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d02b48c6 | 1 | /* crypto/bn/bn_div.c */ |
58964a49 | 2 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
d02b48c6 RE |
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 | ||
73e45b2d | 59 | |
14ae26f2 | 60 | |
84c15db5 | 61 | #include <openssl/bn.h> |
d02b48c6 RE |
62 | #include "cryptlib.h" |
63 | #include "bn_lcl.h" | |
64 | ||
78a0c1f1 | 65 | |
d02b48c6 | 66 | /* The old slow way */ |
4a6222d7 | 67 | #if 0 |
0bde1089 UM |
68 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, |
69 | BN_CTX *ctx) | |
d02b48c6 RE |
70 | { |
71 | int i,nm,nd; | |
9b141126 | 72 | int ret = 0; |
d02b48c6 RE |
73 | BIGNUM *D; |
74 | ||
dfeab068 RE |
75 | bn_check_top(m); |
76 | bn_check_top(d); | |
d02b48c6 RE |
77 | if (BN_is_zero(d)) |
78 | { | |
79 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
80 | return(0); | |
81 | } | |
82 | ||
83 | if (BN_ucmp(m,d) < 0) | |
84 | { | |
85 | if (rem != NULL) | |
86 | { if (BN_copy(rem,m) == NULL) return(0); } | |
87 | if (dv != NULL) BN_zero(dv); | |
88 | return(1); | |
89 | } | |
90 | ||
9b141126 UM |
91 | BN_CTX_start(ctx); |
92 | D = BN_CTX_get(ctx); | |
93 | if (dv == NULL) dv = BN_CTX_get(ctx); | |
94 | if (rem == NULL) rem = BN_CTX_get(ctx); | |
95 | if (D == NULL || dv == NULL || rem == NULL) | |
96 | goto end; | |
d02b48c6 RE |
97 | |
98 | nd=BN_num_bits(d); | |
99 | nm=BN_num_bits(m); | |
9b141126 UM |
100 | if (BN_copy(D,d) == NULL) goto end; |
101 | if (BN_copy(rem,m) == NULL) goto end; | |
d02b48c6 RE |
102 | |
103 | /* The next 2 are needed so we can do a dv->d[0]|=1 later | |
104 | * since BN_lshift1 will only work once there is a value :-) */ | |
105 | BN_zero(dv); | |
2d9dcd4f | 106 | if(bn_wexpand(dv,1) == NULL) goto end; |
d02b48c6 RE |
107 | dv->top=1; |
108 | ||
9b141126 | 109 | if (!BN_lshift(D,D,nm-nd)) goto end; |
d02b48c6 RE |
110 | for (i=nm-nd; i>=0; i--) |
111 | { | |
9b141126 | 112 | if (!BN_lshift1(dv,dv)) goto end; |
d02b48c6 RE |
113 | if (BN_ucmp(rem,D) >= 0) |
114 | { | |
115 | dv->d[0]|=1; | |
9b141126 | 116 | if (!BN_usub(rem,rem,D)) goto end; |
d02b48c6 RE |
117 | } |
118 | /* CAN IMPROVE (and have now :=) */ | |
9b141126 | 119 | if (!BN_rshift1(D,D)) goto end; |
d02b48c6 RE |
120 | } |
121 | rem->neg=BN_is_zero(rem)?0:m->neg; | |
122 | dv->neg=m->neg^d->neg; | |
9b141126 UM |
123 | ret = 1; |
124 | end: | |
125 | BN_CTX_end(ctx); | |
126 | return(ret); | |
d02b48c6 RE |
127 | } |
128 | ||
129 | #else | |
130 | ||
cf1b7d96 RL |
131 | #if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \ |
132 | && !defined(PEDANTIC) && !defined(BN_DIV3W) | |
4a6222d7 | 133 | # if defined(__GNUC__) && __GNUC__>=2 |
5dd955dc | 134 | # if defined(__i386) || defined (__i386__) |
4a6222d7 UM |
135 | /* |
136 | * There were two reasons for implementing this template: | |
137 | * - GNU C generates a call to a function (__udivdi3 to be exact) | |
