x86_64-gcc.c
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1 /* x86_64 BIGNUM accelerator version 0.1, December 2002.
2  *
3  * Implemented by Andy Polyakov <appro@fy.chalmers.se> for the OpenSSL
4  * project.
5  *
6  * Rights for redistribution and usage in source and binary forms are
7  * granted according to the OpenSSL license. Warranty of any kind is
8  * disclaimed.
9  *
10  * Q. Version 0.1? It doesn't sound like Andy, he used to assign real
11  * versions, like 1.0...
12  * A. Well, that's because this code is basically a quick-n-dirty
13  * proof-of-concept hack. As you can see it's implemented with
14  * inline assembler, which means that you're bound to GCC and that
15  * there might be enough room for further improvement.
16  *
17  * Q. Why inline assembler?
18  * A. x86_64 features own ABI which I'm not familiar with. This is
19  * why I decided to let the compiler take care of subroutine
20  * prologue/epilogue as well as register allocation. For reference.
21  * Win64 implements different ABI for AMD64, different from Linux.
22  *
23  * Q. How much faster does it get?
24  * A. 'apps/openssl speed rsa dsa' output with no-asm:
25  *
26  * sign verify sign/s verify/s
27  * rsa 512 bits 0.0006s 0.0001s 1683.8 18456.2
28  * rsa 1024 bits 0.0028s 0.0002s 356.0 6407.0
29  * rsa 2048 bits 0.0172s 0.0005s 58.0 1957.8
30  * rsa 4096 bits 0.1155s 0.0018s 8.7 555.6
31  * sign verify sign/s verify/s
32  * dsa 512 bits 0.0005s 0.0006s 2100.8 1768.3
33  * dsa 1024 bits 0.0014s 0.0018s 692.3 559.2
34  * dsa 2048 bits 0.0049s 0.0061s 204.7 165.0
35  *
36  * 'apps/openssl speed rsa dsa' output with this module:
37  *
38  * sign verify sign/s verify/s
39  * rsa 512 bits 0.0004s 0.0000s 2767.1 33297.9
40  * rsa 1024 bits 0.0012s 0.0001s 867.4 14674.7
41  * rsa 2048 bits 0.0061s 0.0002s 164.0 5270.0
42  * rsa 4096 bits 0.0384s 0.0006s 26.1 1650.8
43  * sign verify sign/s verify/s
44  * dsa 512 bits 0.0002s 0.0003s 4442.2 3786.3
45  * dsa 1024 bits 0.0005s 0.0007s 1835.1 1497.4
46  * dsa 2048 bits 0.0016s 0.0020s 620.4 504.6
47  *
48  * For the reference. IA-32 assembler implementation performs
49  * very much like 64-bit code compiled with no-asm on the same
50  * machine.
51  */
52 
53 #include <openssl/bn.h>
54 
55 // TODO(davidben): Get this file working on MSVC x64.
