x86_64-gcc.c revision 279264
1#include "../bn_lcl.h"
2#if !(defined(__GNUC__) && __GNUC__>=2)
3# include "../bn_asm.c"	/* kind of dirty hack for Sun Studio */
4#else
5/*
6 * x86_64 BIGNUM accelerator version 0.1, December 2002.
7 *
8 * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
9 * project.
10 *
11 * Rights for redistribution and usage in source and binary forms are
12 * granted according to the OpenSSL license. Warranty of any kind is
13 * disclaimed.
14 *
15 * Q. Version 0.1? It doesn't sound like Andy, he used to assign real
16 *    versions, like 1.0...
17 * A. Well, that's because this code is basically a quick-n-dirty
18 *    proof-of-concept hack. As you can see it's implemented with
19 *    inline assembler, which means that you're bound to GCC and that
20 *    there might be enough room for further improvement.
21 *
22 * Q. Why inline assembler?
23 * A. x86_64 features own ABI which I'm not familiar with. This is
24 *    why I decided to let the compiler take care of subroutine
25 *    prologue/epilogue as well as register allocation. For reference.
26 *    Win64 implements different ABI for AMD64, different from Linux.
27 *
28 * Q. How much faster does it get?
29 * A. 'apps/openssl speed rsa dsa' output with no-asm:
30 *
31 *	                  sign    verify    sign/s verify/s
32 *	rsa  512 bits   0.0006s   0.0001s   1683.8  18456.2
33 *	rsa 1024 bits   0.0028s   0.0002s    356.0   6407.0
34 *	rsa 2048 bits   0.0172s   0.0005s     58.0   1957.8
35 *	rsa 4096 bits   0.1155s   0.0018s      8.7    555.6
36 *	                  sign    verify    sign/s verify/s
37 *	dsa  512 bits   0.0005s   0.0006s   2100.8   1768.3
38 *	dsa 1024 bits   0.0014s   0.0018s    692.3    559.2
39 *	dsa 2048 bits   0.0049s   0.0061s    204.7    165.0
40 *
41 *    'apps/openssl speed rsa dsa' output with this module:
42 *
43 *	                  sign    verify    sign/s verify/s
44 *	rsa  512 bits   0.0004s   0.0000s   2767.1  33297.9
45 *	rsa 1024 bits   0.0012s   0.0001s    867.4  14674.7
46 *	rsa 2048 bits   0.0061s   0.0002s    164.0   5270.0
47 *	rsa 4096 bits   0.0384s   0.0006s     26.1   1650.8
48 *	                  sign    verify    sign/s verify/s
49 *	dsa  512 bits   0.0002s   0.0003s   4442.2   3786.3
50 *	dsa 1024 bits   0.0005s   0.0007s   1835.1   1497.4
51 *	dsa 2048 bits   0.0016s   0.0020s    620.4    504.6
52 *
53 *    For the reference. IA-32 assembler implementation performs
54 *    very much like 64-bit code compiled with no-asm on the same
55 *    machine.
