x86_64-mont.pl: futher optimization resulting in up to 48% improvement

(4096-bit RSA sign benchmark on Core2) in comparison to initial version
from 2005.

1 files changed, 1050 insertions, 181 deletions

diff --git a/crypto/bn/asm/x86_64-mont.pl b/crypto/bn/asm/x86_64-mont.pl
index 71b0fe0dd2..4f330b81f3 100755
--- a/crypto/bn/asm/x86_64-mont.pl
+++ b/crypto/bn/asm/x86_64-mont.pl
@@ -21,6 +21,14 @@
 # from platform to platform, but in average it's ~5%/15%/25%/33%
 # for 512-/1024-/2048-/4096-bit RSA *sign* benchmarks respectively.
 
+# August 2011.
+#
+# Unroll and modulo-schedule inner loops in such manner that they
+# are "fallen through" for input lengths of 8, which is critical for
+# 1024-bit RSA *sign*. Average performance improvement in comparison
+# to *initial* version of this module from 2005 is ~0%/30%/40%/45%
+# for 512-/1024-/2048-/4096-bit RSA *sign* benchmarks respectively.
+
 $flavour = shift;
 $output  = shift;
 if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
@@ -56,13 +64,13 @@ $code=<<___;
 .type	bn_mul_mont,\@function,6
 .align	16
 bn_mul_mont:
-	cmp	$ap,$bp
-	jne	.Lmul_enter
-	test	\$1,${num}d
+	test	\$3,${num}d
 	jnz	.Lmul_enter
-	cmp	\$4,${num}d
+	cmp	\$8,${num}d
 	jb	.Lmul_enter
-	jmp	__bn_sqr_enter
+	cmp	$ap,$bp
+	jne	.Lmul4x_enter
+	jmp	.Lsqr4x_enter
 
 .align	16
 .Lmul_enter:
@@ -81,50 +89,65 @@ bn_mul_mont:
 	and	\$-1024,%rsp		# minimize TLB usage
 
 	mov	%r11,8(%rsp,$num,8)	# tp[num+1]=%rsp
-.Lprologue:
+.Lmul_body:
 	mov	$bp,%r12		# reassign $bp
 ___
 		$bp="%r12";
 $code.=<<___;
 	mov	($n0),$n0		# pull n0[0] value
+	mov	($bp),$m0		# m0=bp[0]
+	mov	($ap),%rax
 
 	xor	$i,$i			# i=0
 	xor	$j,$j			# j=0
 
-	mov	($bp),$m0		# m0=bp[0]
-	mov	($ap),%rax
+	mov	$n0,$m1
 	mulq	$m0			# ap[0]*bp[0]
 	mov	%rax,$lo0
-	mov	%rdx,$hi0
+	mov	($np),%rax
 
-	imulq	$n0,%rax		# "tp[0]"*n0
-	mov	%rax,$m1
+	imulq	$lo0,$m1		# "tp[0]"*n0
+	mov	%rdx,$hi0
 
-	mulq	($np)			# np[0]*m1
-	add	$lo0,%rax		# discarded
+	mulq	$m1			# np[0]*m1
+	add	%rax,$lo0		# discarded
+	mov	8($ap),%rax
 	adc	\$0,%rdx
 	mov	%rdx,$hi1
 
 	lea	1($j),$j		# j++
+	jmp	.L1st_enter
+
+.align	16
 .L1st:
+	add	%rax,$hi1
 	mov	($ap,$j,8),%rax
-	mulq	$m0			# ap[j]*bp[0]
-	add	$hi0,%rax
 	adc	\$0,%rdx
-	mov	%rax,$lo0
+	add	$hi0,$hi1		# np[j]*m1+ap[j]*bp[0]
+	mov	$lo0,$hi0
+	adc	\$0,%rdx
+	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$hi1
+
+.L1st_enter:
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$hi0
 	mov	($np,$j,8),%rax
-	mov	%rdx,$hi0
+	adc	\$0,%rdx
+	lea	1($j),$j		# j++
+	mov	%rdx,$lo0
 
 	mulq	$m1			# np[j]*m1
-	add	$hi1,%rax
-	lea	1($j),$j		# j++
+	cmp	$num,$j
+	jne	.L1st
+
+	add	%rax,$hi1
 	adc	\$0,%rdx
-	add	$lo0,%rax		# np[j]*m1+ap[j]*bp[0]
+	add	$hi0,$hi1		# np[j]*m1+ap[j]*bp[0]
 	adc	\$0,%rdx
-	mov	%rax,-16(%rsp,$j,8)	# tp[j-1]
-	cmp	$num,$j
+	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$hi1
-	jl	.L1st
+	mov	$lo0,$hi0
 
