1*2a598d0bSHerbert Xu /* mpi-div.c - MPI functions
2*2a598d0bSHerbert Xu * Copyright (C) 1994, 1996, 1998, 2001, 2002,
3*2a598d0bSHerbert Xu * 2003 Free Software Foundation, Inc.
4*2a598d0bSHerbert Xu *
5*2a598d0bSHerbert Xu * This file is part of Libgcrypt.
6*2a598d0bSHerbert Xu *
7*2a598d0bSHerbert Xu * Note: This code is heavily based on the GNU MP Library.
8*2a598d0bSHerbert Xu * Actually it's the same code with only minor changes in the
9*2a598d0bSHerbert Xu * way the data is stored; this is to support the abstraction
10*2a598d0bSHerbert Xu * of an optional secure memory allocation which may be used
11*2a598d0bSHerbert Xu * to avoid revealing of sensitive data due to paging etc.
12*2a598d0bSHerbert Xu */
13*2a598d0bSHerbert Xu
14*2a598d0bSHerbert Xu #include "mpi-internal.h"
15*2a598d0bSHerbert Xu #include "longlong.h"
16*2a598d0bSHerbert Xu
17*2a598d0bSHerbert Xu void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);
18*2a598d0bSHerbert Xu void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor);
19*2a598d0bSHerbert Xu
mpi_fdiv_r(MPI rem,MPI dividend,MPI divisor)20*2a598d0bSHerbert Xu void mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)
21*2a598d0bSHerbert Xu {
22*2a598d0bSHerbert Xu int divisor_sign = divisor->sign;
23*2a598d0bSHerbert Xu MPI temp_divisor = NULL;
24*2a598d0bSHerbert Xu
25*2a598d0bSHerbert Xu /* We need the original value of the divisor after the remainder has been
26*2a598d0bSHerbert Xu * preliminary calculated. We have to copy it to temporary space if it's
27*2a598d0bSHerbert Xu * the same variable as REM.
28*2a598d0bSHerbert Xu */
29*2a598d0bSHerbert Xu if (rem == divisor) {
30*2a598d0bSHerbert Xu temp_divisor = mpi_copy(divisor);
31*2a598d0bSHerbert Xu divisor = temp_divisor;
32*2a598d0bSHerbert Xu }
33*2a598d0bSHerbert Xu
34*2a598d0bSHerbert Xu mpi_tdiv_r(rem, dividend, divisor);
35*2a598d0bSHerbert Xu
36*2a598d0bSHerbert Xu if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)
37*2a598d0bSHerbert Xu mpi_add(rem, rem, divisor);
38*2a598d0bSHerbert Xu
39*2a598d0bSHerbert Xu if (temp_divisor)
40*2a598d0bSHerbert Xu mpi_free(temp_divisor);
41*2a598d0bSHerbert Xu }
42*2a598d0bSHerbert Xu
mpi_fdiv_q(MPI quot,MPI dividend,MPI divisor)43*2a598d0bSHerbert Xu void mpi_fdiv_q(MPI quot, MPI dividend, MPI divisor)
44*2a598d0bSHerbert Xu {
45*2a598d0bSHerbert Xu MPI tmp = mpi_alloc(mpi_get_nlimbs(quot));
46*2a598d0bSHerbert Xu mpi_fdiv_qr(quot, tmp, dividend, divisor);
47*2a598d0bSHerbert Xu mpi_free(tmp);
48*2a598d0bSHerbert Xu }
49*2a598d0bSHerbert Xu
mpi_fdiv_qr(MPI quot,MPI rem,MPI dividend,MPI divisor)50*2a598d0bSHerbert Xu void mpi_fdiv_qr(MPI quot, MPI rem, MPI dividend, MPI divisor)
51*2a598d0bSHerbert Xu {
52*2a598d0bSHerbert Xu int divisor_sign = divisor->sign;
53*2a598d0bSHerbert Xu MPI temp_divisor = NULL;
54*2a598d0bSHerbert Xu
55*2a598d0bSHerbert Xu if (quot == divisor || rem == divisor) {
56*2a598d0bSHerbert Xu temp_divisor = mpi_copy(divisor);
57*2a598d0bSHerbert Xu divisor = temp_divisor;
58*2a598d0bSHerbert Xu }
59*2a598d0bSHerbert Xu
60*2a598d0bSHerbert Xu mpi_tdiv_qr(quot, rem, dividend, divisor);
61*2a598d0bSHerbert Xu
62*2a598d0bSHerbert Xu if ((divisor_sign ^ dividend->sign) && rem->nlimbs) {
63*2a598d0bSHerbert Xu mpi_sub_ui(quot, quot, 1);
64*2a598d0bSHerbert Xu mpi_add(rem, rem, divisor);
65*2a598d0bSHerbert Xu }
66*2a598d0bSHerbert Xu
67*2a598d0bSHerbert Xu if (temp_divisor)
68*2a598d0bSHerbert Xu mpi_free(temp_divisor);
69*2a598d0bSHerbert Xu }
70*2a598d0bSHerbert Xu
71*2a598d0bSHerbert Xu /* If den == quot, den needs temporary storage.