56 */
57
58#ifdef _WIN64
59#define BN_ULONG unsigned long long
60#else
61#define BN_ULONG unsigned long
62#endif
63
64#undef mul
65#undef mul_add
66#undef sqr
67
68/*
69 * "m"(a), "+m"(r)	is the way to favor DirectPath �-code;
70 * "g"(0)		let the compiler to decide where does it
71 *			want to keep the value of zero;
72 */
73#define mul_add(r,a,word,carry) do {	\
74	register BN_ULONG high,low;	\
75	asm ("mulq %3"			\
76		: "=a"(low),"=d"(high)	\
77		: "a"(word),"m"(a)	\
78		: "cc");		\
79	asm ("addq %2,%0; adcq %3,%1"	\
80		: "+r"(carry),"+d"(high)\
81		: "a"(low),"g"(0)	\
82		: "cc");		\
83	asm ("addq %2,%0; adcq %3,%1"	\
84		: "+m"(r),"+d"(high)	\
85		: "r"(carry),"g"(0)	\
86		: "cc");		\
87	carry=high;			\
88	} while (0)
89
90#define mul(r,a,word,carry) do {	\
91	register BN_ULONG high,low;	\
92	asm ("mulq %3"			\
93		: "=a"(low),"=d"(high)	\
94		: "a"(word),"g"(a)	\
95		: "cc");		\
96	asm ("addq %2,%0; adcq %3,%1"	\
97		: "+r"(carry),"+d"(high)\
98		: "a"(low),"g"(0)	\
99		: "cc");		\
100	(r)=carry, carry=high;		\
101	} while (0)
102
103#define sqr(r0,r1,a)			\
104	asm ("mulq %2"			\
105		: "=a"(r0),"=d"(r1)	\
106		: "a"(a)		\
107		: "cc");
108
109BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
110	{
111	BN_ULONG c1=0;
112
113	if (num <= 0) return(c1);
114
115	while (num&~3)
116		{
117		mul_add(rp[0],ap[0],w,c1);
118		mul_add(rp[1],ap[1],w,c1);
119		mul_add(rp[2],ap[2],w,c1);
120		mul_add(rp[3],ap[3],w,c1);
121		ap+=4; rp+=4; num-=4;
122		}
123	if (num)
124		{
125		mul_add(rp[0],ap[0],w,c1); if (--num==0) return c1;
126		mul_add(rp[1],ap[1],w,c1); if (--num==0) return c1;
127		mul_add(rp[2],ap[2],w,c1); return c1;
128		}
129
130	return(c1);
131	}
132
133BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
134	{
135	BN_ULONG c1=0;
136
137	if (num <= 0) return(c1);
138
139	while (num&~3)
140		{
141		mul(rp[0],ap[0],w,c1);
142		mul(rp[1],ap[1],w,c1);
143		mul(rp[2],ap[2],w,c1);
144		mul(rp[3],ap[3],w,c1);
145		ap+=4; rp+=4; num-=4;
146		}
147	if (num)
148		{
149		mul(rp[0],ap[0],w,c1); if (--num == 0) return c1;
150		mul(rp[1],ap[1],w,c1); if (--num == 0) return c1;
151		mul(rp[2],ap[2],w,c1);
152		}
153	return(c1);
154	}
155
156void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
157        {
158	if (n <= 0) return;
159
160	while (n&~3)
161		{
162		sqr(r[0],r[1],a[0]);
163		sqr(r[2],r[3],a[1]);
164		sqr(r[4],r[5],a[2]);
165		sqr(r[6],r[7],a[3]);
166		a+=4; r+=8; n-=4;
167		}
168	if (n)
169		{
170		sqr(r[0],r[1],a[0]); if (--n == 0) return;
171		sqr(r[2],r[3],a[1]); if (--n == 0) return;
