crypto/bn/bn_asm.c

   1 /* crypto/bn/bn_asm.c */
   2 /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
   3  * All rights reserved.
   4  *
   5  * This package is an SSL implementation written
   6  * by Eric Young (eay@cryptsoft.com).
   7  * The implementation was written so as to conform with Netscapes SSL.
   8  *
   9  * This library is free for commercial and non-commercial use as long as
  10  * the following conditions are aheared to.  The following conditions
  11  * apply to all code found in this distribution, be it the RC4, RSA,
  12  * lhash, DES, etc., code; not just the SSL code.  The SSL documentation
  13  * included with this distribution is covered by the same copyright terms
  14  * except that the holder is Tim Hudson (tjh@cryptsoft.com).
  15  *
  16  * Copyright remains Eric Young's, and as such any Copyright notices in
  17  * the code are not to be removed.
  18  * If this package is used in a product, Eric Young should be given attribution
  19  * as the author of the parts of the library used.
  20  * This can be in the form of a textual message at program startup or
  21  * in documentation (online or textual) provided with the package.
  22  *
  23  * Redistribution and use in source and binary forms, with or without
  24  * modification, are permitted provided that the following conditions
  25  * are met:
  26  * 1. Redistributions of source code must retain the copyright
  27  *    notice, this list of conditions and the following disclaimer.
  28  * 2. Redistributions in binary form must reproduce the above copyright
  29  *    notice, this list of conditions and the following disclaimer in the
  30  *    documentation and/or other materials provided with the distribution.
  31  * 3. All advertising materials mentioning features or use of this software
  32  *    must display the following acknowledgement:
  33  *    "This product includes cryptographic software written by
  34  *     Eric Young (eay@cryptsoft.com)"
  35  *    The word 'cryptographic' can be left out if the rouines from the library
  36  *    being used are not cryptographic related :-).
  37  * 4. If you include any Windows specific code (or a derivative thereof) from
  38  *    the apps directory (application code) you must include an acknowledgement:
  39  *    "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
  40  *
  41  * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
  42  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  43  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  44  * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
  45  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  46  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  47  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  48  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  49  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  50  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  51  * SUCH DAMAGE.
  52  *
  53  * The licence and distribution terms for any publically available version or
  54  * derivative of this code cannot be changed.  i.e. this code cannot simply be
  55  * copied and put under another distribution licence
  56  * [including the GNU Public Licence.]
  57  */
  58
  59 #ifndef BN_DEBUG
  60 # undef NDEBUG /* avoid conflicting definitions */
  61 # define NDEBUG
  62 #endif
  63
  64 #include <stdio.h>
  65 #include <assert.h>
  66 #include "cryptlib.h"
  67 #include "bn_lcl.h"
  68
  69 #if defined(BN_LLONG) || defined(BN_UMULT_HIGH)
  70
  71 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
  72         {
  73         BN_ULONG c1=0;
  74
  75         assert(num >= 0);
  76         if (num <= 0) return(c1);
  77
  78 #ifndef OPENSSL_SMALL_FOOTPRINT
  79         while (num&~3)
  80                 {
  81                 mul_add(rp[0],ap[0],w,c1);
  82                 mul_add(rp[1],ap[1],w,c1);
  83                 mul_add(rp[2],ap[2],w,c1);
  84                 mul_add(rp[3],ap[3],w,c1);
  85                 ap+=4; rp+=4; num-=4;
  86                 }
  87 #endif
  88         while (num)
  89                 {
  90                 mul_add(rp[0],ap[0],w,c1);
  91                 ap++; rp++; num--;
  92                 }
  93
  94         return(c1);
  95         }
  96
  97 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
  98         {
  99         BN_ULONG c1=0;
 100
 101         assert(num >= 0);
 102         if (num <= 0) return(c1);
 103
 104 #ifndef OPENSSL_SMALL_FOOTPRINT
 105         while (num&~3)
 106                 {
 107                 mul(rp[0],ap[0],w,c1);
 108                 mul(rp[1],ap[1],w,c1);
 109                 mul(rp[2],ap[2],w,c1);
 110                 mul(rp[3],ap[3],w,c1);
 111                 ap+=4; rp+=4; num-=4;
 112                 }
 113 #endif
 114         while (num)
 115                 {
 116                 mul(rp[0],ap[0],w,c1);
 117                 ap++; rp++; num--;
 118                 }
 119         return(c1);
 120         }
 121
 122 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
 123         {
 124         assert(n >= 0);