 	xor	%rdx,%rdx
 	add	$hi0,$hi1
@@ -133,51 +156,64 @@ $code.=<<___;
 	mov	%rdx,(%rsp,$num,8)	# store upmost overflow bit
 
 	lea	1($i),$i		# i++
-.align	4
+	jmp	.Louter
+.align	16
 .Louter:
-	xor	$j,$j			# j=0
-
 	mov	($bp,$i,8),$m0		# m0=bp[i]
+	xor	$j,$j			# j=0
 	mov	($ap),%rax		# ap[0]
+	mov	$n0,$m1
+	mov	(%rsp),$lo0
 	mulq	$m0			# ap[0]*bp[i]
-	add	(%rsp),%rax		# ap[0]*bp[i]+tp[0]
+	add	%rax,$lo0		# ap[0]*bp[i]+tp[0]
+	mov	($np),%rax
 	adc	\$0,%rdx
-	mov	%rax,$lo0
-	mov	%rdx,$hi0
 
-	imulq	$n0,%rax		# tp[0]*n0
-	mov	%rax,$m1
+	imulq	$lo0,$m1		# tp[0]*n0
+	mov	%rdx,$hi0
 
-	mulq	($np,$j,8)		# np[0]*m1
-	add	$lo0,%rax		# discarded
-	mov	8(%rsp),$lo0		# tp[1]
+	mulq	$m1			# np[0]*m1
+	add	%rax,$lo0		# discarded
+	mov	8($ap),%rax
 	adc	\$0,%rdx
+	mov	8(%rsp),$lo0		# tp[1]
 	mov	%rdx,$hi1
 
 	lea	1($j),$j		# j++
-	jmp	.Linner
+	jmp	.Linner_enter
+
 .align	16
 .Linner:
+	add	%rax,$hi1
 	mov	($ap,$j,8),%rax
-	mulq	$m0			# ap[j]*bp[i]
-	add	$hi0,%rax
 	adc	\$0,%rdx
-	add	%rax,$lo0		# ap[j]*bp[i]+tp[j]
+	add	$lo0,$hi1		# np[j]*m1+ap[j]*bp[i]+tp[j]
+	mov	(%rsp,$j,8),$lo0
+	adc	\$0,%rdx
+	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$hi1
+
+.Linner_enter:
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$hi0
 	mov	($np,$j,8),%rax
 	adc	\$0,%rdx
+	add	$hi0,$lo0		# ap[j]*bp[i]+tp[j]
 	mov	%rdx,$hi0
+	adc	\$0,$hi0
+	lea	1($j),$j		# j++
 
 	mulq	$m1			# np[j]*m1
-	add	$hi1,%rax
-	lea	1($j),$j		# j++
-	adc	\$0,%rdx
-	add	$lo0,%rax		# np[j]*m1+ap[j]*bp[i]+tp[j]
+	cmp	$num,$j
+	jne	.Linner
+
+	add	%rax,$hi1
 	adc	\$0,%rdx
+	add	$lo0,$hi1		# np[j]*m1+ap[j]*bp[i]+tp[j]
 	mov	(%rsp,$j,8),$lo0
-	cmp	$num,$j
-	mov	%rax,-16(%rsp,$j,8)	# tp[j-1]
+	adc	\$0,%rdx
+	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
 	mov	%rdx,$hi1
-	jl	.Linner
 
 	xor	%rdx,%rdx
 	add	$hi0,$hi1
@@ -191,35 +227,449 @@ $code.=<<___;
 	cmp	$num,$i
 	jl	.Louter
 
-	lea	(%rsp),$ap		# borrow ap for tp
-	lea	-1($num),$j		# j=num-1
-
-	mov	($ap),%rax		# tp[0]
 	xor	$i,$i			# i=0 and clear CF!
+	mov	(%rsp),%rax		# tp[0]
+	lea	(%rsp),$ap		# borrow ap for tp
+	mov	$num,$j			# j=num
 	jmp	.Lsub
 .align	16
 .Lsub:	sbb	($np,$i,8),%rax
 	mov	%rax,($rp,$i,8)		# rp[i]=tp[i]-np[i]
-	dec	$j			# doesn't affect CF!
 	mov	8($ap,$i,8),%rax	# tp[i+1]
 	lea	1($i),$i		# i++
-	jge	.Lsub
+	dec	$j			# doesnn't affect CF!
+	jnz	.Lsub
 
