1#!/usr/bin/env perl
2
3# ====================================================================
4# Written by Andy Polyakov <appro@openssl.org> for the OpenSSL
5# project. The module is, however, dual licensed under OpenSSL and
6# CRYPTOGAMS licenses depending on where you obtain it. For further
7# details see http://www.openssl.org/~appro/cryptogams/.
8# ====================================================================
9
10# August 2011.
11#
12# Companion to x86_64-mont.pl that optimizes cache-timing attack
13# countermeasures. The subroutines are produced by replacing bp[i]
14# references in their x86_64-mont.pl counterparts with cache-neutral
15# references to powers table computed in BN_mod_exp_mont_consttime.
16# In addition subroutine that scatters elements of the powers table
17# is implemented, so that scatter-/gathering can be tuned without
18# bn_exp.c modifications.
19
20# August 2013.
21#
22# Add MULX/AD*X code paths and additional interfaces to optimize for
23# branch prediction unit. For input lengths that are multiples of 8
24# the np argument is not just modulus value, but one interleaved
25# with 0. This is to optimize post-condition...
26
27$flavour = shift;
28$output  = shift;
29if ($flavour =~ /\./) { $output = $flavour; undef $flavour; }
30
31$win64=0; $win64=1 if ($flavour =~ /[nm]asm|mingw64/ || $output =~ /\.asm$/);
32
33$0 =~ m/(.*[\/\\])[^\/\\]+$/; $dir=$1;
34( $xlate="${dir}x86_64-xlate.pl" and -f $xlate ) or
35( $xlate="${dir}../../perlasm/x86_64-xlate.pl" and -f $xlate) or
36die "can't locate x86_64-xlate.pl";
37
38open OUT,"| \"$^X\" $xlate $flavour $output";
39*STDOUT=*OUT;
40
41# In upstream, this is controlled by shelling out to the compiler to check
42# versions, but BoringSSL is intended to be used with pre-generated perlasm
43# output, so this isn't useful anyway.
44#
45# TODO(davidben): Enable this after testing. $addx goes up to 1.
46$addx = 0;
47
48# int bn_mul_mont_gather5(
49$rp="%rdi";	# BN_ULONG *rp,
50$ap="%rsi";	# const BN_ULONG *ap,
51$bp="%rdx";	# const BN_ULONG *bp,
52$np="%rcx";	# const BN_ULONG *np,
53$n0="%r8";	# const BN_ULONG *n0,
54$num="%r9";	# int num,
55		# int idx);	# 0 to 2^5-1, "index" in $bp holding
56				# pre-computed powers of a', interlaced
57				# in such manner that b[0] is $bp[idx],
58				# b[1] is [2^5+idx], etc.
59$lo0="%r10";
60$hi0="%r11";
61$hi1="%r13";
62$i="%r14";
63$j="%r15";
64$m0="%rbx";
65$m1="%rbp";
66
67$code=<<___;
68.text
69
70.extern	OPENSSL_ia32cap_P
71
72.globl	bn_mul_mont_gather5
73.type	bn_mul_mont_gather5,\@function,6
74.align	64
75bn_mul_mont_gather5:
76	test	\$7,${num}d
77	jnz	.Lmul_enter
78___
79$code.=<<___ if ($addx);
80	mov	OPENSSL_ia32cap_P+8(%rip),%r11d
81___
82$code.=<<___;
83	jmp	.Lmul4x_enter
84
85.align	16
86.Lmul_enter:
87	mov	${num}d,${num}d
88	mov	%rsp,%rax
89	mov	`($win64?56:8)`(%rsp),%r10d	# load 7th argument
90	push	%rbx
91	push	%rbp
92	push	%r12
93	push	%r13
94	push	%r14
95	push	%r15
96___
97$code.=<<___ if ($win64);
98	lea	-0x28(%rsp),%rsp
99	movaps	%xmm6,(%rsp)
100	movaps	%xmm7,0x10(%rsp)
101___
102$code.=<<___;
103	lea	2($num),%r11
104	neg	%r11
105	lea	(%rsp,%r11,8),%rsp	# tp=alloca(8*(num+2))
106	and	\$-1024,%rsp		# minimize TLB usage
107
108	mov	%rax,8(%rsp,$num,8)	# tp[num+1]=%rsp
109.Lmul_body:
110	mov	$bp,%r12		# reassign $bp
111___
112		$bp="%r12";
113		$STRIDE=2**5*8;		# 5 is "window size"
114		$N=$STRIDE/4;		# should match cache line size
115$code.=<<___;
116	mov	%r10,%r11
117	shr	\$`log($N/8)/log(2)`,%r10
118	and	\$`$N/8-1`,%r11
119	not	%r10
120	lea	.Lmagic_masks(%rip),%rax
121	and	\$`2**5/($N/8)-1`,%r10	# 5 is "window size"
122	lea	96($bp,%r11,8),$bp	# pointer within 1st cache line
123	movq	0(%rax,%r10,8),%xmm4	# set of masks denoting which
124	movq	8(%rax,%r10,8),%xmm5	# cache line contains element
125	movq	16(%rax,%r10,8),%xmm6	# denoted by 7th argument
126	movq	24(%rax,%r10,8),%xmm7
127
128	movq	`0*$STRIDE/4-96`($bp),%xmm0
129	movq	`1*$STRIDE/4-96`($bp),%xmm1
130	pand	%xmm4,%xmm0
131	movq	`2*$STRIDE/4-96`($bp),%xmm2
132	pand	%xmm5,%xmm1
133	movq	`3*$STRIDE/4-96`($bp),%xmm3
134	pand	%xmm6,%xmm2
135	por	%xmm1,%xmm0
136	pand	%xmm7,%xmm3
137	por	%xmm2,%xmm0
138	lea	$STRIDE($bp),$bp
139	por	%xmm3,%xmm0
140
141	movq	%xmm0,$m0		# m0=bp[0]
142
143	mov	($n0),$n0		# pull n0[0] value
144	mov	($ap),%rax
145
146	xor	$i,$i			# i=0
147	xor	$j,$j			# j=0
148
149	movq	`0*$STRIDE/4-96`($bp),%xmm0
150	movq	`1*$STRIDE/4-96`($bp),%xmm1
151	pand	%xmm4,%xmm0
152	movq	`2*$STRIDE/4-96`($bp),%xmm2
153	pand	%xmm5,%xmm1
154
155	mov	$n0,$m1
156	mulq	$m0			# ap[0]*bp[0]
157	mov	%rax,$lo0
158	mov	($np),%rax
159
160	movq	`3*$STRIDE/4-96`($bp),%xmm3
161	pand	%xmm6,%xmm2
162	por	%xmm1,%xmm0
163	pand	%xmm7,%xmm3
164
165	imulq	$lo0,$m1		# "tp[0]"*n0
166	mov	%rdx,$hi0
167
168	por	%xmm2,%xmm0
169	lea	$STRIDE($bp),$bp
170	por	%xmm3,%xmm0
171
172	mulq	$m1			# np[0]*m1
173	add	%rax,$lo0		# discarded
174	mov	8($ap),%rax
175	adc	\$0,%rdx
176	mov	%rdx,$hi1
177
178	lea	1($j),$j		# j++
179	jmp	.L1st_enter
180
181.align	16
182.L1st:
183	add	%rax,$hi1
184	mov	($ap,$j,8),%rax
185	adc	\$0,%rdx
186	add	$hi0,$hi1		# np[j]*m1+ap[j]*bp[0]
187	mov	$lo0,$hi0
188	adc	\$0,%rdx
189	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
190	mov	%rdx,$hi1
191
192.L1st_enter:
193	mulq	$m0			# ap[j]*bp[0]
194	add	%rax,$hi0
195	mov	($np,$j,8),%rax
196	adc	\$0,%rdx
197	lea	1($j),$j		# j++
198	mov	%rdx,$lo0
199
200	mulq	$m1			# np[j]*m1
201	cmp	$num,$j
202	jne	.L1st
203
204	movq	%xmm0,$m0		# bp[1]
205
206	add	%rax,$hi1
207	mov	($ap),%rax		# ap[0]
208	adc	\$0,%rdx
209	add	$hi0,$hi1		# np[j]*m1+ap[j]*bp[0]
210	adc	\$0,%rdx
211	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
212	mov	%rdx,$hi1
213	mov	$lo0,$hi0
214
215	xor	%rdx,%rdx
216	add	$hi0,$hi1
217	adc	\$0,%rdx
218	mov	$hi1,-8(%rsp,$num,8)
219	mov	%rdx,(%rsp,$num,8)	# store upmost overflow bit
220
221	lea	1($i),$i		# i++
222	jmp	.Louter
223.align	16
224.Louter:
225	xor	$j,$j			# j=0
226	mov	$n0,$m1
227	mov	(%rsp),$lo0
228
229	movq	`0*$STRIDE/4-96`($bp),%xmm0
230	movq	`1*$STRIDE/4-96`($bp),%xmm1
231	pand	%xmm4,%xmm0
232	movq	`2*$STRIDE/4-96`($bp),%xmm2
233	pand	%xmm5,%xmm1
234
235	mulq	$m0			# ap[0]*bp[i]
236	add	%rax,$lo0		# ap[0]*bp[i]+tp[0]
237	mov	($np),%rax
238	adc	\$0,%rdx
239
240	movq	`3*$STRIDE/4-96`($bp),%xmm3
241	pand	%xmm6,%xmm2
242	por	%xmm1,%xmm0
243	pand	%xmm7,%xmm3
244
245	imulq	$lo0,$m1		# tp[0]*n0
246	mov	%rdx,$hi0
247
248	por	%xmm2,%xmm0
249	lea	$STRIDE($bp),$bp
250	por	%xmm3,%xmm0
251
252	mulq	$m1			# np[0]*m1
253	add	%rax,$lo0		# discarded
254	mov	8($ap),%rax
255	adc	\$0,%rdx
256	mov	8(%rsp),$lo0		# tp[1]
257	mov	%rdx,$hi1
258
259	lea	1($j),$j		# j++
260	jmp	.Linner_enter
261
262.align	16
263.Linner:
264	add	%rax,$hi1
265	mov	($ap,$j,8),%rax
266	adc	\$0,%rdx
267	add	$lo0,$hi1		# np[j]*m1+ap[j]*bp[i]+tp[j]
268	mov	(%rsp,$j,8),$lo0
269	adc	\$0,%rdx
270	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
271	mov	%rdx,$hi1
272
273.Linner_enter:
274	mulq	$m0			# ap[j]*bp[i]
275	add	%rax,$hi0
276	mov	($np,$j,8),%rax
277	adc	\$0,%rdx
278	add	$hi0,$lo0		# ap[j]*bp[i]+tp[j]
279	mov	%rdx,$hi0
280	adc	\$0,$hi0
281	lea	1($j),$j		# j++
282
283	mulq	$m1			# np[j]*m1
284	cmp	$num,$j
285	jne	.Linner
286
287	movq	%xmm0,$m0		# bp[i+1]
288
289	add	%rax,$hi1
290	mov	($ap),%rax		# ap[0]
291	adc	\$0,%rdx
292	add	$lo0,$hi1		# np[j]*m1+ap[j]*bp[i]+tp[j]
293	mov	(%rsp,$j,8),$lo0
294	adc	\$0,%rdx
295	mov	$hi1,-16(%rsp,$j,8)	# tp[j-1]
296	mov	%rdx,$hi1
297
298	xor	%rdx,%rdx
299	add	$hi0,$hi1
300	adc	\$0,%rdx
301	add	$lo0,$hi1		# pull upmost overflow bit
302	adc	\$0,%rdx
303	mov	$hi1,-8(%rsp,$num,8)
304	mov	%rdx,(%rsp,$num,8)	# store upmost overflow bit
305
306	lea	1($i),$i		# i++
307	cmp	$num,$i
308	jb	.Louter
309
310	xor	$i,$i			# i=0 and clear CF!
311	mov	(%rsp),%rax		# tp[0]
312	lea	(%rsp),$ap		# borrow ap for tp
313	mov	$num,$j			# j=num
314	jmp	.Lsub
315.align	16
316.Lsub:	sbb	($np,$i,8),%rax
317	mov	%rax,($rp,$i,8)		# rp[i]=tp[i]-np[i]
318	mov	8($ap,$i,8),%rax	# tp[i+1]
319	lea	1($i),$i		# i++
320	dec	$j			# doesnn't affect CF!
321	jnz	.Lsub
322
323	sbb	\$0,%rax		# handle upmost overflow bit
324	xor	$i,$i
325	mov	$num,$j			# j=num
326.align	16
327.Lcopy:					# copy or in-place refresh
328	mov	(%rsp,$i,8),$ap
329	mov	($rp,$i,8),$np
330	xor	$np,$ap			# conditional select:
331	and	%rax,$ap		# ((ap ^ np) & %rax) ^ np
332	xor	$np,$ap			# ap = borrow?tp:rp
333	mov	$i,(%rsp,$i,8)		# zap temporary vector
334	mov	$ap,($rp,$i,8)		# rp[i]=tp[i]
335	lea	1($i),$i
336	sub	\$1,$j
337	jnz	.Lcopy
338
339	mov	8(%rsp,$num,8),%rsi	# restore %rsp
340	mov	\$1,%rax
341___
342$code.=<<___ if ($win64);
343	movaps	-88(%rsi),%xmm6
344	movaps	-72(%rsi),%xmm7
345___
346$code.=<<___;
347	mov	-48(%rsi),%r15
348	mov	-40(%rsi),%r14
349	mov	-32(%rsi),%r13
350	mov	-24(%rsi),%r12
351	mov	-16(%rsi),%rbp
352	mov	-8(%rsi),%rbx
353	lea	(%rsi),%rsp
354.Lmul_epilogue:
355	ret
356.size	bn_mul_mont_gather5,.-bn_mul_mont_gather5
357___
358{{{
359my @A=("%r10","%r11");
360my @N=("%r13","%rdi");
361$code.=<<___;
362.type	bn_mul4x_mont_gather5,\@function,6
363.align	32
364bn_mul4x_mont_gather5:
365.Lmul4x_enter:
366___
367$code.=<<___ if ($addx);
368	and	\$0x80100,%r11d
369	cmp	\$0x80100,%r11d
370	je	.Lmulx4x_enter
371___
372$code.=<<___;
373	.byte	0x67
374	mov	%rsp,%rax
375	push	%rbx
376	push	%rbp
377	push	%r12
378	push	%r13
379	push	%r14
380	push	%r15
381___
382$code.=<<___ if ($win64);
383	lea	-0x28(%rsp),%rsp
384	movaps	%xmm6,(%rsp)
385	movaps	%xmm7,0x10(%rsp)
386___
387$code.=<<___;
388	.byte	0x67
389	mov	${num}d,%r10d
390	shl	\$3,${num}d
391	shl	\$3+2,%r10d		# 4*$num
392	neg	$num			# -$num
393
394	##############################################################
395	# ensure that stack frame doesn't alias with $aptr+4*$num
396	# modulo 4096, which covers ret[num], am[num] and n[2*num]
397	# (see bn_exp.c). this is done to allow memory disambiguation
398	# logic do its magic. [excessive frame is allocated in order
399	# to allow bn_from_mont8x to clear it.]
400	#
401	lea	-64(%rsp,$num,2),%r11
402	sub	$ap,%r11
403	and	\$4095,%r11
404	cmp	%r11,%r10
405	jb	.Lmul4xsp_alt
406	sub	%r11,%rsp		# align with $ap
407	lea	-64(%rsp,$num,2),%rsp	# alloca(128+num*8)
408	jmp	.Lmul4xsp_done
409
410.align	32
411.Lmul4xsp_alt:
412	lea	4096-64(,$num,2),%r10
413	lea	-64(%rsp,$num,2),%rsp	# alloca(128+num*8)
414	sub	%r10,%r11
415	mov	\$0,%r10
416	cmovc	%r10,%r11
417	sub	%r11,%rsp
418.Lmul4xsp_done:
419	and	\$-64,%rsp
420	neg	$num
421
422	mov	%rax,40(%rsp)
423.Lmul4x_body:
424
425	call	mul4x_internal
426
427	mov	40(%rsp),%rsi		# restore %rsp
428	mov	\$1,%rax
429___
430$code.=<<___ if ($win64);
431	movaps	-88(%rsi),%xmm6
432	movaps	-72(%rsi),%xmm7
433___
434$code.=<<___;
435	mov	-48(%rsi),%r15
436	mov	-40(%rsi),%r14
437	mov	-32(%rsi),%r13
438	mov	-24(%rsi),%r12
439	mov	-16(%rsi),%rbp
440	mov	-8(%rsi),%rbx
441	lea	(%rsi),%rsp
442.Lmul4x_epilogue:
443	ret
444.size	bn_mul4x_mont_gather5,.-bn_mul4x_mont_gather5
445
446.type	mul4x_internal,\@abi-omnipotent
447.align	32
448mul4x_internal:
449	shl	\$5,$num
450	mov	`($win64?56:8)`(%rax),%r10d	# load 7th argument
451	lea	256(%rdx,$num),%r13
452	shr	\$5,$num		# restore $num
453___
454		$bp="%r12";
455		$STRIDE=2**5*8;		# 5 is "window size"
456		$N=$STRIDE/4;		# should match cache line size
457		$tp=$i;
458$code.=<<___;
459	mov	%r10,%r11
460	shr	\$`log($N/8)/log(2)`,%r10
461	and	\$`$N/8-1`,%r11
462	not	%r10
463	lea	.Lmagic_masks(%rip),%rax
464	and	\$`2**5/($N/8)-1`,%r10	# 5 is "window size"
465	lea	96(%rdx,%r11,8),$bp	# pointer within 1st cache line
466	movq	0(%rax,%r10,8),%xmm4	# set of masks denoting which
467	movq	8(%rax,%r10,8),%xmm5	# cache line contains element
468	add	\$7,%r11
469	movq	16(%rax,%r10,8),%xmm6	# denoted by 7th argument
470	movq	24(%rax,%r10,8),%xmm7
471	and	\$7,%r11
472
473	movq	`0*$STRIDE/4-96`($bp),%xmm0
474	lea	$STRIDE($bp),$tp	# borrow $tp
475	movq	`1*$STRIDE/4-96`($bp),%xmm1
476	pand	%xmm4,%xmm0
477	movq	`2*$STRIDE/4-96`($bp),%xmm2
478	pand	%xmm5,%xmm1
479	movq	`3*$STRIDE/4-96`($bp),%xmm3
480	pand	%xmm6,%xmm2
481	.byte	0x67
482	por	%xmm1,%xmm0
483	movq	`0*$STRIDE/4-96`($tp),%xmm1
484	.byte	0x67
485	pand	%xmm7,%xmm3
486	.byte	0x67
487	por	%xmm2,%xmm0
488	movq	`1*$STRIDE/4-96`($tp),%xmm2
489	.byte	0x67
490	pand	%xmm4,%xmm1
491	.byte	0x67
492	por	%xmm3,%xmm0
493	movq	`2*$STRIDE/4-96`($tp),%xmm3
494
495	movq	%xmm0,$m0		# m0=bp[0]
496	movq	`3*$STRIDE/4-96`($tp),%xmm0
497	mov	%r13,16+8(%rsp)		# save end of b[num]
498	mov	$rp, 56+8(%rsp)		# save $rp
499
500	mov	($n0),$n0		# pull n0[0] value
501	mov	($ap),%rax
502	lea	($ap,$num),$ap		# end of a[num]
503	neg	$num
504
505	mov	$n0,$m1
506	mulq	$m0			# ap[0]*bp[0]
507	mov	%rax,$A[0]
508	mov	($np),%rax
509
510	pand	%xmm5,%xmm2
511	pand	%xmm6,%xmm3
512	por	%xmm2,%xmm1
513
514	imulq	$A[0],$m1		# "tp[0]"*n0
515	##############################################################
516	# $tp is chosen so that writing to top-most element of the
517	# vector occurs just "above" references to powers table,
518	# "above" modulo cache-line size, which effectively precludes
519	# possibility of memory disambiguation logic failure when
520	# accessing the table.