56 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
57  (defined(__GNUC__) || defined(__clang__))
58 
59 #include "../internal.h"
60 
61 
62 #undef mul
63 #undef mul_add
64 
65 // "m"(a), "+m"(r) is the way to favor DirectPath ยต-code;
66 // "g"(0) let the compiler to decide where does it
67 // want to keep the value of zero;
68 #define mul_add(r, a, word, carry) \
69  do { \
70  register BN_ULONG high, low; \
71  __asm__("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "m"(a) : "cc"); \
72  __asm__("addq %2,%0; adcq %3,%1" \
73  : "+r"(carry), "+d"(high) \
74  : "a"(low), "g"(0) \
75  : "cc"); \
76  __asm__("addq %2,%0; adcq %3,%1" \
77  : "+m"(r), "+d"(high) \
78  : "r"(carry), "g"(0) \
79  : "cc"); \
80  (carry) = high; \
81  } while (0)
82 
83 #define mul(r, a, word, carry) \
84  do { \
85  register BN_ULONG high, low; \
86  __asm__("mulq %3" : "=a"(low), "=d"(high) : "a"(word), "g"(a) : "cc"); \
87  __asm__("addq %2,%0; adcq %3,%1" \
88  : "+r"(carry), "+d"(high) \
89  : "a"(low), "g"(0) \
90  : "cc"); \
91  (r) = (carry); \
92  (carry) = high; \
93  } while (0)
94 #undef sqr
95 #define sqr(r0, r1, a) __asm__("mulq %2" : "=a"(r0), "=d"(r1) : "a"(a) : "cc");
96 
97 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
98  BN_ULONG w) {
99  BN_ULONG c1 = 0;
100 
101  if (num == 0) {
102  return (c1);
103  }
104 
105  while (num & ~3) {
106  mul_add(rp[0], ap[0], w, c1);
107  mul_add(rp[1], ap[1], w, c1);
108  mul_add(rp[2], ap[2], w, c1);
109  mul_add(rp[3], ap[3], w, c1);
110  ap += 4;
111  rp += 4;
112  num -= 4;
113  }
114  if (num) {
115  mul_add(rp[0], ap[0], w, c1);
116  if (--num == 0) {
117  return c1;
118  }
119  mul_add(rp[1], ap[1], w, c1);
120  if (--num == 0) {
121  return c1;
122  }
123  mul_add(rp[2], ap[2], w, c1);
124  return c1;
125  }
126 
127  return c1;
128 }
129 
130 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, size_t num,
131  BN_ULONG w) {
132  BN_ULONG c1 = 0;
133 
134  if (num == 0) {
135  return c1;
136  }
137 
138  while (num & ~3) {
139  mul(rp[0], ap[0], w, c1);
140  mul(rp[1], ap[1], w, c1);
141  mul(rp[2], ap[2], w, c1);
142  mul(rp[3], ap[3], w, c1);
143  ap += 4;
144  rp += 4;
145  num -= 4;
146  }
147  if (num) {
148  mul(rp[0], ap[0], w, c1);
149  if (--num == 0) {
150  return c1;
151  }
152  mul(rp[1], ap[1], w, c1);
153  if (--num == 0) {
154  return c1;
155  }
156  mul(rp[2], ap[2], w, c1);
157  }
158  return c1;
159 }
160 
161 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, size_t n) {
162  if (n == 0) {
163  return;
164  }
165 
166  while (n & ~3) {
