From: Andy Polyakov <appro@openssl.org>
Date: Sun, 15 Feb 2015 21:26:08 +0000 (+0100)
Subject: Add ecp_nistz256-armv8 module.
X-Git-Tag: OpenSSL_1_1_0-pre1~1300
X-Git-Url: https://git.librecmc.org/?a=commitdiff_plain;h=e1613e7c0c692bd9071e04e8fcf1b2a18ebebf0c;p=oweals%2Fopenssl.git

Add ecp_nistz256-armv8 module.

Reviewed-by: Richard Levitte <levitte@openssl.org>
---

diff --git a/crypto/ec/Makefile b/crypto/ec/Makefile
index 542596795e..fa2fc4cbb2 100644
--- a/crypto/ec/Makefile
+++ b/crypto/ec/Makefile
@@ -56,6 +56,7 @@ ecp_nistz256-avx2.s:   asm/ecp_nistz256-avx2.pl
 
 ecp_nistz256-%.S:	asm/ecp_nistz256-%.pl;  $(PERL) $< $(PERLASM_SCHEME) $@
 ecp_nistz256-armv4.o:	ecp_nistz256-armv4.S
+ecp_nistz256-armv8.o:	ecp_nistz256-armv8.S
 
 files:
 	$(PERL) $(TOP)/util/files.pl Makefile >> $(TOP)/MINFO
diff --git a/crypto/ec/asm/ecp_nistz256-armv8.pl b/crypto/ec/asm/ecp_nistz256-armv8.pl
new file mode 100644
index 0000000000..1c9eb6b3fa
--- /dev/null
+++ b/crypto/ec/asm/ecp_nistz256-armv8.pl
@@ -0,0 +1,1567 @@
+#!/usr/bin/env perl
+
+# ====================================================================
+# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
+# project. The module is, however, dual licensed under OpenSSL and
+# CRYPTOGAMS licenses depending on where you obtain it. For further
+# details see http://www.openssl.org/~appro/cryptogams/.
+# ====================================================================
+#
+# ECP_NISTZ256 module for ARMv8.
+#
+# February 2015.
+#
+# Original ECP_NISTZ256 submission targeting x86_64 is detailed in
+# http://eprint.iacr.org/2013/816.
+#
+#			with/without -DECP_NISTZ256_ASM(*)
+# Apple A7		+140-590%
+# Cortex-A53		+135-720%
+# Cortex-A57		+145-570%
+# X-Gene		+120-700%
+# Denver		+150-740%
+#
+# (*)	comparison is not really "fair", because it's compared to C
+#	implementation, unlike other similar cases that is;
+#
+# Ranges denote minimum and maximum improvement coefficients depending
+# on benchmark. Lower coefficients are for ECDSA sign, server-side
+# operation. Keep in mind that +500% means 6x improvement.
+
+$flavour = shift;
+while (($output=shift) && ($output!~/^\w[\w\-]*\.\w+$/)) {}
+
+$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
+( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
+( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
+die "can't locate arm-xlate.pl";
+
+open OUT,"| \"$^X\" $xlate $flavour $output";
+*STDOUT=*OUT;
+
+{
+my ($rp,$ap,$bp,$bi,$a0,$a1,$a2,$a3,$t0,$t1,$t2,$t3,$poly1,$poly3,
+    $acc0,$acc1,$acc2,$acc3,$acc4,$acc5) =
+    map("x$_",(0..17,19,20));
+
+my ($acc6,$acc7)=($ap,$bp);	# used in __ecp_nistz256_sqr_mont
+
+$code.=<<___;
+#include "arm_arch.h"
+
+.text
+___
+########################################################################
+# Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7
+#
+$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
+open TABLE,"<ecp_nistz256_table.c"		or
+open TABLE,"<${dir}../ecp_nistz256_table.c"	or
+die "failed to open ecp_nistz256_table.c:",$!;
+
+use integer;
+
+foreach(<TABLE>) {
+	s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo;
+}
+close TABLE;
+
+# See ecp_nistz256_table.c for explanation for why it's 64*16*37.
+# 64*16*37-1 is because $#arr returns last valid index or @arr, not
+# amount of elements.
+die "insane number of elements" if ($#arr != 64*16*37-1);
+
+$code.=<<___;
+.globl	ecp_nistz256_precomputed
+.type	ecp_nistz256_precomputed,%object
+.align	12
+ecp_nistz256_precomputed:
+___
+########################################################################
+# this conversion smashes P256_POINT_AFFINE by individual bytes with
+# 64 byte interval, similar to
+#	1111222233334444
+#	1234123412341234
+for(1..37) {
+	@tbl = splice(@arr,0,64*16);
+	for($i=0;$i<64;$i++) {
+		undef @line;
+		for($j=0;$j<64;$j++) {
+			push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff;
+		}
+		$code.=".byte\t";
+		$code.=join(',',map { sprintf "0x%02x",$_} @line);
+		$code.="\n";
+	}
+}
+$code.=<<___;
+.size	ecp_nistz256_precomputed,.-ecp_nistz256_precomputed
+.align	5
+.Lpoly:
+.quad	0xffffffffffffffff,0x00000000ffffffff,0x0000000000000000,0xffffffff00000001
+.LRR:	// 2^512 mod P precomputed for NIST P256 polynomial
+.quad	0x0000000000000003,0xfffffffbffffffff,0xfffffffffffffffe,0x00000004fffffffd
+.Lone_mont:
+.quad	0x0000000000000001,0xffffffff00000000,0xffffffffffffffff,0x00000000fffffffe
+.Lone:
+.quad	1,0,0,0
+.asciz	"ECP_NISTZ256 for ARMv8, CRYPTOGAMS by <appro\@openssl.org>"
+
+// void	ecp_nistz256_to_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_to_mont
+.type	ecp_nistz256_to_mont,%function
+.align	6
+ecp_nistz256_to_mont:
+	stp	x29,x30,[sp,#-32]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+
+	ldr	$bi,.LRR		// bp[0]
+	ldp	$a0,$a1,[$ap]
+	ldp	$a2,$a3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+	adr	$bp,.LRR		// &bp[0]
+
+	bl	__ecp_nistz256_mul_mont
+
+	ldp	x19,x20,[sp,#16]
+	ldp	x29,x30,[sp],#32
+	ret
+.size	ecp_nistz256_to_mont,.-ecp_nistz256_to_mont
+
+// void	ecp_nistz256_from_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_from_mont
+.type	ecp_nistz256_from_mont,%function
+.align	4
+ecp_nistz256_from_mont:
+	stp	x29,x30,[sp,#-32]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+
+	mov	$bi,#1			// bp[0]
+	ldp	$a0,$a1,[$ap]
+	ldp	$a2,$a3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+	adr	$bp,.Lone		// &bp[0]
+
+	bl	__ecp_nistz256_mul_mont
+
+	ldp	x19,x20,[sp,#16]
+	ldp	x29,x30,[sp],#32
+	ret
+.size	ecp_nistz256_from_mont,.-ecp_nistz256_from_mont
+
+// void	ecp_nistz256_mul_mont(BN_ULONG x0[4],const BN_ULONG x1[4],
+//					     const BN_ULONG x2[4]);
+.globl	ecp_nistz256_mul_mont
+.type	ecp_nistz256_mul_mont,%function
+.align	4
+ecp_nistz256_mul_mont:
+	stp	x29,x30,[sp,#-32]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+
+	ldr	$bi,[$bp]		// bp[0]
+	ldp	$a0,$a1,[$ap]
+	ldp	$a2,$a3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_mul_mont
+
+	ldp	x19,x20,[sp,#16]
+	ldp	x29,x30,[sp],#32
+	ret
+.size	ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont
+
+// void	ecp_nistz256_sqr_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_sqr_mont
+.type	ecp_nistz256_sqr_mont,%function
+.align	4
+ecp_nistz256_sqr_mont:
