1 | /* mpi-div.c - MPI functions |
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2 | * Copyright (C) 1994, 1996, 1998, 2001, 2002, |
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3 | * 2003 Free Software Foundation, Inc. |
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4 | * |
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5 | * This file is part of Libgcrypt. |
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6 | * |
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7 | * Libgcrypt is free software; you can redistribute it and/or modify |
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8 | * it under the terms of the GNU Lesser General Public License as |
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9 | * published by the Free Software Foundation; either version 2.1 of |
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10 | * the License, or (at your option) any later version. |
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11 | * |
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12 | * Libgcrypt is distributed in the hope that it will be useful, |
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13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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15 | * GNU Lesser General Public License for more details. |
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16 | * |
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17 | * You should have received a copy of the GNU Lesser General Public |
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18 | * License along with this program; if not, write to the Free Software |
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19 | * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA |
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20 | * |
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21 | * Note: This code is heavily based on the GNU MP Library. |
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22 | * Actually it's the same code with only minor changes in the |
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23 | * way the data is stored; this is to support the abstraction |
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24 | * of an optional secure memory allocation which may be used |
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25 | * to avoid revealing of sensitive data due to paging etc. |
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26 | */ |
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27 | |
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28 | #include <config.h> |
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29 | #include <stdio.h> |
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30 | #include <stdlib.h> |
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31 | #include "mpi-internal.h" |
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32 | #include "longlong.h" |
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33 | #include "g10lib.h" |
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34 | |
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35 | |
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36 | void |
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37 | _gcry_mpi_fdiv_r( gcry_mpi_t rem, gcry_mpi_t dividend, gcry_mpi_t divisor ) |
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38 | { |
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39 | int divisor_sign = divisor->sign; |
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40 | gcry_mpi_t temp_divisor = NULL; |
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41 | |
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42 | /* We need the original value of the divisor after the remainder has been |
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43 | * preliminary calculated. We have to copy it to temporary space if it's |
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44 | * the same variable as REM. */ |
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45 | if( rem == divisor ) { |
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46 | temp_divisor = mpi_copy( divisor ); |
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47 | divisor = temp_divisor; |
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48 | } |
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49 | |
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50 | _gcry_mpi_tdiv_r( rem, dividend, divisor ); |
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51 | |
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52 | if( ((divisor_sign?1:0) ^ (dividend->sign?1:0)) && rem->nlimbs ) |
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53 | gcry_mpi_add( rem, rem, divisor); |
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54 | |
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55 | if( temp_divisor ) |
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56 | mpi_free(temp_divisor); |
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57 | } |
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58 | |
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59 | |
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60 | |
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61 | /**************** |
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62 | * Division rounding the quotient towards -infinity. |
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63 | * The remainder gets the same sign as the denominator. |
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64 | * rem is optional |
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65 | */ |
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66 | |
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67 | ulong |
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68 | _gcry_mpi_fdiv_r_ui( gcry_mpi_t rem, gcry_mpi_t dividend, ulong divisor ) |
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69 | { |
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70 | mpi_limb_t rlimb; |
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71 | |
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72 | rlimb = _gcry_mpih_mod_1( dividend->d, dividend->nlimbs, divisor ); |
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73 | if( rlimb && dividend->sign ) |
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74 | rlimb = divisor - rlimb; |
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75 | |
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76 | if( rem ) { |
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77 | rem->d[0] = rlimb; |
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78 | rem->nlimbs = rlimb? 1:0; |
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79 | } |
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80 | return rlimb; |
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81 | } |
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82 | |
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83 | |
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84 | void |
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85 | _gcry_mpi_fdiv_q( gcry_mpi_t quot, gcry_mpi_t dividend, gcry_mpi_t divisor ) |
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86 | { |
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87 | gcry_mpi_t tmp = mpi_alloc( mpi_get_nlimbs(quot) ); |