 125         if (n <= 0) return;
 126
 127 #ifndef OPENSSL_SMALL_FOOTPRINT
 128         while (n&~3)
 129                 {
 130                 sqr(r[0],r[1],a[0]);
 131                 sqr(r[2],r[3],a[1]);
 132                 sqr(r[4],r[5],a[2]);
 133                 sqr(r[6],r[7],a[3]);
 134                 a+=4; r+=8; n-=4;
 135                 }
 136 #endif
 137         while (n)
 138                 {
 139                 sqr(r[0],r[1],a[0]);
 140                 a++; r+=2; n--;
 141                 }
 142         }
 143
 144 #else /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */
 145
 146 BN_ULONG bn_mul_add_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
 147         {
 148         BN_ULONG c=0;
 149         BN_ULONG bl,bh;
 150
 151         assert(num >= 0);
 152         if (num <= 0) return((BN_ULONG)0);
 153
 154         bl=LBITS(w);
 155         bh=HBITS(w);
 156
 157 #ifndef OPENSSL_SMALL_FOOTPRINT
 158         while (num&~3)
 159                 {
 160                 mul_add(rp[0],ap[0],bl,bh,c);
 161                 mul_add(rp[1],ap[1],bl,bh,c);
 162                 mul_add(rp[2],ap[2],bl,bh,c);
 163                 mul_add(rp[3],ap[3],bl,bh,c);
 164                 ap+=4; rp+=4; num-=4;
 165                 }
 166 #endif
 167         while (num)
 168                 {
 169                 mul_add(rp[0],ap[0],bl,bh,c);
 170                 ap++; rp++; num--;
 171                 }
 172         return(c);
 173         }
 174
 175 BN_ULONG bn_mul_words(BN_ULONG *rp, const BN_ULONG *ap, int num, BN_ULONG w)
 176         {
 177         BN_ULONG carry=0;
 178         BN_ULONG bl,bh;
 179
 180         assert(num >= 0);
 181         if (num <= 0) return((BN_ULONG)0);
 182
 183         bl=LBITS(w);
 184         bh=HBITS(w);
 185
 186 #ifndef OPENSSL_SMALL_FOOTPRINT
 187         while (num&~3)
 188                 {
 189                 mul(rp[0],ap[0],bl,bh,carry);
 190                 mul(rp[1],ap[1],bl,bh,carry);
 191                 mul(rp[2],ap[2],bl,bh,carry);
 192                 mul(rp[3],ap[3],bl,bh,carry);
 193                 ap+=4; rp+=4; num-=4;
 194                 }
 195 #endif
 196         while (num)
 197                 {
 198                 mul(rp[0],ap[0],bl,bh,carry);
 199                 ap++; rp++; num--;
 200                 }
 201         return(carry);
 202         }
 203
 204 void bn_sqr_words(BN_ULONG *r, const BN_ULONG *a, int n)
 205         {
 206         assert(n >= 0);
 207         if (n <= 0) return;
 208
 209 #ifndef OPENSSL_SMALL_FOOTPRINT
 210         while (n&~3)
 211                 {
 212                 sqr64(r[0],r[1],a[0]);
 213                 sqr64(r[2],r[3],a[1]);
 214                 sqr64(r[4],r[5],a[2]);
 215                 sqr64(r[6],r[7],a[3]);
 216                 a+=4; r+=8; n-=4;
 217                 }
 218 #endif
 219         while (n)
 220                 {
 221                 sqr64(r[0],r[1],a[0]);
 222                 a++; r+=2; n--;
 223                 }
 224         }
 225
 226 #endif /* !(defined(BN_LLONG) || defined(BN_UMULT_HIGH)) */
 227
 228 #if defined(BN_LLONG) && defined(BN_DIV2W)
 229
 230 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
 231         {
 232         return((BN_ULONG)(((((BN_ULLONG)h)<<BN_BITS2)|l)/(BN_ULLONG)d));
 233         }
 234
 235 #else
 236
 237 /* Divide h,l by d and return the result. */
 238 /* I need to test this some more :-( */
 239 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d)
 240         {
 241         BN_ULONG dh,dl,q,ret=0,th,tl,t;
 242         int i,count=2;
 243
 244         if (d == 0) return(BN_MASK2);
 245
 246         i=BN_num_bits_word(d);
 247         assert((i == BN_BITS2) || (h <= (BN_ULONG)1<<i));
 248
 249         i=BN_BITS2-i;
 250         if (h >= d) h-=d;
 251
 252         if (i)
 253                 {
 254                 d<<=i;
 255                 h=(h<<i)|(l>>(BN_BITS2-i));
 256                 l<<=i;
 257                 }
 258         dh=(d&BN_MASK2h)>>BN_BITS4;
 259         dl=(d&BN_MASK2l);
 260         for (;;)
 261                 {
 262                 if ((h>>BN_BITS4) == dh)
 263                         q=BN_MASK2l;
 264                 else
 265                         q=h/dh;
 266
 267                 th=q*dh;
 268                 tl=dl*q;
 269                 for (;;)
 270                         {
 271                         t=h-th;
 272                         if ((t&BN_MASK2h) ||
 273                                 ((tl) <= (
 274                                         (t<<BN_BITS4)|
 275                                         ((l&BN_MASK2h)>>BN_BITS4))))
 276                                 break;
 277                         q--;
 278                         th-=dh;
 279                         tl-=dl;
 280                         }
 281                 t=(tl>>BN_BITS4);
 282                 tl=(tl<<BN_BITS4)&BN_MASK2h;
 283                 th+=t;
 284
 285                 if (l < tl) th++;
 286                 l-=tl;
 287                 if (h < th)
 288                         {
 289                         h+=d;
 290                         q--;
