lea 1($i),$i # i++
cmp $num,$i
- jl .Louter
+ jb .Louter
xor $i,$i # i=0 and clear CF!
mov (%rsp),%rax # tp[0]
mov $N[1],-32(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
cmp $num,$j
- jl .L1st4x
+ jb .L1st4x
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
mov $N[1],-32(%rsp,$j,8) # tp[j-1]
mov %rdx,$N[0]
cmp $num,$j
- jl .Linner4x
+ jb .Linner4x
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
mov $N[1],(%rsp,$j,8) # store upmost overflow bit
cmp $num,$i
- jl .Louter4x
+ jb .Louter4x
___
{
my @ri=("%rax","%rdx",$m0,$m1);
my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
$code.=<<___;
+.extern bn_sqr8x_internal # see x86_64-mont5 module
+.extern bn_sqrx8x_internal # see x86_64-mont5 module
+
.type bn_sqr8x_mont,\@function,6
.align 32
bn_sqr8x_mont:
.Lsqr8x_enter:
-___
-$code.=<<___ if ($addx);
- and \$0x80100,%r11d
- cmp \$0x80100,%r11d
- je .Lsqrx8x_enter
-___
-$code.=<<___;
+ mov %rsp,%rax
push %rbx
push %rbp
push %r12
push %r14
push %r15
+ mov ${num}d,%r10d
shl \$3,${num}d # convert $num to bytes
- xor %r10,%r10
- mov %rsp,%r11 # put aside %rsp
- sub $num,%r10 # -$num
- mov ($n0),$n0 # *n0
- lea -72(%rsp,%r10,2),%rsp # alloca(frame+2*$num)
- and \$-1024,%rsp # minimize TLB usage
- ##############################################################
- # Stack layout
- #
- # +0 saved $num, used in reduction section
- # +8 &t[2*$num], used in reduction section
- # +32 saved $rptr
- # +40 saved $nptr
- # +48 saved *n0
- # +56 saved %rsp
- # +64 t[2*$num]
- #
- mov $rptr,32(%rsp) # save $rptr
- mov $nptr,40(%rsp)
- mov $n0, 48(%rsp)
- mov %r11, 56(%rsp) # save original %rsp
-.Lsqr8x_body:
+ shl \$3+2,%r10 # 4*$num
+ neg $num
+
##############################################################
- # Squaring part:
- #
- # a) multiply-n-add everything but a[i]*a[i];
- # b) shift result of a) by 1 to the left and accumulate
- # a[i]*a[i] products;
+ # ensure that stack frame doesn't alias with $aptr modulo
+ # 4096. this is done to allow memory disambiguation logic
+ # do its job.
#
- ##############################################################
- # a[1]a[0]
- # a[2]a[0]
- # a[3]a[0]
- # a[2]a[1]
- # a[4]a[0]
- # a[3]a[1]
- # a[5]a[0]
- # a[4]a[1]
- # a[3]a[2]
- # a[6]a[0]
- # a[5]a[1]
- # a[4]a[2]
- # a[7]a[0]
- # a[6]a[1]
- # a[5]a[2]
- # a[4]a[3]
- # a[7]a[1]
- # a[6]a[2]
- # a[5]a[3]
- # a[7]a[2]
- # a[6]a[3]
- # a[5]a[4]
- # a[7]a[3]
- # a[6]a[4]
- # a[7]a[4]
- # a[6]a[5]
- # a[7]a[5]
- # a[7]a[6]
- # a[1]a[0]
- # a[2]a[0]
- # a[3]a[0]
- # a[4]a[0]
- # a[5]a[0]
- # a[6]a[0]
- # a[7]a[0]
- # a[2]a[1]
- # a[3]a[1]
- # a[4]a[1]
- # a[5]a[1]
- # a[6]a[1]
- # a[7]a[1]
- # a[3]a[2]
- # a[4]a[2]
- # a[5]a[2]
- # a[6]a[2]
- # a[7]a[2]
- # a[4]a[3]
- # a[5]a[3]
- # a[6]a[3]
- # a[7]a[3]
- # a[5]a[4]
- # a[6]a[4]
- # a[7]a[4]
- # a[6]a[5]
- # a[7]a[5]
- # a[7]a[6]
- # a[0]a[0]
- # a[1]a[1]
- # a[2]a[2]
- # a[3]a[3]
- # a[4]a[4]
- # a[5]a[5]
- # a[6]a[6]
- # a[7]a[7]
-
- lea 32(%r10),$i # $i=-($num-32)
- lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
-
- mov $num,$j # $j=$num
-
- # comments apply to $num==8 case
- mov -32($aptr,$i),$a0 # a[0]
- lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
- mov -24($aptr,$i),%rax # a[1]
- lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
- mov -16($aptr,$i),$ai # a[2]
- mov %rax,$a1
-
- mul $a0 # a[1]*a[0]
- mov %rax,$A0[0] # a[1]*a[0]
- mov $ai,%rax # a[2]
- mov %rdx,$A0[1]
- mov $A0[0],-24($tptr,$i) # t[1]
-
- mul $a0 # a[2]*a[0]
- add %rax,$A0[1]
- mov $ai,%rax
- adc \$0,%rdx
- mov $A0[1],-16($tptr,$i) # t[2]
- mov %rdx,$A0[0]
-
- lea -16($i),$j # j=-16
-
-
- mov 8($aptr,$j),$ai # a[3]
- mul $a1 # a[2]*a[1]
- mov %rax,$A1[0] # a[2]*a[1]+t[3]
- mov $ai,%rax
- mov %rdx,$A1[1]
-
- lea 16($j),$j
- mul $a0 # a[3]*a[0]
- add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
- mov $ai,%rax
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- add $A1[0],$A0[0]
- adc \$0,$A0[1]
- mov $A0[0],-8($tptr,$j) # t[3]
- jmp .Lsqr4x_1st
-
-.align 32
-.Lsqr4x_1st:
- mov ($aptr,$j),$ai # a[4]
- mul $a1 # a[3]*a[1]
- add %rax,$A1[1] # a[3]*a[1]+t[4]
- mov $ai,%rax
- mov %rdx,$A1[0]
- adc \$0,$A1[0]
-
- mul $a0 # a[4]*a[0]
- add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
- mov $ai,%rax # a[3]
- mov 8($aptr,$j),$ai # a[5]
- mov %rdx,$A0[0]
- adc \$0,$A0[0]
- add $A1[1],$A0[1]
- adc \$0,$A0[0]
-
-
- mul $a1 # a[4]*a[3]
- add %rax,$A1[0] # a[4]*a[3]+t[5]
- mov $ai,%rax
- mov $A0[1],($tptr,$j) # t[4]
- mov %rdx,$A1[1]
- adc \$0,$A1[1]
-
- mul $a0 # a[5]*a[2]
- add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
- mov $ai,%rax
- mov 16($aptr,$j),$ai # a[6]
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- add $A1[0],$A0[0]
- adc \$0,$A0[1]
-
- mul $a1 # a[5]*a[3]
- add %rax,$A1[1] # a[5]*a[3]+t[6]
- mov $ai,%rax
- mov $A0[0],8($tptr,$j) # t[5]
- mov %rdx,$A1[0]
- adc \$0,$A1[0]
-
- mul $a0 # a[6]*a[2]
- add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
- mov $ai,%rax # a[3]
- mov 24($aptr,$j),$ai # a[7]
- mov %rdx,$A0[0]
- adc \$0,$A0[0]
- add $A1[1],$A0[1]
- adc \$0,$A0[0]
-
-
- mul $a1 # a[6]*a[5]
- add %rax,$A1[0] # a[6]*a[5]+t[7]
- mov $ai,%rax
- mov $A0[1],16($tptr,$j) # t[6]
- mov %rdx,$A1[1]
- adc \$0,$A1[1]
-
- mul $a0 # a[7]*a[4]
- add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
- mov $ai,%rax
- lea 32($j),$j
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- add $A1[0],$A0[0]
- adc \$0,$A0[1]
- mov $A0[0],-8($tptr,$j) # t[7]
-
- cmp \$0,$j
- jne .Lsqr4x_1st
-
- mul $a1 # a[7]*a[5]
- add %rax,$A1[1]
- lea 16($i),$i
- adc \$0,%rdx
- add $A0[1],$A1[1]
- adc \$0,%rdx
-
- mov $A1[1],($tptr) # t[8]
- mov %rdx,$A1[0]
- mov %rdx,8($tptr) # t[9]
- jmp .Lsqr4x_outer
-
-.align 32
-.Lsqr4x_outer: # comments apply to $num==6 case
- mov -32($aptr,$i),$a0 # a[0]
- lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
- mov -24($aptr,$i),%rax # a[1]
- lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
- mov -16($aptr,$i),$ai # a[2]
- mov %rax,$a1
-
- mov -24($tptr,$i),$A0[0] # t[1]
- mul $a0 # a[1]*a[0]
- add %rax,$A0[0] # a[1]*a[0]+t[1]
- mov $ai,%rax # a[2]
- adc \$0,%rdx
- mov $A0[0],-24($tptr,$i) # t[1]
- mov %rdx,$A0[1]
-
- mul $a0 # a[2]*a[0]
- add %rax,$A0[1]
- mov $ai,%rax
- adc \$0,%rdx
- add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
- mov %rdx,$A0[0]
- adc \$0,$A0[0]
- mov $A0[1],-16($tptr,$i) # t[2]
-
- lea -16($i),$j # j=-16
- xor $A1[0],$A1[0]
-
-
- mov 8($aptr,$j),$ai # a[3]
- mul $a1 # a[2]*a[1]
- add %rax,$A1[0] # a[2]*a[1]+t[3]
- mov $ai,%rax
- adc \$0,%rdx
- add 8($tptr,$j),$A1[0]
- mov %rdx,$A1[1]
- adc \$0,$A1[1]
-
- mul $a0 # a[3]*a[0]
- add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
- mov $ai,%rax
- adc \$0,%rdx
- add $A1[0],$A0[0]
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- mov $A0[0],8($tptr,$j) # t[3]
-
- lea 16($j),$j
- jmp .Lsqr4x_inner
-
-.align 32
-.Lsqr4x_inner:
- mov ($aptr,$j),$ai # a[4]
- mul $a1 # a[3]*a[1]
- add %rax,$A1[1] # a[3]*a[1]+t[4]
- mov $ai,%rax
- mov %rdx,$A1[0]
- adc \$0,$A1[0]
- add ($tptr,$j),$A1[1]
- adc \$0,$A1[0]
-
- mul $a0 # a[4]*a[0]
- add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
- mov $ai,%rax # a[3]
- mov 8($aptr,$j),$ai # a[5]
- mov %rdx,$A0[0]
- adc \$0,$A0[0]
- add $A1[1],$A0[1]
- adc \$0,$A0[0]
-
- mul $a1 # a[4]*a[3]
- add %rax,$A1[0] # a[4]*a[3]+t[5]
- mov $A0[1],($tptr,$j) # t[4]
- mov $ai,%rax
- mov %rdx,$A1[1]
- adc \$0,$A1[1]
- add 8($tptr,$j),$A1[0]
- lea 16($j),$j # j++
- adc \$0,$A1[1]
-
- mul $a0 # a[5]*a[2]
- add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
- mov $ai,%rax
- adc \$0,%rdx
- add $A1[0],$A0[0]
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
-
- cmp \$0,$j
- jne .Lsqr4x_inner
-
- mul $a1 # a[5]*a[3]
- add %rax,$A1[1]
- adc \$0,%rdx
- add $A0[1],$A1[1]
- adc \$0,%rdx
-
- mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
- mov %rdx,$A1[0]
- mov %rdx,8($tptr) # t[7], "preloaded t[3]" below
-
- add \$16,$i
- jnz .Lsqr4x_outer
-
- # comments apply to $num==4 case
- mov -32($aptr),$a0 # a[0]
- lea 64(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
- mov -24($aptr),%rax # a[1]
- lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
- mov -16($aptr),$ai # a[2]
- mov %rax,$a1
-
- mul $a0 # a[1]*a[0]
- add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
- mov $ai,%rax # a[2]
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
-
- mul $a0 # a[2]*a[0]
- add %rax,$A0[1]
- mov $ai,%rax
- mov $A0[0],-24($tptr) # t[1]
- mov %rdx,$A0[0]
- adc \$0,$A0[0]
- add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
- mov -8($aptr),$ai # a[3]
- adc \$0,$A0[0]
-
- mul $a1 # a[2]*a[1]
- add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
- mov $ai,%rax
- mov $A0[1],-16($tptr) # t[2]
- mov %rdx,$A1[1]
- adc \$0,$A1[1]
-
- mul $a0 # a[3]*a[0]
- add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
- mov $ai,%rax
- mov %rdx,$A0[1]
- adc \$0,$A0[1]
- add $A1[0],$A0[0]
- adc \$0,$A0[1]
- mov $A0[0],-8($tptr) # t[3]
-
- mul $a1 # a[3]*a[1]
- add %rax,$A1[1]
- mov -16($aptr),%rax # a[2]
- adc \$0,%rdx
- add $A0[1],$A1[1]
- adc \$0,%rdx
-
- mov $A1[1],($tptr) # t[4]
- mov %rdx,$A1[0]
- mov %rdx,8($tptr) # t[5]
-
- mul $ai # a[2]*a[3]
-___
-{
-my ($shift,$carry)=($a0,$a1);
-my @S=(@A1,$ai,$n0);
-$code.=<<___;
- add \$16,$i
- xor $shift,$shift
- sub $num,$i # $i=16-$num
- xor $carry,$carry
-
- add $A1[0],%rax # t[5]
- adc \$0,%rdx
- mov %rax,8($tptr) # t[5]
- mov %rdx,16($tptr) # t[6]
- mov $carry,24($tptr) # t[7]
-
- mov -16($aptr,$i),%rax # a[0]
- lea 64(%rsp),$tptr
- xor $A0[0],$A0[0] # t[0]
- mov 8($tptr),$A0[1] # t[1]
-
- lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[1] # | t[2*i]>>63
- mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[0]
- mov -8($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[0],($tptr)
- adc %rdx,$S[1]
-
- lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
- mov $S[1],8($tptr)
- sbb $carry,$carry # mov cf,$carry
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[3] # | t[2*i]>>63
- mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[2]
- mov 0($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[2],16($tptr)
- adc %rdx,$S[3]
- lea 16($i),$i
- mov $S[3],24($tptr)
- sbb $carry,$carry # mov cf,$carry
- lea 64($tptr),$tptr
- jmp .Lsqr4x_shift_n_add
+ lea -64(%rsp,$num,4),%r11
+ mov ($n0),$n0 # *n0
+ sub $aptr,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lsqr8x_sp_alt
+ sub %r11,%rsp # align with $aptr
+ lea -64(%rsp,$num,4),%rsp # alloca(frame+4*$num)
+ jmp .Lsqr8x_sp_done
.align 32
-.Lsqr4x_shift_n_add:
- lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[1] # | t[2*i]>>63
- mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[0]
- mov -8($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[0],-32($tptr)
- adc %rdx,$S[1]
-
- lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
- mov $S[1],-24($tptr)
- sbb $carry,$carry # mov cf,$carry
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[3] # | t[2*i]>>63
- mov 0($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov 8($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[2]
- mov 0($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[2],-16($tptr)
- adc %rdx,$S[3]
-
- lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
- mov $S[3],-8($tptr)
- sbb $carry,$carry # mov cf,$carry
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[1] # | t[2*i]>>63
- mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[0]
- mov 8($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[0],0($tptr)
- adc %rdx,$S[1]
-
- lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
- mov $S[1],8($tptr)
- sbb $carry,$carry # mov cf,$carry
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[3] # | t[2*i]>>63
- mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[2]
- mov 16($aptr,$i),%rax # a[i+1] # prefetch
- mov $S[2],16($tptr)
- adc %rdx,$S[3]
- mov $S[3],24($tptr)
- sbb $carry,$carry # mov cf,$carry
- lea 64($tptr),$tptr
- add \$32,$i
- jnz .Lsqr4x_shift_n_add
-
- lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[1] # | t[2*i]>>63
- mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
- mov $A0[1],$shift # shift=t[2*i+1]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
- adc %rax,$S[0]
- mov -8($aptr),%rax # a[i+1] # prefetch
- mov $S[0],-32($tptr)
- adc %rdx,$S[1]
-
- lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
- mov $S[1],-24($tptr)
- sbb $carry,$carry # mov cf,$carry
- shr \$63,$A0[0]
- lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
- shr \$63,$A0[1]
- or $A0[0],$S[3] # | t[2*i]>>63
- mul %rax # a[i]*a[i]
- neg $carry # mov $carry,cf
- adc %rax,$S[2]
- adc %rdx,$S[3]
- mov $S[2],-16($tptr)
- mov $S[3],-8($tptr)
-___
-}\f
-######################################################################
-# Montgomery reduction part, "word-by-word" algorithm.
-#
-# This new path is inspired by multiple submissions from Intel, by
-# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
-# Vinodh Gopal...
-{
-my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
-
-$code.=<<___;
- mov 40(%rsp),$nptr # pull $nptr
- xor %rax,%rax
- lea ($nptr,$num),%rdx # end of n[]
- lea 64(%rsp,$num,2),$tptr # end of t[] buffer
- mov %rdx,0(%rsp)
- mov $tptr,8(%rsp)
- mov %rax,($tptr) # clear top-most carry bit
- lea 64(%rsp,$num),$tptr # end of initial t[] window
+.Lsqr8x_sp_alt:
+ lea 4096-64(,$num,4),%r10 # 4096-frame-4*$num
+ lea -64(%rsp,$num,4),%rsp # alloca(frame+4*$num)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lsqr8x_sp_done:
+ and \$-64,%rsp
+ mov $num,%r10
neg $num
- jmp .L8x_reduction_loop
-
-.align 32
-.L8x_reduction_loop:
- lea ($tptr,$num),$tptr # start of current t[] window
- mov 8*0($tptr),$m0
- mov 8*1($tptr),%r9
- mov 8*2($tptr),%r10
- mov 8*3($tptr),%r11
- mov 8*4($tptr),%r12
- mov 8*5($tptr),%r13
- mov 8*6($tptr),%r14
- mov 8*7($tptr),%r15
- lea 8*8($tptr),$tptr
-
- mov $m0,%r8
- imulq 48(%rsp),$m0 # n0*a[0]
- mov 8*0($nptr),%rax # n[0]
- mov \$8,%ecx
- jmp .L8x_reduce
-
-.align 32
-.L8x_reduce:
- mulq $m0
- mov 8*1($nptr),%rax # n[1]
- neg %r8
- mov %rdx,%r8
- adc \$0,%r8
-
- mulq $m0
- add %rax,%r9
- mov 8*2($nptr),%rax
- adc \$0,%rdx
- add %r9,%r8
- mov $m0,64-8(%rsp,%rcx,8) # put aside n0*a[i]
- mov %rdx,%r9
- adc \$0,%r9
-
- mulq $m0
- add %rax,%r10
- mov 8*3($nptr),%rax
- adc \$0,%rdx
- add %r10,%r9
- mov 48(%rsp),$carry # pull n0, borrow $carry
- mov %rdx,%r10
- adc \$0,%r10
-
- mulq $m0
- add %rax,%r11
- mov 8*4($nptr),%rax
- adc \$0,%rdx
- imulq %r8,$carry # modulo-scheduled
- add %r11,%r10
- mov %rdx,%r11
- adc \$0,%r11
-
- mulq $m0
- add %rax,%r12
- mov 8*5($nptr),%rax
- adc \$0,%rdx
- add %r12,%r11
- mov %rdx,%r12
- adc \$0,%r12
- mulq $m0
- add %rax,%r13
- mov 8*6($nptr),%rax
- adc \$0,%rdx
- add %r13,%r12
- mov %rdx,%r13
- adc \$0,%r13
-
- mulq $m0
- add %rax,%r14
- mov 8*7($nptr),%rax
- adc \$0,%rdx
- add %r14,%r13
- mov %rdx,%r14
- adc \$0,%r14
+ lea 64(%rsp,$num,2),%r11 # copy of modulus
+ mov $n0, 32(%rsp)
+ mov %rax, 40(%rsp) # save original %rsp
+.Lsqr8x_body:
- mulq $m0
- mov $carry,$m0 # n0*a[i]
- add %rax,%r15
- mov 8*0($nptr),%rax # n[0]
- adc \$0,%rdx
- add %r15,%r14
- mov %rdx,%r15
- adc \$0,%r15
-
- dec %ecx
- jnz .L8x_reduce
-
- lea 8*8($nptr),$nptr
- xor %rax,%rax
- mov 8(%rsp),%rdx # pull end of t[]
- cmp 0(%rsp),$nptr # end of n[]?
- jae .L8x_no_tail
-
- add 8*0($tptr),%r8
- adc 8*1($tptr),%r9
- adc 8*2($tptr),%r10
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- sbb $carry,$carry # top carry
-
- mov 64+56(%rsp),$m0 # pull n0*a[0]
- mov \$8,%ecx
- mov 8*0($nptr),%rax
- jmp .L8x_tail
+ mov $num,$i
+ movq %r11, %xmm2 # save pointer to modulus copy
+ shr \$3+2,$i
+ mov OPENSSL_ia32cap_P+8(%rip),%eax
+ jmp .Lsqr8x_copy_n
.align 32
-.L8x_tail:
- mulq $m0
- add %rax,%r8
- mov 8*1($nptr),%rax
- mov %r8,($tptr) # save result
- mov %rdx,%r8
- adc \$0,%r8
-
- mulq $m0
- add %rax,%r9
- mov 8*2($nptr),%rax
- adc \$0,%rdx
- add %r9,%r8
- lea 8($tptr),$tptr # $tptr++
- mov %rdx,%r9
- adc \$0,%r9
+.Lsqr8x_copy_n:
+ movq 8*0($nptr),%xmm0
+ movq 8*1($nptr),%xmm1
+ movq 8*2($nptr),%xmm3
+ movq 8*3($nptr),%xmm4
+ lea 8*4($nptr),$nptr
+ movdqa %xmm0,16*0(%r11)
+ movdqa %xmm1,16*1(%r11)
+ movdqa %xmm3,16*2(%r11)
+ movdqa %xmm4,16*3(%r11)
+ lea 16*4(%r11),%r11
+ dec $i
+ jnz .Lsqr8x_copy_n
- mulq $m0
- add %rax,%r10
- mov 8*3($nptr),%rax
- adc \$0,%rdx
- add %r10,%r9
- mov %rdx,%r10
- adc \$0,%r10
-
- mulq $m0
- add %rax,%r11
- mov 8*4($nptr),%rax
- adc \$0,%rdx
- add %r11,%r10
- mov %rdx,%r11
- adc \$0,%r11
-
- mulq $m0
- add %rax,%r12
- mov 8*5($nptr),%rax
- adc \$0,%rdx
- add %r12,%r11
- mov %rdx,%r12
- adc \$0,%r12
-
- mulq $m0
- add %rax,%r13
- mov 8*6($nptr),%rax
- adc \$0,%rdx
- add %r13,%r12
- mov %rdx,%r13
- adc \$0,%r13
+ pxor %xmm0,%xmm0
+ movq $rptr,%xmm1 # save $rptr
+ movq %r10, %xmm3 # -$num
+___
+$code.=<<___ if ($addx);
+ and \$0x80100,%eax
+ cmp \$0x80100,%eax
+ jne .Lsqr8x_nox
- mulq $m0
- add %rax,%r14
- mov 8*7($nptr),%rax
- adc \$0,%rdx
- add %r14,%r13
- mov %rdx,%r14
- adc \$0,%r14
+ call bn_sqrx8x_internal # see x86_64-mont5 module
- mulq $m0
- mov 64-16(%rsp,%rcx,8),$m0 # pull n0*a[i]
- add %rax,%r15
- adc \$0,%rdx
- add %r15,%r14
- mov 8*0($nptr),%rax # pull n[0]
- mov %rdx,%r15
- adc \$0,%r15
-
- dec %ecx
- jnz .L8x_tail
-
- lea 8*8($nptr),$nptr
- mov 8(%rsp),%rdx # pull end of t[]
- cmp 0(%rsp),$nptr # end of n[]?
