2 # Copyright 2015-2018 The OpenSSL Project Authors. All Rights Reserved.
4 # Licensed under the Apache License 2.0 (the "License"). You may not use
5 # this file except in compliance with the License. You can obtain a copy
6 # in the file LICENSE in the source distribution or at
7 # https://www.openssl.org/source/license.html
10 # ====================================================================
11 # Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
12 # project. The module is, however, dual licensed under OpenSSL and
13 # CRYPTOGAMS licenses depending on where you obtain it. For further
14 # details see http://www.openssl.org/~appro/cryptogams/.
15 # ====================================================================
17 # ECP_NISTZ256 module for ARMv8.
21 # Original ECP_NISTZ256 submission targeting x86_64 is detailed in
22 # http://eprint.iacr.org/2013/816.
24 # with/without -DECP_NISTZ256_ASM
26 # Cortex-A53 +190-400%
27 # Cortex-A57 +190-350%
30 # Ranges denote minimum and maximum improvement coefficients depending
31 # on benchmark. Lower coefficients are for ECDSA sign, server-side
32 # operation. Keep in mind that +400% means 5x improvement.
35 while (($output=shift) && ($output!~/\w[\w\-]*\.\w+$/)) {}
37 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
38 ( $xlate="${dir}arm-xlate.pl" and -f $xlate ) or
39 ( $xlate="${dir}../../perlasm/arm-xlate.pl" and -f $xlate) or
40 die "can't locate arm-xlate.pl";
42 open OUT,"| \"$^X\" $xlate $flavour $output";
46 my ($rp,$ap,$bp,$bi,$a0,$a1,$a2,$a3,$t0,$t1,$t2,$t3,$poly1,$poly3,
47 $acc0,$acc1,$acc2,$acc3,$acc4,$acc5) =
48 map("x$_",(0..17,19,20));
50 my ($acc6,$acc7)=($ap,$bp); # used in __ecp_nistz256_sqr_mont
57 ########################################################################
58 # Convert ecp_nistz256_table.c to layout expected by ecp_nistz_gather_w7
60 $0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
61 open TABLE,"<ecp_nistz256_table.c" or
62 open TABLE,"<${dir}../ecp_nistz256_table.c" or
63 die "failed to open ecp_nistz256_table.c:",$!;
68 s/TOBN\(\s*(0x[0-9a-f]+),\s*(0x[0-9a-f]+)\s*\)/push @arr,hex($2),hex($1)/geo;
72 # See ecp_nistz256_table.c for explanation for why it's 64*16*37.
73 # 64*16*37-1 is because $#arr returns last valid index or @arr, not
75 die "insane number of elements" if ($#arr != 64*16*37-1);
78 .globl ecp_nistz256_precomputed
79 .type ecp_nistz256_precomputed,%object
81 ecp_nistz256_precomputed:
83 ########################################################################
84 # this conversion smashes P256_POINT_AFFINE by individual bytes with
85 # 64 byte interval, similar to
89 @tbl = splice(@arr,0,64*16);
90 for($i=0;$i<64;$i++) {
92 for($j=0;$j<64;$j++) {
93 push @line,(@tbl[$j*16+$i/4]>>(($i%4)*8))&0xff;
96 $code.=join(',',map { sprintf "0x%02x",$_} @line);
101 .size ecp_nistz256_precomputed,.-ecp_nistz256_precomputed
104 .quad 0xffffffffffffffff,0x00000000ffffffff,0x0000000000000000,0xffffffff00000001
105 .LRR: // 2^512 mod P precomputed for NIST P256 polynomial
106 .quad 0x0000000000000003,0xfffffffbffffffff,0xfffffffffffffffe,0x00000004fffffffd
108 .quad 0x0000000000000001,0xffffffff00000000,0xffffffffffffffff,0x00000000fffffffe
112 .quad 0xf3b9cac2fc632551,0xbce6faada7179e84,0xffffffffffffffff,0xffffffff00000000
114 .quad 0xccd1c8aaee00bc4f
115 .asciz "ECP_NISTZ256 for ARMv8, CRYPTOGAMS by <appro\@openssl.org>"
117 // void ecp_nistz256_to_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
118 .globl ecp_nistz256_to_mont
119 .type ecp_nistz256_to_mont,%function
121 ecp_nistz256_to_mont:
122 .inst 0xd503233f // paciasp
123 stp x29,x30,[sp,#-32]!
127 ldr $bi,.LRR // bp[0]
129 ldp $a2,$a3,[$ap,#16]
132 adr $bp,.LRR // &bp[0]
134 bl __ecp_nistz256_mul_mont
138 .inst 0xd50323bf // autiasp
140 .size ecp_nistz256_to_mont,.-ecp_nistz256_to_mont
142 // void ecp_nistz256_from_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
143 .globl ecp_nistz256_from_mont
144 .type ecp_nistz256_from_mont,%function
146 ecp_nistz256_from_mont:
147 .inst 0xd503233f // paciasp
148 stp x29,x30,[sp,#-32]!
154 ldp $a2,$a3,[$ap,#16]
157 adr $bp,.Lone // &bp[0]
159 bl __ecp_nistz256_mul_mont
163 .inst 0xd50323bf // autiasp
165 .size ecp_nistz256_from_mont,.-ecp_nistz256_from_mont
167 // void ecp_nistz256_mul_mont(BN_ULONG x0[4],const BN_ULONG x1[4],
168 // const BN_ULONG x2[4]);
169 .globl ecp_nistz256_mul_mont
170 .type ecp_nistz256_mul_mont,%function
172 ecp_nistz256_mul_mont:
173 .inst 0xd503233f // paciasp
174 stp x29,x30,[sp,#-32]!
178 ldr $bi,[$bp] // bp[0]
180 ldp $a2,$a3,[$ap,#16]
184 bl __ecp_nistz256_mul_mont
188 .inst 0xd50323bf // autiasp
190 .size ecp_nistz256_mul_mont,.-ecp_nistz256_mul_mont
192 // void ecp_nistz256_sqr_mont(BN_ULONG x0[4],const BN_ULONG x1[4]);
193 .globl ecp_nistz256_sqr_mont
194 .type ecp_nistz256_sqr_mont,%function
196 ecp_nistz256_sqr_mont:
197 .inst 0xd503233f // paciasp
198 stp x29,x30,[sp,#-32]!
203 ldp $a2,$a3,[$ap,#16]
207 bl __ecp_nistz256_sqr_mont
211 .inst 0xd50323bf // autiasp
213 .size ecp_nistz256_sqr_mont,.-ecp_nistz256_sqr_mont
215 // void ecp_nistz256_add(BN_ULONG x0[4],const BN_ULONG x1[4],
216 // const BN_ULONG x2[4]);
217 .globl ecp_nistz256_add
218 .type ecp_nistz256_add,%function
221 .inst 0xd503233f // paciasp
222 stp x29,x30,[sp,#-16]!