138 | * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to | |
139 | * understand why...); | |
140 | * - divl doesn't only calculate quotient, but also leaves | |
141 | * remainder in %edx which we can definitely use here:-) | |
142 | * | |
143 | * <appro@fy.chalmers.se> | |
144 | */ | |
f41154b2 | 145 | #undef bn_div_words |
4a6222d7 UM |
146 | # define bn_div_words(n0,n1,d0) \ |
147 | ({ asm volatile ( \ | |
148 | "divl %4" \ | |
149 | : "=a"(q), "=d"(rem) \ | |
150 | : "a"(n1), "d"(n0), "g"(d0) \ | |
151 | : "cc"); \ | |
152 | q; \ | |
153 | }) | |
154 | # define REMAINDER_IS_ALREADY_CALCULATED | |
2f98abbc AP |
155 | # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG) |
156 | /* | |
157 | * Same story here, but it's 128-bit by 64-bit division. Wow! | |
158 | * <appro@fy.chalmers.se> | |
159 | */ | |
48da9b8f | 160 | # undef bn_div_words |
2f98abbc AP |
161 | # define bn_div_words(n0,n1,d0) \ |
162 | ({ asm volatile ( \ | |
163 | "divq %4" \ | |
164 | : "=a"(q), "=d"(rem) \ | |
165 | : "a"(n1), "d"(n0), "g"(d0) \ | |
166 | : "cc"); \ | |
167 | q; \ | |
168 | }) | |
169 | # define REMAINDER_IS_ALREADY_CALCULATED | |
4a6222d7 UM |
170 | # endif /* __<cpu> */ |
171 | # endif /* __GNUC__ */ | |
cf1b7d96 | 172 | #endif /* OPENSSL_NO_ASM */ |
4a6222d7 | 173 | |
78a0c1f1 | 174 | |
bf3dfe7f | 175 | /* BN_div computes dv := num / divisor, rounding towards |
55525742 | 176 | * zero, and sets up rm such that dv*divisor + rm = num holds. |
78a0c1f1 BM |
177 | * Thus: |
178 | * dv->neg == num->neg ^ divisor->neg (unless the result is zero) | |
179 | * rm->neg == num->neg (unless the remainder is zero) | |
180 | * If 'dv' or 'rm' is NULL, the respective value is not returned. | |
181 | */ | |
84c15db5 BL |
182 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor, |
183 | BN_CTX *ctx) | |
d02b48c6 | 184 | { |
6343829a | 185 | int norm_shift,i,loop; |
d02b48c6 RE |
186 | BIGNUM *tmp,wnum,*snum,*sdiv,*res; |
187 | BN_ULONG *resp,*wnump; | |
188 | BN_ULONG d0,d1; | |
6343829a | 189 | int num_n,div_n; |
bf3dfe7f | 190 | int no_branch=0; |
d02b48c6 | 191 | |
f8d6be3f BM |
192 | /* Invalid zero-padding would have particularly bad consequences |
193 | * in the case of 'num', so don't just rely on bn_check_top() for this one | |
194 | * (bn_check_top() works only for BN_DEBUG builds) */ | |
195 | if (num->top > 0 && num->d[num->top - 1] == 0) | |
196 | { | |
197 | BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED); | |
198 | return 0; | |
199 | } | |
200 | ||
201 | bn_check_top(num); | |
202 | ||
b002265e | 203 | if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) |
bd31fb21 | 204 | { |
bf3dfe7f | 205 | no_branch=1; |
bd31fb21 BM |
206 | } |
207 | ||
8215e7a9 NL |
208 | bn_check_top(dv); |
209 | bn_check_top(rm); | |
f8d6be3f | 210 | /* bn_check_top(num); */ /* 'num' has been checked already */ |