72*2a598d0bSHerbert Xu * If den == rem, den needs temporary storage.
73*2a598d0bSHerbert Xu * If num == quot, num needs temporary storage.
74*2a598d0bSHerbert Xu * If den has temporary storage, it can be normalized while being copied,
75*2a598d0bSHerbert Xu * i.e no extra storage should be allocated.
76*2a598d0bSHerbert Xu */
77*2a598d0bSHerbert Xu
mpi_tdiv_r(MPI rem,MPI num,MPI den)78*2a598d0bSHerbert Xu void mpi_tdiv_r(MPI rem, MPI num, MPI den)
79*2a598d0bSHerbert Xu {
80*2a598d0bSHerbert Xu mpi_tdiv_qr(NULL, rem, num, den);
81*2a598d0bSHerbert Xu }
82*2a598d0bSHerbert Xu
mpi_tdiv_qr(MPI quot,MPI rem,MPI num,MPI den)83*2a598d0bSHerbert Xu void mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)
84*2a598d0bSHerbert Xu {
85*2a598d0bSHerbert Xu mpi_ptr_t np, dp;
86*2a598d0bSHerbert Xu mpi_ptr_t qp, rp;
87*2a598d0bSHerbert Xu mpi_size_t nsize = num->nlimbs;
88*2a598d0bSHerbert Xu mpi_size_t dsize = den->nlimbs;
89*2a598d0bSHerbert Xu mpi_size_t qsize, rsize;
90*2a598d0bSHerbert Xu mpi_size_t sign_remainder = num->sign;
91*2a598d0bSHerbert Xu mpi_size_t sign_quotient = num->sign ^ den->sign;
92*2a598d0bSHerbert Xu unsigned int normalization_steps;
93*2a598d0bSHerbert Xu mpi_limb_t q_limb;
94*2a598d0bSHerbert Xu mpi_ptr_t marker[5];
95*2a598d0bSHerbert Xu int markidx = 0;
96*2a598d0bSHerbert Xu
97*2a598d0bSHerbert Xu /* Ensure space is enough for quotient and remainder.
98*2a598d0bSHerbert Xu * We need space for an extra limb in the remainder, because it's
99*2a598d0bSHerbert Xu * up-shifted (normalized) below.
100*2a598d0bSHerbert Xu */
101*2a598d0bSHerbert Xu rsize = nsize + 1;
102*2a598d0bSHerbert Xu mpi_resize(rem, rsize);
103*2a598d0bSHerbert Xu
104*2a598d0bSHerbert Xu qsize = rsize - dsize; /* qsize cannot be bigger than this. */
105*2a598d0bSHerbert Xu if (qsize <= 0) {
106*2a598d0bSHerbert Xu if (num != rem) {
107*2a598d0bSHerbert Xu rem->nlimbs = num->nlimbs;
108*2a598d0bSHerbert Xu rem->sign = num->sign;
109*2a598d0bSHerbert Xu MPN_COPY(rem->d, num->d, nsize);
110*2a598d0bSHerbert Xu }
111*2a598d0bSHerbert Xu if (quot) {
112*2a598d0bSHerbert Xu /* This needs to follow the assignment to rem, in case the
113*2a598d0bSHerbert Xu * numerator and quotient are the same.