172		sqr(r[4],r[5],a[2]);
173		}
174	}
175
176BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
177{	BN_ULONG ret,waste;
178
179	asm ("divq	%4"
180		: "=a"(ret),"=d"(waste)
181		: "a"(l),"d"(h),"g"(d)
182		: "cc");
183
184	return ret;
185}
186
187BN_ULONG bn_add_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
188{ BN_ULONG ret=0,i=0;
189
190	if (n <= 0) return 0;
191
192	asm volatile (
193	"	subq	%2,%2		\n"
194	".p2align 4			\n"
195	"1:	movq	(%4,%2,8),%0	\n"
196	"	adcq	(%5,%2,8),%0	\n"
197	"	movq	%0,(%3,%2,8)	\n"
198	"	leaq	1(%2),%2	\n"
199	"	loop	1b		\n"
200	"	sbbq	%0,%0		\n"
201		: "=&a"(ret),"+c"(n),"=&r"(i)
202		: "r"(rp),"r"(ap),"r"(bp)
203		: "cc", "memory"
204	);
205
206  return ret&1;
207}
208
209#ifndef SIMICS
210BN_ULONG bn_sub_words (BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,int n)
211{ BN_ULONG ret=0,i=0;
212
213	if (n <= 0) return 0;
214
215	asm volatile (
216	"	subq	%2,%2		\n"
217	".p2align 4			\n"
218	"1:	movq	(%4,%2,8),%0	\n"
219	"	sbbq	(%5,%2,8),%0	\n"
220	"	movq	%0,(%3,%2,8)	\n"
221	"	leaq	1(%2),%2	\n"
222	"	loop	1b		\n"
223	"	sbbq	%0,%0		\n"
224		: "=&a"(ret),"+c"(n),"=&r"(i)
225		: "r"(rp),"r"(ap),"r"(bp)
226		: "cc", "memory"
227	);
228
229  return ret&1;
230}
231#else
232/* Simics 1.4<7 has buggy sbbq:-( */
233#define BN_MASK2 0xffffffffffffffffL
234BN_ULONG bn_sub_words(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
235        {
236	BN_ULONG t1,t2;
237	int c=0;
238
239	if (n <= 0) return((BN_ULONG)0);
240
241	for (;;)
242		{
243		t1=a[0]; t2=b[0];
244		r[0]=(t1-t2-c)&BN_MASK2;
245		if (t1 != t2) c=(t1 < t2);
246		if (--n <= 0) break;
247
248		t1=a[1]; t2=b[1];
249		r[1]=(t1-t2-c)&BN_MASK2;
250		if (t1 != t2) c=(t1 < t2);
251		if (--n <= 0) break;
252
253		t1=a[2]; t2=b[2];
254		r[2]=(t1-t2-c)&BN_MASK2;
255		if (t1 != t2) c=(t1 < t2);
256		if (--n <= 0) break;
257
258		t1=a[3]; t2=b[3];
259		r[3]=(t1-t2-c)&BN_MASK2;
260		if (t1 != t2) c=(t1 < t2);
261		if (--n <= 0) break;
262
263		a+=4;
264		b+=4;
265		r+=4;
266		}
267	return(c);
268	}
269#endif
270
271/* mul_add_c(a,b,c0,c1,c2)  -- c+=a*b for three word number c=(c2,c1,c0) */
272/* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
273/* sqr_add_c(a,i,c0,c1,c2)  -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
274/* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
275
276/*
277 * Keep in mind that carrying into high part of multiplication result
278 * can not overflow, because it cannot be all-ones.
279 */
280#if 0
281/* original macros are kept for reference purposes */
