Root/lib/mpi/mpih-mul.c

1/* mpihelp-mul.c - MPI helper functions
2 * Copyright (C) 1994, 1996, 1998, 1999,
3 * 2000 Free Software Foundation, Inc.
4 *
5 * This file is part of GnuPG.
6 *
7 * GnuPG is free software; you can redistribute it and/or modify
8 * it under the terms of the GNU General Public License as published by
9 * the Free Software Foundation; either version 2 of the License, or
10 * (at your option) any later version.
11 *
12 * GnuPG is distributed in the hope that it will be useful,
13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 * GNU General Public License for more details.
16 *
17 * You should have received a copy of the GNU General Public License
18 * along with this program; if not, write to the Free Software
19 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
20 *
21 * Note: This code is heavily based on the GNU MP Library.
22 * Actually it's the same code with only minor changes in the
23 * way the data is stored; this is to support the abstraction
24 * of an optional secure memory allocation which may be used
25 * to avoid revealing of sensitive data due to paging etc.
26 * The GNU MP Library itself is published under the LGPL;
27 * however I decided to publish this code under the plain GPL.
28 */
29
30#include <linux/string.h>
31#include "mpi-internal.h"
32#include "longlong.h"
33
34#define MPN_MUL_N_RECURSE(prodp, up, vp, size, tspace) \
35    do { \
36        if ((size) < KARATSUBA_THRESHOLD) \
37            mul_n_basecase(prodp, up, vp, size); \
38        else \
39            mul_n(prodp, up, vp, size, tspace); \
40    } while (0);
41
42#define MPN_SQR_N_RECURSE(prodp, up, size, tspace) \
43    do { \
44        if ((size) < KARATSUBA_THRESHOLD) \
45            mpih_sqr_n_basecase(prodp, up, size); \
46        else \
47            mpih_sqr_n(prodp, up, size, tspace); \
48    } while (0);
49
50/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
51 * both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
52 * always stored. Return the most significant limb.
53 *
54 * Argument constraints:
55 * 1. PRODP != UP and PRODP != VP, i.e. the destination
56 * must be distinct from the multiplier and the multiplicand.
57 *
58 *
59 * Handle simple cases with traditional multiplication.
60 *
61 * This is the most critical code of multiplication. All multiplies rely
62 * on this, both small and huge. Small ones arrive here immediately. Huge
63 * ones arrive here as this is the base case for Karatsuba's recursive
64 * algorithm below.
65 */
66
67static mpi_limb_t
68mul_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp, mpi_size_t size)
69{
70    mpi_size_t i;
71    mpi_limb_t cy;
72    mpi_limb_t v_limb;
73
74    /* Multiply by the first limb in V separately, as the result can be
75     * stored (not added) to PROD. We also avoid a loop for zeroing. */
76    v_limb = vp[0];
77    if (v_limb <= 1) {
78        if (v_limb == 1)
79            MPN_COPY(prodp, up, size);
80        else
81            MPN_ZERO(prodp, size);
82        cy = 0;
83    } else
84        cy = mpihelp_mul_1(prodp, up, size, v_limb);
85
86    prodp[size] = cy;
87    prodp++;
88
89    /* For each iteration in the outer loop, multiply one limb from
90     * U with one limb from V, and add it to PROD. */
91    for (i = 1; i < size; i++) {
92        v_limb = vp[i];
93        if (v_limb <= 1) {
94            cy = 0;
95            if (v_limb == 1)
96                cy = mpihelp_add_n(prodp, prodp, up, size);
97        } else
98            cy = mpihelp_addmul_1(prodp, up, size, v_limb);
99
100        prodp[size] = cy;
101        prodp++;
102    }
103
104    return cy;
105}
106
107static void
108mul_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_ptr_t vp,
109        mpi_size_t size, mpi_ptr_t tspace)
110{
111    if (size & 1) {
112        /* The size is odd, and the code below doesn't handle that.
113         * Multiply the least significant (size - 1) limbs with a recursive
114         * call, and handle the most significant limb of S1 and S2
115         * separately.
116         * A slightly faster way to do this would be to make the Karatsuba
117         * code below behave as if the size were even, and let it check for
118         * odd size in the end. I.e., in essence move this code to the end.
119         * Doing so would save us a recursive call, and potentially make the
120         * stack grow a lot less.
121         */
122        mpi_size_t esize = size - 1; /* even size */
123        mpi_limb_t cy_limb;
124
125        MPN_MUL_N_RECURSE(prodp, up, vp, esize, tspace);
126        cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, vp[esize]);
127        prodp[esize + esize] = cy_limb;
128        cy_limb = mpihelp_addmul_1(prodp + esize, vp, size, up[esize]);
129        prodp[esize + size] = cy_limb;
130    } else {
131        /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
132         *
133         * Split U in two pieces, U1 and U0, such that
134         * U = U0 + U1*(B**n),
135         * and V in V1 and V0, such that
136         * V = V0 + V1*(B**n).