167  sqr(r[0], r[1], a[0]);
168  sqr(r[2], r[3], a[1]);
169  sqr(r[4], r[5], a[2]);
170  sqr(r[6], r[7], a[3]);
171  a += 4;
172  r += 8;
173  n -= 4;
174  }
175  if (n) {
176  sqr(r[0], r[1], a[0]);
177  if (--n == 0) {
178  return;
179  }
180  sqr(r[2], r[3], a[1]);
181  if (--n == 0) {
182  return;
183  }
184  sqr(r[4], r[5], a[2]);
185  }
186 }
187 
188 BN_ULONG bn_add_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
189  size_t n) {
190  BN_ULONG ret;
191  size_t i = 0;
192 
193  if (n == 0) {
194  return 0;
195  }
196 
197  __asm__ volatile (
198  " subq %0,%0 \n" // clear carry
199  " jmp 1f \n"
200  ".p2align 4 \n"
201  "1:"
202  " movq (%4,%2,8),%0 \n"
203  " adcq (%5,%2,8),%0 \n"
204  " movq %0,(%3,%2,8) \n"
205  " lea 1(%2),%2 \n"
206  " dec %1 \n"
207  " jnz 1b \n"
208  " sbbq %0,%0 \n"
209  : "=&r"(ret), "+c"(n), "+r"(i)
210  : "r"(rp), "r"(ap), "r"(bp)
211  : "cc", "memory");
212 
213  return ret & 1;
214 }
215 
216 BN_ULONG bn_sub_words(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
217  size_t n) {
218  BN_ULONG ret;
219  size_t i = 0;
220 
221  if (n == 0) {
222  return 0;
223  }
224 
225  __asm__ volatile (
226  " subq %0,%0 \n" // clear borrow
227  " jmp 1f \n"
228  ".p2align 4 \n"
229  "1:"
230  " movq (%4,%2,8),%0 \n"
231  " sbbq (%5,%2,8),%0 \n"
232  " movq %0,(%3,%2,8) \n"
233  " lea 1(%2),%2 \n"
234  " dec %1 \n"
235  " jnz 1b \n"
236  " sbbq %0,%0 \n"
237  : "=&r"(ret), "+c"(n), "+r"(i)
238  : "r"(rp), "r"(ap), "r"(bp)
239  : "cc", "memory");
240 
241  return ret & 1;
242 }
243 
244 // mul_add_c(a,b,c0,c1,c2) -- c+=a*b for three word number c=(c2,c1,c0)
245 // mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0)
246 // sqr_add_c(a,i,c0,c1,c2) -- c+=a[i]^2 for three word number c=(c2,c1,c0)
247 // sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0)
248 
249 // Keep in mind that carrying into high part of multiplication result can not
250 // overflow, because it cannot be all-ones.
251 #define mul_add_c(a, b, c0, c1, c2) \
252  do { \
253  BN_ULONG t1, t2; \
254  __asm__("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \
255  __asm__("addq %3,%0; adcq %4,%1; adcq %5,%2" \
256  : "+r"(c0), "+r"(c1), "+r"(c2) \
257  : "r"(t1), "r"(t2), "g"(0) \
258  : "cc"); \
259  } while (0)
260 
261 #define sqr_add_c(a, i, c0, c1, c2) \
262  do { \
263  BN_ULONG t1, t2; \
264  __asm__("mulq %2" : "=a"(t1), "=d"(t2) : "a"((a)[i]) : "cc"); \
265  __asm__("addq %3,%0; adcq %4,%1; adcq %5,%2" \
266  : "+r"(c0), "+r"(c1), "+r"(c2) \
267  : "r"(t1), "r"(t2), "g"(0) \
268  : "cc"); \