 	sbb	\$0,%rax		# handle upmost overflow bit
+	xor	$i,$i
 	and	%rax,$ap
 	not	%rax
 	mov	$rp,$np
 	and	%rax,$np
-	lea	-1($num),$j
+	mov	$num,$j			# j=num
 	or	$np,$ap			# ap=borrow?tp:rp
 .align	16
 .Lcopy:					# copy or in-place refresh
+	mov	($ap,$i,8),%rax
+	mov	$i,(%rsp,$i,8)		# zap temporary vector
+	mov	%rax,($rp,$i,8)		# rp[i]=tp[i]
+	lea	1($i),$i
+	sub	\$1,$j
+	jnz	.Lcopy
+
+	mov	8(%rsp,$num,8),%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
+.Lmul_epilogue:
+	ret
+.size	bn_mul_mont,.-bn_mul_mont
+___
+{{{
+my @A=("%r10","%r11");
+my @N=("%r13","%rdi");
+$code.=<<___;
+.type	bn_mul4x_mont,\@function,6
+.align	16
+bn_mul4x_mont:
+.Lmul4x_enter:
+	push	%rbx
+	push	%rbp
+	push	%r12
+	push	%r13
+	push	%r14
+	push	%r15
+
+	mov	${num}d,${num}d
+	lea	4($num),%r10
+	mov	%rsp,%r11
+	neg	%r10
+	lea	(%rsp,%r10,8),%rsp	# tp=alloca(8*(num+4))
+	and	\$-1024,%rsp		# minimize TLB usage
+
+	mov	%r11,8(%rsp,$num,8)	# tp[num+1]=%rsp
+.Lmul4x_body:
+	mov	$rp,16(%rsp,$num,8)	# tp[num+2]=$rp
+	mov	%rdx,%r12		# reassign $bp
+___
+		$bp="%r12";
+$code.=<<___;
+	mov	($n0),$n0		# pull n0[0] value
+	mov	($bp),$m0		# m0=bp[0]
+	mov	($ap),%rax
+
+	xor	$i,$i			# i=0
+	xor	$j,$j			# j=0
+
+	mov	$n0,$m1
+	mulq	$m0			# ap[0]*bp[0]
+	mov	%rax,$A[0]
+	mov	($np),%rax
+
+	imulq	$A[0],$m1		# "tp[0]"*n0
+	mov	%rdx,$A[1]
+
+	mulq	$m1			# np[0]*m1
+	add	%rax,$A[0]		# discarded
+	mov	8($ap),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$N[1]
+
+	mulq	$m0
+	add	%rax,$A[1]
+	mov	8($np),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[0]
+
+	mulq	$m1
+	add	%rax,$N[1]
+	mov	16($ap),%rax
+	adc	\$0,%rdx
+	add	$A[1],$N[1]
+	lea	4($j),$j		# j++
+	adc	\$0,%rdx
+	mov	$N[1],(%rsp)
+	mov	%rdx,$N[0]
+	jmp	.L1st4x
+.align	16
+.L1st4x:
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[0]
+	mov	-16($np,$j,8),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[1]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[0]
+	mov	-8($ap,$j,8),%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	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[1]
+	mov	-8($np,$j,8),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[0]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[1]
 	mov	($ap,$j,8),%rax
-	mov	%rax,($rp,$j,8)		# rp[i]=tp[i]
-	mov	$i,(%rsp,$j,8)		# zap temporary vector
+	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	%rdx,$N[0]
+
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[0]
+	mov	($np,$j,8),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[1]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[0]
+	mov	8($ap,$j,8),%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	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[1]
+	mov	8($np,$j,8),%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
+	adc	\$0,%rdx
+	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[0]
+	adc	\$0,%rdx
+	mov	$N[1],-32(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[0]
+	cmp	$num,$j
+	jl	.L1st4x
+
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[0]
+	mov	-16($np,$j,8),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[1]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[0]
+	mov	-8($ap,$j,8),%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	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[0]