225 ldp $acc0,$acc1,[$ap]
227 ldp $acc2,$acc3,[$ap,#16]
228 ldp $t2,$t3,[$bp,#16]
232 bl __ecp_nistz256_add
235 .inst 0xd50323bf // autiasp
237 .size ecp_nistz256_add,.-ecp_nistz256_add
239 // void ecp_nistz256_div_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]);
240 .globl ecp_nistz256_div_by_2
241 .type ecp_nistz256_div_by_2,%function
243 ecp_nistz256_div_by_2:
244 .inst 0xd503233f // paciasp
245 stp x29,x30,[sp,#-16]!
248 ldp $acc0,$acc1,[$ap]
249 ldp $acc2,$acc3,[$ap,#16]
253 bl __ecp_nistz256_div_by_2
256 .inst 0xd50323bf // autiasp
258 .size ecp_nistz256_div_by_2,.-ecp_nistz256_div_by_2
260 // void ecp_nistz256_mul_by_2(BN_ULONG x0[4],const BN_ULONG x1[4]);
261 .globl ecp_nistz256_mul_by_2
262 .type ecp_nistz256_mul_by_2,%function
264 ecp_nistz256_mul_by_2:
265 .inst 0xd503233f // paciasp
266 stp x29,x30,[sp,#-16]!
269 ldp $acc0,$acc1,[$ap]
270 ldp $acc2,$acc3,[$ap,#16]
278 bl __ecp_nistz256_add // ret = a+a // 2*a
281 .inst 0xd50323bf // autiasp
283 .size ecp_nistz256_mul_by_2,.-ecp_nistz256_mul_by_2
285 // void ecp_nistz256_mul_by_3(BN_ULONG x0[4],const BN_ULONG x1[4]);
286 .globl ecp_nistz256_mul_by_3
287 .type ecp_nistz256_mul_by_3,%function
289 ecp_nistz256_mul_by_3:
290 .inst 0xd503233f // paciasp
291 stp x29,x30,[sp,#-16]!
294 ldp $acc0,$acc1,[$ap]
295 ldp $acc2,$acc3,[$ap,#16]
307 bl __ecp_nistz256_add // ret = a+a // 2*a
314 bl __ecp_nistz256_add // ret += a // 2*a+a=3*a
317 .inst 0xd50323bf // autiasp
319 .size ecp_nistz256_mul_by_3,.-ecp_nistz256_mul_by_3
321 // void ecp_nistz256_sub(BN_ULONG x0[4],const BN_ULONG x1[4],
322 // const BN_ULONG x2[4]);
323 .globl ecp_nistz256_sub
324 .type ecp_nistz256_sub,%function
327 .inst 0xd503233f // paciasp
328 stp x29,x30,[sp,#-16]!
331 ldp $acc0,$acc1,[$ap]
332 ldp $acc2,$acc3,[$ap,#16]
336 bl __ecp_nistz256_sub_from
339 .inst 0xd50323bf // autiasp
341 .size ecp_nistz256_sub,.-ecp_nistz256_sub
343 // void ecp_nistz256_neg(BN_ULONG x0[4],const BN_ULONG x1[4]);
344 .globl ecp_nistz256_neg
345 .type ecp_nistz256_neg,%function
348 .inst 0xd503233f // paciasp
349 stp x29,x30,[sp,#-16]!
353 mov $acc0,xzr // a = 0
360 bl __ecp_nistz256_sub_from
363 .inst 0xd50323bf // autiasp
365 .size ecp_nistz256_neg,.-ecp_nistz256_neg
367 // note that __ecp_nistz256_mul_mont expects a[0-3] input pre-loaded
368 // to $a0-$a3 and b[0] - to $bi
369 .type __ecp_nistz256_mul_mont,%function
371 __ecp_nistz256_mul_mont:
372 mul $acc0,$a0,$bi // a[0]*b[0]
375 mul $acc1,$a1,$bi // a[1]*b[0]
378 mul $acc2,$a2,$bi // a[2]*b[0]
381 mul $acc3,$a3,$bi // a[3]*b[0]
383 ldr $bi,[$bp,#8] // b[1]
385 adds $acc1,$acc1,$t0 // accumulate high parts of multiplication
393 for($i=1;$i<4;$i++) {
394 # Reduction iteration is normally performed by accumulating
395 # result of multiplication of modulus by "magic" digit [and
396 # omitting least significant word, which is guaranteed to
397 # be 0], but thanks to special form of modulus and "magic"
398 # digit being equal to least significant word, it can be
399 # performed with additions and subtractions alone. Indeed:
401 # ffff0001.00000000.0000ffff.ffffffff
403 # + xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh
405 # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we
408 # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.abcdefgh
409 # + abcdefgh.abcdefgh.0000abcd.efgh0000.00000000
410 # - 0000abcd.efgh0000.00000000.00000000.abcdefgh
412 # or marking redundant operations:
414 # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.--------
415 # + abcdefgh.abcdefgh.0000abcd.efgh0000.--------
416 # - 0000abcd.efgh0000.--------.--------.--------
419 subs $t2,$acc0,$t0 // "*0xffff0001"
421 adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0]
422 mul $t0,$a0,$bi // lo(a[0]*b[i])
424 mul $t1,$a1,$bi // lo(a[1]*b[i])
425 adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001
426 mul $t2,$a2,$bi // lo(a[2]*b[i])
428 mul $t3,$a3,$bi // lo(a[3]*b[i])
431 adds $acc0,$acc0,$t0 // accumulate low parts of multiplication
432 umulh $t0,$a0,$bi // hi(a[0]*b[i])
434 umulh $t1,$a1,$bi // hi(a[1]*b[i])
436 umulh $t2,$a2,$bi // hi(a[2]*b[i])
438 umulh $t3,$a3,$bi // hi(a[3]*b[i])
441 $code.=<<___ if ($i<3);
442 ldr $bi,[$bp,#8*($i+1)] // b[$i+1]
445 adds $acc1,$acc1,$t0 // accumulate high parts of multiplication
456 subs $t2,$acc0,$t0 // "*0xffff0001"
458 adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0]
460 adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001
464 adds $t0,$acc0,#1 // subs $t0,$acc0,#-1 // tmp = ret-modulus
465 sbcs $t1,$acc1,$poly1
467 sbcs $t3,$acc3,$poly3
468 sbcs xzr,$acc4,xzr // did it borrow?
470 csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus
471 csel $acc1,$acc1,$t1,lo
472 csel $acc2,$acc2,$t2,lo
473 stp $acc0,$acc1,[$rp]
474 csel $acc3,$acc3,$t3,lo
475 stp $acc2,$acc3,[$rp,#16]
478 .size __ecp_nistz256_mul_mont,.-__ecp_nistz256_mul_mont
480 // note that __ecp_nistz256_sqr_mont expects a[0-3] input pre-loaded
482 .type __ecp_nistz256_sqr_mont,%function
484 __ecp_nistz256_sqr_mont:
485 // | | | | | |a1*a0| |
486 // | | | | |a2*a0| | |
487 // | |a3*a2|a3*a0| | | |
488 // | | | |a2*a1| | | |
489 // | | |a3*a1| | | | |
490 // *| | | | | | | | 2|
491 // +|a3*a3|a2*a2|a1*a1|a0*a0|
492 // |--+--+--+--+--+--+--+--|
493 // |A7|A6|A5|A4|A3|A2|A1|A0|, where Ax is $accx, i.e. follow $accx
495 // "can't overflow" below mark carrying into high part of
496 // multiplication result, which can't overflow, because it
497 // can never be all ones.