269  } while (0)
270 
271 #define mul_add_c2(a, b, c0, c1, c2) \
272  do { \
273  BN_ULONG t1, t2; \
274  __asm__("mulq %3" : "=a"(t1), "=d"(t2) : "a"(a), "m"(b) : "cc"); \
275  __asm__("addq %3,%0; adcq %4,%1; adcq %5,%2" \
276  : "+r"(c0), "+r"(c1), "+r"(c2) \
277  : "r"(t1), "r"(t2), "g"(0) \
278  : "cc"); \
279  __asm__("addq %3,%0; adcq %4,%1; adcq %5,%2" \
280  : "+r"(c0), "+r"(c1), "+r"(c2) \
281  : "r"(t1), "r"(t2), "g"(0) \
282  : "cc"); \
283  } while (0)
284 
285 #define sqr_add_c2(a, i, j, c0, c1, c2) mul_add_c2((a)[i], (a)[j], c0, c1, c2)
286 
287 void bn_mul_comba8(BN_ULONG r[16], const BN_ULONG a[8], const BN_ULONG b[8]) {
288  BN_ULONG c1, c2, c3;
289 
290  c1 = 0;
291  c2 = 0;
292  c3 = 0;
293  mul_add_c(a[0], b[0], c1, c2, c3);
294  r[0] = c1;
295  c1 = 0;
296  mul_add_c(a[0], b[1], c2, c3, c1);
297  mul_add_c(a[1], b[0], c2, c3, c1);
298  r[1] = c2;
299  c2 = 0;
300  mul_add_c(a[2], b[0], c3, c1, c2);
301  mul_add_c(a[1], b[1], c3, c1, c2);
302  mul_add_c(a[0], b[2], c3, c1, c2);
303  r[2] = c3;
304  c3 = 0;
305  mul_add_c(a[0], b[3], c1, c2, c3);
306  mul_add_c(a[1], b[2], c1, c2, c3);
307  mul_add_c(a[2], b[1], c1, c2, c3);
308  mul_add_c(a[3], b[0], c1, c2, c3);
309  r[3] = c1;
310  c1 = 0;
311  mul_add_c(a[4], b[0], c2, c3, c1);
312  mul_add_c(a[3], b[1], c2, c3, c1);
313  mul_add_c(a[2], b[2], c2, c3, c1);
314  mul_add_c(a[1], b[3], c2, c3, c1);
315  mul_add_c(a[0], b[4], c2, c3, c1);
316  r[4] = c2;
317  c2 = 0;
318  mul_add_c(a[0], b[5], c3, c1, c2);
319  mul_add_c(a[1], b[4], c3, c1, c2);
320  mul_add_c(a[2], b[3], c3, c1, c2);
321  mul_add_c(a[3], b[2], c3, c1, c2);
322  mul_add_c(a[4], b[1], c3, c1, c2);
323  mul_add_c(a[5], b[0], c3, c1, c2);
324  r[5] = c3;
325  c3 = 0;
326  mul_add_c(a[6], b[0], c1, c2, c3);
327  mul_add_c(a[5], b[1], c1, c2, c3);
328  mul_add_c(a[4], b[2], c1, c2, c3);
329  mul_add_c(a[3], b[3], c1, c2, c3);
330  mul_add_c(a[2], b[4], c1, c2, c3);
331  mul_add_c(a[1], b[5], c1, c2, c3);
332  mul_add_c(a[0], b[6], c1, c2, c3);
333  r[6] = c1;
334  c1 = 0;
335  mul_add_c(a[0], b[7], c2, c3, c1);
336  mul_add_c(a[1], b[6], c2, c3, c1);
337  mul_add_c(a[2], b[5], c2, c3, c1);
338  mul_add_c(a[3], b[4], c2, c3, c1);
339  mul_add_c(a[4], b[3], c2, c3, c1);
340  mul_add_c(a[5], b[2], c2, c3, c1);
341  mul_add_c(a[6], b[1], c2, c3, c1);
342  mul_add_c(a[7], b[0], c2, c3, c1);
343  r[7] = c2;
344  c2 = 0;
345  mul_add_c(a[7], b[1], c3, c1, c2);
346  mul_add_c(a[6], b[2], c3, c1, c2);
347  mul_add_c(a[5], b[3], c3, c1, c2);
348  mul_add_c(a[4], b[4], c3, c1, c2);