521	#
522	lea	64+8(%rsp,%r11,8),$tp
523	mov	%rdx,$A[1]
524
525	pand	%xmm7,%xmm0
526	por	%xmm3,%xmm1
527	lea	2*$STRIDE($bp),$bp
528	por	%xmm1,%xmm0
529
530	mulq	$m1			# np[0]*m1
531	add	%rax,$A[0]		# discarded
532	mov	8($ap,$num),%rax
533	adc	\$0,%rdx
534	mov	%rdx,$N[1]
535
536	mulq	$m0
537	add	%rax,$A[1]
538	mov	16*1($np),%rax		# interleaved with 0, therefore 16*n
539	adc	\$0,%rdx
540	mov	%rdx,$A[0]
541
542	mulq	$m1
543	add	%rax,$N[1]
544	mov	16($ap,$num),%rax
545	adc	\$0,%rdx
546	add	$A[1],$N[1]
547	lea	4*8($num),$j		# j=4
548	lea	16*4($np),$np
549	adc	\$0,%rdx
550	mov	$N[1],($tp)
551	mov	%rdx,$N[0]
552	jmp	.L1st4x
553
554.align	32
555.L1st4x:
556	mulq	$m0			# ap[j]*bp[0]
557	add	%rax,$A[0]
558	mov	-16*2($np),%rax
559	lea	32($tp),$tp
560	adc	\$0,%rdx
561	mov	%rdx,$A[1]
562
563	mulq	$m1			# np[j]*m1
564	add	%rax,$N[0]
565	mov	-8($ap,$j),%rax
566	adc	\$0,%rdx
567	add	$A[0],$N[0]		# np[j]*m1+ap[j]*bp[0]
568	adc	\$0,%rdx
569	mov	$N[0],-24($tp)		# tp[j-1]
570	mov	%rdx,$N[1]
571
572	mulq	$m0			# ap[j]*bp[0]
573	add	%rax,$A[1]
574	mov	-16*1($np),%rax
575	adc	\$0,%rdx
576	mov	%rdx,$A[0]
577
578	mulq	$m1			# np[j]*m1
579	add	%rax,$N[1]
580	mov	($ap,$j),%rax
581	adc	\$0,%rdx
582	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[0]
583	adc	\$0,%rdx
584	mov	$N[1],-16($tp)		# tp[j-1]
585	mov	%rdx,$N[0]
586
587	mulq	$m0			# ap[j]*bp[0]
588	add	%rax,$A[0]
589	mov	16*0($np),%rax
590	adc	\$0,%rdx
591	mov	%rdx,$A[1]
592
593	mulq	$m1			# np[j]*m1
594	add	%rax,$N[0]
595	mov	8($ap,$j),%rax
596	adc	\$0,%rdx
597	add	$A[0],$N[0]		# np[j]*m1+ap[j]*bp[0]
598	adc	\$0,%rdx
599	mov	$N[0],-8($tp)		# tp[j-1]
600	mov	%rdx,$N[1]
601
602	mulq	$m0			# ap[j]*bp[0]
603	add	%rax,$A[1]
604	mov	16*1($np),%rax
605	adc	\$0,%rdx
606	mov	%rdx,$A[0]
607
608	mulq	$m1			# np[j]*m1
609	add	%rax,$N[1]
610	mov	16($ap,$j),%rax
611	adc	\$0,%rdx
612	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[0]
613	lea	16*4($np),$np
614	adc	\$0,%rdx
615	mov	$N[1],($tp)		# tp[j-1]
616	mov	%rdx,$N[0]
617
618	add	\$32,$j			# j+=4
619	jnz	.L1st4x
620
621	mulq	$m0			# ap[j]*bp[0]
622	add	%rax,$A[0]
623	mov	-16*2($np),%rax
624	lea	32($tp),$tp
625	adc	\$0,%rdx
626	mov	%rdx,$A[1]
627
628	mulq	$m1			# np[j]*m1
629	add	%rax,$N[0]
630	mov	-8($ap),%rax
631	adc	\$0,%rdx
632	add	$A[0],$N[0]		# np[j]*m1+ap[j]*bp[0]
633	adc	\$0,%rdx
634	mov	$N[0],-24($tp)		# tp[j-1]
635	mov	%rdx,$N[1]
636
637	mulq	$m0			# ap[j]*bp[0]
638	add	%rax,$A[1]
639	mov	-16*1($np),%rax
640	adc	\$0,%rdx
641	mov	%rdx,$A[0]
642
643	mulq	$m1			# np[j]*m1
644	add	%rax,$N[1]
645	mov	($ap,$num),%rax		# ap[0]
646	adc	\$0,%rdx
647	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[0]
648	adc	\$0,%rdx
649	mov	$N[1],-16($tp)		# tp[j-1]
650	mov	%rdx,$N[0]
651
652	movq	%xmm0,$m0		# bp[1]
653	lea	($np,$num,2),$np	# rewind $np
654
655	xor	$N[1],$N[1]
656	add	$A[0],$N[0]
657	adc	\$0,$N[1]
658	mov	$N[0],-8($tp)
659
660	jmp	.Louter4x
661
662.align	32
663.Louter4x:
664	mov	($tp,$num),$A[0]
665	mov	$n0,$m1
666	mulq	$m0			# ap[0]*bp[i]
667	add	%rax,$A[0]		# ap[0]*bp[i]+tp[0]
668	mov	($np),%rax
669	adc	\$0,%rdx
670
671	movq	`0*$STRIDE/4-96`($bp),%xmm0
672	movq	`1*$STRIDE/4-96`($bp),%xmm1
673	pand	%xmm4,%xmm0
674	movq	`2*$STRIDE/4-96`($bp),%xmm2
675	pand	%xmm5,%xmm1
676	movq	`3*$STRIDE/4-96`($bp),%xmm3
677
678	imulq	$A[0],$m1		# tp[0]*n0
679	.byte	0x67
680	mov	%rdx,$A[1]
681	mov	$N[1],($tp)		# store upmost overflow bit
682
683	pand	%xmm6,%xmm2
684	por	%xmm1,%xmm0
685	pand	%xmm7,%xmm3
686	por	%xmm2,%xmm0
687	lea	($tp,$num),$tp		# rewind $tp
688	lea	$STRIDE($bp),$bp
689	por	%xmm3,%xmm0
690
691	mulq	$m1			# np[0]*m1
692	add	%rax,$A[0]		# "$N[0]", discarded
693	mov	8($ap,$num),%rax
694	adc	\$0,%rdx
695	mov	%rdx,$N[1]
696
697	mulq	$m0			# ap[j]*bp[i]
698	add	%rax,$A[1]
699	mov	16*1($np),%rax		# interleaved with 0, therefore 16*n
700	adc	\$0,%rdx
701	add	8($tp),$A[1]		# +tp[1]
702	adc	\$0,%rdx
703	mov	%rdx,$A[0]
704
705	mulq	$m1			# np[j]*m1
706	add	%rax,$N[1]
707	mov	16($ap,$num),%rax
708	adc	\$0,%rdx
709	add	$A[1],$N[1]		# np[j]*m1+ap[j]*bp[i]+tp[j]
710	lea	4*8($num),$j		# j=4
711	lea	16*4($np),$np
712	adc	\$0,%rdx
713	mov	%rdx,$N[0]
714	jmp	.Linner4x
715
716.align	32
717.Linner4x:
718	mulq	$m0			# ap[j]*bp[i]
719	add	%rax,$A[0]
720	mov	-16*2($np),%rax
721	adc	\$0,%rdx
722	add	16($tp),$A[0]		# ap[j]*bp[i]+tp[j]
723	lea	32($tp),$tp
724	adc	\$0,%rdx
725	mov	%rdx,$A[1]
726
727	mulq	$m1			# np[j]*m1
728	add	%rax,$N[0]
729	mov	-8($ap,$j),%rax
730	adc	\$0,%rdx
731	add	$A[0],$N[0]
732	adc	\$0,%rdx
733	mov	$N[1],-32($tp)		# tp[j-1]
734	mov	%rdx,$N[1]
735
736	mulq	$m0			# ap[j]*bp[i]
737	add	%rax,$A[1]
738	mov	-16*1($np),%rax
739	adc	\$0,%rdx
740	add	-8($tp),$A[1]
741	adc	\$0,%rdx
742	mov	%rdx,$A[0]
743
744	mulq	$m1			# np[j]*m1
745	add	%rax,$N[1]
746	mov	($ap,$j),%rax
747	adc	\$0,%rdx
748	add	$A[1],$N[1]
749	adc	\$0,%rdx
750	mov	$N[0],-24($tp)		# tp[j-1]
751	mov	%rdx,$N[0]
752
753	mulq	$m0			# ap[j]*bp[i]
754	add	%rax,$A[0]
755	mov	16*0($np),%rax
756	adc	\$0,%rdx
757	add	($tp),$A[0]		# ap[j]*bp[i]+tp[j]
758	adc	\$0,%rdx
759	mov	%rdx,$A[1]
760
761	mulq	$m1			# np[j]*m1
762	add	%rax,$N[0]
763	mov	8($ap,$j),%rax
764	adc	\$0,%rdx
765	add	$A[0],$N[0]
766	adc	\$0,%rdx
767	mov	$N[1],-16($tp)		# tp[j-1]
768	mov	%rdx,$N[1]
769
770	mulq	$m0			# ap[j]*bp[i]
771	add	%rax,$A[1]
772	mov	16*1($np),%rax
773	adc	\$0,%rdx
774	add	8($tp),$A[1]
775	adc	\$0,%rdx
776	mov	%rdx,$A[0]
777
778	mulq	$m1			# np[j]*m1
779	add	%rax,$N[1]
780	mov	16($ap,$j),%rax
781	adc	\$0,%rdx
782	add	$A[1],$N[1]
783	lea	16*4($np),$np
784	adc	\$0,%rdx
785	mov	$N[0],-8($tp)		# tp[j-1]
786	mov	%rdx,$N[0]
787
788	add	\$32,$j			# j+=4
789	jnz	.Linner4x
790
791	mulq	$m0			# ap[j]*bp[i]
792	add	%rax,$A[0]
793	mov	-16*2($np),%rax
794	adc	\$0,%rdx
795	add	16($tp),$A[0]		# ap[j]*bp[i]+tp[j]
796	lea	32($tp),$tp
797	adc	\$0,%rdx
798	mov	%rdx,$A[1]
799
800	mulq	$m1			# np[j]*m1
801	add	%rax,$N[0]
802	mov	-8($ap),%rax
803	adc	\$0,%rdx
804	add	$A[0],$N[0]
805	adc	\$0,%rdx
806	mov	$N[1],-32($tp)		# tp[j-1]
807	mov	%rdx,$N[1]
808
809	mulq	$m0			# ap[j]*bp[i]
810	add	%rax,$A[1]
811	mov	$m1,%rax
812	mov	-16*1($np),$m1
813	adc	\$0,%rdx
814	add	-8($tp),$A[1]
815	adc	\$0,%rdx
816	mov	%rdx,$A[0]
817
818	mulq	$m1			# np[j]*m1
819	add	%rax,$N[1]
820	mov	($ap,$num),%rax		# ap[0]
821	adc	\$0,%rdx
822	add	$A[1],$N[1]
823	adc	\$0,%rdx
824	mov	$N[0],-24($tp)		# tp[j-1]
825	mov	%rdx,$N[0]
826
827	movq	%xmm0,$m0		# bp[i+1]
828	mov	$N[1],-16($tp)		# tp[j-1]
829	lea	($np,$num,2),$np	# rewind $np
830
831	xor	$N[1],$N[1]
832	add	$A[0],$N[0]
833	adc	\$0,$N[1]
834	add	($tp),$N[0]		# pull upmost overflow bit
835	adc	\$0,$N[1]		# upmost overflow bit
836	mov	$N[0],-8($tp)
837
838	cmp	16+8(%rsp),$bp
839	jb	.Louter4x
840___
841if (1) {
842$code.=<<___;
843	sub	$N[0],$m1		# compare top-most words
844	adc	$j,$j			# $j is zero
845	or	$j,$N[1]
846	xor	\$1,$N[1]
847	lea	($tp,$num),%rbx		# tptr in .sqr4x_sub
848	lea	($np,$N[1],8),%rbp	# nptr in .sqr4x_sub
849	mov	%r9,%rcx
850	sar	\$3+2,%rcx		# cf=0
851	mov	56+8(%rsp),%rdi		# rptr in .sqr4x_sub
852	jmp	.Lsqr4x_sub
853___
854} else {
855my @ri=("%rax",$bp,$m0,$m1);
856my $rp="%rdx";
857$code.=<<___
858	xor	\$1,$N[1]
859	lea	($tp,$num),$tp		# rewind $tp
860	sar	\$5,$num		# cf=0
861	lea	($np,$N[1],8),$np
862	mov	56+8(%rsp),$rp		# restore $rp
863	jmp	.Lsub4x
864
865.align	32
866.Lsub4x:
867	.byte	0x66
868	mov	8*0($tp),@ri[0]
869	mov	8*1($tp),@ri[1]
870	.byte	0x66
871	sbb	16*0($np),@ri[0]
872	mov	8*2($tp),@ri[2]
873	sbb	16*1($np),@ri[1]
874	mov	3*8($tp),@ri[3]
875	lea	4*8($tp),$tp
876	sbb	16*2($np),@ri[2]
877	mov	@ri[0],8*0($rp)
878	sbb	16*3($np),@ri[3]
879	lea	16*4($np),$np
880	mov	@ri[1],8*1($rp)
881	mov	@ri[2],8*2($rp)
882	mov	@ri[3],8*3($rp)
883	lea	8*4($rp),$rp
884
885	inc	$num
886	jnz	.Lsub4x
887
888	ret
889___
890}
891$code.=<<___;
892.size	mul4x_internal,.-mul4x_internal
893___
894}}}
895{{{
896######################################################################
897# void bn_power5(
898my $rptr="%rdi";	# BN_ULONG *rptr,
899my $aptr="%rsi";	# const BN_ULONG *aptr,
900my $bptr="%rdx";	# const void *table,
901my $nptr="%rcx";	# const BN_ULONG *nptr,
902my $n0  ="%r8";		# const BN_ULONG *n0);
903my $num ="%r9";		# int num, has to be divisible by 8
904			# int pwr
905
906my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
907my @A0=("%r10","%r11");
908my @A1=("%r12","%r13");
909my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
910
911$code.=<<___;
912.globl	bn_power5
913.type	bn_power5,\@function,6
914.align	32
915bn_power5:
916___
917$code.=<<___ if ($addx);
918	mov	OPENSSL_ia32cap_P+8(%rip),%r11d
919	and	\$0x80100,%r11d
920	cmp	\$0x80100,%r11d
921	je	.Lpowerx5_enter
922___
923$code.=<<___;
924	mov	%rsp,%rax
925	push	%rbx
926	push	%rbp
927	push	%r12
928	push	%r13
929	push	%r14
930	push	%r15
931___
932$code.=<<___ if ($win64);
933	lea	-0x28(%rsp),%rsp
934	movaps	%xmm6,(%rsp)
935	movaps	%xmm7,0x10(%rsp)
936___
937$code.=<<___;
938	mov	${num}d,%r10d
939	shl	\$3,${num}d		# convert $num to bytes
940	shl	\$3+2,%r10d		# 4*$num
941	neg	$num
942	mov	($n0),$n0		# *n0
943
944	##############################################################
945	# ensure that stack frame doesn't alias with $aptr+4*$num
946	# modulo 4096, which covers ret[num], am[num] and n[2*num]
947	# (see bn_exp.c). this is done to allow memory disambiguation
948	# logic do its magic.