137         *
138         * UV is then computed recursively using the identity
139         *
140         * 2n n n n
141         * UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
142         * 1 1 1 0 0 1 0 0
143         *
144         * Where B = 2**BITS_PER_MP_LIMB.
145         */
146        mpi_size_t hsize = size >> 1;
147        mpi_limb_t cy;
148        int negflg;
149
150        /* Product H. ________________ ________________
151         * |_____U1 x V1____||____U0 x V0_____|
152         * Put result in upper part of PROD and pass low part of TSPACE
153         * as new TSPACE.
154         */
155        MPN_MUL_N_RECURSE(prodp + size, up + hsize, vp + hsize, hsize,
156                  tspace);
157
158        /* Product M. ________________
159         * |_(U1-U0)(V0-V1)_|
160         */
161        if (mpihelp_cmp(up + hsize, up, hsize) >= 0) {
162            mpihelp_sub_n(prodp, up + hsize, up, hsize);
163            negflg = 0;
164        } else {
165            mpihelp_sub_n(prodp, up, up + hsize, hsize);
166            negflg = 1;
167        }
168        if (mpihelp_cmp(vp + hsize, vp, hsize) >= 0) {
169            mpihelp_sub_n(prodp + hsize, vp + hsize, vp, hsize);
170            negflg ^= 1;
171        } else {
172            mpihelp_sub_n(prodp + hsize, vp, vp + hsize, hsize);
173            /* No change of NEGFLG. */
174        }
175        /* Read temporary operands from low part of PROD.
176         * Put result in low part of TSPACE using upper part of TSPACE
177         * as new TSPACE.
178         */
179        MPN_MUL_N_RECURSE(tspace, prodp, prodp + hsize, hsize,
180                  tspace + size);
181
182        /* Add/copy product H. */
183        MPN_COPY(prodp + hsize, prodp + size, hsize);
184        cy = mpihelp_add_n(prodp + size, prodp + size,
185                   prodp + size + hsize, hsize);
186
187        /* Add product M (if NEGFLG M is a negative number) */
188        if (negflg)
189            cy -=
190                mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace,
191                      size);
192        else
193            cy +=
194                mpihelp_add_n(prodp + hsize, prodp + hsize, tspace,
195                      size);
196
197        /* Product L. ________________ ________________
198         * |________________||____U0 x V0_____|
199         * Read temporary operands from low part of PROD.
200         * Put result in low part of TSPACE using upper part of TSPACE
201         * as new TSPACE.
202         */
203        MPN_MUL_N_RECURSE(tspace, up, vp, hsize, tspace + size);
204
205        /* Add/copy Product L (twice) */
206
207        cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
208        if (cy)
209            mpihelp_add_1(prodp + hsize + size,
210                      prodp + hsize + size, hsize, cy);
211
212        MPN_COPY(prodp, tspace, hsize);
213        cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
214                   hsize);
215        if (cy)
216            mpihelp_add_1(prodp + size, prodp + size, size, 1);
217    }
218}
219
220void mpih_sqr_n_basecase(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size)
221{
222    mpi_size_t i;
223    mpi_limb_t cy_limb;
224    mpi_limb_t v_limb;
225
226    /* Multiply by the first limb in V separately, as the result can be
227     * stored (not added) to PROD. We also avoid a loop for zeroing. */
228    v_limb = up[0];
229    if (v_limb <= 1) {
230        if (v_limb == 1)
231            MPN_COPY(prodp, up, size);
232        else
233            MPN_ZERO(prodp, size);
234        cy_limb = 0;
235    } else
236        cy_limb = mpihelp_mul_1(prodp, up, size, v_limb);
237
238    prodp[size] = cy_limb;
239    prodp++;
240
241    /* For each iteration in the outer loop, multiply one limb from
242     * U with one limb from V, and add it to PROD. */
243    for (i = 1; i < size; i++) {
244        v_limb = up[i];
245        if (v_limb <= 1) {
246            cy_limb = 0;
247            if (v_limb == 1)
248                cy_limb = mpihelp_add_n(prodp, prodp, up, size);
249        } else
250            cy_limb = mpihelp_addmul_1(prodp, up, size, v_limb);
251
252        prodp[size] = cy_limb;
253        prodp++;
254    }
255}
256
257void
258mpih_sqr_n(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t size, mpi_ptr_t tspace)
259{
260    if (size & 1) {
261        /* The size is odd, and the code below doesn't handle that.