349  mul_add_c(a[3], b[5], c3, c1, c2);
350  mul_add_c(a[2], b[6], c3, c1, c2);
351  mul_add_c(a[1], b[7], c3, c1, c2);
352  r[8] = c3;
353  c3 = 0;
354  mul_add_c(a[2], b[7], c1, c2, c3);
355  mul_add_c(a[3], b[6], c1, c2, c3);
356  mul_add_c(a[4], b[5], c1, c2, c3);
357  mul_add_c(a[5], b[4], c1, c2, c3);
358  mul_add_c(a[6], b[3], c1, c2, c3);
359  mul_add_c(a[7], b[2], c1, c2, c3);
360  r[9] = c1;
361  c1 = 0;
362  mul_add_c(a[7], b[3], c2, c3, c1);
363  mul_add_c(a[6], b[4], c2, c3, c1);
364  mul_add_c(a[5], b[5], c2, c3, c1);
365  mul_add_c(a[4], b[6], c2, c3, c1);
366  mul_add_c(a[3], b[7], c2, c3, c1);
367  r[10] = c2;
368  c2 = 0;
369  mul_add_c(a[4], b[7], c3, c1, c2);
370  mul_add_c(a[5], b[6], c3, c1, c2);
371  mul_add_c(a[6], b[5], c3, c1, c2);
372  mul_add_c(a[7], b[4], c3, c1, c2);
373  r[11] = c3;
374  c3 = 0;
375  mul_add_c(a[7], b[5], c1, c2, c3);
376  mul_add_c(a[6], b[6], c1, c2, c3);
377  mul_add_c(a[5], b[7], c1, c2, c3);
378  r[12] = c1;
379  c1 = 0;
380  mul_add_c(a[6], b[7], c2, c3, c1);
381  mul_add_c(a[7], b[6], c2, c3, c1);
382  r[13] = c2;
383  c2 = 0;
384  mul_add_c(a[7], b[7], c3, c1, c2);
385  r[14] = c3;
386  r[15] = c1;
387 }
388 
389 void bn_mul_comba4(BN_ULONG r[8], const BN_ULONG a[4], const BN_ULONG b[4]) {
390  BN_ULONG c1, c2, c3;
391 
392  c1 = 0;
393  c2 = 0;
394  c3 = 0;
395  mul_add_c(a[0], b[0], c1, c2, c3);
396  r[0] = c1;
397  c1 = 0;
398  mul_add_c(a[0], b[1], c2, c3, c1);
399  mul_add_c(a[1], b[0], c2, c3, c1);
400  r[1] = c2;
401  c2 = 0;
402  mul_add_c(a[2], b[0], c3, c1, c2);
403  mul_add_c(a[1], b[1], c3, c1, c2);
404  mul_add_c(a[0], b[2], c3, c1, c2);
405  r[2] = c3;
406  c3 = 0;
407  mul_add_c(a[0], b[3], c1, c2, c3);
408  mul_add_c(a[1], b[2], c1, c2, c3);
409  mul_add_c(a[2], b[1], c1, c2, c3);
410  mul_add_c(a[3], b[0], c1, c2, c3);
411  r[3] = c1;
412  c1 = 0;
413  mul_add_c(a[3], b[1], c2, c3, c1);
414  mul_add_c(a[2], b[2], c2, c3, c1);
415  mul_add_c(a[1], b[3], c2, c3, c1);
416  r[4] = c2;
417  c2 = 0;
418  mul_add_c(a[2], b[3], c3, c1, c2);
419  mul_add_c(a[3], b[2], c3, c1, c2);
420  r[5] = c3;
421  c3 = 0;
422  mul_add_c(a[3], b[3], c1, c2, c3);
423  r[6] = c1;
424  r[7] = c2;
425 }
426 
427 void bn_sqr_comba8(BN_ULONG r[16], const BN_ULONG a[8]) {
428  BN_ULONG c1, c2, c3;
429 
430  c1 = 0;
431  c2 = 0;
432  c3 = 0;
433  sqr_add_c(a, 0, c1, c2, c3);
434  r[0] = c1;
435  c1 = 0;
436  sqr_add_c2(a, 1, 0, c2, c3, c1);
437  r[1] = c2;
438  c2 = 0;
439  sqr_add_c(a, 1, c3, c1, c2);
440  sqr_add_c2(a, 2, 0, c3, c1, c2);
441  r[2] = c3;
442  c3 = 0;