- jae .L8x_tail_done # break out of loop
-
- mov 64+56(%rsp),$m0 # pull n0*a[0]
- neg $carry
- mov 8*0($nptr),%rax # pull n[0]
- adc 8*0($tptr),%r8
- adc 8*1($tptr),%r9
- adc 8*2($tptr),%r10
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- sbb $carry,$carry # top carry
-
- mov \$8,%ecx
- jmp .L8x_tail
+ pxor %xmm0,%xmm0
+ lea 48(%rsp),%rax
+ lea 64(%rsp,$num,2),%rdx
+ shr \$3+2,$num
+ mov 40(%rsp),%rsi # restore %rsp
+ jmp .Lsqr8x_zero
.align 32
-.L8x_tail_done:
- add (%rdx),%r8 # can this overflow?
- xor %rax,%rax
-
- neg $carry
-.L8x_no_tail:
- adc 8*0($tptr),%r8
- adc 8*1($tptr),%r9
- adc 8*2($tptr),%r10
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- adc \$0,%rax # top-most carry
-
- mov 40(%rsp),$nptr # restore $nptr
-
- mov %r8,8*0($tptr) # store top 512 bits
- mov %r9,8*1($tptr)
- mov $nptr,$num # $num is %r9, can't be moved upwards
- mov %r10,8*2($tptr)
- sub 0(%rsp),$num # -$num
- mov %r11,8*3($tptr)
- mov %r12,8*4($tptr)
- mov %r13,8*5($tptr)
- mov %r14,8*6($tptr)
- mov %r15,8*7($tptr)
- lea 8*8($tptr),$tptr
- mov %rax,(%rdx) # store top-most carry
-
- cmp %rdx,$tptr # end of t[]?
- jb .L8x_reduction_loop
-
- neg $num # restore $num
+.Lsqr8x_nox:
___
-}\f
-##############################################################
-# Post-condition, 4x unrolled copy from bn_mul_mont
-#
-{
-my ($tptr,$nptr)=("%rbx",$aptr);
-my @ri=("%rax","%rdx","%r10","%r11");
$code.=<<___;
- mov 64(%rsp,$num),@ri[0] # tp[0]
- lea 64(%rsp,$num),$tptr # upper half of t[2*$num] holds result
- mov 40(%rsp),$nptr # restore $nptr
- shr \$5,$num # num/4
- mov 8($tptr),@ri[1] # t[1]
- xor $i,$i # i=0 and clear CF!
-
- mov 32(%rsp),$rptr # restore $rptr
- sub 0($nptr),@ri[0]
- mov 16($tptr),@ri[2] # t[2]
- mov 24($tptr),@ri[3] # t[3]
- sbb 8($nptr),@ri[1]
- lea -1($num),$j # j=num/4-1
- jmp .Lsqr4x_sub
-.align 32
-.Lsqr4x_sub:
- mov @ri[0],0($rptr) # rp[i]=tp[i]-np[i]
- mov @ri[1],8($rptr) # rp[i]=tp[i]-np[i]
- sbb 16($nptr,$i,8),@ri[2]
- mov 32($tptr,$i,8),@ri[0] # tp[i+1]
- mov 40($tptr,$i,8),@ri[1]
- sbb 24($nptr,$i,8),@ri[3]
- mov @ri[2],16($rptr) # rp[i]=tp[i]-np[i]
- mov @ri[3],24($rptr) # rp[i]=tp[i]-np[i]
- lea 32($rptr),$rptr
- sbb 32($nptr,$i,8),@ri[0]
- mov 48($tptr,$i,8),@ri[2]
- mov 56($tptr,$i,8),@ri[3]
- sbb 40($nptr,$i,8),@ri[1]
- lea 4($i),$i # i++
- dec $j # doesn't affect CF!
- jnz .Lsqr4x_sub
-
- mov @ri[0],0($rptr) # rp[i]=tp[i]-np[i]
- mov 32($tptr,$i,8),@ri[0] # load overflow bit
- sbb 16($nptr,$i,8),@ri[2]
- mov @ri[1],8($rptr) # rp[i]=tp[i]-np[i]
- sbb 24($nptr,$i,8),@ri[3]
- mov @ri[2],16($rptr) # rp[i]=tp[i]-np[i]
-
- sbb \$0,@ri[0] # handle upmost overflow bit
- mov @ri[3],24($rptr) # rp[i]=tp[i]-np[i]
- mov 32(%rsp),$rptr # restore $rptr
- xor $i,$i # i=0
- and @ri[0],$tptr
- not @ri[0]
- mov $rptr,$nptr
- and @ri[0],$nptr
- lea -1($num),$j
- or $nptr,$tptr # tp=borrow?tp:rp
+ call bn_sqr8x_internal # see x86_64-mont5 module
pxor %xmm0,%xmm0
- lea 64(%rsp,$num,8),$nptr
- movdqu ($tptr),%xmm1
- lea ($nptr,$num,8),$nptr
- movdqa %xmm0,64(%rsp) # zap lower half of temporary vector
- movdqa %xmm0,($nptr) # zap upper half of temporary vector
- movdqu %xmm1,($rptr)
- jmp .Lsqr4x_copy
+ lea 48(%rsp),%rax
+ lea 64(%rsp,$num,2),%rdx
+ shr \$3+2,$num
+ mov 40(%rsp),%rsi # restore %rsp
+ jmp .Lsqr8x_zero
+
.align 32
-.Lsqr4x_copy: # copy or in-place refresh
- movdqu 16($tptr,$i),%xmm2
- movdqu 32($tptr,$i),%xmm1
- movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
- movdqa %xmm0,96(%rsp,$i) # zap lower half of temporary vector
- movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
- movdqa %xmm0,32($nptr,$i) # zap upper half of temporary vector
- movdqu %xmm2,16($rptr,$i)
- movdqu %xmm1,32($rptr,$i)
- lea 32($i),$i
- dec $j
- jnz .Lsqr4x_copy
+.Lsqr8x_zero:
+ movdqa %xmm0,16*0(%rax) # wipe t
+ movdqa %xmm0,16*1(%rax)
+ movdqa %xmm0,16*2(%rax)
+ movdqa %xmm0,16*3(%rax)
+ lea 16*4(%rax),%rax
+ movdqa %xmm0,16*0(%rdx) # wipe n
+ movdqa %xmm0,16*1(%rdx)
+ movdqa %xmm0,16*2(%rdx)
+ movdqa %xmm0,16*3(%rdx)
+ lea 16*4(%rdx),%rdx
+ dec $num
+ jnz .Lsqr8x_zero
- movdqu 16($tptr,$i),%xmm2
- movdqa %xmm0,80(%rsp,$i) # zap lower half of temporary vector
- movdqa %xmm0,16($nptr,$i) # zap upper half of temporary vector
- movdqu %xmm2,16($rptr,$i)
-___
-}
-$code.=<<___;
- mov 56(%rsp),%rsi # restore %rsp
mov \$1,%rax
- mov 0(%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
.Lsqr8x_epilogue:
ret
.size bn_sqr8x_mont,.-bn_sqr8x_mont
.align 32
bn_mulx4x_mont:
.Lmulx4x_enter:
+ mov %rsp,%rax
push %rbx
push %rbp
push %r12
shl \$3,${num}d # convert $num to bytes
.byte 0x67
xor %r10,%r10
- mov %rsp,%r11 # put aside %rsp
sub $num,%r10 # -$num
mov ($n0),$n0 # *n0
lea -72(%rsp,%r10),%rsp # alloca(frame+$num+8)
# +16 end of b[num]
# +24 saved n0
# +32 saved rp
- # +40
+ # +40 saved %rsp
# +48 inner counter
- # +56 saved %rsp
+ # +56
# +64 tmp[num+1]
#
mov $num,0(%rsp) # save $num
sub \$1,$num
mov $n0, 24(%rsp) # save *n0
mov $rp, 32(%rsp) # save $rp
+ mov %rax,40(%rsp) # save original %rsp
mov $num,48(%rsp) # inner counter
- mov %r11,56(%rsp) # save original %rsp
jmp .Lmulx4x_body
.align 32
mulx 2*8($aptr),%r12,%rax # ...
adcx %r14,%r12
mulx 3*8($aptr),%r13,%r14
- .byte 0x66,0x66
+ .byte 0x67,0x67
mov $mi,%rdx
adcx %rax,%r13
adcx $zero,%r14 # cf=0
.align 32
.Lmulx4x_outer:
mov ($bptr),%rdx # b[i]
- lea 8($bptr),$bptr
+ lea 8($bptr),$bptr # b++
sub $num,$aptr # rewind $aptr
mov %r15,($tptr) # save top-most carry
- mov 64(%rsp),%r10
- lea 64(%rsp),$tptr
+ lea 64+4*8(%rsp),$tptr
sub $num,$nptr # rewind $nptr
- xor $zero,$zero # cf=0, of=0
- mov %rdx,$bi
- mulx 0*8($aptr),$mi,%rax # a[0]*b[i]
- adox %r10,$mi
- mov 1*8($tptr),%r10
- mulx 1*8($aptr),%r11,%r14 # a[1]*b[i]
- adcx %rax,%r11
- mov $bptr,8(%rsp) # off-load &b[i]
- mulx 2*8($aptr),%r12,%r13 # ...
- adox %r10,%r11
- adcx %r14,%r12
+ mulx 0*8($aptr),$mi,%r11 # a[0]*b[i]
+ xor %ebp,%ebp # xor $zero,$zero # cf=0, of=0
+ mov %rdx,$bi
+ mulx 1*8($aptr),%r14,%r12 # a[1]*b[i]
+ adox -4*8($tptr),$mi
+ adcx %r14,%r11
+ mulx 2*8($aptr),%r15,%r13 # ...
+ adox -3*8($tptr),%r11
+ adcx %r15,%r12
adox $zero,%r12
- .byte 0x66,0x66
adcx $zero,%r13
- mov 2*8($tptr),%r10
- mov $mi,$bptr # borrow $bptr
+ mov $bptr,8(%rsp) # off-load &b[i]
+ .byte 0x67
+ mov $mi,%r15
imulq 24(%rsp),$mi # "t[0]"*n0
- xor $zero,$zero # cf=0, of=0
+ xor %ebp,%ebp # xor $zero,$zero # cf=0, of=0
mulx 3*8($aptr),%rax,%r14
mov $mi,%rdx
- adox %r10,%r12
+ adox -2*8($tptr),%r12
adcx %rax,%r13
- adox 3*8($tptr),%r13
+ adox -1*8($tptr),%r13
adcx $zero,%r14
lea 4*8($aptr),$aptr
- lea 4*8($tptr),$tptr
adox $zero,%r14
mulx 0*8($nptr),%rax,%r10
- adcx %rax,$bptr # discarded
+ adcx %rax,%r15 # discarded
adox %r11,%r10
mulx 1*8($nptr),%rax,%r11
adcx %rax,%r10
mulx 3*8($nptr),%rax,%r15
mov $bi,%rdx
mov %r11,-3*8($tptr)
+ lea 4*8($nptr),$nptr
adcx %rax,%r12
adox $zero,%r15 # of=0
mov 48(%rsp),$bptr # counter value
mov %r12,-2*8($tptr)
- .byte 0x66
- lea 4*8($nptr),$nptr
- #jmp .Lmulx4x_inner
+ jmp .Lmulx4x_inner
.align 32
.Lmulx4x_inner:
- adcx $zero,%r15 # cf=0, modulo-scheduled
- adox 0*8($tptr),%r14
mulx 0*8($aptr),%r10,%rax # a[4]*b[i]
- adcx %r14,%r10
+ adcx $zero,%r15 # cf=0, modulo-scheduled
+ adox %r14,%r10
mulx 1*8($aptr),%r11,%r14 # a[5]*b[i]
+ adcx 0*8($tptr),%r10
adox %rax,%r11
mulx 2*8($aptr),%r12,%rax # ...
adcx 1*8($tptr),%r11
adc $zero,%r15 # modulo-scheduled
sub 0*8($tptr),$zero # pull top-most carry
adc %r15,%r14
+ mov -8($nptr),$mi
sbb %r15,%r15 # top-most carry
mov %r14,-1*8($tptr)
cmp 16(%rsp),$bptr
jne .Lmulx4x_outer
+ sub %r14,$mi # compare top-most words
+ sbb $mi,$mi
+ or $mi,%r15
+
neg $num
xor %rdx,%rdx
mov 32(%rsp),$rptr # restore rp
add \$32,$num
jnz .Lmulx4x_sub
- mov 56(%rsp),%rsi # restore %rsp
+ mov 40(%rsp),%rsi # restore %rsp
mov \$1,%rax
- mov (%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
.Lmulx4x_epilogue:
ret
.size bn_mulx4x_mont,.-bn_mulx4x_mont
___
-}\f{
-######################################################################
-# void bn_sqr8x_mont(
-my $rptr="%rdi"; # const BN_ULONG *rptr,
-my $aptr="%rsi"; # const BN_ULONG *aptr,
-my $bptr="%rdx"; # not used
-my $nptr="%rcx"; # const BN_ULONG *nptr,
-my $n0 ="%r8"; # const BN_ULONG *n0);
-my $num ="%r9"; # int num, has to be divisible by 8
-
-my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
-my @A0=("%r10","%r11");
-my @A1=("%r12","%r13");
-my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
-
-$code.=<<___;
-.type bn_sqrx8x_mont,\@function,6
-.align 32
-bn_sqrx8x_mont:
-.Lsqrx8x_enter:
- push %rbx
- push %rbp
- push %r12
- push %r13
- push %r14
- push %r15
-
- shl \$3,${num}d # convert $num to bytes
- .byte 0x67
- xor %r10,%r10
- mov %rsp,%r11 # put aside %rsp
- sub $num,%r10 # -$num
- mov ($n0),$n0 # *n0
- lea -64(%rsp,%r10,2),%rsp # alloca(frame+2*$num)
- and \$-1024,%rsp # minimize TLB usage
- ##############################################################
- # Stack layout
- #
- # +0 saved $num, used in reduction section
- # +8 &t[2*$num], used in reduction section
- # +16 intermediate carry bit
- # +24 top-most carry bit, used in reduction section
- # +32 saved *n0
- # +48 t[2*$num]
- #
- movq $rptr,%xmm1 # save $rptr
- movq $nptr,%xmm2 # save $nptr
- movq %r10, %xmm3 # -$num
- movq %r11, %xmm4 # save original %rsp
- mov $n0, 32(%rsp)
-___
-$code.=<<___ if ($win64);
- jmp .Lsqrx8x_body
-.align 32
-___
-$code.=<<___;
-.Lsqrx8x_body:
- ##################################################################
- # Squaring part:
- #
- # a) multiply-n-add everything but a[i]*a[i];
- # b) shift result of a) by 1 to the left and accumulate
- # a[i]*a[i] products;
- #
- ##################################################################
- # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
- # a[1]a[0]
- # a[2]a[0]
- # a[3]a[0]
- # a[2]a[1]
- # a[3]a[1]
- # a[3]a[2]
- #
- # a[4]a[0]
- # a[5]a[0]
- # a[6]a[0]
- # a[7]a[0]
- # a[4]a[1]
- # a[5]a[1]
- # a[6]a[1]
- # a[7]a[1]
- # a[4]a[2]
- # a[5]a[2]
- # a[6]a[2]
- # a[7]a[2]
- # a[4]a[3]
- # a[5]a[3]
- # a[6]a[3]
- # a[7]a[3]
- #
- # a[5]a[4]
- # a[6]a[4]
- # a[7]a[4]
- # a[6]a[5]
- # a[7]a[5]
- # a[7]a[6]
- # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
-___
-{
-my ($zero,$carry)=("%rbp","%rcx");
-my $aaptr=$zero;
-$code.=<<___;
- pxor %xmm0,%xmm0
- lea 48(%rsp),$tptr
- lea ($aptr,$num),$aaptr
- mov $num,(%rsp) # save $num
- mov $aaptr,8(%rsp) # save end of $aptr
- jmp .Lsqr8x_zero_start
-
-.align 32
-.byte 0x66,0x66,0x66,0x2e,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
-.Lsqrx8x_zero:
- .byte 0x3e
- movdqa %xmm0,0*8($tptr)
- movdqa %xmm0,2*8($tptr)
- movdqa %xmm0,4*8($tptr)
- movdqa %xmm0,6*8($tptr)
-.Lsqr8x_zero_start: # aligned at 32
- movdqa %xmm0,8*8($tptr)
- movdqa %xmm0,10*8($tptr)
- movdqa %xmm0,12*8($tptr)
- movdqa %xmm0,14*8($tptr)
- lea 16*8($tptr),$tptr
- sub \$64,$num
- jnz .Lsqrx8x_zero
-
- mov 0*8($aptr),%rdx # a[0], modulo-scheduled
- #xor %r9,%r9 # t[1], ex-$num, zero already
- xor %r10,%r10
- xor %r11,%r11
- xor %r12,%r12
- xor %r13,%r13
- xor %r14,%r14
- xor %r15,%r15
- lea 48(%rsp),$tptr
- xor $zero,$zero # cf=0, cf=0
- jmp .Lsqrx8x_outer_loop
-
-.align 32
-.Lsqrx8x_outer_loop:
- mulx 1*8($aptr),%r8,%rax # a[1]*a[0]
- adcx %r9,%r8 # a[1]*a[0]+=t[1]
- adox %rax,%r10
- mulx 2*8($aptr),%r9,%rax # a[2]*a[0]
- adcx %r10,%r9
- adox %rax,%r11
- .byte 0xc4,0xe2,0xab,0xf6,0x86,0x18,0x00,0x00,0x00 # mulx 3*8($aptr),%r10,%rax # ...
- adcx %r11,%r10
- adox %rax,%r12
- .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x20,0x00,0x00,0x00 # mulx 4*8($aptr),%r11,%rax
- adcx %r12,%r11
- adox %rax,%r13
- mulx 5*8($aptr),%r12,%rax
- adcx %r13,%r12
- adox %rax,%r14
- mulx 6*8($aptr),%r13,%rax
- adcx %r14,%r13
- adox %r15,%rax
- mulx 7*8($aptr),%r14,%r15
- mov 1*8($aptr),%rdx # a[1]
- adcx %rax,%r14
- adox $zero,%r15
- adc 8*8($tptr),%r15
- mov %r8,1*8($tptr) # t[1]
- mov %r9,2*8($tptr) # t[2]
- sbb $carry,$carry # mov %cf,$carry
- xor $zero,$zero # cf=0, of=0
-
-
- mulx 2*8($aptr),%r8,%rbx # a[2]*a[1]
- mulx 3*8($aptr),%r9,%rax # a[3]*a[1]
- adcx %r10,%r8
- adox %rbx,%r9
- mulx 4*8($aptr),%r10,%rbx # ...
- adcx %r11,%r9
- adox %rax,%r10
- .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x28,0x00,0x00,0x00 # mulx 5*8($aptr),%r11,%rax
- adcx %r12,%r10
- adox %rbx,%r11
- .byte 0xc4,0xe2,0x9b,0xf6,0x9e,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r12,%rbx
- adcx %r13,%r11
- adox %r14,%r12
- .byte 0xc4,0x62,0x93,0xf6,0xb6,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r13,%r14
- mov 2*8($aptr),%rdx # a[2]
- adcx %rax,%r12
- adox %rbx,%r13
- adcx %r15,%r13
- adox $zero,%r14 # of=0
- adcx $zero,%r14 # cf=0
-
- mov %r8,3*8($tptr) # t[3]
- mov %r9,4*8($tptr) # t[4]
-
- mulx 3*8($aptr),%r8,%rbx # a[3]*a[2]
- mulx 4*8($aptr),%r9,%rax # a[4]*a[2]
- adcx %r10,%r8
- adox %rbx,%r9
- mulx 5*8($aptr),%r10,%rbx # ...
- adcx %r11,%r9
- adox %rax,%r10
- .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r11,%rax
- adcx %r12,%r10
- adox %r13,%r11
- .byte 0xc4,0x62,0x9b,0xf6,0xae,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r12,%r13
- .byte 0x3e
- mov 3*8($aptr),%rdx # a[3]
- adcx %rbx,%r11
- adox %rax,%r12
- adcx %r14,%r12
- mov %r8,5*8($tptr) # t[5]
- mov %r9,6*8($tptr) # t[6]
- mulx 4*8($aptr),%r8,%rax # a[4]*a[3]
- adox $zero,%r13 # of=0
- adcx $zero,%r13 # cf=0
-
- mulx 5*8($aptr),%r9,%rbx # a[5]*a[3]
- adcx %r10,%r8
- adox %rax,%r9
- mulx 6*8($aptr),%r10,%rax # ...
- adcx %r11,%r9
- adox %r12,%r10
- mulx 7*8($aptr),%r11,%r12
- mov 4*8($aptr),%rdx # a[4]
- mov 5*8($aptr),%r14 # a[5]
- adcx %rbx,%r10
- adox %rax,%r11
- mov 6*8($aptr),%r15 # a[6]
- adcx %r13,%r11
- adox $zero,%r12 # of=0
- adcx $zero,%r12 # cf=0
-
- mov %r8,7*8($tptr) # t[7]
- mov %r9,8*8($tptr) # t[8]
-
- mulx %r14,%r9,%rax # a[5]*a[4]
- mov 7*8($aptr),%r8 # a[7]
- adcx %r10,%r9
- mulx %r15,%r10,%rbx # a[6]*a[4]
- adox %rax,%r10
- adcx %r11,%r10
- mulx %r8,%r11,%rax # a[7]*a[4]
- mov %r14,%rdx # a[5]
- adox %rbx,%r11
- adcx %r12,%r11
- #adox $zero,%rax # of=0
- adcx $zero,%rax # cf=0
-
- mulx %r15,%r14,%rbx # a[6]*a[5]
- mulx %r8,%r12,%r13 # a[7]*a[5]
- mov %r15,%rdx # a[6]
- lea 8*8($aptr),$aptr
- adcx %r14,%r11
- adox %rbx,%r12
- adcx %rax,%r12
- adox $zero,%r13
-
- .byte 0x67,0x67
- mulx %r8,%r8,%r14 # a[7]*a[6]
- adcx %r8,%r13
- adcx $zero,%r14
-
- cmp 8(%rsp),$aptr
- je .Lsqrx8x_outer_break
-
- neg $carry # mov $carry,%cf
- mov \$-8,%rcx
- mov $zero,%r15
- mov 8*8($tptr),%r8
- adcx 9*8($tptr),%r9 # +=t[9]
- adcx 10*8($tptr),%r10 # ...