+	add	%rax,$A[1]
+	mov	-8($np,$j,8),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$A[0]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[1]
+	mov	($ap),%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	%rdx,$N[0]
+
+	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
+
+	lea	1($i),$i		# i++
+.align	4
+.Louter4x:
+	mov	($bp,$i,8),$m0		# m0=bp[i]
+	xor	$j,$j			# j=0
+	mov	(%rsp),$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
+
+	imulq	$A[0],$m1		# tp[0]*n0
+	mov	%rdx,$A[1]
+
+	mulq	$m1			# np[0]*m1
+	add	%rax,$A[0]		# "$N[0]", discarded
+	mov	8($ap),%rax
+	adc	\$0,%rdx
+	mov	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[1]
+	mov	8($np),%rax
+	adc	\$0,%rdx
+	add	8(%rsp),$A[1]		# +tp[1]
+	adc	\$0,%rdx
+	mov	%rdx,$A[0]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[1]
+	mov	16($ap),%rax
+	adc	\$0,%rdx
+	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[i]+tp[j]
+	lea	4($j),$j		# j+=2
+	adc	\$0,%rdx
+	mov	$N[1],(%rsp)		# tp[j-1]
+	mov	%rdx,$N[0]
+	jmp	.Linner4x
+.align	16
+.Linner4x:
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[0]
+	mov	-16($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	-16(%rsp,$j,8),$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
+	adc	\$0,%rdx
+	add	$A[0],$N[0]
+	adc	\$0,%rdx
+	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[1]
+	mov	-8($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	-8(%rsp,$j,8),$A[1]
+	adc	\$0,%rdx
+	mov	%rdx,$A[0]
+
+	mulq	$m1			# np[j]*m1
+	add	%rax,$N[1]
+	mov	($ap,$j,8),%rax
+	adc	\$0,%rdx
+	add	$A[1],$N[1]
+	adc	\$0,%rdx
+	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[0]
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[0]
+	mov	($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	(%rsp,$j,8),$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
+	adc	\$0,%rdx
+	add	$A[0],$N[0]
+	adc	\$0,%rdx
+	mov	$N[0],-8(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[1]
+	mov	8($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	8(%rsp,$j,8),$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
+	adc	\$0,%rdx
+	add	$A[1],$N[1]
+	adc	\$0,%rdx
+	mov	$N[1],-32(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[0]
+	cmp	$num,$j
+	jl	.Linner4x
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[0]
+	mov	-16($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	-16(%rsp,$j,8),$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
+	adc	\$0,%rdx
+	add	$A[0],$N[0]
+	adc	\$0,%rdx
+	mov	$N[0],-24(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[1]
+
+	mulq	$m0			# ap[j]*bp[i]
+	add	%rax,$A[1]
+	mov	-8($np,$j,8),%rax
+	adc	\$0,%rdx
+	add	-8(%rsp,$j,8),$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]
+	adc	\$0,%rdx
+	add	$A[1],$N[1]
+	adc	\$0,%rdx
+	mov	$N[1],-16(%rsp,$j,8)	# tp[j-1]
+	mov	%rdx,$N[0]
+
+	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
+
+	cmp	$num,$i
+	jl	.Louter4x
+___
+{
+my @ri=("%rax","%rdx",$m0,$m1);
+$code.=<<___;
+	mov	16(%rsp,$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
+	jmp	.Lsub4x
+.align	16
+.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	$j			# doesnn't affect CF!
+	jnz	.Lsub4x
+
+	mov	@ri[0],0($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
-	jge	.Lcopy
+	jnz	.Lcopy4x
 