 291                         }
 292                 h-=th;
 293
 294                 if (--count == 0) break;
 295
 296                 ret=q<<BN_BITS4;
 297                 h=((h<<BN_BITS4)|(l>>BN_BITS4))&BN_MASK2;
 298                 l=(l&BN_MASK2l)<<BN_BITS4;
 299                 }
 300         ret|=q;
 301         return(ret);
 302         }
 303 #endif /* !defined(BN_LLONG) && defined(BN_DIV2W) */
 304
 305 #ifdef BN_LLONG
 306 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
 307         {
 308         BN_ULLONG ll=0;
 309
 310         assert(n >= 0);
 311         if (n <= 0) return((BN_ULONG)0);
 312
 313 #ifndef OPENSSL_SMALL_FOOTPRINT
 314         while (n&~3)
 315                 {
 316                 ll+=(BN_ULLONG)a[0]+b[0];
 317                 r[0]=(BN_ULONG)ll&BN_MASK2;
 318                 ll>>=BN_BITS2;
 319                 ll+=(BN_ULLONG)a[1]+b[1];
 320                 r[1]=(BN_ULONG)ll&BN_MASK2;
 321                 ll>>=BN_BITS2;
 322                 ll+=(BN_ULLONG)a[2]+b[2];
 323                 r[2]=(BN_ULONG)ll&BN_MASK2;
 324                 ll>>=BN_BITS2;
 325                 ll+=(BN_ULLONG)a[3]+b[3];
 326                 r[3]=(BN_ULONG)ll&BN_MASK2;
 327                 ll>>=BN_BITS2;
 328                 a+=4; b+=4; r+=4; n-=4;
 329                 }
 330 #endif
 331         while (n)
 332                 {
 333                 ll+=(BN_ULLONG)a[0]+b[0];
 334                 r[0]=(BN_ULONG)ll&BN_MASK2;
 335                 ll>>=BN_BITS2;
 336                 a++; b++; r++; n--;
 337                 }
 338         return((BN_ULONG)ll);
 339         }
 340 #else /* !BN_LLONG */
 341 BN_ULONG bn_add_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
 342         {
 343         BN_ULONG c,l,t;
 344
 345         assert(n >= 0);
 346         if (n <= 0) return((BN_ULONG)0);
 347
 348         c=0;
 349 #ifndef OPENSSL_SMALL_FOOTPRINT
 350         while (n&~3)
 351                 {
 352                 t=a[0];
 353                 t=(t+c)&BN_MASK2;
 354                 c=(t < c);
 355                 l=(t+b[0])&BN_MASK2;
 356                 c+=(l < t);
 357                 r[0]=l;
 358                 t=a[1];
 359                 t=(t+c)&BN_MASK2;
 360                 c=(t < c);
 361                 l=(t+b[1])&BN_MASK2;
 362                 c+=(l < t);
 363                 r[1]=l;
 364                 t=a[2];
 365                 t=(t+c)&BN_MASK2;
 366                 c=(t < c);
 367                 l=(t+b[2])&BN_MASK2;
 368                 c+=(l < t);
 369                 r[2]=l;
 370                 t=a[3];
 371                 t=(t+c)&BN_MASK2;
 372                 c=(t < c);
 373                 l=(t+b[3])&BN_MASK2;
 374                 c+=(l < t);
 375                 r[3]=l;
 376                 a+=4; b+=4; r+=4; n-=4;
 377                 }
 378 #endif
 379         while(n)
 380                 {
 381                 t=a[0];
 382                 t=(t+c)&BN_MASK2;
 383                 c=(t < c);
 384                 l=(t+b[0])&BN_MASK2;
 385                 c+=(l < t);
 386                 r[0]=l;
 387                 a++; b++; r++; n--;
 388                 }
 389         return((BN_ULONG)c);
 390         }
 391 #endif /* !BN_LLONG */
 392
 393 BN_ULONG bn_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int n)
 394         {
 395         BN_ULONG t1,t2;
 396         int c=0;
 397
 398         assert(n >= 0);
 399         if (n <= 0) return((BN_ULONG)0);
 400
 401 #ifndef OPENSSL_SMALL_FOOTPRINT
 402         while (n&~3)
 403                 {
 404                 t1=a[0]; t2=b[0];
 405                 r[0]=(t1-t2-c)&BN_MASK2;
 406                 if (t1 != t2) c=(t1 < t2);
 407                 t1=a[1]; t2=b[1];
 408                 r[1]=(t1-t2-c)&BN_MASK2;
 409                 if (t1 != t2) c=(t1 < t2);
 410                 t1=a[2]; t2=b[2];
 411                 r[2]=(t1-t2-c)&BN_MASK2;
 412                 if (t1 != t2) c=(t1 < t2);
 413                 t1=a[3]; t2=b[3];
 414                 r[3]=(t1-t2-c)&BN_MASK2;
 415                 if (t1 != t2) c=(t1 < t2);
 416                 a+=4; b+=4; r+=4; n-=4;
 417                 }
 418 #endif
 419         while (n)
 420                 {
 421                 t1=a[0]; t2=b[0];
 422                 r[0]=(t1-t2-c)&BN_MASK2;
 423                 if (t1 != t2) c=(t1 < t2);
 424                 a++; b++; r++; n--;
 425                 }
 426         return(c);
 427         }
 428
 429 #if defined(BN_MUL_COMBA) && !defined(OPENSSL_SMALL_FOOTPRINT)
 430
 431 #undef bn_mul_comba8
 432 #undef bn_mul_comba4
 433 #undef bn_sqr_comba8
 434 #undef bn_sqr_comba4
 435
 436 /* mul_add_c(a,b,c0,c1,c2)  -- c+=a*b for three word number c=(c2,c1,c0) */
 437 /* mul_add_c2(a,b,c0,c1,c2) -- c+=2*a*b for three word number c=(c2,c1,c0) */
 438 /* sqr_add_c(a,i,c0,c1,c2)  -- c+=a[i]^2 for three word number c=(c2,c1,c0) */
 439 /* sqr_add_c2(a,i,c0,c1,c2) -- c+=2*a[i]*a[j] for three word number c=(c2,c1,c0) */
 440
 441 #ifdef BN_LLONG
 442 /*
 443  * Keep in mind that additions to multiplication result can not
 444  * overflow, because its high half cannot be all-ones.