499 mul $acc1,$a1,$a0 // a[1]*a[0]
501 mul $acc2,$a2,$a0 // a[2]*a[0]
503 mul $acc3,$a3,$a0 // a[3]*a[0]
506 adds $acc2,$acc2,$t1 // accumulate high parts of multiplication
507 mul $t0,$a2,$a1 // a[2]*a[1]
510 mul $t2,$a3,$a1 // a[3]*a[1]
512 adc $acc4,$acc4,xzr // can't overflow
514 mul $acc5,$a3,$a2 // a[3]*a[2]
517 adds $t1,$t1,$t2 // accumulate high parts of multiplication
518 mul $acc0,$a0,$a0 // a[0]*a[0]
519 adc $t2,$t3,xzr // can't overflow
521 adds $acc3,$acc3,$t0 // accumulate low parts of multiplication
524 mul $t1,$a1,$a1 // a[1]*a[1]
527 adc $acc6,$acc6,xzr // can't overflow
529 adds $acc1,$acc1,$acc1 // acc[1-6]*=2
530 mul $t2,$a2,$a2 // a[2]*a[2]
531 adcs $acc2,$acc2,$acc2
533 adcs $acc3,$acc3,$acc3
534 mul $t3,$a3,$a3 // a[3]*a[3]
535 adcs $acc4,$acc4,$acc4
537 adcs $acc5,$acc5,$acc5
538 adcs $acc6,$acc6,$acc6
541 adds $acc1,$acc1,$a0 // +a[i]*a[i]
551 for($i=0;$i<3;$i++) { # reductions, see commentary in
552 # multiplication for details
554 subs $t2,$acc0,$t0 // "*0xffff0001"
556 adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0]
559 adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001
561 adc $acc3,$t3,xzr // can't overflow
565 subs $t2,$acc0,$t0 // "*0xffff0001"
567 adds $acc0,$acc1,$t0 // +=acc[0]<<96 and omit acc[0]
569 adcs $acc2,$acc3,$t2 // +=acc[0]*0xffff0001
570 adc $acc3,$t3,xzr // can't overflow
572 adds $acc0,$acc0,$acc4 // accumulate upper half
573 adcs $acc1,$acc1,$acc5
574 adcs $acc2,$acc2,$acc6
575 adcs $acc3,$acc3,$acc7
578 adds $t0,$acc0,#1 // subs $t0,$acc0,#-1 // tmp = ret-modulus
579 sbcs $t1,$acc1,$poly1
581 sbcs $t3,$acc3,$poly3
582 sbcs xzr,$acc4,xzr // did it borrow?
584 csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus
585 csel $acc1,$acc1,$t1,lo
586 csel $acc2,$acc2,$t2,lo
587 stp $acc0,$acc1,[$rp]
588 csel $acc3,$acc3,$t3,lo
589 stp $acc2,$acc3,[$rp,#16]
592 .size __ecp_nistz256_sqr_mont,.-__ecp_nistz256_sqr_mont
594 // Note that __ecp_nistz256_add expects both input vectors pre-loaded to
595 // $a0-$a3 and $t0-$t3. This is done because it's used in multiple
596 // contexts, e.g. in multiplication by 2 and 3...
597 .type __ecp_nistz256_add,%function
600 adds $acc0,$acc0,$t0 // ret = a+b
604 adc $ap,xzr,xzr // zap $ap
606 adds $t0,$acc0,#1 // subs $t0,$a0,#-1 // tmp = ret-modulus
607 sbcs $t1,$acc1,$poly1
609 sbcs $t3,$acc3,$poly3
610 sbcs xzr,$ap,xzr // did subtraction borrow?
612 csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus
613 csel $acc1,$acc1,$t1,lo
614 csel $acc2,$acc2,$t2,lo
615 stp $acc0,$acc1,[$rp]
616 csel $acc3,$acc3,$t3,lo
617 stp $acc2,$acc3,[$rp,#16]
620 .size __ecp_nistz256_add,.-__ecp_nistz256_add
622 .type __ecp_nistz256_sub_from,%function
624 __ecp_nistz256_sub_from:
626 ldp $t2,$t3,[$bp,#16]
627 subs $acc0,$acc0,$t0 // ret = a-b
631 sbc $ap,xzr,xzr // zap $ap
633 subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = ret+modulus
634 adcs $t1,$acc1,$poly1
637 cmp $ap,xzr // did subtraction borrow?
639 csel $acc0,$acc0,$t0,eq // ret = borrow ? ret+modulus : ret
640 csel $acc1,$acc1,$t1,eq
641 csel $acc2,$acc2,$t2,eq
642 stp $acc0,$acc1,[$rp]
643 csel $acc3,$acc3,$t3,eq
644 stp $acc2,$acc3,[$rp,#16]
647 .size __ecp_nistz256_sub_from,.-__ecp_nistz256_sub_from
649 .type __ecp_nistz256_sub_morf,%function
651 __ecp_nistz256_sub_morf:
653 ldp $t2,$t3,[$bp,#16]
654 subs $acc0,$t0,$acc0 // ret = b-a
658 sbc $ap,xzr,xzr // zap $ap
660 subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = ret+modulus
661 adcs $t1,$acc1,$poly1
664 cmp $ap,xzr // did subtraction borrow?
666 csel $acc0,$acc0,$t0,eq // ret = borrow ? ret+modulus : ret
667 csel $acc1,$acc1,$t1,eq
668 csel $acc2,$acc2,$t2,eq
669 stp $acc0,$acc1,[$rp]
670 csel $acc3,$acc3,$t3,eq
671 stp $acc2,$acc3,[$rp,#16]
674 .size __ecp_nistz256_sub_morf,.-__ecp_nistz256_sub_morf
676 .type __ecp_nistz256_div_by_2,%function
678 __ecp_nistz256_div_by_2:
679 subs $t0,$acc0,#1 // adds $t0,$a0,#-1 // tmp = a+modulus
680 adcs $t1,$acc1,$poly1
682 adcs $t3,$acc3,$poly3
683 adc $ap,xzr,xzr // zap $ap
684 tst $acc0,#1 // is a even?
686 csel $acc0,$acc0,$t0,eq // ret = even ? a : a+modulus
687 csel $acc1,$acc1,$t1,eq
688 csel $acc2,$acc2,$t2,eq
689 csel $acc3,$acc3,$t3,eq
692 lsr $acc0,$acc0,#1 // ret >>= 1
693 orr $acc0,$acc0,$acc1,lsl#63
695 orr $acc1,$acc1,$acc2,lsl#63
697 orr $acc2,$acc2,$acc3,lsl#63
699 stp $acc0,$acc1,[$rp]
700 orr $acc3,$acc3,$ap,lsl#63
701 stp $acc2,$acc3,[$rp,#16]
704 .size __ecp_nistz256_div_by_2,.-__ecp_nistz256_div_by_2
706 ########################################################################
707 # following subroutines are "literal" implementation of those found in
710 ########################################################################
711 # void ecp_nistz256_point_double(P256_POINT *out,const P256_POINT *inp);
714 my ($S,$M,$Zsqr,$tmp0)=map(32*$_,(0..3));
715 # above map() describes stack layout with 4 temporary
716 # 256-bit vectors on top.
