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d02b48c6 1/* crypto/bn/bn_lcl.h */
58964a49 2/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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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.
ae5c8664 8 *
d02b48c6
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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).
ae5c8664 15 *
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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.
ae5c8664 22 *
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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 :-).
ae5c8664 37 * 4. If you include any Windows specific code (or a derivative thereof) from
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38 * the apps directory (application code) you must include an acknowledgement:
39 * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
ae5c8664 40 *
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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.
ae5c8664 52 *
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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 */
dc434bbc 58/* ====================================================================
c24e2f18 59 * Copyright (c) 1998-2018 The OpenSSL Project. All rights reserved.
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60 *
61 * Redistribution and use in source and binary forms, with or without
62 * modification, are permitted provided that the following conditions
63 * are met:
64 *
65 * 1. Redistributions of source code must retain the above copyright
ae5c8664 66 * notice, this list of conditions and the following disclaimer.
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67 *
68 * 2. Redistributions in binary form must reproduce the above copyright
69 * notice, this list of conditions and the following disclaimer in
70 * the documentation and/or other materials provided with the
71 * distribution.
72 *
73 * 3. All advertising materials mentioning features or use of this
74 * software must display the following acknowledgment:
75 * "This product includes software developed by the OpenSSL Project
76 * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
77 *
78 * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
79 * endorse or promote products derived from this software without
80 * prior written permission. For written permission, please contact
81 * openssl-core@openssl.org.
82 *
83 * 5. Products derived from this software may not be called "OpenSSL"
84 * nor may "OpenSSL" appear in their names without prior written
85 * permission of the OpenSSL Project.
86 *
87 * 6. Redistributions of any form whatsoever must retain the following
88 * acknowledgment:
89 * "This product includes software developed by the OpenSSL Project
90 * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
91 *
92 * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
93 * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
94 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
95 * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
96 * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
97 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
98 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
99 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
100 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
101 * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
102 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
103 * OF THE POSSIBILITY OF SUCH DAMAGE.
104 * ====================================================================
105 *
106 * This product includes cryptographic software written by Eric Young
107 * (eay@cryptsoft.com). This product includes software written by Tim
108 * Hudson (tjh@cryptsoft.com).
109 *
110 */
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111
112#ifndef HEADER_BN_LCL_H
ae5c8664 113# define HEADER_BN_LCL_H
d02b48c6 114
ae5c8664 115# include <openssl/bn.h>
c9046a05 116# include "bn_int.h"
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117
118#ifdef __cplusplus
119extern "C" {
120#endif
121
6977c7e2 122/*-
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123 * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
124 *
125 *
126 * For window size 'w' (w >= 2) and a random 'b' bits exponent,
127 * the number of multiplications is a constant plus on average
128 *
129 * 2^(w-1) + (b-w)/(w+1);
130 *
131 * here 2^(w-1) is for precomputing the table (we actually need
132 * entries only for windows that have the lowest bit set), and
133 * (b-w)/(w+1) is an approximation for the expected number of
134 * w-bit windows, not counting the first one.
135 *
136 * Thus we should use
137 *
138 * w >= 6 if b > 671
139 * w = 5 if 671 > b > 239
140 * w = 4 if 239 > b > 79
141 * w = 3 if 79 > b > 23
142 * w <= 2 if 23 > b
143 *
144 * (with draws in between). Very small exponents are often selected
145 * with low Hamming weight, so we use w = 1 for b <= 23.
146 */
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147# if 1
148# define BN_window_bits_for_exponent_size(b) \
149 ((b) > 671 ? 6 : \
150 (b) > 239 ? 5 : \
151 (b) > 79 ? 4 : \
152 (b) > 23 ? 3 : 1)
153# else
154/*
155 * Old SSLeay/OpenSSL table. Maximum window size was 5, so this table differs
156 * for b==1024; but it coincides for other interesting values (b==160,
157 * b==512).
dc434bbc 158 */
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159# define BN_window_bits_for_exponent_size(b) \
160 ((b) > 255 ? 5 : \
161 (b) > 127 ? 4 : \
162 (b) > 17 ? 3 : 1)
163# endif
dc434bbc 164
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165/*
166 * BN_mod_exp_mont_conttime is based on the assumption that the L1 data cache
167 * line width of the target processor is at least the following value.
46a64376 168 */
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169# define MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH ( 64 )
170# define MOD_EXP_CTIME_MIN_CACHE_LINE_MASK (MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH - 1)
46a64376 171
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172/*
173 * Window sizes optimized for fixed window size modular exponentiation
174 * algorithm (BN_mod_exp_mont_consttime). To achieve the security goals of
175 * BN_mode_exp_mont_consttime, the maximum size of the window must not exceed
176 * log_2(MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH). Window size thresholds are
177 * defined for cache line sizes of 32 and 64, cache line sizes where
178 * log_2(32)=5 and log_2(64)=6 respectively. A window size of 7 should only be
179 * used on processors that have a 128 byte or greater cache line size.