949	#
950	lea	-64(%rsp,$num,2),%r11
951	sub	$aptr,%r11
952	and	\$4095,%r11
953	cmp	%r11,%r10
954	jb	.Lpwr_sp_alt
955	sub	%r11,%rsp		# align with $aptr
956	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
957	jmp	.Lpwr_sp_done
958
959.align	32
960.Lpwr_sp_alt:
961	lea	4096-64(,$num,2),%r10	# 4096-frame-2*$num
962	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
963	sub	%r10,%r11
964	mov	\$0,%r10
965	cmovc	%r10,%r11
966	sub	%r11,%rsp
967.Lpwr_sp_done:
968	and	\$-64,%rsp
969	mov	$num,%r10
970	neg	$num
971
972	##############################################################
973	# Stack layout
974	#
975	# +0	saved $num, used in reduction section
976	# +8	&t[2*$num], used in reduction section
977	# +32	saved *n0
978	# +40	saved %rsp
979	# +48	t[2*$num]
980	#
981	mov	$n0,  32(%rsp)
982	mov	%rax, 40(%rsp)		# save original %rsp
983.Lpower5_body:
984	movq	$rptr,%xmm1		# save $rptr
985	movq	$nptr,%xmm2		# save $nptr
986	movq	%r10, %xmm3		# -$num
987	movq	$bptr,%xmm4
988
989	call	__bn_sqr8x_internal
990	call	__bn_sqr8x_internal
991	call	__bn_sqr8x_internal
992	call	__bn_sqr8x_internal
993	call	__bn_sqr8x_internal
994
995	movq	%xmm2,$nptr
996	movq	%xmm4,$bptr
997	mov	$aptr,$rptr
998	mov	40(%rsp),%rax
999	lea	32(%rsp),$n0
1000
1001	call	mul4x_internal
1002
1003	mov	40(%rsp),%rsi		# restore %rsp
1004	mov	\$1,%rax
1005	mov	-48(%rsi),%r15
1006	mov	-40(%rsi),%r14
1007	mov	-32(%rsi),%r13
1008	mov	-24(%rsi),%r12
1009	mov	-16(%rsi),%rbp
1010	mov	-8(%rsi),%rbx
1011	lea	(%rsi),%rsp
1012.Lpower5_epilogue:
1013	ret
1014.size	bn_power5,.-bn_power5
1015
1016.globl	bn_sqr8x_internal
1017.hidden	bn_sqr8x_internal
1018.type	bn_sqr8x_internal,\@abi-omnipotent
1019.align	32
1020bn_sqr8x_internal:
1021__bn_sqr8x_internal:
1022	##############################################################
1023	# Squaring part:
1024	#
1025	# a) multiply-n-add everything but a[i]*a[i];
1026	# b) shift result of a) by 1 to the left and accumulate
1027	#    a[i]*a[i] products;
1028	#
1029	##############################################################
1030	#                                                     a[1]a[0]
1031	#                                                 a[2]a[0]
1032	#                                             a[3]a[0]
1033	#                                             a[2]a[1]
1034	#                                         a[4]a[0]
1035	#                                         a[3]a[1]
1036	#                                     a[5]a[0]
1037	#                                     a[4]a[1]
1038	#                                     a[3]a[2]
1039	#                                 a[6]a[0]
1040	#                                 a[5]a[1]
1041	#                                 a[4]a[2]
1042	#                             a[7]a[0]
1043	#                             a[6]a[1]
1044	#                             a[5]a[2]
1045	#                             a[4]a[3]
1046	#                         a[7]a[1]
1047	#                         a[6]a[2]
1048	#                         a[5]a[3]
1049	#                     a[7]a[2]
1050	#                     a[6]a[3]
1051	#                     a[5]a[4]
1052	#                 a[7]a[3]
1053	#                 a[6]a[4]
1054	#             a[7]a[4]
1055	#             a[6]a[5]
1056	#         a[7]a[5]
1057	#     a[7]a[6]
1058	#                                                     a[1]a[0]
1059	#                                                 a[2]a[0]
1060	#                                             a[3]a[0]
1061	#                                         a[4]a[0]
1062	#                                     a[5]a[0]
1063	#                                 a[6]a[0]
1064	#                             a[7]a[0]
1065	#                                             a[2]a[1]
1066	#                                         a[3]a[1]
1067	#                                     a[4]a[1]
1068	#                                 a[5]a[1]
1069	#                             a[6]a[1]
1070	#                         a[7]a[1]
1071	#                                     a[3]a[2]
1072	#                                 a[4]a[2]
1073	#                             a[5]a[2]
1074	#                         a[6]a[2]
1075	#                     a[7]a[2]
1076	#                             a[4]a[3]
1077	#                         a[5]a[3]
1078	#                     a[6]a[3]
1079	#                 a[7]a[3]
1080	#                     a[5]a[4]
1081	#                 a[6]a[4]
1082	#             a[7]a[4]
1083	#             a[6]a[5]
1084	#         a[7]a[5]
1085	#     a[7]a[6]
1086	#                                                         a[0]a[0]
1087	#                                                 a[1]a[1]
1088	#                                         a[2]a[2]
1089	#                                 a[3]a[3]
1090	#                         a[4]a[4]
1091	#                 a[5]a[5]
1092	#         a[6]a[6]
1093	# a[7]a[7]
1094
1095	lea	32(%r10),$i		# $i=-($num-32)
1096	lea	($aptr,$num),$aptr	# end of a[] buffer, ($aptr,$i)=&ap[2]
1097
1098	mov	$num,$j			# $j=$num
1099
1100					# comments apply to $num==8 case
1101	mov	-32($aptr,$i),$a0	# a[0]
1102	lea	48+8(%rsp,$num,2),$tptr	# end of tp[] buffer, &tp[2*$num]
1103	mov	-24($aptr,$i),%rax	# a[1]
1104	lea	-32($tptr,$i),$tptr	# end of tp[] window, &tp[2*$num-"$i"]
1105	mov	-16($aptr,$i),$ai	# a[2]
1106	mov	%rax,$a1
1107
1108	mul	$a0			# a[1]*a[0]
1109	mov	%rax,$A0[0]		# a[1]*a[0]
1110	 mov	$ai,%rax		# a[2]
1111	mov	%rdx,$A0[1]
1112	mov	$A0[0],-24($tptr,$i)	# t[1]
1113
1114	mul	$a0			# a[2]*a[0]
1115	add	%rax,$A0[1]
1116	 mov	$ai,%rax
1117	adc	\$0,%rdx
1118	mov	$A0[1],-16($tptr,$i)	# t[2]
1119	mov	%rdx,$A0[0]
1120
1121
1122	 mov	-8($aptr,$i),$ai	# a[3]
1123	mul	$a1			# a[2]*a[1]
1124	mov	%rax,$A1[0]		# a[2]*a[1]+t[3]
1125	 mov	$ai,%rax
1126	mov	%rdx,$A1[1]
1127
1128	 lea	($i),$j
1129	mul	$a0			# a[3]*a[0]
1130	add	%rax,$A0[0]		# a[3]*a[0]+a[2]*a[1]+t[3]
1131	 mov	$ai,%rax
1132	mov	%rdx,$A0[1]
1133	adc	\$0,$A0[1]
1134	add	$A1[0],$A0[0]
1135	adc	\$0,$A0[1]
1136	mov	$A0[0],-8($tptr,$j)	# t[3]
1137	jmp	.Lsqr4x_1st
1138
1139.align	32
1140.Lsqr4x_1st:
1141	 mov	($aptr,$j),$ai		# a[4]
1142	mul	$a1			# a[3]*a[1]
1143	add	%rax,$A1[1]		# a[3]*a[1]+t[4]
1144	 mov	$ai,%rax
1145	mov	%rdx,$A1[0]
1146	adc	\$0,$A1[0]
1147
1148	mul	$a0			# a[4]*a[0]
1149	add	%rax,$A0[1]		# a[4]*a[0]+a[3]*a[1]+t[4]
1150	 mov	$ai,%rax		# a[3]
1151	 mov	8($aptr,$j),$ai		# a[5]
1152	mov	%rdx,$A0[0]
1153	adc	\$0,$A0[0]
1154	add	$A1[1],$A0[1]
1155	adc	\$0,$A0[0]
1156
1157
1158	mul	$a1			# a[4]*a[3]
1159	add	%rax,$A1[0]		# a[4]*a[3]+t[5]
1160	 mov	$ai,%rax
1161	 mov	$A0[1],($tptr,$j)	# t[4]
1162	mov	%rdx,$A1[1]
1163	adc	\$0,$A1[1]
1164
1165	mul	$a0			# a[5]*a[2]
1166	add	%rax,$A0[0]		# a[5]*a[2]+a[4]*a[3]+t[5]
1167	 mov	$ai,%rax
1168	 mov	16($aptr,$j),$ai	# a[6]
1169	mov	%rdx,$A0[1]
1170	adc	\$0,$A0[1]
1171	add	$A1[0],$A0[0]
1172	adc	\$0,$A0[1]
1173
1174	mul	$a1			# a[5]*a[3]
1175	add	%rax,$A1[1]		# a[5]*a[3]+t[6]
1176	 mov	$ai,%rax
1177	 mov	$A0[0],8($tptr,$j)	# t[5]
1178	mov	%rdx,$A1[0]
1179	adc	\$0,$A1[0]
1180
1181	mul	$a0			# a[6]*a[2]
1182	add	%rax,$A0[1]		# a[6]*a[2]+a[5]*a[3]+t[6]
1183	 mov	$ai,%rax		# a[3]
1184	 mov	24($aptr,$j),$ai	# a[7]
1185	mov	%rdx,$A0[0]
1186	adc	\$0,$A0[0]
1187	add	$A1[1],$A0[1]
1188	adc	\$0,$A0[0]
1189
1190
1191	mul	$a1			# a[6]*a[5]
1192	add	%rax,$A1[0]		# a[6]*a[5]+t[7]
1193	 mov	$ai,%rax
1194	 mov	$A0[1],16($tptr,$j)	# t[6]
1195	mov	%rdx,$A1[1]
1196	adc	\$0,$A1[1]
1197	 lea	32($j),$j
1198
1199	mul	$a0			# a[7]*a[4]
1200	add	%rax,$A0[0]		# a[7]*a[4]+a[6]*a[5]+t[6]
1201	 mov	$ai,%rax
1202	mov	%rdx,$A0[1]
1203	adc	\$0,$A0[1]
1204	add	$A1[0],$A0[0]
1205	adc	\$0,$A0[1]
1206	mov	$A0[0],-8($tptr,$j)	# t[7]
1207
1208	cmp	\$0,$j
1209	jne	.Lsqr4x_1st
1210
1211	mul	$a1			# a[7]*a[5]
1212	add	%rax,$A1[1]
1213	lea	16($i),$i
1214	adc	\$0,%rdx
1215	add	$A0[1],$A1[1]
1216	adc	\$0,%rdx
1217
1218	mov	$A1[1],($tptr)		# t[8]
1219	mov	%rdx,$A1[0]
1220	mov	%rdx,8($tptr)		# t[9]
1221	jmp	.Lsqr4x_outer
1222
1223.align	32
1224.Lsqr4x_outer:				# comments apply to $num==6 case
1225	mov	-32($aptr,$i),$a0	# a[0]
1226	lea	48+8(%rsp,$num,2),$tptr	# end of tp[] buffer, &tp[2*$num]
1227	mov	-24($aptr,$i),%rax	# a[1]
1228	lea	-32($tptr,$i),$tptr	# end of tp[] window, &tp[2*$num-"$i"]
1229	mov	-16($aptr,$i),$ai	# a[2]
1230	mov	%rax,$a1
1231
1232	mul	$a0			# a[1]*a[0]
1233	mov	-24($tptr,$i),$A0[0]	# t[1]
1234	add	%rax,$A0[0]		# a[1]*a[0]+t[1]
1235	 mov	$ai,%rax		# a[2]
1236	adc	\$0,%rdx
1237	mov	$A0[0],-24($tptr,$i)	# t[1]
1238	mov	%rdx,$A0[1]
1239
1240	mul	$a0			# a[2]*a[0]
1241	add	%rax,$A0[1]
1242	 mov	$ai,%rax
1243	adc	\$0,%rdx
1244	add	-16($tptr,$i),$A0[1]	# a[2]*a[0]+t[2]
1245	mov	%rdx,$A0[0]
1246	adc	\$0,$A0[0]
1247	mov	$A0[1],-16($tptr,$i)	# t[2]
1248
1249	xor	$A1[0],$A1[0]
1250
1251	 mov	-8($aptr,$i),$ai	# a[3]
1252	mul	$a1			# a[2]*a[1]
1253	add	%rax,$A1[0]		# a[2]*a[1]+t[3]
1254	 mov	$ai,%rax
1255	adc	\$0,%rdx
1256	add	-8($tptr,$i),$A1[0]
1257	mov	%rdx,$A1[1]
1258	adc	\$0,$A1[1]
1259
1260	mul	$a0			# a[3]*a[0]
1261	add	%rax,$A0[0]		# a[3]*a[0]+a[2]*a[1]+t[3]
1262	 mov	$ai,%rax
1263	adc	\$0,%rdx
1264	add	$A1[0],$A0[0]
1265	mov	%rdx,$A0[1]
1266	adc	\$0,$A0[1]
1267	mov	$A0[0],-8($tptr,$i)	# t[3]
1268
1269	lea	($i),$j
1270	jmp	.Lsqr4x_inner
1271
1272.align	32
1273.Lsqr4x_inner:
1274	 mov	($aptr,$j),$ai		# a[4]
1275	mul	$a1			# a[3]*a[1]
1276	add	%rax,$A1[1]		# a[3]*a[1]+t[4]
1277	 mov	$ai,%rax
1278	mov	%rdx,$A1[0]
1279	adc	\$0,$A1[0]
1280	add	($tptr,$j),$A1[1]
1281	adc	\$0,$A1[0]
1282
1283	.byte	0x67
1284	mul	$a0			# a[4]*a[0]
1285	add	%rax,$A0[1]		# a[4]*a[0]+a[3]*a[1]+t[4]
1286	 mov	$ai,%rax		# a[3]
1287	 mov	8($aptr,$j),$ai		# a[5]
1288	mov	%rdx,$A0[0]
1289	adc	\$0,$A0[0]
1290	add	$A1[1],$A0[1]
1291	adc	\$0,$A0[0]
1292
1293	mul	$a1			# a[4]*a[3]
1294	add	%rax,$A1[0]		# a[4]*a[3]+t[5]
1295	mov	$A0[1],($tptr,$j)	# t[4]
1296	 mov	$ai,%rax
1297	mov	%rdx,$A1[1]
1298	adc	\$0,$A1[1]
1299	add	8($tptr,$j),$A1[0]
1300	lea	16($j),$j		# j++
1301	adc	\$0,$A1[1]
1302
1303	mul	$a0			# a[5]*a[2]
1304	add	%rax,$A0[0]		# a[5]*a[2]+a[4]*a[3]+t[5]
1305	 mov	$ai,%rax
1306	adc	\$0,%rdx
1307	add	$A1[0],$A0[0]
1308	mov	%rdx,$A0[1]
1309	adc	\$0,$A0[1]
1310	mov	$A0[0],-8($tptr,$j)	# t[5], "preloaded t[1]" below
1311
1312	cmp	\$0,$j
1313	jne	.Lsqr4x_inner
1314
1315	.byte	0x67
1316	mul	$a1			# a[5]*a[3]
1317	add	%rax,$A1[1]
1318	adc	\$0,%rdx
1319	add	$A0[1],$A1[1]
1320	adc	\$0,%rdx
1321
1322	mov	$A1[1],($tptr)		# t[6], "preloaded t[2]" below
1323	mov	%rdx,$A1[0]
1324	mov	%rdx,8($tptr)		# t[7], "preloaded t[3]" below
1325
1326	add	\$16,$i
1327	jnz	.Lsqr4x_outer
1328
1329					# comments apply to $num==4 case
1330	mov	-32($aptr),$a0		# a[0]
1331	lea	48+8(%rsp,$num,2),$tptr	# end of tp[] buffer, &tp[2*$num]
1332	mov	-24($aptr),%rax		# a[1]
1333	lea	-32($tptr,$i),$tptr	# end of tp[] window, &tp[2*$num-"$i"]
1334	mov	-16($aptr),$ai		# a[2]
1335	mov	%rax,$a1
1336
1337	mul	$a0			# a[1]*a[0]
1338	add	%rax,$A0[0]		# a[1]*a[0]+t[1], preloaded t[1]
1339	 mov	$ai,%rax		# a[2]
1340	mov	%rdx,$A0[1]
1341	adc	\$0,$A0[1]
1342
1343	mul	$a0			# a[2]*a[0]
1344	add	%rax,$A0[1]
1345	 mov	$ai,%rax
1346	 mov	$A0[0],-24($tptr)	# t[1]
1347	mov	%rdx,$A0[0]
1348	adc	\$0,$A0[0]
1349	add	$A1[1],$A0[1]		# a[2]*a[0]+t[2], preloaded t[2]
1350	 mov	-8($aptr),$ai		# a[3]
1351	adc	\$0,$A0[0]
1352
1353	mul	$a1			# a[2]*a[1]
1354	add	%rax,$A1[0]		# a[2]*a[1]+t[3], preloaded t[3]
1355	 mov	$ai,%rax
1356	 mov	$A0[1],-16($tptr)	# t[2]
1357	mov	%rdx,$A1[1]
1358	adc	\$0,$A1[1]
1359
1360	mul	$a0			# a[3]*a[0]
1361	add	%rax,$A0[0]		# a[3]*a[0]+a[2]*a[1]+t[3]
1362	 mov	$ai,%rax
1363	mov	%rdx,$A0[1]
