1 | |
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2 | /* |
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3 | * This is a "wrapper" layer that builds on top of the "mpn" layer of gmp. |
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4 | * This layer provides much of the same functionality of the "mpz" |
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5 | * layer of gmp, but the interface it provides is much more like |
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6 | * the interface provided by lip. |
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7 | * |
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8 | * This layer was written under the following assumptions about gmp: |
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9 | * 1) mp_limb_t is an unsigned integral type |
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10 | * 2) sizeof(mp_limb_t) == sizeof(long) or sizeof(mp_limb_t) == 2*sizeof(long) |
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11 | * 3) the number of bits of an mp_limb_t is equal to that of a long, |
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12 | * or twice that of a long |
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13 | * 4) the number of bits of a gmp radix is equal to the number of bits |
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14 | * of an mp_limb_t |
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15 | * |
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16 | * Except for assumption (1), these assumptions are verified in the |
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17 | * installation script, and they should be universally satisfied in practice, |
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18 | * except when gmp is built using the proposed, new "nail" fetaure |
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19 | * (in which some bits of an mp_limb_t are unused). |
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20 | * The code here will not work properly with the "nail" feature; |
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21 | * however, I have (attempted to) identify all such problem spots, |
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22 | * and any other places where assumptions (2-4) are made, |
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23 | * with a comment labeled "DIRT". |
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24 | */ |
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25 | |
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26 | |
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27 | |
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28 | #include <NTL/lip.h> |
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29 | |
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30 | #include <NTL/ctools.h> |
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31 | |
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32 | |
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33 | #include <stdlib.h> |
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34 | #include <stdio.h> |
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35 | #include <math.h> |
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36 | |
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37 | |
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38 | #include <gmp.h> |
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39 | |
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40 | typedef mp_limb_t *_ntl_limb_t_ptr; |
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41 | |
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42 | int _ntl_gmp_hack = 0; |
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43 | |
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44 | #if (__GNU_MP_VERSION < 3) |
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45 | |
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46 | #error "You have to use GNP version >= 3.1" |
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47 | |
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48 | #endif |
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49 | |
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50 | #if ((__GNU_MP_VERSION == 3) && (__GNU_MP_VERSION_MINOR < 1)) |
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51 | |
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52 | #error "You have to use GNP version >= 3.1" |
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53 | |
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54 | #endif |
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55 | |
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56 | |
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57 | |
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58 | /* v 3.1 is supposed mpn_tdiv_qr defined, but it doesn't. |
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59 | Here's a workaround */ |
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60 | |
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61 | #if ((__GNU_MP_VERSION == 3) && (__GNU_MP_VERSION_MINOR == 1) && (__GNU_MP_VERSION_PATCHLEVEL == 0)) |
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62 | |
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63 | #define mpn_tdiv_qr __MPN(tdiv_qr) |
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64 | |
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65 | |
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66 | #ifdef __cplusplus |
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67 | extern "C" |
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68 | #endif |
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69 | void mpn_tdiv_qr(mp_ptr, mp_ptr, mp_size_t, mp_srcptr, mp_size_t, |
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70 | mp_srcptr, mp_size_t); |
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71 | |
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72 | #endif |
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73 | |
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74 | |
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75 | #if (defined(NTL_CXX_ONLY) && !defined(__cplusplus)) |
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76 | #error "CXX_ONLY flag set...must use C++ compiler" |
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77 | #endif |
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78 | |
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79 | |
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80 | union gbigint_header { |
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81 | |
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82 | long info[2]; |
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83 | mp_limb_t alignment; |
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84 | |
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85 | }; |
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86 | |
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87 | /* A bigint is represented as two long's, ALLOC and SIZE, followed by a |
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88 | * vector DATA of mp_limb_t's. |
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89 | * |
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90 | * ALLOC is of the form |
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91 | * (alloc << 2) | continue_flag | frozen_flag |
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92 | * where |