282#define mul_add_c(a,b,c0,c1,c2) {	\
283	BN_ULONG ta=(a),tb=(b);		\
284	t1 = ta * tb;			\
285	t2 = BN_UMULT_HIGH(ta,tb);	\
286	c0 += t1; t2 += (c0<t1)?1:0;	\
287	c1 += t2; c2 += (c1<t2)?1:0;	\
288	}
289
290#define mul_add_c2(a,b,c0,c1,c2) {	\
291	BN_ULONG ta=(a),tb=(b),t0;	\
292	t1 = BN_UMULT_HIGH(ta,tb);	\
293	t0 = ta * tb;			\
294	c0 += t0; t2 = t1+((c0<t0)?1:0);\
295	c1 += t2; c2 += (c1<t2)?1:0;	\
296	c0 += t0; t1 += (c0<t0)?1:0;	\
297	c1 += t1; c2 += (c1<t1)?1:0;	\
298	}
299#else
300#define mul_add_c(a,b,c0,c1,c2)	do {	\
301	asm ("mulq %3"			\
302		: "=a"(t1),"=d"(t2)	\
303		: "a"(a),"m"(b)		\
304		: "cc");		\
305	asm ("addq %2,%0; adcq %3,%1"	\
306		: "+r"(c0),"+d"(t2)	\
307		: "a"(t1),"g"(0)	\
308		: "cc");		\
309	asm ("addq %2,%0; adcq %3,%1"	\
310		: "+r"(c1),"+r"(c2)	\
311		: "d"(t2),"g"(0)	\
312		: "cc");		\
313	} while (0)
314
315#define sqr_add_c(a,i,c0,c1,c2)	do {	\
316	asm ("mulq %2"			\
317		: "=a"(t1),"=d"(t2)	\
318		: "a"(a[i])		\
319		: "cc");		\
320	asm ("addq %2,%0; adcq %3,%1"	\
321		: "+r"(c0),"+d"(t2)	\
322		: "a"(t1),"g"(0)	\
323		: "cc");		\
324	asm ("addq %2,%0; adcq %3,%1"	\
325		: "+r"(c1),"+r"(c2)	\
326		: "d"(t2),"g"(0)	\
327		: "cc");		\
328	} while (0)
329
330#define mul_add_c2(a,b,c0,c1,c2) do {	\
331	asm ("mulq %3"			\
332		: "=a"(t1),"=d"(t2)	\
333		: "a"(a),"m"(b)		\
334		: "cc");		\
335	asm ("addq %3,%0; adcq %4,%1; adcq %5,%2"	\
336		: "+r"(c0),"+r"(c1),"+r"(c2)		\
337		: "r"(t1),"r"(t2),"g"(0)		\
338		: "cc");				\
339	asm ("addq %3,%0; adcq %4,%1; adcq %5,%2"	\
340		: "+r"(c0),"+r"(c1),"+r"(c2)		\
341		: "r"(t1),"r"(t2),"g"(0)		\
342		: "cc");				\
343	} while (0)
344#endif
345
346#define sqr_add_c2(a,i,j,c0,c1,c2)	\
347	mul_add_c2((a)[i],(a)[j],c0,c1,c2)
348
349void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
350	{
351	BN_ULONG t1,t2;
352	BN_ULONG c1,c2,c3;
353
354	c1=0;
355	c2=0;
356	c3=0;
357	mul_add_c(a[0],b[0],c1,c2,c3);
358	r[0]=c1;
359	c1=0;
360	mul_add_c(a[0],b[1],c2,c3,c1);
361	mul_add_c(a[1],b[0],c2,c3,c1);
362	r[1]=c2;
363	c2=0;
364	mul_add_c(a[2],b[0],c3,c1,c2);
365	mul_add_c(a[1],b[1],c3,c1,c2);
366	mul_add_c(a[0],b[2],c3,c1,c2);
367	r[2]=c3;
368	c3=0;
369	mul_add_c(a[0],b[3],c1,c2,c3);
370	mul_add_c(a[1],b[2],c1,c2,c3);
371	mul_add_c(a[2],b[1],c1,c2,c3);
372	mul_add_c(a[3],b[0],c1,c2,c3);
373	r[3]=c1;
374	c1=0;
375	mul_add_c(a[4],b[0],c2,c3,c1);
376	mul_add_c(a[3],b[1],c2,c3,c1);
377	mul_add_c(a[2],b[2],c2,c3,c1);
378	mul_add_c(a[1],b[3],c2,c3,c1);
379	mul_add_c(a[0],b[4],c2,c3,c1);
380	r[4]=c2;
381	c2=0;
382	mul_add_c(a[0],b[5],c3,c1,c2);
