From: Andy Polyakov <appro@openssl.org>
Date: Mon, 9 Dec 2013 20:02:24 +0000 (+0100)
Subject: bn/asm/x86_64-mont5.pl: add MULX/AD*X code path.
X-Git-Tag: master-post-reformat~1053
X-Git-Url: https://git.openssl.org/?p=openssl.git;a=commitdiff_plain;h=ec9cc70f72454b8d4a84247c86159613cee83b81;hp=d1671f4f1a39d938499c67efe5d4a14c34c09b31

bn/asm/x86_64-mont5.pl: add MULX/AD*X code path.

This also eliminates code duplication between x86_64-mont and x86_64-mont
and optimizes even original non-MULX code.
---

diff --git a/crypto/bn/asm/x86_64-mont.pl b/crypto/bn/asm/x86_64-mont.pl
index b6db337457..38039286be 100755
--- a/crypto/bn/asm/x86_64-mont.pl
+++ b/crypto/bn/asm/x86_64-mont.pl
@@ -261,7 +261,7 @@ $code.=<<___;
 
 	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]
@@ -442,7 +442,7 @@ $code.=<<___;
 	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]
@@ -590,7 +590,7 @@ $code.=<<___;
 	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]
@@ -636,7 +636,7 @@ $code.=<<___;
 	mov	$N[1],(%rsp,$j,8)	# store upmost overflow bit
 
 	cmp	$num,$i
-	jl	.Louter4x
+	jb	.Louter4x
 ___
 {
 my @ri=("%rax","%rdx",$m0,$m1);
@@ -743,17 +743,14 @@ my @A1=("%r12","%r13");
 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
@@ -761,908 +758,119 @@ $code.=<<___;
 	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)
-___
-}
-######################################################################
-# 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 $num
+.Lsqr8x_nox:
 ___
-}
-##############################################################
-# Post-condition, 4x unrolled copy from bn_mul_mont
-#
-{
-my ($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
@@ -1677,6 +885,7 @@ $code.=<<___;
 .align	32
 bn_mulx4x_mont:
 .Lmulx4x_enter:
+	mov	%rsp,%rax
 	push	%rbx
 	push	%rbp
 	push	%r12
@@ -1687,7 +896,6 @@ bn_mulx4x_mont:
 	shl	\$3,${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)
@@ -1700,9 +908,9 @@ bn_mulx4x_mont:
 	# +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 $num
@@ -1711,8 +919,8 @@ bn_mulx4x_mont:
 	sub	\$1,$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
@@ -1776,7 +984,7 @@ $code.=<<___;
 	mulx	2*8($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
@@ -1817,45 +1025,41 @@ $code.=<<___;
 .align	32
 .Lmulx4x_outer:
 	mov	($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
@@ -1867,22 +1071,21 @@ $code.=<<___;
 	mulx	3*8($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
@@ -1925,12 +1128,17 @@ $code.=<<___;
 	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
@@ -1977,797 +1185,19 @@ $code.=<<___;
 	add	\$32,$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
 ___
-}{
-######################################################################
-# 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)
-___
-}{
-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),$tptr		# end of t[] buffer
-___
-}
-######################################################################
-# Montgomery reduction part, "word-by-word" algorithm.
-#
-# This new path is inspired by multiple submissions from Intel, by
-# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
-# Vinodh Gopal...
-{
-my ($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		# -$num
-	jmp	.Lsqrx8x_post
-___
-}
-##############################################################
-# Post-condition, 8x unrolled
-#
-{
-my ($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>"
@@ -2868,8 +1298,7 @@ sqr_handler:
 	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
@@ -2942,10 +1371,6 @@ $code.=<<___ if ($addx);
 	.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
@@ -2968,10 +1393,6 @@ $code.=<<___ if ($addx);
 	.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[]
 ___
 }
 
diff --git a/crypto/bn/asm/x86_64-mont5.pl b/crypto/bn/asm/x86_64-mont5.pl
index 93257376ac..265ee7d13a 100755
--- a/crypto/bn/asm/x86_64-mont5.pl
+++ b/crypto/bn/asm/x86_64-mont5.pl
@@ -17,6 +17,13 @@
 # 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; }
@@ -74,10 +81,8 @@ $code=<<___;
 .type	bn_mul_mont_gather5,\@function,6
 .align	64
 bn_mul_mont_gather5:
-	test	\$3,${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
@@ -88,6 +93,7 @@ $code.=<<___;
 .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
@@ -100,10 +106,8 @@ $code.=<<___ if ($win64);
 	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))
@@ -309,7 +313,7 @@ $code.=<<___;
 