114*2a598d0bSHerbert Xu */
115*2a598d0bSHerbert Xu quot->nlimbs = 0;
116*2a598d0bSHerbert Xu quot->sign = 0;
117*2a598d0bSHerbert Xu }
118*2a598d0bSHerbert Xu return;
119*2a598d0bSHerbert Xu }
120*2a598d0bSHerbert Xu
121*2a598d0bSHerbert Xu if (quot)
122*2a598d0bSHerbert Xu mpi_resize(quot, qsize);
123*2a598d0bSHerbert Xu
124*2a598d0bSHerbert Xu /* Read pointers here, when reallocation is finished. */
125*2a598d0bSHerbert Xu np = num->d;
126*2a598d0bSHerbert Xu dp = den->d;
127*2a598d0bSHerbert Xu rp = rem->d;
128*2a598d0bSHerbert Xu
129*2a598d0bSHerbert Xu /* Optimize division by a single-limb divisor. */
130*2a598d0bSHerbert Xu if (dsize == 1) {
131*2a598d0bSHerbert Xu mpi_limb_t rlimb;
132*2a598d0bSHerbert Xu if (quot) {
133*2a598d0bSHerbert Xu qp = quot->d;
134*2a598d0bSHerbert Xu rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);
135*2a598d0bSHerbert Xu qsize -= qp[qsize - 1] == 0;
136*2a598d0bSHerbert Xu quot->nlimbs = qsize;
137*2a598d0bSHerbert Xu quot->sign = sign_quotient;
138*2a598d0bSHerbert Xu } else
139*2a598d0bSHerbert Xu rlimb = mpihelp_mod_1(np, nsize, dp[0]);
140*2a598d0bSHerbert Xu rp[0] = rlimb;
141*2a598d0bSHerbert Xu rsize = rlimb != 0?1:0;
142*2a598d0bSHerbert Xu rem->nlimbs = rsize;
143*2a598d0bSHerbert Xu rem->sign = sign_remainder;
144*2a598d0bSHerbert Xu return;
145*2a598d0bSHerbert Xu }
146*2a598d0bSHerbert Xu
147*2a598d0bSHerbert Xu
148*2a598d0bSHerbert Xu if (quot) {
149*2a598d0bSHerbert Xu qp = quot->d;
150*2a598d0bSHerbert Xu /* Make sure QP and NP point to different objects. Otherwise the
151*2a598d0bSHerbert Xu * numerator would be gradually overwritten by the quotient limbs.
152*2a598d0bSHerbert Xu */
153*2a598d0bSHerbert Xu if (qp == np) { /* Copy NP object to temporary space. */
154*2a598d0bSHerbert Xu np = marker[markidx++] = mpi_alloc_limb_space(nsize);
155*2a598d0bSHerbert Xu MPN_COPY(np, qp, nsize);
156*2a598d0bSHerbert Xu }
157*2a598d0bSHerbert Xu } else /* Put quotient at top of remainder. */
158*2a598d0bSHerbert Xu qp = rp + dsize;
159*2a598d0bSHerbert Xu
160*2a598d0bSHerbert Xu normalization_steps = count_leading_zeros(dp[dsize - 1]);
161*2a598d0bSHerbert Xu
162*2a598d0bSHerbert Xu /* Normalize the denominator, i.e. make its most significant bit set by
163*2a598d0bSHerbert Xu * shifting it NORMALIZATION_STEPS bits to the left. Also shift the
164*2a598d0bSHerbert Xu * numerator the same number of steps (to keep the quotient the same!).
165*2a598d0bSHerbert Xu */
166*2a598d0bSHerbert Xu if (normalization_steps) {
167*2a598d0bSHerbert Xu mpi_ptr_t tp;
168*2a598d0bSHerbert Xu mpi_limb_t nlimb;
169*2a598d0bSHerbert Xu
170*2a598d0bSHerbert Xu /* Shift up the denominator setting the most significant bit of
171*2a598d0bSHerbert Xu * the most significant word. Use temporary storage not to clobber
172*2a598d0bSHerbert Xu * the original contents of the denominator.