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93 | * - alloc is the number of allocated mp_limb_t's, |
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94 | * - continue flag is either 2 or 0, |
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95 | * - frozen_flag is either 1 or 0. |
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96 | * If frozen_flag is set, then the space for this bigint is *not* |
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97 | * managed by the _ntl_gsetlength and _ntl_gfree routines, |
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98 | * but are instead managed by the vec_ZZ_p and ZZVec routines. |
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99 | * The continue_flag is only set when the frozen_flag is set. |
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100 | * |
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101 | * SIZE is the number of mp_limb_t's actually |
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102 | * used by the bigint, with the sign of SIZE having |
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103 | * the sign of the bigint. |
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104 | * Note that the zero bigint is represented as SIZE=0. |
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105 | * |
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106 | * Bigint's are accessed through a handle, which is pointer to void. |
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107 | * A null handle logically represents the bigint zero. |
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108 | * This is done so that the interface presented to higher level |
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109 | * routines is essentially the same as that of NTL's traditional |
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110 | * long integer package. |
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111 | * |
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112 | * The components ALLOC, SIZE, and DATA are all accessed through |
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113 | * macros using pointer casts. While all of may seem a bit dirty, |
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114 | * it should be quite portable: objects are never referenced |
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115 | * through pointers of different types, and no alignmement |
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116 | * problems should arise. |
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117 | * |
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118 | * Actually, mp_limb_t is usually the type unsigned long. |
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119 | * However, on some 64-bit platforms, the type long is only 32 bits, |
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120 | * and gmp makes mp_limb_t unsigned long long in this case. |
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121 | * This is fairly rare, as the industry standard for Unix is to |
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122 | * have 64-bit longs on 64-bit machines. |
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123 | */ |
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124 | |
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125 | #if 1 |
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126 | |
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127 | #define ALLOC(p) (((long *) (p))[0]) |
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128 | #define SIZE(p) (((long *) (p))[1]) |
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129 | #define DATA(p) ((mp_limb_t *) (((long *) (p)) + 2)) |
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130 | |
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131 | #define STORAGE(len) ((long)(2*sizeof(long) + (len)*sizeof(mp_limb_t))) |
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132 | |
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133 | /* DIRT: STORAGE computes the number of bytes to allocate for a bigint |
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134 | * of maximal SIZE len. This should be computed so that one |
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135 | * can store several such bigints in a contiguous array |
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136 | * of memory without breaking any alignment requirements. |
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137 | * Currently, it is assumed (and explicitly checked in the NTL installation |
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138 | * script) that sizeof(mp_limb_t) is either sizeof(long) or |
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139 | * 2*sizeof(long), and therfore, nothing special needs to |
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140 | * be done to enfoce alignment requirements. If this assumption |
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141 | * should change, then the storage layout for bigints must be |
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142 | * re-designed. |
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143 | */ |
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144 | |
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145 | #define MustAlloc(c, len) (!(c) || (ALLOC(c) >> 2) < (len)) |
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146 | |
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147 | |
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148 | |
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149 | #define GET_SIZE_NEG(sz, neg, p) \ |
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150 | do \ |
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151 | { \ |
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152 | long _s; \ |
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153 | _s = SIZE(p); \ |
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154 | if (_s < 0) { \ |
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155 | sz = -_s; \ |
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156 | neg = 1; \ |
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157 | } \ |
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158 | else { \ |
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159 | sz = _s; \ |
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160 | neg = 0; \ |
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161 | } \ |
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162 | } \ |
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163 | while (0) |
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164 | |
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165 | #define STRIP(sz, p) \ |
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166 | do \ |
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167 | { \ |
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168 | long _i; \ |
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169 | _i = sz - 1; \ |
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170 | while (_i >= 0 && p[_i] == 0) _i--; \ |
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171 | sz = _i + 1; \ |
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172 | } \ |
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173 | while (0) |
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174 | |
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175 | #define ZEROP(p) (!p || !SIZE(p)) |