262         * Multiply the least significant (size - 1) limbs with a recursive
263         * call, and handle the most significant limb of S1 and S2
264         * separately.
265         * A slightly faster way to do this would be to make the Karatsuba
266         * code below behave as if the size were even, and let it check for
267         * odd size in the end. I.e., in essence move this code to the end.
268         * Doing so would save us a recursive call, and potentially make the
269         * stack grow a lot less.
270         */
271        mpi_size_t esize = size - 1; /* even size */
272        mpi_limb_t cy_limb;
273
274        MPN_SQR_N_RECURSE(prodp, up, esize, tspace);
275        cy_limb = mpihelp_addmul_1(prodp + esize, up, esize, up[esize]);
276        prodp[esize + esize] = cy_limb;
277        cy_limb = mpihelp_addmul_1(prodp + esize, up, size, up[esize]);
278
279        prodp[esize + size] = cy_limb;
280    } else {
281        mpi_size_t hsize = size >> 1;
282        mpi_limb_t cy;
283
284        /* Product H. ________________ ________________
285         * |_____U1 x U1____||____U0 x U0_____|
286         * Put result in upper part of PROD and pass low part of TSPACE
287         * as new TSPACE.
288         */
289        MPN_SQR_N_RECURSE(prodp + size, up + hsize, hsize, tspace);
290
291        /* Product M. ________________
292         * |_(U1-U0)(U0-U1)_|
293         */
294        if (mpihelp_cmp(up + hsize, up, hsize) >= 0)
295            mpihelp_sub_n(prodp, up + hsize, up, hsize);
296        else
297            mpihelp_sub_n(prodp, up, up + hsize, hsize);
298
299        /* Read temporary operands from low part of PROD.
300         * Put result in low part of TSPACE using upper part of TSPACE
301         * as new TSPACE. */
302        MPN_SQR_N_RECURSE(tspace, prodp, hsize, tspace + size);
303
304        /* Add/copy product H */
305        MPN_COPY(prodp + hsize, prodp + size, hsize);
306        cy = mpihelp_add_n(prodp + size, prodp + size,
307                   prodp + size + hsize, hsize);
308
309        /* Add product M (if NEGFLG M is a negative number). */
310        cy -= mpihelp_sub_n(prodp + hsize, prodp + hsize, tspace, size);
311
312        /* Product L. ________________ ________________
313         * |________________||____U0 x U0_____|
314         * Read temporary operands from low part of PROD.
315         * Put result in low part of TSPACE using upper part of TSPACE
316         * as new TSPACE. */
317        MPN_SQR_N_RECURSE(tspace, up, hsize, tspace + size);
318
319        /* Add/copy Product L (twice). */
320        cy += mpihelp_add_n(prodp + hsize, prodp + hsize, tspace, size);
321        if (cy)
322            mpihelp_add_1(prodp + hsize + size,
323                      prodp + hsize + size, hsize, cy);
324
325        MPN_COPY(prodp, tspace, hsize);
326        cy = mpihelp_add_n(prodp + hsize, prodp + hsize, tspace + hsize,
327                   hsize);
328        if (cy)
329            mpihelp_add_1(prodp + size, prodp + size, size, 1);
330    }
331}
332
333int
334mpihelp_mul_karatsuba_case(mpi_ptr_t prodp,
335               mpi_ptr_t up, mpi_size_t usize,
336               mpi_ptr_t vp, mpi_size_t vsize,
337               struct karatsuba_ctx *ctx)
338{
339    mpi_limb_t cy;
340
341    if (!ctx->tspace || ctx->tspace_size < vsize) {
342        if (ctx->tspace)
343            mpi_free_limb_space(ctx->tspace);
344        ctx->tspace = mpi_alloc_limb_space(2 * vsize);
345        if (!ctx->tspace)
346            return -ENOMEM;
347        ctx->tspace_size = vsize;
348    }
349
350    MPN_MUL_N_RECURSE(prodp, up, vp, vsize, ctx->tspace);
351
352    prodp += vsize;
353    up += vsize;
354    usize -= vsize;
355    if (usize >= vsize) {
356        if (!ctx->tp || ctx->tp_size < vsize) {
357            if (ctx->tp)
358                mpi_free_limb_space(ctx->tp);
359            ctx->tp = mpi_alloc_limb_space(2 * vsize);
360            if (!ctx->tp) {
361                if (ctx->tspace)
362                    mpi_free_limb_space(ctx->tspace);
363                ctx->tspace = NULL;
364                return -ENOMEM;
365            }
366            ctx->tp_size = vsize;
367        }
368
369        do {
