x86_64 assembler pack update from HEAD.

3 files changed, 2877 insertions, 68 deletions

diff --git a/crypto/bn/asm/x86_64-gf2m.pl b/crypto/bn/asm/x86_64-gf2m.pl
new file mode 100644
index 0000000000..1658acbbdd
--- /dev/null
+++ b/crypto/bn/asm/x86_64-gf2m.pl
@@ -0,0 +1,389 @@
+#!/usr/bin/env perl
+#
+# ====================================================================
+# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
+# project. The module is, however, dual licensed under OpenSSL and
+# CRYPTOGAMS licenses depending on where you obtain it. For further
+# details see http://www.openssl.org/~appro/cryptogams/.
+# ====================================================================
+#
+# May 2011
+#
+# The module implements bn_GF2m_mul_2x2 polynomial multiplication used
+# in bn_gf2m.c. It's kind of low-hanging mechanical port from C for
+# the time being... Except that it has two code paths: code suitable
+# for any x86_64 CPU and PCLMULQDQ one suitable for Westmere and
+# later. Improvement varies from one benchmark and µ-arch to another.
+# Vanilla code path is at most 20% faster than compiler-generated code
+# [not very impressive], while PCLMULQDQ - whole 85%-160% better on
+# 163- and 571-bit ECDH benchmarks on Intel CPUs. Keep in mind that
+# these coefficients are not ones for bn_GF2m_mul_2x2 itself, as not
+# all CPU time is burnt in it...
+
+$flavour = shift;
+$output  = shift;
+if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
+
+$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
+
+$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
+( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
+( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
+die "can't locate x86_64-xlate.pl";
+
+open STDOUT,"| $^X $xlate $flavour $output";
+
+($lo,$hi)=("%rax","%rdx");	$a=$lo;
+($i0,$i1)=("%rsi","%rdi");
+($t0,$t1)=("%rbx","%rcx");
+($b,$mask)=("%rbp","%r8");
+($a1,$a2,$a4,$a8,$a12,$a48)=map("%r$_",(9..15));
+($R,$Tx)=("%xmm0","%xmm1");
+
+$code.=<<___;
+.text
+
+.type	_mul_1x1,\@abi-omnipotent
+.align	16
+_mul_1x1:
+	sub	\$128+8,%rsp
+	mov	\$-1,$a1
+	lea	($a,$a),$i0
+	shr	\$3,$a1
+	lea	(,$a,4),$i1
+	and	$a,$a1			# a1=a&0x1fffffffffffffff
+	lea	(,$a,8),$a8
+	sar	\$63,$a			# broadcast 63rd bit
+	lea	($a1,$a1),$a2
+	sar	\$63,$i0		# broadcast 62nd bit
+	lea	(,$a1,4),$a4
+	and	$b,$a