+	stp	x29,x30,[sp,#-32]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+
+	ldp	$a0,$a1,[$ap]
+	ldp	$a2,$a3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_sqr_mont
+
+	ldp	x19,x20,[sp,#16]
+	ldp	x29,x30,[sp],#32
+	ret
+.size	ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont
+
+// void	ecp_nistz256_add(BN_ULONG x0[4],const BN_ULONG x1[4],
+//					const BN_ULONG x2[4]);
+.globl	ecp_nistz256_add
+.type	ecp_nistz256_add,%function
+.align	4
+ecp_nistz256_add:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	ldp	$acc0,$acc1,[$ap]
+	ldp	$t0,$t1,[$bp]
+	ldp	$acc2,$acc3,[$ap,#16]
+	ldp	$t2,$t3,[$bp,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_add
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_add,.-ecp_nistz256_add
+
+// void	ecp_nistz256_div_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_div_by_2
+.type	ecp_nistz256_div_by_2,%function
+.align	4
+ecp_nistz256_div_by_2:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	ldp	$acc0,$acc1,[$ap]
+	ldp	$acc2,$acc3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_div_by_2
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2
+
+// void	ecp_nistz256_mul_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_mul_by_2
+.type	ecp_nistz256_mul_by_2,%function
+.align	4
+ecp_nistz256_mul_by_2:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	ldp	$acc0,$acc1,[$ap]
+	ldp	$acc2,$acc3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+
+	bl	__ecp_nistz256_add	// ret = a+a	// 2*a
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2
+
+// void	ecp_nistz256_mul_by_3(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_mul_by_3
+.type	ecp_nistz256_mul_by_3,%function
+.align	4
+ecp_nistz256_mul_by_3:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	ldp	$acc0,$acc1,[$ap]
+	ldp	$acc2,$acc3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	mov	$a0,$acc0
+	mov	$a1,$acc1
+	mov	$a2,$acc2
+	mov	$a3,$acc3
+
+	bl	__ecp_nistz256_add	// ret = a+a	// 2*a
+
+	mov	$t0,$a0
+	mov	$t1,$a1
+	mov	$t2,$a2
+	mov	$t3,$a3
+
+	bl	__ecp_nistz256_add	// ret += a	// 2*a+a=3*a
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3
+
+// void	ecp_nistz256_sub(BN_ULONG x0[4],const BN_ULONG x1[4],
+//				        const BN_ULONG x2[4]);
+.globl	ecp_nistz256_sub
+.type	ecp_nistz256_sub,%function
+.align	4
+ecp_nistz256_sub:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	ldp	$acc0,$acc1,[$ap]
+	ldp	$acc2,$acc3,[$ap,#16]
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_sub_from
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_sub,.-ecp_nistz256_sub
+
+// void	ecp_nistz256_neg(BN_ULONG x0[4],const BN_ULONG x1[4]);
+.globl	ecp_nistz256_neg
+.type	ecp_nistz256_neg,%function
+.align	4
+ecp_nistz256_neg:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	mov	$bp,$ap
+	mov	$acc0,xzr		// a = 0
+	mov	$acc1,xzr
+	mov	$acc2,xzr
+	mov	$acc3,xzr
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	bl	__ecp_nistz256_sub_from
+
+	ldp	x29,x30,[sp],#16
+	ret
+.size	ecp_nistz256_neg,.-ecp_nistz256_neg
+
+// note that __ecp_nistz256_mul_mont expects a[0-3] input pre-loaded
+// to $a0-$a3 and b[0] - to $bi
+.type	__ecp_nistz256_mul_mont,%function
+.align	4
+__ecp_nistz256_mul_mont:
+	mul	$acc0,$a0,$bi		// a[0]*b[0]
+	umulh	$t0,$a0,$bi
+
+	mul	$acc1,$a1,$bi		// a[1]*b[0]
+	umulh	$t1,$a1,$bi
+
+	mul	$acc2,$a2,$bi		// a[2]*b[0]
+	umulh	$t2,$a2,$bi
+
+	mul	$acc3,$a3,$bi		// a[3]*b[0]
+	umulh	$t3,$a3,$bi
+	ldr	$bi,[$bp,#8]		// b[1]
+
+	adds	$acc1,$acc1,$t0		// accumulate high parts of multiplication
+	 lsl	$t0,$acc0,#32
+	adcs	$acc2,$acc2,$t1
+	 lsr	$t1,$acc0,#32
+	adcs	$acc3,$acc3,$t2
+	adc	$acc4,xzr,$t3
+	mov	$acc5,xzr
+___
+for($i=1;$i<4;$i++) {
+        # Reduction iteration is normally performed by accumulating
+        # result of multiplication of modulus by "magic" digit [and
+        # omitting least significant word, which is guaranteed to
+        # be 0], but thanks to special form of modulus and "magic"
+        # digit being equal to least significant word, it can be
+        # performed with additions and subtractions alone. Indeed:
+        #
+        #            ffff0001.00000000.0000ffff.ffffffff
+        # *                                     abcdefgh
+        # + xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh
+        #
+        # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we
+        # rewrite above as:
+        #
+        #   xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh
+        # + abcdefgh.abcdefgh.0000abcd.efgh0000.00000000
+        # - 0000abcd.efgh0000.00000000.00000000.abcdefgh
+        #
+        # or marking redundant operations:
+        #
+        #   xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.--------
+        # + abcdefgh.abcdefgh.0000abcd.efgh0000.--------
+        # - 0000abcd.efgh0000.--------.--------.--------
+
+$code.=<<___;
+	subs	$t2,$acc0,$t0		// "*0xffff0001"
+	sbc	$t3,$acc0,$t1
+	adds	$acc0,$acc1,$t0		// +=acc[0]<<96 and omit acc[0]
+	 mul	$t0,$a0,$bi		// lo(a[0]*b[i])
+	adcs	$acc1,$acc2,$t1
+	 mul	$t1,$a1,$bi		// lo(a[1]*b[i])
+	adcs	$acc2,$acc3,$t2		// +=acc[0]*0xffff0001
+	 mul	$t2,$a2,$bi		// lo(a[2]*b[i])
+	adcs	$acc3,$acc4,$t3
+	 mul	$t3,$a3,$bi		// lo(a[3]*b[i])
+	adc	$acc4,$acc5,xzr
+
+	adds	$acc0,$acc0,$t0		// accumulate low parts of multiplication
+	 umulh	$t0,$a0,$bi		// hi(a[0]*b[i])
+	adcs	$acc1,$acc1,$t1
+	 umulh	$t1,$a1,$bi		// hi(a[1]*b[i])
+	adcs	$acc2,$acc2,$t2
+	 umulh	$t2,$a2,$bi		// hi(a[2]*b[i])
+	adcs	$acc3,$acc3,$t3
+	 umulh	$t3,$a3,$bi		// hi(a[3]*b[i])
+	adc	$acc4,$acc4,xzr
+___
+$code.=<<___	if ($i<3);
+	ldr	$bi,[$bp,#8*($i+1)]	// b[$i+1]
+___
+$code.=<<___;
+	adds	$acc1,$acc1,$t0		// accumulate high parts of multiplication
+	 lsl	$t0,$acc0,#32
+	adcs	$acc2,$acc2,$t1
+	 lsr	$t1,$acc0,#32
+	adcs	$acc3,$acc3,$t2
+	adcs	$acc4,$acc4,$t3
+	adc	$acc5,xzr,xzr
+___
+}
+$code.=<<___;
+	// last reduction
+	subs	$t2,$acc0,$t0		// "*0xffff0001"
+	sbc	$t3,$acc0,$t1
+	adds	$acc0,$acc1,$t0		// +=acc[0]<<96 and omit acc[0]
+	adcs	$acc1,$acc2,$t1
+	adcs	$acc2,$acc3,$t2		// +=acc[0]*0xffff0001
+	adcs	$acc3,$acc4,$t3
+	adc	$acc4,$acc5,xzr
+
+	adds	$t0,$acc0,#1		// subs	$t0,$acc0,#-1 // tmp = ret-modulus
+	sbcs	$t1,$acc1,$poly1
+	sbcs	$t2,$acc2,xzr
+	sbcs	$t3,$acc3,$poly3
+	sbcs	xzr,$acc4,xzr		// did it borrow?