 	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]
@@ -345,18 +349,17 @@ $code.=<<___;
 	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
@@ -366,7 +369,7 @@ my @A=("%r10","%r11");
 my @N=("%r13","%rdi");
 $code.=<<___;
 .type	bn_mul4x_mont_gather5,\@function,6
-.align	16
+.align	32
 bn_mul4x_mont_gather5:
 .Lmul4x_enter:
 ___
@@ -376,8 +379,8 @@ $code.=<<___ if ($addx);
 	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
@@ -389,23 +392,78 @@ $code.=<<___ if ($win64);
 	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
@@ -413,458 +471,465 @@ $code.=<<___;
 	not	%r10
 	lea	.Lmagic_masks(%rip),%rax
 	and	\$`2**5/($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
+{{{
+######################################################################
+# 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
@@ -879,142 +944,1296 @@ $code.=<<___ if ($win64);
 	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)
+___
+}
+######################################################################
+# 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
+___
+}
+##############################################################
+# 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,$num
+	jnz	.Lfrom_mont_zero
+
+	mov	\$1,%rax
+	mov	-48(%rsi),%r15
+	mov	-40(%rsi),%r14
+	mov	-32(%rsi),%r13
+	mov	-24(%rsi),%r12
+	mov	-16(%rsi),%rbp
+	mov	-8(%rsi),%rbx
+	lea	(%rsi),%rsp
+.Lfrom_epilogue:
+	ret
+.size	bn_from_mont8x,.-bn_from_mont8x
+___
+}
+}}}
+
+if ($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
@@ -1022,125 +2241,114 @@ $code.=<<___;
 	lea	4*8($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
@@ -1149,120 +2357,885 @@ $code.=<<___;
 	adcx	3*8($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
+___
+}{
+######################################################################
+# 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)
+___
+}{
+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 ($win64);
-	movaps	(%rsi),%xmm6
-	movaps	0x10(%rsi),%xmm7
-	lea	0x28(%rsi),%rsi
+}
+######################################################################
+# Montgomery reduction part, "word-by-word" algorithm.
+#
+# This new path is inspired by multiple submissions from Intel, by
+# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
+# Vinodh Gopal...
+{
+my ($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),$tptr	# start of current t[] window
+	cmp	8+8(%rsp),%r8		# end of t[]?
+	jb	.Lsqrx8x_reduction_loop
 ___
+}
+##############################################################
+# Post-condition, 4x unrolled
+#
+{
+my ($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
@@ -1294,13 +3267,13 @@ $code.=<<___ if ($win64);
 	.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
@@ -1308,15 +3281,16 @@ $code.=<<___;
 	jmp	.Lgather
 .align	16
 .Lgather:
-	movq	`0*$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
@@ -1380,26 +3354,27 @@ mul_handler:
 	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
@@ -1466,6 +3441,24 @@ mul_handler:
 	.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
+___
+$code.=<<___;
 	.rva	.LSEH_begin_bn_gather5
 	.rva	.LSEH_end_bn_gather5
 	.rva	.LSEH_info_bn_gather5
@@ -1475,12 +3468,36 @@ mul_handler:
 .LSEH_info_bn_mul_mont_gather5:
 	.byte	9,0,0,0
 	.rva	mul_handler
-	.rva	.Lmul_alloca,.Lmul_body,.Lmul_epilogue		# HandlerData[]
+	.rva	.Lmul_body,.Lmul_epilogue		# HandlerData[]
 .align	8
 .LSEH_info_bn_mul4x_mont_gather5:
 	.byte	9,0,0,0
 	.rva	mul_handler
-	.rva	.Lmul4x_alloca,.Lmul4x_body,.Lmul4x_epilogue	# HandlerData[]
+	.rva	.Lmul4x_body,.Lmul4x_epilogue		# HandlerData[]
+.align	8
+.LSEH_info_bn_power5:
+	.byte	9,0,0,0
+	.rva	mul_handler
+	.rva	.Lpower5_body,.Lpower5_epilogue		# HandlerData[]
+.align	8
+.LSEH_info_bn_from_mont8x:
+	.byte	9,0,0,0
+	.rva	mul_handler
+	.rva	.Lfrom_body,.Lfrom_epilogue		# HandlerData[]
+___
+$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
diff --git a/crypto/bn/bn_exp.c b/crypto/bn/bn_exp.c
index 6e3a7264d5..baeda372cf 100644
--- a/crypto/bn/bn_exp.c
+++ b/crypto/bn/bn_exp.c
@@ -726,7 +726,11 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	else
 #endif
 #if defined(OPENSSL_BN_ASM_MONT5)
-	if (window==6 && bits<=1024) window=5;	/* ~5% improvement of 2048-bit RSA sign */
+	if (window>=5)
+		{
+		window=5;	/* ~5% improvement for RSA2048 sign, and even for RSA4096 */
+		if ((top&7)==0)	powerbufLen += 2*top*sizeof(m->d[0]);
+		}
 #endif
 	(void)0;
 