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176 | |
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177 | #define ONEP(p) (p && SIZE(p) == 1 && DATA(p)[0] == 1) |
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178 | |
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179 | #define SWAP_BIGINT(a, b) \ |
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180 | do \ |
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181 | { \ |
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182 | _ntl_gbigint _t; \ |
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183 | _t = a; \ |
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184 | a = b; \ |
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185 | b = _t; \ |
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186 | } \ |
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187 | while (0) |
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188 | |
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189 | #define SWAP_LONG(a, b) \ |
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190 | do \ |
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191 | { \ |
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192 | long _t; \ |
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193 | _t = a; \ |
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194 | a = b; \ |
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195 | b = _t; \ |
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196 | } \ |
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197 | while (0) |
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198 | |
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199 | #define SWAP_LIMB_PTR(a, b) \ |
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200 | do \ |
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201 | { \ |
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202 | _ntl_limb_t_ptr _t; \ |
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203 | _t = a; \ |
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204 | a = b; \ |
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205 | b = _t; \ |
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206 | } \ |
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207 | while (0) |
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208 | |
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209 | #define COUNT_BITS(cnt, a) \ |
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210 | do \ |
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211 | { \ |
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212 | long _i = 0; \ |
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213 | mp_limb_t _a = (a); \ |
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214 | \ |
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215 | while (_a>=256) \ |
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216 | _i += 8, _a >>= 8; \ |
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217 | if (_a >=16) \ |
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218 | _i += 4, _a >>= 4; \ |
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219 | if (_a >= 4) \ |
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220 | _i += 2, _a >>= 2; \ |
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221 | if (_a >= 2) \ |
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222 | _i += 2; \ |
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223 | else if (_a >= 1) \ |
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224 | _i++; \ |
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225 | \ |
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226 | cnt = _i; \ |
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227 | } \ |
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228 | while (0) |
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229 | |
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230 | #else |
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231 | |
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232 | /* These are C++ inline functions that are equivalent to the above |
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233 | * macros. They are mainly intended as a debugging aid. |
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234 | */ |
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235 | |
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236 | |
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237 | inline long& ALLOC(_ntl_gbigint p) |
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238 | { return (((long *) p)[0]); } |
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239 | |
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240 | inline long& SIZE(_ntl_gbigint p) |
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241 | { return (((long *) p)[1]); } |
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242 | |
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243 | inline mp_limb_t * DATA(_ntl_gbigint p) |
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244 | { return ((mp_limb_t *) (((long *) (p)) + 2)); } |
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245 | |
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246 | inline long STORAGE(long len) |
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247 | { return ((long)(2*sizeof(long) + (len)*sizeof(mp_limb_t))); } |
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248 | |
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249 | inline long MustAlloc(_ntl_gbigint c, long len) |
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250 | { return (!(c) || (ALLOC(c) >> 2) < (len)); } |
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251 | |
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252 | |
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253 | inline void GET_SIZE_NEG(long& sz, long& neg, _ntl_gbigint p) |
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254 | { |
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255 | long s; |
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256 | s = SIZE(p); |
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257 | if (s < 0) { |
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258 | sz = -s; |
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259 | neg = 1; |
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260 | } |
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261 | else { |
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262 | sz = s; |
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263 | neg = 0; |
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264 | } |
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265 | } |
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266 | |
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267 | inline void STRIP(long& sz, mp_limb_t *p) |
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268 | { |
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269 | long i; |
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270 | i = sz - 1; |
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271 | while (i >= 0 && p[i] == 0) i--; |
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272 | sz = i + 1; |
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273 | } |
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274 | |
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275 | inline long ZEROP(_ntl_gbigint p) |
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276 | { |