+	sar	\$63,$i1		# boardcast 61st bit
+	mov	$a,$hi			# $a is $lo
+	shl	\$63,$lo
+	and	$b,$i0
+	shr	\$1,$hi
+	mov	$i0,$t1
+	shl	\$62,$i0
+	and	$b,$i1
+	shr	\$2,$t1
+	xor	$i0,$lo
+	mov	$i1,$t0
+	shl	\$61,$i1
+	xor	$t1,$hi
+	shr	\$3,$t0
+	xor	$i1,$lo
+	xor	$t0,$hi
+
+	mov	$a1,$a12
+	movq	\$0,0(%rsp)		# tab[0]=0
+	xor	$a2,$a12		# a1^a2
+	mov	$a1,8(%rsp)		# tab[1]=a1
+	 mov	$a4,$a48
+	mov	$a2,16(%rsp)		# tab[2]=a2
+	 xor	$a8,$a48		# a4^a8
+	mov	$a12,24(%rsp)		# tab[3]=a1^a2
+
+	xor	$a4,$a1
+	mov	$a4,32(%rsp)		# tab[4]=a4
+	xor	$a4,$a2
+	mov	$a1,40(%rsp)		# tab[5]=a1^a4
+	xor	$a4,$a12
+	mov	$a2,48(%rsp)		# tab[6]=a2^a4
+	 xor	$a48,$a1		# a1^a4^a4^a8=a1^a8
+	mov	$a12,56(%rsp)		# tab[7]=a1^a2^a4
+	 xor	$a48,$a2		# a2^a4^a4^a8=a1^a8
+
+	mov	$a8,64(%rsp)		# tab[8]=a8
+	xor	$a48,$a12		# a1^a2^a4^a4^a8=a1^a2^a8
+	mov	$a1,72(%rsp)		# tab[9]=a1^a8
+	 xor	$a4,$a1			# a1^a8^a4
+	mov	$a2,80(%rsp)		# tab[10]=a2^a8
+	 xor	$a4,$a2			# a2^a8^a4
+	mov	$a12,88(%rsp)		# tab[11]=a1^a2^a8
+
+	xor	$a4,$a12		# a1^a2^a8^a4
+	mov	$a48,96(%rsp)		# tab[12]=a4^a8
+	 mov	$mask,$i0
+	mov	$a1,104(%rsp)		# tab[13]=a1^a4^a8
+	 and	$b,$i0
+	mov	$a2,112(%rsp)		# tab[14]=a2^a4^a8
+	 shr	\$4,$b
+	mov	$a12,120(%rsp)		# tab[15]=a1^a2^a4^a8
+	 mov	$mask,$i1
+	 and	$b,$i1
+	 shr	\$4,$b
+
+	movq	(%rsp,$i0,8),$R		# half of calculations is done in SSE2
+	mov	$mask,$i0
+	and	$b,$i0
+	shr	\$4,$b
+___
+    for ($n=1;$n<8;$n++) {
+	$code.=<<___;
+	mov	(%rsp,$i1,8),$t1
+	mov	$mask,$i1
+	mov	$t1,$t0
+	shl	\$`8*$n-4`,$t1
+	and	$b,$i1
+	 movq	(%rsp,$i0,8),$Tx
+	shr	\$`64-(8*$n-4)`,$t0
+	xor	$t1,$lo
+	 pslldq	\$$n,$Tx
+	 mov	$mask,$i0
+	shr	\$4,$b
+	xor	$t0,$hi
+	 and	$b,$i0
+	 shr	\$4,$b
+	 pxor	$Tx,$R
+___
+    }
+$code.=<<___;
+	mov	(%rsp,$i1,8),$t1
+	mov	$t1,$t0
+	shl	\$`8*$n-4`,$t1
+	movq	$R,$i0
+	shr	\$`64-(8*$n-4)`,$t0
+	xor	$t1,$lo
+	psrldq	\$8,$R
+	xor	$t0,$hi
+	movq	$R,$i1
+	xor	$i0,$lo
+	xor	$i1,$hi
+
+	add	\$128+8,%rsp
+	ret
+.Lend_mul_1x1:
+.size	_mul_1x1,.-_mul_1x1
+___
+
+($rp,$a1,$a0,$b1,$b0) = $win64?	("%rcx","%rdx","%r8", "%r9","%r10") :	# Win64 order
+				("%rdi","%rsi","%rdx","%rcx","%r8");	# Unix order
+
+$code.=<<___;
+.extern	OPENSSL_ia32cap_P
+.globl	bn_GF2m_mul_2x2
+.type	bn_GF2m_mul_2x2,\@abi-omnipotent
+.align	16
+bn_GF2m_mul_2x2:
+	mov	OPENSSL_ia32cap_P(%rip),%rax
+	bt	\$33,%rax
+	jnc	.Lvanilla_mul_2x2
+
+	movq		$a1,%xmm0
+	movq		$b1,%xmm1
+	movq		$a0,%xmm2
