1/* mpi-div.c  -  MPI functions
  2 * Copyright (C) 1994, 1996, 1998, 2001, 2002,
  3 *               2003 Free Software Foundation, Inc.
  4 *
  5 * This file is part of Libgcrypt.
  6 *
  7 * Note: This code is heavily based on the GNU MP Library.
  8 *	 Actually it's the same code with only minor changes in the
  9 *	 way the data is stored; this is to support the abstraction
 10 *	 of an optional secure memory allocation which may be used
 11 *	 to avoid revealing of sensitive data due to paging etc.
 12 */
 13
 14#include "mpi-internal.h"
 15#include "longlong.h"
 16
 17void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
 18void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
 19
 20void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
 21{
 22	int divisor_sign = divisor->sign;
 23	MPI temp_divisor = NULL;
 24
 25	/* We need the original value of the divisor after the remainder has been
 26	 * preliminary calculated.	We have to copy it to temporary space if it's
 27	 * the same variable as REM.
 28	 */
 29	if (rem == divisor) {
 30		temp_divisor = mpi_copy(divisor);
 31		divisor = temp_divisor;
 32	}
 33
 34	mpi_tdiv_r(rem, dividend, divisor);
 35
 36	if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
 37		mpi_add(rem, rem, divisor);
 38
 39	if (temp_divisor)
 40		mpi_free(temp_divisor);
 41}
 42
 43void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
 44{
 45	MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
 46	mpi_fdiv_qr(quot, tmp, dividend, divisor);
 47	mpi_free(tmp);
 48}
 49
 50void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
 51{
 52	int divisor_sign = divisor->sign;
 53	MPI temp_divisor = NULL;
 54
 55	if (quot == divisor || rem == divisor) {
 56		temp_divisor = mpi_copy(divisor);
 57		divisor = temp_divisor;
 58	}
 59
 60	mpi_tdiv_qr(quot, rem, dividend, divisor);
 61
 62	if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
 63		mpi_sub_ui(quot, quot, 1);
 64		mpi_add(rem, rem, divisor);
 65	}
 66
 67	if (temp_divisor)
 68		mpi_free(temp_divisor);
 69}
 70
 71/* If den == quot, den needs temporary storage.
 72 * If den == rem, den needs temporary storage.
 73 * If num == quot, num needs temporary storage.
 74 * If den has temporary storage, it can be normalized while being copied,
 75 *   i.e no extra storage should be allocated.
 76 */
 77
 78void mpi_tdiv_r(MPI rem, MPI num, MPI den)
 79{
 80	mpi_tdiv_qr(NULL, rem, num, den);
 81}
 82
 83void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
 84{
 85	mpi_ptr_t np, dp;
 86	mpi_ptr_t qp, rp;
 87	mpi_size_t nsize = num->nlimbs;
 88	mpi_size_t dsize = den->nlimbs;
 89	mpi_size_t qsize, rsize;
 90	mpi_size_t sign_remainder = num->sign;
 91	mpi_size_t sign_quotient = num->sign ^ den->sign;
 92	unsigned int normalization_steps;
 93	mpi_limb_t q_limb;
 94	mpi_ptr_t marker[5];
 95	int markidx = 0;
 96
 97	/* Ensure space is enough for quotient and remainder.
 98	 * We need space for an extra limb in the remainder, because it's
 99	 * up-shifted (normalized) below.
100	 */
101	rsize = nsize + 1;
102	mpi_resize(rem, rsize);
103
104	qsize = rsize - dsize;	  /* qsize cannot be bigger than this.	*/
105	if (qsize <= 0) {
106		if (num != rem) {
107			rem->nlimbs = num->nlimbs;
108			rem->sign = num->sign;
109			MPN_COPY(rem->d, num->d, nsize);
110		}
111		if (quot) {
112			/* This needs to follow the assignment to rem, in case the
113			 * numerator and quotient are the same.
114			 */
115			quot->nlimbs = 0;
116			quot->sign = 0;
117		}
118		return;
119	}
120
121	if (quot)
122		mpi_resize(quot, qsize);
123
124	/* Read pointers here, when reallocation is finished.  */
125	np = num->d;
126	dp = den->d;
127	rp = rem->d;
128
129	/* Optimize division by a single-limb divisor.  */
130	if (dsize == 1) {
131		mpi_limb_t rlimb;
132		if (quot) {
133			qp = quot->d;
134			rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
135			qsize -= qp[qsize - 1] == 0;
136			quot->nlimbs = qsize;
137			quot->sign = sign_quotient;
138		} else
139			rlimb = mpihelp_mod_1(np, nsize, dp[0]);
140		rp[0] = rlimb;
141		rsize = rlimb != 0?1:0;
142		rem->nlimbs = rsize;
143		rem->sign = sign_remainder;
144		return;
145	}
146
147
148	if (quot) {
149		qp = quot->d;
150		/* Make sure QP and NP point to different objects.  Otherwise the
151		 * numerator would be gradually overwritten by the quotient limbs.
152		 */
153		if (qp == np) { /* Copy NP object to temporary space.  */
154			np = marker[markidx++] = mpi_alloc_limb_space(nsize);
155			MPN_COPY(np, qp, nsize);
156		}
157	} else /* Put quotient at top of remainder. */
158		qp = rp + dsize;
159
160	normalization_steps = count_leading_zeros(dp[dsize - 1]);
161
162	/* Normalize the denominator, i.e. make its most significant bit set by
163	 * shifting it NORMALIZATION_STEPS bits to the left.  Also shift the
164	 * numerator the same number of steps (to keep the quotient the same!).
165	 */
166	if (normalization_steps) {
167		mpi_ptr_t tp;
168		mpi_limb_t nlimb;
169
170		/* Shift up the denominator setting the most significant bit of
171		 * the most significant word.  Use temporary storage not to clobber
172		 * the original contents of the denominator.
173		 */
174		tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
175		mpihelp_lshift(tp, dp, dsize, normalization_steps);
176		dp = tp;
177
178		/* Shift up the numerator, possibly introducing a new most
179		 * significant word.  Move the shifted numerator in the remainder
180		 * meanwhile.
181		 */
182		nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
183		if (nlimb) {
184			rp[nsize] = nlimb;
185			rsize = nsize + 1;
186		} else
187			rsize = nsize;
188	} else {
189		/* The denominator is already normalized, as required.	Copy it to
190		 * temporary space if it overlaps with the quotient or remainder.
191		 */
192		if (dp == rp || (quot && (dp == qp))) {
193			mpi_ptr_t tp;
194
195			tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
196			MPN_COPY(tp, dp, dsize);
197			dp = tp;
198		}
199
200		/* Move the numerator to the remainder.  */
201		if (rp != np)
202			MPN_COPY(rp, np, nsize);
203
204		rsize = nsize;
205	}
206
207	q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
208
209	if (quot) {
210		qsize = rsize - dsize;
211		if (q_limb) {
212			qp[qsize] = q_limb;
213			qsize += 1;
214		}
215
216		quot->nlimbs = qsize;
217		quot->sign = sign_quotient;
218	}
219
220	rsize = dsize;
221	MPN_NORMALIZE(rp, rsize);
222
223	if (normalization_steps && rsize) {
224		mpihelp_rshift(rp, rp, rsize, normalization_steps);
225		rsize -= rp[rsize - 1] == 0?1:0;
226	}
227
228	rem->nlimbs = rsize;
229	rem->sign	= sign_remainder;
230	while (markidx) {
231		markidx--;
232		mpi_free_limb_space(marker[markidx]);
233	}
234}