# subtract m
|
|
|
|
mov (+$pData_offset)(%rsp), %rbx
|
|
|
|
add \$$M, %rbx
|
|
|
|
|
|
|
|
sub (+8*0)(%rbx), %r8
|
|
|
|
sbb (+8*1)(%rbx), %r9
|
|
|
|
sbb (+8*2)(%rbx), %r10
|
|
|
|
sbb (+8*3)(%rbx), %r11
|
|
|
|
sbb (+8*4)(%rbx), %r12
|
|
|
|
sbb (+8*5)(%rbx), %r13
|
|
|
|
sbb (+8*6)(%rbx), %r14
|
|
|
|
sbb (+8*7)(%rbx), %r15
|
|
|
|
|
|
|
|
# if Carry is clear, replace result with difference
|
|
|
|
mov (+8*0)(%rax), %rsi
|
|
|
|
mov (+8*1)(%rax), %rdi
|
|
|
|
mov (+8*2)(%rax), %rcx
|
|
|
|
mov (+8*3)(%rax), %rdx
|
|
|
|
cmovnc %r8, %rsi
|
|
|
|
cmovnc %r9, %rdi
|
|
|
|
cmovnc %r10, %rcx
|
|
|
|
cmovnc %r11, %rdx
|
|
|
|
mov %rsi, (+8*0)(%rax)
|
|
|
|
mov %rdi, (+8*1)(%rax)
|
|
|
|
mov %rcx, (+8*2)(%rax)
|
|
|
|
mov %rdx, (+8*3)(%rax)
|
|
|
|
|
|
|
|
mov (+8*4)(%rax), %rsi
|
|
|
|
mov (+8*5)(%rax), %rdi
|
|
|
|
mov (+8*6)(%rax), %rcx
|
|
|
|
mov (+8*7)(%rax), %rdx
|
|
|
|
cmovnc %r12, %rsi
|
|
|
|
cmovnc %r13, %rdi
|
|
|
|
cmovnc %r14, %rcx
|
|
|
|
cmovnc %r15, %rdx
|
|
|
|
mov %rsi, (+8*4)(%rax)
|
|
|
|
mov %rdi, (+8*5)(%rax)
|
|
|
|
mov %rcx, (+8*6)(%rax)
|
|
|
|
mov %rdx, (+8*7)(%rax)
|
|
|
|
|
|
|
|
mov (+$rsp_offset)(%rsp), %rsi
|
|
|
|
mov 0(%rsi),%r15
|
|
|
|
mov 8(%rsi),%r14
|
|
|
|
mov 16(%rsi),%r13
|
|
|
|
mov 24(%rsi),%r12
|
|
|
|
mov 32(%rsi),%rbx
|
|
|
|
mov 40(%rsi),%rbp
|
|
|
|
lea 48(%rsi),%rsp
|
|
|
|
.Lepilogue:
|
|
|
|
ret
|
|
|
|
.size mod_exp_512, . - mod_exp_512
|
|
|
|
___
|
|
|
|
|
|
|
|
if ($win64) {
|
|
|
|
# EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
|
|
|
|
# CONTEXT *context,DISPATCHER_CONTEXT *disp)
|
|
|
|
my $rec="%rcx";
|
|
|
|
my $frame="%rdx";
|
|
|
|
my $context="%r8";
|
|
|
|
my $disp="%r9";
|
|
|
|
|
|
|
|
$code.=<<___;
|
|
|
|
.extern __imp_RtlVirtualUnwind
|
|
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.type mod_exp_512_se_handler,\@abi-omnipotent
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.align 16
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mod_exp_512_se_handler:
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push %rsi
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push %rdi
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push %rbx
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push %rbp
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push %r12
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push %r13
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push %r14
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push %r15
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pushfq
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sub \$64,%rsp
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mov 120($context),%rax # pull context->Rax
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mov 248($context),%rbx # pull context->Rip
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lea .Lbody(%rip),%r10
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cmp %r10,%rbx # context->Rip<prologue label
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jb .Lin_prologue
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mov 152($context),%rax # pull context->Rsp
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lea .Lepilogue(%rip),%r10
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cmp %r10,%rbx # context->Rip>=epilogue label
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jae .Lin_prologue
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mov $rsp_offset(%rax),%rax # pull saved Rsp
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mov 32(%rax),%rbx
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mov 40(%rax),%rbp
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mov 24(%rax),%r12
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mov 16(%rax),%r13
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mov 8(%rax),%r14
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mov 0(%rax),%r15
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lea 48(%rax),%rax
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mov %rbx,144($context) # restore context->Rbx
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mov %rbp,160($context) # restore context->Rbp
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mov %r12,216($context) # restore context->R12
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mov %r13,224($context) # restore context->R13
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mov %r14,232($context) # restore context->R14
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mov %r15,240($context) # restore context->R15
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.Lin_prologue:
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mov 8(%rax),%rdi
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mov 16(%rax),%rsi
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mov %rax,152($context) # restore context->Rsp
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mov %rsi,168($context) # restore context->Rsi
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mov %rdi,176($context) # restore context->Rdi
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mov 40($disp),%rdi # disp->ContextRecord
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mov $context,%rsi # context
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mov \$154,%ecx # sizeof(CONTEXT)
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.long 0xa548f3fc # cld; rep movsq
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mov $disp,%rsi
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xor %rcx,%rcx # arg1, UNW_FLAG_NHANDLER
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mov 8(%rsi),%rdx # arg2, disp->ImageBase
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mov 0(%rsi),%r8 # arg3, disp->ControlPc
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mov 16(%rsi),%r9 # arg4, disp->FunctionEntry
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mov 40(%rsi),%r10 # disp->ContextRecord
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lea 56(%rsi),%r11 # &disp->HandlerData
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lea 24(%rsi),%r12 # &disp->EstablisherFrame
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mov %r10,32(%rsp) # arg5
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mov %r11,40(%rsp) # arg6
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mov %r12,48(%rsp) # arg7
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mov %rcx,56(%rsp) # arg8, (NULL)
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call *__imp_RtlVirtualUnwind(%rip)
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mov \$1,%eax # ExceptionContinueSearch
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add \$64,%rsp
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popfq
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pop %r15
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pop %r14
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pop %r13
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pop %r12
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pop %rbp
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pop %rbx
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pop %rdi
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pop %rsi
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ret
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.size mod_exp_512_se_handler,.-mod_exp_512_se_handler
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.section .pdata
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.align 4
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.rva .LSEH_begin_mod_exp_512
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.rva .LSEH_end_mod_exp_512
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.rva .LSEH_info_mod_exp_512
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.section .xdata
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.align 8
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.LSEH_info_mod_exp_512:
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.byte 9,0,0,0
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.rva mod_exp_512_se_handler
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___
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}
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sub reg_part {
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my ($reg,$conv)=@_;
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if ($reg =~ /%r[0-9]+/) { $reg .= $conv; }
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elsif ($conv eq "b") { $reg =~ s/%[er]([^x]+)x?/%$1l/; }
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elsif ($conv eq "w") { $reg =~ s/%[er](.+)/%$1/; }
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elsif ($conv eq "d") { $reg =~ s/%[er](.+)/%e$1/; }
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return $reg;
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}
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$code =~ s/(%[a-z0-9]+)#([bwd])/reg_part($1,$2)/gem;
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$code =~ s/\`([^\`]*)\`/eval $1/gem;
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$code =~ s/(\(\+[^)]+\))/eval $1/gem;
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print $code;
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close STDOUT;
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