 445  */
 446 #define mul_add_c(a,b,c0,c1,c2)         do {    \
 447         BN_ULONG hi;                            \
 448         BN_ULLONG t = (BN_ULLONG)(a)*(b);       \
 449         t += c0;                /* no carry */  \
 450         c0 = (BN_ULONG)Lw(t);                   \
 451         hi = (BN_ULONG)Hw(t);                   \
 452         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 453         } while(0)
 454
 455 #define mul_add_c2(a,b,c0,c1,c2)        do {    \
 456         BN_ULONG hi;                            \
 457         BN_ULLONG t = (BN_ULLONG)(a)*(b);       \
 458         BN_ULLONG tt = t+c0;    /* no carry */  \
 459         c0 = (BN_ULONG)Lw(tt);                  \
 460         hi = (BN_ULONG)Hw(tt);                  \
 461         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 462         t += c0;                /* no carry */  \
 463         c0 = (BN_ULONG)Lw(t);                   \
 464         hi = (BN_ULONG)Hw(t);                   \
 465         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 466         } while(0)
 467
 468 #define sqr_add_c(a,i,c0,c1,c2)         do {    \
 469         BN_ULONG hi;                            \
 470         BN_ULLONG t = (BN_ULLONG)a[i]*a[i];     \
 471         t += c0;                /* no carry */  \
 472         c0 = (BN_ULONG)Lw(t);                   \
 473         hi = (BN_ULONG)Hw(t);                   \
 474         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 475         } while(0)
 476
 477 #define sqr_add_c2(a,i,j,c0,c1,c2) \
 478         mul_add_c2((a)[i],(a)[j],c0,c1,c2)
 479
 480 #elif defined(BN_UMULT_LOHI)
 481 /*
 482  * Keep in mind that additions to hi can not overflow, because
 483  * the high word of a multiplication result cannot be all-ones.
 484  */
 485 #define mul_add_c(a,b,c0,c1,c2)         do {    \
 486         BN_ULONG ta = (a), tb = (b);            \
 487         BN_ULONG lo, hi;                        \
 488         BN_UMULT_LOHI(lo,hi,ta,tb);             \
 489         c0 += lo; hi += (c0<lo)?1:0;            \
 490         c1 += hi; c2 += (c1<hi)?1:0;            \
 491         } while(0)
 492
 493 #define mul_add_c2(a,b,c0,c1,c2)        do {    \
 494         BN_ULONG ta = (a), tb = (b);            \
 495         BN_ULONG lo, hi, tt;                    \
 496         BN_UMULT_LOHI(lo,hi,ta,tb);             \
 497         c0 += lo; tt = hi+((c0<lo)?1:0);        \
 498         c1 += tt; c2 += (c1<tt)?1:0;            \
 499         c0 += lo; hi += (c0<lo)?1:0;            \
 500         c1 += hi; c2 += (c1<hi)?1:0;            \
 501         } while(0)
 502
 503 #define sqr_add_c(a,i,c0,c1,c2)         do {    \
 504         BN_ULONG ta = (a)[i];                   \
 505         BN_ULONG lo, hi;                        \
 506         BN_UMULT_LOHI(lo,hi,ta,ta);             \
 507         c0 += lo; hi += (c0<lo)?1:0;            \
 508         c1 += hi; c2 += (c1<hi)?1:0;            \
 509         } while(0)
 510
 511 #define sqr_add_c2(a,i,j,c0,c1,c2)      \
 512         mul_add_c2((a)[i],(a)[j],c0,c1,c2)
 513
 514 #elif defined(BN_UMULT_HIGH)
 515 /*
 516  * Keep in mind that additions to hi can not overflow, because
 517  * the high word of a multiplication result cannot be all-ones.
 518  */
 519 #define mul_add_c(a,b,c0,c1,c2)         do {    \
 520         BN_ULONG ta = (a), tb = (b);            \
 521         BN_ULONG lo = ta * tb;                  \
 522         BN_ULONG hi = BN_UMULT_HIGH(ta,tb);     \
 523         c0 += lo; hi += (c0<lo)?1:0;            \
 524         c1 += hi; c2 += (c1<hi)?1:0;            \
 525         } while(0)
 526
 527 #define mul_add_c2(a,b,c0,c1,c2)        do {    \
 528         BN_ULONG ta = (a), tb = (b), tt;        \
 529         BN_ULONG lo = ta * tb;                  \
 530         BN_ULONG hi = BN_UMULT_HIGH(ta,tb);     \
 531         c0 += lo; tt = hi + ((c0<lo)?1:0);      \
 532         c1 += tt; c2 += (c1<tt)?1:0;            \
 533         c0 += lo; hi += (c0<lo)?1:0;            \
 534         c1 += hi; c2 += (c1<hi)?1:0;            \
 535         } while(0)
 536
 537 #define sqr_add_c(a,i,c0,c1,c2)         do {    \
 538         BN_ULONG ta = (a)[i];                   \
 539         BN_ULONG lo = ta * ta;                  \
 540         BN_ULONG hi = BN_UMULT_HIGH(ta,ta);     \
 541         c0 += lo; hi += (c0<lo)?1:0;            \
 542         c1 += hi; c2 += (c1<hi)?1:0;            \
 543         } while(0)
 544
 545 #define sqr_add_c2(a,i,j,c0,c1,c2)      \
 546         mul_add_c2((a)[i],(a)[j],c0,c1,c2)
 547
 548 #else /* !BN_LLONG */
 549 /*
 550  * Keep in mind that additions to hi can not overflow, because
 551  * the high word of a multiplication result cannot be all-ones.