- adcx 11*8($tptr),%r11
- adc 12*8($tptr),%r12
- adc 13*8($tptr),%r13
- adc 14*8($tptr),%r14
- adc 15*8($tptr),%r15
- lea ($aptr),$aaptr
- lea 2*8*8($tptr),$tptr
- sbb %rax,%rax # mov %cf,$carry
-
- mov -64($aptr),%rdx # a[0]
- mov %rax,16(%rsp) # offload $carry
- mov $tptr,24(%rsp)
-
- #lea 8*8($tptr),$tptr # see 2*8*8($tptr) above
- xor %eax,%eax # cf=0, of=0
- jmp .Lsqrx8x_loop
-
-.align 32
-.Lsqrx8x_loop:
- mov %r8,%rbx
- mulx 0*8($aaptr),%rax,%r8 # a[8]*a[i]
- adcx %rax,%rbx # +=t[8]
- adox %r9,%r8
-
- mulx 1*8($aaptr),%rax,%r9 # ...
- adcx %rax,%r8
- adox %r10,%r9
-
- mulx 2*8($aaptr),%rax,%r10
- adcx %rax,%r9
- adox %r11,%r10
-
- mulx 3*8($aaptr),%rax,%r11
- adcx %rax,%r10
- adox %r12,%r11
-
- .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 4*8($aaptr),%rax,%r12
- adcx %rax,%r11
- adox %r13,%r12
-
- mulx 5*8($aaptr),%rax,%r13
- adcx %rax,%r12
- adox %r14,%r13
-
- mulx 6*8($aaptr),%rax,%r14
- mov %rbx,($tptr,%rcx,8) # store t[8+i]
- mov \$0,%ebx
- adcx %rax,%r13
- adox %r15,%r14
-
- .byte 0xc4,0x62,0xfb,0xf6,0xbd,0x38,0x00,0x00,0x00 # mulx 7*8($aaptr),%rax,%r15
- mov 8($aptr,%rcx,8),%rdx # a[i]
- adcx %rax,%r14
- adox %rbx,%r15 # %rbx is 0, of=0
- adcx %rbx,%r15 # cf=0
-
- .byte 0x67
- inc %rcx # of=0
- jnz .Lsqrx8x_loop
-
- lea 8*8($aaptr),$aaptr
- mov \$-8,%rcx
- cmp 8(%rsp),$aaptr # done?
- je .Lsqrx8x_break
-
- sub 16(%rsp),%rbx # mov 16(%rsp),%cf
- .byte 0x66
- mov -64($aptr),%rdx
- adcx 0*8($tptr),%r8
- adcx 1*8($tptr),%r9
- adc 2*8($tptr),%r10
- adc 3*8($tptr),%r11
- adc 4*8($tptr),%r12
- adc 5*8($tptr),%r13
- adc 6*8($tptr),%r14
- adc 7*8($tptr),%r15
- lea 8*8($tptr),$tptr
- .byte 0x67
- sbb %rax,%rax # mov %cf,%rax
- xor %ebx,%ebx # cf=0, of=0
- mov %rax,16(%rsp) # offload carry
- jmp .Lsqrx8x_loop
-
-.align 32
-.Lsqrx8x_break:
- sub 16(%rsp),%r8 # consume last carry
- mov 24(%rsp),$carry # initial $tptr, borrow $carry
- mov 0*8($aptr),%rdx # a[8], modulo-scheduled
- xor %ebp,%ebp # xor $zero,$zero
- mov %r8,0*8($tptr)
- cmp $carry,$tptr # cf=0, of=0
- je .Lsqrx8x_outer_loop
-
- mov %r9,1*8($tptr)
- mov 1*8($carry),%r9
- mov %r10,2*8($tptr)
- mov 2*8($carry),%r10
- mov %r11,3*8($tptr)
- mov 3*8($carry),%r11
- mov %r12,4*8($tptr)
- mov 4*8($carry),%r12
- mov %r13,5*8($tptr)
- mov 5*8($carry),%r13
- mov %r14,6*8($tptr)
- mov 6*8($carry),%r14
- mov %r15,7*8($tptr)
- mov 7*8($carry),%r15
- mov $carry,$tptr
- jmp .Lsqrx8x_outer_loop
-
-.align 32
-.Lsqrx8x_outer_break:
- mov %r9,9*8($tptr) # t[9]
- movq %xmm3,%rcx # -$num
- mov %r10,10*8($tptr) # ...
- mov %r11,11*8($tptr)
- mov %r12,12*8($tptr)
- mov %r13,13*8($tptr)
- mov %r14,14*8($tptr)
-___
-}\f{
-my $i="%rcx";
-$code.=<<___;
- lea 48(%rsp),$tptr
- mov ($aptr,$i),%rdx # a[0]
-
- mov 8($tptr),$A0[1] # t[1]
- xor $A0[0],$A0[0] # t[0], of=0, cf=0
- mov (%rsp),$num # restore $num
- adox $A0[1],$A0[1]
- mov 16($tptr),$A1[0] # t[2] # prefetch
- mov 24($tptr),$A1[1] # t[3] # prefetch
- nop
- #jmp .Lsqrx4x_shift_n_add # happens to be aligned
-
-.align 32
-.Lsqrx4x_shift_n_add:
- mulx %rdx,%rax,%rbx
- adox $A1[0],$A1[0]
- adcx $A0[0],%rax
- .byte 0x48,0x8b,0x94,0x0e,0x08,0x00,0x00,0x00 # mov 8($aptr,$i),%rdx # a[i+1] # prefetch
- .byte 0x4c,0x8b,0x97,0x20,0x00,0x00,0x00 # mov 32($tptr),$A0[0] # t[2*i+4] # prefetch
- adox $A1[1],$A1[1]
- adcx $A0[1],%rbx
- mov 40($tptr),$A0[1] # t[2*i+4+1] # prefetch
- mov %rax,0($tptr)
- mov %rbx,8($tptr)
-
- mulx %rdx,%rax,%rbx
- adox $A0[0],$A0[0]
- adcx $A1[0],%rax
- mov 16($aptr,$i),%rdx # a[i+2] # prefetch
- mov 48($tptr),$A1[0] # t[2*i+6] # prefetch
- adox $A0[1],$A0[1]
- adcx $A1[1],%rbx
- mov 56($tptr),$A1[1] # t[2*i+6+1] # prefetch
- mov %rax,16($tptr)
- mov %rbx,24($tptr)
-
- mulx %rdx,%rax,%rbx
- adox $A1[0],$A1[0]
- adcx $A0[0],%rax
- mov 24($aptr,$i),%rdx # a[i+3] # prefetch
- lea 32($i),$i
- mov 64($tptr),$A0[0] # t[2*i+8] # prefetch
- adox $A1[1],$A1[1]
- adcx $A0[1],%rbx
- mov 72($tptr),$A0[1] # t[2*i+8+1] # prefetch
- mov %rax,32($tptr)
- mov %rbx,40($tptr)
-
- mulx %rdx,%rax,%rbx
- adox $A0[0],$A0[0]
- adcx $A1[0],%rax
- jrcxz .Lsqrx4x_shift_n_add_break
- .byte 0x48,0x8b,0x94,0x0e,0x00,0x00,0x00,0x00 # mov 0($aptr,$i),%rdx # a[i+4] # prefetch
- adox $A0[1],$A0[1]
- adcx $A1[1],%rbx
- mov 80($tptr),$A1[0] # t[2*i+10] # prefetch
- mov 88($tptr),$A1[1] # t[2*i+10+1] # prefetch
- mov %rax,48($tptr)
- mov %rbx,56($tptr)
- lea 64($tptr),$tptr
- nop
- jmp .Lsqrx4x_shift_n_add
-
-.align 32
-.Lsqrx4x_shift_n_add_break:
- adcx $A1[1],%rbx
- mov %rax,48($tptr)
- mov %rbx,56($tptr)
- lea 64($tptr),$tptr # end of t[] buffer
-___
-}\f
-######################################################################
-# Montgomery reduction part, "word-by-word" algorithm.
-#
-# This new path is inspired by multiple submissions from Intel, by
-# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
-# Vinodh Gopal...
-{
-my ($nptr,$carry,$m0)=("%rbp","%rsi","%rdx");
-
-$code.=<<___;
- movq %xmm2,$nptr
- xor %eax,%eax # initial top-most carry bit
- mov 32(%rsp),%rbx # n0
- mov 48(%rsp),%rdx # "%r8", 8*0($tptr)
- lea -64($nptr,$num),%rcx # end of n[]
- #lea 48(%rsp,$num,2),$tptr # end of t[] buffer
- mov %rcx, 0(%rsp) # save end of n[]
- mov $tptr,8(%rsp) # save end of t[]
-
- lea 48(%rsp),$tptr # initial t[] window
- jmp .Lsqrx8x_reduction_loop
-
-.align 32
-.Lsqrx8x_reduction_loop:
- mov 8*1($tptr),%r9
- mov 8*2($tptr),%r10
- mov 8*3($tptr),%r11
- mov 8*4($tptr),%r12
- mov %rdx,%r8
- imulq %rbx,%rdx # n0*a[i]
- mov 8*5($tptr),%r13
- mov 8*6($tptr),%r14
- mov 8*7($tptr),%r15
- mov %rax,24(%rsp) # store top-most carry bit
-
- lea 8*8($tptr),$tptr
- xor $carry,$carry # cf=0,of=0
- mov \$-8,%rcx
- jmp .Lsqrx8x_reduce
-
-.align 32
-.Lsqrx8x_reduce:
- mov %r8, %rbx
- mulx 8*0($nptr),%rax,%r8 # n[0]
- adcx %rbx,%rax # discarded
- adox %r9,%r8
-
- mulx 8*1($nptr),%rbx,%r9 # n[1]
- adcx %rbx,%r8
- adox %r10,%r9
-
- mulx 8*2($nptr),%rbx,%r10
- adcx %rbx,%r9
- adox %r11,%r10
-
- mulx 8*3($nptr),%rbx,%r11
- adcx %rbx,%r10
- adox %r12,%r11
-
- .byte 0xc4,0x62,0xe3,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rbx,%r12
- mov %rdx,%rax
- mov %r8,%rdx
- adcx %rbx,%r11
- adox %r13,%r12
-
- mulx 32(%rsp),%rbx,%rdx # %rdx discarded
- mov %rax,%rdx
- mov %rax,48+64(%rsp,%rcx,8) # put aside n0*a[i]
-
- mulx 8*5($nptr),%rax,%r13
- adcx %rax,%r12
- adox %r14,%r13
-
- mulx 8*6($nptr),%rax,%r14
- adcx %rax,%r13
- adox %r15,%r14
-
- mulx 8*7($nptr),%rax,%r15
- mov %rbx,%rdx
- adcx %rax,%r14
- adox $carry,%r15 # $carry is 0
- adcx $carry,%r15 # cf=0
-
- .byte 0x67
- inc %rcx # of=0
- jnz .Lsqrx8x_reduce
-
- .byte 0x66,0x67
- mov $carry,%rax # xor %rax,%rax
- cmp 0(%rsp),$nptr # end of n[]?
- jae .Lsqrx8x_no_tail
-
- mov 48(%rsp),%rdx # pull n0*a[0]
- add 8*0($tptr),%r8
- lea 8*8($nptr),$nptr
- mov \$-8,%rcx
- adc 8*1($tptr),%r9
- adc 8*2($tptr),%r10
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- lea 8*8($tptr),$tptr
- sbb %rax,%rax # top carry
-
- xor $carry,$carry # of=0, cf=0
- mov %rax,16(%rsp)
- jmp .Lsqrx8x_tail
-
-.align 32
-.Lsqrx8x_tail:
- mov %r8,%rbx
- mulx 8*0($nptr),%rax,%r8
- adcx %rax,%rbx
- adox %r9,%r8
-
- mulx 8*1($nptr),%rax,%r9
- adcx %rax,%r8
- adox %r10,%r9
-
- mulx 8*2($nptr),%rax,%r10
- adcx %rax,%r9
- adox %r11,%r10
-
- mulx 8*3($nptr),%rax,%r11
- adcx %rax,%r10
- adox %r12,%r11
-
- .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 8*4($nptr),%rax,%r12
- adcx %rax,%r11
- adox %r13,%r12
-
- mulx 8*5($nptr),%rax,%r13
- adcx %rax,%r12
- adox %r14,%r13
-
- mulx 8*6($nptr),%rax,%r14
- adcx %rax,%r13
- adox %r15,%r14
-
- mulx 8*7($nptr),%rax,%r15
- mov 48+72(%rsp,%rcx,8),%rdx # pull n0*a[i]
- adcx %rax,%r14
- .byte 0x67
- adox $carry,%r15
- mov %rbx,($tptr,%rcx,8) # save result
- mov %r8,%rbx
- adcx $carry,%r15 # cf=0
-
- inc %rcx # of=0
- jnz .Lsqrx8x_tail
-
- cmp 0(%rsp),$nptr # end of n[]?
- jae .Lsqrx8x_tail_done # break out of loop
-
- sub 16(%rsp),$carry # mov 16(%rsp),%cf
- mov 48(%rsp),%rdx # pull n0*a[0]
- lea 8*8($nptr),$nptr
- adc 8*0($tptr),%r8
- adc 8*1($tptr),%r9
- adc 8*2($tptr),%r10
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- lea 8*8($tptr),$tptr
- mov \$-8,%rcx
- sbb %rax,%rax
-
- xor $carry,$carry # of=0, cf=0
- mov %rax,16(%rsp)
- jmp .Lsqrx8x_tail
-
-.align 32
-.Lsqrx8x_tail_done:
- add 24(%rsp),%r8 # can this overflow?
- mov $carry,%rax # xor %rax,%rax
-
- sub 16(%rsp),$carry # mov 16(%rsp),%cf
-.Lsqrx8x_no_tail: # %cf is 0 if jumped here
- adc 8*0($tptr),%r8
- movq %xmm3,%rcx
- adc 8*1($tptr),%r9
- movq %xmm2,$nptr # restore $nptr
- adc 8*2($tptr),%r10
- lea 8*8($tptr),$carry # borrow $carry
- adc 8*3($tptr),%r11
- adc 8*4($tptr),%r12
- adc 8*5($tptr),%r13
- adc 8*6($tptr),%r14
- adc 8*7($tptr),%r15
- adc %rax,%rax # top-most carry
-
- mov 32(%rsp),%rbx # n0
- mov 8*8($tptr,%rcx),%rdx # modulo-scheduled "%r8"
-
- mov %r8,8*0($tptr) # store top 512 bits
- mov %r9,8*1($tptr)
- mov %r10,8*2($tptr)
- mov %r11,8*3($tptr)
- mov %r12,8*4($tptr)
- mov %r13,8*5($tptr)
- mov %r14,8*6($tptr)
- mov %r15,8*7($tptr)
-
- lea 8*8($tptr,%rcx),$tptr # start of current t[] window
- cmp 8(%rsp),$carry # end of t[]?
- jb .Lsqrx8x_reduction_loop
-
- mov %rcx,%rdx # -$num
- jmp .Lsqrx8x_post
-___
-}\f
-##############################################################
-# Post-condition, 8x unrolled
-#
-{
-my ($rptr,$nptr,$lptr,$i)=($aptr,"%rbp","%rbx","%rcx");
-my @ri=map("%r$_",(10..13));
-my @ni=map("%r$_",(14..15));
-$code.=<<___;
-.align 32
-.Lsqrx8x_post:
- neg %rdx # restore $num
- neg %rax # top-most carry as mask
- mov 0*8($nptr),%r8
- mov 1*8($nptr),%r9
- lea ($nptr,%rdx),$nptr # end of $nptr
- lea 48(%rsp,%rdx),$lptr # end of lower half of t[2*num]
- lea 48(%rsp,%rdx),$tptr
- .byte 0x67
- xor %rdx,%rdx
- movq %xmm1,$rptr # restore $rptr
-
- neg %r8
- jmp .Lsqrx8x_sub_entry
-
-.byte 0x66,0x66,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
-.Lsqrx8x_sub:
- mov 0*8($nptr,$i),%r8
- mov 1*8($nptr,$i),%r9
- not %r8
-.Lsqrx8x_sub_entry: # aligned at 32
- mov 2*8($nptr,$i),%r10
- not %r9
- and %rax,%r8
- mov 3*8($nptr,$i),%r11
- not %r10
- and %rax,%r9
- mov 4*8($nptr,$i),%r12
- not %r11
- and %rax,%r10
- mov 5*8($nptr,$i),%r13
- not %r12
- and %rax,%r11
- mov 6*8($nptr,$i),%r14
- not %r13
- and %rax,%r12
- mov 7*8($nptr,$i),%r15
- not %r14
- and %rax,%r13
- movdqa %xmm0,0*8($lptr,$i) # zap lower half
- not %r15
- and %rax,%r14
- movdqa %xmm0,2*8($lptr,$i)
- and %rax,%r15
-
- neg %edx # mov %edx,%cf
- movdqa %xmm0,4*8($lptr,$i)
- adc 0*8($tptr),%r8
- mov %r8,0*8($rptr) # result
- adc 1*8($tptr),%r9
- movdqa %xmm0,6*8($lptr,$i)
- adc 2*8($tptr),%r10
- mov %r9,1*8($rptr)
- adc 3*8($tptr),%r11
- movdqa %xmm0,0*8($tptr) # zap upper half
- adc 4*8($tptr),%r12
- mov %r10,2*8($rptr)
- adc 5*8($tptr),%r13
- movdqa %xmm0,2*8($tptr)
- adc 6*8($tptr),%r14
- mov %r11,3*8($rptr)
- adc 7*8($tptr),%r15
- sbb %edx,%edx # mov %cf,%edx
- movdqa %xmm0,4*8($tptr)
- movdqa %xmm0,6*8($tptr)
- lea 8*8($tptr),$tptr
- mov %r12,4*8($rptr)
- mov %r13,5*8($rptr)
- mov %r14,6*8($rptr)
- mov %r15,7*8($rptr)
- lea 8*8($rptr),$rptr
-
- add \$64,$i
- jnz .Lsqrx8x_sub
-___
-}
-$code.=<<___;
- movq %xmm4,%rsi # restore %rsp
- mov \$1,%rax
- mov 0(%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
-.Lsqrx8x_epilogue:
- ret
-.size bn_sqrx8x_mont,.-bn_sqrx8x_mont
-___
}}}
$code.=<<___;
.asciz "Montgomery Multiplication for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
cmp %r10,%rbx # context->Rip>=.Lsqr_epilogue
jae .Lcommon_seh_tail
- mov 56(%rax),%rax # pull saved stack pointer
- lea 48(%rax),%rax
+ mov 40(%rax),%rax # pull saved stack pointer
mov -8(%rax),%rbx
mov -16(%rax),%rbp
.rva .LSEH_begin_bn_mulx4x_mont
.rva .LSEH_end_bn_mulx4x_mont
.rva .LSEH_info_bn_mulx4x_mont
-
- .rva .LSEH_begin_bn_sqrx8x_mont
- .rva .LSEH_end_bn_sqrx8x_mont
- .rva .LSEH_info_bn_sqrx8x_mont
___
$code.=<<___;
.section .xdata
.byte 9,0,0,0
.rva sqr_handler
.rva .Lmulx4x_body,.Lmulx4x_epilogue # HandlerData[]
-.LSEH_info_bn_sqrx8x_mont:
- .byte 9,0,0,0
- .rva sqr_handler
- .rva .Lsqrx8x_body,.Lsqrx8x_epilogue # HandlerData[]
___
}
# is implemented, so that scatter-/gathering can be tuned without
# bn_exp.c modifications.
+# August 2013.
+#
+# Add MULX/AD*X code paths and additional interfaces to optimize for
+# branch prediction unit. For input lengths that are multiples of 8
+# the np argument is not just modulus value, but one interleaved
+# with 0. This is to optimize post-condition...
+
$flavour = shift;
$output = shift;
if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
.type bn_mul_mont_gather5,\@function,6
.align 64
bn_mul_mont_gather5:
- test \$3,${num}d
+ test \$7,${num}d
jnz .Lmul_enter
- cmp \$8,${num}d
- jb .Lmul_enter
___
$code.=<<___ if ($addx);
mov OPENSSL_ia32cap_P+8(%rip),%r11d
.align 16
.Lmul_enter:
mov ${num}d,${num}d
+ mov %rsp,%rax
mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
push %rbx
push %rbp
lea -0x28(%rsp),%rsp
movaps %xmm6,(%rsp)
movaps %xmm7,0x10(%rsp)
-.Lmul_alloca:
___
$code.=<<___;
- mov %rsp,%rax
lea 2($num),%r11
neg %r11
lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+2))
lea 1($i),$i # i++
cmp $num,$i
- jl .Louter
+ jb .Louter
xor $i,$i # i=0 and clear CF!
mov (%rsp),%rax # tp[0]
mov \$1,%rax
___
$code.=<<___ if ($win64);
- movaps (%rsi),%xmm6
- movaps 0x10(%rsi),%xmm7
- lea 0x28(%rsi),%rsi
+ movaps -88(%rsi),%xmm6
+ movaps -72(%rsi),%xmm7
___
$code.=<<___;
- mov (%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
.Lmul_epilogue:
ret
.size bn_mul_mont_gather5,.-bn_mul_mont_gather5
my @N=("%r13","%rdi");
$code.=<<___;
.type bn_mul4x_mont_gather5,\@function,6
-.align 16
+.align 32
bn_mul4x_mont_gather5:
.Lmul4x_enter:
___
je .Lmulx4x_enter
___
$code.=<<___;
- mov ${num}d,${num}d
- mov `($win64?56:8)`(%rsp),%r10d # load 7th argument
+ .byte 0x67
+ mov %rsp,%rax
push %rbx
push %rbp
push %r12
lea -0x28(%rsp),%rsp
movaps %xmm6,(%rsp)
movaps %xmm7,0x10(%rsp)
-.Lmul4x_alloca:
___
$code.=<<___;
- mov %rsp,%rax
- lea 4($num),%r11
- neg %r11
- lea (%rsp,%r11,8),%rsp # tp=alloca(8*(num+4))
- and \$-1024,%rsp # minimize TLB usage
+ .byte 0x67
+ mov ${num}d,%r10d
+ shl \$3,${num}d
+ shl \$3+2,%r10d # 4*$num
+ neg $num # -$num
- mov %rax,8(%rsp,$num,8) # tp[num+1]=%rsp
+ ##############################################################
+ # ensure that stack frame doesn't alias with $aptr+4*$num
+ # modulo 4096, which covers ret[num], am[num] and n[2*num]
+ # (see bn_exp.c). this is done to allow memory disambiguation
+ # logic do its magic. [excessive frame is allocated in order
+ # to allow bn_from_mont8x to clear it.]
