1 /* mpi-div.c - MPI functions
2 * Copyright (C) 1994, 1996 Free Software Foundation, Inc.
3 * Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
5 * This file is part of GnuPG.
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.
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.
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
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.
30 #include <linux/string.h>
31 #include "mpi-internal.h"
36 mpi_fdiv_r( MPI rem, MPI dividend, MPI divisor )
39 int divisor_sign = divisor->sign;
40 MPI temp_divisor = NULL;
42 /* We need the original value of the divisor after the remainder has been
43 * preliminary calculated. We have to copy it to temporary space if it's
44 * the same variable as REM. */
45 if( rem == divisor ) {
46 if (mpi_copy( &temp_divisor, divisor ) < 0) goto nomem;
47 divisor = temp_divisor;
50 if (mpi_tdiv_qr(NULL, rem, dividend, divisor ) < 0) goto nomem;
51 if( ((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs )
52 if (mpi_add( rem, rem, divisor) < 0) goto nomem;
58 mpi_free(temp_divisor);
64 * Division rounding the quotient towards -infinity.
65 * The remainder gets the same sign as the denominator.
70 mpi_fdiv_r_ui( MPI rem, MPI dividend, ulong divisor )
74 rlimb = mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );
75 if( rlimb && dividend->sign )
76 rlimb = divisor - rlimb;
80 rem->nlimbs = rlimb? 1:0;
87 mpi_fdiv_q( MPI quot, MPI dividend, MPI divisor )
89 MPI tmp = mpi_alloc( mpi_get_nlimbs(quot) );
92 mpi_fdiv_qr( quot, tmp, dividend, divisor);
98 mpi_fdiv_qr( MPI quot, MPI rem, MPI dividend, MPI divisor )
100 int divisor_sign = divisor->sign;
101 MPI temp_divisor = NULL;
103 if( quot == divisor || rem == divisor ) {
104 if (mpi_copy( &temp_divisor, divisor ) < 0);
106 divisor = temp_divisor;
109 if (mpi_tdiv_qr( quot, rem, dividend, divisor ) < 0)
112 if( (divisor_sign ^ dividend->sign) && rem->nlimbs ) {
113 if (mpi_sub_ui( quot, quot, 1 ) < 0)
115 if (mpi_add( rem, rem, divisor) < 0)
120 mpi_free(temp_divisor);
125 mpi_free(temp_divisor);
130 /* If den == quot, den needs temporary storage.
131 * If den == rem, den needs temporary storage.
132 * If num == quot, num needs temporary storage.
133 * If den has temporary storage, it can be normalized while being copied,
134 * i.e no extra storage should be allocated.
138 mpi_tdiv_r( MPI rem, MPI num, MPI den)
140 return mpi_tdiv_qr(NULL, rem, num, den );
144 mpi_tdiv_qr( MPI quot, MPI rem, MPI num, MPI den)
149 mpi_size_t nsize = num->nlimbs;
150 mpi_size_t dsize = den->nlimbs;
151 mpi_size_t qsize, rsize;
152 mpi_size_t sign_remainder = num->sign;
153 mpi_size_t sign_quotient = num->sign ^ den->sign;
154 unsigned normalization_steps;
159 memset(marker,0,sizeof(marker));
161 /* Ensure space is enough for quotient and remainder.
162 * We need space for an extra limb in the remainder, because it's
163 * up-shifted (normalized) below. */
165 if (mpi_resize( rem, rsize) < 0) goto nomem;
167 qsize = rsize - dsize; /* qsize cannot be bigger than this. */
170 rem->nlimbs = num->nlimbs;
171 rem->sign = num->sign;
172 MPN_COPY(rem->d, num->d, nsize);
175 /* This needs to follow the assignment to rem, in case the
176 * numerator and quotient are the same. */
184 if (mpi_resize( quot, qsize) < 0) goto nomem;
186 /* Read pointers here, when reallocation is finished. */
191 /* Optimize division by a single-limb divisor. */
196 rlimb = mpihelp_divmod_1( qp, np, nsize, dp[0] );
197 qsize -= qp[qsize - 1] == 0;
198 quot->nlimbs = qsize;
199 quot->sign = sign_quotient;
202 rlimb = mpihelp_mod_1( np, nsize, dp[0] );
204 rsize = rlimb != 0?1:0;
206 rem->sign = sign_remainder;
213 /* Make sure QP and NP point to different objects. Otherwise the
214 * numerator would be gradually overwritten by the quotient limbs. */
215 if(qp == np) { /* Copy NP object to temporary space. */
216 np = marker[markidx++] = mpi_alloc_limb_space(nsize);
217 MPN_COPY(np, qp, nsize);
220 else /* Put quotient at top of remainder. */
223 count_leading_zeros( normalization_steps, dp[dsize - 1] );
225 /* Normalize the denominator, i.e. make its most significant bit set by
226 * shifting it NORMALIZATION_STEPS bits to the left. Also shift the
227 * numerator the same number of steps (to keep the quotient the same!).
229 if( normalization_steps ) {
233 /* Shift up the denominator setting the most significant bit of
234 * the most significant word. Use temporary storage not to clobber
235 * the original contents of the denominator. */
236 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
238 mpihelp_lshift( tp, dp, dsize, normalization_steps );
241 /* Shift up the numerator, possibly introducing a new most
242 * significant word. Move the shifted numerator in the remainder
244 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
253 /* The denominator is already normalized, as required. Copy it to
254 * temporary space if it overlaps with the quotient or remainder. */
255 if( dp == rp || (quot && (dp == qp))) {
258 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
260 MPN_COPY( tp, dp, dsize );
264 /* Move the numerator to the remainder. */
266 MPN_COPY(rp, np, nsize);
271 q_limb = mpihelp_divrem( qp, 0, rp, rsize, dp, dsize );
274 qsize = rsize - dsize;
280 quot->nlimbs = qsize;
281 quot->sign = sign_quotient;
285 MPN_NORMALIZE (rp, rsize);
287 if( normalization_steps && rsize ) {
288 mpihelp_rshift(rp, rp, rsize, normalization_steps);
289 rsize -= rp[rsize - 1] == 0?1:0;
293 rem->sign = sign_remainder;
298 mpi_free_limb_space(marker[--markidx]);
303 mpi_tdiv_q_2exp( MPI w, MPI u, unsigned count )
305 mpi_size_t usize, wsize;
309 limb_cnt = count / BITS_PER_MPI_LIMB;
310 wsize = usize - limb_cnt;
311 if( limb_cnt >= usize )
317 if (RESIZE_IF_NEEDED( w, wsize ) < 0)
322 count %= BITS_PER_MPI_LIMB;
324 mpihelp_rshift( wp, up + limb_cnt, wsize, count );
325 wsize -= !wp[wsize - 1];
328 MPN_COPY_INCR( wp, up + limb_cnt, wsize);
337 * Check whether dividend is divisible by divisor
338 * (note: divisor must fit into a limb)
341 mpi_divisible_ui(MPI dividend, ulong divisor )
343 return !mpihelp_mod_1( dividend->d, dividend->nlimbs, divisor );