+
+	csel	$acc0,$acc0,$t0,lo	// ret = borrow ? ret : ret-modulus
+	csel	$acc1,$acc1,$t1,lo
+	csel	$acc2,$acc2,$t2,lo
+	stp	$acc0,$acc1,[$rp]
+	csel	$acc3,$acc3,$t3,lo
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont
+
+// note that __ecp_nistz256_sqr_mont expects a[0-3] input pre-loaded
+// to $a0-$a3
+.type	__ecp_nistz256_sqr_mont,%function
+.align	4
+__ecp_nistz256_sqr_mont:
+	//  |  |  |  |  |  |a1*a0|  |
+	//  |  |  |  |  |a2*a0|  |  |
+	//  |  |a3*a2|a3*a0|  |  |  |
+	//  |  |  |  |a2*a1|  |  |  |
+	//  |  |  |a3*a1|  |  |  |  |
+	// *|  |  |  |  |  |  |  | 2|
+	// +|a3*a3|a2*a2|a1*a1|a0*a0|
+	//  |--+--+--+--+--+--+--+--|
+	//  |A7|A6|A5|A4|A3|A2|A1|A0|, where Ax is $accx, i.e. follow $accx
+	//
+	//  "can't overflow" below mark carrying into high part of
+	//  multiplication result, which can't overflow, because it
+	//  can never be all ones.
+
+	mul	$acc1,$a1,$a0		// a[1]*a[0]
+	umulh	$t1,$a1,$a0
+	mul	$acc2,$a2,$a0		// a[2]*a[0]
+	umulh	$t2,$a2,$a0
+	mul	$acc3,$a3,$a0		// a[3]*a[0]
+	umulh	$acc4,$a3,$a0
+
+	adds	$acc2,$acc2,$t1		// accumulate high parts of multiplication
+	 mul	$t0,$a2,$a1		// a[2]*a[1]
+	 umulh	$t1,$a2,$a1
+	adcs	$acc3,$acc3,$t2
+	 mul	$t2,$a3,$a1		// a[3]*a[1]
+	 umulh	$t3,$a3,$a1
+	adc	$acc4,$acc4,xzr		// can't overflow
+
+	mul	$acc5,$a3,$a2		// a[3]*a[2]
+	umulh	$acc6,$a3,$a2
+
+	adds	$t1,$t1,$t2		// accumulate high parts of multiplication
+	 mul	$acc0,$a0,$a0		// a[0]*a[0]
+	adc	$t2,$t3,xzr		// can't overflow
+
+	adds	$acc3,$acc3,$t0		// accumulate low parts of multiplication
+	 umulh	$a0,$a0,$a0
+	adcs	$acc4,$acc4,$t1
+	 mul	$t1,$a1,$a1		// a[1]*a[1]
+	adcs	$acc5,$acc5,$t2
+	 umulh	$a1,$a1,$a1
+	adc	$acc6,$acc6,xzr		// can't overflow
+
+	adds	$acc1,$acc1,$acc1	// acc[1-6]*=2
+	 mul	$t2,$a2,$a2		// a[2]*a[2]
+	adcs	$acc2,$acc2,$acc2
+	 umulh	$a2,$a2,$a2
+	adcs	$acc3,$acc3,$acc3
+	 mul	$t3,$a3,$a3		// a[3]*a[3]
+	adcs	$acc4,$acc4,$acc4
+	 umulh	$a3,$a3,$a3
+	adcs	$acc5,$acc5,$acc5
+	adcs	$acc6,$acc6,$acc6
+	adc	$acc7,xzr,xzr
+
+	adds	$acc1,$acc1,$a0		// +a[i]*a[i]
+	adcs	$acc2,$acc2,$t1
+	adcs	$acc3,$acc3,$a1
+	adcs	$acc4,$acc4,$t2
+	adcs	$acc5,$acc5,$a2
+	 lsl	$t0,$acc0,#32
+	adcs	$acc6,$acc6,$t3
+	 lsr	$t1,$acc0,#32
+	adc	$acc7,$acc7,$a3
+___
+for($i=0;$i<3;$i++) {			# reductions, see commentary in
+					# multiplication for details
+$code.=<<___;
+	subs	$t2,$acc0,$t0		// "*0xffff0001"
+	sbc	$t3,$acc0,$t1
+	adds	$acc0,$acc1,$t0		// +=acc[0]<<96 and omit acc[0]
+	adcs	$acc1,$acc2,$t1
+	 lsl	$t0,$acc0,#32
+	adcs	$acc2,$acc3,$t2		// +=acc[0]*0xffff0001
+	 lsr	$t1,$acc0,#32
+	adc	$acc3,$t3,xzr		// can't overflow
+___
+}
+$code.=<<___;
+	subs	$t2,$acc0,$t0		// "*0xffff0001"
+	sbc	$t3,$acc0,$t1
+	adds	$acc0,$acc1,$t0		// +=acc[0]<<96 and omit acc[0]
+	adcs	$acc1,$acc2,$t1
+	adcs	$acc2,$acc3,$t2		// +=acc[0]*0xffff0001
+	adc	$acc3,$t3,xzr		// can't overflow
+
+	adds	$acc0,$acc0,$acc4	// accumulate upper half
+	adcs	$acc1,$acc1,$acc5
+	adcs	$acc2,$acc2,$acc6
+	adcs	$acc3,$acc3,$acc7
+	adc	$acc4,xzr,xzr
+
+	adds	$t0,$acc0,#1		// subs	$t0,$acc0,#-1 // tmp = ret-modulus
+	sbcs	$t1,$acc1,$poly1
+	sbcs	$t2,$acc2,xzr
+	sbcs	$t3,$acc3,$poly3
+	sbcs	xzr,$acc4,xzr		// did it borrow?
+
+	csel	$acc0,$acc0,$t0,lo	// ret = borrow ? ret : ret-modulus
+	csel	$acc1,$acc1,$t1,lo
+	csel	$acc2,$acc2,$t2,lo
+	stp	$acc0,$acc1,[$rp]
+	csel	$acc3,$acc3,$t3,lo
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_sqr_mont,.-__ecp_nistz256_sqr_mont
+
+// Note that __ecp_nistz256_add expects both input vectors pre-loaded to
+// $a0-$a3 and $t0-$t3. This is done because it's used in multiple
+// contexts, e.g. in multiplication by 2 and 3...
+.type	__ecp_nistz256_add,%function
+.align	4
+__ecp_nistz256_add:
+	adds	$acc0,$acc0,$t0		// ret = a+b
+	adcs	$acc1,$acc1,$t1
+	adcs	$acc2,$acc2,$t2
+	adcs	$acc3,$acc3,$t3
+	adc	$ap,xzr,xzr		// zap $ap
+
+	adds	$t0,$acc0,#1		// subs	$t0,$a0,#-1 // tmp = ret-modulus
+	sbcs	$t1,$acc1,$poly1
+	sbcs	$t2,$acc2,xzr
+	sbc	$t3,$acc3,$poly3
+	cmp	$ap,xzr			// did addition carry?
+
+	csel	$acc0,$acc0,$t0,eq	// ret = carry ? ret-modulus : ret
+	csel	$acc1,$acc1,$t1,eq
+	csel	$acc2,$acc2,$t2,eq
+	stp	$acc0,$acc1,[$rp]
+	csel	$acc3,$acc3,$t3,eq
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_add,.-__ecp_nistz256_add
+
+.type	__ecp_nistz256_sub_from,%function
+.align	4
+__ecp_nistz256_sub_from:
+	ldp	$t0,$t1,[$bp]
+	ldp	$t2,$t3,[$bp,#16]
+	subs	$acc0,$acc0,$t0		// ret = a-b
+	sbcs	$acc1,$acc1,$t1
+	sbcs	$acc2,$acc2,$t2
+	sbcs	$acc3,$acc3,$t3
+	sbc	$ap,xzr,xzr		// zap $ap
+
+	subs	$t0,$acc0,#1		// adds	$t0,$a0,#-1 // tmp = ret+modulus
+	adcs	$t1,$acc1,$poly1
+	adcs	$t2,$acc2,xzr
+	adc	$t3,$acc3,$poly3
+	cmp	$ap,xzr			// did subtraction borrow?