+ #
+ lea -64(%rsp,$num,2),%r11
+ sub $ap,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lmul4xsp_alt
+ sub %r11,%rsp # align with $ap
+ lea -64(%rsp,$num,2),%rsp # alloca(128+num*8)
+ jmp .Lmul4xsp_done
+
+.align 32
+.Lmul4xsp_alt:
+ lea 4096-64(,$num,2),%r10
+ lea -64(%rsp,$num,2),%rsp # alloca(128+num*8)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lmul4xsp_done:
+ and \$-64,%rsp
+ neg $num
+
+ mov %rax,40(%rsp)
.Lmul4x_body:
- mov $rp,16(%rsp,$num,8) # tp[num+2]=$rp
- mov %rdx,%r12 # reassign $bp
+
+ call mul4x_internal
+
+ mov 40(%rsp),%rsi # restore %rsp
+ mov \$1,%rax
+___
+$code.=<<___ if ($win64);
+ movaps -88(%rsi),%xmm6
+ movaps -72(%rsi),%xmm7
+___
+$code.=<<___;
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
+.Lmul4x_epilogue:
+ ret
+.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
+
+.type mul4x_internal,\@abi-omnipotent
+.align 32
+mul4x_internal:
+ shl \$5,$num
+ mov `($win64?56:8)`(%rax),%r10d # load 7th argument
+ lea 256(%rdx,$num),%r13
+ shr \$5,$num # restore $num
___
$bp="%r12";
$STRIDE=2**5*8; # 5 is "window size"
$N=$STRIDE/4; # should match cache line size
+ $tp=$i;
$code.=<<___;
mov %r10,%r11
shr \$`log($N/8)/log(2)`,%r10
not %r10
lea .Lmagic_masks(%rip),%rax
and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
- lea 96($bp,%r11,8),$bp # pointer within 1st cache line
+ lea 96(%rdx,%r11,8),$bp # pointer within 1st cache line
movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
movq 8(%rax,%r10,8),%xmm5 # cache line contains element
+ add \$7,%r11
movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
movq 24(%rax,%r10,8),%xmm7
+ and \$7,%r11
movq `0*$STRIDE/4-96`($bp),%xmm0
+ lea $STRIDE($bp),$tp # borrow $tp
movq `1*$STRIDE/4-96`($bp),%xmm1
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bp),%xmm2
pand %xmm5,%xmm1
movq `3*$STRIDE/4-96`($bp),%xmm3
pand %xmm6,%xmm2
+ .byte 0x67
por %xmm1,%xmm0
+ movq `0*$STRIDE/4-96`($tp),%xmm1
+ .byte 0x67
pand %xmm7,%xmm3
+ .byte 0x67
por %xmm2,%xmm0
- lea $STRIDE($bp),$bp
+ movq `1*$STRIDE/4-96`($tp),%xmm2
+ .byte 0x67
+ pand %xmm4,%xmm1
+ .byte 0x67
por %xmm3,%xmm0
+ movq `2*$STRIDE/4-96`($tp),%xmm3
movq %xmm0,$m0 # m0=bp[0]
+ movq `3*$STRIDE/4-96`($tp),%xmm0
+ mov %r13,16+8(%rsp) # save end of b[num]
+ mov $rp, 56+8(%rsp) # save $rp
+
mov ($n0),$n0 # pull n0[0] value
mov ($ap),%rax
-
- xor $i,$i # i=0
- xor $j,$j # j=0
-
- movq `0*$STRIDE/4-96`($bp),%xmm0
- movq `1*$STRIDE/4-96`($bp),%xmm1
- pand %xmm4,%xmm0
- movq `2*$STRIDE/4-96`($bp),%xmm2
- pand %xmm5,%xmm1
+ lea ($ap,$num),$ap # end of a[num]
+ neg $num
mov $n0,$m1
mulq $m0 # ap[0]*bp[0]
mov %rax,$A[0]
mov ($np),%rax
- movq `3*$STRIDE/4-96`($bp),%xmm3
- pand %xmm6,%xmm2
- por %xmm1,%xmm0
- pand %xmm7,%xmm3
+ pand %xmm5,%xmm2
+ pand %xmm6,%xmm3
+ por %xmm2,%xmm1
imulq $A[0],$m1 # "tp[0]"*n0
+ ##############################################################
+ # $tp is chosen so that writing to top-most element of the
+ # vector occurs just "above" references to powers table,
+ # "above" modulo cache-line size, which effectively precludes
+ # possibility of memory disambiguation logic failure when
+ # accessing the table.
+ #
+ lea 64+8(%rsp,%r11,8),$tp
mov %rdx,$A[1]
- por %xmm2,%xmm0
- lea $STRIDE($bp),$bp
- por %xmm3,%xmm0
+ pand %xmm7,%xmm0
+ por %xmm3,%xmm1
+ lea 2*$STRIDE($bp),$bp
+ por %xmm1,%xmm0
mulq $m1 # np[0]*m1
add %rax,$A[0] # discarded
- mov 8($ap),%rax
+ mov 8($ap,$num),%rax
adc \$0,%rdx
mov %rdx,$N[1]
mulq $m0
add %rax,$A[1]
- mov 8($np),%rax
+ mov 16*1($np),%rax # interleaved with 0, therefore 16*n
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1
add %rax,$N[1]
- mov 16($ap),%rax
+ mov 16($ap,$num),%rax
adc \$0,%rdx
add $A[1],$N[1]
- lea 4($j),$j # j++
+ lea 4*8($num),$j # j=4
+ lea 16*4($np),$np
adc \$0,%rdx
- mov $N[1],(%rsp)
+ mov $N[1],($tp)
mov %rdx,$N[0]
jmp .L1st4x
-.align 16
+
+.align 32
.L1st4x:
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
- mov -16($np,$j,8),%rax
+ mov -16*2($np),%rax
+ lea 32($tp),$tp
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov -8($ap,$j,8),%rax
+ mov -8($ap,$j),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
- mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-24($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
- mov -8($np,$j,8),%rax
+ mov -16*1($np),%rax
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov ($ap,$j,8),%rax
+ mov ($ap,$j),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
- mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-16($tp) # tp[j-1]
mov %rdx,$N[0]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
- mov ($np,$j,8),%rax
+ mov 16*0($np),%rax
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov 8($ap,$j,8),%rax
+ mov 8($ap,$j),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
- mov $N[0],-8(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-8($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
- mov 8($np,$j,8),%rax
+ mov 16*1($np),%rax
adc \$0,%rdx
- lea 4($j),$j # j++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov -16($ap,$j,8),%rax
+ mov 16($ap,$j),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
+ lea 16*4($np),$np
adc \$0,%rdx
- mov $N[1],-32(%rsp,$j,8) # tp[j-1]
+ mov $N[1],($tp) # tp[j-1]
mov %rdx,$N[0]
- cmp $num,$j
- jl .L1st4x
+
+ add \$32,$j # j+=4
+ jnz .L1st4x
mulq $m0 # ap[j]*bp[0]
add %rax,$A[0]
- mov -16($np,$j,8),%rax
+ mov -16*2($np),%rax
+ lea 32($tp),$tp
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov -8($ap,$j,8),%rax
+ mov -8($ap),%rax
adc \$0,%rdx
add $A[0],$N[0] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
- mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-24($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[0]
add %rax,$A[1]
- mov -8($np,$j,8),%rax
+ mov -16*1($np),%rax
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov ($ap),%rax # ap[0]
+ mov ($ap,$num),%rax # ap[0]
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[0]
adc \$0,%rdx
- mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-16($tp) # tp[j-1]
mov %rdx,$N[0]
movq %xmm0,$m0 # bp[1]
+ lea ($np,$num,2),$np # rewind $np
xor $N[1],$N[1]
add $A[0],$N[0]
adc \$0,$N[1]
- mov $N[0],-8(%rsp,$j,8)
- mov $N[1],(%rsp,$j,8) # store upmost overflow bit
+ mov $N[0],-8($tp)
- lea 1($i),$i # i++
-.align 4
-.Louter4x:
- xor $j,$j # j=0
- movq `0*$STRIDE/4-96`($bp),%xmm0
- movq `1*$STRIDE/4-96`($bp),%xmm1
- pand %xmm4,%xmm0
- movq `2*$STRIDE/4-96`($bp),%xmm2
- pand %xmm5,%xmm1
+ jmp .Louter4x
- mov (%rsp),$A[0]
+.align 32
+.Louter4x:
+ mov ($tp,$num),$A[0]
mov $n0,$m1
mulq $m0 # ap[0]*bp[i]
add %rax,$A[0] # ap[0]*bp[i]+tp[0]
mov ($np),%rax
adc \$0,%rdx
+ movq `0*$STRIDE/4-96`($bp),%xmm0
+ movq `1*$STRIDE/4-96`($bp),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bp),%xmm2
+ pand %xmm5,%xmm1
movq `3*$STRIDE/4-96`($bp),%xmm3
- pand %xmm6,%xmm2
- por %xmm1,%xmm0
- pand %xmm7,%xmm3
imulq $A[0],$m1 # tp[0]*n0
+ .byte 0x67
mov %rdx,$A[1]
+ mov $N[1],($tp) # store upmost overflow bit
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ pand %xmm7,%xmm3
por %xmm2,%xmm0
+ lea ($tp,$num),$tp # rewind $tp
lea $STRIDE($bp),$bp
por %xmm3,%xmm0
mulq $m1 # np[0]*m1
add %rax,$A[0] # "$N[0]", discarded
- mov 8($ap),%rax
+ mov 8($ap,$num),%rax
adc \$0,%rdx
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
- mov 8($np),%rax
+ mov 16*1($np),%rax # interleaved with 0, therefore 16*n
adc \$0,%rdx
- add 8(%rsp),$A[1] # +tp[1]
+ add 8($tp),$A[1] # +tp[1]
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov 16($ap),%rax
+ mov 16($ap,$num),%rax
adc \$0,%rdx
add $A[1],$N[1] # np[j]*m1+ap[j]*bp[i]+tp[j]
- lea 4($j),$j # j+=2
+ lea 4*8($num),$j # j=4
+ lea 16*4($np),$np
adc \$0,%rdx
mov %rdx,$N[0]
jmp .Linner4x
-.align 16
+
+.align 32
.Linner4x:
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
- mov -16($np,$j,8),%rax
+ mov -16*2($np),%rax
adc \$0,%rdx
- add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
+ lea 32($tp),$tp
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov -8($ap,$j,8),%rax
+ mov -8($ap,$j),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
- mov $N[1],-32(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-32($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
- mov -8($np,$j,8),%rax
+ mov -16*1($np),%rax
adc \$0,%rdx
- add -8(%rsp,$j,8),$A[1]
+ add -8($tp),$A[1]
adc \$0,%rdx
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov ($ap,$j,8),%rax
+ mov ($ap,$j),%rax
adc \$0,%rdx
add $A[1],$N[1]
adc \$0,%rdx
- mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-24($tp) # tp[j-1]
mov %rdx,$N[0]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
- mov ($np,$j,8),%rax
+ mov 16*0($np),%rax
adc \$0,%rdx
- add (%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ add ($tp),$A[0] # ap[j]*bp[i]+tp[j]
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov 8($ap,$j,8),%rax
+ mov 8($ap,$j),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
- mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-16($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
- mov 8($np,$j,8),%rax
+ mov 16*1($np),%rax
adc \$0,%rdx
- add 8(%rsp,$j,8),$A[1]
+ add 8($tp),$A[1]
adc \$0,%rdx
- lea 4($j),$j # j++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov -16($ap,$j,8),%rax
+ mov 16($ap,$j),%rax
adc \$0,%rdx
add $A[1],$N[1]
+ lea 16*4($np),$np
adc \$0,%rdx
- mov $N[0],-40(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-8($tp) # tp[j-1]
mov %rdx,$N[0]
- cmp $num,$j
- jl .Linner4x
+
+ add \$32,$j # j+=4
+ jnz .Linner4x
mulq $m0 # ap[j]*bp[i]
add %rax,$A[0]
- mov -16($np,$j,8),%rax
+ mov -16*2($np),%rax
adc \$0,%rdx
- add -16(%rsp,$j,8),$A[0] # ap[j]*bp[i]+tp[j]
+ add 16($tp),$A[0] # ap[j]*bp[i]+tp[j]
+ lea 32($tp),$tp
adc \$0,%rdx
mov %rdx,$A[1]
mulq $m1 # np[j]*m1
add %rax,$N[0]
- mov -8($ap,$j,8),%rax
+ mov -8($ap),%rax
adc \$0,%rdx
add $A[0],$N[0]
adc \$0,%rdx
- mov $N[1],-32(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-32($tp) # tp[j-1]
mov %rdx,$N[1]
mulq $m0 # ap[j]*bp[i]
add %rax,$A[1]
- mov -8($np,$j,8),%rax
+ mov $m1,%rax
+ mov -16*1($np),$m1
adc \$0,%rdx
- add -8(%rsp,$j,8),$A[1]
+ add -8($tp),$A[1]
adc \$0,%rdx
- lea 1($i),$i # i++
mov %rdx,$A[0]
mulq $m1 # np[j]*m1
add %rax,$N[1]
- mov ($ap),%rax # ap[0]
+ mov ($ap,$num),%rax # ap[0]
adc \$0,%rdx
add $A[1],$N[1]
adc \$0,%rdx
- mov $N[0],-24(%rsp,$j,8) # tp[j-1]
+ mov $N[0],-24($tp) # tp[j-1]
mov %rdx,$N[0]
movq %xmm0,$m0 # bp[i+1]
- mov $N[1],-16(%rsp,$j,8) # tp[j-1]
+ mov $N[1],-16($tp) # tp[j-1]
+ lea ($np,$num,2),$np # rewind $np
xor $N[1],$N[1]
add $A[0],$N[0]
adc \$0,$N[1]
- add (%rsp,$num,8),$N[0] # pull upmost overflow bit
- adc \$0,$N[1]
- mov $N[0],-8(%rsp,$j,8)
- mov $N[1],(%rsp,$j,8) # store upmost overflow bit
+ add ($tp),$N[0] # pull upmost overflow bit
+ adc \$0,$N[1] # upmost overflow bit
+ mov $N[0],-8($tp)
- cmp $num,$i
- jl .Louter4x
+ cmp 16+8(%rsp),$bp
+ jb .Louter4x
___
-{
-my @ri=("%rax","%rdx",$m0,$m1);
+if (1) {
$code.=<<___;
- mov 16(%rsp,$num,8),$rp # restore $rp
- mov 0(%rsp),@ri[0] # tp[0]
- pxor %xmm0,%xmm0
- mov 8(%rsp),@ri[1] # tp[1]
- shr \$2,$num # num/=4
- lea (%rsp),$ap # borrow ap for tp
- xor $i,$i # i=0 and clear CF!
-
- sub 0($np),@ri[0]
- mov 16($ap),@ri[2] # tp[2]
- mov 24($ap),@ri[3] # tp[3]
- sbb 8($np),@ri[1]
- lea -1($num),$j # j=num/4-1
+ sub $N[0],$m1 # compare top-most words
+ adc $j,$j # $j is zero
+ or $j,$N[1]
+ xor \$1,$N[1]
+ lea ($tp,$num),%rbx # tptr in .sqr4x_sub
+ lea ($np,$N[1],8),%rbp # nptr in .sqr4x_sub
+ mov %r9,%rcx
+ sar \$3+2,%rcx # cf=0
+ mov 56+8(%rsp),%rdi # rptr in .sqr4x_sub
+ jmp .Lsqr4x_sub
+___
+} else {
+my @ri=("%rax",$bp,$m0,$m1);
+my $rp="%rdx";
+$code.=<<___
+ xor \$1,$N[1]
+ lea ($tp,$num),$tp # rewind $tp
+ sar \$5,$num # cf=0
+ lea ($np,$N[1],8),$np
+ mov 56+8(%rsp),$rp # restore $rp
jmp .Lsub4x
-.align 16
+
+.align 32
.Lsub4x:
- mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
- mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
- sbb 16($np,$i,8),@ri[2]
- mov 32($ap,$i,8),@ri[0] # tp[i+1]
- mov 40($ap,$i,8),@ri[1]
- sbb 24($np,$i,8),@ri[3]
- mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
- mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
- sbb 32($np,$i,8),@ri[0]
- mov 48($ap,$i,8),@ri[2]
- mov 56($ap,$i,8),@ri[3]
- sbb 40($np,$i,8),@ri[1]
- lea 4($i),$i # i++
- dec $j # doesnn't affect CF!
+ .byte 0x66
+ mov 8*0($tp),@ri[0]
+ mov 8*1($tp),@ri[1]
+ .byte 0x66
+ sbb 16*0($np),@ri[0]
+ mov 8*2($tp),@ri[2]
+ sbb 16*1($np),@ri[1]
+ mov 3*8($tp),@ri[3]
+ lea 4*8($tp),$tp
+ sbb 16*2($np),@ri[2]
+ mov @ri[0],8*0($rp)
+ sbb 16*3($np),@ri[3]
+ lea 16*4($np),$np
+ mov @ri[1],8*1($rp)
+ mov @ri[2],8*2($rp)
+ mov @ri[3],8*3($rp)
+ lea 8*4($rp),$rp
+
+ inc $num
jnz .Lsub4x
- mov @ri[0],0($rp,$i,8) # rp[i]=tp[i]-np[i]
- mov 32($ap,$i,8),@ri[0] # load overflow bit
- sbb 16($np,$i,8),@ri[2]
- mov @ri[1],8($rp,$i,8) # rp[i]=tp[i]-np[i]
- sbb 24($np,$i,8),@ri[3]
- mov @ri[2],16($rp,$i,8) # rp[i]=tp[i]-np[i]
-
- sbb \$0,@ri[0] # handle upmost overflow bit
- mov @ri[3],24($rp,$i,8) # rp[i]=tp[i]-np[i]
- xor $i,$i # i=0
- and @ri[0],$ap
- not @ri[0]
- mov $rp,$np
- and @ri[0],$np
- lea -1($num),$j
- or $np,$ap # ap=borrow?tp:rp
-
- movdqu ($ap),%xmm1
- movdqa %xmm0,(%rsp)
- movdqu %xmm1,($rp)
- jmp .Lcopy4x
-.align 16
-.Lcopy4x: # copy or in-place refresh
- movdqu 16($ap,$i),%xmm2
- movdqu 32($ap,$i),%xmm1
- movdqa %xmm0,16(%rsp,$i)
- movdqu %xmm2,16($rp,$i)
- movdqa %xmm0,32(%rsp,$i)
- movdqu %xmm1,32($rp,$i)
- lea 32($i),$i
- dec $j
- jnz .Lcopy4x
-
- shl \$2,$num
- movdqu 16($ap,$i),%xmm2
- movdqa %xmm0,16(%rsp,$i)
- movdqu %xmm2,16($rp,$i)
+ ret
___
}
$code.=<<___;
- mov 8(%rsp,$num,8),%rsi # restore %rsp
- mov \$1,%rax
-___
-$code.=<<___ if ($win64);
- movaps (%rsi),%xmm6
- movaps 0x10(%rsi),%xmm7
- lea 0x28(%rsi),%rsi
-___
-$code.=<<___;
- mov (%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
-.Lmul4x_epilogue:
- ret
-.size bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
+.size mul4x_internal,.-mul4x_internal
___
}}}
-if ($addx) {{{
-my $bp="%rdx"; # original value
+\f{{{
+######################################################################
+# void bn_power5(
+my $rptr="%rdi"; # BN_ULONG *rptr,
+my $aptr="%rsi"; # const BN_ULONG *aptr,
+my $bptr="%rdx"; # const void *table,
+my $nptr="%rcx"; # const BN_ULONG *nptr,
+my $n0 ="%r8"; # const BN_ULONG *n0);
+my $num ="%r9"; # int num, has to be divisible by 8
+ # int pwr
+
+my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
+my @A0=("%r10","%r11");
+my @A1=("%r12","%r13");
+my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
$code.=<<___;
-.type bn_mulx4x_mont_gather5,\@function,6
+.globl bn_power5
+.type bn_power5,\@function,6
.align 32
-bn_mulx4x_mont_gather5:
-.Lmulx4x_enter:
+bn_power5:
+___
+$code.=<<___ if ($addx);
+ mov OPENSSL_ia32cap_P+8(%rip),%r11d
+ and \$0x80100,%r11d
+ cmp \$0x80100,%r11d
+ je .Lpowerx5_enter
+___
+$code.=<<___;
mov %rsp,%rax
push %rbx
push %rbp
movaps %xmm7,0x10(%rsp)
___
$code.=<<___;
+ mov ${num}d,%r10d
shl \$3,${num}d # convert $num to bytes
- xor %r10,%r10
- mov %rsp,%r11 # put aside %rsp
- sub $num,%r10 # -$num
+ shl \$3+2,%r10d # 4*$num
+ neg $num
mov ($n0),$n0 # *n0
- lea -72(%rsp,%r10),%rsp # alloca(frame+$num+8)
- and \$-128,%rsp
+
+ ##############################################################
+ # ensure that stack frame doesn't alias with $aptr+4*$num
+ # modulo 4096, which covers ret[num], am[num] and n[2*num]
+ # (see bn_exp.c). this is done to allow memory disambiguation
+ # logic do its magic.