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88 | _gcry_mpi_fdiv_qr( quot, tmp, dividend, divisor); |
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89 | mpi_free(tmp); |
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90 | } |
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91 | |
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92 | void |
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93 | _gcry_mpi_fdiv_qr( gcry_mpi_t quot, gcry_mpi_t rem, gcry_mpi_t dividend, gcry_mpi_t divisor ) |
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94 | { |
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95 | int divisor_sign = divisor->sign; |
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96 | gcry_mpi_t temp_divisor = NULL; |
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97 | |
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98 | if( quot == divisor || rem == divisor ) { |
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99 | temp_divisor = mpi_copy( divisor ); |
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100 | divisor = temp_divisor; |
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101 | } |
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102 | |
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103 | _gcry_mpi_tdiv_qr( quot, rem, dividend, divisor ); |
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104 | |
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105 | if( (divisor_sign ^ dividend->sign) && rem->nlimbs ) { |
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106 | gcry_mpi_sub_ui( quot, quot, 1 ); |
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107 | gcry_mpi_add( rem, rem, divisor); |
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108 | } |
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109 | |
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110 | if( temp_divisor ) |
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111 | mpi_free(temp_divisor); |
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112 | } |
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113 | |
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114 | |
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115 | /* If den == quot, den needs temporary storage. |
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116 | * If den == rem, den needs temporary storage. |
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117 | * If num == quot, num needs temporary storage. |
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118 | * If den has temporary storage, it can be normalized while being copied, |
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119 | * i.e no extra storage should be allocated. |
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120 | */ |
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121 | |
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122 | void |
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123 | _gcry_mpi_tdiv_r( gcry_mpi_t rem, gcry_mpi_t num, gcry_mpi_t den) |
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124 | { |
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125 | _gcry_mpi_tdiv_qr(NULL, rem, num, den ); |
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126 | } |
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127 | |
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128 | void |
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129 | _gcry_mpi_tdiv_qr( gcry_mpi_t quot, gcry_mpi_t rem, gcry_mpi_t num, gcry_mpi_t den) |
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130 | { |
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131 | mpi_ptr_t np, dp; |
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132 | mpi_ptr_t qp, rp; |
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133 | mpi_size_t nsize = num->nlimbs; |
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134 | mpi_size_t dsize = den->nlimbs; |
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135 | mpi_size_t qsize, rsize; |
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136 | mpi_size_t sign_remainder = num->sign; |
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137 | mpi_size_t sign_quotient = num->sign ^ den->sign; |
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138 | unsigned normalization_steps; |
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139 | mpi_limb_t q_limb; |
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140 | mpi_ptr_t marker[5]; |
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141 | unsigned int marker_nlimbs[5]; |
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142 | int markidx=0; |
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143 | |
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144 | /* Ensure space is enough for quotient and remainder. |
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145 | * We need space for an extra limb in the remainder, because it's |
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146 | * up-shifted (normalized) below. */ |
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147 | rsize = nsize + 1; |
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148 | mpi_resize( rem, rsize); |
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149 | |
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150 | qsize = rsize - dsize; /* qsize cannot be bigger than this. */ |
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151 | if( qsize <= 0 ) { |
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152 | if( num != rem ) { |
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153 | rem->nlimbs = num->nlimbs; |
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154 | rem->sign = num->sign; |
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155 | MPN_COPY(rem->d, num->d, nsize); |
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156 | } |
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157 | if( quot ) { |
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158 | /* This needs to follow the assignment to rem, in case the |
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159 | * numerator and quotient are the same. */ |
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160 | quot->nlimbs = 0; |
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161 | quot->sign = 0; |
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162 | } |
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163 | return; |
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164 | } |
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165 | |
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166 | if( quot ) |
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167 | mpi_resize( quot, qsize); |
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168 | |
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169 | /* Read pointers here, when reallocation is finished. */ |
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170 | np = num->d; |
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171 | dp = den->d; |
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172 | rp = rem->d; |
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173 | |
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174 | /* Optimize division by a single-limb divisor. */ |
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175 | if( dsize == 1 ) { |
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176 | mpi_limb_t rlimb; |