717 my ($rp_real,$ap_real) = map("x$_",(21,22));
720 .globl ecp_nistz256_point_double
721 .type ecp_nistz256_point_double,%function
723 ecp_nistz256_point_double:
724 .inst 0xd503233f // paciasp
725 stp x29,x30,[sp,#-80]!
732 ldp $acc0,$acc1,[$ap,#32]
734 ldp $acc2,$acc3,[$ap,#48]
740 ldp $a0,$a1,[$ap_real,#64] // forward load for p256_sqr_mont
743 ldp $a2,$a3,[$ap_real,#64+16]
745 bl __ecp_nistz256_add // p256_mul_by_2(S, in_y);
748 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Zsqr, in_z);
750 ldp $t0,$t1,[$ap_real]
751 ldp $t2,$t3,[$ap_real,#16]
752 mov $a0,$acc0 // put Zsqr aside for p256_sub
757 bl __ecp_nistz256_add // p256_add(M, Zsqr, in_x);
760 mov $acc0,$a0 // restore Zsqr
762 ldp $a0,$a1,[sp,#$S] // forward load for p256_sqr_mont
765 ldp $a2,$a3,[sp,#$S+16]
767 bl __ecp_nistz256_sub_morf // p256_sub(Zsqr, in_x, Zsqr);
770 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(S, S);
772 ldr $bi,[$ap_real,#32]
773 ldp $a0,$a1,[$ap_real,#64]
774 ldp $a2,$a3,[$ap_real,#64+16]
777 bl __ecp_nistz256_mul_mont // p256_mul_mont(tmp0, in_z, in_y);
781 ldp $a0,$a1,[sp,#$S] // forward load for p256_sqr_mont
784 ldp $a2,$a3,[sp,#$S+16]
786 bl __ecp_nistz256_add // p256_mul_by_2(res_z, tmp0);
789 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(tmp0, S);
791 ldr $bi,[sp,#$Zsqr] // forward load for p256_mul_mont
793 ldp $a2,$a3,[sp,#$M+16]
795 bl __ecp_nistz256_div_by_2 // p256_div_by_2(res_y, tmp0);
799 bl __ecp_nistz256_mul_mont // p256_mul_mont(M, M, Zsqr);
801 mov $t0,$acc0 // duplicate M
805 mov $a0,$acc0 // put M aside
810 bl __ecp_nistz256_add
811 mov $t0,$a0 // restore M
813 ldr $bi,[$ap_real] // forward load for p256_mul_mont
817 ldp $a2,$a3,[sp,#$S+16]
818 bl __ecp_nistz256_add // p256_mul_by_3(M, M);
822 bl __ecp_nistz256_mul_mont // p256_mul_mont(S, S, in_x);
826 ldp $a0,$a1,[sp,#$M] // forward load for p256_sqr_mont
829 ldp $a2,$a3,[sp,#$M+16]
831 bl __ecp_nistz256_add // p256_mul_by_2(tmp0, S);
834 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(res_x, M);
837 bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, tmp0);
841 bl __ecp_nistz256_sub_morf // p256_sub(S, S, res_x);
844 mov $a0,$acc0 // copy S
849 bl __ecp_nistz256_mul_mont // p256_mul_mont(S, S, M);
853 bl __ecp_nistz256_sub_from // p256_sub(res_y, S, res_y);
855 add sp,x29,#0 // destroy frame
856 ldp x19,x20,[x29,#16]
857 ldp x21,x22,[x29,#32]
859 .inst 0xd50323bf // autiasp
861 .size ecp_nistz256_point_double,.-ecp_nistz256_point_double
865 ########################################################################
866 # void ecp_nistz256_point_add(P256_POINT *out,const P256_POINT *in1,
867 # const P256_POINT *in2);
869 my ($res_x,$res_y,$res_z,
870 $H,$Hsqr,$R,$Rsqr,$Hcub,
871 $U1,$U2,$S1,$S2)=map(32*$_,(0..11));
872 my ($Z1sqr, $Z2sqr) = ($Hsqr, $Rsqr);
873 # above map() describes stack layout with 12 temporary
874 # 256-bit vectors on top.
875 my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26));
878 .globl ecp_nistz256_point_add
879 .type ecp_nistz256_point_add,%function
881 ecp_nistz256_point_add:
882 .inst 0xd503233f // paciasp
883 stp x29,x30,[sp,#-80]!
891 ldp $a0,$a1,[$bp,#64] // in2_z
892 ldp $a2,$a3,[$bp,#64+16]
900 orr $in2infty,$t0,$t2
902 csetm $in2infty,ne // !in2infty
904 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z2sqr, in2_z);
906 ldp $a0,$a1,[$ap_real,#64] // in1_z
907 ldp $a2,$a3,[$ap_real,#64+16]
910 orr $in1infty,$t0,$t2
912 csetm $in1infty,ne // !in1infty
914 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z1sqr, in1_z);
916 ldr $bi,[$bp_real,#64]
917 ldp $a0,$a1,[sp,#$Z2sqr]
918 ldp $a2,$a3,[sp,#$Z2sqr+16]
921 bl __ecp_nistz256_mul_mont // p256_mul_mont(S1, Z2sqr, in2_z);
923 ldr $bi,[$ap_real,#64]
924 ldp $a0,$a1,[sp,#$Z1sqr]
925 ldp $a2,$a3,[sp,#$Z1sqr+16]
928 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, Z1sqr, in1_z);
930 ldr $bi,[$ap_real,#32]
931 ldp $a0,$a1,[sp,#$S1]
932 ldp $a2,$a3,[sp,#$S1+16]
935 bl __ecp_nistz256_mul_mont // p256_mul_mont(S1, S1, in1_y);
937 ldr $bi,[$bp_real,#32]
938 ldp $a0,$a1,[sp,#$S2]
939 ldp $a2,$a3,[sp,#$S2+16]
942 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S2, in2_y);
945 ldr $bi,[sp,#$Z2sqr] // forward load for p256_mul_mont
946 ldp $a0,$a1,[$ap_real]
947 ldp $a2,$a3,[$ap_real,#16]
949 bl __ecp_nistz256_sub_from // p256_sub(R, S2, S1);
951 orr $acc0,$acc0,$acc1 // see if result is zero
952 orr $acc2,$acc2,$acc3
953 orr $temp,$acc0,$acc2
957 bl __ecp_nistz256_mul_mont // p256_mul_mont(U1, in1_x, Z2sqr);
960 ldp $a0,$a1,[$bp_real]
961 ldp $a2,$a3,[$bp_real,#16]
964 bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, in2_x, Z1sqr);
967 ldp $a0,$a1,[sp,#$R] // forward load for p256_sqr_mont
968 ldp $a2,$a3,[sp,#$R+16]
970 bl __ecp_nistz256_sub_from // p256_sub(H, U2, U1);
972 orr $acc0,$acc0,$acc1 // see if result is zero
973 orr $acc2,$acc2,$acc3
974 orr $acc0,$acc0,$acc2
976 b.ne .Ladd_proceed // is_equal(U1,U2)?