1364	adc	\$0,$A0[1]
1365	add	$A1[0],$A0[0]
1366	adc	\$0,$A0[1]
1367	mov	$A0[0],-8($tptr)	# t[3]
1368
1369	mul	$a1			# a[3]*a[1]
1370	add	%rax,$A1[1]
1371	 mov	-16($aptr),%rax		# a[2]
1372	adc	\$0,%rdx
1373	add	$A0[1],$A1[1]
1374	adc	\$0,%rdx
1375
1376	mov	$A1[1],($tptr)		# t[4]
1377	mov	%rdx,$A1[0]
1378	mov	%rdx,8($tptr)		# t[5]
1379
1380	mul	$ai			# a[2]*a[3]
1381___
1382{
1383my ($shift,$carry)=($a0,$a1);
1384my @S=(@A1,$ai,$n0);
1385$code.=<<___;
1386	 add	\$16,$i
1387	 xor	$shift,$shift
1388	 sub	$num,$i			# $i=16-$num
1389	 xor	$carry,$carry
1390
1391	add	$A1[0],%rax		# t[5]
1392	adc	\$0,%rdx
1393	mov	%rax,8($tptr)		# t[5]
1394	mov	%rdx,16($tptr)		# t[6]
1395	mov	$carry,24($tptr)	# t[7]
1396
1397	 mov	-16($aptr,$i),%rax	# a[0]
1398	lea	48+8(%rsp),$tptr
1399	 xor	$A0[0],$A0[0]		# t[0]
1400	 mov	8($tptr),$A0[1]		# t[1]
1401
1402	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
1403	shr	\$63,$A0[0]
1404	lea	($j,$A0[1],2),$S[1]	# t[2*i+1]<<1 |
1405	shr	\$63,$A0[1]
1406	or	$A0[0],$S[1]		# | t[2*i]>>63
1407	 mov	16($tptr),$A0[0]	# t[2*i+2]	# prefetch
1408	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1409	mul	%rax			# a[i]*a[i]
1410	neg	$carry			# mov $carry,cf
1411	 mov	24($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1412	adc	%rax,$S[0]
1413	 mov	-8($aptr,$i),%rax	# a[i+1]	# prefetch
1414	mov	$S[0],($tptr)
1415	adc	%rdx,$S[1]
1416
1417	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
1418	 mov	$S[1],8($tptr)
1419	 sbb	$carry,$carry		# mov cf,$carry
1420	shr	\$63,$A0[0]
1421	lea	($j,$A0[1],2),$S[3]	# t[2*i+1]<<1 |
1422	shr	\$63,$A0[1]
1423	or	$A0[0],$S[3]		# | t[2*i]>>63
1424	 mov	32($tptr),$A0[0]	# t[2*i+2]	# prefetch
1425	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1426	mul	%rax			# a[i]*a[i]
1427	neg	$carry			# mov $carry,cf
1428	 mov	40($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1429	adc	%rax,$S[2]
1430	 mov	0($aptr,$i),%rax	# a[i+1]	# prefetch
1431	mov	$S[2],16($tptr)
1432	adc	%rdx,$S[3]
1433	lea	16($i),$i
1434	mov	$S[3],24($tptr)
1435	sbb	$carry,$carry		# mov cf,$carry
1436	lea	64($tptr),$tptr
1437	jmp	.Lsqr4x_shift_n_add
1438
1439.align	32
1440.Lsqr4x_shift_n_add:
1441	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
1442	shr	\$63,$A0[0]
1443	lea	($j,$A0[1],2),$S[1]	# t[2*i+1]<<1 |
1444	shr	\$63,$A0[1]
1445	or	$A0[0],$S[1]		# | t[2*i]>>63
1446	 mov	-16($tptr),$A0[0]	# t[2*i+2]	# prefetch
1447	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1448	mul	%rax			# a[i]*a[i]
1449	neg	$carry			# mov $carry,cf
1450	 mov	-8($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1451	adc	%rax,$S[0]
1452	 mov	-8($aptr,$i),%rax	# a[i+1]	# prefetch
1453	mov	$S[0],-32($tptr)
1454	adc	%rdx,$S[1]
1455
1456	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
1457	 mov	$S[1],-24($tptr)
1458	 sbb	$carry,$carry		# mov cf,$carry
1459	shr	\$63,$A0[0]
1460	lea	($j,$A0[1],2),$S[3]	# t[2*i+1]<<1 |
1461	shr	\$63,$A0[1]
1462	or	$A0[0],$S[3]		# | t[2*i]>>63
1463	 mov	0($tptr),$A0[0]		# t[2*i+2]	# prefetch
1464	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1465	mul	%rax			# a[i]*a[i]
1466	neg	$carry			# mov $carry,cf
1467	 mov	8($tptr),$A0[1]		# t[2*i+2+1]	# prefetch
1468	adc	%rax,$S[2]
1469	 mov	0($aptr,$i),%rax	# a[i+1]	# prefetch
1470	mov	$S[2],-16($tptr)
1471	adc	%rdx,$S[3]
1472
1473	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
1474	 mov	$S[3],-8($tptr)
1475	 sbb	$carry,$carry		# mov cf,$carry
1476	shr	\$63,$A0[0]
1477	lea	($j,$A0[1],2),$S[1]	# t[2*i+1]<<1 |
1478	shr	\$63,$A0[1]
1479	or	$A0[0],$S[1]		# | t[2*i]>>63
1480	 mov	16($tptr),$A0[0]	# t[2*i+2]	# prefetch
1481	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1482	mul	%rax			# a[i]*a[i]
1483	neg	$carry			# mov $carry,cf
1484	 mov	24($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1485	adc	%rax,$S[0]
1486	 mov	8($aptr,$i),%rax	# a[i+1]	# prefetch
1487	mov	$S[0],0($tptr)
1488	adc	%rdx,$S[1]
1489
1490	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1 | shift
1491	 mov	$S[1],8($tptr)
1492	 sbb	$carry,$carry		# mov cf,$carry
1493	shr	\$63,$A0[0]
1494	lea	($j,$A0[1],2),$S[3]	# t[2*i+1]<<1 |
1495	shr	\$63,$A0[1]
1496	or	$A0[0],$S[3]		# | t[2*i]>>63
1497	 mov	32($tptr),$A0[0]	# t[2*i+2]	# prefetch
1498	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1499	mul	%rax			# a[i]*a[i]
1500	neg	$carry			# mov $carry,cf
1501	 mov	40($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1502	adc	%rax,$S[2]
1503	 mov	16($aptr,$i),%rax	# a[i+1]	# prefetch
1504	mov	$S[2],16($tptr)
1505	adc	%rdx,$S[3]
1506	mov	$S[3],24($tptr)
1507	sbb	$carry,$carry		# mov cf,$carry
1508	lea	64($tptr),$tptr
1509	add	\$32,$i
1510	jnz	.Lsqr4x_shift_n_add
1511
1512	lea	($shift,$A0[0],2),$S[0]	# t[2*i]<<1 | shift
1513	.byte	0x67
1514	shr	\$63,$A0[0]
1515	lea	($j,$A0[1],2),$S[1]	# t[2*i+1]<<1 |
1516	shr	\$63,$A0[1]
1517	or	$A0[0],$S[1]		# | t[2*i]>>63
1518	 mov	-16($tptr),$A0[0]	# t[2*i+2]	# prefetch
1519	mov	$A0[1],$shift		# shift=t[2*i+1]>>63
1520	mul	%rax			# a[i]*a[i]
1521	neg	$carry			# mov $carry,cf
1522	 mov	-8($tptr),$A0[1]	# t[2*i+2+1]	# prefetch
1523	adc	%rax,$S[0]
1524	 mov	-8($aptr),%rax		# a[i+1]	# prefetch
1525	mov	$S[0],-32($tptr)
1526	adc	%rdx,$S[1]
1527
1528	lea	($shift,$A0[0],2),$S[2]	# t[2*i]<<1|shift
1529	 mov	$S[1],-24($tptr)
1530	 sbb	$carry,$carry		# mov cf,$carry
1531	shr	\$63,$A0[0]
1532	lea	($j,$A0[1],2),$S[3]	# t[2*i+1]<<1 |
1533	shr	\$63,$A0[1]
1534	or	$A0[0],$S[3]		# | t[2*i]>>63
1535	mul	%rax			# a[i]*a[i]
1536	neg	$carry			# mov $carry,cf
1537	adc	%rax,$S[2]
1538	adc	%rdx,$S[3]
1539	mov	$S[2],-16($tptr)
1540	mov	$S[3],-8($tptr)
1541___
1542}
1543######################################################################
1544# Montgomery reduction part, "word-by-word" algorithm.
1545#
1546# This new path is inspired by multiple submissions from Intel, by
1547# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
1548# Vinodh Gopal...
1549{
1550my ($nptr,$tptr,$carry,$m0)=("%rbp","%rdi","%rsi","%rbx");
1551
1552$code.=<<___;
1553	movq	%xmm2,$nptr
1554sqr8x_reduction:
1555	xor	%rax,%rax
1556	lea	($nptr,$num,2),%rcx	# end of n[]
1557	lea	48+8(%rsp,$num,2),%rdx	# end of t[] buffer
1558	mov	%rcx,0+8(%rsp)
1559	lea	48+8(%rsp,$num),$tptr	# end of initial t[] window
1560	mov	%rdx,8+8(%rsp)
1561	neg	$num
1562	jmp	.L8x_reduction_loop
1563
1564.align	32
1565.L8x_reduction_loop:
1566	lea	($tptr,$num),$tptr	# start of current t[] window
1567	.byte	0x66
1568	mov	8*0($tptr),$m0
1569	mov	8*1($tptr),%r9
1570	mov	8*2($tptr),%r10
1571	mov	8*3($tptr),%r11
1572	mov	8*4($tptr),%r12
1573	mov	8*5($tptr),%r13
1574	mov	8*6($tptr),%r14
1575	mov	8*7($tptr),%r15
1576	mov	%rax,(%rdx)		# store top-most carry bit
1577	lea	8*8($tptr),$tptr
1578
1579	.byte	0x67
1580	mov	$m0,%r8
1581	imulq	32+8(%rsp),$m0		# n0*a[0]
1582	mov	16*0($nptr),%rax	# n[0]
1583	mov	\$8,%ecx
1584	jmp	.L8x_reduce
1585
1586.align	32
1587.L8x_reduce:
1588	mulq	$m0
1589	 mov	16*1($nptr),%rax	# n[1]
1590	neg	%r8
1591	mov	%rdx,%r8
1592	adc	\$0,%r8
1593
1594	mulq	$m0
1595	add	%rax,%r9
1596	 mov	16*2($nptr),%rax
1597	adc	\$0,%rdx
1598	add	%r9,%r8
1599	 mov	$m0,48-8+8(%rsp,%rcx,8)	# put aside n0*a[i]
1600	mov	%rdx,%r9
1601	adc	\$0,%r9
1602
1603	mulq	$m0
1604	add	%rax,%r10
1605	 mov	16*3($nptr),%rax
1606	adc	\$0,%rdx
1607	add	%r10,%r9
1608	 mov	32+8(%rsp),$carry	# pull n0, borrow $carry
1609	mov	%rdx,%r10
1610	adc	\$0,%r10
1611
1612	mulq	$m0
1613	add	%rax,%r11
1614	 mov	16*4($nptr),%rax
1615	adc	\$0,%rdx
1616	 imulq	%r8,$carry		# modulo-scheduled
1617	add	%r11,%r10
1618	mov	%rdx,%r11
1619	adc	\$0,%r11
1620
1621	mulq	$m0
1622	add	%rax,%r12
1623	 mov	16*5($nptr),%rax
1624	adc	\$0,%rdx
1625	add	%r12,%r11
1626	mov	%rdx,%r12
1627	adc	\$0,%r12
1628
1629	mulq	$m0
1630	add	%rax,%r13
1631	 mov	16*6($nptr),%rax
1632	adc	\$0,%rdx
1633	add	%r13,%r12
1634	mov	%rdx,%r13
1635	adc	\$0,%r13
1636
1637	mulq	$m0
1638	add	%rax,%r14
1639	 mov	16*7($nptr),%rax
1640	adc	\$0,%rdx
1641	add	%r14,%r13
1642	mov	%rdx,%r14
1643	adc	\$0,%r14
1644
1645	mulq	$m0
1646	 mov	$carry,$m0		# n0*a[i]
1647	add	%rax,%r15
1648	 mov	16*0($nptr),%rax	# n[0]
1649	adc	\$0,%rdx
1650	add	%r15,%r14
1651	mov	%rdx,%r15
1652	adc	\$0,%r15
1653
1654	dec	%ecx
1655	jnz	.L8x_reduce
1656
1657	lea	16*8($nptr),$nptr
1658	xor	%rax,%rax
1659	mov	8+8(%rsp),%rdx		# pull end of t[]
1660	cmp	0+8(%rsp),$nptr		# end of n[]?
1661	jae	.L8x_no_tail
1662
1663	.byte	0x66
1664	add	8*0($tptr),%r8
1665	adc	8*1($tptr),%r9
1666	adc	8*2($tptr),%r10
1667	adc	8*3($tptr),%r11
1668	adc	8*4($tptr),%r12
1669	adc	8*5($tptr),%r13
1670	adc	8*6($tptr),%r14
1671	adc	8*7($tptr),%r15
1672	sbb	$carry,$carry		# top carry
1673
1674	mov	48+56+8(%rsp),$m0	# pull n0*a[0]
1675	mov	\$8,%ecx
1676	mov	16*0($nptr),%rax
1677	jmp	.L8x_tail
1678
1679.align	32
1680.L8x_tail:
1681	mulq	$m0
1682	add	%rax,%r8
1683	 mov	16*1($nptr),%rax
1684	 mov	%r8,($tptr)		# save result
1685	mov	%rdx,%r8
1686	adc	\$0,%r8
1687
1688	mulq	$m0
1689	add	%rax,%r9
1690	 mov	16*2($nptr),%rax
1691	adc	\$0,%rdx
1692	add	%r9,%r8
1693	 lea	8($tptr),$tptr		# $tptr++
1694	mov	%rdx,%r9
1695	adc	\$0,%r9
1696
1697	mulq	$m0
1698	add	%rax,%r10
1699	 mov	16*3($nptr),%rax
1700	adc	\$0,%rdx
1701	add	%r10,%r9
1702	mov	%rdx,%r10
1703	adc	\$0,%r10
1704
1705	mulq	$m0
1706	add	%rax,%r11
1707	 mov	16*4($nptr),%rax
1708	adc	\$0,%rdx
1709	add	%r11,%r10
1710	mov	%rdx,%r11
1711	adc	\$0,%r11
1712
1713	mulq	$m0
1714	add	%rax,%r12
1715	 mov	16*5($nptr),%rax
1716	adc	\$0,%rdx
1717	add	%r12,%r11
1718	mov	%rdx,%r12
1719	adc	\$0,%r12
1720
1721	mulq	$m0
1722	add	%rax,%r13
1723	 mov	16*6($nptr),%rax
1724	adc	\$0,%rdx
1725	add	%r13,%r12
1726	mov	%rdx,%r13
1727	adc	\$0,%r13
1728
1729	mulq	$m0
1730	add	%rax,%r14
1731	 mov	16*7($nptr),%rax
1732	adc	\$0,%rdx
1733	add	%r14,%r13
1734	mov	%rdx,%r14
1735	adc	\$0,%r14
1736
1737	mulq	$m0
1738	 mov	48-16+8(%rsp,%rcx,8),$m0# pull n0*a[i]
1739	add	%rax,%r15
1740	adc	\$0,%rdx
1741	add	%r15,%r14
1742	 mov	16*0($nptr),%rax	# pull n[0]
1743	mov	%rdx,%r15
1744	adc	\$0,%r15
1745
1746	dec	%ecx
1747	jnz	.L8x_tail
1748
1749	lea	16*8($nptr),$nptr
1750	mov	8+8(%rsp),%rdx		# pull end of t[]
1751	cmp	0+8(%rsp),$nptr		# end of n[]?
1752	jae	.L8x_tail_done		# break out of loop
1753
1754	 mov	48+56+8(%rsp),$m0	# pull n0*a[0]
1755	neg	$carry
1756	 mov	8*0($nptr),%rax		# pull n[0]
1757	adc	8*0($tptr),%r8
1758	adc	8*1($tptr),%r9
1759	adc	8*2($tptr),%r10
1760	adc	8*3($tptr),%r11
1761	adc	8*4($tptr),%r12
1762	adc	8*5($tptr),%r13
1763	adc	8*6($tptr),%r14
1764	adc	8*7($tptr),%r15
1765	sbb	$carry,$carry		# top carry
1766
1767	mov	\$8,%ecx
1768	jmp	.L8x_tail
1769
1770.align	32
1771.L8x_tail_done:
1772	add	(%rdx),%r8		# can this overflow?
1773	adc	\$0,%r9
1774	adc	\$0,%r10
1775	adc	\$0,%r11
1776	adc	\$0,%r12
1777	adc	\$0,%r13
1778	adc	\$0,%r14
1779	adc	\$0,%r15		# can't overflow, because we
1780					# started with "overhung" part
1781					# of multiplication
1782	xor	%rax,%rax
1783
1784	neg	$carry
1785.L8x_no_tail:
1786	adc	8*0($tptr),%r8
1787	adc	8*1($tptr),%r9
1788	adc	8*2($tptr),%r10
1789	adc	8*3($tptr),%r11
1790	adc	8*4($tptr),%r12
1791	adc	8*5($tptr),%r13
1792	adc	8*6($tptr),%r14
1793	adc	8*7($tptr),%r15
1794	adc	\$0,%rax		# top-most carry
1795	 mov	-16($nptr),%rcx		# np[num-1]
1796	 xor	$carry,$carry
1797
1798	movq	%xmm2,$nptr		# restore $nptr
1799
1800	mov	%r8,8*0($tptr)		# store top 512 bits
1801	mov	%r9,8*1($tptr)
1802	 movq	%xmm3,$num		# $num is %r9, can't be moved upwards
1803	mov	%r10,8*2($tptr)
1804	mov	%r11,8*3($tptr)
1805	mov	%r12,8*4($tptr)
1806	mov	%r13,8*5($tptr)
1807	mov	%r14,8*6($tptr)
1808	mov	%r15,8*7($tptr)
1809	lea	8*8($tptr),$tptr
1810
1811	cmp	%rdx,$tptr		# end of t[]?