+
+	csel	$acc0,$acc0,$t0,eq	// ret = borrow ? ret+modulus : ret
+	csel	$acc1,$acc1,$t1,eq
+	csel	$acc2,$acc2,$t2,eq
+	stp	$acc0,$acc1,[$rp]
+	csel	$acc3,$acc3,$t3,eq
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from
+
+.type	__ecp_nistz256_sub_morf,%function
+.align	4
+__ecp_nistz256_sub_morf:
+	ldp	$t0,$t1,[$bp]
+	ldp	$t2,$t3,[$bp,#16]
+	subs	$acc0,$t0,$acc0		// ret = b-a
+	sbcs	$acc1,$t1,$acc1
+	sbcs	$acc2,$t2,$acc2
+	sbcs	$acc3,$t3,$acc3
+	sbc	$ap,xzr,xzr		// zap $ap
+
+	subs	$t0,$acc0,#1		// adds	$t0,$a0,#-1 // tmp = ret+modulus
+	adcs	$t1,$acc1,$poly1
+	adcs	$t2,$acc2,xzr
+	adc	$t3,$acc3,$poly3
+	cmp	$ap,xzr			// did subtraction borrow?
+
+	csel	$acc0,$acc0,$t0,eq	// ret = borrow ? ret+modulus : ret
+	csel	$acc1,$acc1,$t1,eq
+	csel	$acc2,$acc2,$t2,eq
+	stp	$acc0,$acc1,[$rp]
+	csel	$acc3,$acc3,$t3,eq
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf
+
+.type	__ecp_nistz256_div_by_2,%function
+.align	4
+__ecp_nistz256_div_by_2:
+	subs	$t0,$acc0,#1		// adds	$t0,$a0,#-1 // tmp = a+modulus
+	adcs	$t1,$acc1,$poly1
+	adcs	$t2,$acc2,xzr
+	adcs	$t3,$acc3,$poly3
+	adc	$ap,xzr,xzr		// zap $ap
+	tst	$acc0,#1		// is a even?
+
+	csel	$acc0,$acc0,$t0,eq	// ret = even ? a : a+modulus 
+	csel	$acc1,$acc1,$t1,eq
+	csel	$acc2,$acc2,$t2,eq
+	csel	$acc3,$acc3,$t3,eq
+	csel	$ap,xzr,$ap,eq
+
+	lsr	$acc0,$acc0,#1		// ret >>= 1
+	orr	$acc0,$acc0,$acc1,lsl#63
+	lsr	$acc1,$acc1,#1
+	orr	$acc1,$acc1,$acc2,lsl#63
+	lsr	$acc2,$acc2,#1
+	orr	$acc2,$acc2,$acc3,lsl#63
+	lsr	$acc3,$acc3,#1
+	stp	$acc0,$acc1,[$rp]
+	orr	$acc3,$acc3,$ap,lsl#63
+	stp	$acc2,$acc3,[$rp,#16]
+
+	ret
+.size	__ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2
+___
+########################################################################
+# following subroutines are "literal" implemetation of those found in
+# ecp_nistz256.c
+#
+########################################################################
+# void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp);
+#
+{
+my ($S,$M,$Zsqr,$tmp0)=map(32*$_,(0..3));
+# above map() describes stack layout with 4 temporary
+# 256-bit vectors on top.
+my ($rp_real,$ap_real) = map("x$_",(21,22));
+
+$code.=<<___;
+.globl	ecp_nistz256_point_double
+.type	ecp_nistz256_point_double,%function
+.align	5
+ecp_nistz256_point_double:
+	stp	x29,x30,[sp,#-48]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+	stp	x21,x22,[sp,#32]
+	sub	sp,sp,#32*4
+
+	ldp	$acc0,$acc1,[$ap,#32]
+	 mov	$rp_real,$rp
+	ldp	$acc2,$acc3,[$ap,#48]
+	 mov	$ap_real,$ap
+	 ldr	$poly1,.Lpoly+8
+	mov	$t0,$acc0
+	 ldr	$poly3,.Lpoly+24
+	mov	$t1,$acc1
+	 ldp	$a0,$a1,[$ap_real,#64]	// forward load for p256_sqr_mont
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	 ldp	$a2,$a3,[$ap_real,#64+16]
+	add	$rp,sp,#$S
+	bl	__ecp_nistz256_add	// p256_mul_by_2(S, in_y);
+
+	add	$rp,sp,#$Zsqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Zsqr, in_z);
+
+	ldp	$t0,$t1,[$ap_real]
+	ldp	$t2,$t3,[$ap_real,#16]
+	mov	$a0,$acc0		// put Zsqr aside for p256_sub
+	mov	$a1,$acc1
+	mov	$a2,$acc2
+	mov	$a3,$acc3
+	add	$rp,sp,#$M
+	bl	__ecp_nistz256_add	// p256_add(M, Zsqr, in_x);
+
+	add	$bp,$ap_real,#0
+	mov	$acc0,$a0		// restore Zsqr
+	mov	$acc1,$a1
+	 ldp	$a0,$a1,[sp,#$S]	// forward load for p256_sqr_mont
+	mov	$acc2,$a2
+	mov	$acc3,$a3
+	 ldp	$a2,$a3,[sp,#$S+16]
+	add	$rp,sp,#$Zsqr
+	bl	__ecp_nistz256_sub_morf	// p256_sub(Zsqr, in_x, Zsqr);
+
+	add	$rp,sp,#$S
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(S, S);
+
+	ldr	$bi,[$ap_real,#32]
+	ldp	$a0,$a1,[$ap_real,#64]
+	ldp	$a2,$a3,[$ap_real,#64+16]
+	add	$bp,$ap_real,#32
+	add	$rp,sp,#$tmp0
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(tmp0, in_z, in_y);
+
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	 ldp	$a0,$a1,[sp,#$S]	// forward load for p256_sqr_mont
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	 ldp	$a2,$a3,[sp,#$S+16]
+	add	$rp,$rp_real,#64
+	bl	__ecp_nistz256_add	// p256_mul_by_2(res_z, tmp0);
+
+	add	$rp,sp,#$tmp0
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(tmp0, S);
+
+	 ldr	$bi,[sp,#$Zsqr]		// forward load for p256_mul_mont
+	 ldp	$a0,$a1,[sp,#$M]
+	 ldp	$a2,$a3,[sp,#$M+16]
+	add	$rp,$rp_real,#32
+	bl	__ecp_nistz256_div_by_2	// p256_div_by_2(res_y, tmp0);
+
+	add	$bp,sp,#$Zsqr
+	add	$rp,sp,#$M
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(M, M, Zsqr);
+
+	mov	$t0,$acc0		// duplicate M
+	mov	$t1,$acc1
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	mov	$a0,$acc0		// put M aside
+	mov	$a1,$acc1
+	mov	$a2,$acc2
+	mov	$a3,$acc3
+	add	$rp,sp,#$M
+	bl	__ecp_nistz256_add
+	mov	$t0,$a0			// restore M
+	mov	$t1,$a1
+	 ldr	$bi,[$ap_real]		// forward load for p256_mul_mont
+	mov	$t2,$a2
+	 ldp	$a0,$a1,[sp,#$S]
+	mov	$t3,$a3
+	 ldp	$a2,$a3,[sp,#$S+16]
+	bl	__ecp_nistz256_add	// p256_mul_by_3(M, M);
+
+	add	$bp,$ap_real,#0
+	add	$rp,sp,#$S
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S, S, in_x);
+
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	 ldp	$a0,$a1,[sp,#$M]	// forward load for p256_sqr_mont
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	 ldp	$a2,$a3,[sp,#$M+16]
+	add	$rp,sp,#$tmp0
+	bl	__ecp_nistz256_add	// p256_mul_by_2(tmp0, S);
+
+	add	$rp,$rp_real,#0
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(res_x, M);
+
+	add	$bp,sp,#$tmp0
+	bl	__ecp_nistz256_sub_from	// p256_sub(res_x, res_x, tmp0);
+
+	add	$bp,sp,#$S
+	add	$rp,sp,#$S
+	bl	__ecp_nistz256_sub_morf	// p256_sub(S, S, res_x);
+
+	ldr	$bi,[sp,#$M]
+	mov	$a0,$acc0		// copy S
+	mov	$a1,$acc1
+	mov	$a2,$acc2
+	mov	$a3,$acc3
+	add	$bp,sp,#$M
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S, S, M);
+
+	add	$bp,$rp_real,#32
+	add	$rp,$rp_real,#32
+	bl	__ecp_nistz256_sub_from	// p256_sub(res_y, S, res_y);
+
+	add	sp,x29,#0		// destroy frame
+	ldp	x19,x20,[x29,#16]
+	ldp	x21,x22,[x29,#32]
+	ldp	x29,x30,[sp],#48
+	ret
+.size	ecp_nistz256_point_double,.-ecp_nistz256_point_double
+___
+}
+
+########################################################################
+# void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1,
+#			      const P256_POINT *in2);
+{
+my ($res_x,$res_y,$res_z,
+    $H,$Hsqr,$R,$Rsqr,$Hcub,
+    $U1,$U2,$S1,$S2)=map(32*$_,(0..11));
+my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr);
+# above map() describes stack layout with 12 temporary
+# 256-bit vectors on top.
