Training courses

Kernel and Embedded Linux

Bootlin training courses

Embedded Linux, kernel,
Yocto Project, Buildroot, real-time,
graphics, boot time, debugging...

Bootlin logo

Elixir Cross Referencer

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
/* mpihelp-mul.c  -  MPI helper functions
 * Copyright (C) 1994, 1996, 1998, 1999,
 *               2000 Free Software Foundation, Inc.
 *
 * This file is part of GnuPG.
 *
 * GnuPG is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * GnuPG is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
 *
 * Note: This code is heavily based on the GNU MP Library.
 *	 Actually it's the same code with only minor changes in the
 *	 way the data is stored; this is to support the abstraction
 *	 of an optional secure memory allocation which may be used
 *	 to avoid revealing of sensitive data due to paging etc.
 *	 The GNU MP Library itself is published under the LGPL;
 *	 however I decided to publish this code under the plain GPL.
 */

#include <linux/string.h>
#include "mpi-internal.h"
#include "longlong.h"

#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace)		\
	do {							\
		if ((size) < KARATSUBA_THRESHOLD)		\
			mul_n_basecase(prodp, up, vp, size);	\
		else						\
			mul_n(prodp, up, vp, size, tspace);	\
	} while (0);

#define MPN_SQR_N_RECURSE(prodp, up, size, tspace)		\
	do {							\
		if ((size) < KARATSUBA_THRESHOLD)		\
			mpih_sqr_n_basecase(prodp, up, size);	\
		else						\
			mpih_sqr_n(prodp, up, size, tspace);	\
	} while (0);

/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
 * both with SIZE limbs, and store the result at PRODP.  2 * SIZE limbs are
 * always stored.  Return the most significant limb.
 *
 * Argument constraints:
 * 1. PRODP != UP and PRODP != VP, i.e. the destination
 *    must be distinct from the multiplier and the multiplicand.
 *
 *
 * Handle simple cases with traditional multiplication.
 *
 * This is the most critical code of multiplication.  All multiplies rely
 * on this, both small and huge.  Small ones arrive here immediately.  Huge
 * ones arrive here as this is the base case for Karatsuba's recursive
 * algorithm below.
 */

static mpi_limb_t
mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
{
	mpi_size_t i;
	mpi_limb_t cy;
	mpi_limb_t v_limb;

	/* Multiply by the first limb in V separately, as the result can be
	 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
	v_limb = vp[0];
	if (v_limb <= 1) {
		if (v_limb == 1)
			MPN_COPY(prodp, up, size);
		else
			MPN_ZERO(prodp, size);
		cy = 0;
	} else
		cy = mpihelp_mul_1(prodp, up, size, v_limb);

	prodp[size] = cy;
	prodp++;

	/* For each iteration in the outer loop, multiply one limb from
	 * U with one limb from V, and add it to PROD.  */
	for (i = 1; i < size; i++) {
		v_limb = vp[i];
		if (v_limb <= 1) {
			cy = 0;
			if (v_limb == 1)
				cy = mpihelp_add_n(prodp, prodp, up, size);
		} else
			cy = mpihelp_addmul_1(prodp, up, size, v_limb);

		prodp[size] = cy;
		prodp++;
	}

	return cy;
}

static void
mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
		mpi_size_t size, mpi_ptr_t tspace)
{
	if (size & 1) {
		/* The size is odd, and the code below doesn't handle that.
		 * Multiply the least significant (size - 1) limbs with a recursive
		 * call, and handle the most significant limb of S1 and S2
		 * separately.
		 * A slightly faster way to do this would be to make the Karatsuba
		 * code below behave as if the size were even, and let it check for
		 * odd size in the end.  I.e., in essence move this code to the end.
		 * Doing so would save us a recursive call, and potentially make the
		 * stack grow a lot less.
		 */
		mpi_size_t esize = size - 1;	/* even size */
		mpi_limb_t cy_limb;

		MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
		cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
		prodp[esize + esize] = cy_limb;
		cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
		prodp[esize + size] = cy_limb;
	} else {
		/* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
		 *
		 * Split U in two pieces, U1 and U0, such that
		 * U = U0 + U1*(B**n),
		 * and V in V1 and V0, such that
		 * V = V0 + V1*(B**n).
		 *
		 * UV is then computed recursively using the identity
		 *
		 *        2n   n          n                     n
		 * UV = (B  + B )U V  +  B (U -U )(V -V )  +  (B + 1)U V
		 *                1 1        1  0   0  1              0 0
		 *
		 * Where B = 2**BITS_PER_MP_LIMB.
		 */
		mpi_size_t hsize = size >> 1;
		mpi_limb_t cy;
		int negflg;