+	shl	\$2,$num
+	movdqu	16($ap,$i),%xmm2
+	movdqa	%xmm0,16(%rsp,$i)
+	movdqu	%xmm2,16($rp,$i)
+___
+}
+$code.=<<___;
 	mov	8(%rsp,$num,8),%rsi	# restore %rsp
 	mov	\$1,%rax
 	mov	(%rsi),%r15
@@ -229,19 +679,21 @@ $code.=<<___;
 	mov	32(%rsi),%rbp
 	mov	40(%rsi),%rbx
 	lea	48(%rsi),%rsp
-.Lepilogue:
+.Lmul4x_epilogue:
 	ret
-.size	bn_mul_mont,.-bn_mul_mont
+.size	bn_mul4x_mont,.-bn_mul4x_mont
 ___
+}}}
 {{{
 ######################################################################
-# void bn_sqr_mont(
+# void bn_sqr4x_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 even and not less than 4
+my $num ="%r9";		# int num, has to be divisible by 4 and
+			# not less than 8
 
 my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
 my @A0=("%r10","%r11");
@@ -249,10 +701,10 @@ my @A1=("%r12","%r13");
 my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
 
 $code.=<<___;
-.type	bn_sqr_mont,\@function,5
+.type	bn_sqr4x_mont,\@function,6
 .align	16
-bn_sqr_mont:
-__bn_sqr_enter:
+bn_sqr4x_mont:
+.Lsqr4x_enter:
 	push	%rbx
 	push	%rbp
 	push	%r12
@@ -282,7 +734,7 @@ __bn_sqr_enter:
 	mov	$nptr,40(%rsp)
 	mov	$n0,  48(%rsp)
 	mov	%r11, 56(%rsp)		# save original %rsp
-.Lsqr_body:
+.Lsqr4x_body:
 	##############################################################
 	# Squaring part:
 	#
@@ -290,51 +742,167 @@ __bn_sqr_enter:
 	# b) shift result of a) by 1 to the left and accumulate
 	#    a[i]*a[i] products;
 	#
-	lea	16(%r10),$i		# $i=-($num-16)
+	lea	32(%r10),$i		# $i=-($num-32)
 	lea	($aptr,$num),$aptr	# end of a[] buffer, ($aptr,$i)=&ap[2]
 
 	mov	$num,$j			# $j=$num
-	pxor	%xmm0,%xmm0
-	lea	64(%rsp),$tptr
-.Lbzero:				# clear t[$num]
-	movdqa	%xmm0,($tptr)
-	lea	16($tptr),$tptr
-	sub	\$16,$j
-	jnz	.Lbzero
-	jmp	.Lsqr_outer
+
+					# 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]
+
+	xor	$A0[0],$A0[0]
+	mul	$a0			# a[2]*a[0]
+	add	%rax,$A0[1]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[0]
+	mov	$A0[1],-16($tptr,$i)	# t[2]
+
+	lea	-16($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]
+
+	xor	$A0[1],$A0[1]
+	add	$A1[0],$A0[0]
+	 lea	16($j),$j
+	adc	\$0,$A0[1]
+	mul	$a0			# a[3]*a[0]
+	add	%rax,$A0[0]		# a[3]*a[0]+a[2]*a[1]+t[3]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-8($tptr,$j)	# t[3]
+	jmp	.Lsqr4x_1st
 
 .align	16
-.Lsqr_outer:				# comments apply to $num==4 case
-	mov	-16($aptr,$i),$a0	# a[0]
+.Lsqr4x_1st:
+	 mov	($aptr,$j),$ai		# a[4]
+	xor	$A1[0],$A1[0]
+	mul	$a1			# a[3]*a[1]
+	add	%rax,$A1[1]		# a[3]*a[1]+t[4]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[0]
+
+	xor	$A0[0],$A0[0]
+	add	$A1[1],$A0[1]
+	adc	\$0,$A0[0]
+	mul	$a0			# a[4]*a[0]
+	add	%rax,$A0[1]		# a[4]*a[0]+a[3]*a[1]+t[4]
+	 mov	$ai,%rax		# a[3]
+	adc	%rdx,$A0[0]
+	mov	$A0[1],($tptr,$j)	# t[4]
+
+
+	 mov	8($aptr,$j),$ai		# a[5]
+	xor	$A1[1],$A1[1]
+	mul	$a1			# a[4]*a[3]
+	add	%rax,$A1[0]		# a[4]*a[3]+t[5]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[1]
+
+	xor	$A0[1],$A0[1]
+	add	$A1[0],$A0[0]
+	 lea	16($j),$j
+	adc	\$0,$A0[1]
+	mul	$a0			# a[5]*a[2]
+	add	%rax,$A0[0]		# a[5]*a[2]+a[4]*a[3]+t[5]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-8($tptr,$j)	# t[5]
+
+	 mov	($aptr,$j),$ai		# a[6]
+	xor	$A1[0],$A1[0]
+	mul	$a1			# a[5]*a[3]
+	add	%rax,$A1[1]		# a[5]*a[3]+t[6]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[0]
+
+	xor	$A0[0],$A0[0]
+	add	$A1[1],$A0[1]
+	adc	\$0,$A0[0]
+	mul	$a0			# a[6]*a[2]
+	add	%rax,$A0[1]		# a[6]*a[2]+a[5]*a[3]+t[6]
+	 mov	$ai,%rax		# a[3]
+	adc	%rdx,$A0[0]
+	mov	$A0[1],($tptr,$j)	# t[6]
+
+
+	 mov	8($aptr,$j),$ai		# a[7]
+	xor	$A1[1],$A1[1]
+	mul	$a1			# a[6]*a[5]
+	add	%rax,$A1[0]		# a[6]*a[5]+t[7]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[1]
+
+	xor	$A0[1],$A0[1]
+	add	$A1[0],$A0[0]
+	 lea	16($j),$j
+	adc	\$0,$A0[1]
+	mul	$a0			# a[7]*a[4]
+	add	%rax,$A0[0]		# a[7]*a[4]+a[6]*a[5]+t[6]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-8($tptr,$j)	# t[7]
+
+	cmp	\$0,$j
+	jne	.Lsqr4x_1st
+
+	xor	$A1[0],$A1[0]
+	add	$A0[1],$A1[1]
+	adc	\$0,$A1[0]
+	mul	$a1			# a[7]*a[5]
+	add	%rax,$A1[1]
+	adc	%rdx,$A1[0]
+
+	mov	$A1[1],($tptr)		# t[8]
+	lea	16($i),$i
+	mov	$A1[0],8($tptr)		# t[9]
+	jmp	.Lsqr4x_outer
+
+.align	16
+.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*$num]
-	mov	-8($aptr,$i),%rax	# a[1]
-	lea	-16($tptr,$i),$tptr	# end of tp[] window, &tp[2*$num-"$i"]
-	mov	($aptr,$i),$ai		# a[2]
+	mov	-24($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	-8($tptr,$i),$A0[0]	# t[1]
+	mov	-24($tptr,$i),$A0[0]	# t[1]
 	xor	$A0[1],$A0[1]
 	mul	$a0			# a[1]*a[0]
 	add	%rax,$A0[0]		# a[1]*a[0]+t[1]
 	 mov	$ai,%rax		# a[2]
 	adc	%rdx,$A0[1]
-	mov	$A0[0],-8($tptr,$i)	# t[1]
+	mov	$A0[0],-24($tptr,$i)	# t[1]
 