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277 | return !p || !SIZE(p); |
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278 | } |
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279 | |
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280 | inline long ONEP(_ntl_gbigint p) |
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281 | { |
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282 | return p && SIZE(p) == 1 && DATA(p)[0] == 1; |
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283 | } |
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284 | |
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285 | inline void SWAP_BIGINT(_ntl_gbigint& a, _ntl_gbigint& b) |
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286 | { |
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287 | _ntl_gbigint t; |
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288 | t = a; |
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289 | a = b; |
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290 | b = t; |
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291 | } |
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292 | |
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293 | inline void SWAP_LONG(long& a, long& b) |
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294 | { |
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295 | long t; |
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296 | t = a; |
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297 | a = b; |
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298 | b = t; |
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299 | } |
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300 | |
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301 | inline void SWAP_LIMB_PTR(_ntl_limb_t_ptr& a, _ntl_limb_t_ptr& b) |
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302 | { |
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303 | _ntl_limb_t_ptr t; |
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304 | t = a; |
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305 | a = b; |
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306 | b = t; |
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307 | } |
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308 | |
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309 | |
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310 | inline void COUNT_BITS(long& cnt, mp_limb_t a) |
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311 | { |
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312 | long i = 0; |
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313 | |
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314 | while (a>=256) |
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315 | i += 8, a >>= 8; |
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316 | if (a >=16) |
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317 | i += 4, a >>= 4; |
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318 | if (a >= 4) |
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319 | i += 2, a >>= 2; |
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320 | if (a >= 2) |
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321 | i += 2; |
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322 | else if (a >= 1) |
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323 | i++; |
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324 | |
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325 | cnt = i; |
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326 | } |
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327 | |
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328 | #endif |
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329 | |
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330 | #define STORAGE_OVF(len) NTL_OVERFLOW(len, sizeof(mp_limb_t), 2*sizeof(long)) |
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331 | |
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332 | |
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333 | |
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334 | static |
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335 | void ghalt(char *c) |
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336 | { |
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337 | fprintf(stderr,"fatal error:\n %s\nexit...\n",c); |
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338 | fflush(stderr); |
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339 | abort(); |
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340 | } |
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341 | |
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342 | |
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343 | #define MIN_SETL (4) |
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344 | /* _ntl_gsetlength allocates a multiple of MIN_SETL digits */ |
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345 | |
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346 | |
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347 | |
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348 | void _ntl_gsetlength(_ntl_gbigint *v, long len) |
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349 | { |
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350 | _ntl_gbigint x = *v; |
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351 | |
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352 | if (len < 0) |
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353 | ghalt("negative size allocation in _ntl_zgetlength"); |
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354 | |
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355 | if (NTL_OVERFLOW(len, NTL_ZZ_NBITS, 0)) |
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356 | ghalt("size too big in _ntl_gsetlength"); |
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357 | |
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358 | #ifdef NTL_SMALL_MP_SIZE_T |
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359 | /* this makes sure that numbers don't get too big for GMP */ |
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360 | if (len >= (1L << (NTL_BITS_PER_INT-4))) |
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361 | ghalt("size too big for GMP"); |
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362 | #endif |
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363 | |
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364 | |
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365 | if (x) { |
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366 | long oldlen = ALLOC(x); |
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367 | long fixed = oldlen & 1; |
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368 | oldlen = oldlen >> 2; |
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369 | |
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370 | if (fixed) { |
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371 | if (len > oldlen) |
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372 | ghalt("internal error: can't grow this _ntl_gbigint"); |
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373 | else |
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374 | return; |
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375 | } |
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376 | |
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377 | if (len <= oldlen) return; |
