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 
17 void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
18 void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
19 
mpi_fdiv_r(MPI rem,MPI dividend,MPI divisor)20 void 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 
mpi_fdiv_q(MPI quot,MPI dividend,MPI divisor)43 void 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 
mpi_fdiv_qr(MPI quot,MPI rem,MPI dividend,MPI divisor)50 void 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 
mpi_tdiv_r(MPI rem,MPI num,MPI den)78 void mpi_tdiv_r(MPI rem, MPI num, MPI den)
79 {
80 	mpi_tdiv_qr(NULL, rem, num, den);
81 }
82 
mpi_tdiv_qr(MPI quot,MPI rem,MPI num,MPI den)83 void 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 }
235