 	xor	$A0[0],$A0[0]
-	add	($tptr,$i),$A0[1]	# a[2]*a[0]+t[2]
+	add	-16($tptr,$i),$A0[1]	# a[2]*a[0]+t[2]
 	adc	\$0,$A0[0]
 	mul	$a0			# a[2]*a[0]
 	add	%rax,$A0[1]
 	 mov	$ai,%rax
 	adc	%rdx,$A0[0]
-	mov	$A0[1],($tptr,$i)	# t[2]
+	mov	$A0[1],-16($tptr,$i)	# t[2]
 
-	lea	($i),$j			# j=-16
+	lea	-16($i),$j		# j=-16
 	xor	$A1[0],$A1[0]
-	jmp	.Lsqr_inner
 
-.align	16
-.Lsqr_inner:
+
 	 mov	8($aptr,$j),$ai		# a[3]
 	xor	$A1[1],$A1[1]
 	add	8($tptr,$j),$A1[0]
@@ -353,9 +921,11 @@ __bn_sqr_enter:
 	adc	%rdx,$A0[1]
 	mov	$A0[0],8($tptr,$j)	# t[3]
 
-	add	\$16,$j
-	jz	.Lsqr_inner_done
+	lea	16($j),$j
+	jmp	.Lsqr4x_inner
 
+.align	16
+.Lsqr4x_inner:
 	 mov	($aptr,$j),$ai		# a[4]
 	xor	$A1[0],$A1[0]
 	add	($tptr,$j),$A1[1]
@@ -373,10 +943,86 @@ __bn_sqr_enter:
 	 mov	$ai,%rax		# a[3]
 	adc	%rdx,$A0[0]
 	mov	$A0[1],($tptr,$j)	# t[4]
-	jmp	.Lsqr_inner
 
-.align	16
-.Lsqr_inner_done:
+	 mov	8($aptr,$j),$ai		# a[5]
+	xor	$A1[1],$A1[1]
+	add	8($tptr,$j),$A1[0]
+	adc	\$0,$A1[1]
+	mul	$a1			# a[4]*a[3]
+	add	%rax,$A1[0]		# a[4]*a[3]+t[5]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[1]
+
+	xor	$A0[1],$A0[1]
+	add	$A1[0],$A0[0]
+	lea	16($j),$j		# j++
+	adc	\$0,$A0[1]
+	mul	$a0			# a[5]*a[2]
+	add	%rax,$A0[0]		# a[5]*a[2]+a[4]*a[3]+t[5]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-8($tptr,$j)	# t[5]
+
+	cmp	\$0,$j
+	jne	.Lsqr4x_inner
+
+	xor	$A1[0],$A1[0]
+	add	$A0[1],$A1[1]
+	adc	\$0,$A1[0]
+	mul	$a1			# a[5]*a[3]
+	add	%rax,$A1[1]
+	adc	%rdx,$A1[0]
+
+	mov	$A1[1],($tptr)		# t[6]
+	mov	$A1[0],8($tptr)		# t[7]
+
+	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,$a1
+
+	mov	-24($tptr),$A0[0]	# t[1]
+	xor	$A0[1],$A0[1]
+	mul	$a0			# a[1]*a[0]
+	add	%rax,$A0[0]		# a[1]*a[0]+t[1]
+	 mov	$ai,%rax		# a[2]
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-24($tptr)	# t[1]
+
+	xor	$A0[0],$A0[0]
+	add	-16($tptr),$A0[1]	# a[2]*a[0]+t[2]
+	adc	\$0,$A0[0]
+	mul	$a0			# a[2]*a[0]
+	add	%rax,$A0[1]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[0]
+	mov	$A0[1],-16($tptr)	# t[2]
+
+	xor	$A1[0],$A1[0]
+	 mov	-8($aptr),$ai		# a[3]
+	xor	$A1[1],$A1[1]
+	add	-8($tptr),$A1[0]
+	adc	\$0,$A1[1]
+	mul	$a1			# a[2]*a[1]
+	add	%rax,$A1[0]		# a[2]*a[1]+t[3]
+	 mov	$ai,%rax
+	adc	%rdx,$A1[1]
+
+	xor	$A0[1],$A0[1]
+	add	$A1[0],$A0[0]
+	adc	\$0,$A0[1]
+	mul	$a0			# a[3]*a[0]
+	add	%rax,$A0[0]		# a[3]*a[0]+a[2]*a[1]+t[3]
+	 mov	$ai,%rax
+	adc	%rdx,$A0[1]
+	mov	$A0[0],-8($tptr)	# t[3]
+
 	xor	$A1[0],$A1[0]
 	add	$A0[1],$A1[1]
 	adc	\$0,$A1[0]
@@ -388,17 +1034,15 @@ __bn_sqr_enter:
 	mov	$A1[1],($tptr)		# t[4]
 	mov	$A1[0],8($tptr)		# t[5]
 