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378 | |
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379 | len++; /* always allocate at least one more than requested */ |
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380 | |
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381 | oldlen = (long) (oldlen * 1.2); /* always increase by at least 20% */ |
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382 | if (len < oldlen) |
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383 | len = oldlen; |
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384 | |
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385 | /* round up to multiple of MIN_SETL */ |
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386 | len = ((len+(MIN_SETL-1))/MIN_SETL)*MIN_SETL; |
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387 | |
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388 | /* test len again */ |
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389 | if (NTL_OVERFLOW(len, NTL_ZZ_NBITS, 0)) |
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390 | ghalt("size too big in _ntl_gsetlength"); |
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391 | |
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392 | if (STORAGE_OVF(len)) |
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393 | ghalt("reallocation failed in _ntl_gsetlength"); |
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394 | |
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395 | ALLOC(x) = len << 2; |
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396 | if (!(x = (_ntl_gbigint)NTL_REALLOC((void *) x, 1, STORAGE(len), 0))) { |
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397 | ghalt("reallocation failed in _ntl_gsetlength"); |
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398 | } |
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399 | } |
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400 | else { |
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401 | len++; |
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402 | len = ((len+(MIN_SETL-1))/MIN_SETL)*MIN_SETL; |
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403 | |
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404 | /* test len again */ |
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405 | if (NTL_OVERFLOW(len, NTL_ZZ_NBITS, 0)) |
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406 | ghalt("size too big in _ntl_gsetlength"); |
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407 | |
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408 | if (STORAGE_OVF(len)) |
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409 | ghalt("reallocation failed in _ntl_gsetlength"); |
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410 | |
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411 | if (!(x = (_ntl_gbigint)NTL_MALLOC(1, STORAGE(len), 0))) { |
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412 | ghalt("allocation failed in _ntl_gsetlength"); |
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413 | } |
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414 | ALLOC(x) = len << 2; |
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415 | SIZE(x) = 0; |
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416 | } |
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417 | |
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418 | *v = x; |
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419 | } |
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420 | |
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421 | void _ntl_gfree(_ntl_gbigint *xx) |
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422 | { |
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423 | _ntl_gbigint x = *xx; |
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424 | |
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425 | if (!x) |
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426 | return; |
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427 | |
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428 | if (ALLOC(x) & 1) |
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429 | ghalt("Internal error: can't free this _ntl_gbigint"); |
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430 | |
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431 | free((void*) x); |
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432 | *xx = 0; |
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433 | return; |
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434 | } |
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435 | |
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436 | void |
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437 | _ntl_gswap(_ntl_gbigint *a, _ntl_gbigint *b) |
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438 | { |
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439 | _ntl_gbigint c; |
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440 | |
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441 | if ((*a && (ALLOC(*a) & 1)) || (*b && (ALLOC(*b) & 1))) { |
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442 | static _ntl_gbigint t = 0; |
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443 | _ntl_gcopy(*a, &t); |
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444 | _ntl_gcopy(*b, a); |
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445 | _ntl_gcopy(t, b); |
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446 | return; |
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447 | } |
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448 | |
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449 | c = *a; |
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450 | *a = *b; |
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451 | *b = c; |
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452 | } |
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453 | |
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454 | |
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455 | void _ntl_gcopy(_ntl_gbigint a, _ntl_gbigint *bb) |
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456 | { |
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457 | _ntl_gbigint b; |
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458 | long sa, abs_sa, i; |
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459 | mp_limb_t *adata, *bdata; |
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460 | |
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461 | b = *bb; |
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462 | |
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463 | if (!a || (sa = SIZE(a)) == 0) { |
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464 | if (b) SIZE(b) = 0; |
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465 | } |
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466 | else { |
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467 | if (a != b) { |
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468 | if (sa >= 0) |
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469 | abs_sa = sa; |
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470 | else |
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471 | abs_sa = -sa; |
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472 | |
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473 | if (MustAlloc(b, abs_sa)) { |
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474 | _ntl_gsetlength(&b, abs_sa); |