+___
+$code.=<<___ if ($win64);
+	movq		40(%rsp),%xmm3
+___
+$code.=<<___ if (!$win64);
+	movq		$b0,%xmm3
+___
+$code.=<<___;
+	movdqa		%xmm0,%xmm4
+	movdqa		%xmm1,%xmm5
+	pclmulqdq	\$0,%xmm1,%xmm0	# a1·b1
+	pxor		%xmm2,%xmm4
+	pxor		%xmm3,%xmm5
+	pclmulqdq	\$0,%xmm3,%xmm2	# a0·b0
+	pclmulqdq	\$0,%xmm5,%xmm4	# (a0+a1)·(b0+b1)
+	xorps		%xmm0,%xmm4
+	xorps		%xmm2,%xmm4	# (a0+a1)·(b0+b1)-a0·b0-a1·b1
+	movdqa		%xmm4,%xmm5
+	pslldq		\$8,%xmm4
+	psrldq		\$8,%xmm5
+	pxor		%xmm4,%xmm2
+	pxor		%xmm5,%xmm0
+	movdqu		%xmm2,0($rp)
+	movdqu		%xmm0,16($rp)
+	ret
+
+.align	16
+.Lvanilla_mul_2x2:
+	lea	-8*17(%rsp),%rsp
+___
+$code.=<<___ if ($win64);
+	mov	`8*17+40`(%rsp),$b0
+	mov	%rdi,8*15(%rsp)
+	mov	%rsi,8*16(%rsp)
+___
+$code.=<<___;
+	mov	%r14,8*10(%rsp)
+	mov	%r13,8*11(%rsp)
+	mov	%r12,8*12(%rsp)
+	mov	%rbp,8*13(%rsp)
+	mov	%rbx,8*14(%rsp)
+.Lbody_mul_2x2:
+	mov	$rp,32(%rsp)		# save the arguments
+	mov	$a1,40(%rsp)
+	mov	$a0,48(%rsp)
+	mov	$b1,56(%rsp)
+	mov	$b0,64(%rsp)
+
+	mov	\$0xf,$mask
+	mov	$a1,$a
+	mov	$b1,$b
+	call	_mul_1x1		# a1·b1
+	mov	$lo,16(%rsp)
+	mov	$hi,24(%rsp)
+
+	mov	48(%rsp),$a
+	mov	64(%rsp),$b
+	call	_mul_1x1		# a0·b0
+	mov	$lo,0(%rsp)
+	mov	$hi,8(%rsp)
+
+	mov	40(%rsp),$a
+	mov	56(%rsp),$b
+	xor	48(%rsp),$a
+	xor	64(%rsp),$b
+	call	_mul_1x1		# (a0+a1)·(b0+b1)
+___
+	@r=("%rbx","%rcx","%rdi","%rsi");
+$code.=<<___;
+	mov	0(%rsp),@r[0]
+	mov	8(%rsp),@r[1]
+	mov	16(%rsp),@r[2]
+	mov	24(%rsp),@r[3]
+	mov	32(%rsp),%rbp
+
+	xor	$hi,$lo
+	xor	@r[1],$hi
+	xor	@r[0],$lo
+	mov	@r[0],0(%rbp)
+	xor	@r[2],$hi
+	mov	@r[3],24(%rbp)
+	xor	@r[3],$lo
+	xor	@r[3],$hi
+	xor	$hi,$lo
+	mov	$hi,16(%rbp)
+	mov	$lo,8(%rbp)
+
+	mov	8*10(%rsp),%r14
+	mov	8*11(%rsp),%r13
+	mov	8*12(%rsp),%r12
+	mov	8*13(%rsp),%rbp
+	mov	8*14(%rsp),%rbx
+___
+$code.=<<___ if ($win64);
+	mov	8*15(%rsp),%rdi
+	mov	8*16(%rsp),%rsi
+___
+$code.=<<___;
+	lea	8*17(%rsp),%rsp
+	ret
+.Lend_mul_2x2:
+.size	bn_GF2m_mul_2x2,.-bn_GF2m_mul_2x2
+.asciz	"GF(2^m) Multiplication for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
+.align	16
+___
+
+# EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
+#               CONTEXT *context,DISPATCHER_CONTEXT *disp)
+if ($win64) {
+$rec="%rcx";
+$frame="%rdx";
+$context="%r8";
+$disp="%r9";
+
+$code.=<<___;
+.extern __imp_RtlVirtualUnwind
+
+.type	se_handler,\@abi-omnipotent
+.align	16
+se_handler:
+	push	%rsi