+my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26));
+
+$code.=<<___;
+.globl	ecp_nistz256_point_add
+.type	ecp_nistz256_point_add,%function
+.align	5
+ecp_nistz256_point_add:
+	stp	x29,x30,[sp,#-80]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+	stp	x21,x22,[sp,#32]
+	stp	x23,x24,[sp,#48]
+	stp	x25,x26,[sp,#64]
+	sub	sp,sp,#32*12
+
+	ldp	$a0,$a1,[$bp]
+	ldp	$a2,$a3,[$bp,#16]
+	ldp	$t0,$t1,[$bp,#32]
+	ldp	$t2,$t3,[$bp,#48]
+	 mov	$rp_real,$rp
+	 mov	$ap_real,$ap
+	 mov	$bp_real,$bp
+	orr	$a0,$a0,$a1
+	orr	$a2,$a2,$a3
+	 ldp	$acc0,$acc1,[$ap]
+	orr	$t0,$t0,$t1
+	orr	$t2,$t2,$t3
+	 ldp	$acc2,$acc3,[$ap,#16]
+	orr	$a0,$a0,$a2
+	orr	$t2,$t0,$t2
+	 ldp	$t0,$t1,[$ap,#32]
+	orr	$in2infty,$a0,$t2
+	cmp	$in2infty,#0
+	 ldp	$t2,$t3,[$ap,#48]
+	csetm	$in2infty,ne		// !in2infty
+
+	 ldp	$a0,$a1,[$bp_real,#64]	// forward load for p256_sqr_mont
+	orr	$acc0,$acc0,$acc1
+	orr	$acc2,$acc2,$acc3
+	 ldp	$a2,$a3,[$bp_real,#64+16]
+	orr	$t0,$t0,$t1
+	orr	$t2,$t2,$t3
+	orr	$acc0,$acc0,$acc2
+	orr	$t0,$t0,$t2
+	orr	$in1infty,$acc0,$t0
+	cmp	$in1infty,#0
+	 ldr	$poly1,.Lpoly+8
+	 ldr	$poly3,.Lpoly+24
+	csetm	$in1infty,ne		// !in1infty
+
+	add	$rp,sp,#$Z2sqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Z2sqr, in2_z);
+
+	ldp	$a0,$a1,[$ap_real,#64]
+	ldp	$a2,$a3,[$ap_real,#64+16]
+	add	$rp,sp,#$Z1sqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Z1sqr, in1_z);
+
+	ldr	$bi,[$bp_real,#64]
+	ldp	$a0,$a1,[sp,#$Z2sqr]
+	ldp	$a2,$a3,[sp,#$Z2sqr+16]
+	add	$bp,$bp_real,#64
+	add	$rp,sp,#$S1
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S1, Z2sqr, in2_z);
+
+	ldr	$bi,[$ap_real,#64]
+	ldp	$a0,$a1,[sp,#$Z1sqr]
+	ldp	$a2,$a3,[sp,#$Z1sqr+16]
+	add	$bp,$ap_real,#64
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, Z1sqr, in1_z);
+
+	ldr	$bi,[$ap_real,#32]
+	ldp	$a0,$a1,[sp,#$S1]
+	ldp	$a2,$a3,[sp,#$S1+16]
+	add	$bp,$ap_real,#32
+	add	$rp,sp,#$S1
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S1, S1, in1_y);
+
+	ldr	$bi,[$bp_real,#32]
+	ldp	$a0,$a1,[sp,#$S2]
+	ldp	$a2,$a3,[sp,#$S2+16]
+	add	$bp,$bp_real,#32
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, S2, in2_y);
+
+	add	$bp,sp,#$S1
+	 ldr	$bi,[sp,#$Z2sqr]	// forward load for p256_mul_mont
+	 ldp	$a0,$a1,[$ap_real]
+	 ldp	$a2,$a3,[$ap_real,#16]
+	add	$rp,sp,#$R
+	bl	__ecp_nistz256_sub_from	// p256_sub(R, S2, S1);
+
+	orr	$acc0,$acc0,$acc1	// see if result is zero
+	orr	$acc2,$acc2,$acc3
+	orr	$temp,$acc0,$acc2
+
+	add	$bp,sp,#$Z2sqr
+	add	$rp,sp,#$U1
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(U1, in1_x, Z2sqr);
+
+	ldr	$bi,[sp,#$Z1sqr]
+	ldp	$a0,$a1,[$bp_real]
+	ldp	$a2,$a3,[$bp_real,#16]
+	add	$bp,sp,#$Z1sqr
+	add	$rp,sp,#$U2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(U2, in2_x, Z1sqr);
+
+	add	$bp,sp,#$U1
+	 ldp	$a0,$a1,[sp,#$R]	// forward load for p256_sqr_mont
+	 ldp	$a2,$a3,[sp,#$R+16]
+	add	$rp,sp,#$H
+	bl	__ecp_nistz256_sub_from	// p256_sub(H, U2, U1);
+
+	orr	$acc0,$acc0,$acc1	// see if result is zero
+	orr	$acc2,$acc2,$acc3
+	orr	$acc0,$acc0,$acc2
+	tst	$acc0,$acc0
+	b.ne	.Ladd_proceed		// is_equal(U1,U2)?
+
+	tst	$in1infty,$in2infty
+	b.eq	.Ladd_proceed		// (in1infty || in2infty)?
+
+	tst	$temp,$temp
+	b.eq	.Ladd_proceed		// is_equal(S1,S2)?