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475 | *bb = b; |
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476 | } |
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477 | |
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478 | adata = DATA(a); |
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479 | bdata = DATA(b); |
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480 | |
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481 | for (i = 0; i < abs_sa; i++) |
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482 | bdata[i] = adata[i]; |
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483 | |
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484 | SIZE(b) = sa; |
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485 | } |
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486 | } |
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487 | } |
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488 | |
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489 | |
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490 | void _ntl_gzero(_ntl_gbigint *aa) |
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491 | { |
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492 | _ntl_gbigint a = *aa; |
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493 | |
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494 | if (a) SIZE(a) = 0; |
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495 | } |
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496 | |
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497 | void _ntl_gone(_ntl_gbigint *aa) |
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498 | { |
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499 | _ntl_gbigint a = *aa; |
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500 | if (!a) { |
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501 | _ntl_gsetlength(&a, 1); |
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502 | *aa = a; |
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503 | } |
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504 | |
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505 | SIZE(a) = 1; |
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506 | DATA(a)[0] = 1; |
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507 | } |
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508 | |
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509 | long _ntl_giszero(_ntl_gbigint a) |
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510 | { |
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511 | return ZEROP(a); |
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512 | } |
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513 | |
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514 | long _ntl_godd(_ntl_gbigint a) |
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515 | { |
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516 | if (ZEROP(a)) |
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517 | return 0; |
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518 | else |
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519 | return DATA(a)[0]&1; |
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520 | } |
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521 | |
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522 | long _ntl_gbit(_ntl_gbigint a, long p) |
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523 | { |
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524 | long bl; |
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525 | long sa; |
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526 | mp_limb_t wh; |
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527 | |
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528 | if (p < 0 || !a) return 0; |
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529 | |
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530 | bl = p/NTL_ZZ_NBITS; |
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531 | wh = ((mp_limb_t) 1) << (p - NTL_ZZ_NBITS*bl); |
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532 | |
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533 | sa = SIZE(a); |
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534 | if (sa < 0) sa = -sa; |
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535 | |
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536 | if (sa <= bl) return 0; |
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537 | if (DATA(a)[bl] & wh) return 1; |
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538 | return 0; |
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539 | } |
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540 | |
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541 | void _ntl_glowbits(_ntl_gbigint a, long b, _ntl_gbigint *cc) |
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542 | { |
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543 | _ntl_gbigint c; |
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544 | |
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545 | long bl; |
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546 | long wh; |
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547 | long sa; |
---|
548 | long i; |
---|
549 | mp_limb_t *adata, *cdata; |
---|
550 | |
---|
551 | if (ZEROP(a) || (b<=0)) { |
---|
552 | _ntl_gzero(cc); |
---|
553 | return; |
---|
554 | } |
---|
555 | |
---|
556 | bl = b/NTL_ZZ_NBITS; |
---|
557 | wh = b - NTL_ZZ_NBITS*bl; |
---|
558 | if (wh != 0) |
---|
559 | bl++; |
---|
560 | else |
---|
561 | wh = NTL_ZZ_NBITS; |
---|
562 | |
---|
563 | sa = SIZE(a); |
---|
564 | if (sa < 0) sa = -sa; |
---|
565 | |
---|
566 | if (sa < bl) { |
---|
567 | _ntl_gcopy(a,cc); |
---|
568 | _ntl_gabs(cc); |
---|
569 | return; |
---|
570 | } |
---|
571 | |
---|
572 | c = *cc; |
---|
573 | |
---|
574 | /* a won't move if c aliases a */ |
---|
575 | _ntl_gsetlength(&c, bl); |
---|
576 | *cc = c; |
---|
577 | |
---|
578 | adata = DATA(a); |
---|
579 | cdata = DATA(c); |
---|
580 | |
---|
581 | for (i = 0; i < bl-1; i++) |
---|
582 | cdata[i] = adata[i]; |
---|
583 | |
---|
584 | if (wh == NTL_ZZ_NBITS) |
---|
585 | cdata[bl-1] = adata[bl-1]; |
---|
586 | else |
---|
587 | cdata[bl-1] = adata[bl-1] & ((((mp_limb_t) 1) << wh) - ((mp_limb_t) 1)); |
---|
588 | |
---|
589 | STRIP(bl, cdata); |
---|
590 | SIZE(c) = bl; |
---|
591 | } |
---|
592 | |
---|
593 | long _ntl_gslowbits(_ntl_gbigint a, long p) |
---|
594 | { |
---|
595 | static _ntl_gbigint x = 0; |
---|
596 | |
---|
597 | if (p > NTL_BITS_PER_LONG) |
---|
598 | p = NTL_BITS_PER_LONG; |
---|
599 | |
---|
600 | _ntl_glowbits(a, p, &x); |
---|
601 | |
---|
602 | return _ntl_gtoint(x); |
---|
603 | } |
---|
604 | |
---|
605 | long _ntl_gsetbit(_ntl_gbigint *a, long b) |
---|
606 | { |
---|
607 | long bl; |
---|
608 | long sa, aneg; |
---|
609 | long i; |
---|
610 | mp_limb_t wh, *adata, tmp; |
---|
611 | |
---|
612 | if (b<0) ghalt("_ntl_gsetbit: negative index"); |
---|
613 | |
---|
614 | if (ZEROP(*a)) { |
---|
615 | _ntl_gintoz(1, a); |
---|
616 | _ntl_glshift(*a, b, a); |
---|
617 | return 0; |
---|
618 | } |
---|
619 | |
---|
620 | bl = (b/NTL_ZZ_NBITS); |
---|
621 | wh = ((mp_limb_t) 1) << (b - NTL_ZZ_NBITS*bl); |
---|
622 | |
---|
623 | GET_SIZE_NEG(sa, aneg, *a); |
---|
624 | |
---|
625 | if (sa > bl) { |
---|
626 | adata = DATA(*a); |
---|
627 | tmp = adata[bl] & wh; |
---|
628 | adata[bl] |= wh; |
---|
629 | if (tmp) return 1; |
---|
630 | return 0; |
---|