46a64376 180 */
ae5c8664 181# if MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 64
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182
183# define BN_window_bits_for_ctime_exponent_size(b) \
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184 ((b) > 937 ? 6 : \
185 (b) > 306 ? 5 : \
186 (b) > 89 ? 4 : \
187 (b) > 22 ? 3 : 1)
188# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (6)
46a64376 189
ae5c8664 190# elif MOD_EXP_CTIME_MIN_CACHE_LINE_WIDTH == 32
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191
192# define BN_window_bits_for_ctime_exponent_size(b) \
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193 ((b) > 306 ? 5 : \
194 (b) > 89 ? 4 : \
195 (b) > 22 ? 3 : 1)
196# define BN_MAX_WINDOW_BITS_FOR_CTIME_EXPONENT_SIZE (5)
46a64376 197
ae5c8664 198# endif
46a64376 199
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200/* Pentium pro 16,16,16,32,64 */
201/* Alpha 16,16,16,16.64 */
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202# define BN_MULL_SIZE_NORMAL (16)/* 32 */
203# define BN_MUL_RECURSIVE_SIZE_NORMAL (16)/* 32 less than */
204# define BN_SQR_RECURSIVE_SIZE_NORMAL (16)/* 32 */
205# define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32)/* 32 */
206# define BN_MONT_CTX_SET_SIZE_WORD (64)/* 32 */
207
208/*
209 * 2011-02-22 SMS. In various places, a size_t variable or a type cast to
210 * size_t was used to perform integer-only operations on pointers. This
211 * failed on VMS with 64-bit pointers (CC /POINTER_SIZE = 64) because size_t
212 * is still only 32 bits. What's needed in these cases is an integer type
213 * with the same size as a pointer, which size_t is not certain to be. The
214 * only fix here is VMS-specific.
fd6a72fa 215 */
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216# if defined(OPENSSL_SYS_VMS)
217# if __INITIAL_POINTER_SIZE == 64
218# define PTR_SIZE_INT long long
219# else /* __INITIAL_POINTER_SIZE == 64 */
220# define PTR_SIZE_INT int
221# endif /* __INITIAL_POINTER_SIZE == 64 [else] */
222# elif !defined(PTR_SIZE_INT) /* defined(OPENSSL_SYS_VMS) */
223# define PTR_SIZE_INT size_t
224# endif /* defined(OPENSSL_SYS_VMS) [else] */
225
226# if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) && !defined(PEDANTIC)
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227/*
228 * BN_UMULT_HIGH section.
229 *
230 * No, I'm not trying to overwhelm you when stating that the
231 * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
232 * you to be impressed when I say that if the compiler doesn't
233 * support 2*N integer type, then you have to replace every N*N
234 * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
235 * and additions which unavoidably results in severe performance
236 * penalties. Of course provided that the hardware is capable of
237 * producing 2*N result... That's when you normally start
238 * considering assembler implementation. However! It should be
239 * pointed out that some CPUs (most notably Alpha, PowerPC and
240 * upcoming IA-64 family:-) provide *separate* instruction
241 * calculating the upper half of the product placing the result
242 * into a general purpose register. Now *if* the compiler supports
243 * inline assembler, then it's not impossible to implement the
244 * "bignum" routines (and have the compiler optimize 'em)
245 * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
246 * macro is about:-)
247 *
ae5c8664 248 * <appro@fy.chalmers.se>
fb81ac5e 249 */
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250# if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
251# if defined(__DECC)
252# include <c_asm.h>
253# define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
254# elif defined(__GNUC__) && __GNUC__>=2
255# define BN_UMULT_HIGH(a,b) ({ \
256 register BN_ULONG ret; \
257 asm ("umulh %1,%2,%0" \
258 : "=r"(ret) \
259 : "r"(a), "r"(b)); \
260 ret; })
261# endif /* compiler */
262# elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
263# if defined(__GNUC__) && __GNUC__>=2
264# define BN_UMULT_HIGH(a,b) ({ \
265 register BN_ULONG ret; \
266 asm ("mulhdu %0,%1,%2" \
267 : "=r"(ret) \
268 : "r"(a), "r"(b)); \
269 ret; })
270# endif /* compiler */
271# elif (defined(__x86_64) || defined(__x86_64__)) && \