+
+	eor	$a0,$a0,$a0
+	eor	$a1,$a1,$a1
+	stp	$a0,$a1,[$rp_real]
+	stp	$a0,$a1,[$rp_real,#16]
+	stp	$a0,$a1,[$rp_real,#32]
+	stp	$a0,$a1,[$rp_real,#48]
+	stp	$a0,$a1,[$rp_real,#64]
+	stp	$a0,$a1,[$rp_real,#80]
+	b	.Ladd_done
+
+.align	4
+.Ladd_proceed:
+	add	$rp,sp,#$Rsqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Rsqr, R);
+
+	ldr	$bi,[$ap_real,#64]
+	ldp	$a0,$a1,[sp,#$H]
+	ldp	$a2,$a3,[sp,#$H+16]
+	add	$bp,$ap_real,#64
+	add	$rp,sp,#$res_z
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(res_z, H, in1_z);
+
+	ldp	$a0,$a1,[sp,#$H]
+	ldp	$a2,$a3,[sp,#$H+16]
+	add	$rp,sp,#$Hsqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Hsqr, H);
+
+	ldr	$bi,[$bp_real,#64]
+	ldp	$a0,$a1,[sp,#$res_z]
+	ldp	$a2,$a3,[sp,#$res_z+16]
+	add	$bp,$bp_real,#64
+	add	$rp,sp,#$res_z
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(res_z, res_z, in2_z);
+
+	ldr	$bi,[sp,#$H]
+	ldp	$a0,$a1,[sp,#$Hsqr]
+	ldp	$a2,$a3,[sp,#$Hsqr+16]
+	add	$bp,sp,#$H
+	add	$rp,sp,#$Hcub
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(Hcub, Hsqr, H);
+
+	ldr	$bi,[sp,#$Hsqr]
+	ldp	$a0,$a1,[sp,#$U1]
+	ldp	$a2,$a3,[sp,#$U1+16]
+	add	$bp,sp,#$Hsqr
+	add	$rp,sp,#$U2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(U2, U1, Hsqr);
+
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	add	$rp,sp,#$Hsqr
+	bl	__ecp_nistz256_add	// p256_mul_by_2(Hsqr, U2);
+
+	add	$bp,sp,#$Rsqr
+	add	$rp,sp,#$res_x
+	bl	__ecp_nistz256_sub_morf	// p256_sub(res_x, Rsqr, Hsqr);
+
+	add	$bp,sp,#$Hcub
+	bl	__ecp_nistz256_sub_from	//  p256_sub(res_x, res_x, Hcub);
+
+	add	$bp,sp,#$U2
+	 ldr	$bi,[sp,#$Hcub]		// forward load for p256_mul_mont
+	 ldp	$a0,$a1,[sp,#$S1]
+	 ldp	$a2,$a3,[sp,#$S1+16]
+	add	$rp,sp,#$res_y
+	bl	__ecp_nistz256_sub_morf	// p256_sub(res_y, U2, res_x);
+
+	add	$bp,sp,#$Hcub
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, S1, Hcub);
+
+	ldr	$bi,[sp,#$R]
+	ldp	$a0,$a1,[sp,#$res_y]
+	ldp	$a2,$a3,[sp,#$res_y+16]
+	add	$bp,sp,#$R
+	add	$rp,sp,#$res_y
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(res_y, res_y, R);
+
+	add	$bp,sp,#$S2
+	bl	__ecp_nistz256_sub_from	// p256_sub(res_y, res_y, S2);
+
+	ldp	$a0,$a1,[sp,#$res_x]		// res
+	ldp	$a2,$a3,[sp,#$res_x+16]
+	ldp	$t0,$t1,[$bp_real]		// in2
+	ldp	$t2,$t3,[$bp_real,#16]
+___
+for($i=0;$i<64;$i+=32) {		# conditional moves
+$code.=<<___;
+	ldp	$acc0,$acc1,[$ap_real,#$i]	// in1
+	cmp	$in1infty,#0			// !$in1intfy, remember?
+	ldp	$acc2,$acc3,[$ap_real,#$i+16]
+	csel	$t0,$a0,$t0,ne
+	csel	$t1,$a1,$t1,ne
+	ldp	$a0,$a1,[sp,#$res_x+$i+32]	// res
+	csel	$t2,$a2,$t2,ne
+	csel	$t3,$a3,$t3,ne
+	cmp	$in2infty,#0			// !$in2intfy, remember?
+	ldp	$a2,$a3,[sp,#$res_x+$i+48]
+	csel	$acc0,$t0,$acc0,ne
+	csel	$acc1,$t1,$acc1,ne
+	ldp	$t0,$t1,[$bp_real,#$i+32]	// in2
+	csel	$acc2,$t2,$acc2,ne
+	csel	$acc3,$t3,$acc3,ne
+	ldp	$t2,$t3,[$bp_real,#$i+48]
+	stp	$acc0,$acc1,[$rp_real,#$i]
+	stp	$acc2,$acc3,[$rp_real,#$i+16]
+___
+}
+$code.=<<___;
+	ldp	$acc0,$acc1,[$ap_real,#$i]	// in1
+	cmp	$in1infty,#0			// !$in1intfy, remember?
+	ldp	$acc2,$acc3,[$ap_real,#$i+16]
+	csel	$t0,$a0,$t0,ne
+	csel	$t1,$a1,$t1,ne
+	csel	$t2,$a2,$t2,ne
+	csel	$t3,$a3,$t3,ne
+	cmp	$in2infty,#0			// !$in2intfy, remember?
+	csel	$acc0,$t0,$acc0,ne
+	csel	$acc1,$t1,$acc1,ne
+	csel	$acc2,$t2,$acc2,ne
+	csel	$acc3,$t3,$acc3,ne
+	stp	$acc0,$acc1,[$rp_real,#$i]
+	stp	$acc2,$acc3,[$rp_real,#$i+16]
+
+.Ladd_done:
+	add	sp,x29,#0	// destroy frame
+	ldp	x19,x20,[x29,#16]
+	ldp	x21,x22,[x29,#32]
+	ldp	x23,x24,[x29,#48]
+	ldp	x25,x26,[x29,#64]
+	ldp	x29,x30,[sp],#80
+	ret
+.size	ecp_nistz256_point_add,.-ecp_nistz256_point_add
+___
+}
+
+########################################################################
+# void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1,
+#				     const P256_POINT_AFFINE *in2);
+{
+my ($res_x,$res_y,$res_z,
+    $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..9));
+my $Z1sqr = $S2;
+# above map() describes stack layout with 10 temporary
+# 256-bit vectors on top.
+my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26));
+
+$code.=<<___;
+.globl	ecp_nistz256_point_add_affine
+.type	ecp_nistz256_point_add_affine,%function
+.align	5
+ecp_nistz256_point_add_affine:
+	stp	x29,x30,[sp,#-80]!
+	add	x29,sp,#0
+	stp	x19,x20,[sp,#16]
+	stp	x21,x22,[sp,#32]
+	stp	x23,x24,[sp,#48]
+	stp	x25,x26,[sp,#64]
+	sub	sp,sp,#32*10
+
+	mov	$rp_real,$rp
+	mov	$ap_real,$ap
+	mov	$bp_real,$bp