+ #
+ lea -64(%rsp,$num,2),%r11
+ sub $aptr,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lpwr_sp_alt
+ sub %r11,%rsp # align with $aptr
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ jmp .Lpwr_sp_done
+
+.align 32
+.Lpwr_sp_alt:
+ lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lpwr_sp_done:
+ and \$-64,%rsp
+ mov $num,%r10
+ neg $num
+
##############################################################
# Stack layout
- # +0 num
- # +8 off-loaded &b[i]
- # +16 end of b[num]
- # +24 saved n0
- # +32 saved rp
- # +40
- # +48 inner counter
- # +56 saved %rsp
- # +64 tmp[num+1]
#
- mov $num,0(%rsp) # save $num
- shl \$5,$num
- lea 256($bp,$num),%r10
- shr \$5+5,$num
- mov %r10,16(%rsp) # end of b[num]
- sub \$1,$num
- mov $n0, 24(%rsp) # save *n0
- mov $rp, 32(%rsp) # save $rp
- mov $num,48(%rsp) # inner counter
- mov %r11,56(%rsp) # save original %rsp
- jmp .Lmulx4x_body
+ # +0 saved $num, used in reduction section
+ # +8 &t[2*$num], used in reduction section
+ # +32 saved *n0
+ # +40 saved %rsp
+ # +48 t[2*$num]
+ #
+ mov $n0, 32(%rsp)
+ mov %rax, 40(%rsp) # save original %rsp
+.Lpower5_body:
+ movq $rptr,%xmm1 # save $rptr
+ movq $nptr,%xmm2 # save $nptr
+ movq %r10, %xmm3 # -$num
+ movq $bptr,%xmm4
+
+ call __bn_sqr8x_internal
+ call __bn_sqr8x_internal
+ call __bn_sqr8x_internal
+ call __bn_sqr8x_internal
+ call __bn_sqr8x_internal
+
+ mov %xmm2,$nptr
+ movq %xmm4,$bptr
+ mov $aptr,$rptr
+ mov 40(%rsp),%rax
+ lea 32(%rsp),$n0
+
+ call mul4x_internal
+
+ mov 40(%rsp),%rsi # restore %rsp
+ mov \$1,%rax
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
+.Lpower5_epilogue:
+ ret
+.size bn_power5,.-bn_power5
+.globl bn_sqr8x_internal
+.hidden bn_sqr8x_internal
+.type bn_sqr8x_internal,\@abi-omnipotent
.align 32
-.Lmulx4x_body:
+bn_sqr8x_internal:
+__bn_sqr8x_internal:
+ ##############################################################
+ # Squaring part:
+ #
+ # a) multiply-n-add everything but a[i]*a[i];
+ # b) shift result of a) by 1 to the left and accumulate
+ # a[i]*a[i] products;
+ #
+ ##############################################################
+ # a[1]a[0]
+ # a[2]a[0]
+ # a[3]a[0]
+ # a[2]a[1]
+ # a[4]a[0]
+ # a[3]a[1]
+ # a[5]a[0]
+ # a[4]a[1]
+ # a[3]a[2]
+ # a[6]a[0]
+ # a[5]a[1]
+ # a[4]a[2]
+ # a[7]a[0]
+ # a[6]a[1]
+ # a[5]a[2]
+ # a[4]a[3]
+ # a[7]a[1]
+ # a[6]a[2]
+ # a[5]a[3]
+ # a[7]a[2]
+ # a[6]a[3]
+ # a[5]a[4]
+ # a[7]a[3]
+ # a[6]a[4]
+ # a[7]a[4]
+ # a[6]a[5]
+ # a[7]a[5]
+ # a[7]a[6]
+ # a[1]a[0]
+ # a[2]a[0]
+ # a[3]a[0]
+ # a[4]a[0]
+ # a[5]a[0]
+ # a[6]a[0]
+ # a[7]a[0]
+ # a[2]a[1]
+ # a[3]a[1]
+ # a[4]a[1]
+ # a[5]a[1]
+ # a[6]a[1]
+ # a[7]a[1]
+ # a[3]a[2]
+ # a[4]a[2]
+ # a[5]a[2]
+ # a[6]a[2]
+ # a[7]a[2]
+ # a[4]a[3]
+ # a[5]a[3]
+ # a[6]a[3]
+ # a[7]a[3]
+ # a[5]a[4]
+ # a[6]a[4]
+ # a[7]a[4]
+ # a[6]a[5]
+ # a[7]a[5]
+ # a[7]a[6]
+ # a[0]a[0]
+ # a[1]a[1]
+ # a[2]a[2]
+ # a[3]a[3]
+ # a[4]a[4]
+ # a[5]a[5]
+ # a[6]a[6]
+ # a[7]a[7]
+
+ lea 32(%r10),$i # $i=-($num-32)
+ lea ($aptr,$num),$aptr # end of a[] buffer, ($aptr,$i)=&ap[2]
+
+ mov $num,$j # $j=$num
+
+ # comments apply to $num==8 case
+ mov -32($aptr,$i),$a0 # a[0]
+ lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
+ mov -24($aptr,$i),%rax # a[1]
+ lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
+ mov -16($aptr,$i),$ai # a[2]
+ mov %rax,$a1
+
+ mul $a0 # a[1]*a[0]
+ mov %rax,$A0[0] # a[1]*a[0]
+ mov $ai,%rax # a[2]
+ mov %rdx,$A0[1]
+ mov $A0[0],-24($tptr,$i) # t[1]
+
+ mul $a0 # a[2]*a[0]
+ add %rax,$A0[1]
+ mov $ai,%rax
+ adc \$0,%rdx
+ mov $A0[1],-16($tptr,$i) # t[2]
+ mov %rdx,$A0[0]
+
+
+ mov -8($aptr,$i),$ai # a[3]
+ mul $a1 # a[2]*a[1]
+ mov %rax,$A1[0] # a[2]*a[1]+t[3]
+ mov $ai,%rax
+ mov %rdx,$A1[1]
+
+ lea ($i),$j
+ mul $a0 # a[3]*a[0]
+ add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
+ mov $ai,%rax
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ add $A1[0],$A0[0]
+ adc \$0,$A0[1]
+ mov $A0[0],-8($tptr,$j) # t[3]
+ jmp .Lsqr4x_1st
+
+.align 32
+.Lsqr4x_1st:
+ mov ($aptr,$j),$ai # a[4]
+ mul $a1 # a[3]*a[1]
+ add %rax,$A1[1] # a[3]*a[1]+t[4]
+ mov $ai,%rax
+ mov %rdx,$A1[0]
+ adc \$0,$A1[0]
+
+ mul $a0 # a[4]*a[0]
+ add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
+ mov $ai,%rax # a[3]
+ mov 8($aptr,$j),$ai # a[5]
+ mov %rdx,$A0[0]
+ adc \$0,$A0[0]
+ add $A1[1],$A0[1]
+ adc \$0,$A0[0]
+
+
+ mul $a1 # a[4]*a[3]
+ add %rax,$A1[0] # a[4]*a[3]+t[5]
+ mov $ai,%rax
+ mov $A0[1],($tptr,$j) # t[4]
+ mov %rdx,$A1[1]
+ adc \$0,$A1[1]
+
+ mul $a0 # a[5]*a[2]
+ add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
+ mov $ai,%rax
+ mov 16($aptr,$j),$ai # a[6]
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ add $A1[0],$A0[0]
+ adc \$0,$A0[1]
+
+ mul $a1 # a[5]*a[3]
+ add %rax,$A1[1] # a[5]*a[3]+t[6]
+ mov $ai,%rax
+ mov $A0[0],8($tptr,$j) # t[5]
+ mov %rdx,$A1[0]
+ adc \$0,$A1[0]
+
+ mul $a0 # a[6]*a[2]
+ add %rax,$A0[1] # a[6]*a[2]+a[5]*a[3]+t[6]
+ mov $ai,%rax # a[3]
+ mov 24($aptr,$j),$ai # a[7]
+ mov %rdx,$A0[0]
+ adc \$0,$A0[0]
+ add $A1[1],$A0[1]
+ adc \$0,$A0[0]
+
+
+ mul $a1 # a[6]*a[5]
+ add %rax,$A1[0] # a[6]*a[5]+t[7]
+ mov $ai,%rax
+ mov $A0[1],16($tptr,$j) # t[6]
+ mov %rdx,$A1[1]
+ adc \$0,$A1[1]
+ lea 32($j),$j
+
+ mul $a0 # a[7]*a[4]
+ add %rax,$A0[0] # a[7]*a[4]+a[6]*a[5]+t[6]
+ mov $ai,%rax
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ add $A1[0],$A0[0]
+ adc \$0,$A0[1]
+ mov $A0[0],-8($tptr,$j) # t[7]
+
+ cmp \$0,$j
+ jne .Lsqr4x_1st
+
+ mul $a1 # a[7]*a[5]
+ add %rax,$A1[1]
+ lea 16($i),$i
+ adc \$0,%rdx
+ add $A0[1],$A1[1]
+ adc \$0,%rdx
+
+ mov $A1[1],($tptr) # t[8]
+ mov %rdx,$A1[0]
+ mov %rdx,8($tptr) # t[9]
+ jmp .Lsqr4x_outer
+
+.align 32
+.Lsqr4x_outer: # comments apply to $num==6 case
+ mov -32($aptr,$i),$a0 # a[0]
+ lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
+ mov -24($aptr,$i),%rax # a[1]
+ lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
+ mov -16($aptr,$i),$ai # a[2]
+ mov %rax,$a1
+
+ mul $a0 # a[1]*a[0]
+ mov -24($tptr,$i),$A0[0] # t[1]
+ add %rax,$A0[0] # a[1]*a[0]+t[1]
+ mov $ai,%rax # a[2]
+ adc \$0,%rdx
+ mov $A0[0],-24($tptr,$i) # t[1]
+ mov %rdx,$A0[1]
+
+ mul $a0 # a[2]*a[0]
+ add %rax,$A0[1]
+ mov $ai,%rax
+ adc \$0,%rdx
+ add -16($tptr,$i),$A0[1] # a[2]*a[0]+t[2]
+ mov %rdx,$A0[0]
+ adc \$0,$A0[0]
+ mov $A0[1],-16($tptr,$i) # t[2]
+
+ xor $A1[0],$A1[0]
+
+ mov -8($aptr,$i),$ai # a[3]
+ mul $a1 # a[2]*a[1]
+ add %rax,$A1[0] # a[2]*a[1]+t[3]
+ mov $ai,%rax
+ adc \$0,%rdx
+ add -8($tptr,$i),$A1[0]
+ mov %rdx,$A1[1]
+ adc \$0,$A1[1]
+
+ mul $a0 # a[3]*a[0]
+ add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
+ mov $ai,%rax
+ adc \$0,%rdx
+ add $A1[0],$A0[0]
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ mov $A0[0],-8($tptr,$i) # t[3]
+
+ lea ($i),$j
+ jmp .Lsqr4x_inner
+
+.align 32
+.Lsqr4x_inner:
+ mov ($aptr,$j),$ai # a[4]
+ mul $a1 # a[3]*a[1]
+ add %rax,$A1[1] # a[3]*a[1]+t[4]
+ mov $ai,%rax
+ mov %rdx,$A1[0]
+ adc \$0,$A1[0]
+ add ($tptr,$j),$A1[1]
+ adc \$0,$A1[0]
+
+ .byte 0x67
+ mul $a0 # a[4]*a[0]
+ add %rax,$A0[1] # a[4]*a[0]+a[3]*a[1]+t[4]
+ mov $ai,%rax # a[3]
+ mov 8($aptr,$j),$ai # a[5]
+ mov %rdx,$A0[0]
+ adc \$0,$A0[0]
+ add $A1[1],$A0[1]
+ adc \$0,$A0[0]
+
+ mul $a1 # a[4]*a[3]
+ add %rax,$A1[0] # a[4]*a[3]+t[5]
+ mov $A0[1],($tptr,$j) # t[4]
+ mov $ai,%rax
+ mov %rdx,$A1[1]
+ adc \$0,$A1[1]
+ add 8($tptr,$j),$A1[0]
+ lea 16($j),$j # j++
+ adc \$0,$A1[1]
+
+ mul $a0 # a[5]*a[2]
+ add %rax,$A0[0] # a[5]*a[2]+a[4]*a[3]+t[5]
+ mov $ai,%rax
+ adc \$0,%rdx
+ add $A1[0],$A0[0]
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ mov $A0[0],-8($tptr,$j) # t[5], "preloaded t[1]" below
+
+ cmp \$0,$j
+ jne .Lsqr4x_inner
+
+ .byte 0x67
+ mul $a1 # a[5]*a[3]
+ add %rax,$A1[1]
+ adc \$0,%rdx
+ add $A0[1],$A1[1]
+ adc \$0,%rdx
+
+ mov $A1[1],($tptr) # t[6], "preloaded t[2]" below
+ mov %rdx,$A1[0]
+ mov %rdx,8($tptr) # t[7], "preloaded t[3]" below
+
+ add \$16,$i
+ jnz .Lsqr4x_outer
+
+ # comments apply to $num==4 case
+ mov -32($aptr),$a0 # a[0]
+ lea 48+8(%rsp,$num,2),$tptr # end of tp[] buffer, &tp[2*$num]
+ mov -24($aptr),%rax # a[1]
+ lea -32($tptr,$i),$tptr # end of tp[] window, &tp[2*$num-"$i"]
+ mov -16($aptr),$ai # a[2]
+ mov %rax,$a1
+
+ mul $a0 # a[1]*a[0]
+ add %rax,$A0[0] # a[1]*a[0]+t[1], preloaded t[1]
+ mov $ai,%rax # a[2]
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+
+ mul $a0 # a[2]*a[0]
+ add %rax,$A0[1]
+ mov $ai,%rax
+ mov $A0[0],-24($tptr) # t[1]
+ mov %rdx,$A0[0]
+ adc \$0,$A0[0]
+ add $A1[1],$A0[1] # a[2]*a[0]+t[2], preloaded t[2]
+ mov -8($aptr),$ai # a[3]
+ adc \$0,$A0[0]
+
+ mul $a1 # a[2]*a[1]
+ add %rax,$A1[0] # a[2]*a[1]+t[3], preloaded t[3]
+ mov $ai,%rax
+ mov $A0[1],-16($tptr) # t[2]
+ mov %rdx,$A1[1]
+ adc \$0,$A1[1]
+
+ mul $a0 # a[3]*a[0]
+ add %rax,$A0[0] # a[3]*a[0]+a[2]*a[1]+t[3]
+ mov $ai,%rax
+ mov %rdx,$A0[1]
+ adc \$0,$A0[1]
+ add $A1[0],$A0[0]
+ adc \$0,$A0[1]
+ mov $A0[0],-8($tptr) # t[3]
+
+ mul $a1 # a[3]*a[1]
+ add %rax,$A1[1]
+ mov -16($aptr),%rax # a[2]
+ adc \$0,%rdx
+ add $A0[1],$A1[1]
+ adc \$0,%rdx
+
+ mov $A1[1],($tptr) # t[4]
+ mov %rdx,$A1[0]
+ mov %rdx,8($tptr) # t[5]
+
+ mul $ai # a[2]*a[3]
___
-my ($aptr, $bptr, $nptr, $tptr, $mi, $bi, $zero, $num)=
- ("%rsi","%rdi","%rcx","%rbx","%r8","%r9","%rbp","%rax");
-my $rptr=$bptr;
-my $STRIDE=2**5*8; # 5 is "window size"
-my $N=$STRIDE/4; # should match cache line size
+{
+my ($shift,$carry)=($a0,$a1);
+my @S=(@A1,$ai,$n0);
$code.=<<___;
- mov `($win64?56:8)`(%rax),%r10d # load 7th argument
- mov %r10,%r11
- shr \$`log($N/8)/log(2)`,%r10
- and \$`$N/8-1`,%r11
- not %r10
- lea .Lmagic_masks(%rip),%rax
- and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
- lea 96($bp,%r11,8),$bptr # pointer within 1st cache line
- movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
- movq 8(%rax,%r10,8),%xmm5 # cache line contains element
- movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
- movq 24(%rax,%r10,8),%xmm7
+ add \$16,$i
+ xor $shift,$shift
+ sub $num,$i # $i=16-$num
+ xor $carry,$carry
+
+ add $A1[0],%rax # t[5]
+ adc \$0,%rdx
+ mov %rax,8($tptr) # t[5]
+ mov %rdx,16($tptr) # t[6]
+ mov $carry,24($tptr) # t[7]
+
+ mov -16($aptr,$i),%rax # a[0]
+ lea 48+8(%rsp),$tptr
+ xor $A0[0],$A0[0] # t[0]
+ mov 8($tptr),$A0[1] # t[1]
+
+ lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[1] # | t[2*i]>>63
+ mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[0]
+ mov -8($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[0],($tptr)
+ adc %rdx,$S[1]
+
+ lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
+ mov $S[1],8($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[3] # | t[2*i]>>63
+ mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[2]
+ mov 0($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[2],16($tptr)
+ adc %rdx,$S[3]
+ lea 16($i),$i
+ mov $S[3],24($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ lea 64($tptr),$tptr
+ jmp .Lsqr4x_shift_n_add
- movq `0*$STRIDE/4-96`($bptr),%xmm0
- movq `1*$STRIDE/4-96`($bptr),%xmm1
- pand %xmm4,%xmm0
- movq `2*$STRIDE/4-96`($bptr),%xmm2
- pand %xmm5,%xmm1
- movq `3*$STRIDE/4-96`($bptr),%xmm3
- pand %xmm6,%xmm2
- por %xmm1,%xmm0
- pand %xmm7,%xmm3
- por %xmm2,%xmm0
- lea $STRIDE($bptr),$bptr
- por %xmm3,%xmm0
+.align 32
+.Lsqr4x_shift_n_add:
+ lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[1] # | t[2*i]>>63
+ mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[0]
+ mov -8($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[0],-32($tptr)
+ adc %rdx,$S[1]
+
+ lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
+ mov $S[1],-24($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[3] # | t[2*i]>>63
+ mov 0($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov 8($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[2]
+ mov 0($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[2],-16($tptr)
+ adc %rdx,$S[3]
+
+ lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
+ mov $S[3],-8($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[1] # | t[2*i]>>63
+ mov 16($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov 24($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[0]
+ mov 8($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[0],0($tptr)
+ adc %rdx,$S[1]
+
+ lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1 | shift
+ mov $S[1],8($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[3] # | t[2*i]>>63
+ mov 32($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov 40($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[2]
+ mov 16($aptr,$i),%rax # a[i+1] # prefetch
+ mov $S[2],16($tptr)
+ adc %rdx,$S[3]
+ mov $S[3],24($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ lea 64($tptr),$tptr
+ add \$32,$i
+ jnz .Lsqr4x_shift_n_add
+
+ lea ($shift,$A0[0],2),$S[0] # t[2*i]<<1 | shift
+ .byte 0x67
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[1] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[1] # | t[2*i]>>63
+ mov -16($tptr),$A0[0] # t[2*i+2] # prefetch
+ mov $A0[1],$shift # shift=t[2*i+1]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ mov -8($tptr),$A0[1] # t[2*i+2+1] # prefetch
+ adc %rax,$S[0]
+ mov -8($aptr),%rax # a[i+1] # prefetch
+ mov $S[0],-32($tptr)
+ adc %rdx,$S[1]
+
+ lea ($shift,$A0[0],2),$S[2] # t[2*i]<<1|shift
+ mov $S[1],-24($tptr)
+ sbb $carry,$carry # mov cf,$carry
+ shr \$63,$A0[0]
+ lea ($j,$A0[1],2),$S[3] # t[2*i+1]<<1 |
+ shr \$63,$A0[1]
+ or $A0[0],$S[3] # | t[2*i]>>63
+ mul %rax # a[i]*a[i]
+ neg $carry # mov $carry,cf
+ adc %rax,$S[2]
+ adc %rdx,$S[3]
+ mov $S[2],-16($tptr)
+ mov $S[3],-8($tptr)
+___
+}\f
+######################################################################
+# Montgomery reduction part, "word-by-word" algorithm.
+#
+# This new path is inspired by multiple submissions from Intel, by
+# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
+# Vinodh Gopal...
+{
+my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
- movq %xmm0,%rdx # bp[0]
- movq `0*$STRIDE/4-96`($bptr),%xmm0
- movq `1*$STRIDE/4-96`($bptr),%xmm1
- pand %xmm4,%xmm0
- movq `2*$STRIDE/4-96`($bptr),%xmm2
- pand %xmm5,%xmm1
+$code.=<<___;
+ movq %xmm2,$nptr
+sqr8x_reduction:
+ xor %rax,%rax
+ lea ($nptr,$num,2),%rcx # end of n[]
+ lea 48+8(%rsp,$num,2),%rdx # end of t[] buffer
+ mov %rcx,0+8(%rsp)
+ lea 48+8(%rsp,$num),$tptr # end of initial t[] window
+ mov %rdx,8+8(%rsp)
+ neg $num
+ jmp .L8x_reduction_loop
- lea 64+32(%rsp),$tptr
- mov %rdx,$bi
- xor $zero,$zero # of=0,cf=0
+.align 32
+.L8x_reduction_loop:
+ lea ($tptr,$num),$tptr # start of current t[] window
+ .byte 0x66
+ mov 8*0($tptr),$m0
+ mov 8*1($tptr),%r9
+ mov 8*2($tptr),%r10
+ mov 8*3($tptr),%r11
+ mov 8*4($tptr),%r12
+ mov 8*5($tptr),%r13
+ mov 8*6($tptr),%r14
+ mov 8*7($tptr),%r15
+ mov %rax,(%rdx) # store top-most carry bit
+ lea 8*8($tptr),$tptr
+
+ .byte 0x67
+ mov $m0,%r8
+ imulq 32+8(%rsp),$m0 # n0*a[0]
+ mov 16*0($nptr),%rax # n[0]
+ mov \$8,%ecx
+ jmp .L8x_reduce
- mulx 0*8($aptr),$mi,%rax # a[0]*b[0]
- mulx 1*8($aptr),%r11,%r14 # a[1]*b[0]
- adcx %rax,%r11
- mulx 2*8($aptr),%r12,%r13 # ...
- adcx %r14,%r12
- adcx $zero,%r13
+.align 32
+.L8x_reduce:
+ mulq $m0
+ mov 16*1($nptr),%rax # n[1]
+ neg %r8
+ mov %rdx,%r8
+ adc \$0,%r8
- movq `3*$STRIDE/4-96`($bptr),%xmm3
- lea $STRIDE($bptr),%r10 # next &b[i]
- pand %xmm6,%xmm2
- por %xmm1,%xmm0
- pand %xmm7,%xmm3
+ mulq $m0
+ add %rax,%r9
+ mov 16*2($nptr),%rax
+ adc \$0,%rdx
+ add %r9,%r8
+ mov $m0,48-8+8(%rsp,%rcx,8) # put aside n0*a[i]
+ mov %rdx,%r9
+ adc \$0,%r9
- mov $mi,$bptr # borrow $bptr
- imulq 24(%rsp),$mi # "t[0]"*n0
- xor $zero,$zero # cf=0, of=0
+ mulq $m0
+ add %rax,%r10
+ mov 16*3($nptr),%rax
+ adc \$0,%rdx
+ add %r10,%r9
+ mov 32+8(%rsp),$carry # pull n0, borrow $carry
+ mov %rdx,%r10
+ adc \$0,%r10
- por %xmm2,%xmm0
- por %xmm3,%xmm0
- mov %r10,8(%rsp) # off-load &b[i]
+ mulq $m0
+ add %rax,%r11
+ mov 16*4($nptr),%rax
+ adc \$0,%rdx
+ imulq %r8,$carry # modulo-scheduled
+ add %r11,%r10
+ mov %rdx,%r11
+ adc \$0,%r11
- mulx 3*8($aptr),%rax,%r14
- mov $mi,%rdx
- lea 4*8($aptr),$aptr
- adcx %rax,%r13
- adcx $zero,%r14 # cf=0
+ mulq $m0
+ add %rax,%r12
+ mov 16*5($nptr),%rax
+ adc \$0,%rdx
+ add %r12,%r11
+ mov %rdx,%r12
+ adc \$0,%r12
- mulx 0*8($nptr),%rax,%r10
- adcx %rax,$bptr # discarded
- adox %r11,%r10
- mulx 1*8($nptr),%rax,%r11
- adcx %rax,%r10
- adox %r12,%r11
- mulx 2*8($nptr),%rax,%r12
- mov 48(%rsp),$bptr # counter value
- mov %r10,-4*8($tptr)
- adcx %rax,%r11
- adox %r13,%r12
- mulx 3*8($nptr),%rax,%r15
- mov $bi,%rdx
- mov %r11,-3*8($tptr)
- adcx %rax,%r12
- adox $zero,%r15 # of=0
- lea 4*8($nptr),$nptr
- mov %r12,-2*8($tptr)
+ mulq $m0
+ add %rax,%r13
+ mov 16*6($nptr),%rax
+ adc \$0,%rdx
+ add %r13,%r12
+ mov %rdx,%r13
+ adc \$0,%r13
+
+ mulq $m0
+ add %rax,%r14
+ mov 16*7($nptr),%rax
+ adc \$0,%rdx
+ add %r14,%r13
+ mov %rdx,%r14
+ adc \$0,%r14
- jmp .Lmulx4x_1st
+ mulq $m0
+ mov $carry,$m0 # n0*a[i]
+ add %rax,%r15
+ mov 16*0($nptr),%rax # n[0]
+ adc \$0,%rdx
+ add %r15,%r14
+ mov %rdx,%r15
+ adc \$0,%r15
+
+ dec %ecx
+ jnz .L8x_reduce
+
+ lea 16*8($nptr),$nptr
+ xor %rax,%rax
+ mov 8+8(%rsp),%rdx # pull end of t[]
+ cmp 0+8(%rsp),$nptr # end of n[]?