631 | } |
---|
632 | else { |
---|
633 | _ntl_gsetlength(a, bl+1); |
---|
634 | adata = DATA(*a); |
---|
635 | for (i = sa; i < bl; i++) |
---|
636 | adata[i] = 0; |
---|
637 | adata[bl] = wh; |
---|
638 | |
---|
639 | sa = bl+1; |
---|
640 | if (aneg) sa = -sa; |
---|
641 | SIZE(*a) = sa; |
---|
642 | return 0; |
---|
643 | } |
---|
644 | } |
---|
645 | |
---|
646 | long _ntl_gswitchbit(_ntl_gbigint *a, long b) |
---|
647 | { |
---|
648 | long bl; |
---|
649 | long sa, aneg; |
---|
650 | long i; |
---|
651 | mp_limb_t wh, *adata, tmp; |
---|
652 | |
---|
653 | if (b<0) ghalt("_ntl_gswitchbit: negative index"); |
---|
654 | |
---|
655 | |
---|
656 | if (ZEROP(*a)) { |
---|
657 | _ntl_gintoz(1, a); |
---|
658 | _ntl_glshift(*a, b, a); |
---|
659 | return 0; |
---|
660 | } |
---|
661 | |
---|
662 | bl = (b/NTL_ZZ_NBITS); |
---|
663 | wh = ((mp_limb_t) 1) << (b - NTL_ZZ_NBITS*bl); |
---|
664 | |
---|
665 | GET_SIZE_NEG(sa, aneg, *a); |
---|
666 | |
---|
667 | if (sa > bl) { |
---|
668 | adata = DATA(*a); |
---|
669 | tmp = adata[bl] & wh; |
---|
670 | adata[bl] ^= wh; |
---|
671 | |
---|
672 | if (bl == sa-1) { |
---|
673 | STRIP(sa, adata); |
---|
674 | if (aneg) sa = -sa; |
---|
675 | SIZE(*a) = sa; |
---|
676 | } |
---|
677 | |
---|
678 | if (tmp) return 1; |
---|
679 | return 0; |
---|
680 | } |
---|
681 | else { |
---|
682 | _ntl_gsetlength(a, bl+1); |
---|
683 | adata = DATA(*a); |
---|
684 | for (i = sa; i < bl; i++) |
---|
685 | adata[i] = 0; |
---|
686 | adata[bl] = wh; |
---|
687 | |
---|
688 | sa = bl+1; |
---|
689 | if (aneg) sa = -sa; |
---|
690 | SIZE(*a) = sa; |
---|
691 | return 0; |
---|
692 | } |
---|
693 | } |
---|
694 | |
---|
695 | long |
---|
696 | _ntl_gweights( |
---|
697 | long aa |
---|
698 | ) |
---|
699 | { |
---|
700 | unsigned long a; |
---|
701 | long res = 0; |
---|
702 | if (aa < 0) |
---|
703 | a = -((unsigned long) aa); |
---|
704 | else |
---|
705 | a = aa; |
---|
706 | |
---|
707 | while (a) { |
---|
708 | if (a & 1) res ++; |
---|
709 | a >>= 1; |
---|
710 | } |
---|
711 | return (res); |
---|
712 | } |
---|
713 | |
---|
714 | static long |
---|
715 | gweights_mp_limb( |
---|
716 | mp_limb_t a |
---|
717 | ) |
---|
718 | { |
---|
719 | long res = 0; |
---|
720 | |
---|
721 | while (a) { |
---|
722 | if (a & 1) res ++; |
---|
723 | a >>= 1; |
---|
724 | } |
---|
725 | return (res); |
---|
726 | } |
---|
727 | |
---|
728 | long |
---|
729 | _ntl_gweight( |
---|
730 | _ntl_gbigint a |
---|
731 | ) |
---|
732 | { |
---|
733 | long i; |
---|
734 | long sa; |
---|
735 | mp_limb_t *adata; |
---|
736 | long res; |
---|
737 | |
---|
738 | if (!a) return (0); |
---|
739 | |
---|
740 | sa = SIZE(a); |
---|
741 | if (sa < 0) sa = -sa; |
---|
742 | adata = DATA(a); |
---|
743 | |
---|
744 | res = 0; |
---|
745 | for (i = 0; i < sa; i++) |
---|
746 | res += gweights_mp_limb(adata[i]); |
---|
747 | |
---|
748 | return (res); |
---|
749 | } |
---|
750 | |
---|
751 | long |
---|
752 | _ntl_g2logs( |
---|
753 | long aa |
---|
754 | ) |
---|
755 | { |
---|
756 | long i = 0; |
---|
757 | unsigned long a; |
---|
758 | |
---|
759 | if (aa < 0) |
---|
760 | a = - ((unsigned long) aa); |
---|
761 | else |
---|
762 | a = aa; |
---|
763 | |
---|
764 | while (a>=256) |
---|
765 | i += 8, a >>= 8; |
---|
766 | if (a >=16) |
---|
767 | i += 4, a >>= 4; |
---|
768 | if (a >= 4) |
---|
769 | i += 2, a >>= 2; |
---|
770 | if (a >= 2) |
---|
771 | i += 2; |
---|
772 | else if (a >= 1) |
---|
773 | i++; |
---|
774 | return (i); |
---|
775 | } |
---|
776 | |
---|
777 | long _ntl_g2log(_ntl_gbigint a) |
---|
778 | { |
---|
779 | long la; |
---|
780 | long t; |
---|
781 | |
---|
782 | if (!a) return 0; |
---|
783 | la = SIZE(a); |
---|
784 | if (la == 0) return 0; |
---|
785 | if (la < 0) la = -la; |
---|
786 | COUNT_BITS(t, DATA(a)[la-1]); |
---|
787 | return NTL_ZZ_NBITS*(la - 1) + t; |
---|
788 | } |
---|
789 | |
---|
790 | |
---|
791 | |
---|
792 | long _ntl_gmakeodd(_ntl_gbigint *nn) |
---|
793 | { |
---|
794 | _ntl_gbigint n = *nn; |
---|
795 | long shift; |
---|
796 | mp_limb_t *ndata; |
---|
797 | mp_limb_t i; |
---|
798 | |
---|
799 | if (ZEROP(n)) |
---|
800 | return (0); |
---|
801 | |
---|
802 | shift = 0; |
---|
803 | ndata = DATA(n); |
---|
804 | |
---|
805 | while (ndata[shift] == 0) |
---|
806 | shift++; |
---|
807 | |
---|
808 | i = ndata[shift]; |
---|
809 | |
---|
810 | shift = NTL_ZZ_NBITS * shift; |
---|
811 | |
---|
812 | while ((i & 1) == 0) { |
---|
813 | shift++; |
---|
814 | i >>= 1; |
---|
815 | } |
---|
816 | _ntl_grshift(n, shift, &n); |
---|
817 | return shift; |
---|
818 | } |
---|
819 | |
---|
820 | |
---|
821 | long _ntl_gnumtwos(_ntl_gbigint n) |
---|
822 | { |
---|
823 | long shift; |
---|
824 | mp_limb_t *ndata; |
---|
825 | mp_limb_t i; |
---|
826 | |
---|
827 | if (ZEROP(n)) |
---|
828 | return (0); |
---|
829 | |
---|
830 | shift = 0; |
---|
831 | ndata = DATA(n); |
---|
832 | |
---|
833 | while (ndata[shift] == 0) |
---|
834 | shift++; |
---|
835 | |
---|
836 | i = ndata[shift]; |
---|
837 | |
---|
838 | shift = NTL_ZZ_NBITS * shift; |
---|
839 | |
---|
840 | while ((i & 1) == 0) { |
---|
841 | shift++; |
---|
842 | i >>= 1; |
---|
843 | } |
---|
844 | |
---|
845 | return shift; |
---|
846 | } |
---|
847 | |
---|
848 | |
---|
849 | void _ntl_gand(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
850 | { |
---|
851 | _ntl_gbigint c; |
---|
852 | long sa; |
---|
853 | long sb; |
---|
854 | long sm; |
---|
855 | long i; |
---|
856 | long a_alias, b_alias; |
---|
857 | mp_limb_t *adata, *bdata, *cdata; |
---|
858 | |
---|
859 | if (ZEROP(a) || ZEROP(b)) { |
---|
860 | _ntl_gzero(cc); |
---|
861 | return; |
---|
862 | } |
---|
863 | |
---|
864 | c = *cc; |
---|
865 | a_alias = (a == c); |
---|
866 | b_alias = (b == c); |
---|
867 | |
---|
868 | sa = SIZE(a); |
---|
869 | if (sa < 0) sa = -sa; |
---|
870 | |
---|
871 | sb = SIZE(b); |
---|
872 | if (sb < 0) sb = -sb; |
---|
873 | |
---|
874 | sm = (sa > sb ? sb : sa); |
---|
875 | |
---|
876 | _ntl_gsetlength(&c, sm); |
---|
877 | if (a_alias) a = c; |
---|
878 | if (b_alias) b = c; |
---|
879 | *cc = c; |
---|
880 | |
---|
881 | adata = DATA(a); |
---|
882 | bdata = DATA(b); |
---|
883 | cdata = DATA(c); |
---|
884 | |
---|
885 | for (i = 0; i < sm; i++) |
---|
886 | cdata[i] = adata[i] & bdata[i]; |
---|
887 | |
---|
888 | STRIP(sm, cdata); |
---|
889 | SIZE(c) = sm; |
---|
890 | } |
---|
891 | |
---|
892 | |
---|
893 | void _ntl_gxor(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
894 | { |
---|
895 | _ntl_gbigint c; |
---|
896 | long sa; |
---|
897 | long sb; |
---|
898 | long sm; |
---|
899 | long la; |
---|
900 | long i; |
---|
901 | long a_alias, b_alias; |
---|
902 | mp_limb_t *adata, *bdata, *cdata; |
---|
903 | |
---|
904 | if (ZEROP(a)) { |
---|
905 | _ntl_gcopy(b,cc); |
---|
906 | _ntl_gabs(cc); |
---|
907 | return; |
---|
908 | } |
---|
909 | |
---|
910 | if (ZEROP(b)) { |
---|
911 | _ntl_gcopy(a,cc); |
---|
912 | _ntl_gabs(cc); |
---|
913 | return; |
---|
914 | } |
---|
915 | |
---|
916 | c = *cc; |
---|
917 | a_alias = (a == c); |
---|
918 | b_alias = (b == c); |
---|
919 | |
---|
920 | sa = SIZE(a); |
---|
921 | if (sa < 0) sa = -sa; |
---|
922 | |
---|
923 | sb = SIZE(b); |
---|
924 | if (sb < 0) sb = -sb; |
---|
925 | |
---|
926 | if (sa > sb) { |
---|
927 | la = sa; |
---|
928 | sm = sb; |
---|
929 | } |
---|
930 | else { |
---|
931 | la = sb; |
---|
932 | sm = sa; |
---|
933 | } |
---|
934 | |
---|
935 | _ntl_gsetlength(&c, la); |
---|
936 | if (a_alias) a = c; |
---|
937 | if (b_alias) b = c; |
---|
938 | *cc = c; |
---|
939 | |
---|
940 | adata = DATA(a); |