978 tst $in1infty,$in2infty
979 b.eq .Ladd_proceed // (in1infty || in2infty)?
982 b.eq .Ladd_double // is_equal(S1,S2)?
986 stp $a0,$a1,[$rp_real]
987 stp $a0,$a1,[$rp_real,#16]
988 stp $a0,$a1,[$rp_real,#32]
989 stp $a0,$a1,[$rp_real,#48]
990 stp $a0,$a1,[$rp_real,#64]
991 stp $a0,$a1,[$rp_real,#80]
998 ldp x23,x24,[x29,#48]
999 ldp x25,x26,[x29,#64]
1000 add sp,sp,#32*(12-4) // difference in stack frames
1006 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Rsqr, R);
1008 ldr $bi,[$ap_real,#64]
1009 ldp $a0,$a1,[sp,#$H]
1010 ldp $a2,$a3,[sp,#$H+16]
1011 add $bp,$ap_real,#64
1013 bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, H, in1_z);
1015 ldp $a0,$a1,[sp,#$H]
1016 ldp $a2,$a3,[sp,#$H+16]
1018 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Hsqr, H);
1020 ldr $bi,[$bp_real,#64]
1021 ldp $a0,$a1,[sp,#$res_z]
1022 ldp $a2,$a3,[sp,#$res_z+16]
1023 add $bp,$bp_real,#64
1025 bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, res_z, in2_z);
1028 ldp $a0,$a1,[sp,#$Hsqr]
1029 ldp $a2,$a3,[sp,#$Hsqr+16]
1032 bl __ecp_nistz256_mul_mont // p256_mul_mont(Hcub, Hsqr, H);
1035 ldp $a0,$a1,[sp,#$U1]
1036 ldp $a2,$a3,[sp,#$U1+16]
1039 bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, U1, Hsqr);
1046 bl __ecp_nistz256_add // p256_mul_by_2(Hsqr, U2);
1050 bl __ecp_nistz256_sub_morf // p256_sub(res_x, Rsqr, Hsqr);
1053 bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, Hcub);
1056 ldr $bi,[sp,#$Hcub] // forward load for p256_mul_mont
1057 ldp $a0,$a1,[sp,#$S1]
1058 ldp $a2,$a3,[sp,#$S1+16]
1060 bl __ecp_nistz256_sub_morf // p256_sub(res_y, U2, res_x);
1064 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S1, Hcub);
1067 ldp $a0,$a1,[sp,#$res_y]
1068 ldp $a2,$a3,[sp,#$res_y+16]
1071 bl __ecp_nistz256_mul_mont // p256_mul_mont(res_y, res_y, R);
1074 bl __ecp_nistz256_sub_from // p256_sub(res_y, res_y, S2);
1076 ldp $a0,$a1,[sp,#$res_x] // res
1077 ldp $a2,$a3,[sp,#$res_x+16]
1078 ldp $t0,$t1,[$bp_real] // in2
1079 ldp $t2,$t3,[$bp_real,#16]
1081 for($i=0;$i<64;$i+=32) { # conditional moves
1083 ldp $acc0,$acc1,[$ap_real,#$i] // in1
1084 cmp $in1infty,#0 // !$in1intfy, remember?
1085 ldp $acc2,$acc3,[$ap_real,#$i+16]
1088 ldp $a0,$a1,[sp,#$res_x+$i+32] // res
1091 cmp $in2infty,#0 // !$in2intfy, remember?
1092 ldp $a2,$a3,[sp,#$res_x+$i+48]
1093 csel $acc0,$t0,$acc0,ne
1094 csel $acc1,$t1,$acc1,ne
1095 ldp $t0,$t1,[$bp_real,#$i+32] // in2
1096 csel $acc2,$t2,$acc2,ne
1097 csel $acc3,$t3,$acc3,ne
1098 ldp $t2,$t3,[$bp_real,#$i+48]
1099 stp $acc0,$acc1,[$rp_real,#$i]
1100 stp $acc2,$acc3,[$rp_real,#$i+16]
1104 ldp $acc0,$acc1,[$ap_real,#$i] // in1
1105 cmp $in1infty,#0 // !$in1intfy, remember?
1106 ldp $acc2,$acc3,[$ap_real,#$i+16]
1111 cmp $in2infty,#0 // !$in2intfy, remember?
1112 csel $acc0,$t0,$acc0,ne
1113 csel $acc1,$t1,$acc1,ne
1114 csel $acc2,$t2,$acc2,ne
1115 csel $acc3,$t3,$acc3,ne
1116 stp $acc0,$acc1,[$rp_real,#$i]
1117 stp $acc2,$acc3,[$rp_real,#$i+16]
1120 add sp,x29,#0 // destroy frame
1121 ldp x19,x20,[x29,#16]
1122 ldp x21,x22,[x29,#32]
1123 ldp x23,x24,[x29,#48]
1124 ldp x25,x26,[x29,#64]
1125 ldp x29,x30,[sp],#80
1126 .inst 0xd50323bf // autiasp
1128 .size ecp_nistz256_point_add,.-ecp_nistz256_point_add
1132 ########################################################################
1133 # void ecp_nistz256_point_add_affine(P256_POINT *out,const P256_POINT *in1,
1134 # const P256_POINT_AFFINE *in2);
1136 my ($res_x,$res_y,$res_z,
1137 $U2,$S2,$H,$R,$Hsqr,$Hcub,$Rsqr)=map(32*$_,(0..9));
1139 # above map() describes stack layout with 10 temporary
1140 # 256-bit vectors on top.
1141 my ($rp_real,$ap_real,$bp_real,$in1infty,$in2infty,$temp)=map("x$_",(21..26));
1144 .globl ecp_nistz256_point_add_affine
1145 .type ecp_nistz256_point_add_affine,%function
1147 ecp_nistz256_point_add_affine:
1148 .inst 0xd503233f // paciasp
1149 stp x29,x30,[sp,#-80]!