 552  */
 553 #define mul_add_c(a,b,c0,c1,c2)         do {    \
 554         BN_ULONG lo = LBITS(a), hi = HBITS(a);  \
 555         BN_ULONG bl = LBITS(b), bh = HBITS(b);  \
 556         mul64(lo,hi,bl,bh);                     \
 557         c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
 558         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 559         } while(0)
 560
 561 #define mul_add_c2(a,b,c0,c1,c2)        do {    \
 562         BN_ULONG tt;                            \
 563         BN_ULONG lo = LBITS(a), hi = HBITS(a);  \
 564         BN_ULONG bl = LBITS(b), bh = HBITS(b);  \
 565         mul64(lo,hi,bl,bh);                     \
 566         tt = hi;                                \
 567         c0 = (c0+lo)&BN_MASK2; if (c0<lo) tt++; \
 568         c1 = (c1+tt)&BN_MASK2; if (c1<tt) c2++; \
 569         c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
 570         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 571         } while(0)
 572
 573 #define sqr_add_c(a,i,c0,c1,c2)         do {    \
 574         BN_ULONG lo, hi;                        \
 575         sqr64(lo,hi,(a)[i]);                    \
 576         c0 = (c0+lo)&BN_MASK2; if (c0<lo) hi++; \
 577         c1 = (c1+hi)&BN_MASK2; if (c1<hi) c2++; \
 578         } while(0)
 579
 580 #define sqr_add_c2(a,i,j,c0,c1,c2) \
 581         mul_add_c2((a)[i],(a)[j],c0,c1,c2)
 582 #endif /* !BN_LLONG */
 583
 584 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
 585         {
 586         BN_ULONG c1,c2,c3;
 587
 588         c1=0;
 589         c2=0;
 590         c3=0;
 591         mul_add_c(a[0],b[0],c1,c2,c3);
 592         r[0]=c1;
 593         c1=0;
 594         mul_add_c(a[0],b[1],c2,c3,c1);
 595         mul_add_c(a[1],b[0],c2,c3,c1);
 596         r[1]=c2;
 597         c2=0;
 598         mul_add_c(a[2],b[0],c3,c1,c2);
 599         mul_add_c(a[1],b[1],c3,c1,c2);
 600         mul_add_c(a[0],b[2],c3,c1,c2);
 601         r[2]=c3;
 602         c3=0;
 603         mul_add_c(a[0],b[3],c1,c2,c3);
 604         mul_add_c(a[1],b[2],c1,c2,c3);
 605         mul_add_c(a[2],b[1],c1,c2,c3);
 606         mul_add_c(a[3],b[0],c1,c2,c3);
 607         r[3]=c1;
 608         c1=0;
 609         mul_add_c(a[4],b[0],c2,c3,c1);
 610         mul_add_c(a[3],b[1],c2,c3,c1);
 611         mul_add_c(a[2],b[2],c2,c3,c1);
 612         mul_add_c(a[1],b[3],c2,c3,c1);
 613         mul_add_c(a[0],b[4],c2,c3,c1);
 614         r[4]=c2;
 615         c2=0;
 616         mul_add_c(a[0],b[5],c3,c1,c2);
 617         mul_add_c(a[1],b[4],c3,c1,c2);
 618         mul_add_c(a[2],b[3],c3,c1,c2);
 619         mul_add_c(a[3],b[2],c3,c1,c2);
 620         mul_add_c(a[4],b[1],c3,c1,c2);
 621         mul_add_c(a[5],b[0],c3,c1,c2);
 622         r[5]=c3;
 623         c3=0;
 624         mul_add_c(a[6],b[0],c1,c2,c3);
 625         mul_add_c(a[5],b[1],c1,c2,c3);
 626         mul_add_c(a[4],b[2],c1,c2,c3);
 627         mul_add_c(a[3],b[3],c1,c2,c3);
 628         mul_add_c(a[2],b[4],c1,c2,c3);
 629         mul_add_c(a[1],b[5],c1,c2,c3);
 630         mul_add_c(a[0],b[6],c1,c2,c3);
 631         r[6]=c1;
 632         c1=0;
 633         mul_add_c(a[0],b[7],c2,c3,c1);
 634         mul_add_c(a[1],b[6],c2,c3,c1);
 635         mul_add_c(a[2],b[5],c2,c3,c1);
 636         mul_add_c(a[3],b[4],c2,c3,c1);
 637         mul_add_c(a[4],b[3],c2,c3,c1);
 638         mul_add_c(a[5],b[2],c2,c3,c1);
 639         mul_add_c(a[6],b[1],c2,c3,c1);
 640         mul_add_c(a[7],b[0],c2,c3,c1);
 641         r[7]=c2;
 642         c2=0;
 643         mul_add_c(a[7],b[1],c3,c1,c2);
 644         mul_add_c(a[6],b[2],c3,c1,c2);
 645         mul_add_c(a[5],b[3],c3,c1,c2);
 646         mul_add_c(a[4],b[4],c3,c1,c2);
 647         mul_add_c(a[3],b[5],c3,c1,c2);
 648         mul_add_c(a[2],b[6],c3,c1,c2);
 649         mul_add_c(a[1],b[7],c3,c1,c2);
 650         r[8]=c3;
 651         c3=0;
 652         mul_add_c(a[2],b[7],c1,c2,c3);
 653         mul_add_c(a[3],b[6],c1,c2,c3);
 654         mul_add_c(a[4],b[5],c1,c2,c3);
 655         mul_add_c(a[5],b[4],c1,c2,c3);
 656         mul_add_c(a[6],b[3],c1,c2,c3);
 657         mul_add_c(a[7],b[2],c1,c2,c3);