1812	jb	.L8x_reduction_loop
1813___
1814}
1815##############################################################
1816# Post-condition, 4x unrolled
1817#
1818{
1819my ($tptr,$nptr)=("%rbx","%rbp");
1820$code.=<<___;
1821	#xor	%rsi,%rsi		# %rsi was $carry above
1822	sub	%r15,%rcx		# compare top-most words
1823	lea	(%rdi,$num),$tptr	# %rdi was $tptr above
1824	adc	%rsi,%rsi
1825	mov	$num,%rcx
1826	or	%rsi,%rax
1827	movq	%xmm1,$rptr		# restore $rptr
1828	xor	\$1,%rax
1829	movq	%xmm1,$aptr		# prepare for back-to-back call
1830	lea	($nptr,%rax,8),$nptr
1831	sar	\$3+2,%rcx		# cf=0
1832	jmp	.Lsqr4x_sub
1833
1834.align	32
1835.Lsqr4x_sub:
1836	.byte	0x66
1837	mov	8*0($tptr),%r12
1838	mov	8*1($tptr),%r13
1839	sbb	16*0($nptr),%r12
1840	mov	8*2($tptr),%r14
1841	sbb	16*1($nptr),%r13
1842	mov	8*3($tptr),%r15
1843	lea	8*4($tptr),$tptr
1844	sbb	16*2($nptr),%r14
1845	mov	%r12,8*0($rptr)
1846	sbb	16*3($nptr),%r15
1847	lea	16*4($nptr),$nptr
1848	mov	%r13,8*1($rptr)
1849	mov	%r14,8*2($rptr)
1850	mov	%r15,8*3($rptr)
1851	lea	8*4($rptr),$rptr
1852
1853	inc	%rcx			# pass %cf
1854	jnz	.Lsqr4x_sub
1855___
1856}
1857$code.=<<___;
1858	mov	$num,%r10		# prepare for back-to-back call
1859	neg	$num			# restore $num
1860	ret
1861.size	bn_sqr8x_internal,.-bn_sqr8x_internal
1862___
1863{
1864$code.=<<___;
1865.globl	bn_from_montgomery
1866.type	bn_from_montgomery,\@abi-omnipotent
1867.align	32
1868bn_from_montgomery:
1869	testl	\$7,`($win64?"48(%rsp)":"%r9d")`
1870	jz	bn_from_mont8x
1871	xor	%eax,%eax
1872	ret
1873.size	bn_from_montgomery,.-bn_from_montgomery
1874
1875.type	bn_from_mont8x,\@function,6
1876.align	32
1877bn_from_mont8x:
1878	.byte	0x67
1879	mov	%rsp,%rax
1880	push	%rbx
1881	push	%rbp
1882	push	%r12
1883	push	%r13
1884	push	%r14
1885	push	%r15
1886___
1887$code.=<<___ if ($win64);
1888	lea	-0x28(%rsp),%rsp
1889	movaps	%xmm6,(%rsp)
1890	movaps	%xmm7,0x10(%rsp)
1891___
1892$code.=<<___;
1893	.byte	0x67
1894	mov	${num}d,%r10d
1895	shl	\$3,${num}d		# convert $num to bytes
1896	shl	\$3+2,%r10d		# 4*$num
1897	neg	$num
1898	mov	($n0),$n0		# *n0
1899
1900	##############################################################
1901	# ensure that stack frame doesn't alias with $aptr+4*$num
1902	# modulo 4096, which covers ret[num], am[num] and n[2*num]
1903	# (see bn_exp.c). this is done to allow memory disambiguation
1904	# logic do its magic.
1905	#
1906	lea	-64(%rsp,$num,2),%r11
1907	sub	$aptr,%r11
1908	and	\$4095,%r11
1909	cmp	%r11,%r10
1910	jb	.Lfrom_sp_alt
1911	sub	%r11,%rsp		# align with $aptr
1912	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
1913	jmp	.Lfrom_sp_done
1914
1915.align	32
1916.Lfrom_sp_alt:
1917	lea	4096-64(,$num,2),%r10	# 4096-frame-2*$num
1918	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
1919	sub	%r10,%r11
1920	mov	\$0,%r10
1921	cmovc	%r10,%r11
1922	sub	%r11,%rsp
1923.Lfrom_sp_done:
1924	and	\$-64,%rsp
1925	mov	$num,%r10
1926	neg	$num
1927
1928	##############################################################
1929	# Stack layout
1930	#
1931	# +0	saved $num, used in reduction section
1932	# +8	&t[2*$num], used in reduction section
1933	# +32	saved *n0
1934	# +40	saved %rsp
1935	# +48	t[2*$num]
1936	#
1937	mov	$n0,  32(%rsp)
1938	mov	%rax, 40(%rsp)		# save original %rsp
1939.Lfrom_body:
1940	mov	$num,%r11
1941	lea	48(%rsp),%rax
1942	pxor	%xmm0,%xmm0
1943	jmp	.Lmul_by_1
1944
1945.align	32
1946.Lmul_by_1:
1947	movdqu	($aptr),%xmm1
1948	movdqu	16($aptr),%xmm2
1949	movdqu	32($aptr),%xmm3
1950	movdqa	%xmm0,(%rax,$num)
1951	movdqu	48($aptr),%xmm4
1952	movdqa	%xmm0,16(%rax,$num)
1953	.byte	0x48,0x8d,0xb6,0x40,0x00,0x00,0x00	# lea	64($aptr),$aptr
1954	movdqa	%xmm1,(%rax)
1955	movdqa	%xmm0,32(%rax,$num)
1956	movdqa	%xmm2,16(%rax)
1957	movdqa	%xmm0,48(%rax,$num)
1958	movdqa	%xmm3,32(%rax)
1959	movdqa	%xmm4,48(%rax)
1960	lea	64(%rax),%rax
1961	sub	\$64,%r11
1962	jnz	.Lmul_by_1
1963
1964	movq	$rptr,%xmm1
1965	movq	$nptr,%xmm2
1966	.byte	0x67
1967	mov	$nptr,%rbp
1968	movq	%r10, %xmm3		# -num
1969___
1970$code.=<<___ if ($addx);
1971	mov	OPENSSL_ia32cap_P+8(%rip),%r11d
1972	and	\$0x80100,%r11d
1973	cmp	\$0x80100,%r11d
1974	jne	.Lfrom_mont_nox
1975
1976	lea	(%rax,$num),$rptr
1977	call	sqrx8x_reduction
1978
1979	pxor	%xmm0,%xmm0
1980	lea	48(%rsp),%rax
1981	mov	40(%rsp),%rsi		# restore %rsp
1982	jmp	.Lfrom_mont_zero
1983
1984.align	32
1985.Lfrom_mont_nox:
1986___
1987$code.=<<___;
1988	call	sqr8x_reduction
1989
1990	pxor	%xmm0,%xmm0
1991	lea	48(%rsp),%rax
1992	mov	40(%rsp),%rsi		# restore %rsp
1993	jmp	.Lfrom_mont_zero
1994
1995.align	32
1996.Lfrom_mont_zero:
1997	movdqa	%xmm0,16*0(%rax)
1998	movdqa	%xmm0,16*1(%rax)
1999	movdqa	%xmm0,16*2(%rax)
2000	movdqa	%xmm0,16*3(%rax)
2001	lea	16*4(%rax),%rax
2002	sub	\$32,$num
2003	jnz	.Lfrom_mont_zero
2004
2005	mov	\$1,%rax
2006	mov	-48(%rsi),%r15
2007	mov	-40(%rsi),%r14
2008	mov	-32(%rsi),%r13
2009	mov	-24(%rsi),%r12
2010	mov	-16(%rsi),%rbp
2011	mov	-8(%rsi),%rbx
2012	lea	(%rsi),%rsp
2013.Lfrom_epilogue:
2014	ret
2015.size	bn_from_mont8x,.-bn_from_mont8x
2016___
2017}
2018}}}
2019
2020if ($addx) {{{
2021my $bp="%rdx";	# restore original value
2022
2023$code.=<<___;
2024.type	bn_mulx4x_mont_gather5,\@function,6
2025.align	32
2026bn_mulx4x_mont_gather5:
2027.Lmulx4x_enter:
2028	.byte	0x67
2029	mov	%rsp,%rax
2030	push	%rbx
2031	push	%rbp
2032	push	%r12
2033	push	%r13
2034	push	%r14
2035	push	%r15
2036___
2037$code.=<<___ if ($win64);
2038	lea	-0x28(%rsp),%rsp
2039	movaps	%xmm6,(%rsp)
2040	movaps	%xmm7,0x10(%rsp)
2041___
2042$code.=<<___;
2043	.byte	0x67
2044	mov	${num}d,%r10d
2045	shl	\$3,${num}d		# convert $num to bytes
2046	shl	\$3+2,%r10d		# 4*$num
2047	neg	$num			# -$num
2048	mov	($n0),$n0		# *n0
2049
2050	##############################################################
2051	# ensure that stack frame doesn't alias with $aptr+4*$num
2052	# modulo 4096, which covers a[num], ret[num] and n[2*num]
2053	# (see bn_exp.c). this is done to allow memory disambiguation
2054	# logic do its magic. [excessive frame is allocated in order
2055	# to allow bn_from_mont8x to clear it.]
2056	#
2057	lea	-64(%rsp,$num,2),%r11
2058	sub	$ap,%r11
2059	and	\$4095,%r11
2060	cmp	%r11,%r10
2061	jb	.Lmulx4xsp_alt
2062	sub	%r11,%rsp		# align with $aptr
2063	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+$num)
2064	jmp	.Lmulx4xsp_done
2065
2066.align	32
2067.Lmulx4xsp_alt:
2068	lea	4096-64(,$num,2),%r10	# 4096-frame-$num
2069	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+$num)
2070	sub	%r10,%r11
2071	mov	\$0,%r10
2072	cmovc	%r10,%r11
2073	sub	%r11,%rsp
2074.Lmulx4xsp_done:
2075	and	\$-64,%rsp		# ensure alignment
2076	##############################################################
2077	# Stack layout
2078	# +0	-num
2079	# +8	off-loaded &b[i]
2080	# +16	end of b[num]
2081	# +24	inner counter
2082	# +32	saved n0
2083	# +40	saved %rsp
2084	# +48
2085	# +56	saved rp
2086	# +64	tmp[num+1]
2087	#
2088	mov	$n0, 32(%rsp)		# save *n0
2089	mov	%rax,40(%rsp)		# save original %rsp
2090.Lmulx4x_body:
2091	call	mulx4x_internal
2092
2093	mov	40(%rsp),%rsi		# restore %rsp
2094	mov	\$1,%rax
2095___
2096$code.=<<___ if ($win64);
2097	movaps	-88(%rsi),%xmm6
2098	movaps	-72(%rsi),%xmm7
2099___
2100$code.=<<___;
2101	mov	-48(%rsi),%r15
2102	mov	-40(%rsi),%r14
2103	mov	-32(%rsi),%r13
2104	mov	-24(%rsi),%r12
2105	mov	-16(%rsi),%rbp
2106	mov	-8(%rsi),%rbx
2107	lea	(%rsi),%rsp
2108.Lmulx4x_epilogue:
2109	ret
2110.size	bn_mulx4x_mont_gather5,.-bn_mulx4x_mont_gather5
2111
2112.type	mulx4x_internal,\@abi-omnipotent
2113.align	32
2114mulx4x_internal:
2115	.byte	0x4c,0x89,0x8c,0x24,0x08,0x00,0x00,0x00	# mov	$num,8(%rsp)		# save -$num
2116	.byte	0x67
2117	neg	$num			# restore $num
2118	shl	\$5,$num
2119	lea	256($bp,$num),%r13
2120	shr	\$5+5,$num
2121	mov	`($win64?56:8)`(%rax),%r10d	# load 7th argument
2122	sub	\$1,$num
2123	mov	%r13,16+8(%rsp)		# end of b[num]
2124	mov	$num,24+8(%rsp)		# inner counter
2125	mov	$rp, 56+8(%rsp)		# save $rp
2126___
2127my ($aptr, $bptr, $nptr, $tptr, $mi,  $bi,  $zero, $num)=
2128   ("%rsi","%rdi","%rcx","%rbx","%r8","%r9","%rbp","%rax");
2129my $rptr=$bptr;
2130my $STRIDE=2**5*8;		# 5 is "window size"
2131my $N=$STRIDE/4;		# should match cache line size
2132$code.=<<___;
2133	mov	%r10,%r11
2134	shr	\$`log($N/8)/log(2)`,%r10
2135	and	\$`$N/8-1`,%r11
2136	not	%r10
2137	lea	.Lmagic_masks(%rip),%rax
2138	and	\$`2**5/($N/8)-1`,%r10	# 5 is "window size"
2139	lea	96($bp,%r11,8),$bptr	# pointer within 1st cache line
2140	movq	0(%rax,%r10,8),%xmm4	# set of masks denoting which
2141	movq	8(%rax,%r10,8),%xmm5	# cache line contains element
2142	add	\$7,%r11
2143	movq	16(%rax,%r10,8),%xmm6	# denoted by 7th argument
2144	movq	24(%rax,%r10,8),%xmm7
2145	and	\$7,%r11
2146
2147	movq	`0*$STRIDE/4-96`($bptr),%xmm0
2148	lea	$STRIDE($bptr),$tptr	# borrow $tptr
2149	movq	`1*$STRIDE/4-96`($bptr),%xmm1
2150	pand	%xmm4,%xmm0
2151	movq	`2*$STRIDE/4-96`($bptr),%xmm2
2152	pand	%xmm5,%xmm1
2153	movq	`3*$STRIDE/4-96`($bptr),%xmm3
2154	pand	%xmm6,%xmm2
2155	por	%xmm1,%xmm0
2156	movq	`0*$STRIDE/4-96`($tptr),%xmm1
2157	pand	%xmm7,%xmm3
2158	por	%xmm2,%xmm0
2159	movq	`1*$STRIDE/4-96`($tptr),%xmm2
2160	por	%xmm3,%xmm0
2161	.byte	0x67,0x67
2162	pand	%xmm4,%xmm1
2163	movq	`2*$STRIDE/4-96`($tptr),%xmm3
2164
2165	movq	%xmm0,%rdx		# bp[0]
2166	movq	`3*$STRIDE/4-96`($tptr),%xmm0
2167	lea	2*$STRIDE($bptr),$bptr	# next &b[i]
2168	pand	%xmm5,%xmm2
2169	.byte	0x67,0x67
2170	pand	%xmm6,%xmm3
2171	##############################################################
2172	# $tptr is chosen so that writing to top-most element of the
2173	# vector occurs just "above" references to powers table,
2174	# "above" modulo cache-line size, which effectively precludes
2175	# possibility of memory disambiguation logic failure when
2176	# accessing the table.
2177	#
2178	lea	64+8*4+8(%rsp,%r11,8),$tptr
2179
2180	mov	%rdx,$bi
2181	mulx	0*8($aptr),$mi,%rax	# a[0]*b[0]
2182	mulx	1*8($aptr),%r11,%r12	# a[1]*b[0]
2183	add	%rax,%r11
2184	mulx	2*8($aptr),%rax,%r13	# ...
2185	adc	%rax,%r12
2186	adc	\$0,%r13
2187	mulx	3*8($aptr),%rax,%r14
2188
2189	mov	$mi,%r15
2190	imulq	32+8(%rsp),$mi		# "t[0]"*n0
2191	xor	$zero,$zero		# cf=0, of=0
2192	mov	$mi,%rdx
2193
2194	por	%xmm2,%xmm1
2195	pand	%xmm7,%xmm0
2196	por	%xmm3,%xmm1
2197	mov	$bptr,8+8(%rsp)		# off-load &b[i]
2198	por	%xmm1,%xmm0
2199
2200	.byte	0x48,0x8d,0xb6,0x20,0x00,0x00,0x00	# lea	4*8($aptr),$aptr
2201	adcx	%rax,%r13
2202	adcx	$zero,%r14		# cf=0
2203
2204	mulx	0*16($nptr),%rax,%r10
2205	adcx	%rax,%r15		# discarded
2206	adox	%r11,%r10
2207	mulx	1*16($nptr),%rax,%r11
2208	adcx	%rax,%r10
2209	adox	%r12,%r11
2210	mulx	2*16($nptr),%rax,%r12
2211	mov	24+8(%rsp),$bptr	# counter value
2212	.byte	0x66
2213	mov	%r10,-8*4($tptr)
2214	adcx	%rax,%r11
2215	adox	%r13,%r12
2216	mulx	3*16($nptr),%rax,%r15
2217	 .byte	0x67,0x67
2218	 mov	$bi,%rdx
2219	mov	%r11,-8*3($tptr)
2220	adcx	%rax,%r12
2221	adox	$zero,%r15		# of=0
2222	.byte	0x48,0x8d,0x89,0x40,0x00,0x00,0x00	# lea	4*16($nptr),$nptr
2223	mov	%r12,-8*2($tptr)
2224	#jmp	.Lmulx4x_1st
2225
2226.align	32
2227.Lmulx4x_1st:
2228	adcx	$zero,%r15		# cf=0, modulo-scheduled
2229	mulx	0*8($aptr),%r10,%rax	# a[4]*b[0]
2230	adcx	%r14,%r10
2231	mulx	1*8($aptr),%r11,%r14	# a[5]*b[0]
2232	adcx	%rax,%r11
2233	mulx	2*8($aptr),%r12,%rax	# ...
2234	adcx	%r14,%r12
2235	mulx	3*8($aptr),%r13,%r14
2236	 .byte	0x67,0x67
2237	 mov	$mi,%rdx
2238	adcx	%rax,%r13
2239	adcx	$zero,%r14		# cf=0
2240	lea	4*8($aptr),$aptr
2241	lea	4*8($tptr),$tptr
2242
2243	adox	%r15,%r10
2244	mulx	0*16($nptr),%rax,%r15
2245	adcx	%rax,%r10
2246	adox	%r15,%r11
2247	mulx	1*16($nptr),%rax,%r15
2248	adcx	%rax,%r11
2249	adox	%r15,%r12
2250	mulx	2*16($nptr),%rax,%r15
2251	mov	%r10,-5*8($tptr)
2252	adcx	%rax,%r12
2253	mov	%r11,-4*8($tptr)
2254	adox	%r15,%r13
2255	mulx	3*16($nptr),%rax,%r15
2256	 mov	$bi,%rdx
2257	mov	%r12,-3*8($tptr)
2258	adcx	%rax,%r13
2259	adox	$zero,%r15
2260	lea	4*16($nptr),$nptr
2261	mov	%r13,-2*8($tptr)
2262
2263	dec	$bptr			# of=0, pass cf
2264	jnz	.Lmulx4x_1st
2265
2266	mov	8(%rsp),$num		# load -num
2267	movq	%xmm0,%rdx		# bp[1]
2268	adc	$zero,%r15		# modulo-scheduled
2269	lea	($aptr,$num),$aptr	# rewind $aptr
2270	add	%r15,%r14
2271	mov	8+8(%rsp),$bptr		# re-load &b[i]
2272	adc	$zero,$zero		# top-most carry
2273	mov	%r14,-1*8($tptr)
2274	jmp	.Lmulx4x_outer
2275
2276.align	32
2277.Lmulx4x_outer:
2278	mov	$zero,($tptr)		# save top-most carry
2279	lea	4*8($tptr,$num),$tptr	# rewind $tptr
2280	mulx	0*8($aptr),$mi,%r11	# a[0]*b[i]
2281	xor	$zero,$zero		# cf=0, of=0
2282	mov	%rdx,$bi
2283	mulx	1*8($aptr),%r14,%r12	# a[1]*b[i]
2284	adox	-4*8($tptr),$mi		# +t[0]
2285	adcx	%r14,%r11
2286	mulx	2*8($aptr),%r15,%r13	# ...