1151 stp x19,x20,[sp,#16]
1152 stp x21,x22,[sp,#32]
1153 stp x23,x24,[sp,#48]
1154 stp x25,x26,[sp,#64]
1161 ldr $poly3,.Lpoly+24
1163 ldp $a0,$a1,[$ap,#64] // in1_z
1164 ldp $a2,$a3,[$ap,#64+16]
1167 orr $in1infty,$t0,$t2
1169 csetm $in1infty,ne // !in1infty
1171 ldp $acc0,$acc1,[$bp] // in2_x
1172 ldp $acc2,$acc3,[$bp,#16]
1173 ldp $t0,$t1,[$bp,#32] // in2_y
1174 ldp $t2,$t3,[$bp,#48]
1175 orr $acc0,$acc0,$acc1
1176 orr $acc2,$acc2,$acc3
1179 orr $acc0,$acc0,$acc2
1181 orr $in2infty,$acc0,$t0
1183 csetm $in2infty,ne // !in2infty
1186 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Z1sqr, in1_z);
1195 bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, Z1sqr, in2_x);
1198 ldr $bi,[$ap_real,#64] // forward load for p256_mul_mont
1199 ldp $a0,$a1,[sp,#$Z1sqr]
1200 ldp $a2,$a3,[sp,#$Z1sqr+16]
1202 bl __ecp_nistz256_sub_from // p256_sub(H, U2, in1_x);
1204 add $bp,$ap_real,#64
1206 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, Z1sqr, in1_z);
1208 ldr $bi,[$ap_real,#64]
1209 ldp $a0,$a1,[sp,#$H]
1210 ldp $a2,$a3,[sp,#$H+16]
1211 add $bp,$ap_real,#64
1213 bl __ecp_nistz256_mul_mont // p256_mul_mont(res_z, H, in1_z);
1215 ldr $bi,[$bp_real,#32]
1216 ldp $a0,$a1,[sp,#$S2]
1217 ldp $a2,$a3,[sp,#$S2+16]
1218 add $bp,$bp_real,#32
1220 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, S2, in2_y);
1222 add $bp,$ap_real,#32
1223 ldp $a0,$a1,[sp,#$H] // forward load for p256_sqr_mont
1224 ldp $a2,$a3,[sp,#$H+16]
1226 bl __ecp_nistz256_sub_from // p256_sub(R, S2, in1_y);
1229 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Hsqr, H);
1231 ldp $a0,$a1,[sp,#$R]
1232 ldp $a2,$a3,[sp,#$R+16]
1234 bl __ecp_nistz256_sqr_mont // p256_sqr_mont(Rsqr, R);
1237 ldp $a0,$a1,[sp,#$Hsqr]
1238 ldp $a2,$a3,[sp,#$Hsqr+16]
1241 bl __ecp_nistz256_mul_mont // p256_mul_mont(Hcub, Hsqr, H);
1244 ldp $a0,$a1,[sp,#$Hsqr]
1245 ldp $a2,$a3,[sp,#$Hsqr+16]
1248 bl __ecp_nistz256_mul_mont // p256_mul_mont(U2, in1_x, Hsqr);
1255 bl __ecp_nistz256_add // p256_mul_by_2(Hsqr, U2);
1259 bl __ecp_nistz256_sub_morf // p256_sub(res_x, Rsqr, Hsqr);
1262 bl __ecp_nistz256_sub_from // p256_sub(res_x, res_x, Hcub);
1265 ldr $bi,[$ap_real,#32] // forward load for p256_mul_mont
1266 ldp $a0,$a1,[sp,#$Hcub]
1267 ldp $a2,$a3,[sp,#$Hcub+16]
1269 bl __ecp_nistz256_sub_morf // p256_sub(res_y, U2, res_x);
1271 add $bp,$ap_real,#32
1273 bl __ecp_nistz256_mul_mont // p256_mul_mont(S2, in1_y, Hcub);
1276 ldp $a0,$a1,[sp,#$res_y]
1277 ldp $a2,$a3,[sp,#$res_y+16]
1280 bl __ecp_nistz256_mul_mont // p256_mul_mont(res_y, res_y, R);
1283 bl __ecp_nistz256_sub_from // p256_sub(res_y, res_y, S2);
1285 ldp $a0,$a1,[sp,#$res_x] // res
1286 ldp $a2,$a3,[sp,#$res_x+16]
1287 ldp $t0,$t1,[$bp_real] // in2
1288 ldp $t2,$t3,[$bp_real,#16]
1290 for($i=0;$i<64;$i+=32) { # conditional moves
1292 ldp $acc0,$acc1,[$ap_real,#$i] // in1
1293 cmp $in1infty,#0 // !$in1intfy, remember?
1294 ldp $acc2,$acc3,[$ap_real,#$i+16]
1297 ldp $a0,$a1,[sp,#$res_x+$i+32] // res
1300 cmp $in2infty,#0 // !$in2intfy, remember?
1301 ldp $a2,$a3,[sp,#$res_x+$i+48]
1302 csel $acc0,$t0,$acc0,ne
1303 csel $acc1,$t1,$acc1,ne
1304 ldp $t0,$t1,[$bp_real,#$i+32] // in2
1305 csel $acc2,$t2,$acc2,ne
1306 csel $acc3,$t3,$acc3,ne
1307 ldp $t2,$t3,[$bp_real,#$i+48]
1308 stp $acc0,$acc1,[$rp_real,#$i]
1309 stp $acc2,$acc3,[$rp_real,#$i+16]
1311 $code.=<<___ if ($i == 0);
1312 adr $bp_real,.Lone_mont-64
1316 ldp $acc0,$acc1,[$ap_real,#$i] // in1
1317 cmp $in1infty,#0 // !$in1intfy, remember?
1318 ldp $acc2,$acc3,[$ap_real,#$i+16]
1323 cmp $in2infty,#0 // !$in2intfy, remember?
1324 csel $acc0,$t0,$acc0,ne
1325 csel $acc1,$t1,$acc1,ne
1326 csel $acc2,$t2,$acc2,ne
1327 csel $acc3,$t3,$acc3,ne
1328 stp $acc0,$acc1,[$rp_real,#$i]
1329 stp $acc2,$acc3,[$rp_real,#$i+16]
1331 add sp,x29,#0 // destroy frame
1332 ldp x19,x20,[x29,#16]
1333 ldp x21,x22,[x29,#32]
1334 ldp x23,x24,[x29,#48]
1335 ldp x25,x26,[x29,#64]
1336 ldp x29,x30,[sp],#80
1337 .inst 0xd50323bf // autiasp
1339 .size ecp_nistz256_point_add_affine,.-ecp_nistz256_point_add_affine
1343 my ($ord0,$ord1) = ($poly1,$poly3);
1344 my ($ord2,$ord3,$ordk,$t4) = map("x$_",(21..24));
1348 ////////////////////////////////////////////////////////////////////////
1349 // void ecp_nistz256_ord_mul_mont(uint64_t res[4], uint64_t a[4],
1351 .globl ecp_nistz256_ord_mul_mont
1352 .type ecp_nistz256_ord_mul_mont,%function
1354 ecp_nistz256_ord_mul_mont:
1355 stp x29,x30,[sp,#-64]!