dfeab068 RE |
211 | bn_check_top(divisor); |
212 | ||
58964a49 | 213 | if (BN_is_zero(divisor)) |
d02b48c6 RE |
214 | { |
215 | BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); | |
216 | return(0); | |
217 | } | |
218 | ||
bf3dfe7f | 219 | if (!no_branch && BN_ucmp(num,divisor) < 0) |
d02b48c6 RE |
220 | { |
221 | if (rm != NULL) | |
222 | { if (BN_copy(rm,num) == NULL) return(0); } | |
223 | if (dv != NULL) BN_zero(dv); | |
224 | return(1); | |
225 | } | |
226 | ||
9b141126 UM |
227 | BN_CTX_start(ctx); |
228 | tmp=BN_CTX_get(ctx); | |
9b141126 UM |
229 | snum=BN_CTX_get(ctx); |
230 | sdiv=BN_CTX_get(ctx); | |
d02b48c6 | 231 | if (dv == NULL) |
9b141126 | 232 | res=BN_CTX_get(ctx); |
d02b48c6 | 233 | else res=dv; |
d70323f1 DSH |
234 | if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL) |
235 | goto err; | |
d02b48c6 RE |
236 | |
237 | /* First we normalise the numbers */ | |
238 | norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2); | |
9cdf87f1 | 239 | if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err; |
d02b48c6 RE |
240 | sdiv->neg=0; |
241 | norm_shift+=BN_BITS2; | |
9cdf87f1 | 242 | if (!(BN_lshift(snum,num,norm_shift))) goto err; |
d02b48c6 | 243 | snum->neg=0; |
d02b48c6 | 244 | |
bf3dfe7f | 245 | if (no_branch) |
d02b48c6 | 246 | { |
bf3dfe7f AP |
247 | /* Since we don't know whether snum is larger than sdiv, |
248 | * we pad snum with enough zeroes without changing its | |
249 | * value. | |
250 | */ | |
251 | if (snum->top <= sdiv->top+1) | |
56c7754c | 252 | { |
bf3dfe7f AP |
253 | if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err; |
254 | for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0; | |
255 | snum->top = sdiv->top + 2; | |
56c7754c | 256 | } |
bf3dfe7f | 257 | else |
bd31fb21 | 258 | { |
bf3dfe7f AP |
259 | if (bn_wexpand(snum, snum->top + 1) == NULL) goto err; |
260 | snum->d[snum->top] = 0; | |
261 | snum->top ++; | |
bd31fb21 | 262 | } |
bd31fb21 BM |
263 | } |
264 | ||
265 | div_n=sdiv->top; | |
266 | num_n=snum->top; | |
267 | loop=num_n-div_n; | |
268 | /* Lets setup a 'window' into snum | |
269 | * This is the part that corresponds to the current | |
270 | * 'area' being divided */ | |
271 | wnum.neg = 0; | |
272 | wnum.d = &(snum->d[loop]); | |
273 | wnum.top = div_n; | |
274 | /* only needed when BN_ucmp messes up the values between top and max */ | |
275 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */ | |
276 | ||
277 | /* Get the top 2 words of sdiv */ | |
278 | /* div_n=sdiv->top; */ | |
279 | d0=sdiv->d[div_n-1]; | |
280 | d1=(div_n == 1)?0:sdiv->d[div_n-2]; | |
281 | ||
282 | /* pointer to the 'top' of snum */ | |
283 | wnump= &(snum->d[num_n-1]); | |
284 | ||
285 | /* Setup to 'res' */ | |
286 | res->neg= (num->neg^divisor->neg); | |
6343829a | 287 | if (!bn_wexpand(res,(loop+1))) goto err; |