+ jae .L8x_no_tail
+
+ .byte 0x66
+ add 8*0($tptr),%r8
+ adc 8*1($tptr),%r9
+ adc 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ sbb $carry,$carry # top carry
+
+ mov 48+56+8(%rsp),$m0 # pull n0*a[0]
+ mov \$8,%ecx
+ mov 16*0($nptr),%rax
+ jmp .L8x_tail
.align 32
-.Lmulx4x_1st:
- adcx $zero,%r15 # cf=0, modulo-scheduled
- mulx 0*8($aptr),%r10,%rax # a[4]*b[0]
- adcx %r14,%r10
- mulx 1*8($aptr),%r11,%r14 # a[5]*b[0]
- adcx %rax,%r11
- mulx 2*8($aptr),%r12,%rax # ...
+.L8x_tail:
+ mulq $m0
+ add %rax,%r8
+ mov 16*1($nptr),%rax
+ mov %r8,($tptr) # save result
+ mov %rdx,%r8
+ adc \$0,%r8
+
+ mulq $m0
+ add %rax,%r9
+ mov 16*2($nptr),%rax
+ adc \$0,%rdx
+ add %r9,%r8
+ lea 8($tptr),$tptr # $tptr++
+ mov %rdx,%r9
+ adc \$0,%r9
+
+ mulq $m0
+ add %rax,%r10
+ mov 16*3($nptr),%rax
+ adc \$0,%rdx
+ add %r10,%r9
+ mov %rdx,%r10
+ adc \$0,%r10
+
+ mulq $m0
+ add %rax,%r11
+ mov 16*4($nptr),%rax
+ adc \$0,%rdx
+ add %r11,%r10
+ mov %rdx,%r11
+ adc \$0,%r11
+
+ mulq $m0
+ add %rax,%r12
+ mov 16*5($nptr),%rax
+ adc \$0,%rdx
+ add %r12,%r11
+ mov %rdx,%r12
+ adc \$0,%r12
+
+ mulq $m0
+ add %rax,%r13
+ mov 16*6($nptr),%rax
+ adc \$0,%rdx
+ add %r13,%r12
+ mov %rdx,%r13
+ adc \$0,%r13
+
+ mulq $m0
+ add %rax,%r14
+ mov 16*7($nptr),%rax
+ adc \$0,%rdx
+ add %r14,%r13
+ mov %rdx,%r14
+ adc \$0,%r14
+
+ mulq $m0
+ mov 48-16+8(%rsp,%rcx,8),$m0# pull n0*a[i]
+ add %rax,%r15
+ adc \$0,%rdx
+ add %r15,%r14
+ mov 16*0($nptr),%rax # pull n[0]
+ mov %rdx,%r15
+ adc \$0,%r15
+
+ dec %ecx
+ jnz .L8x_tail
+
+ lea 16*8($nptr),$nptr
+ mov 8+8(%rsp),%rdx # pull end of t[]
+ cmp 0+8(%rsp),$nptr # end of n[]?
+ jae .L8x_tail_done # break out of loop
+
+ mov 48+56+8(%rsp),$m0 # pull n0*a[0]
+ neg $carry
+ mov 8*0($nptr),%rax # pull n[0]
+ adc 8*0($tptr),%r8
+ adc 8*1($tptr),%r9
+ adc 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ sbb $carry,$carry # top carry
+
+ mov \$8,%ecx
+ jmp .L8x_tail
+
+.align 32
+.L8x_tail_done:
+ add (%rdx),%r8 # can this overflow?
+ xor %rax,%rax
+
+ neg $carry
+.L8x_no_tail:
+ adc 8*0($tptr),%r8
+ adc 8*1($tptr),%r9
+ adc 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ adc \$0,%rax # top-most carry
+ mov -16($nptr),%rcx # np[num-1]
+ xor $carry,$carry
+
+ movq %xmm2,$nptr # restore $nptr
+
+ mov %r8,8*0($tptr) # store top 512 bits
+ mov %r9,8*1($tptr)
+ movq %xmm3,$num # $num is %r9, can't be moved upwards
+ mov %r10,8*2($tptr)
+ mov %r11,8*3($tptr)
+ mov %r12,8*4($tptr)
+ mov %r13,8*5($tptr)
+ mov %r14,8*6($tptr)
+ mov %r15,8*7($tptr)
+ lea 8*8($tptr),$tptr
+
+ cmp %rdx,$tptr # end of t[]?
+ jb .L8x_reduction_loop
+___
+}\f
+##############################################################
+# Post-condition, 4x unrolled
+#
+{
+my ($tptr,$nptr)=("%rbx","%rbp");
+$code.=<<___;
+ #xor %rsi,%rsi # %rsi was $carry above
+ sub %r15,%rcx # compare top-most words
+ lea (%rdi,$num),$tptr # %rdi was $tptr above
+ adc %rsi,%rsi
+ mov $num,%rcx
+ or %rsi,%rax
+ movq %xmm1,$rptr # restore $rptr
+ xor \$1,%rax
+ movq %xmm1,$aptr # prepare for back-to-back call
+ lea ($nptr,%rax,8),$nptr
+ sar \$3+2,%rcx # cf=0
+ jmp .Lsqr4x_sub
+
+.align 32
+.Lsqr4x_sub:
+ .byte 0x66
+ mov 8*0($tptr),%r12
+ mov 8*1($tptr),%r13
+ sbb 16*0($nptr),%r12
+ mov 8*2($tptr),%r14
+ sbb 16*1($nptr),%r13
+ mov 8*3($tptr),%r15
+ lea 8*4($tptr),$tptr
+ sbb 16*2($nptr),%r14
+ mov %r12,8*0($rptr)
+ sbb 16*3($nptr),%r15
+ lea 16*4($nptr),$nptr
+ mov %r13,8*1($rptr)
+ mov %r14,8*2($rptr)
+ mov %r15,8*3($rptr)
+ lea 8*4($rptr),$rptr
+
+ inc %rcx # pass %cf
+ jnz .Lsqr4x_sub
+___
+}
+$code.=<<___;
+ mov $num,%r10 # prepare for back-to-back call
+ neg $num # restore $num
+ ret
+.size bn_sqr8x_internal,.-bn_sqr8x_internal
+___
+{
+$code.=<<___;
+.globl bn_from_montgomery
+.type bn_from_montgomery,\@abi-omnipotent
+.align 32
+bn_from_montgomery:
+ testl \$7,`($win64?"48(%rsp)":"%r9d")`
+ jz bn_from_mont8x
+ xor %eax,%eax
+ ret
+.size bn_from_montgomery,.-bn_from_montgomery
+
+.type bn_from_mont8x,\@function,6
+.align 32
+bn_from_mont8x:
+ .byte 0x67
+ mov %rsp,%rax
+ push %rbx
+ push %rbp
+ push %r12
+ push %r13
+ push %r14
+ push %r15
+___
+$code.=<<___ if ($win64);
+ lea -0x28(%rsp),%rsp
+ movaps %xmm6,(%rsp)
+ movaps %xmm7,0x10(%rsp)
+___
+$code.=<<___;
+ .byte 0x67
+ mov ${num}d,%r10d
+ shl \$3,${num}d # convert $num to bytes
+ shl \$3+2,%r10d # 4*$num
+ neg $num
+ mov ($n0),$n0 # *n0
+
+ ##############################################################
+ # ensure that stack frame doesn't alias with $aptr+4*$num
+ # modulo 4096, which covers ret[num], am[num] and n[2*num]
+ # (see bn_exp.c). this is done to allow memory disambiguation
+ # logic do its magic.
+ #
+ lea -64(%rsp,$num,2),%r11
+ sub $aptr,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lfrom_sp_alt
+ sub %r11,%rsp # align with $aptr
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ jmp .Lfrom_sp_done
+
+.align 32
+.Lfrom_sp_alt:
+ lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lfrom_sp_done:
+ and \$-64,%rsp
+ mov $num,%r10
+ neg $num
+
+ ##############################################################
+ # Stack layout
+ #
+ # +0 saved $num, used in reduction section
+ # +8 &t[2*$num], used in reduction section
+ # +32 saved *n0
+ # +40 saved %rsp
+ # +48 t[2*$num]
+ #
+ mov $n0, 32(%rsp)
+ mov %rax, 40(%rsp) # save original %rsp
+.Lfrom_body:
+ mov $num,%r11
+ lea 48(%rsp),%rax
+ pxor %xmm0,%xmm0
+ jmp .Lmul_by_1
+
+.align 32
+.Lmul_by_1:
+ movdqu ($aptr),%xmm1
+ movdqu 16($aptr),%xmm2
+ movdqu 32($aptr),%xmm3
+ movdqa %xmm0,(%rax,$num)
+ movdqu 48($aptr),%xmm4
+ movdqa %xmm0,16(%rax,$num)
+ .byte 0x48,0x8d,0xb6,0x40,0x00,0x00,0x00 # lea 64($aptr),$aptr
+ movdqa %xmm1,(%rax)
+ movdqa %xmm0,32(%rax,$num)
+ movdqa %xmm2,16(%rax)
+ movdqa %xmm0,48(%rax,$num)
+ movdqa %xmm3,32(%rax)
+ movdqa %xmm4,48(%rax)
+ lea 64(%rax),%rax
+ sub \$64,%r11
+ jnz .Lmul_by_1
+
+ movq $rptr,%xmm1
+ movq $nptr,%xmm2
+ .byte 0x67
+ mov $nptr,%rbp
+ movq %r10, %xmm3 # -num
+___
+$code.=<<___ if ($addx);
+ mov OPENSSL_ia32cap_P+8(%rip),%r11d
+ and \$0x80100,%r11d
+ cmp \$0x80100,%r11d
+ jne .Lfrom_mont_nox
+
+ lea (%rax,$num),$rptr
+ call sqrx8x_reduction
+
+ pxor %xmm0,%xmm0
+ lea 48(%rsp),%rax
+ mov 40(%rsp),%rsi # restore %rsp
+ jmp .Lfrom_mont_zero
+
+.align 32
+.Lfrom_mont_nox:
+___
+$code.=<<___;
+ call sqr8x_reduction
+
+ pxor %xmm0,%xmm0
+ lea 48(%rsp),%rax
+ mov 40(%rsp),%rsi # restore %rsp
+ jmp .Lfrom_mont_zero
+
+.align 32
+.Lfrom_mont_zero:
+ movdqa %xmm0,16*0(%rax)
+ movdqa %xmm0,16*1(%rax)
+ movdqa %xmm0,16*2(%rax)
+ movdqa %xmm0,16*3(%rax)
+ lea 16*4(%rax),%rax
+ sub \$32,$num
+ jnz .Lfrom_mont_zero
+
+ mov \$1,%rax
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
+.Lfrom_epilogue:
+ ret
+.size bn_from_mont8x,.-bn_from_mont8x
+___
+}
+}}}
+\f
+if ($addx) {{{
+my $bp="%rdx"; # restore original value
+
+$code.=<<___;
+.type bn_mulx4x_mont_gather5,\@function,6
+.align 32
+bn_mulx4x_mont_gather5:
+.Lmulx4x_enter:
+ .byte 0x67
+ mov %rsp,%rax
+ push %rbx
+ push %rbp
+ push %r12
+ push %r13
+ push %r14
+ push %r15
+___
+$code.=<<___ if ($win64);
+ lea -0x28(%rsp),%rsp
+ movaps %xmm6,(%rsp)
+ movaps %xmm7,0x10(%rsp)
+___
+$code.=<<___;
+ .byte 0x67
+ mov ${num}d,%r10d
+ shl \$3,${num}d # convert $num to bytes
+ shl \$3+2,%r10d # 4*$num
+ neg $num # -$num
+ mov ($n0),$n0 # *n0
+
+ ##############################################################
+ # ensure that stack frame doesn't alias with $aptr+4*$num
+ # modulo 4096, which covers a[num], ret[num] and n[2*num]
+ # (see bn_exp.c). this is done to allow memory disambiguation
+ # logic do its magic. [excessive frame is allocated in order
+ # to allow bn_from_mont8x to clear it.]
+ #
+ lea -64(%rsp,$num,2),%r11
+ sub $ap,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lmulx4xsp_alt
+ sub %r11,%rsp # align with $aptr
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+$num)
+ jmp .Lmulx4xsp_done
+
+.align 32
+.Lmulx4xsp_alt:
+ lea 4096-64(,$num,2),%r10 # 4096-frame-$num
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+$num)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lmulx4xsp_done:
+ and \$-64,%rsp # ensure alignment
+ ##############################################################
+ # Stack layout
+ # +0 -num
+ # +8 off-loaded &b[i]
+ # +16 end of b[num]
+ # +24 inner counter
+ # +32 saved n0
+ # +40 saved %rsp
+ # +48
+ # +56 saved rp
+ # +64 tmp[num+1]
+ #
+ mov $n0, 32(%rsp) # save *n0
+ mov %rax,40(%rsp) # save original %rsp
+.Lmulx4x_body:
+ call mulx4x_internal
+
+ mov 40(%rsp),%rsi # restore %rsp
+ mov \$1,%rax
+___
+$code.=<<___ if ($win64);
+ movaps -88(%rsi),%xmm6
+ movaps -72(%rsi),%xmm7
+___
+$code.=<<___;
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
+.Lmulx4x_epilogue:
+ ret
+.size bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
+
+.type mulx4x_internal,\@abi-omnipotent
+.align 32
+mulx4x_internal:
+ .byte 0x4c,0x89,0x8c,0x24,0x08,0x00,0x00,0x00 # mov $num,8(%rsp) # save -$num
+ .byte 0x67
+ neg $num # restore $num
+ shl \$5,$num
+ lea 256($bp,$num),%r13
+ shr \$5+5,$num
+ mov `($win64?56:8)`(%rax),%r10d # load 7th argument
+ sub \$1,$num
+ mov %r13,16+8(%rsp) # end of b[num]
+ mov $num,24+8(%rsp) # inner counter
+ mov $rp, 56+8(%rsp) # save $rp
+___
+my ($aptr, $bptr, $nptr, $tptr, $mi, $bi, $zero, $num)=
+ ("%rsi","%rdi","%rcx","%rbx","%r8","%r9","%rbp","%rax");
+my $rptr=$bptr;
+my $STRIDE=2**5*8; # 5 is "window size"
+my $N=$STRIDE/4; # should match cache line size
+$code.=<<___;
+ mov %r10,%r11
+ shr \$`log($N/8)/log(2)`,%r10
+ and \$`$N/8-1`,%r11
+ not %r10
+ lea .Lmagic_masks(%rip),%rax
+ and \$`2**5/($N/8)-1`,%r10 # 5 is "window size"
+ lea 96($bp,%r11,8),$bptr # pointer within 1st cache line
+ movq 0(%rax,%r10,8),%xmm4 # set of masks denoting which
+ movq 8(%rax,%r10,8),%xmm5 # cache line contains element
+ add \$7,%r11
+ movq 16(%rax,%r10,8),%xmm6 # denoted by 7th argument
+ movq 24(%rax,%r10,8),%xmm7
+ and \$7,%r11
+
+ movq `0*$STRIDE/4-96`($bptr),%xmm0
+ lea $STRIDE($bptr),$tptr # borrow $tptr
+ movq `1*$STRIDE/4-96`($bptr),%xmm1
+ pand %xmm4,%xmm0
+ movq `2*$STRIDE/4-96`($bptr),%xmm2
+ pand %xmm5,%xmm1
+ movq `3*$STRIDE/4-96`($bptr),%xmm3
+ pand %xmm6,%xmm2
+ por %xmm1,%xmm0
+ movq `0*$STRIDE/4-96`($tptr),%xmm1
+ pand %xmm7,%xmm3
+ por %xmm2,%xmm0
+ movq `1*$STRIDE/4-96`($tptr),%xmm2
+ por %xmm3,%xmm0
+ .byte 0x67,0x67
+ pand %xmm4,%xmm1
+ movq `2*$STRIDE/4-96`($tptr),%xmm3
+
+ movq %xmm0,%rdx # bp[0]
+ movq `3*$STRIDE/4-96`($tptr),%xmm0
+ lea 2*$STRIDE($bptr),$bptr # next &b[i]
+ pand %xmm5,%xmm2
+ .byte 0x67,0x67
+ pand %xmm6,%xmm3
+ ##############################################################
+ # $tptr is chosen so that writing to top-most element of the
+ # vector occurs just "above" references to powers table,
+ # "above" modulo cache-line size, which effectively precludes
+ # possibility of memory disambiguation logic failure when
+ # accessing the table.
+ #
+ lea 64+8*4+8(%rsp,%r11,8),$tptr
+
+ mov %rdx,$bi
+ mulx 0*8($aptr),$mi,%rax # a[0]*b[0]
+ mulx 1*8($aptr),%r11,%r12 # a[1]*b[0]
+ add %rax,%r11
+ mulx 2*8($aptr),%rax,%r13 # ...
+ adc %rax,%r12
+ adc \$0,%r13
+ mulx 3*8($aptr),%rax,%r14
+
+ mov $mi,%r15
+ imulq 32+8(%rsp),$mi # "t[0]"*n0
+ xor $zero,$zero # cf=0, of=0
+ mov $mi,%rdx
+
+ por %xmm2,%xmm1
+ pand %xmm7,%xmm0
+ por %xmm3,%xmm1
+ mov $bptr,8+8(%rsp) # off-load &b[i]
+ por %xmm1,%xmm0
+
+ .byte 0x48,0x8d,0xb6,0x20,0x00,0x00,0x00 # lea 4*8($aptr),$aptr
+ adcx %rax,%r13
+ adcx $zero,%r14 # cf=0
+
+ mulx 0*16($nptr),%rax,%r10
+ adcx %rax,%r15 # discarded
+ adox %r11,%r10
+ mulx 1*16($nptr),%rax,%r11
+ adcx %rax,%r10
+ adox %r12,%r11
+ mulx 2*16($nptr),%rax,%r12
+ mov 24+8(%rsp),$bptr # counter value
+ .byte 0x66
+ mov %r10,-8*4($tptr)
+ adcx %rax,%r11
+ adox %r13,%r12
+ mulx 3*16($nptr),%rax,%r15
+ .byte 0x67,0x67
+ mov $bi,%rdx
+ mov %r11,-8*3($tptr)
+ adcx %rax,%r12
+ adox $zero,%r15 # of=0
+ .byte 0x48,0x8d,0x89,0x40,0x00,0x00,0x00 # lea 4*16($nptr),$nptr
+ mov %r12,-8*2($tptr)
+ #jmp .Lmulx4x_1st
+
+.align 32
+.Lmulx4x_1st:
+ adcx $zero,%r15 # cf=0, modulo-scheduled
+ mulx 0*8($aptr),%r10,%rax # a[4]*b[0]
+ adcx %r14,%r10
+ mulx 1*8($aptr),%r11,%r14 # a[5]*b[0]
+ adcx %rax,%r11
+ mulx 2*8($aptr),%r12,%rax # ...
adcx %r14,%r12
mulx 3*8($aptr),%r13,%r14
- .byte 0x66,0x66
+ .byte 0x67,0x67
mov $mi,%rdx
adcx %rax,%r13
adcx $zero,%r14 # cf=0
lea 4*8($tptr),$tptr
adox %r15,%r10
- mulx 0*8($nptr),%rax,%r15
+ mulx 0*16($nptr),%rax,%r15
adcx %rax,%r10
adox %r15,%r11
- mulx 1*8($nptr),%rax,%r15
+ mulx 1*16($nptr),%rax,%r15
adcx %rax,%r11
adox %r15,%r12
- .byte 0x3e
- mulx 2*8($nptr),%rax,%r15
+ mulx 2*16($nptr),%rax,%r15
mov %r10,-5*8($tptr)
- mov %r11,-4*8($tptr)
adcx %rax,%r12
+ mov %r11,-4*8($tptr)
adox %r15,%r13
- mulx 3*8($nptr),%rax,%r15
+ mulx 3*16($nptr),%rax,%r15
mov $bi,%rdx
mov %r12,-3*8($tptr)
adcx %rax,%r13
adox $zero,%r15
- lea 4*8($nptr),$nptr
+ lea 4*16($nptr),$nptr
mov %r13,-2*8($tptr)
dec $bptr # of=0, pass cf
jnz .Lmulx4x_1st
- mov 0(%rsp),$num # load num
- mov 8(%rsp),$bptr # re-load &b[i]
+ mov 8(%rsp),$num # load -num
movq %xmm0,%rdx # bp[1]
adc $zero,%r15 # modulo-scheduled
+ lea ($aptr,$num),$aptr # rewind $aptr
add %r15,%r14
- sbb %r15,%r15 # top-most carry
+ mov 8+8(%rsp),$bptr # re-load &b[i]
+ adc $zero,$zero # top-most carry
mov %r14,-1*8($tptr)
jmp .Lmulx4x_outer
.align 32
.Lmulx4x_outer:
- sub $num,$aptr # rewind $aptr
- mov %r15,($tptr) # save top-most carry
- mov 64(%rsp),%r10
- lea 64(%rsp),$tptr
- sub $num,$nptr # rewind $nptr
+ mov $zero,($tptr) # save top-most carry
+ lea 4*8($tptr,$num),$tptr # rewind $tptr
+ mulx 0*8($aptr),$mi,%r11 # a[0]*b[i]
xor $zero,$zero # cf=0, of=0
mov %rdx,$bi
+ mulx 1*8($aptr),%r14,%r12 # a[1]*b[i]
+ adox -4*8($tptr),$mi # +t[0]
+ adcx %r14,%r11
+ mulx 2*8($aptr),%r15,%r13 # ...