2287	adox	-3*8($tptr),%r11
2288	adcx	%r15,%r12
2289	mulx	3*8($aptr),%rdx,%r14
2290	adox	-2*8($tptr),%r12
2291	adcx	%rdx,%r13
2292	lea	($nptr,$num,2),$nptr	# rewind $nptr
2293	lea	4*8($aptr),$aptr
2294	adox	-1*8($tptr),%r13
2295	adcx	$zero,%r14
2296	adox	$zero,%r14
2297
2298	.byte	0x67
2299	mov	$mi,%r15
2300	imulq	32+8(%rsp),$mi		# "t[0]"*n0
2301
2302	movq	`0*$STRIDE/4-96`($bptr),%xmm0
2303	.byte	0x67,0x67
2304	mov	$mi,%rdx
2305	movq	`1*$STRIDE/4-96`($bptr),%xmm1
2306	.byte	0x67
2307	pand	%xmm4,%xmm0
2308	movq	`2*$STRIDE/4-96`($bptr),%xmm2
2309	.byte	0x67
2310	pand	%xmm5,%xmm1
2311	movq	`3*$STRIDE/4-96`($bptr),%xmm3
2312	add	\$$STRIDE,$bptr		# next &b[i]
2313	.byte	0x67
2314	pand	%xmm6,%xmm2
2315	por	%xmm1,%xmm0
2316	pand	%xmm7,%xmm3
2317	xor	$zero,$zero		# cf=0, of=0
2318	mov	$bptr,8+8(%rsp)		# off-load &b[i]
2319
2320	mulx	0*16($nptr),%rax,%r10
2321	adcx	%rax,%r15		# discarded
2322	adox	%r11,%r10
2323	mulx	1*16($nptr),%rax,%r11
2324	adcx	%rax,%r10
2325	adox	%r12,%r11
2326	mulx	2*16($nptr),%rax,%r12
2327	adcx	%rax,%r11
2328	adox	%r13,%r12
2329	mulx	3*16($nptr),%rax,%r15
2330	 mov	$bi,%rdx
2331	 por	%xmm2,%xmm0
2332	mov	24+8(%rsp),$bptr	# counter value
2333	mov	%r10,-8*4($tptr)
2334	 por	%xmm3,%xmm0
2335	adcx	%rax,%r12
2336	mov	%r11,-8*3($tptr)
2337	adox	$zero,%r15		# of=0
2338	mov	%r12,-8*2($tptr)
2339	lea	4*16($nptr),$nptr
2340	jmp	.Lmulx4x_inner
2341
2342.align	32
2343.Lmulx4x_inner:
2344	mulx	0*8($aptr),%r10,%rax	# a[4]*b[i]
2345	adcx	$zero,%r15		# cf=0, modulo-scheduled
2346	adox	%r14,%r10
2347	mulx	1*8($aptr),%r11,%r14	# a[5]*b[i]
2348	adcx	0*8($tptr),%r10
2349	adox	%rax,%r11
2350	mulx	2*8($aptr),%r12,%rax	# ...
2351	adcx	1*8($tptr),%r11
2352	adox	%r14,%r12
2353	mulx	3*8($aptr),%r13,%r14
2354	 mov	$mi,%rdx
2355	adcx	2*8($tptr),%r12
2356	adox	%rax,%r13
2357	adcx	3*8($tptr),%r13
2358	adox	$zero,%r14		# of=0
2359	lea	4*8($aptr),$aptr
2360	lea	4*8($tptr),$tptr
2361	adcx	$zero,%r14		# cf=0
2362
2363	adox	%r15,%r10
2364	mulx	0*16($nptr),%rax,%r15
2365	adcx	%rax,%r10
2366	adox	%r15,%r11
2367	mulx	1*16($nptr),%rax,%r15
2368	adcx	%rax,%r11
2369	adox	%r15,%r12
2370	mulx	2*16($nptr),%rax,%r15
2371	mov	%r10,-5*8($tptr)
2372	adcx	%rax,%r12
2373	adox	%r15,%r13
2374	mov	%r11,-4*8($tptr)
2375	mulx	3*16($nptr),%rax,%r15
2376	 mov	$bi,%rdx
2377	lea	4*16($nptr),$nptr
2378	mov	%r12,-3*8($tptr)
2379	adcx	%rax,%r13
2380	adox	$zero,%r15
2381	mov	%r13,-2*8($tptr)
2382
2383	dec	$bptr			# of=0, pass cf
2384	jnz	.Lmulx4x_inner
2385
2386	mov	0+8(%rsp),$num		# load -num
2387	movq	%xmm0,%rdx		# bp[i+1]
2388	adc	$zero,%r15		# modulo-scheduled
2389	sub	0*8($tptr),$bptr	# pull top-most carry to %cf
2390	mov	8+8(%rsp),$bptr		# re-load &b[i]
2391	mov	16+8(%rsp),%r10
2392	adc	%r15,%r14
2393	lea	($aptr,$num),$aptr	# rewind $aptr
2394	adc	$zero,$zero		# top-most carry
2395	mov	%r14,-1*8($tptr)
2396
2397	cmp	%r10,$bptr
2398	jb	.Lmulx4x_outer
2399
2400	mov	-16($nptr),%r10
2401	xor	%r15,%r15
2402	sub	%r14,%r10		# compare top-most words
2403	adc	%r15,%r15
2404	or	%r15,$zero
2405	xor	\$1,$zero
2406	lea	($tptr,$num),%rdi	# rewind $tptr
2407	lea	($nptr,$num,2),$nptr	# rewind $nptr
2408	.byte	0x67,0x67
2409	sar	\$3+2,$num		# cf=0
2410	lea	($nptr,$zero,8),%rbp
2411	mov	56+8(%rsp),%rdx		# restore rp
2412	mov	$num,%rcx
2413	jmp	.Lsqrx4x_sub		# common post-condition
2414.size	mulx4x_internal,.-mulx4x_internal
2415___
2416}{
2417######################################################################
2418# void bn_power5(
2419my $rptr="%rdi";	# BN_ULONG *rptr,
2420my $aptr="%rsi";	# const BN_ULONG *aptr,
2421my $bptr="%rdx";	# const void *table,
2422my $nptr="%rcx";	# const BN_ULONG *nptr,
2423my $n0  ="%r8";		# const BN_ULONG *n0);
2424my $num ="%r9";		# int num, has to be divisible by 8
2425			# int pwr);
2426
2427my ($i,$j,$tptr)=("%rbp","%rcx",$rptr);
2428my @A0=("%r10","%r11");
2429my @A1=("%r12","%r13");
2430my ($a0,$a1,$ai)=("%r14","%r15","%rbx");
2431
2432$code.=<<___;
2433.type	bn_powerx5,\@function,6
2434.align	32
2435bn_powerx5:
2436.Lpowerx5_enter:
2437	.byte	0x67
2438	mov	%rsp,%rax
2439	push	%rbx
2440	push	%rbp
2441	push	%r12
2442	push	%r13
2443	push	%r14
2444	push	%r15
2445___
2446$code.=<<___ if ($win64);
2447	lea	-0x28(%rsp),%rsp
2448	movaps	%xmm6,(%rsp)
2449	movaps	%xmm7,0x10(%rsp)
2450___
2451$code.=<<___;
2452	.byte	0x67
2453	mov	${num}d,%r10d
2454	shl	\$3,${num}d		# convert $num to bytes
2455	shl	\$3+2,%r10d		# 4*$num
2456	neg	$num
2457	mov	($n0),$n0		# *n0
2458
2459	##############################################################
2460	# ensure that stack frame doesn't alias with $aptr+4*$num
2461	# modulo 4096, which covers ret[num], am[num] and n[2*num]
2462	# (see bn_exp.c). this is done to allow memory disambiguation
2463	# logic do its magic.
2464	#
2465	lea	-64(%rsp,$num,2),%r11
2466	sub	$aptr,%r11
2467	and	\$4095,%r11
2468	cmp	%r11,%r10
2469	jb	.Lpwrx_sp_alt
2470	sub	%r11,%rsp		# align with $aptr
2471	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
2472	jmp	.Lpwrx_sp_done
2473
2474.align	32
2475.Lpwrx_sp_alt:
2476	lea	4096-64(,$num,2),%r10	# 4096-frame-2*$num
2477	lea	-64(%rsp,$num,2),%rsp	# alloca(frame+2*$num)
2478	sub	%r10,%r11
2479	mov	\$0,%r10
2480	cmovc	%r10,%r11
2481	sub	%r11,%rsp
2482.Lpwrx_sp_done:
2483	and	\$-64,%rsp
2484	mov	$num,%r10
2485	neg	$num
2486
2487	##############################################################
2488	# Stack layout
2489	#
2490	# +0	saved $num, used in reduction section
2491	# +8	&t[2*$num], used in reduction section
2492	# +16	intermediate carry bit
2493	# +24	top-most carry bit, used in reduction section
2494	# +32	saved *n0
2495	# +40	saved %rsp
2496	# +48	t[2*$num]
2497	#
2498	pxor	%xmm0,%xmm0
2499	movq	$rptr,%xmm1		# save $rptr
2500	movq	$nptr,%xmm2		# save $nptr
2501	movq	%r10, %xmm3		# -$num
2502	movq	$bptr,%xmm4
2503	mov	$n0,  32(%rsp)
2504	mov	%rax, 40(%rsp)		# save original %rsp
2505.Lpowerx5_body:
2506
2507	call	__bn_sqrx8x_internal
2508	call	__bn_sqrx8x_internal
2509	call	__bn_sqrx8x_internal
2510	call	__bn_sqrx8x_internal
2511	call	__bn_sqrx8x_internal
2512
2513	mov	%r10,$num		# -num
2514	mov	$aptr,$rptr
2515	movq	%xmm2,$nptr
2516	movq	%xmm4,$bptr
2517	mov	40(%rsp),%rax
2518
2519	call	mulx4x_internal
2520
2521	mov	40(%rsp),%rsi		# restore %rsp
2522	mov	\$1,%rax
2523___
2524$code.=<<___ if ($win64);
2525	movaps	-88(%rsi),%xmm6
2526	movaps	-72(%rsi),%xmm7
2527___
2528$code.=<<___;
2529	mov	-48(%rsi),%r15
2530	mov	-40(%rsi),%r14
2531	mov	-32(%rsi),%r13
2532	mov	-24(%rsi),%r12
2533	mov	-16(%rsi),%rbp
2534	mov	-8(%rsi),%rbx
2535	lea	(%rsi),%rsp
2536.Lpowerx5_epilogue:
2537	ret
2538.size	bn_powerx5,.-bn_powerx5
2539
2540.globl	bn_sqrx8x_internal
2541.hidden	bn_sqrx8x_internal
2542.type	bn_sqrx8x_internal,\@abi-omnipotent
2543.align	32
2544bn_sqrx8x_internal:
2545__bn_sqrx8x_internal:
2546	##################################################################
2547	# Squaring part:
2548	#
2549	# a) multiply-n-add everything but a[i]*a[i];
2550	# b) shift result of a) by 1 to the left and accumulate
2551	#    a[i]*a[i] products;
2552	#
2553	##################################################################
2554	# a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
2555	#                                                     a[1]a[0]
2556	#                                                 a[2]a[0]
2557	#                                             a[3]a[0]
2558	#                                             a[2]a[1]
2559	#                                         a[3]a[1]
2560	#                                     a[3]a[2]
2561	#
2562	#                                         a[4]a[0]
2563	#                                     a[5]a[0]
2564	#                                 a[6]a[0]
2565	#                             a[7]a[0]
2566	#                                     a[4]a[1]
2567	#                                 a[5]a[1]
2568	#                             a[6]a[1]
2569	#                         a[7]a[1]
2570	#                                 a[4]a[2]
2571	#                             a[5]a[2]
2572	#                         a[6]a[2]
2573	#                     a[7]a[2]
2574	#                             a[4]a[3]
2575	#                         a[5]a[3]
2576	#                     a[6]a[3]
2577	#                 a[7]a[3]
2578	#
2579	#                     a[5]a[4]
2580	#                 a[6]a[4]
2581	#             a[7]a[4]
2582	#             a[6]a[5]
2583	#         a[7]a[5]
2584	#     a[7]a[6]
2585	# a[7]a[7]a[6]a[6]a[5]a[5]a[4]a[4]a[3]a[3]a[2]a[2]a[1]a[1]a[0]a[0]
2586___
2587{
2588my ($zero,$carry)=("%rbp","%rcx");
2589my $aaptr=$zero;
2590$code.=<<___;
2591	lea	48+8(%rsp),$tptr
2592	lea	($aptr,$num),$aaptr
2593	mov	$num,0+8(%rsp)			# save $num
2594	mov	$aaptr,8+8(%rsp)		# save end of $aptr
2595	jmp	.Lsqr8x_zero_start
2596
2597.align	32
2598.byte	0x66,0x66,0x66,0x2e,0x0f,0x1f,0x84,0x00,0x00,0x00,0x00,0x00
2599.Lsqrx8x_zero:
2600	.byte	0x3e
2601	movdqa	%xmm0,0*8($tptr)
2602	movdqa	%xmm0,2*8($tptr)
2603	movdqa	%xmm0,4*8($tptr)
2604	movdqa	%xmm0,6*8($tptr)
2605.Lsqr8x_zero_start:			# aligned at 32
2606	movdqa	%xmm0,8*8($tptr)
2607	movdqa	%xmm0,10*8($tptr)
2608	movdqa	%xmm0,12*8($tptr)
2609	movdqa	%xmm0,14*8($tptr)
2610	lea	16*8($tptr),$tptr
2611	sub	\$64,$num
2612	jnz	.Lsqrx8x_zero
2613
2614	mov	0*8($aptr),%rdx		# a[0], modulo-scheduled
2615	#xor	%r9,%r9			# t[1], ex-$num, zero already
2616	xor	%r10,%r10
2617	xor	%r11,%r11
2618	xor	%r12,%r12
2619	xor	%r13,%r13
2620	xor	%r14,%r14
2621	xor	%r15,%r15
2622	lea	48+8(%rsp),$tptr
2623	xor	$zero,$zero		# cf=0, cf=0
2624	jmp	.Lsqrx8x_outer_loop
2625
2626.align	32
2627.Lsqrx8x_outer_loop:
2628	mulx	1*8($aptr),%r8,%rax	# a[1]*a[0]
2629	adcx	%r9,%r8			# a[1]*a[0]+=t[1]
2630	adox	%rax,%r10
2631	mulx	2*8($aptr),%r9,%rax	# a[2]*a[0]
2632	adcx	%r10,%r9
2633	adox	%rax,%r11
2634	.byte	0xc4,0xe2,0xab,0xf6,0x86,0x18,0x00,0x00,0x00	# mulx	3*8($aptr),%r10,%rax	# ...
2635	adcx	%r11,%r10
2636	adox	%rax,%r12
2637	.byte	0xc4,0xe2,0xa3,0xf6,0x86,0x20,0x00,0x00,0x00	# mulx	4*8($aptr),%r11,%rax
2638	adcx	%r12,%r11
2639	adox	%rax,%r13
2640	mulx	5*8($aptr),%r12,%rax
2641	adcx	%r13,%r12
2642	adox	%rax,%r14
2643	mulx	6*8($aptr),%r13,%rax
2644	adcx	%r14,%r13
2645	adox	%r15,%rax
2646	mulx	7*8($aptr),%r14,%r15
2647	 mov	1*8($aptr),%rdx		# a[1]
2648	adcx	%rax,%r14
2649	adox	$zero,%r15
2650	adc	8*8($tptr),%r15
2651	mov	%r8,1*8($tptr)		# t[1]
2652	mov	%r9,2*8($tptr)		# t[2]
2653	sbb	$carry,$carry		# mov %cf,$carry
2654	xor	$zero,$zero		# cf=0, of=0
2655
2656
2657	mulx	2*8($aptr),%r8,%rbx	# a[2]*a[1]
2658	mulx	3*8($aptr),%r9,%rax	# a[3]*a[1]
2659	adcx	%r10,%r8
2660	adox	%rbx,%r9
2661	mulx	4*8($aptr),%r10,%rbx	# ...
2662	adcx	%r11,%r9
2663	adox	%rax,%r10
2664	.byte	0xc4,0xe2,0xa3,0xf6,0x86,0x28,0x00,0x00,0x00	# mulx	5*8($aptr),%r11,%rax
2665	adcx	%r12,%r10
2666	adox	%rbx,%r11
2667	.byte	0xc4,0xe2,0x9b,0xf6,0x9e,0x30,0x00,0x00,0x00	# mulx	6*8($aptr),%r12,%rbx
2668	adcx	%r13,%r11
2669	adox	%r14,%r12
2670	.byte	0xc4,0x62,0x93,0xf6,0xb6,0x38,0x00,0x00,0x00	# mulx	7*8($aptr),%r13,%r14
2671	 mov	2*8($aptr),%rdx		# a[2]
2672	adcx	%rax,%r12
2673	adox	%rbx,%r13
2674	adcx	%r15,%r13
2675	adox	$zero,%r14		# of=0
2676	adcx	$zero,%r14		# cf=0
2677
2678	mov	%r8,3*8($tptr)		# t[3]
2679	mov	%r9,4*8($tptr)		# t[4]
2680
2681	mulx	3*8($aptr),%r8,%rbx	# a[3]*a[2]
2682	mulx	4*8($aptr),%r9,%rax	# a[4]*a[2]
2683	adcx	%r10,%r8
2684	adox	%rbx,%r9
2685	mulx	5*8($aptr),%r10,%rbx	# ...