1357 stp x19,x20,[sp,#16]
1358 stp x21,x22,[sp,#32]
1359 stp x23,x24,[sp,#48]
1362 ldr $bi,[$bp] // bp[0]
1364 ldp $a2,$a3,[$ap,#16]
1366 ldp $ord0,$ord1,[$ordk,#0]
1367 ldp $ord2,$ord3,[$ordk,#16]
1368 ldr $ordk,[$ordk,#32]
1370 mul $acc0,$a0,$bi // a[0]*b[0]
1373 mul $acc1,$a1,$bi // a[1]*b[0]
1376 mul $acc2,$a2,$bi // a[2]*b[0]
1379 mul $acc3,$a3,$bi // a[3]*b[0]
1384 adds $acc1,$acc1,$t0 // accumulate high parts of multiplication
1385 adcs $acc2,$acc2,$t1
1386 adcs $acc3,$acc3,$t2
1390 for ($i=1;$i<4;$i++) {
1391 ################################################################
1392 # ffff0000.ffffffff.yyyyyyyy.zzzzzzzz
1394 # + xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx
1396 # Now observing that ff..ff*x = (2^n-1)*x = 2^n*x-x, we
1399 # xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx.xxxxxxxx
1400 # - 0000abcd.efgh0000.abcdefgh.00000000.00000000
1401 # + abcdefgh.abcdefgh.yzayzbyz.cyzdyzey.zfyzgyzh
1403 ldr $bi,[$bp,#8*$i] // b[i]
1406 subs $acc2,$acc2,$t4
1408 sbcs $acc3,$acc3,$t0
1409 sbcs $acc4,$acc4,$t1
1422 adds $acc0,$acc1,$t2
1424 adcs $acc1,$acc2,$t3
1426 adcs $acc2,$acc3,$t4
1427 adcs $acc3,$acc4,$t4
1430 adds $acc0,$acc0,$t0 // accumulate low parts
1432 adcs $acc1,$acc1,$t1
1434 adcs $acc2,$acc2,$t2
1436 adcs $acc3,$acc3,$t3
1440 adds $acc1,$acc1,$t0 // accumulate high parts
1441 adcs $acc2,$acc2,$t1
1442 adcs $acc3,$acc3,$t2
1443 adcs $acc4,$acc4,$t3
1448 lsl $t0,$t4,#32 // last reduction
1449 subs $acc2,$acc2,$t4
1451 sbcs $acc3,$acc3,$t0
1452 sbcs $acc4,$acc4,$t1
1463 adds $acc0,$acc1,$t2
1464 adcs $acc1,$acc2,$t3
1465 adcs $acc2,$acc3,$t4
1466 adcs $acc3,$acc4,$t4
1469 subs $t0,$acc0,$ord0 // ret -= modulus
1470 sbcs $t1,$acc1,$ord1
1471 sbcs $t2,$acc2,$ord2
1472 sbcs $t3,$acc3,$ord3
1475 csel $acc0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus
1476 csel $acc1,$acc1,$t1,lo
1477 csel $acc2,$acc2,$t2,lo
1478 stp $acc0,$acc1,[$rp]
1479 csel $acc3,$acc3,$t3,lo
1480 stp $acc2,$acc3,[$rp,#16]
1482 ldp x19,x20,[sp,#16]
1483 ldp x21,x22,[sp,#32]
1484 ldp x23,x24,[sp,#48]
1487 .size ecp_nistz256_ord_mul_mont,.-ecp_nistz256_ord_mul_mont
1489 ////////////////////////////////////////////////////////////////////////
1490 // void ecp_nistz256_ord_sqr_mont(uint64_t res[4], uint64_t a[4],
1492 .globl ecp_nistz256_ord_sqr_mont
1493 .type ecp_nistz256_ord_sqr_mont,%function
1495 ecp_nistz256_ord_sqr_mont:
1496 stp x29,x30,[sp,#-64]!
1498 stp x19,x20,[sp,#16]
1499 stp x21,x22,[sp,#32]
1500 stp x23,x24,[sp,#48]
1504 ldp $a2,$a3,[$ap,#16]
1506 ldp $ord0,$ord1,[$ordk,#0]
1507 ldp $ord2,$ord3,[$ordk,#16]
1508 ldr $ordk,[$ordk,#32]
1514 ////////////////////////////////////////////////////////////////
1515 // | | | | | |a1*a0| |
1516 // | | | | |a2*a0| | |
1517 // | |a3*a2|a3*a0| | | |
1518 // | | | |a2*a1| | | |
1519 // | | |a3*a1| | | | |
1520 // *| | | | | | | | 2|
1521 // +|a3*a3|a2*a2|a1*a1|a0*a0|
1522 // |--+--+--+--+--+--+--+--|
1523 // |A7|A6|A5|A4|A3|A2|A1|A0|, where Ax is $accx, i.e. follow $accx
1525 // "can't overflow" below mark carrying into high part of
1526 // multiplication result, which can't overflow, because it
1527 // can never be all ones.
1529 mul $acc1,$a1,$a0 // a[1]*a[0]
1531 mul $acc2,$a2,$a0 // a[2]*a[0]
1533 mul $acc3,$a3,$a0 // a[3]*a[0]
1536 adds $acc2,$acc2,$t1 // accumulate high parts of multiplication
1537 mul $t0,$a2,$a1 // a[2]*a[1]
1539 adcs $acc3,$acc3,$t2
1540 mul $t2,$a3,$a1 // a[3]*a[1]
1542 adc $acc4,$acc4,xzr // can't overflow
1544 mul $acc5,$a3,$a2 // a[3]*a[2]
1547 adds $t1,$t1,$t2 // accumulate high parts of multiplication
1548 mul $acc0,$a0,$a0 // a[0]*a[0]
1549 adc $t2,$t3,xzr // can't overflow
1551 adds $acc3,$acc3,$t0 // accumulate low parts of multiplication
1553 adcs $acc4,$acc4,$t1
1554 mul $t1,$a1,$a1 // a[1]*a[1]
1555 adcs $acc5,$acc5,$t2
1557 adc $acc6,$acc6,xzr // can't overflow
1559 adds $acc1,$acc1,$acc1 // acc[1-6]*=2
1560 mul $t2,$a2,$a2 // a[2]*a[2]
1561 adcs $acc2,$acc2,$acc2
1563 adcs $acc3,$acc3,$acc3
1564 mul $t3,$a3,$a3 // a[3]*a[3]
1565 adcs $acc4,$acc4,$acc4
1567 adcs $acc5,$acc5,$acc5
1568 adcs $acc6,$acc6,$acc6
1571 adds $acc1,$acc1,$a0 // +a[i]*a[i]
1573 adcs $acc2,$acc2,$t1
1574 adcs $acc3,$acc3,$a1
1575 adcs $acc4,$acc4,$t2
1576 adcs $acc5,$acc5,$a2
1577 adcs $acc6,$acc6,$t3
1580 for($i=0; $i<4; $i++) { # reductions
1590 adds $acc0,$acc1,$t2
1591 adcs $acc1,$acc2,$t3
1592 adcs $acc2,$acc3,$t4
1593 adc $acc3,xzr,$t4 // can't overflow
1595 $code.=<<___ if ($i<3);
1600 subs $acc1,$acc1,$t4
1602 sbcs $acc2,$acc2,$t0
1603 sbc $acc3,$acc3,$t1 // can't borrow
1605 ($t3,$t4) = ($t4,$t3);
1608 adds $acc0,$acc0,$acc4 // accumulate upper half
1609 adcs $acc1,$acc1,$acc5
1610 adcs $acc2,$acc2,$acc6
1611 adcs $acc3,$acc3,$acc7
1614 subs $t0,$acc0,$ord0 // ret -= modulus
1615 sbcs $t1,$acc1,$ord1
1616 sbcs $t2,$acc2,$ord2
1617 sbcs $t3,$acc3,$ord3
1620 csel $a0,$acc0,$t0,lo // ret = borrow ? ret : ret-modulus
1621 csel $a1,$acc1,$t1,lo
1622 csel $a2,$acc2,$t2,lo
1623 csel $a3,$acc3,$t3,lo
1625 cbnz $bp,.Loop_ord_sqr
1628 stp $a2,$a3,[$rp,#16]
1630 ldp x19,x20,[sp,#16]
1631 ldp x21,x22,[sp,#32]
1632 ldp x23,x24,[sp,#48]
1635 .size ecp_nistz256_ord_sqr_mont,.-ecp_nistz256_ord_sqr_mont
1639 ########################################################################
1640 # scatter-gather subroutines
1642 my ($out,$inp,$index,$mask)=map("x$_",(0..3));
1644 // void ecp_nistz256_scatter_w5(void *x0,const P256_POINT *x1,
1646 .globl ecp_nistz256_scatter_w5
1647 .type ecp_nistz256_scatter_w5,%function
1649 ecp_nistz256_scatter_w5:
1650 stp x29,x30,[sp,#-16]!