+	push	%rdi
+	push	%rbx
+	push	%rbp
+	push	%r12
+	push	%r13
+	push	%r14
+	push	%r15
+	pushfq
+	sub	\$64,%rsp
+
+	mov	152($context),%rax	# pull context->Rsp
+	mov	248($context),%rbx	# pull context->Rip
+
+	lea	.Lbody_mul_2x2(%rip),%r10
+	cmp	%r10,%rbx		# context->Rip<"prologue" label
+	jb	.Lin_prologue
+
+	mov	8*10(%rax),%r14		# mimic epilogue
+	mov	8*11(%rax),%r13
+	mov	8*12(%rax),%r12
+	mov	8*13(%rax),%rbp
+	mov	8*14(%rax),%rbx
+	mov	8*15(%rax),%rdi
+	mov	8*16(%rax),%rsi
+
+	mov	%rbx,144($context)	# restore context->Rbx
+	mov	%rbp,160($context)	# restore context->Rbp
+	mov	%rsi,168($context)	# restore context->Rsi
+	mov	%rdi,176($context)	# restore context->Rdi
+	mov	%r12,216($context)	# restore context->R12
+	mov	%r13,224($context)	# restore context->R13
+	mov	%r14,232($context)	# restore context->R14
+
+.Lin_prologue:
+	lea	8*17(%rax),%rax
+	mov	%rax,152($context)	# restore context->Rsp
+
+	mov	40($disp),%rdi		# disp->ContextRecord
+	mov	$context,%rsi		# context
+	mov	\$154,%ecx		# sizeof(CONTEXT)
+	.long	0xa548f3fc		# cld; rep movsq
+
+	mov	$disp,%rsi
+	xor	%rcx,%rcx		# arg1, UNW_FLAG_NHANDLER
+	mov	8(%rsi),%rdx		# arg2, disp->ImageBase
+	mov	0(%rsi),%r8		# arg3, disp->ControlPc
+	mov	16(%rsi),%r9		# arg4, disp->FunctionEntry
+	mov	40(%rsi),%r10		# disp->ContextRecord
+	lea	56(%rsi),%r11		# &disp->HandlerData
+	lea	24(%rsi),%r12		# &disp->EstablisherFrame
+	mov	%r10,32(%rsp)		# arg5
+	mov	%r11,40(%rsp)		# arg6
+	mov	%r12,48(%rsp)		# arg7
+	mov	%rcx,56(%rsp)		# arg8, (NULL)
+	call	*__imp_RtlVirtualUnwind(%rip)
+
+	mov	\$1,%eax		# ExceptionContinueSearch
+	add	\$64,%rsp
+	popfq
+	pop	%r15
+	pop	%r14
+	pop	%r13
+	pop	%r12
+	pop	%rbp
+	pop	%rbx
+	pop	%rdi
+	pop	%rsi
+	ret
+.size	se_handler,.-se_handler
+
+.section	.pdata
+.align	4
+	.rva	_mul_1x1
+	.rva	.Lend_mul_1x1
+	.rva	.LSEH_info_1x1
+
+	.rva	.Lvanilla_mul_2x2
+	.rva	.Lend_mul_2x2
+	.rva	.LSEH_info_2x2
+.section	.xdata
+.align	8
+.LSEH_info_1x1:
+	.byte	0x01,0x07,0x02,0x00
+	.byte	0x07,0x01,0x11,0x00	# sub rsp,128+8
+.LSEH_info_2x2:
+	.byte	9,0,0,0
+	.rva	se_handler
+___
+}
+
+$code =~ s/\`([^\`]*)\`/eval($1)/gem;
+print $code;
+close STDOUT;
diff --git a/crypto/bn/asm/x86_64-mont.pl b/crypto/bn/asm/x86_64-mont.pl
index 3b7a6f243f..5d79b35e1c 100755
--- a/crypto/bn/asm/x86_64-mont.pl
+++ b/crypto/bn/asm/x86_64-mont.pl
@@ -1,7 +1,7 @@
 #!/usr/bin/env perl
 