-	add	\$16,$i
-	jnz	.Lsqr_outer
-
 	mul	$ai			# a[2]*a[3]
 ___
 {
 my ($shift,$carry)=($a0,$a1);
+my @S=(@A1,$ai,$n0);
 $code.=<<___;
-	 add	\$8,$i
+	 add	\$16,$i
 	 xor	$shift,$shift
-	 sub	$num,$i			# $i=8-$num
+	 sub	$num,$i			# $i=16-$num
 	 xor	$carry,$carry
 
 	add	$A1[0],%rax		# t[5]
@@ -407,44 +1051,147 @@ $code.=<<___;
 	mov	%rdx,16($tptr)		# t[6]
 	mov	$carry,24($tptr)	# t[7]
 
-	 mov	-8($aptr,$i),%rax	# a[0]
+	 mov	-16($aptr,$i),%rax	# a[0]
 	lea	64(%rsp,$num,2),$tptr
-	 mov	-16($tptr,$i,2),$A0[0]	# t[0]
-	 mov	-8($tptr,$i,2),$A0[1]	# t[1]
-	jmp	.Lsqr_shift_n_add
+	 xor	$A0[0],$A0[0]		# t[0]
+	 mov	-24($tptr,$i,2),$A0[1]	# t[1]
 
-.align	16
-.Lsqr_shift_n_add:
-	lea	($shift,$A0[0],2),$A1[0]# t[2*i]<<1 | shift
+	lea	($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($tptr,$i,2),$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,$i,2),$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,$i,2)
+	adc	%rdx,$S[1]
+
+	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
+	 mov	$S[1],-24($tptr,$i,2)
+	 sbb	$carry,$carry		# mov cf,$carry
 	shr	\$63,$A0[0]
-	lea	(,$A0[1],2),$A1[1]	# t[2*i+1]<<1 |
+	lea	($j,$A0[1],2),$S[3]	# t[2*i+1]<<1 |
 	shr	\$63,$A0[1]
-	or	$A0[0],$A1[1]		# | t[2*i]>>63
+	or	$A0[0],$S[3]		# | t[2*i]>>63
 	 mov	0($tptr,$i,2),$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,$i,2),$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,$i,2)
+	adc	%rdx,$S[3]
+	lea	16($i),$i
+	mov	$S[3],-40($tptr,$i,2)
+	sbb	$carry,$carry		# mov cf,$carry
+	jmp	.Lsqr4x_shift_n_add
+
+.align	16
+.Lsqr4x_shift_n_add:
+	lea	($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($tptr,$i,2),$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,$i,2),$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,$i,2)
+	adc	%rdx,$S[1]
+
+	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
+	 mov	$S[1],-24($tptr,$i,2)
+	 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($tptr,$i,2),$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 $carry,cf
-	adc	%rax,$A1[0]
+	 mov	8($tptr,$i,2),$A0[1]	# t[2*i+2+1]	# prefetch
+	adc	%rax,$S[2]
 	 mov	0($aptr,$i),%rax	# a[i+1]	# prefetch
-	adc	%rdx,$A1[1]
-	mov	$A1[0],-16($tptr,$i,2)
+	mov	$S[2],-16($tptr,$i,2)
+	adc	%rdx,$S[3]
+
+	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
+	 mov	$S[3],-8($tptr,$i,2)
+	 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($tptr,$i,2),$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,$i,2),$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,$i,2)
+	adc	%rdx,$S[1]
+
+	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
+	 mov	$S[1],8($tptr,$i,2)
+	 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($tptr,$i,2),$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,$i,2),$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,$i,2)
+	adc	%rdx,$S[3]
+	mov	$S[3],24($tptr,$i,2)
 	sbb	$carry,$carry		# mov cf,$carry
-	mov	$A1[1],-8($tptr,$i,2)
-	add	\$8,$i
-	jnz	.Lsqr_shift_n_add
+	add	\$32,$i
+	jnz	.Lsqr4x_shift_n_add
 