@@ -734,7 +738,7 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	 * powers of am, am itself and tmp.
 	 */
 	numPowers = 1 << window;
-	powerbufLen = sizeof(m->d[0])*(top*numPowers +
+	powerbufLen += sizeof(m->d[0])*(top*numPowers +
 				((2*top)>numPowers?(2*top):numPowers));
 #ifdef alloca
 	if (powerbufLen < 3072)
@@ -912,14 +916,26 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 			void *table,size_t power);
 	void bn_gather5(BN_ULONG *out,size_t num,
 			void *table,size_t power);
+	void bn_power5(BN_ULONG *rp,const BN_ULONG *ap,
+			const void *table,const BN_ULONG *np,
+			const BN_ULONG *n0,int num,int power);
+	int bn_get_bits5(const BN_ULONG *ap,int off);
+	int bn_from_montgomery(BN_ULONG *rp,const BN_ULONG *ap,
+			const BN_ULONG *not_used,const BN_ULONG *np,
+			const BN_ULONG *n0,int num);
 
-	BN_ULONG *np=mont->N.d, *n0=mont->n0;
+	BN_ULONG *np=mont->N.d, *n0=mont->n0, *np2;
 
 	/* BN_to_montgomery can contaminate words above .top
 	 * [in BN_DEBUG[_DEBUG] build]... */
 	for (i=am.top; i<top; i++)	am.d[i]=0;
 	for (i=tmp.top; i<top; i++)	tmp.d[i]=0;
 
+	if (top&7)
+		np2 = np;
+	else
+		for (np2=am.d+top,i=0; i<top; i++) np2[2*i]=np[i];
+
 	bn_scatter5(tmp.d,top,powerbuf,0);
 	bn_scatter5(am.d,am.top,powerbuf,1);
 	bn_mul_mont(tmp.d,am.d,am.d,np,n0,top);
@@ -929,7 +945,7 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	for (i=3; i<32; i++)
 		{
 		/* Calculate a^i = a^(i-1) * a */
-		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
 		bn_scatter5(tmp.d,top,powerbuf,i);
 		}
 #else
@@ -942,7 +958,7 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	for (i=3; i<8; i+=2)
 		{
 		int j;
-		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
 		bn_scatter5(tmp.d,top,powerbuf,i);
 		for (j=2*i; j<32; j*=2)
 			{
@@ -952,14 +968,14 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 		}
 	for (; i<16; i+=2)
 		{
-		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
 		bn_scatter5(tmp.d,top,powerbuf,i);
 		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
 		bn_scatter5(tmp.d,top,powerbuf,2*i);
 		}
 	for (; i<32; i+=2)
 		{
-		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np,n0,top,i-1);
+		bn_mul_mont_gather5(tmp.d,am.d,powerbuf,np2,n0,top,i-1);
 		bn_scatter5(tmp.d,top,powerbuf,i);
 		}
 #endif
@@ -971,7 +987,8 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 	/* Scan the exponent one window at a time starting from the most
 	 * significant bits.
 	 */
-	while (bits >= 0)
+	if (top&7)
+	    while (bits >= 0)
 		{
 		for (wvalue=0, i=0; i<5; i++,bits--)
 			wvalue = (wvalue<<1)+BN_is_bit_set(p,bits);
@@ -983,9 +1000,24 @@ int BN_mod_exp_mont_consttime(BIGNUM *rr, const BIGNUM *a, const BIGNUM *p,
 		bn_mul_mont(tmp.d,tmp.d,tmp.d,np,n0,top);
 		bn_mul_mont_gather5(tmp.d,tmp.d,powerbuf,np,n0,top,wvalue);
 		}
+	else
+	    {
+	    while (bits >= 0)
+		{
+		wvalue = bn_get_bits5(p->d,bits-4);
+		bits-=5;
+		bn_power5(tmp.d,tmp.d,powerbuf,np2,n0,top,wvalue);
+		}
+	    }
 
+	ret=bn_from_montgomery(tmp.d,tmp.d,NULL,np2,n0,top);
 	tmp.top=top;
 	bn_correct_top(&tmp);
+	if (ret)
+		{
+		if (!BN_copy(rr,&tmp)) ret=0;
+		goto err; /* non-zero ret means it's not error */
+		}
 	}
     else
 #endif