383	mul_add_c(a[1],b[4],c3,c1,c2);
384	mul_add_c(a[2],b[3],c3,c1,c2);
385	mul_add_c(a[3],b[2],c3,c1,c2);
386	mul_add_c(a[4],b[1],c3,c1,c2);
387	mul_add_c(a[5],b[0],c3,c1,c2);
388	r[5]=c3;
389	c3=0;
390	mul_add_c(a[6],b[0],c1,c2,c3);
391	mul_add_c(a[5],b[1],c1,c2,c3);
392	mul_add_c(a[4],b[2],c1,c2,c3);
393	mul_add_c(a[3],b[3],c1,c2,c3);
394	mul_add_c(a[2],b[4],c1,c2,c3);
395	mul_add_c(a[1],b[5],c1,c2,c3);
396	mul_add_c(a[0],b[6],c1,c2,c3);
397	r[6]=c1;
398	c1=0;
399	mul_add_c(a[0],b[7],c2,c3,c1);
400	mul_add_c(a[1],b[6],c2,c3,c1);
401	mul_add_c(a[2],b[5],c2,c3,c1);
402	mul_add_c(a[3],b[4],c2,c3,c1);
403	mul_add_c(a[4],b[3],c2,c3,c1);
404	mul_add_c(a[5],b[2],c2,c3,c1);
405	mul_add_c(a[6],b[1],c2,c3,c1);
406	mul_add_c(a[7],b[0],c2,c3,c1);
407	r[7]=c2;
408	c2=0;
409	mul_add_c(a[7],b[1],c3,c1,c2);
410	mul_add_c(a[6],b[2],c3,c1,c2);
411	mul_add_c(a[5],b[3],c3,c1,c2);
412	mul_add_c(a[4],b[4],c3,c1,c2);
413	mul_add_c(a[3],b[5],c3,c1,c2);
414	mul_add_c(a[2],b[6],c3,c1,c2);
415	mul_add_c(a[1],b[7],c3,c1,c2);
416	r[8]=c3;
417	c3=0;
418	mul_add_c(a[2],b[7],c1,c2,c3);
419	mul_add_c(a[3],b[6],c1,c2,c3);
420	mul_add_c(a[4],b[5],c1,c2,c3);
421	mul_add_c(a[5],b[4],c1,c2,c3);
422	mul_add_c(a[6],b[3],c1,c2,c3);
423	mul_add_c(a[7],b[2],c1,c2,c3);
424	r[9]=c1;
425	c1=0;
426	mul_add_c(a[7],b[3],c2,c3,c1);
427	mul_add_c(a[6],b[4],c2,c3,c1);
428	mul_add_c(a[5],b[5],c2,c3,c1);
429	mul_add_c(a[4],b[6],c2,c3,c1);
430	mul_add_c(a[3],b[7],c2,c3,c1);
431	r[10]=c2;
432	c2=0;
433	mul_add_c(a[4],b[7],c3,c1,c2);
434	mul_add_c(a[5],b[6],c3,c1,c2);
435	mul_add_c(a[6],b[5],c3,c1,c2);
436	mul_add_c(a[7],b[4],c3,c1,c2);
437	r[11]=c3;
438	c3=0;
439	mul_add_c(a[7],b[5],c1,c2,c3);
440	mul_add_c(a[6],b[6],c1,c2,c3);
441	mul_add_c(a[5],b[7],c1,c2,c3);
442	r[12]=c1;
443	c1=0;
444	mul_add_c(a[6],b[7],c2,c3,c1);
445	mul_add_c(a[7],b[6],c2,c3,c1);
446	r[13]=c2;
447	c2=0;
448	mul_add_c(a[7],b[7],c3,c1,c2);
449	r[14]=c3;
450	r[15]=c1;
451	}
452
453void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
454	{
455	BN_ULONG t1,t2;
456	BN_ULONG c1,c2,c3;
457
458	c1=0;
459	c2=0;
460	c3=0;
461	mul_add_c(a[0],b[0],c1,c2,c3);
462	r[0]=c1;
463	c1=0;
464	mul_add_c(a[0],b[1],c2,c3,c1);
465	mul_add_c(a[1],b[0],c2,c3,c1);
466	r[1]=c2;
467	c2=0;
468	mul_add_c(a[2],b[0],c3,c1,c2);
469	mul_add_c(a[1],b[1],c3,c1,c2);
470	mul_add_c(a[0],b[2],c3,c1,c2);
471	r[2]=c3;
472	c3=0;
473	mul_add_c(a[0],b[3],c1,c2,c3);
474	mul_add_c(a[1],b[2],c1,c2,c3);
475	mul_add_c(a[2],b[1],c1,c2,c3);
476	mul_add_c(a[3],b[0],c1,c2,c3);
477	r[3]=c1;
478	c1=0;
479	mul_add_c(a[3],b[1],c2,c3,c1);