2686	adcx	%r11,%r9
2687	adox	%rax,%r10
2688	.byte	0xc4,0xe2,0xa3,0xf6,0x86,0x30,0x00,0x00,0x00	# mulx	6*8($aptr),%r11,%rax
2689	adcx	%r12,%r10
2690	adox	%r13,%r11
2691	.byte	0xc4,0x62,0x9b,0xf6,0xae,0x38,0x00,0x00,0x00	# mulx	7*8($aptr),%r12,%r13
2692	.byte	0x3e
2693	 mov	3*8($aptr),%rdx		# a[3]
2694	adcx	%rbx,%r11
2695	adox	%rax,%r12
2696	adcx	%r14,%r12
2697	mov	%r8,5*8($tptr)		# t[5]
2698	mov	%r9,6*8($tptr)		# t[6]
2699	 mulx	4*8($aptr),%r8,%rax	# a[4]*a[3]
2700	adox	$zero,%r13		# of=0
2701	adcx	$zero,%r13		# cf=0
2702
2703	mulx	5*8($aptr),%r9,%rbx	# a[5]*a[3]
2704	adcx	%r10,%r8
2705	adox	%rax,%r9
2706	mulx	6*8($aptr),%r10,%rax	# ...
2707	adcx	%r11,%r9
2708	adox	%r12,%r10
2709	mulx	7*8($aptr),%r11,%r12
2710	 mov	4*8($aptr),%rdx		# a[4]
2711	 mov	5*8($aptr),%r14		# a[5]
2712	adcx	%rbx,%r10
2713	adox	%rax,%r11
2714	 mov	6*8($aptr),%r15		# a[6]
2715	adcx	%r13,%r11
2716	adox	$zero,%r12		# of=0
2717	adcx	$zero,%r12		# cf=0
2718
2719	mov	%r8,7*8($tptr)		# t[7]
2720	mov	%r9,8*8($tptr)		# t[8]
2721
2722	mulx	%r14,%r9,%rax		# a[5]*a[4]
2723	 mov	7*8($aptr),%r8		# a[7]
2724	adcx	%r10,%r9
2725	mulx	%r15,%r10,%rbx		# a[6]*a[4]
2726	adox	%rax,%r10
2727	adcx	%r11,%r10
2728	mulx	%r8,%r11,%rax		# a[7]*a[4]
2729	 mov	%r14,%rdx		# a[5]
2730	adox	%rbx,%r11
2731	adcx	%r12,%r11
2732	#adox	$zero,%rax		# of=0
2733	adcx	$zero,%rax		# cf=0
2734
2735	mulx	%r15,%r14,%rbx		# a[6]*a[5]
2736	mulx	%r8,%r12,%r13		# a[7]*a[5]
2737	 mov	%r15,%rdx		# a[6]
2738	 lea	8*8($aptr),$aptr
2739	adcx	%r14,%r11
2740	adox	%rbx,%r12
2741	adcx	%rax,%r12
2742	adox	$zero,%r13
2743
2744	.byte	0x67,0x67
2745	mulx	%r8,%r8,%r14		# a[7]*a[6]
2746	adcx	%r8,%r13
2747	adcx	$zero,%r14
2748
2749	cmp	8+8(%rsp),$aptr
2750	je	.Lsqrx8x_outer_break
2751
2752	neg	$carry			# mov $carry,%cf
2753	mov	\$-8,%rcx
2754	mov	$zero,%r15
2755	mov	8*8($tptr),%r8
2756	adcx	9*8($tptr),%r9		# +=t[9]
2757	adcx	10*8($tptr),%r10	# ...
2758	adcx	11*8($tptr),%r11
2759	adc	12*8($tptr),%r12
2760	adc	13*8($tptr),%r13
2761	adc	14*8($tptr),%r14
2762	adc	15*8($tptr),%r15
2763	lea	($aptr),$aaptr
2764	lea	2*64($tptr),$tptr
2765	sbb	%rax,%rax		# mov %cf,$carry
2766
2767	mov	-64($aptr),%rdx		# a[0]
2768	mov	%rax,16+8(%rsp)		# offload $carry
2769	mov	$tptr,24+8(%rsp)
2770
2771	#lea	8*8($tptr),$tptr	# see 2*8*8($tptr) above
2772	xor	%eax,%eax		# cf=0, of=0
2773	jmp	.Lsqrx8x_loop
2774
2775.align	32
2776.Lsqrx8x_loop:
2777	mov	%r8,%rbx
2778	mulx	0*8($aaptr),%rax,%r8	# a[8]*a[i]
2779	adcx	%rax,%rbx		# +=t[8]
2780	adox	%r9,%r8
2781
2782	mulx	1*8($aaptr),%rax,%r9	# ...
2783	adcx	%rax,%r8
2784	adox	%r10,%r9
2785
2786	mulx	2*8($aaptr),%rax,%r10
2787	adcx	%rax,%r9
2788	adox	%r11,%r10
2789
2790	mulx	3*8($aaptr),%rax,%r11
2791	adcx	%rax,%r10
2792	adox	%r12,%r11
2793
2794	.byte	0xc4,0x62,0xfb,0xf6,0xa5,0x20,0x00,0x00,0x00	# mulx	4*8($aaptr),%rax,%r12
2795	adcx	%rax,%r11
2796	adox	%r13,%r12
2797
2798	mulx	5*8($aaptr),%rax,%r13
2799	adcx	%rax,%r12
2800	adox	%r14,%r13
2801
2802	mulx	6*8($aaptr),%rax,%r14
2803	 mov	%rbx,($tptr,%rcx,8)	# store t[8+i]
2804	 mov	\$0,%ebx
2805	adcx	%rax,%r13
2806	adox	%r15,%r14
2807
2808	.byte	0xc4,0x62,0xfb,0xf6,0xbd,0x38,0x00,0x00,0x00	# mulx	7*8($aaptr),%rax,%r15
2809	 mov	8($aptr,%rcx,8),%rdx	# a[i]
2810	adcx	%rax,%r14
2811	adox	%rbx,%r15		# %rbx is 0, of=0
2812	adcx	%rbx,%r15		# cf=0
2813
2814	.byte	0x67
2815	inc	%rcx			# of=0
2816	jnz	.Lsqrx8x_loop
2817
2818	lea	8*8($aaptr),$aaptr
2819	mov	\$-8,%rcx
2820	cmp	8+8(%rsp),$aaptr	# done?
2821	je	.Lsqrx8x_break
2822
2823	sub	16+8(%rsp),%rbx		# mov 16(%rsp),%cf
2824	.byte	0x66
2825	mov	-64($aptr),%rdx
2826	adcx	0*8($tptr),%r8
2827	adcx	1*8($tptr),%r9
2828	adc	2*8($tptr),%r10
2829	adc	3*8($tptr),%r11
2830	adc	4*8($tptr),%r12
2831	adc	5*8($tptr),%r13
2832	adc	6*8($tptr),%r14
2833	adc	7*8($tptr),%r15
2834	lea	8*8($tptr),$tptr
2835	.byte	0x67
2836	sbb	%rax,%rax		# mov %cf,%rax
2837	xor	%ebx,%ebx		# cf=0, of=0
2838	mov	%rax,16+8(%rsp)		# offload carry
2839	jmp	.Lsqrx8x_loop
2840
2841.align	32
2842.Lsqrx8x_break:
2843	sub	16+8(%rsp),%r8		# consume last carry
2844	mov	24+8(%rsp),$carry	# initial $tptr, borrow $carry
2845	mov	0*8($aptr),%rdx		# a[8], modulo-scheduled
2846	xor	%ebp,%ebp		# xor	$zero,$zero
2847	mov	%r8,0*8($tptr)
2848	cmp	$carry,$tptr		# cf=0, of=0
2849	je	.Lsqrx8x_outer_loop
2850
2851	mov	%r9,1*8($tptr)
2852	 mov	1*8($carry),%r9
2853	mov	%r10,2*8($tptr)
2854	 mov	2*8($carry),%r10
2855	mov	%r11,3*8($tptr)
2856	 mov	3*8($carry),%r11
2857	mov	%r12,4*8($tptr)
2858	 mov	4*8($carry),%r12
2859	mov	%r13,5*8($tptr)
2860	 mov	5*8($carry),%r13
2861	mov	%r14,6*8($tptr)
2862	 mov	6*8($carry),%r14
2863	mov	%r15,7*8($tptr)
2864	 mov	7*8($carry),%r15
2865	mov	$carry,$tptr
2866	jmp	.Lsqrx8x_outer_loop
2867
2868.align	32
2869.Lsqrx8x_outer_break:
2870	mov	%r9,9*8($tptr)		# t[9]
2871	 movq	%xmm3,%rcx		# -$num
2872	mov	%r10,10*8($tptr)	# ...
2873	mov	%r11,11*8($tptr)
2874	mov	%r12,12*8($tptr)
2875	mov	%r13,13*8($tptr)
2876	mov	%r14,14*8($tptr)
2877___
2878}{
2879my $i="%rcx";
2880$code.=<<___;
2881	lea	48+8(%rsp),$tptr
2882	mov	($aptr,$i),%rdx		# a[0]
2883
2884	mov	8($tptr),$A0[1]		# t[1]
2885	xor	$A0[0],$A0[0]		# t[0], of=0, cf=0
2886	mov	0+8(%rsp),$num		# restore $num
2887	adox	$A0[1],$A0[1]
2888	 mov	16($tptr),$A1[0]	# t[2]	# prefetch
2889	 mov	24($tptr),$A1[1]	# t[3]	# prefetch
2890	#jmp	.Lsqrx4x_shift_n_add	# happens to be aligned
2891
2892.align	32
2893.Lsqrx4x_shift_n_add:
2894	mulx	%rdx,%rax,%rbx
2895	 adox	$A1[0],$A1[0]
2896	adcx	$A0[0],%rax
2897	 .byte	0x48,0x8b,0x94,0x0e,0x08,0x00,0x00,0x00	# mov	8($aptr,$i),%rdx	# a[i+1]	# prefetch
2898	 .byte	0x4c,0x8b,0x97,0x20,0x00,0x00,0x00	# mov	32($tptr),$A0[0]	# t[2*i+4]	# prefetch
2899	 adox	$A1[1],$A1[1]
2900	adcx	$A0[1],%rbx
2901	 mov	40($tptr),$A0[1]		# t[2*i+4+1]	# prefetch
2902	mov	%rax,0($tptr)
2903	mov	%rbx,8($tptr)
2904
2905	mulx	%rdx,%rax,%rbx
2906	 adox	$A0[0],$A0[0]
2907	adcx	$A1[0],%rax
2908	 mov	16($aptr,$i),%rdx	# a[i+2]	# prefetch
2909	 mov	48($tptr),$A1[0]	# t[2*i+6]	# prefetch
2910	 adox	$A0[1],$A0[1]
2911	adcx	$A1[1],%rbx
2912	 mov	56($tptr),$A1[1]	# t[2*i+6+1]	# prefetch
2913	mov	%rax,16($tptr)
2914	mov	%rbx,24($tptr)
2915
2916	mulx	%rdx,%rax,%rbx
2917	 adox	$A1[0],$A1[0]
2918	adcx	$A0[0],%rax
2919	 mov	24($aptr,$i),%rdx	# a[i+3]	# prefetch
2920	 lea	32($i),$i
2921	 mov	64($tptr),$A0[0]	# t[2*i+8]	# prefetch
2922	 adox	$A1[1],$A1[1]
2923	adcx	$A0[1],%rbx
2924	 mov	72($tptr),$A0[1]	# t[2*i+8+1]	# prefetch
2925	mov	%rax,32($tptr)
2926	mov	%rbx,40($tptr)
2927
2928	mulx	%rdx,%rax,%rbx
2929	 adox	$A0[0],$A0[0]
2930	adcx	$A1[0],%rax
2931	jrcxz	.Lsqrx4x_shift_n_add_break
2932	 .byte	0x48,0x8b,0x94,0x0e,0x00,0x00,0x00,0x00	# mov	0($aptr,$i),%rdx	# a[i+4]	# prefetch
2933	 adox	$A0[1],$A0[1]
2934	adcx	$A1[1],%rbx
2935	 mov	80($tptr),$A1[0]	# t[2*i+10]	# prefetch
2936	 mov	88($tptr),$A1[1]	# t[2*i+10+1]	# prefetch
2937	mov	%rax,48($tptr)
2938	mov	%rbx,56($tptr)
2939	lea	64($tptr),$tptr
2940	nop
2941	jmp	.Lsqrx4x_shift_n_add
2942
2943.align	32
2944.Lsqrx4x_shift_n_add_break:
2945	adcx	$A1[1],%rbx
2946	mov	%rax,48($tptr)
2947	mov	%rbx,56($tptr)
2948	lea	64($tptr),$tptr		# end of t[] buffer
2949___
2950}
2951######################################################################
2952# Montgomery reduction part, "word-by-word" algorithm.
2953#
2954# This new path is inspired by multiple submissions from Intel, by
2955# Shay Gueron, Vlad Krasnov, Erdinc Ozturk, James Guilford,
2956# Vinodh Gopal...
2957{
2958my ($nptr,$carry,$m0)=("%rbp","%rsi","%rdx");
2959
2960$code.=<<___;
2961	movq	%xmm2,$nptr
2962sqrx8x_reduction:
2963	xor	%eax,%eax		# initial top-most carry bit
2964	mov	32+8(%rsp),%rbx		# n0
2965	mov	48+8(%rsp),%rdx		# "%r8", 8*0($tptr)
2966	lea	-128($nptr,$num,2),%rcx	# end of n[]
2967	#lea	48+8(%rsp,$num,2),$tptr	# end of t[] buffer
2968	mov	%rcx, 0+8(%rsp)		# save end of n[]
2969	mov	$tptr,8+8(%rsp)		# save end of t[]
2970
2971	lea	48+8(%rsp),$tptr		# initial t[] window
2972	jmp	.Lsqrx8x_reduction_loop
2973
2974.align	32
2975.Lsqrx8x_reduction_loop:
2976	mov	8*1($tptr),%r9
2977	mov	8*2($tptr),%r10
2978	mov	8*3($tptr),%r11
2979	mov	8*4($tptr),%r12
2980	mov	%rdx,%r8
2981	imulq	%rbx,%rdx		# n0*a[i]
2982	mov	8*5($tptr),%r13
2983	mov	8*6($tptr),%r14
2984	mov	8*7($tptr),%r15
2985	mov	%rax,24+8(%rsp)		# store top-most carry bit
2986
2987	lea	8*8($tptr),$tptr
2988	xor	$carry,$carry		# cf=0,of=0
2989	mov	\$-8,%rcx
2990	jmp	.Lsqrx8x_reduce
2991
2992.align	32
2993.Lsqrx8x_reduce:
2994	mov	%r8, %rbx
2995	mulx	16*0($nptr),%rax,%r8	# n[0]
2996	adcx	%rbx,%rax		# discarded
2997	adox	%r9,%r8
2998
2999	mulx	16*1($nptr),%rbx,%r9	# n[1]
3000	adcx	%rbx,%r8
3001	adox	%r10,%r9
3002
3003	mulx	16*2($nptr),%rbx,%r10
3004	adcx	%rbx,%r9
3005	adox	%r11,%r10
3006
3007	mulx	16*3($nptr),%rbx,%r11
3008	adcx	%rbx,%r10
3009	adox	%r12,%r11
3010
3011	.byte	0xc4,0x62,0xe3,0xf6,0xa5,0x40,0x00,0x00,0x00	# mulx	16*4($nptr),%rbx,%r12
3012	 mov	%rdx,%rax
3013	 mov	%r8,%rdx
3014	adcx	%rbx,%r11
3015	adox	%r13,%r12
3016
3017	 mulx	32+8(%rsp),%rbx,%rdx	# %rdx discarded
3018	 mov	%rax,%rdx
3019	 mov	%rax,64+48+8(%rsp,%rcx,8)	# put aside n0*a[i]
3020
3021	mulx	16*5($nptr),%rax,%r13
3022	adcx	%rax,%r12
3023	adox	%r14,%r13
3024
3025	mulx	16*6($nptr),%rax,%r14
3026	adcx	%rax,%r13
3027	adox	%r15,%r14
3028
3029	mulx	16*7($nptr),%rax,%r15
3030	 mov	%rbx,%rdx
3031	adcx	%rax,%r14
3032	adox	$carry,%r15		# $carry is 0
3033	adcx	$carry,%r15		# cf=0
3034
3035	.byte	0x67,0x67,0x67
3036	inc	%rcx			# of=0
3037	jnz	.Lsqrx8x_reduce
3038
3039	mov	$carry,%rax		# xor	%rax,%rax
3040	cmp	0+8(%rsp),$nptr		# end of n[]?
3041	jae	.Lsqrx8x_no_tail
3042
3043	mov	48+8(%rsp),%rdx		# pull n0*a[0]
3044	add	8*0($tptr),%r8
3045	lea	16*8($nptr),$nptr
3046	mov	\$-8,%rcx
3047	adcx	8*1($tptr),%r9
3048	adcx	8*2($tptr),%r10
3049	adc	8*3($tptr),%r11
3050	adc	8*4($tptr),%r12
3051	adc	8*5($tptr),%r13
3052	adc	8*6($tptr),%r14
3053	adc	8*7($tptr),%r15
3054	lea	8*8($tptr),$tptr
3055	sbb	%rax,%rax		# top carry
3056
3057	xor	$carry,$carry		# of=0, cf=0
3058	mov	%rax,16+8(%rsp)
3059	jmp	.Lsqrx8x_tail
3060
3061.align	32
3062.Lsqrx8x_tail:
3063	mov	%r8,%rbx
3064	mulx	16*0($nptr),%rax,%r8
3065	adcx	%rax,%rbx
3066	adox	%r9,%r8
3067
3068	mulx	16*1($nptr),%rax,%r9
3069	adcx	%rax,%r8
3070	adox	%r10,%r9
3071
3072	mulx	16*2($nptr),%rax,%r10
3073	adcx	%rax,%r9
3074	adox	%r11,%r10
3075
3076	mulx	16*3($nptr),%rax,%r11
3077	adcx	%rax,%r10
3078	adox	%r12,%r11
3079
3080	.byte	0xc4,0x62,0xfb,0xf6,0xa5,0x40,0x00,0x00,0x00	# mulx	16*4($nptr),%rax,%r12
3081	adcx	%rax,%r11
3082	adox	%r13,%r12
3083
3084	mulx	16*5($nptr),%rax,%r13
3085	adcx	%rax,%r12
3086	adox	%r14,%r13
3087
3088	mulx	16*6($nptr),%rax,%r14
3089	adcx	%rax,%r13
3090	adox	%r15,%r14
3091
3092	mulx	16*7($nptr),%rax,%r15
3093	 mov	72+48+8(%rsp,%rcx,8),%rdx	# pull n0*a[i]
3094	adcx	%rax,%r14
3095	adox	$carry,%r15
3096	 mov	%rbx,($tptr,%rcx,8)	# save result
3097	 mov	%r8,%rbx
3098	adcx	$carry,%r15		# cf=0
3099
3100	inc	%rcx			# of=0
3101	jnz	.Lsqrx8x_tail
3102
3103	cmp	0+8(%rsp),$nptr		# end of n[]?