173*2a598d0bSHerbert Xu */
174*2a598d0bSHerbert Xu tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
175*2a598d0bSHerbert Xu mpihelp_lshift(tp, dp, dsize, normalization_steps);
176*2a598d0bSHerbert Xu dp = tp;
177*2a598d0bSHerbert Xu
178*2a598d0bSHerbert Xu /* Shift up the numerator, possibly introducing a new most
179*2a598d0bSHerbert Xu * significant word. Move the shifted numerator in the remainder
180*2a598d0bSHerbert Xu * meanwhile.
181*2a598d0bSHerbert Xu */
182*2a598d0bSHerbert Xu nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);
183*2a598d0bSHerbert Xu if (nlimb) {
184*2a598d0bSHerbert Xu rp[nsize] = nlimb;
185*2a598d0bSHerbert Xu rsize = nsize + 1;
186*2a598d0bSHerbert Xu } else
187*2a598d0bSHerbert Xu rsize = nsize;
188*2a598d0bSHerbert Xu } else {
189*2a598d0bSHerbert Xu /* The denominator is already normalized, as required. Copy it to
190*2a598d0bSHerbert Xu * temporary space if it overlaps with the quotient or remainder.
191*2a598d0bSHerbert Xu */
192*2a598d0bSHerbert Xu if (dp == rp || (quot && (dp == qp))) {
193*2a598d0bSHerbert Xu mpi_ptr_t tp;
194*2a598d0bSHerbert Xu
195*2a598d0bSHerbert Xu tp = marker[markidx++] = mpi_alloc_limb_space(dsize);
196*2a598d0bSHerbert Xu MPN_COPY(tp, dp, dsize);
197*2a598d0bSHerbert Xu dp = tp;
198*2a598d0bSHerbert Xu }
199*2a598d0bSHerbert Xu
200*2a598d0bSHerbert Xu /* Move the numerator to the remainder. */
201*2a598d0bSHerbert Xu if (rp != np)
202*2a598d0bSHerbert Xu MPN_COPY(rp, np, nsize);
203*2a598d0bSHerbert Xu
204*2a598d0bSHerbert Xu rsize = nsize;
205*2a598d0bSHerbert Xu }
206*2a598d0bSHerbert Xu
207*2a598d0bSHerbert Xu q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);
208*2a598d0bSHerbert Xu
209*2a598d0bSHerbert Xu if (quot) {
210*2a598d0bSHerbert Xu qsize = rsize - dsize;
211*2a598d0bSHerbert Xu if (q_limb) {
212*2a598d0bSHerbert Xu qp[qsize] = q_limb;
213*2a598d0bSHerbert Xu qsize += 1;
214*2a598d0bSHerbert Xu }
215*2a598d0bSHerbert Xu
216*2a598d0bSHerbert Xu quot->nlimbs = qsize;
217*2a598d0bSHerbert Xu quot->sign = sign_quotient;
218*2a598d0bSHerbert Xu }
219*2a598d0bSHerbert Xu
220*2a598d0bSHerbert Xu rsize = dsize;
221*2a598d0bSHerbert Xu MPN_NORMALIZE(rp, rsize);
222*2a598d0bSHerbert Xu
223*2a598d0bSHerbert Xu if (normalization_steps && rsize) {
224*2a598d0bSHerbert Xu mpihelp_rshift(rp, rp, rsize, normalization_steps);
225*2a598d0bSHerbert Xu rsize -= rp[rsize - 1] == 0?1:0;
226*2a598d0bSHerbert Xu }
227*2a598d0bSHerbert Xu
228*2a598d0bSHerbert Xu rem->nlimbs = rsize;
229*2a598d0bSHerbert Xu rem->sign = sign_remainder;
230*2a598d0bSHerbert Xu while (markidx) {
231*2a598d0bSHerbert Xu markidx--;
232*2a598d0bSHerbert Xu mpi_free_limb_space(marker[markidx]);
233*2a598d0bSHerbert Xu }
234*2a598d0bSHerbert Xu }
235