-	lea	($shift,$A0[0],2),$A1[0]# t[2*i]<<1|shift
+	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
 	shr	\$63,$A0[0]
-	lea	(,$A0[1],2),$A1[1]	# t[2*i+1]<<1 |
+	lea	($j,$A0[1],2),$S[1]	# t[2*i+1]<<1 |
 	shr	\$63,$A0[1]
-	or	$A0[0],$A1[1]		# | t[2*i]>>63
+	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 $carry,cf
-	adc	%rax,$A1[0]
-	adc	%rdx,$A1[1]
-	mov	$A1[0],-16($tptr)
-	mov	$A1[1],-8($tptr)
+	 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)
 ___
 }
 ##############################################################
@@ -456,6 +1203,7 @@ my ($m0,$m1)=($a0,$a1);
 my @Ni=("%rbx","%r9");
 $code.=<<___;
 	mov	40(%rsp),$nptr		# restore $nptr
+	mov	48(%rsp),$n0		# restore *n0
 	xor	$j,$j
 	mov	$num,0(%rsp)		# save $num
 	sub	$num,$j			# $j=-$num
@@ -471,10 +1219,10 @@ $code.=<<___;
 	mov	8($nptr,$j),$Ni[1]	# n[1]		# modsched #
 	 imulq	$A0[0],$m0		# m0=t[0]*n0	# modsched #
 	 mov	%rax,$Ni[0]		#		# modsched #
-	jmp	.Lmont_outer
+	jmp	.Lsqr4x_mont_outer
 
 .align	16
-.Lmont_outer:
+.Lsqr4x_mont_outer:
 	xor	$A0[1],$A0[1]
 	mul	$m0			# n[0]*m0
 	add	%rax,$A0[0]		# n[0]*m0+t[0]
@@ -491,12 +1239,8 @@ $code.=<<___;
 	adc	%rdx,$A0[0]
 
 	imulq	$A0[1],$m1
-	lea	16($j),$j
-	jmp	.Lmont_inner
 
-.align	16
-.Lmont_inner:
-	mov	($nptr,$j),$Ni[0]	# n[2]
+	mov	16($nptr,$j),$Ni[0]	# n[2]
 	xor	$A1[1],$A1[1]
 	add	$A0[1],$A1[0]
 	adc	\$0,$A1[1]
@@ -504,17 +1248,17 @@ $code.=<<___;
 	add	%rax,$A1[0]		# n[0]*m1+"t[1]"
 	 mov	$Ni[0],%rax
 	adc	%rdx,$A1[1]
-	mov	$A1[0],-8($tptr,$j)	# "t[1]"
+	mov	$A1[0],8($tptr,$j)	# "t[1]"
 
 	xor	$A0[1],$A0[1]
-	add	($tptr,$j),$A0[0]
+	add	16($tptr,$j),$A0[0]
 	adc	\$0,$A0[1]
 	mul	$m0			# n[2]*m0
 	add	%rax,$A0[0]		# n[2]*m0+t[2]
 	 mov	$Ni[1],%rax
 	adc	%rdx,$A0[1]
 
-	mov	8($nptr,$j),$Ni[1]	# n[3]
+	mov	24($nptr,$j),$Ni[1]	# n[3]
 	xor	$A1[0],$A1[0]
 	add	$A0[0],$A1[1]
 	adc	\$0,$A1[0]
@@ -522,18 +1266,95 @@ $code.=<<___;
 	add	%rax,$A1[1]		# n[1]*m1+"t[2]"
 	 mov	$Ni[1],%rax
 	adc	%rdx,$A1[0]
-	mov	$A1[1],($tptr,$j)	# "t[2]"
+	mov	$A1[1],16($tptr,$j)	# "t[2]"
 
 	xor	$A0[0],$A0[0]
-	add	8($tptr,$j),$A0[1]