480	mul_add_c(a[2],b[2],c2,c3,c1);
481	mul_add_c(a[1],b[3],c2,c3,c1);
482	r[4]=c2;
483	c2=0;
484	mul_add_c(a[2],b[3],c3,c1,c2);
485	mul_add_c(a[3],b[2],c3,c1,c2);
486	r[5]=c3;
487	c3=0;
488	mul_add_c(a[3],b[3],c1,c2,c3);
489	r[6]=c1;
490	r[7]=c2;
491	}
492
493void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
494	{
495	BN_ULONG t1,t2;
496	BN_ULONG c1,c2,c3;
497
498	c1=0;
499	c2=0;
500	c3=0;
501	sqr_add_c(a,0,c1,c2,c3);
502	r[0]=c1;
503	c1=0;
504	sqr_add_c2(a,1,0,c2,c3,c1);
505	r[1]=c2;
506	c2=0;
507	sqr_add_c(a,1,c3,c1,c2);
508	sqr_add_c2(a,2,0,c3,c1,c2);
509	r[2]=c3;
510	c3=0;
511	sqr_add_c2(a,3,0,c1,c2,c3);
512	sqr_add_c2(a,2,1,c1,c2,c3);
513	r[3]=c1;
514	c1=0;
515	sqr_add_c(a,2,c2,c3,c1);
516	sqr_add_c2(a,3,1,c2,c3,c1);
517	sqr_add_c2(a,4,0,c2,c3,c1);
518	r[4]=c2;
519	c2=0;
520	sqr_add_c2(a,5,0,c3,c1,c2);
521	sqr_add_c2(a,4,1,c3,c1,c2);
522	sqr_add_c2(a,3,2,c3,c1,c2);
523	r[5]=c3;
524	c3=0;
525	sqr_add_c(a,3,c1,c2,c3);
526	sqr_add_c2(a,4,2,c1,c2,c3);
527	sqr_add_c2(a,5,1,c1,c2,c3);
528	sqr_add_c2(a,6,0,c1,c2,c3);
529	r[6]=c1;
530	c1=0;
531	sqr_add_c2(a,7,0,c2,c3,c1);
532	sqr_add_c2(a,6,1,c2,c3,c1);
533	sqr_add_c2(a,5,2,c2,c3,c1);
534	sqr_add_c2(a,4,3,c2,c3,c1);
535	r[7]=c2;
536	c2=0;
537	sqr_add_c(a,4,c3,c1,c2);
538	sqr_add_c2(a,5,3,c3,c1,c2);
539	sqr_add_c2(a,6,2,c3,c1,c2);
540	sqr_add_c2(a,7,1,c3,c1,c2);
541	r[8]=c3;
542	c3=0;
543	sqr_add_c2(a,7,2,c1,c2,c3);
544	sqr_add_c2(a,6,3,c1,c2,c3);
545	sqr_add_c2(a,5,4,c1,c2,c3);
546	r[9]=c1;
547	c1=0;
548	sqr_add_c(a,5,c2,c3,c1);
549	sqr_add_c2(a,6,4,c2,c3,c1);
550	sqr_add_c2(a,7,3,c2,c3,c1);
551	r[10]=c2;
552	c2=0;
553	sqr_add_c2(a,7,4,c3,c1,c2);
554	sqr_add_c2(a,6,5,c3,c1,c2);
555	r[11]=c3;
556	c3=0;
557	sqr_add_c(a,6,c1,c2,c3);
558	sqr_add_c2(a,7,5,c1,c2,c3);
559	r[12]=c1;
560	c1=0;
561	sqr_add_c2(a,7,6,c2,c3,c1);
562	r[13]=c2;
563	c2=0;
564	sqr_add_c(a,7,c3,c1,c2);
565	r[14]=c3;
566	r[15]=c1;
567	}
568
569void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
570	{
571	BN_ULONG t1,t2;
572	BN_ULONG c1,c2,c3;
573
574	c1=0;
575	c2=0;
576	c3=0;
577	sqr_add_c(a,0,c1,c2,c3);
578	r[0]=c1;
579	c1=0;
580	sqr_add_c2(a,1,0,c2,c3,c1);
581	r[1]=c2;
582	c2=0;
583	sqr_add_c(a,1,c3,c1,c2);
584	sqr_add_c2(a,2,0,c3,c1,c2);
585	r[2]=c3;
586	c3=0;
587	sqr_add_c2(a,3,0,c1,c2,c3);
588	sqr_add_c2(a,2,1,c1,c2,c3);
589	r[3]=c1;
590	c1=0;
591	sqr_add_c(a,2,c2,c3,c1);
592	sqr_add_c2(a,3,1,c2,c3,c1);
593	r[4]=c2;
594	c2=0;
595	sqr_add_c2(a,3,2,c3,c1,c2);
596	r[5]=c3;
597	c3=0;
598	sqr_add_c(a,3,c1,c2,c3);
599	r[6]=c1;
600	r[7]=c2;
601	}
602#endif
603