bf3dfe7f | 288 | res->top=loop-no_branch; |
bd31fb21 BM |
289 | resp= &(res->d[loop-1]); |
290 | ||
291 | /* space for temp */ | |
6343829a | 292 | if (!bn_wexpand(tmp,(div_n+1))) goto err; |
bd31fb21 | 293 | |
bf3dfe7f AP |
294 | if (!no_branch) |
295 | { | |
296 | if (BN_ucmp(&wnum,sdiv) >= 0) | |
297 | { | |
298 | /* If BN_DEBUG_RAND is defined BN_ucmp changes (via | |
299 | * bn_pollute) the const bignum arguments => | |
300 | * clean the values between top and max again */ | |
301 | bn_clear_top2max(&wnum); | |
302 | bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n); | |
303 | *resp=1; | |
304 | } | |
305 | else | |
306 | res->top--; | |
307 | } | |
308 | ||
bd31fb21 BM |
309 | /* if res->top == 0 then clear the neg value otherwise decrease |
310 | * the resp pointer */ | |
311 | if (res->top == 0) | |
312 | res->neg = 0; | |
9e989810 GT |
313 | else |
314 | resp--; | |
d02b48c6 | 315 | |
9e989810 | 316 | for (i=0; i<loop-1; i++, wnump--, resp--) |
d02b48c6 | 317 | { |
0dd25e36 | 318 | BN_ULONG q,l0; |
9e989810 GT |
319 | /* the first part of the loop uses the top two words of |
320 | * snum and sdiv to calculate a BN_ULONG q such that | |
321 | * | wnum - sdiv * q | < sdiv */ | |
cf1b7d96 | 322 | #if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM) |
500230ee | 323 | BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG); |
0bbd0352 | 324 | q=bn_div_3_words(wnump,d1,d0); |
0dd25e36 | 325 | #else |
4c22909e | 326 | BN_ULONG n0,n1,rem=0; |
d02b48c6 | 327 | |
d02b48c6 RE |
328 | n0=wnump[0]; |
329 | n1=wnump[-1]; | |
330 | if (n0 == d0) | |
331 | q=BN_MASK2; | |
4a6222d7 UM |
332 | else /* n0 < d0 */ |
333 | { | |
334 | #ifdef BN_LLONG | |
335 | BN_ULLONG t2; | |
336 | ||
4c22909e | 337 | #if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words) |
8e1589ec | 338 | q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0); |
0dd25e36 | 339 | #else |
dfeab068 | 340 | q=bn_div_words(n0,n1,d0); |
3c801fa4 RL |
341 | #ifdef BN_DEBUG_LEVITTE |
342 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
343 | X) -> 0x%08X\n", | |
344 | n0, n1, d0, q); | |
345 | #endif | |
0dd25e36 | 346 | #endif |
0dd25e36 | 347 | |
fe7cd164 | 348 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 UM |
349 | /* |
350 | * rem doesn't have to be BN_ULLONG. The least we | |
351 | * know it's less that d0, isn't it? | |
352 | */ | |
353 | rem=(n1-q*d0)&BN_MASK2; | |
4c22909e | 354 | #endif |
4a6222d7 UM |
355 | t2=(BN_ULLONG)d1*q; |
356 | ||
357 | for (;;) | |
358 | { | |
359 | if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2])) | |
360 | break; | |
361 | q--; | |
362 | rem += d0; | |
363 | if (rem < d0) break; /* don't let rem overflow */ | |
364 | t2 -= d1; | |
365 | } | |
366 | #else /* !BN_LLONG */ | |
56c7754c | 367 | BN_ULONG t2l,t2h; |
0dd25e36 | 368 | |
4a6222d7 | 369 | q=bn_div_words(n0,n1,d0); |
3c801fa4 RL |