1653 add $out,$out,$index,lsl#2
1655 ldp x4,x5,[$inp] // X
1656 ldp x6,x7,[$inp,#16]
1657 str w4,[$out,#64*0-4]
1659 str w5,[$out,#64*1-4]
1661 str w6,[$out,#64*2-4]
1663 str w7,[$out,#64*3-4]
1665 str w4,[$out,#64*4-4]
1666 str w5,[$out,#64*5-4]
1667 str w6,[$out,#64*6-4]
1668 str w7,[$out,#64*7-4]
1671 ldp x4,x5,[$inp,#32] // Y
1672 ldp x6,x7,[$inp,#48]
1673 str w4,[$out,#64*0-4]
1675 str w5,[$out,#64*1-4]
1677 str w6,[$out,#64*2-4]
1679 str w7,[$out,#64*3-4]
1681 str w4,[$out,#64*4-4]
1682 str w5,[$out,#64*5-4]
1683 str w6,[$out,#64*6-4]
1684 str w7,[$out,#64*7-4]
1687 ldp x4,x5,[$inp,#64] // Z
1688 ldp x6,x7,[$inp,#80]
1689 str w4,[$out,#64*0-4]
1691 str w5,[$out,#64*1-4]
1693 str w6,[$out,#64*2-4]
1695 str w7,[$out,#64*3-4]
1697 str w4,[$out,#64*4-4]
1698 str w5,[$out,#64*5-4]
1699 str w6,[$out,#64*6-4]
1700 str w7,[$out,#64*7-4]
1704 .size ecp_nistz256_scatter_w5,.-ecp_nistz256_scatter_w5
1706 // void ecp_nistz256_gather_w5(P256_POINT *x0,const void *x1,
1708 .globl ecp_nistz256_gather_w5
1709 .type ecp_nistz256_gather_w5,%function
1711 ecp_nistz256_gather_w5:
1712 stp x29,x30,[sp,#-16]!
1717 add $index,$index,x3
1718 add $inp,$inp,$index,lsl#2
1726 ldr w10,[$inp,#64*6]
1727 ldr w11,[$inp,#64*7]
1731 orr x6,x6,x10,lsl#32
1732 orr x7,x7,x11,lsl#32
1737 stp x4,x5,[$out] // X
1738 stp x6,x7,[$out,#16]
1746 ldr w10,[$inp,#64*6]
1747 ldr w11,[$inp,#64*7]
1751 orr x6,x6,x10,lsl#32
1752 orr x7,x7,x11,lsl#32
1757 stp x4,x5,[$out,#32] // Y
1758 stp x6,x7,[$out,#48]
1766 ldr w10,[$inp,#64*6]
1767 ldr w11,[$inp,#64*7]
1770 orr x6,x6,x10,lsl#32
1771 orr x7,x7,x11,lsl#32
1776 stp x4,x5,[$out,#64] // Z
1777 stp x6,x7,[$out,#80]
1781 .size ecp_nistz256_gather_w5,.-ecp_nistz256_gather_w5
1783 // void ecp_nistz256_scatter_w7(void *x0,const P256_POINT_AFFINE *x1,
1785 .globl ecp_nistz256_scatter_w7
1786 .type ecp_nistz256_scatter_w7,%function
1788 ecp_nistz256_scatter_w7:
1789 stp x29,x30,[sp,#-16]!
1792 add $out,$out,$index
1796 subs $index,$index,#1
1797 prfm pstl1strm,[$out,#4096+64*0]
1798 prfm pstl1strm,[$out,#4096+64*1]
1799 prfm pstl1strm,[$out,#4096+64*2]
1800 prfm pstl1strm,[$out,#4096+64*3]
1801 prfm pstl1strm,[$out,#4096+64*4]
1802 prfm pstl1strm,[$out,#4096+64*5]
1803 prfm pstl1strm,[$out,#4096+64*6]
1804 prfm pstl1strm,[$out,#4096+64*7]
1805 strb w3,[$out,#64*0]
1807 strb w3,[$out,#64*1]
1809 strb w3,[$out,#64*2]
1811 strb w3,[$out,#64*3]
1813 strb w3,[$out,#64*4]
1815 strb w3,[$out,#64*5]
1817 strb w3,[$out,#64*6]
1819 strb w3,[$out,#64*7]
1821 b.ne .Loop_scatter_w7
1825 .size ecp_nistz256_scatter_w7,.-ecp_nistz256_scatter_w7
1827 // void ecp_nistz256_gather_w7(P256_POINT_AFFINE *x0,const void *x1,
1829 .globl ecp_nistz256_gather_w7
1830 .type ecp_nistz256_gather_w7,%function
1832 ecp_nistz256_gather_w7:
1833 stp x29,x30,[sp,#-16]!
1838 add $index,$index,x3
1839 add $inp,$inp,$index
1843 ldrb w4,[$inp,#64*0]
1844 prfm pldl1strm,[$inp,#4096+64*0]
1845 subs $index,$index,#1
1846 ldrb w5,[$inp,#64*1]
1847 prfm pldl1strm,[$inp,#4096+64*1]
1848 ldrb w6,[$inp,#64*2]
1849 prfm pldl1strm,[$inp,#4096+64*2]
1850 ldrb w7,[$inp,#64*3]
1851 prfm pldl1strm,[$inp,#4096+64*3]
1852 ldrb w8,[$inp,#64*4]
1853 prfm pldl1strm,[$inp,#4096+64*4]
1854 ldrb w9,[$inp,#64*5]
1855 prfm pldl1strm,[$inp,#4096+64*5]
1856 ldrb w10,[$inp,#64*6]
1857 prfm pldl1strm,[$inp,#4096+64*6]
1858 ldrb w11,[$inp,#64*7]
1859 prfm pldl1strm,[$inp,#4096+64*7]
1865 orr x10,x10,x11,lsl#8
1867 orr x4,x4,x10,lsl#48
1870 b.ne .Loop_gather_w7
1874 .size ecp_nistz256_gather_w7,.-ecp_nistz256_gather_w7
1878 foreach (split("\n",$code)) {
1879 s/\`([^\`]*)\`/eval $1/ge;
1883 close STDOUT; # enforce flush