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177 | if( quot ) { |
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178 | qp = quot->d; |
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179 | rlimb = _gcry_mpih_divmod_1( qp, np, nsize, dp[0] ); |
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180 | qsize -= qp[qsize - 1] == 0; |
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181 | quot->nlimbs = qsize; |
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182 | quot->sign = sign_quotient; |
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183 | } |
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184 | else |
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185 | rlimb = _gcry_mpih_mod_1( np, nsize, dp[0] ); |
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186 | rp[0] = rlimb; |
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187 | rsize = rlimb != 0?1:0; |
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188 | rem->nlimbs = rsize; |
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189 | rem->sign = sign_remainder; |
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190 | return; |
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191 | } |
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192 | |
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193 | |
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194 | if( quot ) { |
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195 | qp = quot->d; |
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196 | /* Make sure QP and NP point to different objects. Otherwise the |
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197 | * numerator would be gradually overwritten by the quotient limbs. */ |
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198 | if(qp == np) { /* Copy NP object to temporary space. */ |
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199 | marker_nlimbs[markidx] = nsize; |
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200 | np = marker[markidx++] = mpi_alloc_limb_space(nsize, |
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201 | mpi_is_secure(quot)); |
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202 | MPN_COPY(np, qp, nsize); |
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203 | } |
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204 | } |
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205 | else /* Put quotient at top of remainder. */ |
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206 | qp = rp + dsize; |
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207 | |
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208 | count_leading_zeros( normalization_steps, dp[dsize - 1] ); |
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209 | |
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210 | /* Normalize the denominator, i.e. make its most significant bit set by |
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211 | * shifting it NORMALIZATION_STEPS bits to the left. Also shift the |
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212 | * numerator the same number of steps (to keep the quotient the same!). |
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213 | */ |
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214 | if( normalization_steps ) { |
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215 | mpi_ptr_t tp; |
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216 | mpi_limb_t nlimb; |
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217 | |
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218 | /* Shift up the denominator setting the most significant bit of |
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219 | * the most significant word. Use temporary storage not to clobber |
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220 | * the original contents of the denominator. */ |
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221 | marker_nlimbs[markidx] = dsize; |
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222 | tp = marker[markidx++] = mpi_alloc_limb_space(dsize,mpi_is_secure(den)); |
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223 | _gcry_mpih_lshift( tp, dp, dsize, normalization_steps ); |
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224 | dp = tp; |
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225 | |
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226 | /* Shift up the numerator, possibly introducing a new most |
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227 | * significant word. Move the shifted numerator in the remainder |
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228 | * meanwhile. */ |
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229 | nlimb = _gcry_mpih_lshift(rp, np, nsize, normalization_steps); |
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230 | if( nlimb ) { |
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231 | rp[nsize] = nlimb; |
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232 | rsize = nsize + 1; |
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233 | } |
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234 | else |
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235 | rsize = nsize; |
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236 | } |
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237 | else { |
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238 | /* The denominator is already normalized, as required. Copy it to |
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239 | * temporary space if it overlaps with the quotient or remainder. */ |
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240 | if( dp == rp || (quot && (dp == qp))) { |
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241 | mpi_ptr_t tp; |
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242 | |
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243 | marker_nlimbs[markidx] = dsize; |
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244 | tp = marker[markidx++] = mpi_alloc_limb_space(dsize, |
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245 | mpi_is_secure(den)); |
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246 | MPN_COPY( tp, dp, dsize ); |
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247 | dp = tp; |
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248 | } |
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249 | |
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250 | /* Move the numerator to the remainder. */ |
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251 | if( rp != np ) |
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252 | MPN_COPY(rp, np, nsize); |
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253 | |
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254 | rsize = nsize; |
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255 | } |
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256 | |
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257 | q_limb = _gcry_mpih_divrem( qp, 0, rp, rsize, dp, dsize ); |
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258 | |
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259 | if( quot ) { |
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260 | qsize = rsize - dsize; |
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261 | if(q_limb) { |
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262 | qp[qsize] = q_limb; |