370 | #ifdef BN_DEBUG_LEVITTE |
371 | fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\ | |
372 | X) -> 0x%08X\n", | |
373 | n0, n1, d0, q); | |
374 | #endif | |
fe7cd164 | 375 | #ifndef REMAINDER_IS_ALREADY_CALCULATED |
4a6222d7 | 376 | rem=(n1-q*d0)&BN_MASK2; |
4c22909e | 377 | #endif |
4a6222d7 | 378 | |
2f98abbc AP |
379 | #if defined(BN_UMULT_LOHI) |
380 | BN_UMULT_LOHI(t2l,t2h,d1,q); | |
381 | #elif defined(BN_UMULT_HIGH) | |
4a6222d7 UM |
382 | t2l = d1 * q; |
383 | t2h = BN_UMULT_HIGH(d1,q); | |
fb81ac5e | 384 | #else |
56c7754c DSH |
385 | { |
386 | BN_ULONG ql, qh; | |
4a6222d7 UM |
387 | t2l=LBITS(d1); t2h=HBITS(d1); |
388 | ql =LBITS(q); qh =HBITS(q); | |
389 | mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */ | |
56c7754c | 390 | } |
fb81ac5e | 391 | #endif |
0dd25e36 | 392 | |
4a6222d7 UM |
393 | for (;;) |
394 | { | |
395 | if ((t2h < rem) || | |
396 | ((t2h == rem) && (t2l <= wnump[-2]))) | |
397 | break; | |
398 | q--; | |
399 | rem += d0; | |
400 | if (rem < d0) break; /* don't let rem overflow */ | |
401 | if (t2l < d1) t2h--; t2l -= d1; | |
402 | } | |
403 | #endif /* !BN_LLONG */ | |
d02b48c6 | 404 | } |
4c22909e | 405 | #endif /* !BN_DIV3W */ |
4a6222d7 | 406 | |
58964a49 | 407 | l0=bn_mul_words(tmp->d,sdiv->d,div_n,q); |
d02b48c6 | 408 | tmp->d[div_n]=l0; |
9e989810 GT |
409 | wnum.d--; |
410 | /* ingore top values of the bignums just sub the two | |
411 | * BN_ULONG arrays with bn_sub_words */ | |
412 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1)) | |
d02b48c6 | 413 | { |
9e989810 GT |
414 | /* Note: As we have considered only the leading |
415 | * two BN_ULONGs in the calculation of q, sdiv * q | |
416 | * might be greater than wnum (but then (q-1) * sdiv | |
417 | * is less or equal than wnum) | |
418 | */ | |
d02b48c6 | 419 | q--; |
9e989810 GT |
420 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n)) |
421 | /* we can't have an overflow here (assuming | |
422 | * that q != 0, but if q == 0 then tmp is | |
423 | * zero anyway) */ | |
424 | (*wnump)++; | |
d02b48c6 | 425 | } |
9e989810 GT |
426 | /* store part of the result */ |
427 | *resp = q; | |
d02b48c6 | 428 | } |
a8aa764d | 429 | bn_correct_top(snum); |
d02b48c6 RE |
430 | if (rm != NULL) |
431 | { | |
3d2e469c DSH |
432 | /* Keep a copy of the neg flag in num because if rm==num |
433 | * BN_rshift() will overwrite it. | |
434 | */ | |
435 | int neg = num->neg; | |
d02b48c6 | 436 | BN_rshift(rm,snum,norm_shift); |
78a0c1f1 | 437 | if (!BN_is_zero(rm)) |
3d2e469c | 438 | rm->neg = neg; |
d870740c | 439 | bn_check_top(rm); |
d02b48c6 | 440 | } |
bf3dfe7f | 441 | if (no_branch) bn_correct_top(res); |
9b141126 | 442 | BN_CTX_end(ctx); |
d02b48c6 RE |
443 | return(1); |
444 | err: | |
8215e7a9 | 445 | bn_check_top(rm); |
4a6222d7 | 446 | BN_CTX_end(ctx); |
d02b48c6 RE |
447 | return(0); |
448 | } | |
d02b48c6 | 449 | #endif |