 658         r[9]=c1;
 659         c1=0;
 660         mul_add_c(a[7],b[3],c2,c3,c1);
 661         mul_add_c(a[6],b[4],c2,c3,c1);
 662         mul_add_c(a[5],b[5],c2,c3,c1);
 663         mul_add_c(a[4],b[6],c2,c3,c1);
 664         mul_add_c(a[3],b[7],c2,c3,c1);
 665         r[10]=c2;
 666         c2=0;
 667         mul_add_c(a[4],b[7],c3,c1,c2);
 668         mul_add_c(a[5],b[6],c3,c1,c2);
 669         mul_add_c(a[6],b[5],c3,c1,c2);
 670         mul_add_c(a[7],b[4],c3,c1,c2);
 671         r[11]=c3;
 672         c3=0;
 673         mul_add_c(a[7],b[5],c1,c2,c3);
 674         mul_add_c(a[6],b[6],c1,c2,c3);
 675         mul_add_c(a[5],b[7],c1,c2,c3);
 676         r[12]=c1;
 677         c1=0;
 678         mul_add_c(a[6],b[7],c2,c3,c1);
 679         mul_add_c(a[7],b[6],c2,c3,c1);
 680         r[13]=c2;
 681         c2=0;
 682         mul_add_c(a[7],b[7],c3,c1,c2);
 683         r[14]=c3;
 684         r[15]=c1;
 685         }
 686
 687 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
 688         {
 689         BN_ULONG c1,c2,c3;
 690
 691         c1=0;
 692         c2=0;
 693         c3=0;
 694         mul_add_c(a[0],b[0],c1,c2,c3);
 695         r[0]=c1;
 696         c1=0;
 697         mul_add_c(a[0],b[1],c2,c3,c1);
 698         mul_add_c(a[1],b[0],c2,c3,c1);
 699         r[1]=c2;
 700         c2=0;
 701         mul_add_c(a[2],b[0],c3,c1,c2);
 702         mul_add_c(a[1],b[1],c3,c1,c2);
 703         mul_add_c(a[0],b[2],c3,c1,c2);
 704         r[2]=c3;
 705         c3=0;
 706         mul_add_c(a[0],b[3],c1,c2,c3);
 707         mul_add_c(a[1],b[2],c1,c2,c3);
 708         mul_add_c(a[2],b[1],c1,c2,c3);
 709         mul_add_c(a[3],b[0],c1,c2,c3);
 710         r[3]=c1;
 711         c1=0;
 712         mul_add_c(a[3],b[1],c2,c3,c1);
 713         mul_add_c(a[2],b[2],c2,c3,c1);
 714         mul_add_c(a[1],b[3],c2,c3,c1);
 715         r[4]=c2;
 716         c2=0;
 717         mul_add_c(a[2],b[3],c3,c1,c2);
 718         mul_add_c(a[3],b[2],c3,c1,c2);
 719         r[5]=c3;
 720         c3=0;
 721         mul_add_c(a[3],b[3],c1,c2,c3);
 722         r[6]=c1;
 723         r[7]=c2;
 724         }
 725
 726 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
 727         {
 728         BN_ULONG c1,c2,c3;
 729
 730         c1=0;
 731         c2=0;
 732         c3=0;
 733         sqr_add_c(a,0,c1,c2,c3);
 734         r[0]=c1;
 735         c1=0;
 736         sqr_add_c2(a,1,0,c2,c3,c1);
 737         r[1]=c2;
 738         c2=0;
 739         sqr_add_c(a,1,c3,c1,c2);
 740         sqr_add_c2(a,2,0,c3,c1,c2);
 741         r[2]=c3;
 742         c3=0;
 743         sqr_add_c2(a,3,0,c1,c2,c3);
 744         sqr_add_c2(a,2,1,c1,c2,c3);
 745         r[3]=c1;
 746         c1=0;
 747         sqr_add_c(a,2,c2,c3,c1);
 748         sqr_add_c2(a,3,1,c2,c3,c1);
 749         sqr_add_c2(a,4,0,c2,c3,c1);
 750         r[4]=c2;
 751         c2=0;
 752         sqr_add_c2(a,5,0,c3,c1,c2);
 753         sqr_add_c2(a,4,1,c3,c1,c2);
 754         sqr_add_c2(a,3,2,c3,c1,c2);
 755         r[5]=c3;
 756         c3=0;
 757         sqr_add_c(a,3,c1,c2,c3);
 758         sqr_add_c2(a,4,2,c1,c2,c3);
 759         sqr_add_c2(a,5,1,c1,c2,c3);
 760         sqr_add_c2(a,6,0,c1,c2,c3);
 761         r[6]=c1;
 762         c1=0;
 763         sqr_add_c2(a,7,0,c2,c3,c1);
 764         sqr_add_c2(a,6,1,c2,c3,c1);
 765         sqr_add_c2(a,5,2,c2,c3,c1);
 766         sqr_add_c2(a,4,3,c2,c3,c1);
 767         r[7]=c2;
 768         c2=0;
 769         sqr_add_c(a,4,c3,c1,c2);
 770         sqr_add_c2(a,5,3,c3,c1,c2);
 771         sqr_add_c2(a,6,2,c3,c1,c2);
 772         sqr_add_c2(a,7,1,c3,c1,c2);
 773         r[8]=c3;
 774         c3=0;
 775         sqr_add_c2(a,7,2,c1,c2,c3);
 776         sqr_add_c2(a,6,3,c1,c2,c3);
 777         sqr_add_c2(a,5,4,c1,c2,c3);
 778         r[9]=c1;
 779         c1=0;
 780         sqr_add_c(a,5,c2,c3,c1);
 781         sqr_add_c2(a,6,4,c2,c3,c1);
 782         sqr_add_c2(a,7,3,c2,c3,c1);
 783         r[10]=c2;
 784         c2=0;
 785         sqr_add_c2(a,7,4,c3,c1,c2);
 786         sqr_add_c2(a,6,5,c3,c1,c2);
 787         r[11]=c3;
 788         c3=0;
 789         sqr_add_c(a,6,c1,c2,c3);
 790         sqr_add_c2(a,7,5,c1,c2,c3);