122396f2 272 (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
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273# if defined(__GNUC__) && __GNUC__>=2
274# define BN_UMULT_HIGH(a,b) ({ \
275 register BN_ULONG ret,discard; \
276 asm ("mulq %3" \
277 : "=a"(discard),"=d"(ret) \
278 : "a"(a), "g"(b) \
279 : "cc"); \
280 ret; })
281# define BN_UMULT_LOHI(low,high,a,b) \
282 asm ("mulq %3" \
283 : "=a"(low),"=d"(high) \
284 : "a"(a),"g"(b) \
285 : "cc");
286# endif
287# elif (defined(_M_AMD64) || defined(_M_X64)) && defined(SIXTY_FOUR_BIT)
288# if defined(_MSC_VER) && _MSC_VER>=1400
289unsigned __int64 __umulh(unsigned __int64 a, unsigned __int64 b);
290unsigned __int64 _umul128(unsigned __int64 a, unsigned __int64 b,
291 unsigned __int64 *h);
292# pragma intrinsic(__umulh,_umul128)
293# define BN_UMULT_HIGH(a,b) __umulh((a),(b))
294# define BN_UMULT_LOHI(low,high,a,b) ((low)=_umul128((a),(b),&(high)))
295# endif
296# elif defined(__mips) && (defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG))
297# if defined(__GNUC__) && __GNUC__>=2
78ac7fa1 298# if __GNUC__>4 || (__GNUC__>=4 && __GNUC_MINOR__>=4)
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299 /* "h" constraint is no more since 4.4 */
300# define BN_UMULT_HIGH(a,b) (((__uint128_t)(a)*(b))>>64)
301# define BN_UMULT_LOHI(low,high,a,b) ({ \
302 __uint128_t ret=(__uint128_t)(a)*(b); \
303 (high)=ret>>64; (low)=ret; })
304# else
305# define BN_UMULT_HIGH(a,b) ({ \
306 register BN_ULONG ret; \
307 asm ("dmultu %1,%2" \
308 : "=h"(ret) \
309 : "r"(a), "r"(b) : "l"); \
310 ret; })
d46a1a61 311# define BN_UMULT_LOHI(low,high,a,b)\
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312 asm ("dmultu %2,%3" \
313 : "=l"(low),"=h"(high) \
314 : "r"(a), "r"(b));
d46a1a61 315# endif
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316# endif
317# elif defined(__aarch64__) && defined(SIXTY_FOUR_BIT_LONG)
318# if defined(__GNUC__) && __GNUC__>=2
319# define BN_UMULT_HIGH(a,b) ({ \
320 register BN_ULONG ret; \
321 asm ("umulh %0,%1,%2" \
322 : "=r"(ret) \
323 : "r"(a), "r"(b)); \
324 ret; })
325# endif
326# endif /* cpu */
327# endif /* OPENSSL_NO_ASM */
fb81ac5e 328
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329/*************************************************************
330 * Using the long long type
331 */
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332# define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
333# define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
334
335# ifdef BN_DEBUG_RAND
336# define bn_clear_top2max(a) \
337 { \
338 int ind = (a)->dmax - (a)->top; \
339 BN_ULONG *ftl = &(a)->d[(a)->top-1]; \
340 for (; ind != 0; ind--) \
341 *(++ftl) = 0x0; \
342 }
343# else
344# define bn_clear_top2max(a)
345# endif
346
347# ifdef BN_LLONG
348# define mul_add(r,a,w,c) { \
349 BN_ULLONG t; \
350 t=(BN_ULLONG)w * (a) + (r) + (c); \
351 (r)= Lw(t); \
352 (c)= Hw(t); \
353 }
354
355# define mul(r,a,w,c) { \
356 BN_ULLONG t; \
357 t=(BN_ULLONG)w * (a) + (c); \
358 (r)= Lw(t); \
359 (c)= Hw(t); \
360 }
361
362# define sqr(r0,r1,a) { \
363 BN_ULLONG t; \
364 t=(BN_ULLONG)(a)*(a); \
365 (r0)=Lw(t); \
366 (r1)=Hw(t); \
367 }
368
369# elif defined(BN_UMULT_LOHI)
370# define mul_add(r,a,w,c) { \
371 BN_ULONG high,low,ret,tmp=(a); \
372 ret = (r); \
373 BN_UMULT_LOHI(low,high,w,tmp); \
374 ret += (c); \
375 (c) = (ret<(c))?1:0; \
376 (c) += high; \
377 ret += low; \
378 (c) += (ret<low)?1:0; \
379 (r) = ret; \
380 }
381
382# define mul(r,a,w,c) { \
383 BN_ULONG high,low,ret,ta=(a); \
384 BN_UMULT_LOHI(low,high,w,ta); \
385 ret = low + (c); \
386 (c) = high; \
387 (c) += (ret<low)?1:0; \
388 (r) = ret; \
389 }
390
391# define sqr(r0,r1,a) { \
392 BN_ULONG tmp=(a); \
393 BN_UMULT_LOHI(r0,r1,tmp,tmp); \
394 }
395
396# elif defined(BN_UMULT_HIGH)
397# define mul_add(r,a,w,c) { \
398 BN_ULONG high,low,ret,tmp=(a); \
399 ret = (r); \
400 high= BN_UMULT_HIGH(w,tmp); \
401 ret += (c); \
402 low = (w) * tmp; \
403 (c) = (ret<(c))?1:0; \
404 (c) += high; \
405 ret += low; \
406 (c) += (ret<low)?1:0; \
407 (r) = ret; \
408 }
409
410# define mul(r,a,w,c) { \
411 BN_ULONG high,low,ret,ta=(a); \
412 low = (w) * ta; \
413 high= BN_UMULT_HIGH(w,ta); \