		/* Product H.      ________________  ________________
		 *                |_____U1 x V1____||____U0 x V0_____|
		 * Put result in upper part of PROD and pass low part of TSPACE
		 * as new TSPACE.
		 */
		MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
				  tspace);

		/* Product M.      ________________
		 *                |_(U1-U0)(V0-V1)_|
		 */
		if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
			mpihelp_sub_n(prodp, up + hsize, up, hsize);
			negflg = 0;
		} else {
			mpihelp_sub_n(prodp, up, up + hsize, hsize);
			negflg = 1;
		}
		if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
			mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
			negflg ^= 1;
		} else {
			mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
			/* No change of NEGFLG.  */
		}
		/* Read temporary operands from low part of PROD.
		 * Put result in low part of TSPACE using upper part of TSPACE
		 * as new TSPACE.
		 */
		MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
				  tspace + size);

		/* Add/copy product H. */
		MPN_COPY(prodp + hsize, prodp + size, hsize);
		cy = mpihelp_add_n(prodp + size, prodp + size,
				   prodp + size + hsize, hsize);

		/* Add product M (if NEGFLG M is a negative number) */
		if (negflg)
			cy -=
			    mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
					  size);
		else
			cy +=
			    mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
					  size);

		/* Product L.      ________________  ________________
		 *                |________________||____U0 x V0_____|
		 * Read temporary operands from low part of PROD.
		 * Put result in low part of TSPACE using upper part of TSPACE
		 * as new TSPACE.
		 */
		MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);

		/* Add/copy Product L (twice) */

		cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
		if (cy)
			mpihelp_add_1(prodp + hsize + size,
				      prodp + hsize + size, hsize, cy);

		MPN_COPY(prodp, tspace, hsize);
		cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
				   hsize);
		if (cy)
			mpihelp_add_1(prodp + size, prodp + size, size, 1);
	}
}

void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
{
	mpi_size_t i;
	mpi_limb_t cy_limb;
	mpi_limb_t v_limb;

	/* Multiply by the first limb in V separately, as the result can be
	 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
	v_limb = up[0];
	if (v_limb <= 1) {
		if (v_limb == 1)
			MPN_COPY(prodp, up, size);
		else
			MPN_ZERO(prodp, size);
		cy_limb = 0;
	} else
		cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);

	prodp[size] = cy_limb;
	prodp++;

	/* For each iteration in the outer loop, multiply one limb from
	 * U with one limb from V, and add it to PROD.  */
	for (i = 1; i < size; i++) {
		v_limb = up[i];
		if (v_limb <= 1) {
			cy_limb = 0;
			if (v_limb == 1)
				cy_limb = mpihelp_add_n(prodp, prodp, up, size);
		} else
			cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);

		prodp[size] = cy_limb;
		prodp++;
	}
}

void
mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
{
	if (size & 1) {
		/* The size is odd, and the code below doesn't handle that.
		 * Multiply the least significant (size - 1) limbs with a recursive
		 * call, and handle the most significant limb of S1 and S2
		 * separately.
		 * A slightly faster way to do this would be to make the Karatsuba
		 * code below behave as if the size were even, and let it check for
		 * odd size in the end.  I.e., in essence move this code to the end.
		 * Doing so would save us a recursive call, and potentially make the
		 * stack grow a lot less.
		 */
		mpi_size_t esize = size - 1;	/* even size */
		mpi_limb_t cy_limb;

		MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
		cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
		prodp[esize + esize] = cy_limb;
		cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);

		prodp[esize + size] = cy_limb;
	} else {
		mpi_size_t hsize = size >> 1;
		mpi_limb_t cy;

		/* Product H.      ________________  ________________
		 *                |_____U1 x U1____||____U0 x U0_____|
		 * Put result in upper part of PROD and pass low part of TSPACE
		 * as new TSPACE.
		 */
		MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);

		/* Product M.      ________________
		 *                |_(U1-U0)(U0-U1)_|
		 */
		if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
			mpihelp_sub_n(prodp, up + hsize, up, hsize);
		else
			mpihelp_sub_n(prodp, up, up + hsize, hsize);

		/* Read temporary operands from low part of PROD.
		 * Put result in low part of TSPACE using upper part of TSPACE
		 * as new TSPACE.  */
		MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);

		/* Add/copy product H  */
		MPN_COPY(prodp + hsize, prodp + size, hsize);
		cy = mpihelp_add_n(prodp + size, prodp + size,
				   prodp + size + hsize, hsize);

		/* Add product M (if NEGFLG M is a negative number).  */
		cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);

		/* Product L.      ________________  ________________
		 *                |________________||____U0 x U0_____|
		 * Read temporary operands from low part of PROD.
		 * Put result in low part of TSPACE using upper part of TSPACE
		 * as new TSPACE.  */
		MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);