 791         r[12]=c1;
 792         c1=0;
 793         sqr_add_c2(a,7,6,c2,c3,c1);
 794         r[13]=c2;
 795         c2=0;
 796         sqr_add_c(a,7,c3,c1,c2);
 797         r[14]=c3;
 798         r[15]=c1;
 799         }
 800
 801 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
 802         {
 803         BN_ULONG c1,c2,c3;
 804
 805         c1=0;
 806         c2=0;
 807         c3=0;
 808         sqr_add_c(a,0,c1,c2,c3);
 809         r[0]=c1;
 810         c1=0;
 811         sqr_add_c2(a,1,0,c2,c3,c1);
 812         r[1]=c2;
 813         c2=0;
 814         sqr_add_c(a,1,c3,c1,c2);
 815         sqr_add_c2(a,2,0,c3,c1,c2);
 816         r[2]=c3;
 817         c3=0;
 818         sqr_add_c2(a,3,0,c1,c2,c3);
 819         sqr_add_c2(a,2,1,c1,c2,c3);
 820         r[3]=c1;
 821         c1=0;
 822         sqr_add_c(a,2,c2,c3,c1);
 823         sqr_add_c2(a,3,1,c2,c3,c1);
 824         r[4]=c2;
 825         c2=0;
 826         sqr_add_c2(a,3,2,c3,c1,c2);
 827         r[5]=c3;
 828         c3=0;
 829         sqr_add_c(a,3,c1,c2,c3);
 830         r[6]=c1;
 831         r[7]=c2;
 832         }
 833
 834 #ifdef OPENSSL_NO_ASM
 835 #ifdef OPENSSL_BN_ASM_MONT
 836 #include <alloca.h>
 837 /*
 838  * This is essentially reference implementation, which may or may not
 839  * result in performance improvement. E.g. on IA-32 this routine was
 840  * observed to give 40% faster rsa1024 private key operations and 10%
 841  * faster rsa4096 ones, while on AMD64 it improves rsa1024 sign only
 842  * by 10% and *worsens* rsa4096 sign by 15%. Once again, it's a
 843  * reference implementation, one to be used as starting point for
 844  * platform-specific assembler. Mentioned numbers apply to compiler
 845  * generated code compiled with and without -DOPENSSL_BN_ASM_MONT and
 846  * can vary not only from platform to platform, but even for compiler
 847  * versions. Assembler vs. assembler improvement coefficients can
 848  * [and are known to] differ and are to be documented elsewhere.
 849  */
 850 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0p, int num)
 851         {
 852         BN_ULONG c0,c1,ml,*tp,n0;
 853 #ifdef mul64
 854         BN_ULONG mh;
 855 #endif
 856         volatile BN_ULONG *vp;
 857         int i=0,j;
 858
 859 #if 0   /* template for platform-specific implementation */
 860         if (ap==bp)     return bn_sqr_mont(rp,ap,np,n0p,num);
 861 #endif
 862         vp = tp = alloca((num+2)*sizeof(BN_ULONG));
 863
 864         n0 = *n0p;
 865
 866         c0 = 0;
 867         ml = bp[0];
 868 #ifdef mul64
 869         mh = HBITS(ml);
 870         ml = LBITS(ml);
 871         for (j=0;j<num;++j)
 872                 mul(tp[j],ap[j],ml,mh,c0);
 873 #else
 874         for (j=0;j<num;++j)
 875                 mul(tp[j],ap[j],ml,c0);
 876 #endif
 877
 878         tp[num]   = c0;
 879         tp[num+1] = 0;
 880         goto enter;
 881
 882         for(i=0;i<num;i++)
 883                 {
 884                 c0 = 0;
 885                 ml = bp[i];
 886 #ifdef mul64
 887                 mh = HBITS(ml);
 888                 ml = LBITS(ml);
 889                 for (j=0;j<num;++j)
 890                         mul_add(tp[j],ap[j],ml,mh,c0);
 891 #else
 892                 for (j=0;j<num;++j)
 893                         mul_add(tp[j],ap[j],ml,c0);
 894 #endif
 895                 c1 = (tp[num] + c0)&BN_MASK2;
 896                 tp[num]   = c1;
 897                 tp[num+1] = (c1<c0?1:0);
 898         enter:
 899                 c1  = tp[0];
 900                 ml = (c1*n0)&BN_MASK2;
 901                 c0 = 0;
 902 #ifdef mul64
 903                 mh = HBITS(ml);
 904                 ml = LBITS(ml);
 905                 mul_add(c1,np[0],ml,mh,c0);
 906 #else
 907                 mul_add(c1,ml,np[0],c0);
 908 #endif
 909                 for(j=1;j<num;j++)
 910                         {
 911                         c1 = tp[j];
 912 #ifdef mul64
 913                         mul_add(c1,np[j],ml,mh,c0);
 914 #else
 915                         mul_add(c1,ml,np[j],c0);
 916 #endif
 917                         tp[j-1] = c1&BN_MASK2;