+ adox -3*8($tptr),%r11
+ adcx %r15,%r12
+ mulx 3*8($aptr),%rdx,%r14
+ adox -2*8($tptr),%r12
+ adcx %rdx,%r13
+ lea ($nptr,$num,2),$nptr # rewind $nptr
+ lea 4*8($aptr),$aptr
+ adox -1*8($tptr),%r13
+ adcx $zero,%r14
+ adox $zero,%r14
+
+ .byte 0x67
+ mov $mi,%r15
+ imulq 32+8(%rsp),$mi # "t[0]"*n0
movq `0*$STRIDE/4-96`($bptr),%xmm0
+ .byte 0x67,0x67
+ mov $mi,%rdx
movq `1*$STRIDE/4-96`($bptr),%xmm1
+ .byte 0x67
pand %xmm4,%xmm0
movq `2*$STRIDE/4-96`($bptr),%xmm2
+ .byte 0x67
pand %xmm5,%xmm1
-
- mulx 0*8($aptr),$mi,%rax # a[0]*b[i]
- adox %r10,$mi
- mov 1*8($tptr),%r10
- mulx 1*8($aptr),%r11,%r14 # a[1]*b[i]
- adcx %rax,%r11
- mulx 2*8($aptr),%r12,%r13 # ...
- adox %r10,%r11
- adcx %r14,%r12
- adox $zero,%r12
- adcx $zero,%r13
-
movq `3*$STRIDE/4-96`($bptr),%xmm3
- lea $STRIDE($bptr),%r10 # next &b[i]
+ add \$$STRIDE,$bptr # next &b[i]
+ .byte 0x67
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
-
- mov $mi,$bptr # borrow $bptr
- imulq 24(%rsp),$mi # "t[0]"*n0
xor $zero,$zero # cf=0, of=0
+ mov $bptr,8+8(%rsp) # off-load &b[i]
- por %xmm2,%xmm0
- por %xmm3,%xmm0
- mov %r10,8(%rsp) # off-load &b[i]
- mov 2*8($tptr),%r10
-
- mulx 3*8($aptr),%rax,%r14
- mov $mi,%rdx
- adox %r10,%r12
- adcx %rax,%r13
- adox 3*8($tptr),%r13
- adcx $zero,%r14
- lea 4*8($aptr),$aptr
- lea 4*8($tptr),$tptr
- adox $zero,%r14
-
- mulx 0*8($nptr),%rax,%r10
- adcx %rax,$bptr # discarded
+ mulx 0*16($nptr),%rax,%r10
+ adcx %rax,%r15 # discarded
adox %r11,%r10
- mulx 1*8($nptr),%rax,%r11
+ mulx 1*16($nptr),%rax,%r11
adcx %rax,%r10
adox %r12,%r11
- mulx 2*8($nptr),%rax,%r12
- .byte 0x3e
- mov %r10,-4*8($tptr)
- .byte 0x3e
- mov 0*8($tptr),%r10
+ mulx 2*16($nptr),%rax,%r12
adcx %rax,%r11
adox %r13,%r12
- mulx 3*8($nptr),%rax,%r15
+ mulx 3*16($nptr),%rax,%r15
mov $bi,%rdx
- mov %r11,-3*8($tptr)
+ por %xmm2,%xmm0
+ mov 24+8(%rsp),$bptr # counter value
+ mov %r10,-8*4($tptr)
+ por %xmm3,%xmm0
adcx %rax,%r12
+ mov %r11,-8*3($tptr)
adox $zero,%r15 # of=0
- mov 48(%rsp),$bptr # counter value
- mov %r12,-2*8($tptr)
- lea 4*8($nptr),$nptr
-
+ mov %r12,-8*2($tptr)
+ lea 4*16($nptr),$nptr
jmp .Lmulx4x_inner
.align 32
.Lmulx4x_inner:
- adcx $zero,%r15 # cf=0, modulo-scheduled
- adox %r10,%r14
mulx 0*8($aptr),%r10,%rax # a[4]*b[i]
- mov 1*8($tptr),%r13
- adcx %r14,%r10
+ adcx $zero,%r15 # cf=0, modulo-scheduled
+ adox %r14,%r10
mulx 1*8($aptr),%r11,%r14 # a[5]*b[i]
+ adcx 0*8($tptr),%r10
adox %rax,%r11
mulx 2*8($aptr),%r12,%rax # ...
- adcx %r13,%r11
+ adcx 1*8($tptr),%r11
adox %r14,%r12
mulx 3*8($aptr),%r13,%r14
mov $mi,%rdx
adcx 3*8($tptr),%r13
adox $zero,%r14 # of=0
lea 4*8($aptr),$aptr
- .byte 0x48,0x8d,0x9b,0x20,0x00,0x00,0x00 # lea 4*8($tptr),$tptr
+ lea 4*8($tptr),$tptr
adcx $zero,%r14 # cf=0
adox %r15,%r10
- .byte 0x3e,0xc4,0x62,0xfb,0xf6,0x79,0x00 # mulx 0*8($nptr),%rax,%r15
+ mulx 0*16($nptr),%rax,%r15
adcx %rax,%r10
adox %r15,%r11
- mulx 1*8($nptr),%rax,%r15
+ mulx 1*16($nptr),%rax,%r15
adcx %rax,%r11
adox %r15,%r12
- mulx 2*8($nptr),%rax,%r15
+ mulx 2*16($nptr),%rax,%r15
mov %r10,-5*8($tptr)
- mov 0*8($tptr),%r10
adcx %rax,%r12
adox %r15,%r13
- mulx 3*8($nptr),%rax,%r15
- mov $bi,%rdx
mov %r11,-4*8($tptr)
+ mulx 3*16($nptr),%rax,%r15
+ mov $bi,%rdx
+ lea 4*16($nptr),$nptr
mov %r12,-3*8($tptr)
adcx %rax,%r13
adox $zero,%r15
- lea 4*8($nptr),$nptr
mov %r13,-2*8($tptr)
dec $bptr # of=0, pass cf
jnz .Lmulx4x_inner
- mov 0(%rsp),$num # load num
- mov 8(%rsp),$bptr # re-load &b[i]
+ mov 0+8(%rsp),$num # load -num
movq %xmm0,%rdx # bp[i+1]
adc $zero,%r15 # modulo-scheduled
- sub %r10,$zero # pull top-most carry
+ sub 0*8($tptr),$bptr # pull top-most carry to %cf
+ mov 8+8(%rsp),$bptr # re-load &b[i]
+ mov 16+8(%rsp),%r10
adc %r15,%r14
- sbb %r15,%r15 # top-most carry
+ lea ($aptr,$num),$aptr # rewind $aptr
+ adc $zero,$zero # top-most carry
mov %r14,-1*8($tptr)
- cmp 16(%rsp),$bptr
+ cmp %r10,$bptr
jb .Lmulx4x_outer
+ mov -16($nptr),%r10
+ xor %r15,%r15
+ sub %r14,%r10 # compare top-most words
+ adc %r15,%r15
+ or %r15,$zero
+ xor \$1,$zero
+ lea ($tptr,$num),%rdi # rewind $tptr
+ lea ($nptr,$num,2),$nptr # rewind $nptr
+ .byte 0x67,0x67
+ sar \$3+2,$num # cf=0
+ lea ($nptr,$zero,8),%rbp
+ mov 56+8(%rsp),%rdx # restore rp
+ mov $num,%rcx
+ jmp .Lsqrx4x_sub # common post-condition
+.size mulx4x_internal,.-mulx4x_internal
+___
+}\f{
+######################################################################
+# void bn_power5(
+my $rptr="%rdi"; # BN_ULONG *rptr,
+my $aptr="%rsi"; # const BN_ULONG *aptr,
+my $bptr="%rdx"; # const void *table,
+my $nptr="%rcx"; # const BN_ULONG *nptr,
+my $n0 ="%r8"; # const BN_ULONG *n0);
+my $num ="%r9"; # int num, has to be divisible by 8
+ # int pwr);
+
+my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
+my @A0=("%r10","%r11");
+my @A1=("%r12","%r13");
+my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
+
+$code.=<<___;
+.type bn_powerx5,\@function,6
+.align 32
+bn_powerx5:
+.Lpowerx5_enter:
+ .byte 0x67
+ mov %rsp,%rax
+ push %rbx
+ push %rbp
+ push %r12
+ push %r13
+ push %r14
+ push %r15
+___
+$code.=<<___ if ($win64);
+ lea -0x28(%rsp),%rsp
+ movaps %xmm6,(%rsp)
+ movaps %xmm7,0x10(%rsp)
+___
+$code.=<<___;
+ .byte 0x67
+ mov ${num}d,%r10d
+ shl \$3,${num}d # convert $num to bytes
+ shl \$3+2,%r10d # 4*$num
neg $num
- mov 32(%rsp),$rptr # restore rp
- lea 64(%rsp),$tptr
+ mov ($n0),$n0 # *n0
- xor %rdx,%rdx
+ ##############################################################
+ # ensure that stack frame doesn't alias with $aptr+4*$num
+ # modulo 4096, which covers ret[num], am[num] and n[2*num]
+ # (see bn_exp.c). this is done to allow memory disambiguation
+ # logic do its magic.
+ #
+ lea -64(%rsp,$num,2),%r11
+ sub $aptr,%r11
+ and \$4095,%r11
+ cmp %r11,%r10
+ jb .Lpwrx_sp_alt
+ sub %r11,%rsp # align with $aptr
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ jmp .Lpwrx_sp_done
+
+.align 32
+.Lpwrx_sp_alt:
+ lea 4096-64(,$num,2),%r10 # 4096-frame-2*$num
+ lea -64(%rsp,$num,2),%rsp # alloca(frame+2*$num)
+ sub %r10,%r11
+ mov \$0,%r10
+ cmovc %r10,%r11
+ sub %r11,%rsp
+.Lpwrx_sp_done:
+ and \$-64,%rsp
+ mov $num,%r10
+ neg $num
+
+ ##############################################################
+ # Stack layout
+ #
+ # +0 saved $num, used in reduction section
+ # +8 &t[2*$num], used in reduction section
+ # +16 intermediate carry bit
+ # +24 top-most carry bit, used in reduction section
+ # +32 saved *n0
+ # +40 saved %rsp
+ # +48 t[2*$num]
+ #
pxor %xmm0,%xmm0
- mov 0*8($nptr,$num),%r8
- mov 1*8($nptr,$num),%r9
- neg %r8
- jmp .Lmulx4x_sub_entry
+ movq $rptr,%xmm1 # save $rptr
+ movq $nptr,%xmm2 # save $nptr
+ movq %r10, %xmm3 # -$num
+ movq $bptr,%xmm4
+ mov $n0, 32(%rsp)
+ mov %rax, 40(%rsp) # save original %rsp
+.Lpowerx5_body:
+
+ call __bn_sqrx8x_internal
+ call __bn_sqrx8x_internal
+ call __bn_sqrx8x_internal
+ call __bn_sqrx8x_internal
+ call __bn_sqrx8x_internal
+
+ mov %r10,$num # -num
+ mov $aptr,$rptr
+ movq %xmm2,$nptr
+ movq %xmm4,$bptr
+ mov 40(%rsp),%rax
+
+ call mulx4x_internal
+
+ mov 40(%rsp),%rsi # restore %rsp
+ mov \$1,%rax
+___
+$code.=<<___ if ($win64);
+ movaps -88(%rsi),%xmm6
+ movaps -72(%rsi),%xmm7
+___
+$code.=<<___;
+ mov -48(%rsi),%r15
+ mov -40(%rsi),%r14
+ mov -32(%rsi),%r13
+ mov -24(%rsi),%r12
+ mov -16(%rsi),%rbp
+ mov -8(%rsi),%rbx
+ lea (%rsi),%rsp
+.Lpowerx5_epilogue:
+ ret
+.size bn_powerx5,.-bn_powerx5
+.globl bn_sqrx8x_internal
+.hidden bn_sqrx8x_internal
+.type bn_sqrx8x_internal,\@abi-omnipotent
.align 32
-.Lmulx4x_sub:
- mov 0*8($nptr,$num),%r8
- mov 1*8($nptr,$num),%r9
- not %r8
-.Lmulx4x_sub_entry:
- mov 2*8($nptr,$num),%r10
- not %r9
- and %r15,%r8
- mov 3*8($nptr,$num),%r11
- not %r10
- and %r15,%r9
- not %r11
- and %r15,%r10
- and %r15,%r11
-
- neg %rdx # mov %rdx,%cf
- adc 0*8($tptr),%r8
- adc 1*8($tptr),%r9
- movdqa %xmm0,($tptr)
+bn_sqrx8x_internal:
+__bn_sqrx8x_internal:
+ ##################################################################
+ # Squaring part:
+ #
+ # a) multiply-n-add everything but a[i]*a[i];
+ # b) shift result of a) by 1 to the left and accumulate
+ # a[i]*a[i] products;
+ #
+ ##################################################################
+ # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
+ # a[1]a[0]
+ # a[2]a[0]
+ # a[3]a[0]
+ # a[2]a[1]
+ # a[3]a[1]
+ # a[3]a[2]
+ #
+ # a[4]a[0]
+ # a[5]a[0]
+ # a[6]a[0]
+ # a[7]a[0]
+ # a[4]a[1]
+ # a[5]a[1]
+ # a[6]a[1]
+ # a[7]a[1]
+ # a[4]a[2]
+ # a[5]a[2]
+ # a[6]a[2]
+ # a[7]a[2]
+ # a[4]a[3]
+ # a[5]a[3]
+ # a[6]a[3]
+ # a[7]a[3]
+ #
+ # a[5]a[4]
+ # a[6]a[4]
+ # a[7]a[4]
+ # a[6]a[5]
+ # a[7]a[5]
+ # a[7]a[6]
+ # a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
+___
+{
+my ($zero,$carry)=("%rbp","%rcx");
+my $aaptr=$zero;
+$code.=<<___;
+ lea 48+8(%rsp),$tptr
+ lea ($aptr,$num),$aaptr
+ mov $num,0+8(%rsp) # save $num
+ mov $aaptr,8+8(%rsp) # save end of $aptr
+ jmp .Lsqr8x_zero_start
+
+.align 32
+.byte 0x66,0x66,0x66,0x2e,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
+.Lsqrx8x_zero:
+ .byte 0x3e
+ movdqa %xmm0,0*8($tptr)
+ movdqa %xmm0,2*8($tptr)
+ movdqa %xmm0,4*8($tptr)
+ movdqa %xmm0,6*8($tptr)
+.Lsqr8x_zero_start: # aligned at 32
+ movdqa %xmm0,8*8($tptr)
+ movdqa %xmm0,10*8($tptr)
+ movdqa %xmm0,12*8($tptr)
+ movdqa %xmm0,14*8($tptr)
+ lea 16*8($tptr),$tptr
+ sub \$64,$num
+ jnz .Lsqrx8x_zero
+
+ mov 0*8($aptr),%rdx # a[0], modulo-scheduled
+ #xor %r9,%r9 # t[1], ex-$num, zero already
+ xor %r10,%r10
+ xor %r11,%r11
+ xor %r12,%r12
+ xor %r13,%r13
+ xor %r14,%r14
+ xor %r15,%r15
+ lea 48+8(%rsp),$tptr
+ xor $zero,$zero # cf=0, cf=0
+ jmp .Lsqrx8x_outer_loop
+
+.align 32
+.Lsqrx8x_outer_loop:
+ mulx 1*8($aptr),%r8,%rax # a[1]*a[0]
+ adcx %r9,%r8 # a[1]*a[0]+=t[1]
+ adox %rax,%r10
+ mulx 2*8($aptr),%r9,%rax # a[2]*a[0]
+ adcx %r10,%r9
+ adox %rax,%r11
+ .byte 0xc4,0xe2,0xab,0xf6,0x86,0x18,0x00,0x00,0x00 # mulx 3*8($aptr),%r10,%rax # ...
+ adcx %r11,%r10
+ adox %rax,%r12
+ .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x20,0x00,0x00,0x00 # mulx 4*8($aptr),%r11,%rax
+ adcx %r12,%r11
+ adox %rax,%r13
+ mulx 5*8($aptr),%r12,%rax
+ adcx %r13,%r12
+ adox %rax,%r14
+ mulx 6*8($aptr),%r13,%rax
+ adcx %r14,%r13
+ adox %r15,%rax
+ mulx 7*8($aptr),%r14,%r15
+ mov 1*8($aptr),%rdx # a[1]
+ adcx %rax,%r14
+ adox $zero,%r15
+ adc 8*8($tptr),%r15
+ mov %r8,1*8($tptr) # t[1]
+ mov %r9,2*8($tptr) # t[2]
+ sbb $carry,$carry # mov %cf,$carry
+ xor $zero,$zero # cf=0, of=0
+
+
+ mulx 2*8($aptr),%r8,%rbx # a[2]*a[1]
+ mulx 3*8($aptr),%r9,%rax # a[3]*a[1]
+ adcx %r10,%r8
+ adox %rbx,%r9
+ mulx 4*8($aptr),%r10,%rbx # ...
+ adcx %r11,%r9
+ adox %rax,%r10
+ .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x28,0x00,0x00,0x00 # mulx 5*8($aptr),%r11,%rax
+ adcx %r12,%r10
+ adox %rbx,%r11
+ .byte 0xc4,0xe2,0x9b,0xf6,0x9e,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r12,%rbx
+ adcx %r13,%r11
+ adox %r14,%r12
+ .byte 0xc4,0x62,0x93,0xf6,0xb6,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r13,%r14
+ mov 2*8($aptr),%rdx # a[2]
+ adcx %rax,%r12
+ adox %rbx,%r13
+ adcx %r15,%r13
+ adox $zero,%r14 # of=0
+ adcx $zero,%r14 # cf=0
+
+ mov %r8,3*8($tptr) # t[3]
+ mov %r9,4*8($tptr) # t[4]
+
+ mulx 3*8($aptr),%r8,%rbx # a[3]*a[2]
+ mulx 4*8($aptr),%r9,%rax # a[4]*a[2]
+ adcx %r10,%r8
+ adox %rbx,%r9
+ mulx 5*8($aptr),%r10,%rbx # ...
+ adcx %r11,%r9
+ adox %rax,%r10
+ .byte 0xc4,0xe2,0xa3,0xf6,0x86,0x30,0x00,0x00,0x00 # mulx 6*8($aptr),%r11,%rax
+ adcx %r12,%r10
+ adox %r13,%r11
+ .byte 0xc4,0x62,0x9b,0xf6,0xae,0x38,0x00,0x00,0x00 # mulx 7*8($aptr),%r12,%r13
+ .byte 0x3e
+ mov 3*8($aptr),%rdx # a[3]
+ adcx %rbx,%r11
+ adox %rax,%r12
+ adcx %r14,%r12
+ mov %r8,5*8($tptr) # t[5]
+ mov %r9,6*8($tptr) # t[6]
+ mulx 4*8($aptr),%r8,%rax # a[4]*a[3]
+ adox $zero,%r13 # of=0
+ adcx $zero,%r13 # cf=0
+
+ mulx 5*8($aptr),%r9,%rbx # a[5]*a[3]
+ adcx %r10,%r8
+ adox %rax,%r9
+ mulx 6*8($aptr),%r10,%rax # ...
+ adcx %r11,%r9
+ adox %r12,%r10
+ mulx 7*8($aptr),%r11,%r12
+ mov 4*8($aptr),%rdx # a[4]
+ mov 5*8($aptr),%r14 # a[5]
+ adcx %rbx,%r10
+ adox %rax,%r11
+ mov 6*8($aptr),%r15 # a[6]
+ adcx %r13,%r11
+ adox $zero,%r12 # of=0
+ adcx $zero,%r12 # cf=0
+
+ mov %r8,7*8($tptr) # t[7]
+ mov %r9,8*8($tptr) # t[8]
+
+ mulx %r14,%r9,%rax # a[5]*a[4]
+ mov 7*8($aptr),%r8 # a[7]
+ adcx %r10,%r9
+ mulx %r15,%r10,%rbx # a[6]*a[4]
+ adox %rax,%r10
+ adcx %r11,%r10
+ mulx %r8,%r11,%rax # a[7]*a[4]
+ mov %r14,%rdx # a[5]
+ adox %rbx,%r11
+ adcx %r12,%r11
+ #adox $zero,%rax # of=0
+ adcx $zero,%rax # cf=0
+
+ mulx %r15,%r14,%rbx # a[6]*a[5]
+ mulx %r8,%r12,%r13 # a[7]*a[5]
+ mov %r15,%rdx # a[6]
+ lea 8*8($aptr),$aptr
+ adcx %r14,%r11
+ adox %rbx,%r12
+ adcx %rax,%r12
+ adox $zero,%r13
+
+ .byte 0x67,0x67
+ mulx %r8,%r8,%r14 # a[7]*a[6]
+ adcx %r8,%r13
+ adcx $zero,%r14
+
+ cmp 8+8(%rsp),$aptr
+ je .Lsqrx8x_outer_break
+
+ neg $carry # mov $carry,%cf
+ mov \$-8,%rcx
+ mov $zero,%r15
+ mov 8*8($tptr),%r8
+ adcx 9*8($tptr),%r9 # +=t[9]
+ adcx 10*8($tptr),%r10 # ...
+ adcx 11*8($tptr),%r11
+ adc 12*8($tptr),%r12
+ adc 13*8($tptr),%r13
+ adc 14*8($tptr),%r14
+ adc 15*8($tptr),%r15
+ lea ($aptr),$aaptr
+ lea 2*64($tptr),$tptr
+ sbb %rax,%rax # mov %cf,$carry
+
+ mov -64($aptr),%rdx # a[0]
+ mov %rax,16+8(%rsp) # offload $carry
+ mov $tptr,24+8(%rsp)
+
+ #lea 8*8($tptr),$tptr # see 2*8*8($tptr) above
+ xor %eax,%eax # cf=0, of=0
+ jmp .Lsqrx8x_loop
+
+.align 32
+.Lsqrx8x_loop:
+ mov %r8,%rbx
+ mulx 0*8($aaptr),%rax,%r8 # a[8]*a[i]
+ adcx %rax,%rbx # +=t[8]
+ adox %r9,%r8
+
+ mulx 1*8($aaptr),%rax,%r9 # ...
+ adcx %rax,%r8
+ adox %r10,%r9
+
+ mulx 2*8($aaptr),%rax,%r10
+ adcx %rax,%r9
+ adox %r11,%r10
+
+ mulx 3*8($aaptr),%rax,%r11
+ adcx %rax,%r10
+ adox %r12,%r11
+
+ .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00 # mulx 4*8($aaptr),%rax,%r12
+ adcx %rax,%r11
+ adox %r13,%r12
+
+ mulx 5*8($aaptr),%rax,%r13
+ adcx %rax,%r12
+ adox %r14,%r13
+
+ mulx 6*8($aaptr),%rax,%r14
+ mov %rbx,($tptr,%rcx,8) # store t[8+i]
+ mov \$0,%ebx
+ adcx %rax,%r13
+ adox %r15,%r14
+
+ .byte 0xc4,0x62,0xfb,0xf6,0xbd,0x38,0x00,0x00,0x00 # mulx 7*8($aaptr),%rax,%r15
+ mov 8($aptr,%rcx,8),%rdx # a[i]
+ adcx %rax,%r14
+ adox %rbx,%r15 # %rbx is 0, of=0
+ adcx %rbx,%r15 # cf=0
+
+ .byte 0x67
+ inc %rcx # of=0
+ jnz .Lsqrx8x_loop
+
+ lea 8*8($aaptr),$aaptr
+ mov \$-8,%rcx
+ cmp 8+8(%rsp),$aaptr # done?