+	ldr	$poly1,.Lpoly+8
+	ldr	$poly3,.Lpoly+24
+
+	ldp	$a0,$a1,[$ap]
+	ldp	$a2,$a3,[$ap,#16]
+	ldp	$t0,$t1,[$ap,#32]
+	ldp	$t2,$t3,[$ap,#48]
+	orr	$a0,$a0,$a1
+	orr	$a2,$a2,$a3
+	orr	$t0,$t0,$t1
+	orr	$t2,$t2,$t3
+	orr	$a0,$a0,$a2
+	orr	$t0,$t0,$t2
+	orr	$in1infty,$a0,$t0
+	cmp	$in1infty,#0
+	csetm	$in1infty,ne		// !in1infty
+
+	ldp	$a0,$a1,[$bp]
+	ldp	$a2,$a3,[$bp,#16]
+	ldp	$t0,$t1,[$bp,#32]
+	ldp	$t2,$t3,[$bp,#48]
+	orr	$a0,$a0,$a1
+	orr	$a2,$a2,$a3
+	orr	$t0,$t0,$t1
+	orr	$t2,$t2,$t3
+	orr	$a0,$a0,$a2
+	orr	$t0,$t0,$t2
+	orr	$in2infty,$a0,$t0
+	cmp	$in2infty,#0
+	csetm	$in2infty,ne		// !in2infty
+
+	ldp	$a0,$a1,[$ap_real,#64]
+	ldp	$a2,$a3,[$ap_real,#64+16]
+	add	$rp,sp,#$Z1sqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Z1sqr, in1_z);
+
+	mov	$a0,$acc0
+	mov	$a1,$acc1
+	mov	$a2,$acc2
+	mov	$a3,$acc3
+	ldr	$bi,[$bp_real]
+	add	$bp,$bp_real,#0
+	add	$rp,sp,#$U2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(U2, Z1sqr, in2_x);
+
+	add	$bp,$ap_real,#0
+	 ldr	$bi,[$ap_real,#64]	// forward load for p256_mul_mont
+	 ldp	$a0,$a1,[sp,#$Z1sqr]
+	 ldp	$a2,$a3,[sp,#$Z1sqr+16]
+	add	$rp,sp,#$H
+	bl	__ecp_nistz256_sub_from	// p256_sub(H, U2, in1_x);
+
+	add	$bp,$ap_real,#64
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, Z1sqr, in1_z);
+
+	ldr	$bi,[$ap_real,#64]
+	ldp	$a0,$a1,[sp,#$H]
+	ldp	$a2,$a3,[sp,#$H+16]
+	add	$bp,$ap_real,#64
+	add	$rp,sp,#$res_z
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(res_z, H, in1_z);
+
+	ldr	$bi,[$bp_real,#32]
+	ldp	$a0,$a1,[sp,#$S2]
+	ldp	$a2,$a3,[sp,#$S2+16]
+	add	$bp,$bp_real,#32
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, S2, in2_y);
+
+	add	$bp,$ap_real,#32
+	 ldp	$a0,$a1,[sp,#$H]	// forward load for p256_sqr_mont
+	 ldp	$a2,$a3,[sp,#$H+16]
+	add	$rp,sp,#$R
+	bl	__ecp_nistz256_sub_from	// p256_sub(R, S2, in1_y);
+
+	add	$rp,sp,#$Hsqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Hsqr, H);
+
+	ldp	$a0,$a1,[sp,#$R]
+	ldp	$a2,$a3,[sp,#$R+16]
+	add	$rp,sp,#$Rsqr
+	bl	__ecp_nistz256_sqr_mont	// p256_sqr_mont(Rsqr, R);
+
+	ldr	$bi,[sp,#$H]
+	ldp	$a0,$a1,[sp,#$Hsqr]
+	ldp	$a2,$a3,[sp,#$Hsqr+16]
+	add	$bp,sp,#$H
+	add	$rp,sp,#$Hcub
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(Hcub, Hsqr, H);
+
+	ldr	$bi,[$ap_real]
+	ldp	$a0,$a1,[sp,#$Hsqr]
+	ldp	$a2,$a3,[sp,#$Hsqr+16]
+	add	$bp,$ap_real,#0
+	add	$rp,sp,#$U2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(U2, in1_x, Hsqr);
+
+	mov	$t0,$acc0
+	mov	$t1,$acc1
+	mov	$t2,$acc2
+	mov	$t3,$acc3
+	add	$rp,sp,#$Hsqr
+	bl	__ecp_nistz256_add	// p256_mul_by_2(Hsqr, U2);
+
+	add	$bp,sp,#$Rsqr
+	add	$rp,sp,#$res_x
+	bl	__ecp_nistz256_sub_morf	// p256_sub(res_x, Rsqr, Hsqr);
+
+	add	$bp,sp,#$Hcub
+	bl	__ecp_nistz256_sub_from	//  p256_sub(res_x, res_x, Hcub);
+
+	add	$bp,sp,#$U2
+	 ldr	$bi,[$ap_real,#32]	// forward load for p256_mul_mont
+	 ldp	$a0,$a1,[sp,#$Hcub]
+	 ldp	$a2,$a3,[sp,#$Hcub+16]
+	add	$rp,sp,#$res_y
+	bl	__ecp_nistz256_sub_morf	// p256_sub(res_y, U2, res_x);
+
+	add	$bp,$ap_real,#32
+	add	$rp,sp,#$S2
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(S2, in1_y, Hcub);
+
+	ldr	$bi,[sp,#$R]
+	ldp	$a0,$a1,[sp,#$res_y]
+	ldp	$a2,$a3,[sp,#$res_y+16]
+	add	$bp,sp,#$R
+	add	$rp,sp,#$res_y
+	bl	__ecp_nistz256_mul_mont	// p256_mul_mont(res_y, res_y, R);
+
+	add	$bp,sp,#$S2
+	bl	__ecp_nistz256_sub_from	// p256_sub(res_y, res_y, S2);
+
+	ldp	$a0,$a1,[sp,#$res_x]		// res
+	ldp	$a2,$a3,[sp,#$res_x+16]
+	ldp	$t0,$t1,[$bp_real]		// in2
+	ldp	$t2,$t3,[$bp_real,#16]
+___
+for($i=0;$i<64;$i+=32) {		# conditional moves
+$code.=<<___;
+	ldp	$acc0,$acc1,[$ap_real,#$i]	// in1
+	cmp	$in1infty,#0			// !$in1intfy, remember?
+	ldp	$acc2,$acc3,[$ap_real,#$i+16]
+	csel	$t0,$a0,$t0,ne
+	csel	$t1,$a1,$t1,ne
+	ldp	$a0,$a1,[sp,#$res_x+$i+32]	// res
+	csel	$t2,$a2,$t2,ne
+	csel	$t3,$a3,$t3,ne
+	cmp	$in2infty,#0			// !$in2intfy, remember?
+	ldp	$a2,$a3,[sp,#$res_x+$i+48]
+	csel	$acc0,$t0,$acc0,ne
+	csel	$acc1,$t1,$acc1,ne
+	ldp	$t0,$t1,[$bp_real,#$i+32]	// in2
+	csel	$acc2,$t2,$acc2,ne
+	csel	$acc3,$t3,$acc3,ne
+	ldp	$t2,$t3,[$bp_real,#$i+48]
+	stp	$acc0,$acc1,[$rp_real,#$i]
+	stp	$acc2,$acc3,[$rp_real,#$i+16]
+___
+}
+$code.=<<___;
+	ldp	$acc0,$acc1,[$ap_real,#$i]	// in1
+	cmp	$in1infty,#0			// !$in1intfy, remember?
+	ldp	$acc2,$acc3,[$ap_real,#$i+16]
+	csel	$t0,$a0,$t0,ne
+	csel	$t1,$a1,$t1,ne
+	csel	$t2,$a2,$t2,ne
+	csel	$t3,$a3,$t3,ne
+	cmp	$in2infty,#0			// !$in2intfy, remember?