3104	jae	.Lsqrx8x_tail_done	# break out of loop
3105
3106	sub	16+8(%rsp),$carry	# mov 16(%rsp),%cf
3107	 mov	48+8(%rsp),%rdx		# pull n0*a[0]
3108	 lea	16*8($nptr),$nptr
3109	adc	8*0($tptr),%r8
3110	adc	8*1($tptr),%r9
3111	adc	8*2($tptr),%r10
3112	adc	8*3($tptr),%r11
3113	adc	8*4($tptr),%r12
3114	adc	8*5($tptr),%r13
3115	adc	8*6($tptr),%r14
3116	adc	8*7($tptr),%r15
3117	lea	8*8($tptr),$tptr
3118	sbb	%rax,%rax
3119	sub	\$8,%rcx		# mov	\$-8,%rcx
3120
3121	xor	$carry,$carry		# of=0, cf=0
3122	mov	%rax,16+8(%rsp)
3123	jmp	.Lsqrx8x_tail
3124
3125.align	32
3126.Lsqrx8x_tail_done:
3127	add	24+8(%rsp),%r8		# can this overflow?
3128	adc	\$0,%r9
3129	adc	\$0,%r10
3130	adc	\$0,%r11
3131	adc	\$0,%r12
3132	adc	\$0,%r13
3133	adc	\$0,%r14
3134	adc	\$0,%r15		# can't overflow, because we
3135					# started with "overhung" part
3136					# of multiplication
3137	mov	$carry,%rax		# xor	%rax,%rax
3138
3139	sub	16+8(%rsp),$carry	# mov 16(%rsp),%cf
3140.Lsqrx8x_no_tail:			# %cf is 0 if jumped here
3141	adc	8*0($tptr),%r8
3142	 movq	%xmm3,%rcx
3143	adc	8*1($tptr),%r9
3144	 mov	16*7($nptr),$carry
3145	 movq	%xmm2,$nptr		# restore $nptr
3146	adc	8*2($tptr),%r10
3147	adc	8*3($tptr),%r11
3148	adc	8*4($tptr),%r12
3149	adc	8*5($tptr),%r13
3150	adc	8*6($tptr),%r14
3151	adc	8*7($tptr),%r15
3152	adc	%rax,%rax		# top-most carry
3153
3154	mov	32+8(%rsp),%rbx		# n0
3155	mov	8*8($tptr,%rcx),%rdx	# modulo-scheduled "%r8"
3156
3157	mov	%r8,8*0($tptr)		# store top 512 bits
3158	 lea	8*8($tptr),%r8		# borrow %r8
3159	mov	%r9,8*1($tptr)
3160	mov	%r10,8*2($tptr)
3161	mov	%r11,8*3($tptr)
3162	mov	%r12,8*4($tptr)
3163	mov	%r13,8*5($tptr)
3164	mov	%r14,8*6($tptr)
3165	mov	%r15,8*7($tptr)
3166
3167	lea	8*8($tptr,%rcx),$tptr	# start of current t[] window
3168	cmp	8+8(%rsp),%r8		# end of t[]?
3169	jb	.Lsqrx8x_reduction_loop
3170___
3171}
3172##############################################################
3173# Post-condition, 4x unrolled
3174#
3175{
3176my ($rptr,$nptr)=("%rdx","%rbp");
3177my @ri=map("%r$_",(10..13));
3178my @ni=map("%r$_",(14..15));
3179$code.=<<___;
3180	xor	%ebx,%ebx
3181	sub	%r15,%rsi		# compare top-most words
3182	adc	%rbx,%rbx
3183	mov	%rcx,%r10		# -$num
3184	or	%rbx,%rax
3185	mov	%rcx,%r9		# -$num
3186	xor	\$1,%rax
3187	sar	\$3+2,%rcx		# cf=0
3188	#lea	48+8(%rsp,%r9),$tptr
3189	lea	($nptr,%rax,8),$nptr
3190	movq	%xmm1,$rptr		# restore $rptr
3191	movq	%xmm1,$aptr		# prepare for back-to-back call
3192	jmp	.Lsqrx4x_sub
3193
3194.align	32
3195.Lsqrx4x_sub:
3196	.byte	0x66
3197	mov	8*0($tptr),%r12
3198	mov	8*1($tptr),%r13
3199	sbb	16*0($nptr),%r12
3200	mov	8*2($tptr),%r14
3201	sbb	16*1($nptr),%r13
3202	mov	8*3($tptr),%r15
3203	lea	8*4($tptr),$tptr
3204	sbb	16*2($nptr),%r14
3205	mov	%r12,8*0($rptr)
3206	sbb	16*3($nptr),%r15
3207	lea	16*4($nptr),$nptr
3208	mov	%r13,8*1($rptr)
3209	mov	%r14,8*2($rptr)
3210	mov	%r15,8*3($rptr)
3211	lea	8*4($rptr),$rptr
3212
3213	inc	%rcx
3214	jnz	.Lsqrx4x_sub
3215___
3216}
3217$code.=<<___;
3218	neg	%r9			# restore $num
3219
3220	ret
3221.size	bn_sqrx8x_internal,.-bn_sqrx8x_internal
3222___
3223}}}
3224{
3225my ($inp,$num,$tbl,$idx)=$win64?("%rcx","%edx","%r8", "%r9d") : # Win64 order
3226				("%rdi","%esi","%rdx","%ecx");  # Unix order
3227my $out=$inp;
3228my $STRIDE=2**5*8;
3229my $N=$STRIDE/4;
3230
3231$code.=<<___;
3232.globl	bn_scatter5
3233.type	bn_scatter5,\@abi-omnipotent
3234.align	16
3235bn_scatter5:
3236	cmp	\$0, $num
3237	jz	.Lscatter_epilogue
3238	lea	($tbl,$idx,8),$tbl
3239.Lscatter:
3240	mov	($inp),%rax
3241	lea	8($inp),$inp
3242	mov	%rax,($tbl)
3243	lea	32*8($tbl),$tbl
3244	sub	\$1,$num
3245	jnz	.Lscatter
3246.Lscatter_epilogue:
3247	ret
3248.size	bn_scatter5,.-bn_scatter5
3249
3250.globl	bn_gather5
3251.type	bn_gather5,\@abi-omnipotent
3252.align	16
3253bn_gather5:
3254___
3255$code.=<<___ if ($win64);
3256.LSEH_begin_bn_gather5:
3257	# I can't trust assembler to use specific encoding:-(
3258	.byte	0x48,0x83,0xec,0x28		#sub	\$0x28,%rsp
3259	.byte	0x0f,0x29,0x34,0x24		#movaps	%xmm6,(%rsp)
3260	.byte	0x0f,0x29,0x7c,0x24,0x10	#movdqa	%xmm7,0x10(%rsp)
3261___
3262$code.=<<___;
3263	mov	$idx,%r11d
3264	shr	\$`log($N/8)/log(2)`,$idx
3265	and	\$`$N/8-1`,%r11
3266	not	$idx
3267	lea	.Lmagic_masks(%rip),%rax
3268	and	\$`2**5/($N/8)-1`,$idx	# 5 is "window size"
3269	lea	128($tbl,%r11,8),$tbl	# pointer within 1st cache line
3270	movq	0(%rax,$idx,8),%xmm4	# set of masks denoting which
3271	movq	8(%rax,$idx,8),%xmm5	# cache line contains element
3272	movq	16(%rax,$idx,8),%xmm6	# denoted by 7th argument
3273	movq	24(%rax,$idx,8),%xmm7
3274	jmp	.Lgather
3275.align	16
3276.Lgather:
3277	movq	`0*$STRIDE/4-128`($tbl),%xmm0
3278	movq	`1*$STRIDE/4-128`($tbl),%xmm1
3279	pand	%xmm4,%xmm0
3280	movq	`2*$STRIDE/4-128`($tbl),%xmm2
3281	pand	%xmm5,%xmm1
3282	movq	`3*$STRIDE/4-128`($tbl),%xmm3
3283	pand	%xmm6,%xmm2
3284	por	%xmm1,%xmm0
3285	pand	%xmm7,%xmm3
3286	.byte	0x67,0x67
3287	por	%xmm2,%xmm0
3288	lea	$STRIDE($tbl),$tbl
3289	por	%xmm3,%xmm0
3290
3291	movq	%xmm0,($out)		# m0=bp[0]
3292	lea	8($out),$out
3293	sub	\$1,$num
3294	jnz	.Lgather
3295___
3296$code.=<<___ if ($win64);
3297	movaps	(%rsp),%xmm6
3298	movaps	0x10(%rsp),%xmm7
3299	lea	0x28(%rsp),%rsp
3300___
3301$code.=<<___;
3302	ret
3303.LSEH_end_bn_gather5:
3304.size	bn_gather5,.-bn_gather5
3305___
3306}
3307$code.=<<___;
3308.align	64
3309.Lmagic_masks:
3310	.long	0,0, 0,0, 0,0, -1,-1
3311	.long	0,0, 0,0, 0,0,  0,0
3312.asciz	"Montgomery Multiplication with scatter/gather for x86_64, CRYPTOGAMS by <appro\@openssl.org>"
3313___
3314
3315# EXCEPTION_DISPOSITION handler (EXCEPTION_RECORD *rec,ULONG64 frame,
3316#		CONTEXT *context,DISPATCHER_CONTEXT *disp)
3317if ($win64) {
3318$rec="%rcx";
3319$frame="%rdx";
3320$context="%r8";
3321$disp="%r9";
3322
3323$code.=<<___;
3324.extern	__imp_RtlVirtualUnwind
3325.type	mul_handler,\@abi-omnipotent
3326.align	16
3327mul_handler:
3328	push	%rsi
3329	push	%rdi
3330	push	%rbx
3331	push	%rbp
3332	push	%r12
3333	push	%r13
3334	push	%r14
3335	push	%r15
3336	pushfq
3337	sub	\$64,%rsp
3338
3339	mov	120($context),%rax	# pull context->Rax
3340	mov	248($context),%rbx	# pull context->Rip
3341
3342	mov	8($disp),%rsi		# disp->ImageBase
3343	mov	56($disp),%r11		# disp->HandlerData
3344
3345	mov	0(%r11),%r10d		# HandlerData[0]
3346	lea	(%rsi,%r10),%r10	# end of prologue label
3347	cmp	%r10,%rbx		# context->Rip<end of prologue label
3348	jb	.Lcommon_seh_tail
3349
3350	mov	152($context),%rax	# pull context->Rsp
3351
3352	mov	4(%r11),%r10d		# HandlerData[1]
3353	lea	(%rsi,%r10),%r10	# epilogue label
3354	cmp	%r10,%rbx		# context->Rip>=epilogue label
3355	jae	.Lcommon_seh_tail
3356
3357	lea	.Lmul_epilogue(%rip),%r10
3358	cmp	%r10,%rbx
3359	jb	.Lbody_40
3360
3361	mov	192($context),%r10	# pull $num
3362	mov	8(%rax,%r10,8),%rax	# pull saved stack pointer
3363	jmp	.Lbody_proceed
3364
3365.Lbody_40:
3366	mov	40(%rax),%rax		# pull saved stack pointer
3367.Lbody_proceed:
3368
3369	movaps	-88(%rax),%xmm0
3370	movaps	-72(%rax),%xmm1
3371
3372	mov	-8(%rax),%rbx
3373	mov	-16(%rax),%rbp
3374	mov	-24(%rax),%r12
3375	mov	-32(%rax),%r13
3376	mov	-40(%rax),%r14
3377	mov	-48(%rax),%r15
3378	mov	%rbx,144($context)	# restore context->Rbx
3379	mov	%rbp,160($context)	# restore context->Rbp
3380	mov	%r12,216($context)	# restore context->R12
3381	mov	%r13,224($context)	# restore context->R13
3382	mov	%r14,232($context)	# restore context->R14
3383	mov	%r15,240($context)	# restore context->R15
3384	movups	%xmm0,512($context)	# restore context->Xmm6
3385	movups	%xmm1,528($context)	# restore context->Xmm7
3386
3387.Lcommon_seh_tail:
3388	mov	8(%rax),%rdi
3389	mov	16(%rax),%rsi
3390	mov	%rax,152($context)	# restore context->Rsp
3391	mov	%rsi,168($context)	# restore context->Rsi
3392	mov	%rdi,176($context)	# restore context->Rdi
3393
3394	mov	40($disp),%rdi		# disp->ContextRecord
3395	mov	$context,%rsi		# context
3396	mov	\$154,%ecx		# sizeof(CONTEXT)
3397	.long	0xa548f3fc		# cld; rep movsq
3398
3399	mov	$disp,%rsi
3400	xor	%rcx,%rcx		# arg1, UNW_FLAG_NHANDLER
3401	mov	8(%rsi),%rdx		# arg2, disp->ImageBase
3402	mov	0(%rsi),%r8		# arg3, disp->ControlPc
3403	mov	16(%rsi),%r9		# arg4, disp->FunctionEntry
3404	mov	40(%rsi),%r10		# disp->ContextRecord
3405	lea	56(%rsi),%r11		# &disp->HandlerData
3406	lea	24(%rsi),%r12		# &disp->EstablisherFrame
3407	mov	%r10,32(%rsp)		# arg5
3408	mov	%r11,40(%rsp)		# arg6
3409	mov	%r12,48(%rsp)		# arg7
3410	mov	%rcx,56(%rsp)		# arg8, (NULL)
3411	call	*__imp_RtlVirtualUnwind(%rip)
3412
3413	mov	\$1,%eax		# ExceptionContinueSearch
3414	add	\$64,%rsp
3415	popfq
3416	pop	%r15
3417	pop	%r14
3418	pop	%r13
3419	pop	%r12
3420	pop	%rbp
3421	pop	%rbx
3422	pop	%rdi
3423	pop	%rsi
3424	ret
3425.size	mul_handler,.-mul_handler
3426
3427.section	.pdata
3428.align	4
3429	.rva	.LSEH_begin_bn_mul_mont_gather5
3430	.rva	.LSEH_end_bn_mul_mont_gather5
3431	.rva	.LSEH_info_bn_mul_mont_gather5
3432
3433	.rva	.LSEH_begin_bn_mul4x_mont_gather5
3434	.rva	.LSEH_end_bn_mul4x_mont_gather5
3435	.rva	.LSEH_info_bn_mul4x_mont_gather5
3436
3437	.rva	.LSEH_begin_bn_power5
3438	.rva	.LSEH_end_bn_power5
3439	.rva	.LSEH_info_bn_power5
3440
3441	.rva	.LSEH_begin_bn_from_mont8x
3442	.rva	.LSEH_end_bn_from_mont8x
3443	.rva	.LSEH_info_bn_from_mont8x
3444___
3445$code.=<<___ if ($addx);
3446	.rva	.LSEH_begin_bn_mulx4x_mont_gather5
3447	.rva	.LSEH_end_bn_mulx4x_mont_gather5
3448	.rva	.LSEH_info_bn_mulx4x_mont_gather5
3449
3450	.rva	.LSEH_begin_bn_powerx5
3451	.rva	.LSEH_end_bn_powerx5
3452	.rva	.LSEH_info_bn_powerx5
3453___
3454$code.=<<___;
3455	.rva	.LSEH_begin_bn_gather5
3456	.rva	.LSEH_end_bn_gather5
3457	.rva	.LSEH_info_bn_gather5
3458
3459.section	.xdata
3460.align	8
3461.LSEH_info_bn_mul_mont_gather5:
3462	.byte	9,0,0,0
3463	.rva	mul_handler
3464	.rva	.Lmul_body,.Lmul_epilogue		# HandlerData[]
3465.align	8
3466.LSEH_info_bn_mul4x_mont_gather5:
3467	.byte	9,0,0,0
3468	.rva	mul_handler
3469	.rva	.Lmul4x_body,.Lmul4x_epilogue		# HandlerData[]
3470.align	8
3471.LSEH_info_bn_power5:
3472	.byte	9,0,0,0
3473	.rva	mul_handler
3474	.rva	.Lpower5_body,.Lpower5_epilogue		# HandlerData[]
3475.align	8
3476.LSEH_info_bn_from_mont8x:
3477	.byte	9,0,0,0
3478	.rva	mul_handler
3479	.rva	.Lfrom_body,.Lfrom_epilogue		# HandlerData[]
3480___
3481$code.=<<___ if ($addx);
3482.align	8
3483.LSEH_info_bn_mulx4x_mont_gather5:
3484	.byte	9,0,0,0
3485	.rva	mul_handler
3486	.rva	.Lmulx4x_body,.Lmulx4x_epilogue		# HandlerData[]
3487.align	8
3488.LSEH_info_bn_powerx5:
3489	.byte	9,0,0,0
3490	.rva	mul_handler
3491	.rva	.Lpowerx5_body,.Lpowerx5_epilogue	# HandlerData[]
3492___
3493$code.=<<___;
3494.align	8
3495.LSEH_info_bn_gather5:
3496        .byte   0x01,0x0d,0x05,0x00
3497        .byte   0x0d,0x78,0x01,0x00	#movaps	0x10(rsp),xmm7
3498        .byte   0x08,0x68,0x00,0x00	#movaps	(rsp),xmm6
3499        .byte   0x04,0x42,0x00,0x00	#sub	rsp,0x28
3500.align	8
3501___
3502}
3503
3504$code =~ s/\`([^\`]*)\`/eval($1)/gem;
3505
3506print $code;
3507close STDOUT;
3508