414 ret = low + (c); \
415 (c) = high; \
416 (c) += (ret<low)?1:0; \
417 (r) = ret; \
418 }
419
420# define sqr(r0,r1,a) { \
421 BN_ULONG tmp=(a); \
422 (r0) = tmp * tmp; \
423 (r1) = BN_UMULT_HIGH(tmp,tmp); \
424 }
425
426# else
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427/*************************************************************
428 * No long long type
429 */
430
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431# define LBITS(a) ((a)&BN_MASK2l)
432# define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
433# define L2HBITS(a) (((a)<<BN_BITS4)&BN_MASK2)
d02b48c6 434
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435# define LLBITS(a) ((a)&BN_MASKl)
436# define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
437# define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
d02b48c6 438
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439# define mul64(l,h,bl,bh) \
440 { \
441 BN_ULONG m,m1,lt,ht; \
d02b48c6 442 \
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443 lt=l; \
444 ht=h; \
445 m =(bh)*(lt); \
446 lt=(bl)*(lt); \
447 m1=(bl)*(ht); \
448 ht =(bh)*(ht); \
449 m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS((BN_ULONG)1); \
450 ht+=HBITS(m); \
451 m1=L2HBITS(m); \
452 lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
453 (l)=lt; \
454 (h)=ht; \
455 }
456
457# define sqr64(lo,ho,in) \
458 { \
459 BN_ULONG l,h,m; \
d02b48c6 460 \
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461 h=(in); \
462 l=LBITS(h); \
463 h=HBITS(h); \
464 m =(l)*(h); \
465 l*=l; \
466 h*=h; \
467 h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
468 m =(m&BN_MASK2l)<<(BN_BITS4+1); \
469 l=(l+m)&BN_MASK2; if (l < m) h++; \
470 (lo)=l; \
471 (ho)=h; \
472 }
473
474# define mul_add(r,a,bl,bh,c) { \
475 BN_ULONG l,h; \
d02b48c6 476 \
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477 h= (a); \
478 l=LBITS(h); \
479 h=HBITS(h); \
480 mul64(l,h,(bl),(bh)); \
d02b48c6 481 \
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482 /* non-multiply part */ \
483 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
484 (c)=(r); \
485 l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
486 (c)=h&BN_MASK2; \
487 (r)=l; \
488 }
489
490# define mul(r,a,bl,bh,c) { \
491 BN_ULONG l,h; \
d02b48c6 492 \
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493 h= (a); \
494 l=LBITS(h); \
495 h=HBITS(h); \
496 mul64(l,h,(bl),(bh)); \
d02b48c6 497 \
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498 /* non-multiply part */ \
499 l+=(c); if ((l&BN_MASK2) < (c)) h++; \
500 (c)=h&BN_MASK2; \
501 (r)=l&BN_MASK2; \
502 }
503# endif /* !BN_LLONG */
504
505# if defined(OPENSSL_DOING_MAKEDEPEND) && defined(OPENSSL_FIPS)
506# undef bn_div_words
507# endif
508
509void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb);
510void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
511void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b);
cbd48ba6 512void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, int n, BN_ULONG *tmp);
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513void bn_sqr_comba8(BN_ULONG *r, const BN_ULONG *a);
514void bn_sqr_comba4(BN_ULONG *r, const BN_ULONG *a);
515int bn_cmp_words(const BN_ULONG *a, const BN_ULONG *b, int n);
516int bn_cmp_part_words(const BN_ULONG *a, const BN_ULONG *b, int cl, int dl);
517void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
518 int dna, int dnb, BN_ULONG *t);
519void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b,
520 int n, int tna, int tnb, BN_ULONG *t);
521void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2, BN_ULONG *t);
522void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n);
523void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
524 BN_ULONG *t);
525void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2,
526 BN_ULONG *t);
d5c21afd 527BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
ae5c8664 528 int cl, int dl);
6343829a 529BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
ae5c8664
MC
530 int cl, int dl);
531int bn_mul_mont(BN_ULONG *rp, const BN_ULONG *ap, const BN_ULONG *bp,
532 const BN_ULONG *np, const BN_ULONG *n0, int num);
58964a49 533
d02b48c6
RE
534#ifdef __cplusplus
535}
536#endif
537
538#endif