+	csel	$acc0,$t0,$acc0,ne
+	csel	$acc1,$t1,$acc1,ne
+	csel	$acc2,$t2,$acc2,ne
+	csel	$acc3,$t3,$acc3,ne
+	stp	$acc0,$acc1,[$rp_real,#$i]
+	stp	$acc2,$acc3,[$rp_real,#$i+16]
+
+	add	sp,x29,#0		// destroy frame
+	ldp	x19,x20,[x29,#16]
+	ldp	x21,x22,[x29,#32]
+	ldp	x23,x24,[x29,#48]
+	ldp	x25,x26,[x29,#64]
+	ldp	x29,x30,[sp],#80
+	ret
+.size	ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine
+___
+}	}
+
+########################################################################
+# scatter-gather subroutines
+{
+my ($out,$inp,$index,$mask)=map("x$_",(0..3));
+$code.=<<___;
+// void	ecp_nistz256_scatter_w5(void *x0,const P256_POINT *x1,
+//					 int x2);
+.globl	ecp_nistz256_scatter_w5
+.type	ecp_nistz256_scatter_w5,%function
+.align	4
+ecp_nistz256_scatter_w5:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	add	$out,$out,$index,lsl#2
+
+	ldp	x4,x5,[$inp]		// X
+	ldp	x6,x7,[$inp,#16]
+	str	w4,[$out,#64*0-4]
+	lsr	x4,x4,#32
+	str	w5,[$out,#64*1-4]
+	lsr	x5,x5,#32
+	str	w6,[$out,#64*2-4]
+	lsr	x6,x6,#32
+	str	w7,[$out,#64*3-4]
+	lsr	x7,x7,#32
+	str	w4,[$out,#64*4-4]
+	str	w5,[$out,#64*5-4]
+	str	w6,[$out,#64*6-4]
+	str	w7,[$out,#64*7-4]
+	add	$out,$out,#64*8
+
+	ldp	x4,x5,[$inp,#32]	// Y
+	ldp	x6,x7,[$inp,#48]
+	str	w4,[$out,#64*0-4]
+	lsr	x4,x4,#32
+	str	w5,[$out,#64*1-4]
+	lsr	x5,x5,#32
+	str	w6,[$out,#64*2-4]
+	lsr	x6,x6,#32
+	str	w7,[$out,#64*3-4]
+	lsr	x7,x7,#32
+	str	w4,[$out,#64*4-4]
+	str	w5,[$out,#64*5-4]
+	str	w6,[$out,#64*6-4]
+	str	w7,[$out,#64*7-4]
+	add	$out,$out,#64*8
+
+	ldp	x4,x5,[$inp,#64]	// Z
+	ldp	x6,x7,[$inp,#80]
+	str	w4,[$out,#64*0-4]
+	lsr	x4,x4,#32
+	str	w5,[$out,#64*1-4]
+	lsr	x5,x5,#32
+	str	w6,[$out,#64*2-4]
+	lsr	x6,x6,#32
+	str	w7,[$out,#64*3-4]
+	lsr	x7,x7,#32
+	str	w4,[$out,#64*4-4]
+	str	w5,[$out,#64*5-4]
+	str	w6,[$out,#64*6-4]
+	str	w7,[$out,#64*7-4]
+
+	ldr	x29,[sp],#16
+	ret
+.size	ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5
+
+// void	ecp_nistz256_gather_w5(P256_POINT *x0,const void *x1,
+//					      int x2);
+.globl	ecp_nistz256_gather_w5
+.type	ecp_nistz256_gather_w5,%function
+.align	4
+ecp_nistz256_gather_w5:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	cmp	$index,xzr
+	csetm	x3,ne
+	add	$index,$index,x3
+	add	$inp,$inp,$index,lsl#2
+
+	ldr	w4,[$inp,#64*0]
+	ldr	w5,[$inp,#64*1]
+	ldr	w6,[$inp,#64*2]
+	ldr	w7,[$inp,#64*3]
+	ldr	w8,[$inp,#64*4]
+	ldr	w9,[$inp,#64*5]
+	ldr	w10,[$inp,#64*6]
+	ldr	w11,[$inp,#64*7]
+	add	$inp,$inp,#64*8
+	orr	x4,x4,x8,lsl#32
+	orr	x5,x5,x9,lsl#32
+	orr	x6,x6,x10,lsl#32
+	orr	x7,x7,x11,lsl#32
+	csel	x4,x4,xzr,ne
+	csel	x5,x5,xzr,ne
+	csel	x6,x6,xzr,ne
+	csel	x7,x7,xzr,ne
+	stp	x4,x5,[$out]		// X
+	stp	x6,x7,[$out,#16]
+
+	ldr	w4,[$inp,#64*0]
+	ldr	w5,[$inp,#64*1]
+	ldr	w6,[$inp,#64*2]
+	ldr	w7,[$inp,#64*3]
+	ldr	w8,[$inp,#64*4]
+	ldr	w9,[$inp,#64*5]
+	ldr	w10,[$inp,#64*6]
+	ldr	w11,[$inp,#64*7]
+	add	$inp,$inp,#64*8
+	orr	x4,x4,x8,lsl#32
+	orr	x5,x5,x9,lsl#32
+	orr	x6,x6,x10,lsl#32
+	orr	x7,x7,x11,lsl#32
+	csel	x4,x4,xzr,ne
+	csel	x5,x5,xzr,ne
+	csel	x6,x6,xzr,ne
+	csel	x7,x7,xzr,ne
+	stp	x4,x5,[$out,#32]	// Y
+	stp	x6,x7,[$out,#48]
+
+	ldr	w4,[$inp,#64*0]
+	ldr	w5,[$inp,#64*1]
+	ldr	w6,[$inp,#64*2]
+	ldr	w7,[$inp,#64*3]
+	ldr	w8,[$inp,#64*4]
+	ldr	w9,[$inp,#64*5]
+	ldr	w10,[$inp,#64*6]
+	ldr	w11,[$inp,#64*7]
+	orr	x4,x4,x8,lsl#32
+	orr	x5,x5,x9,lsl#32
+	orr	x6,x6,x10,lsl#32
+	orr	x7,x7,x11,lsl#32
+	csel	x4,x4,xzr,ne
+	csel	x5,x5,xzr,ne
+	csel	x6,x6,xzr,ne
+	csel	x7,x7,xzr,ne
+	stp	x4,x5,[$out,#64]	// Z
+	stp	x6,x7,[$out,#80]
+
+	ldr	x29,[sp],#16
+	ret
+.size	ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5
+
+// void	ecp_nistz256_scatter_w7(void *x0,const P256_POINT_AFFINE *x1,
+//					 int x2);
+.globl	ecp_nistz256_scatter_w7
+.type	ecp_nistz256_scatter_w7,%function
+.align	4
+ecp_nistz256_scatter_w7:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	add	$out,$out,$index
+	mov	$index,#64/8
+.Loop_scatter_w7:
+	ldr	x3,[$inp],#8
+	subs	$index,$index,#1
+	prfm	pstl1strm,[$out,#4096+64*0]
+	prfm	pstl1strm,[$out,#4096+64*1]
+	prfm	pstl1strm,[$out,#4096+64*2]
+	prfm	pstl1strm,[$out,#4096+64*3]
+	prfm	pstl1strm,[$out,#4096+64*4]
+	prfm	pstl1strm,[$out,#4096+64*5]
+	prfm	pstl1strm,[$out,#4096+64*6]
+	prfm	pstl1strm,[$out,#4096+64*7]
+	strb	w3,[$out,#64*0-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*1-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*2-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*3-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*4-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*5-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*6-1]
+	lsr	x3,x3,#8
+	strb	w3,[$out,#64*7-1]
+	add	$out,$out,#64*8
+	b.ne	.Loop_scatter_w7
+
+	ldr	x29,[sp],#16
+	ret
+.size	ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7
+
+// void	ecp_nistz256_gather_w7(P256_POINT_AFFINE *x0,const void *x1,
+//						     int x2);
+.globl	ecp_nistz256_gather_w7
+.type	ecp_nistz256_gather_w7,%function
+.align	4
+ecp_nistz256_gather_w7:
+	stp	x29,x30,[sp,#-16]!
+	add	x29,sp,#0
+
+	cmp	$index,xzr
+	csetm	x3,ne
+	add	$index,$index,x3
+	add	$inp,$inp,$index
+	mov	$index,#64/8
+	nop
+.Loop_gather_w7:
+	ldrb	w4,[$inp,#64*0]
+	prfm	pldl1strm,[$inp,#4096+64*0]
+	subs	$index,$index,#1
+	ldrb	w5,[$inp,#64*1]
+	prfm	pldl1strm,[$inp,#4096+64*1]
+	ldrb	w6,[$inp,#64*2]
+	prfm	pldl1strm,[$inp,#4096+64*2]
+	ldrb	w7,[$inp,#64*3]
+	prfm	pldl1strm,[$inp,#4096+64*3]
+	ldrb	w8,[$inp,#64*4]
+	prfm	pldl1strm,[$inp,#4096+64*4]
+	ldrb	w9,[$inp,#64*5]
+	prfm	pldl1strm,[$inp,#4096+64*5]
+	ldrb	w10,[$inp,#64*6]
+	prfm	pldl1strm,[$inp,#4096+64*6]
+	ldrb	w11,[$inp,#64*7]
+	prfm	pldl1strm,[$inp,#4096+64*7]
+	add	$inp,$inp,#64*8
+	orr	x4,x4,x5,lsl#8
+	orr	x6,x6,x7,lsl#8
+	orr	x8,x8,x9,lsl#8
+	orr	x4,x4,x6,lsl#16
+	orr	x10,x10,x11,lsl#8
+	orr	x4,x4,x8,lsl#32
+	orr	x4,x4,x10,lsl#48
+	and	x4,x4,x3
+	str	x4,[$out],#8
+	b.ne	.Loop_gather_w7
+
+	ldr	x29,[sp],#16
+	ret
+.size	ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7
+___
+}
+
+foreach (split("\n",$code)) {
+	s/\`([^\`]*)\`/eval $1/ge;
+
+	print $_,"\n";
+}
+close STDOUT;	# enforce flush