231 lines · c
1/* mpi-div.c - MPI functions2 * 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 the9 * way the data is stored; this is to support the abstraction10 * of an optional secure memory allocation which may be used11 * to avoid revealing of sensitive data due to paging etc.12 */13 14#include "mpi-internal.h"15#include "longlong.h"16 17int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den);18 19int mpi_fdiv_r(MPI rem, MPI dividend, MPI divisor)20{21 int divisor_sign = divisor->sign;22 MPI temp_divisor = NULL;23 int err;24 25 /* We need the original value of the divisor after the remainder has been26 * preliminary calculated. We have to copy it to temporary space if it's27 * the same variable as REM.28 */29 if (rem == divisor) {30 temp_divisor = mpi_copy(divisor);31 if (!temp_divisor)32 return -ENOMEM;33 divisor = temp_divisor;34 }35 36 err = mpi_tdiv_r(rem, dividend, divisor);37 if (err)38 goto free_temp_divisor;39 40 if (((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs)41 err = mpi_add(rem, rem, divisor);42 43free_temp_divisor:44 mpi_free(temp_divisor);45 46 return err;47}48 49/* If den == quot, den needs temporary storage.50 * If den == rem, den needs temporary storage.51 * If num == quot, num needs temporary storage.52 * If den has temporary storage, it can be normalized while being copied,53 * i.e no extra storage should be allocated.54 */55 56int mpi_tdiv_r(MPI rem, MPI num, MPI den)57{58 return mpi_tdiv_qr(NULL, rem, num, den);59}60 61int mpi_tdiv_qr(MPI quot, MPI rem, MPI num, MPI den)62{63 mpi_ptr_t np, dp;64 mpi_ptr_t qp, rp;65 mpi_size_t nsize = num->nlimbs;66 mpi_size_t dsize = den->nlimbs;67 mpi_size_t qsize, rsize;68 mpi_size_t sign_remainder = num->sign;69 mpi_size_t sign_quotient = num->sign ^ den->sign;70 unsigned int normalization_steps;71 mpi_limb_t q_limb;72 mpi_ptr_t marker[5];73 int markidx = 0;74 int err;75 76 /* Ensure space is enough for quotient and remainder.77 * We need space for an extra limb in the remainder, because it's78 * up-shifted (normalized) below.79 */80 rsize = nsize + 1;81 err = mpi_resize(rem, rsize);82 if (err)83 return err;84 85 qsize = rsize - dsize; /* qsize cannot be bigger than this. */86 if (qsize <= 0) {87 if (num != rem) {88 rem->nlimbs = num->nlimbs;89 rem->sign = num->sign;90 MPN_COPY(rem->d, num->d, nsize);91 }92 if (quot) {93 /* This needs to follow the assignment to rem, in case the94 * numerator and quotient are the same.95 */96 quot->nlimbs = 0;97 quot->sign = 0;98 }99 return 0;100 }101 102 if (quot) {103 err = mpi_resize(quot, qsize);104 if (err)105 return err;106 }107 108 /* Read pointers here, when reallocation is finished. */109 np = num->d;110 dp = den->d;111 rp = rem->d;112 113 /* Optimize division by a single-limb divisor. */114 if (dsize == 1) {115 mpi_limb_t rlimb;116 if (quot) {117 qp = quot->d;118 rlimb = mpihelp_divmod_1(qp, np, nsize, dp[0]);119 qsize -= qp[qsize - 1] == 0;120 quot->nlimbs = qsize;121 quot->sign = sign_quotient;122 } else123 rlimb = mpihelp_mod_1(np, nsize, dp[0]);124 rp[0] = rlimb;125 rsize = rlimb != 0?1:0;126 rem->nlimbs = rsize;127 rem->sign = sign_remainder;128 return 0;129 }130 131 err = -ENOMEM;132 if (quot) {133 qp = quot->d;134 /* Make sure QP and NP point to different objects. Otherwise the135 * numerator would be gradually overwritten by the quotient limbs.136 */137 if (qp == np) { /* Copy NP object to temporary space. */138 np = marker[markidx++] = mpi_alloc_limb_space(nsize);139 if (!np)140 goto out_free_marker;141 MPN_COPY(np, qp, nsize);142 }143 } else /* Put quotient at top of remainder. */144 qp = rp + dsize;145 146 normalization_steps = count_leading_zeros(dp[dsize - 1]);147 148 /* Normalize the denominator, i.e. make its most significant bit set by149 * shifting it NORMALIZATION_STEPS bits to the left. Also shift the150 * numerator the same number of steps (to keep the quotient the same!).151 */152 if (normalization_steps) {153 mpi_ptr_t tp;154 mpi_limb_t nlimb;155 156 /* Shift up the denominator setting the most significant bit of157 * the most significant word. Use temporary storage not to clobber158 * the original contents of the denominator.159 */160 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);161 if (!tp)162 goto out_free_marker;163 mpihelp_lshift(tp, dp, dsize, normalization_steps);164 dp = tp;165 166 /* Shift up the numerator, possibly introducing a new most167 * significant word. Move the shifted numerator in the remainder168 * meanwhile.169 */170 nlimb = mpihelp_lshift(rp, np, nsize, normalization_steps);171 if (nlimb) {172 rp[nsize] = nlimb;173 rsize = nsize + 1;174 } else175 rsize = nsize;176 } else {177 /* The denominator is already normalized, as required. Copy it to178 * temporary space if it overlaps with the quotient or remainder.179 */180 if (dp == rp || (quot && (dp == qp))) {181 mpi_ptr_t tp;182 183 tp = marker[markidx++] = mpi_alloc_limb_space(dsize);184 if (!tp)185 goto out_free_marker;186 MPN_COPY(tp, dp, dsize);187 dp = tp;188 }189 190 /* Move the numerator to the remainder. */191 if (rp != np)192 MPN_COPY(rp, np, nsize);193 194 rsize = nsize;195 }196 197 q_limb = mpihelp_divrem(qp, 0, rp, rsize, dp, dsize);198 199 if (quot) {200 qsize = rsize - dsize;201 if (q_limb) {202 qp[qsize] = q_limb;203 qsize += 1;204 }205 206 quot->nlimbs = qsize;207 quot->sign = sign_quotient;208 }209 210 rsize = dsize;211 MPN_NORMALIZE(rp, rsize);212 213 if (normalization_steps && rsize) {214 mpihelp_rshift(rp, rp, rsize, normalization_steps);215 rsize -= rp[rsize - 1] == 0?1:0;216 }217 218 rem->nlimbs = rsize;219 rem->sign = sign_remainder;220 221 err = 0;222 223out_free_marker:224 while (markidx) {225 markidx--;226 mpi_free_limb_space(marker[markidx]);227 }228 229 return err;230}231