 # ====================================================================
-# Written by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
+# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
 # project. The module is, however, dual licensed under OpenSSL and
 # CRYPTOGAMS licenses depending on where you obtain it. For further
 # details see http://www.openssl.org/~appro/cryptogams/.
@@ -15,6 +15,20 @@
 # respectful 50%. It remains to be seen if loop unrolling and
 # dedicated squaring routine can provide further improvement...
 
+# July 2011.
+#
+# Add dedicated squaring procedure. Performance improvement varies
+# 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; }
@@ -37,7 +51,6 @@ $n0="%r8";	# const BN_ULONG *n0,
 $num="%r9";	# int num);
 $lo0="%r10";
 $hi0="%r11";
-$bp="%r12";	# reassign $bp
 $hi1="%r13";
 $i="%r14";
 $j="%r15";
@@ -51,6 +64,16 @@ $code=<<___;
 .type	bn_mul_mont,\@function,6
 .align	16
 bn_mul_mont:
+	test	\$3,${num}d
+	jnz	.Lmul_enter
+	cmp	\$8,${num}d
+	jb	.Lmul_enter
+	cmp	$ap,$bp
+	jne	.Lmul4x_enter
+	jmp	.Lsqr4x_enter
+
+.align	16
+.Lmul_enter:
 	push	%rbx
 	push	%rbp
 	push	%r12
@@ -66,48 +89,66 @@ bn_mul_mont:
 	and	\$-1024,%rsp		# minimize TLB usage
 
 	mov	%r11,8(%rsp,$num,8)	# tp[num+1]=%rsp
-.Lprologue:
-	mov	%rdx,$bp		# $bp reassigned, remember?
-
+.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,$hi1
+	mov	($ap),%rax		# ap[0]
 	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
@@ -116,50 +157,64 @@ bn_mul_mont:
 	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),$m0		# m0=bp[i]
-	mov	($ap),%rax		# ap[0]
+	xor	$j,$j			# j=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++
-.align	4
+	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,$hi1
+	mov	($ap),%rax		# ap[0]
 	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
@@ -173,35 +228,449 @@ bn_mul_mont:
 	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
@@ -211,9 +680,823 @@ bn_mul_mont:
 	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_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 $num ="%r9";		# int num, has to be divisible by 4 and
+			# not less than 8
+
+my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
+my @A0=("%r10","%r11");
+my @A1=("%r12","%r13");
+my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
+
+$code.=<<___;
+.type	bn_sqr4x_mont,\@function,6
+.align	16
+bn_sqr4x_mont:
+.Lsqr4x_enter:
+	push	%rbx
+	push	%rbp
+	push	%r12
+	push	%r13
+	push	%r14
+	push	%r15
+
+	shl	\$3,${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	$n0,  48(%rsp)
+	mov	%r11, 56(%rsp)		# save original %rsp
+.Lsqr4x_body:
+	##############################################################
+	# Squaring part:
+	#
+	# a) multiply-n-add everything but a[i]*a[i];
+	# b) shift result of a) by 1 to the left and accumulate
+	#    a[i]*a[i] products;
+	#
+	lea	32(%r10),$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]
+
+	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,$j)	# t[3]
+	jmp	.Lsqr4x_1st
+
+.align	16
+.Lsqr4x_1st:
+	 mov	($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]
+	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,$j)	# t[5]
+
+	 mov	16($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	$A0[1],16($tptr,$j)	# t[6]
+
+
+	 mov	24($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	32($j),$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]
+