+ je .Lsqrx8x_break
+
+ sub 16+8(%rsp),%rbx # mov 16(%rsp),%cf
+ .byte 0x66
+ mov -64($aptr),%rdx
+ adcx 0*8($tptr),%r8
+ adcx 1*8($tptr),%r9
adc 2*8($tptr),%r10
adc 3*8($tptr),%r11
- movdqa %xmm0,16($tptr)
- lea 4*8($tptr),$tptr
- sbb %rdx,%rdx # mov %cf,%rdx
+ adc 4*8($tptr),%r12
+ adc 5*8($tptr),%r13
+ adc 6*8($tptr),%r14
+ adc 7*8($tptr),%r15
+ lea 8*8($tptr),$tptr
+ .byte 0x67
+ sbb %rax,%rax # mov %cf,%rax
+ xor %ebx,%ebx # cf=0, of=0
+ mov %rax,16+8(%rsp) # offload carry
+ jmp .Lsqrx8x_loop
- mov %r8,0*8($rptr)
- mov %r9,1*8($rptr)
- mov %r10,2*8($rptr)
- mov %r11,3*8($rptr)
- lea 4*8($rptr),$rptr
+.align 32
+.Lsqrx8x_break:
+ sub 16+8(%rsp),%r8 # consume last carry
+ mov 24+8(%rsp),$carry # initial $tptr, borrow $carry
+ mov 0*8($aptr),%rdx # a[8], modulo-scheduled
+ xor %ebp,%ebp # xor $zero,$zero
+ mov %r8,0*8($tptr)
+ cmp $carry,$tptr # cf=0, of=0
+ je .Lsqrx8x_outer_loop
+
+ mov %r9,1*8($tptr)
+ mov 1*8($carry),%r9
+ mov %r10,2*8($tptr)
+ mov 2*8($carry),%r10
+ mov %r11,3*8($tptr)
+ mov 3*8($carry),%r11
+ mov %r12,4*8($tptr)
+ mov 4*8($carry),%r12
+ mov %r13,5*8($tptr)
+ mov 5*8($carry),%r13
+ mov %r14,6*8($tptr)
+ mov 6*8($carry),%r14
+ mov %r15,7*8($tptr)
+ mov 7*8($carry),%r15
+ mov $carry,$tptr
+ jmp .Lsqrx8x_outer_loop
- add \$32,$num
- jnz .Lmulx4x_sub
+.align 32
+.Lsqrx8x_outer_break:
+ mov %r9,9*8($tptr) # t[9]
+ movq %xmm3,%rcx # -$num
+ mov %r10,10*8($tptr) # ...
+ mov %r11,11*8($tptr)
+ mov %r12,12*8($tptr)
+ mov %r13,13*8($tptr)
+ mov %r14,14*8($tptr)
+___
+}\f{
+my $i="%rcx";
+$code.=<<___;
+ lea 48+8(%rsp),$tptr
+ mov ($aptr,$i),%rdx # a[0]
- mov 56(%rsp),%rsi # restore %rsp
- mov \$1,%rax
+ mov 8($tptr),$A0[1] # t[1]
+ xor $A0[0],$A0[0] # t[0], of=0, cf=0
+ mov 0+8(%rsp),$num # restore $num
+ adox $A0[1],$A0[1]
+ mov 16($tptr),$A1[0] # t[2] # prefetch
+ mov 24($tptr),$A1[1] # t[3] # prefetch
+ #jmp .Lsqrx4x_shift_n_add # happens to be aligned
+
+.align 32
+.Lsqrx4x_shift_n_add:
+ mulx %rdx,%rax,%rbx
+ adox $A1[0],$A1[0]
+ adcx $A0[0],%rax
+ .byte 0x48,0x8b,0x94,0x0e,0x08,0x00,0x00,0x00 # mov 8($aptr,$i),%rdx # a[i+1] # prefetch
+ .byte 0x4c,0x8b,0x97,0x20,0x00,0x00,0x00 # mov 32($tptr),$A0[0] # t[2*i+4] # prefetch
+ adox $A1[1],$A1[1]
+ adcx $A0[1],%rbx
+ mov 40($tptr),$A0[1] # t[2*i+4+1] # prefetch
+ mov %rax,0($tptr)
+ mov %rbx,8($tptr)
+
+ mulx %rdx,%rax,%rbx
+ adox $A0[0],$A0[0]
+ adcx $A1[0],%rax
+ mov 16($aptr,$i),%rdx # a[i+2] # prefetch
+ mov 48($tptr),$A1[0] # t[2*i+6] # prefetch
+ adox $A0[1],$A0[1]
+ adcx $A1[1],%rbx
+ mov 56($tptr),$A1[1] # t[2*i+6+1] # prefetch
+ mov %rax,16($tptr)
+ mov %rbx,24($tptr)
+
+ mulx %rdx,%rax,%rbx
+ adox $A1[0],$A1[0]
+ adcx $A0[0],%rax
+ mov 24($aptr,$i),%rdx # a[i+3] # prefetch
+ lea 32($i),$i
+ mov 64($tptr),$A0[0] # t[2*i+8] # prefetch
+ adox $A1[1],$A1[1]
+ adcx $A0[1],%rbx
+ mov 72($tptr),$A0[1] # t[2*i+8+1] # prefetch
+ mov %rax,32($tptr)
+ mov %rbx,40($tptr)
+
+ mulx %rdx,%rax,%rbx
+ adox $A0[0],$A0[0]
+ adcx $A1[0],%rax
+ jrcxz .Lsqrx4x_shift_n_add_break
+ .byte 0x48,0x8b,0x94,0x0e,0x00,0x00,0x00,0x00 # mov 0($aptr,$i),%rdx # a[i+4] # prefetch
+ adox $A0[1],$A0[1]
+ adcx $A1[1],%rbx
+ mov 80($tptr),$A1[0] # t[2*i+10] # prefetch
+ mov 88($tptr),$A1[1] # t[2*i+10+1] # prefetch
+ mov %rax,48($tptr)
+ mov %rbx,56($tptr)
+ lea 64($tptr),$tptr
+ nop
+ jmp .Lsqrx4x_shift_n_add
+
+.align 32
+.Lsqrx4x_shift_n_add_break:
+ adcx $A1[1],%rbx
+ mov %rax,48($tptr)
+ mov %rbx,56($tptr)
+ lea 64($tptr),$tptr # end of t[] buffer
___
-$code.=<<___ if ($win64);
- movaps (%rsi),%xmm6
- movaps 0x10(%rsi),%xmm7
- lea 0x28(%rsi),%rsi
+}\f
+######################################################################
+# Montgomery reduction part, "word-by-word" algorithm.
+#
+# This new path is inspired by multiple submissions from Intel, by
+# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
+# Vinodh Gopal...
+{
+my ($nptr,$carry,$m0)=("%rbp","%rsi","%rdx");
+
+$code.=<<___;
+ movq %xmm2,$nptr
+sqrx8x_reduction:
+ xor %eax,%eax # initial top-most carry bit
+ mov 32+8(%rsp),%rbx # n0
+ mov 48+8(%rsp),%rdx # "%r8", 8*0($tptr)
+ lea -128($nptr,$num,2),%rcx # end of n[]
+ #lea 48+8(%rsp,$num,2),$tptr # end of t[] buffer
+ mov %rcx, 0+8(%rsp) # save end of n[]
+ mov $tptr,8+8(%rsp) # save end of t[]
+
+ lea 48+8(%rsp),$tptr # initial t[] window
+ jmp .Lsqrx8x_reduction_loop
+
+.align 32
+.Lsqrx8x_reduction_loop:
+ mov 8*1($tptr),%r9
+ mov 8*2($tptr),%r10
+ mov 8*3($tptr),%r11
+ mov 8*4($tptr),%r12
+ mov %rdx,%r8
+ imulq %rbx,%rdx # n0*a[i]
+ mov 8*5($tptr),%r13
+ mov 8*6($tptr),%r14
+ mov 8*7($tptr),%r15
+ mov %rax,24+8(%rsp) # store top-most carry bit
+
+ lea 8*8($tptr),$tptr
+ xor $carry,$carry # cf=0,of=0
+ mov \$-8,%rcx
+ jmp .Lsqrx8x_reduce
+
+.align 32
+.Lsqrx8x_reduce:
+ mov %r8, %rbx
+ mulx 16*0($nptr),%rax,%r8 # n[0]
+ adcx %rbx,%rax # discarded
+ adox %r9,%r8
+
+ mulx 16*1($nptr),%rbx,%r9 # n[1]
+ adcx %rbx,%r8
+ adox %r10,%r9
+
+ mulx 16*2($nptr),%rbx,%r10
+ adcx %rbx,%r9
+ adox %r11,%r10
+
+ mulx 16*3($nptr),%rbx,%r11
+ adcx %rbx,%r10
+ adox %r12,%r11
+
+ .byte 0xc4,0x62,0xe3,0xf6,0xa5,0x40,0x00,0x00,0x00 # mulx 16*4($nptr),%rbx,%r12
+ mov %rdx,%rax
+ mov %r8,%rdx
+ adcx %rbx,%r11
+ adox %r13,%r12
+
+ mulx 32+8(%rsp),%rbx,%rdx # %rdx discarded
+ mov %rax,%rdx
+ mov %rax,64+48+8(%rsp,%rcx,8) # put aside n0*a[i]
+
+ mulx 16*5($nptr),%rax,%r13
+ adcx %rax,%r12
+ adox %r14,%r13
+
+ mulx 16*6($nptr),%rax,%r14
+ adcx %rax,%r13
+ adox %r15,%r14
+
+ mulx 16*7($nptr),%rax,%r15
+ mov %rbx,%rdx
+ adcx %rax,%r14
+ adox $carry,%r15 # $carry is 0
+ adcx $carry,%r15 # cf=0
+
+ .byte 0x67,0x67,0x67
+ inc %rcx # of=0
+ jnz .Lsqrx8x_reduce
+
+ mov $carry,%rax # xor %rax,%rax
+ cmp 0+8(%rsp),$nptr # end of n[]?
+ jae .Lsqrx8x_no_tail
+
+ mov 48+8(%rsp),%rdx # pull n0*a[0]
+ add 8*0($tptr),%r8
+ lea 16*8($nptr),$nptr
+ mov \$-8,%rcx
+ adcx 8*1($tptr),%r9
+ adcx 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ lea 8*8($tptr),$tptr
+ sbb %rax,%rax # top carry
+
+ xor $carry,$carry # of=0, cf=0
+ mov %rax,16+8(%rsp)
+ jmp .Lsqrx8x_tail
+
+.align 32
+.Lsqrx8x_tail:
+ mov %r8,%rbx
+ mulx 16*0($nptr),%rax,%r8
+ adcx %rax,%rbx
+ adox %r9,%r8
+
+ mulx 16*1($nptr),%rax,%r9
+ adcx %rax,%r8
+ adox %r10,%r9
+
+ mulx 16*2($nptr),%rax,%r10
+ adcx %rax,%r9
+ adox %r11,%r10
+
+ mulx 16*3($nptr),%rax,%r11
+ adcx %rax,%r10
+ adox %r12,%r11
+
+ .byte 0xc4,0x62,0xfb,0xf6,0xa5,0x40,0x00,0x00,0x00 # mulx 16*4($nptr),%rax,%r12
+ adcx %rax,%r11
+ adox %r13,%r12
+
+ mulx 16*5($nptr),%rax,%r13
+ adcx %rax,%r12
+ adox %r14,%r13
+
+ mulx 16*6($nptr),%rax,%r14
+ adcx %rax,%r13
+ adox %r15,%r14
+
+ mulx 16*7($nptr),%rax,%r15
+ mov 72+48+8(%rsp,%rcx,8),%rdx # pull n0*a[i]
+ adcx %rax,%r14
+ adox $carry,%r15
+ mov %rbx,($tptr,%rcx,8) # save result
+ mov %r8,%rbx
+ adcx $carry,%r15 # cf=0
+
+ inc %rcx # of=0
+ jnz .Lsqrx8x_tail
+
+ cmp 0+8(%rsp),$nptr # end of n[]?
+ jae .Lsqrx8x_tail_done # break out of loop
+
+ sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
+ mov 48+8(%rsp),%rdx # pull n0*a[0]
+ lea 16*8($nptr),$nptr
+ adc 8*0($tptr),%r8
+ adc 8*1($tptr),%r9
+ adc 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ lea 8*8($tptr),$tptr
+ sbb %rax,%rax
+ sub \$8,%rcx # mov \$-8,%rcx
+
+ xor $carry,$carry # of=0, cf=0
+ mov %rax,16+8(%rsp)
+ jmp .Lsqrx8x_tail
+
+.align 32
+.Lsqrx8x_tail_done:
+ add 24+8(%rsp),%r8 # can this overflow?
+ mov $carry,%rax # xor %rax,%rax
+
+ sub 16+8(%rsp),$carry # mov 16(%rsp),%cf
+.Lsqrx8x_no_tail: # %cf is 0 if jumped here
+ adc 8*0($tptr),%r8
+ movq %xmm3,%rcx
+ adc 8*1($tptr),%r9
+ mov 16*7($nptr),$carry
+ movq %xmm2,$nptr # restore $nptr
+ adc 8*2($tptr),%r10
+ adc 8*3($tptr),%r11
+ adc 8*4($tptr),%r12
+ adc 8*5($tptr),%r13
+ adc 8*6($tptr),%r14
+ adc 8*7($tptr),%r15
+ adc %rax,%rax # top-most carry
+
+ mov 32+8(%rsp),%rbx # n0
+ mov 8*8($tptr,%rcx),%rdx # modulo-scheduled "%r8"
+
+ mov %r8,8*0($tptr) # store top 512 bits
+ lea 8*8($tptr),%r8 # borrow %r8
+ mov %r9,8*1($tptr)
+ mov %r10,8*2($tptr)
+ mov %r11,8*3($tptr)
+ mov %r12,8*4($tptr)
+ mov %r13,8*5($tptr)
+ mov %r14,8*6($tptr)
+ mov %r15,8*7($tptr)
+
+ lea 8*8($tptr,%rcx),$tptr # start of current t[] window
+ cmp 8+8(%rsp),%r8 # end of t[]?
+ jb .Lsqrx8x_reduction_loop
___
+}\f
+##############################################################
+# Post-condition, 4x unrolled
+#
+{
+my ($rptr,$nptr)=("%rdx","%rbp");
+my @ri=map("%r$_",(10..13));
+my @ni=map("%r$_",(14..15));
$code.=<<___;
- mov (%rsi),%r15
- mov 8(%rsi),%r14
- mov 16(%rsi),%r13
- mov 24(%rsi),%r12
- mov 32(%rsi),%rbp
- mov 40(%rsi),%rbx
- lea 48(%rsi),%rsp
-.Lmulx4x_epilogue:
+ xor %rbx,%rbx
+ sub %r15,%rsi # compare top-most words
+ adc %rbx,%rbx
+ mov %rcx,%r10 # -$num
+ .byte 0x67
+ or %rbx,%rax
+ .byte 0x67
+ mov %rcx,%r9 # -$num
+ xor \$1,%rax
+ sar \$3+2,%rcx # cf=0
+ #lea 48+8(%rsp,%r9),$tptr
+ lea ($nptr,%rax,8),$nptr
+ movq %xmm1,$rptr # restore $rptr
+ movq %xmm1,$aptr # prepare for back-to-back call
+ jmp .Lsqrx4x_sub
+
+.align 32
+.Lsqrx4x_sub:
+ .byte 0x66
+ mov 8*0($tptr),%r12
+ mov 8*1($tptr),%r13
+ sbb 16*0($nptr),%r12
+ mov 8*2($tptr),%r14
+ sbb 16*1($nptr),%r13
+ mov 8*3($tptr),%r15
+ lea 8*4($tptr),$tptr
+ sbb 16*2($nptr),%r14
+ mov %r12,8*0($rptr)
+ sbb 16*3($nptr),%r15
+ lea 16*4($nptr),$nptr
+ mov %r13,8*1($rptr)
+ mov %r14,8*2($rptr)
+ mov %r15,8*3($rptr)
+ lea 8*4($rptr),$rptr
+
+ inc %rcx
+ jnz .Lsqrx4x_sub
+___
+}
+$code.=<<___;
+ neg %r9 # restore $num
+
ret
-.size bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
+.size bn_sqrx8x_internal,.-bn_sqrx8x_internal
___
}}}
{
-my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%rdx","%r8", "%r9") : # Win64 order
- ("%rdi","%rsi","%rdx","%rcx"); # Unix order
+my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%edx","%r8", "%r9d") : # Win64 order
+ ("%rdi","%esi","%rdx","%ecx"); # Unix order
my $out=$inp;
my $STRIDE=2**5*8;
my $N=$STRIDE/4;
$code.=<<___;
+.globl bn_get_bits5
+.type bn_get_bits5,\@abi-omnipotent
+.align 16
+bn_get_bits5:
+ mov $inp,%r10
+ mov $num,%ecx
+ shr \$3,$num
+ movzw (%r10,$num),%eax
+ and \$7,%ecx
+ shrl %cl,%eax
+ and \$31,%eax
+ ret
+.size bn_get_bits5,.-bn_get_bits5
+
.globl bn_scatter5
.type bn_scatter5,\@abi-omnipotent
.align 16
.byte 0x0f,0x29,0x7c,0x24,0x10 #movdqa %xmm7,0x10(%rsp)
___
$code.=<<___;
- mov $idx,%r11
+ mov $idx,%r11d
shr \$`log($N/8)/log(2)`,$idx
and \$`$N/8-1`,%r11
not $idx
lea .Lmagic_masks(%rip),%rax
and \$`2**5/($N/8)-1`,$idx # 5 is "window size"
- lea 96($tbl,%r11,8),$tbl # pointer within 1st cache line
+ lea 128($tbl,%r11,8),$tbl # pointer within 1st cache line
movq 0(%rax,$idx,8),%xmm4 # set of masks denoting which
movq 8(%rax,$idx,8),%xmm5 # cache line contains element
movq 16(%rax,$idx,8),%xmm6 # denoted by 7th argument
jmp .Lgather
.align 16
.Lgather:
- movq `0*$STRIDE/4-96`($tbl),%xmm0
- movq `1*$STRIDE/4-96`($tbl),%xmm1
+ movq `0*$STRIDE/4-128`($tbl),%xmm0
+ movq `1*$STRIDE/4-128`($tbl),%xmm1
pand %xmm4,%xmm0
- movq `2*$STRIDE/4-96`($tbl),%xmm2
+ movq `2*$STRIDE/4-128`($tbl),%xmm2
pand %xmm5,%xmm1
- movq `3*$STRIDE/4-96`($tbl),%xmm3
+ movq `3*$STRIDE/4-128`($tbl),%xmm3
pand %xmm6,%xmm2
por %xmm1,%xmm0
pand %xmm7,%xmm3
+ .byte 0x67,0x67
por %xmm2,%xmm0
lea $STRIDE($tbl),$tbl
por %xmm3,%xmm0
cmp %r10,%rbx # context->Rip<end of prologue label
jb .Lcommon_seh_tail
- lea `40+48`(%rax),%rax
-
- mov 4(%r11),%r10d # HandlerData[1]
- lea (%rsi,%r10),%r10 # end of alloca label
- cmp %r10,%rbx # context->Rip<end of alloca label
- jb .Lcommon_seh_tail
-
mov 152($context),%rax # pull context->Rsp
- mov 8(%r11),%r10d # HandlerData[2]
+ mov 4(%r11),%r10d # HandlerData[1]
lea (%rsi,%r10),%r10 # epilogue label
cmp %r10,%rbx # context->Rip>=epilogue label
jae .Lcommon_seh_tail
+ lea .Lmul_epilogue(%rip),%r10
+ cmp %r10,%rbx
+ jb .Lbody_40
+
mov 192($context),%r10 # pull $num
mov 8(%rax,%r10,8),%rax # pull saved stack pointer
+ jmp .Lbody_proceed
- movaps (%rax),%xmm0
- movaps 16(%rax),%xmm1
- lea `40+48`(%rax),%rax
+.Lbody_40:
+ mov 40(%rax),%rax # pull saved stack pointer
+.Lbody_proceed:
+
+ movaps -88(%rax),%xmm0
+ movaps -72(%rax),%xmm1
mov -8(%rax),%rbx
mov -16(%rax),%rbp
.rva .LSEH_end_bn_mul4x_mont_gather5
.rva .LSEH_info_bn_mul4x_mont_gather5
+ .rva .LSEH_begin_bn_power5
+ .rva .LSEH_end_bn_power5
+ .rva .LSEH_info_bn_power5
+
+ .rva .LSEH_begin_bn_from_mont8x
+ .rva .LSEH_end_bn_from_mont8x
+ .rva .LSEH_info_bn_from_mont8x
+___
+$code.=<<___ if ($addx);
+ .rva .LSEH_begin_bn_mulx4x_mont_gather5
+ .rva .LSEH_end_bn_mulx4x_mont_gather5
+ .rva .LSEH_info_bn_mulx4x_mont_gather5
+
+ .rva .LSEH_begin_bn_powerx5
+ .rva .LSEH_end_bn_powerx5
+ .rva .LSEH_info_bn_powerx5
+___
+$code.=<<___;
.rva .LSEH_begin_bn_gather5
.rva .LSEH_end_bn_gather5
.rva .LSEH_info_bn_gather5
.LSEH_info_bn_mul_mont_gather5:
.byte 9,0,0,0
.rva mul_handler
- .rva .Lmul_alloca,.Lmul_body,.Lmul_epilogue # HandlerData[]
+ .rva .Lmul_body,.Lmul_epilogue # HandlerData[]
.align 8
.LSEH_info_bn_mul4x_mont_gather5:
.byte 9,0,0,0
.rva mul_handler
- .rva .Lmul4x_alloca,.Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
+ .rva .Lmul4x_body,.Lmul4x_epilogue # HandlerData[]
+.align 8
+.LSEH_info_bn_power5:
+ .byte 9,0,0,0
+ .rva mul_handler
+ .rva .Lpower5_body,.Lpower5_epilogue # HandlerData[]
+.align 8
+.LSEH_info_bn_from_mont8x:
+ .byte 9,0,0,0
+ .rva mul_handler
+ .rva .Lfrom_body,.Lfrom_epilogue # HandlerData[]
+___
+$code.=<<___ if ($addx);
+.align 8
+.LSEH_info_bn_mulx4x_mont_gather5:
+ .byte 9,0,0,0
+ .rva mul_handler
+ .rva .Lmulx4x_body,.Lmulx4x_epilogue # HandlerData[]
+.align 8
+.LSEH_info_bn_powerx5:
+ .byte 9,0,0,0
+ .rva mul_handler
+ .rva .Lpowerx5_body,.Lpowerx5_epilogue # HandlerData[]
+___
+$code.=<<___;
.align 8
.LSEH_info_bn_gather5:
.byte 0x01,0x0d,0x05,0x00
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