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#!/usr/bin/env perl
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# ====================================================================
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# Written by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
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# project. The module is, however, dual licensed under OpenSSL and
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# CRYPTOGAMS licenses depending on where you obtain it. For further
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# details see http://www.openssl.org/~appro/cryptogams/.
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# ====================================================================
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# January 2007.
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# Montgomery multiplication for ARMv4.
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#
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# Performance improvement naturally varies among CPU implementations
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# and compilers. The code was observed to provide +65-35% improvement
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# [depending on key length, less for longer keys] on ARM920T, and
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# +115-80% on Intel IXP425. This is compared to pre-bn_mul_mont code
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# base and compiler generated code with in-lined umull and even umlal
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# instructions. The latter means that this code didn't really have an
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# "advantage" of utilizing some "secret" instruction.
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#
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# The code is interoperable with Thumb ISA and is rather compact, less
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# than 1/2KB. Windows CE port would be trivial, as it's exclusively
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# about decorations, ABI and instruction syntax are identical.
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$num="r0"; # starts as num argument, but holds &tp[num-1]
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$ap="r1";
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$bp="r2"; $bi="r2"; $rp="r2";
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$np="r3";
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$tp="r4";
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$aj="r5";
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$nj="r6";
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$tj="r7";
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$n0="r8";
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########### # r9 is reserved by ELF as platform specific, e.g. TLS pointer
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$alo="r10"; # sl, gcc uses it to keep @GOT
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$ahi="r11"; # fp
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$nlo="r12"; # ip
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########### # r13 is stack pointer
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$nhi="r14"; # lr
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########### # r15 is program counter
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#### argument block layout relative to &tp[num-1], a.k.a. $num
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$_rp="$num,#12*4";
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# ap permanently resides in r1
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$_bp="$num,#13*4";
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# np permanently resides in r3
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$_n0="$num,#14*4";
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$_num="$num,#15*4"; $_bpend=$_num;
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$code=<<___;
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.text
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.global bn_mul_mont
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.type bn_mul_mont,%function
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.align 2
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bn_mul_mont:
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stmdb sp!,{r0,r2} @ sp points at argument block
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ldr $num,[sp,#3*4] @ load num
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cmp $num,#2
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movlt r0,#0
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addlt sp,sp,#2*4
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blt .Labrt
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stmdb sp!,{r4-r12,lr} @ save 10 registers
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mov $num,$num,lsl#2 @ rescale $num for byte count
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sub sp,sp,$num @ alloca(4*num)
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sub sp,sp,#4 @ +extra dword
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sub $num,$num,#4 @ "num=num-1"
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add $tp,$bp,$num @ &bp[num-1]
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add $num,sp,$num @ $num to point at &tp[num-1]
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ldr $n0,[$_n0] @ &n0
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ldr $bi,[$bp] @ bp[0]
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ldr $aj,[$ap],#4 @ ap[0],ap++
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ldr $nj,[$np],#4 @ np[0],np++
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ldr $n0,[$n0] @ *n0
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str $tp,[$_bpend] @ save &bp[num]
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umull $alo,$ahi,$aj,$bi @ ap[0]*bp[0]
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str $n0,[$_n0] @ save n0 value
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mul $n0,$alo,$n0 @ "tp[0]"*n0
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mov $nlo,#0
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umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"t[0]"
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mov $tp,sp
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.L1st:
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ldr $aj,[$ap],#4 @ ap[j],ap++
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mov $alo,$ahi
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mov $ahi,#0
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umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[0]
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ldr $nj,[$np],#4 @ np[j],np++
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mov $nhi,#0
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umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0
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adds $nlo,$nlo,$alo