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263 | qsize += 1; |
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264 | } |
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265 | |
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266 | quot->nlimbs = qsize; |
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267 | quot->sign = sign_quotient; |
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268 | } |
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269 | |
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270 | rsize = dsize; |
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271 | MPN_NORMALIZE (rp, rsize); |
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272 | |
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273 | if( normalization_steps && rsize ) { |
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274 | _gcry_mpih_rshift(rp, rp, rsize, normalization_steps); |
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275 | rsize -= rp[rsize - 1] == 0?1:0; |
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276 | } |
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277 | |
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278 | rem->nlimbs = rsize; |
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279 | rem->sign = sign_remainder; |
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280 | while( markidx ) |
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281 | { |
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282 | markidx--; |
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283 | _gcry_mpi_free_limb_space (marker[markidx], marker_nlimbs[markidx]); |
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284 | } |
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285 | } |
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286 | |
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287 | void |
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288 | _gcry_mpi_tdiv_q_2exp( gcry_mpi_t w, gcry_mpi_t u, unsigned int count ) |
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289 | { |
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290 | mpi_size_t usize, wsize; |
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291 | mpi_size_t limb_cnt; |
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292 | |
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293 | usize = u->nlimbs; |
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294 | limb_cnt = count / BITS_PER_MPI_LIMB; |
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295 | wsize = usize - limb_cnt; |
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296 | if( limb_cnt >= usize ) |
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297 | w->nlimbs = 0; |
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298 | else { |
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299 | mpi_ptr_t wp; |
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300 | mpi_ptr_t up; |
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301 | |
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302 | RESIZE_IF_NEEDED( w, wsize ); |
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303 | wp = w->d; |
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304 | up = u->d; |
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305 | |
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306 | count %= BITS_PER_MPI_LIMB; |
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307 | if( count ) { |
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308 | _gcry_mpih_rshift( wp, up + limb_cnt, wsize, count ); |
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309 | wsize -= !wp[wsize - 1]; |
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310 | } |
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311 | else { |
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312 | MPN_COPY_INCR( wp, up + limb_cnt, wsize); |
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313 | } |
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314 | |
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315 | w->nlimbs = wsize; |
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316 | } |
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317 | } |
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318 | |
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319 | /**************** |
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320 | * Check whether dividend is divisible by divisor |
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321 | * (note: divisor must fit into a limb) |
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322 | */ |
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323 | int |
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324 | _gcry_mpi_divisible_ui(gcry_mpi_t dividend, ulong divisor ) |
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325 | { |
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326 | return !_gcry_mpih_mod_1( dividend->d, dividend->nlimbs, divisor ); |
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327 | } |
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328 | |
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329 | |
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330 | void |
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331 | gcry_mpi_div (gcry_mpi_t quot, gcry_mpi_t rem, gcry_mpi_t dividend, gcry_mpi_t divisor, int round) |
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332 | { |
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333 | if (!round) |
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334 | { |
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335 | if (!rem) |
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336 | { |
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337 | gcry_mpi_t tmp = mpi_alloc (mpi_get_nlimbs(quot)); |
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338 | _gcry_mpi_tdiv_qr (quot, tmp, dividend, divisor); |
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339 | mpi_free (tmp); |
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340 | } |
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341 | else |
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342 | _gcry_mpi_tdiv_qr (quot, rem, dividend, divisor); |
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343 | } |
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344 | else if (round < 0) |
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345 | { |
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346 | if (!rem) |
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347 | _gcry_mpi_fdiv_q (quot, dividend, divisor); |
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348 | else if (!quot) |
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349 | _gcry_mpi_fdiv_r (rem, dividend, divisor); |
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350 | else |
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351 | _gcry_mpi_fdiv_qr (quot, rem, dividend, divisor); |
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352 | } |
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353 | else |
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354 | log_bug ("mpi rounding to ceiling not yet implemented\n"); |
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355 | } |
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