370            MPN_MUL_N_RECURSE(ctx->tp, up, vp, vsize, ctx->tspace);
371            cy = mpihelp_add_n(prodp, prodp, ctx->tp, vsize);
372            mpihelp_add_1(prodp + vsize, ctx->tp + vsize, vsize,
373                      cy);
374            prodp += vsize;
375            up += vsize;
376            usize -= vsize;
377        } while (usize >= vsize);
378    }
379
380    if (usize) {
381        if (usize < KARATSUBA_THRESHOLD) {
382            mpi_limb_t tmp;
383            if (mpihelp_mul(ctx->tspace, vp, vsize, up, usize, &tmp)
384                < 0)
385                return -ENOMEM;
386        } else {
387            if (!ctx->next) {
388                ctx->next = kzalloc(sizeof *ctx, GFP_KERNEL);
389                if (!ctx->next)
390                    return -ENOMEM;
391            }
392            if (mpihelp_mul_karatsuba_case(ctx->tspace,
393                               vp, vsize,
394                               up, usize,
395                               ctx->next) < 0)
396                return -ENOMEM;
397        }
398
399        cy = mpihelp_add_n(prodp, prodp, ctx->tspace, vsize);
400        mpihelp_add_1(prodp + vsize, ctx->tspace + vsize, usize, cy);
401    }
402
403    return 0;
404}
405
406void mpihelp_release_karatsuba_ctx(struct karatsuba_ctx *ctx)
407{
408    struct karatsuba_ctx *ctx2;
409
410    if (ctx->tp)
411        mpi_free_limb_space(ctx->tp);
412    if (ctx->tspace)
413        mpi_free_limb_space(ctx->tspace);
414    for (ctx = ctx->next; ctx; ctx = ctx2) {
415        ctx2 = ctx->next;
416        if (ctx->tp)
417            mpi_free_limb_space(ctx->tp);
418        if (ctx->tspace)
419            mpi_free_limb_space(ctx->tspace);
420        kfree(ctx);
421    }
422}
423
424/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
425 * and v (pointed to by VP, with VSIZE limbs), and store the result at
426 * PRODP. USIZE + VSIZE limbs are always stored, but if the input
427 * operands are normalized. Return the most significant limb of the
428 * result.
429 *
430 * NOTE: The space pointed to by PRODP is overwritten before finished
431 * with U and V, so overlap is an error.
432 *
433 * Argument constraints:
434 * 1. USIZE >= VSIZE.
435 * 2. PRODP != UP and PRODP != VP, i.e. the destination
436 * must be distinct from the multiplier and the multiplicand.
437 */
438
439int
440mpihelp_mul(mpi_ptr_t prodp, mpi_ptr_t up, mpi_size_t usize,
441        mpi_ptr_t vp, mpi_size_t vsize, mpi_limb_t *_result)
442{
443    mpi_ptr_t prod_endp = prodp + usize + vsize - 1;
444    mpi_limb_t cy;
445    struct karatsuba_ctx ctx;
446
447    if (vsize < KARATSUBA_THRESHOLD) {
448        mpi_size_t i;
449        mpi_limb_t v_limb;
450
451        if (!vsize) {
452            *_result = 0;
453            return 0;
454        }
455
456        /* Multiply by the first limb in V separately, as the result can be
457         * stored (not added) to PROD. We also avoid a loop for zeroing. */
458        v_limb = vp[0];
459        if (v_limb <= 1) {
460            if (v_limb == 1)
461                MPN_COPY(prodp, up, usize);
462            else
463                MPN_ZERO(prodp, usize);
464            cy = 0;
465        } else
466            cy = mpihelp_mul_1(prodp, up, usize, v_limb);
467
468        prodp[usize] = cy;
469        prodp++;
470
471        /* For each iteration in the outer loop, multiply one limb from
472         * U with one limb from V, and add it to PROD. */
473        for (i = 1; i < vsize; i++) {
474            v_limb = vp[i];
475            if (v_limb <= 1) {
476                cy = 0;
477                if (v_limb == 1)
478                    cy = mpihelp_add_n(prodp, prodp, up,
479                               usize);
480            } else
481                cy = mpihelp_addmul_1(prodp, up, usize, v_limb);
482
483            prodp[usize] = cy;
484            prodp++;
485        }
486
487        *_result = cy;
488        return 0;
489    }
490
491    memset(&ctx, 0, sizeof ctx);
492    if (mpihelp_mul_karatsuba_case(prodp, up, usize, vp, vsize, &ctx) < 0)
493        return -ENOMEM;
494    mpihelp_release_karatsuba_ctx(&ctx);
495    *_result = *prod_endp;
496    return 0;
497}
498

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