 918                         }
 919                 c1        = (tp[num] + c0)&BN_MASK2;
 920                 tp[num-1] = c1;
 921                 tp[num]   = tp[num+1] + (c1<c0?1:0);
 922                 }
 923
 924         if (tp[num]!=0 || tp[num-1]>=np[num-1])
 925                 {
 926                 c0 = bn_sub_words(rp,tp,np,num);
 927                 if (tp[num]!=0 || c0==0)
 928                         {
 929                         for(i=0;i<num+2;i++)    vp[i] = 0;
 930                         return 1;
 931                         }
 932                 }
 933         for(i=0;i<num;i++)      rp[i] = tp[i],  vp[i] = 0;
 934         vp[num]   = 0;
 935         vp[num+1] = 0;
 936         return 1;
 937         }
 938 #else
 939 /*
 940  * Return value of 0 indicates that multiplication/convolution was not
 941  * performed to signal the caller to fall down to alternative/original
 942  * code-path.
 943  */
 944 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num)
 945 {       return 0;       }
 946 #endif /* OPENSSL_BN_ASM_MONT */
 947 #endif
 948
 949 #else /* !BN_MUL_COMBA */
 950
 951 /* hmm... is it faster just to do a multiply? */
 952 #undef bn_sqr_comba4
 953 void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a)
 954         {
 955         BN_ULONG t[8];
 956         bn_sqr_normal(r,a,4,t);
 957         }
 958
 959 #undef bn_sqr_comba8
 960 void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a)
 961         {
 962         BN_ULONG t[16];
 963         bn_sqr_normal(r,a,8,t);
 964         }
 965
 966 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
 967         {
 968         r[4]=bn_mul_words(    &(r[0]),a,4,b[0]);
 969         r[5]=bn_mul_add_words(&(r[1]),a,4,b[1]);
 970         r[6]=bn_mul_add_words(&(r[2]),a,4,b[2]);
 971         r[7]=bn_mul_add_words(&(r[3]),a,4,b[3]);
 972         }
 973
 974 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b)
 975         {
 976         r[ 8]=bn_mul_words(    &(r[0]),a,8,b[0]);
 977         r[ 9]=bn_mul_add_words(&(r[1]),a,8,b[1]);
 978         r[10]=bn_mul_add_words(&(r[2]),a,8,b[2]);
 979         r[11]=bn_mul_add_words(&(r[3]),a,8,b[3]);
 980         r[12]=bn_mul_add_words(&(r[4]),a,8,b[4]);
 981         r[13]=bn_mul_add_words(&(r[5]),a,8,b[5]);
 982         r[14]=bn_mul_add_words(&(r[6]),a,8,b[6]);
 983         r[15]=bn_mul_add_words(&(r[7]),a,8,b[7]);
 984         }
 985
 986 #ifdef OPENSSL_NO_ASM
 987 #ifdef OPENSSL_BN_ASM_MONT
 988 #include <alloca.h>
 989 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0p, int num)
 990         {
 991         BN_ULONG c0,c1,*tp,n0=*n0p;
 992         volatile BN_ULONG *vp;
 993         int i=0,j;
 994
 995         vp = tp = alloca((num+2)*sizeof(BN_ULONG));
 996
 997         for(i=0;i<=num;i++)     tp[i]=0;
 998
 999         for(i=0;i<num;i++)
1000                 {
1001                 c0         = bn_mul_add_words(tp,ap,num,bp[i]);
1002                 c1         = (tp[num] + c0)&BN_MASK2;
1003                 tp[num]    = c1;
1004                 tp[num+1]  = (c1<c0?1:0);
1005
1006                 c0         = bn_mul_add_words(tp,np,num,tp[0]*n0);
1007                 c1         = (tp[num] + c0)&BN_MASK2;
1008                 tp[num]    = c1;
1009                 tp[num+1] += (c1<c0?1:0);
1010                 for(j=0;j<=num;j++)     tp[j]=tp[j+1];
1011                 }
1012
1013         if (tp[num]!=0 || tp[num-1]>=np[num-1])
1014                 {
1015                 c0 = bn_sub_words(rp,tp,np,num);
1016                 if (tp[num]!=0 || c0==0)
1017                         {
1018                         for(i=0;i<num+2;i++)    vp[i] = 0;
1019                         return 1;
1020                         }
1021                 }
1022         for(i=0;i<num;i++)      rp[i] = tp[i],  vp[i] = 0;
1023         vp[num]   = 0;
1024         vp[num+1] = 0;
1025         return 1;
1026         }
1027 #else
1028 int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp, const BN_ULONG *np,const BN_ULONG *n0, int num)
1029 {       return 0;       }
1030 #endif /* OPENSSL_BN_ASM_MONT */
1031 #endif
1032
1033 #endif /* !BN_MUL_COMBA */