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str $nlo,[$tp],#4 @ tp[j-1]=,tp++
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adc $nlo,$nhi,#0
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cmp $tp,$num
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bne .L1st
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adds $nlo,$nlo,$ahi
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mov $nhi,#0
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adc $nhi,$nhi,#0
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ldr $tp,[$_bp] @ restore bp
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str $nlo,[$num] @ tp[num-1]=
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ldr $n0,[$_n0] @ restore n0
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str $nhi,[$num,#4] @ tp[num]=
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.Louter:
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sub $tj,$num,sp @ "original" $num-1 value
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sub $ap,$ap,$tj @ "rewind" ap to &ap[1]
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sub $np,$np,$tj @ "rewind" np to &np[1]
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ldr $bi,[$tp,#4]! @ *(++bp)
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ldr $aj,[$ap,#-4] @ ap[0]
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ldr $nj,[$np,#-4] @ np[0]
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ldr $alo,[sp] @ tp[0]
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ldr $tj,[sp,#4] @ tp[1]
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mov $ahi,#0
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umlal $alo,$ahi,$aj,$bi @ ap[0]*bp[i]+tp[0]
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str $tp,[$_bp] @ save bp
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mul $n0,$alo,$n0
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mov $nlo,#0
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umlal $alo,$nlo,$nj,$n0 @ np[0]*n0+"tp[0]"
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mov $tp,sp
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.Linner:
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ldr $aj,[$ap],#4 @ ap[j],ap++
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adds $alo,$ahi,$tj @ +=tp[j]
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mov $ahi,#0
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umlal $alo,$ahi,$aj,$bi @ ap[j]*bp[i]
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ldr $nj,[$np],#4 @ np[j],np++
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mov $nhi,#0
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umlal $nlo,$nhi,$nj,$n0 @ np[j]*n0
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ldr $tj,[$tp,#8] @ tp[j+1]
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adc $ahi,$ahi,#0
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adds $nlo,$nlo,$alo
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str $nlo,[$tp],#4 @ tp[j-1]=,tp++
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adc $nlo,$nhi,#0
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cmp $tp,$num
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bne .Linner
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adds $nlo,$nlo,$ahi
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mov $nhi,#0
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adc $nhi,$nhi,#0
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adds $nlo,$nlo,$tj
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adc $nhi,$nhi,#0
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ldr $tp,[$_bp] @ restore bp
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ldr $tj,[$_bpend] @ restore &bp[num]
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str $nlo,[$num] @ tp[num-1]=
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ldr $n0,[$_n0] @ restore n0
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str $nhi,[$num,#4] @ tp[num]=
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cmp $tp,$tj
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bne .Louter
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ldr $rp,[$_rp] @ pull rp
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add $num,$num,#4 @ $num to point at &tp[num]
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sub $aj,$num,sp @ "original" num value
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mov $tp,sp @ "rewind" $tp
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mov $ap,$tp @ "borrow" $ap
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sub $np,$np,$aj @ "rewind" $np to &np[0]
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subs $tj,$tj,$tj @ "clear" carry flag
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.Lsub: ldr $tj,[$tp],#4
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ldr $nj,[$np],#4
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sbcs $tj,$tj,$nj @ tp[j]-np[j]
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str $tj,[$rp],#4 @ rp[j]=
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teq $tp,$num @ preserve carry
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bne .Lsub
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sbcs $nhi,$nhi,#0 @ upmost carry
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mov $tp,sp @ "rewind" $tp
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sub $rp,$rp,$aj @ "rewind" $rp
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and $ap,$tp,$nhi
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bic $np,$rp,$nhi
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orr $ap,$ap,$np @ ap=borrow?tp:rp
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.Lcopy: ldr $tj,[$ap],#4 @ copy or in-place refresh
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str sp,[$tp],#4 @ zap tp
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str $tj,[$rp],#4
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cmp $tp,$num
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bne .Lcopy
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add sp,$num,#4 @ skip over tp[num+1]
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ldmia sp!,{r4-r12,lr} @ restore registers
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add sp,sp,#2*4 @ skip over {r0,r2}
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mov r0,#1
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.Labrt: tst lr,#1
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moveq pc,lr @ be binary compatible with V4, yet
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bx lr @ interoperable with Thumb ISA:-)
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.size bn_mul_mont,.-bn_mul_mont
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.asciz "Montgomery multiplication for ARMv4, CRYPTOGAMS by <appro\@openssl.org>"
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.align 2
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___
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$code =~ s/\bbx\s+lr\b/.word\t0xe12fff1e/gm; # make it possible to compile with -march=armv4
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print $code;
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close STDOUT;
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