		/* Add/copy Product L (twice).  */
		cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
		if (cy)
			mpihelp_add_1(prodp + hsize + size,
				      prodp + hsize + size, hsize, cy);

		MPN_COPY(prodp, tspace, hsize);
		cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
				   hsize);
		if (cy)
			mpihelp_add_1(prodp + size, prodp + size, size, 1);
	}
}

int
mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
			   mpi_ptr_t up, mpi_size_t usize,
			   mpi_ptr_t vp, mpi_size_t vsize,
			   struct karatsuba_ctx *ctx)
{
	mpi_limb_t cy;

	if (!ctx->tspace || ctx->tspace_size < vsize) {
		if (ctx->tspace)
			mpi_free_limb_space(ctx->tspace);
		ctx->tspace = mpi_alloc_limb_space(2 * vsize);
		if (!ctx->tspace)
			return -ENOMEM;
		ctx->tspace_size = vsize;
	}

	MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);

	prodp += vsize;
	up += vsize;
	usize -= vsize;
	if (usize >= vsize) {
		if (!ctx->tp || ctx->tp_size < vsize) {
			if (ctx->tp)
				mpi_free_limb_space(ctx->tp);
			ctx->tp = mpi_alloc_limb_space(2 * vsize);
			if (!ctx->tp) {
				if (ctx->tspace)
					mpi_free_limb_space(ctx->tspace);
				ctx->tspace = NULL;
				return -ENOMEM;
			}
			ctx->tp_size = vsize;
		}

		do {
			MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
			cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
			mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
				      cy);
			prodp += vsize;
			up += vsize;
			usize -= vsize;
		} while (usize >= vsize);
	}

	if (usize) {
		if (usize < KARATSUBA_THRESHOLD) {
			mpi_limb_t tmp;
			if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
			    < 0)
				return -ENOMEM;
		} else {
			if (!ctx->next) {
				ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
				if (!ctx->next)
					return -ENOMEM;
			}
			if (mpihelp_mul_karatsuba_case(ctx->tspace,
						       vp, vsize,
						       up, usize,
						       ctx->next) < 0)
				return -ENOMEM;
		}

		cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
		mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
	}

	return 0;
}

void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx)
{
	struct karatsuba_ctx *ctx2;

	if (ctx->tp)
		mpi_free_limb_space(ctx->tp);
	if (ctx->tspace)
		mpi_free_limb_space(ctx->tspace);
	for (ctx = ctx->next; ctx; ctx = ctx2) {
		ctx2 = ctx->next;
		if (ctx->tp)
			mpi_free_limb_space(ctx->tp);
		if (ctx->tspace)
			mpi_free_limb_space(ctx->tspace);
		kfree(ctx);
	}
}

/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
 * and v (pointed to by VP, with VSIZE limbs), and store the result at
 * PRODP.  USIZE + VSIZE limbs are always stored, but if the input
 * operands are normalized.  Return the most significant limb of the
 * result.
 *
 * NOTE: The space pointed to by PRODP is overwritten before finished
 * with U and V, so overlap is an error.
 *
 * Argument constraints:
 * 1. USIZE >= VSIZE.
 * 2. PRODP != UP and PRODP != VP, i.e. the destination
 *    must be distinct from the multiplier and the multiplicand.
 */

int
mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
	    mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
{
	mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
	mpi_limb_t cy;
	struct karatsuba_ctx ctx;

	if (vsize < KARATSUBA_THRESHOLD) {
		mpi_size_t i;
		mpi_limb_t v_limb;

		if (!vsize) {
			*_result = 0;
			return 0;
		}

		/* Multiply by the first limb in V separately, as the result can be
		 * stored (not added) to PROD.  We also avoid a loop for zeroing.  */
		v_limb = vp[0];
		if (v_limb <= 1) {
			if (v_limb == 1)
				MPN_COPY(prodp, up, usize);
			else
				MPN_ZERO(prodp, usize);
			cy = 0;
		} else
			cy = mpihelp_mul_1(prodp, up, usize, v_limb);

		prodp[usize] = cy;
		prodp++;

		/* For each iteration in the outer loop, multiply one limb from
		 * U with one limb from V, and add it to PROD.  */
		for (i = 1; i < vsize; i++) {
			v_limb = vp[i];
			if (v_limb <= 1) {
				cy = 0;
				if (v_limb == 1)
					cy = mpihelp_add_n(prodp, prodp, up,
							   usize);
			} else
				cy = mpihelp_addmul_1(prodp, up, usize, v_limb);

			prodp[usize] = cy;
			prodp++;
		}

		*_result = cy;
		return 0;
	}

	memset(&ctx, 0, sizeof ctx);
	if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
		return -ENOMEM;
	mpihelp_release_karatsuba_ctx(&ctx);
	*_result = *prod_endp;
	return 0;
}