443  sqr_add_c2(a, 3, 0, c1, c2, c3);
444  sqr_add_c2(a, 2, 1, c1, c2, c3);
445  r[3] = c1;
446  c1 = 0;
447  sqr_add_c(a, 2, c2, c3, c1);
448  sqr_add_c2(a, 3, 1, c2, c3, c1);
449  sqr_add_c2(a, 4, 0, c2, c3, c1);
450  r[4] = c2;
451  c2 = 0;
452  sqr_add_c2(a, 5, 0, c3, c1, c2);
453  sqr_add_c2(a, 4, 1, c3, c1, c2);
454  sqr_add_c2(a, 3, 2, c3, c1, c2);
455  r[5] = c3;
456  c3 = 0;
457  sqr_add_c(a, 3, c1, c2, c3);
458  sqr_add_c2(a, 4, 2, c1, c2, c3);
459  sqr_add_c2(a, 5, 1, c1, c2, c3);
460  sqr_add_c2(a, 6, 0, c1, c2, c3);
461  r[6] = c1;
462  c1 = 0;
463  sqr_add_c2(a, 7, 0, c2, c3, c1);
464  sqr_add_c2(a, 6, 1, c2, c3, c1);
465  sqr_add_c2(a, 5, 2, c2, c3, c1);
466  sqr_add_c2(a, 4, 3, c2, c3, c1);
467  r[7] = c2;
468  c2 = 0;
469  sqr_add_c(a, 4, c3, c1, c2);
470  sqr_add_c2(a, 5, 3, c3, c1, c2);
471  sqr_add_c2(a, 6, 2, c3, c1, c2);
472  sqr_add_c2(a, 7, 1, c3, c1, c2);
473  r[8] = c3;
474  c3 = 0;
475  sqr_add_c2(a, 7, 2, c1, c2, c3);
476  sqr_add_c2(a, 6, 3, c1, c2, c3);
477  sqr_add_c2(a, 5, 4, c1, c2, c3);
478  r[9] = c1;
479  c1 = 0;
480  sqr_add_c(a, 5, c2, c3, c1);
481  sqr_add_c2(a, 6, 4, c2, c3, c1);
482  sqr_add_c2(a, 7, 3, c2, c3, c1);
483  r[10] = c2;
484  c2 = 0;
485  sqr_add_c2(a, 7, 4, c3, c1, c2);
486  sqr_add_c2(a, 6, 5, c3, c1, c2);
487  r[11] = c3;
488  c3 = 0;
489  sqr_add_c(a, 6, c1, c2, c3);
490  sqr_add_c2(a, 7, 5, c1, c2, c3);
491  r[12] = c1;
492  c1 = 0;
493  sqr_add_c2(a, 7, 6, c2, c3, c1);
494  r[13] = c2;
495  c2 = 0;
496  sqr_add_c(a, 7, c3, c1, c2);
497  r[14] = c3;
498  r[15] = c1;
499 }
500 
501 void bn_sqr_comba4(BN_ULONG r[8], const BN_ULONG a[4]) {
502  BN_ULONG c1, c2, c3;
503 
504  c1 = 0;
505  c2 = 0;
506  c3 = 0;
507  sqr_add_c(a, 0, c1, c2, c3);
508  r[0] = c1;
509  c1 = 0;
510  sqr_add_c2(a, 1, 0, c2, c3, c1);
511  r[1] = c2;
512  c2 = 0;
513  sqr_add_c(a, 1, c3, c1, c2);
514  sqr_add_c2(a, 2, 0, c3, c1, c2);
515  r[2] = c3;
516  c3 = 0;
517  sqr_add_c2(a, 3, 0, c1, c2, c3);
518  sqr_add_c2(a, 2, 1, c1, c2, c3);
519  r[3] = c1;
520  c1 = 0;
521  sqr_add_c(a, 2, c2, c3, c1);
522  sqr_add_c2(a, 3, 1, c2, c3, c1);
523  r[4] = c2;
524  c2 = 0;
525  sqr_add_c2(a, 3, 2, c3, c1, c2);
526  r[5] = c3;
527  c3 = 0;
528  sqr_add_c(a, 3, c1, c2, c3);
529  r[6] = c1;
530  r[7] = c2;
531 }
532 
533 #undef mul_add
534 #undef mul
535 #undef sqr
536 #undef mul_add_c
537 #undef sqr_add_c
538 #undef mul_add_c2
539 #undef sqr_add_c2
540 
541 #endif // !NO_ASM && X86_64 && (__GNUC__ || __clang__)
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autogenerated on Fri May 16 2025 03:00:56