---|
941 | bdata = DATA(b); |
---|
942 | cdata = DATA(c); |
---|
943 | |
---|
944 | for (i = 0; i < sm; i ++) |
---|
945 | cdata[i] = adata[i] ^ bdata[i]; |
---|
946 | |
---|
947 | if (sa > sb) |
---|
948 | for (;i < la; i++) cdata[i] = adata[i]; |
---|
949 | else |
---|
950 | for (;i < la; i++) cdata[i] = bdata[i]; |
---|
951 | |
---|
952 | STRIP(la, cdata); |
---|
953 | SIZE(c) = la; |
---|
954 | } |
---|
955 | |
---|
956 | |
---|
957 | void _ntl_gor(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
958 | { |
---|
959 | _ntl_gbigint c; |
---|
960 | long sa; |
---|
961 | long sb; |
---|
962 | long sm; |
---|
963 | long la; |
---|
964 | long i; |
---|
965 | long a_alias, b_alias; |
---|
966 | mp_limb_t *adata, *bdata, *cdata; |
---|
967 | |
---|
968 | if (ZEROP(a)) { |
---|
969 | _ntl_gcopy(b,cc); |
---|
970 | _ntl_gabs(cc); |
---|
971 | return; |
---|
972 | } |
---|
973 | |
---|
974 | if (ZEROP(b)) { |
---|
975 | _ntl_gcopy(a,cc); |
---|
976 | _ntl_gabs(cc); |
---|
977 | return; |
---|
978 | } |
---|
979 | |
---|
980 | c = *cc; |
---|
981 | a_alias = (a == c); |
---|
982 | b_alias = (b == c); |
---|
983 | |
---|
984 | sa = SIZE(a); |
---|
985 | if (sa < 0) sa = -sa; |
---|
986 | |
---|
987 | sb = SIZE(b); |
---|
988 | if (sb < 0) sb = -sb; |
---|
989 | |
---|
990 | if (sa > sb) { |
---|
991 | la = sa; |
---|
992 | sm = sb; |
---|
993 | } |
---|
994 | else { |
---|
995 | la = sb; |
---|
996 | sm = sa; |
---|
997 | } |
---|
998 | |
---|
999 | _ntl_gsetlength(&c, la); |
---|
1000 | if (a_alias) a = c; |
---|
1001 | if (b_alias) b = c; |
---|
1002 | *cc = c; |
---|
1003 | |
---|
1004 | adata = DATA(a); |
---|
1005 | bdata = DATA(b); |
---|
1006 | cdata = DATA(c); |
---|
1007 | |
---|
1008 | for (i = 0; i < sm; i ++) |
---|
1009 | cdata[i] = adata[i] | bdata[i]; |
---|
1010 | |
---|
1011 | if (sa > sb) |
---|
1012 | for (;i < la; i++) cdata[i] = adata[i]; |
---|
1013 | else |
---|
1014 | for (;i < la; i++) cdata[i] = bdata[i]; |
---|
1015 | |
---|
1016 | STRIP(la, cdata); |
---|
1017 | SIZE(c) = la; |
---|
1018 | } |
---|
1019 | |
---|
1020 | |
---|
1021 | void _ntl_gnegate(_ntl_gbigint *aa) |
---|
1022 | { |
---|
1023 | _ntl_gbigint a = *aa; |
---|
1024 | if (a) SIZE(a) = -SIZE(a); |
---|
1025 | } |
---|
1026 | |
---|
1027 | |
---|
1028 | /* |
---|
1029 | * DIRT: this implementation of _ntl_gintoz relies crucially |
---|
1030 | * on the assumption that the number of bits per limb_t is at least |
---|
1031 | * equal to the number of bits per long. |
---|
1032 | */ |
---|
1033 | |
---|
1034 | void _ntl_gintoz(long d, _ntl_gbigint *aa) |
---|
1035 | { |
---|
1036 | _ntl_gbigint a = *aa; |
---|
1037 | |
---|
1038 | if (d == 0) { |
---|
1039 | if (a) SIZE(a) = 0; |
---|
1040 | } |
---|
1041 | else if (d > 0) { |
---|
1042 | if (!a) { |
---|
1043 | _ntl_gsetlength(&a, 1); |
---|
1044 | *aa = a; |
---|
1045 | } |
---|
1046 | |
---|
1047 | SIZE(a) = 1; |
---|
1048 | DATA(a)[0] = d; |
---|
1049 | } |
---|
1050 | else { |
---|
1051 | if (!a) { |
---|
1052 | _ntl_gsetlength(&a, 1); |
---|
1053 | *aa = a; |
---|
1054 | } |
---|
1055 | |
---|
1056 | SIZE(a) = -1; |
---|
1057 | DATA(a)[0] = -((mp_limb_t) d); /* careful! */ |
---|
1058 | } |
---|
1059 | } |
---|
1060 | |
---|
1061 | |
---|
1062 | /* |
---|
1063 | * DIRT: this implementation of _ntl_guintoz relies crucially |
---|
1064 | * on the assumption that the number of bits per limb_t is at least |
---|
1065 | * equal to the number of bits per long. |
---|
1066 | */ |
---|
1067 | |
---|
1068 | void _ntl_guintoz(unsigned long d, _ntl_gbigint *aa) |
---|
1069 | { |
---|
1070 | _ntl_gbigint a = *aa; |
---|
1071 | |
---|
1072 | if (d == 0) { |
---|
1073 | if (a) SIZE(a) = 0; |
---|
1074 | } |
---|
1075 | else { |
---|
1076 | if (!a) { |
---|
1077 | _ntl_gsetlength(&a, 1); |
---|
1078 | *aa = a; |
---|
1079 | } |
---|
1080 | |
---|
1081 | SIZE(a) = 1; |
---|
1082 | DATA(a)[0] = d; |
---|
1083 | } |
---|
1084 | } |
---|
1085 | |
---|
1086 | |
---|
1087 | long _ntl_gtoint(_ntl_gbigint a) |
---|
1088 | { |
---|
1089 | unsigned long res = _ntl_gtouint(a); |
---|
1090 | return NTL_ULONG_TO_LONG(res); |
---|
1091 | } |
---|
1092 | |
---|
1093 | /* |
---|
1094 | * DIRT: this implementation of _ntl_gtouint relies crucially |
---|
1095 | * on the assumption that the number of bits per limb_t is at least |
---|
1096 | * equal to the number of bits per long. |
---|
1097 | */ |
---|
1098 | |
---|
1099 | unsigned long _ntl_gtouint(_ntl_gbigint a) |
---|
1100 | { |
---|
1101 | if (ZEROP(a)) |
---|
1102 | return 0; |
---|
1103 | |
---|
1104 | if (SIZE(a) > 0) |
---|
1105 | return DATA(a)[0]; |
---|
1106 | |
---|
1107 | return -DATA(a)[0]; |
---|
1108 | } |
---|
1109 | |
---|
1110 | |
---|
1111 | long _ntl_gcompare(_ntl_gbigint a, _ntl_gbigint b) |
---|
1112 | { |
---|
1113 | long sa, sb, cmp; |
---|
1114 | mp_limb_t *adata, *bdata; |
---|
1115 | |
---|
1116 | if (!a) |
---|
1117 | sa = 0; |
---|
1118 | else |
---|
1119 | sa = SIZE(a); |
---|
1120 | |
---|
1121 | if (!b) |
---|
1122 | sb = 0; |
---|
1123 | else |
---|
1124 | sb = SIZE(b); |
---|
1125 | |
---|
1126 | if (sa != sb) { |
---|
1127 | if (sa > sb) |
---|
1128 | return 1; |
---|
1129 | else |
---|
1130 | return -1; |
---|
1131 | } |
---|
1132 | |
---|
1133 | if (sa == 0) |
---|
1134 | return 0; |
---|
1135 | |
---|
1136 | adata = DATA(a); |
---|
1137 | bdata = DATA(b); |
---|
1138 | |
---|
1139 | if (sa > 0) { |
---|
1140 | cmp = mpn_cmp(adata, bdata, sa); |
---|
1141 | |
---|
1142 | if (cmp > 0) |
---|
1143 | return 1; |
---|
1144 | else if (cmp < 0) |
---|
1145 | return -1; |
---|
1146 | else |
---|
1147 | return 0; |
---|
1148 | } |
---|
1149 | else { |
---|
1150 | cmp = mpn_cmp(adata, bdata, -sa); |
---|
1151 | |
---|
1152 | if (cmp > 0) |
---|
1153 | return -1; |
---|
1154 | else if (cmp < 0) |
---|
1155 | return 1; |
---|
1156 | else |
---|
1157 | return 0; |
---|
1158 | } |
---|
1159 | } |
---|
1160 | |
---|
1161 | |
---|
1162 | long _ntl_gsign(_ntl_gbigint a) |
---|
1163 | { |
---|
1164 | long sa; |
---|
1165 | |
---|
1166 | if (!a) return 0; |
---|
1167 | |
---|
1168 | sa = SIZE(a); |
---|
1169 | if (sa > 0) return 1; |
---|
1170 | if (sa == 0) return 0; |
---|
1171 | return -1; |
---|
1172 | } |
---|
1173 | |
---|
1174 | void _ntl_gabs(_ntl_gbigint *pa) |
---|
1175 | { |
---|
1176 | _ntl_gbigint a = *pa; |
---|
1177 | |
---|
1178 | if (!a) return; |
---|
1179 | if (SIZE(a) < 0) SIZE(a) = -SIZE(a); |
---|
1180 | } |
---|
1181 | |
---|
1182 | long _ntl_gscompare(_ntl_gbigint a, long b) |
---|
1183 | { |
---|
1184 | if (b == 0) { |
---|
1185 | long sa; |
---|
1186 | if (!a) return 0; |
---|
1187 | sa = SIZE(a); |
---|
1188 | if (sa > 0) return 1; |
---|
1189 | if (sa == 0) return 0; |
---|
1190 | return -1; |
---|
1191 | } |
---|
1192 | else { |
---|
1193 | static _ntl_gbigint B = 0; |
---|
1194 | _ntl_gintoz(b, &B); |
---|
1195 | return _ntl_gcompare(a, B); |
---|
1196 | } |
---|
1197 | } |
---|
1198 | |
---|
1199 | |
---|
1200 | void _ntl_glshift(_ntl_gbigint n, long k, _ntl_gbigint *rres) |
---|
1201 | { |
---|
1202 | _ntl_gbigint res; |
---|
1203 | mp_limb_t *ndata, *resdata, *resdata1; |
---|
1204 | long limb_cnt, i, sn, nneg, sres; |
---|
1205 | long n_alias; |
---|
1206 | |
---|
1207 | if (ZEROP(n)) { |
---|
1208 | _ntl_gzero(rres); |
---|
1209 | return; |
---|
1210 | } |
---|
1211 | |
---|
1212 | res = *rres; |
---|
1213 | n_alias = (n == res); |
---|
1214 | |
---|
1215 | if (!k) { |
---|
1216 | if (!n_alias) |
---|
1217 | _ntl_gcopy(n, rres); |
---|
1218 | return; |
---|
1219 | } |
---|
1220 | |
---|
1221 | if (k < 0) { |
---|
1222 | if (k < -NTL_MAX_LONG) |
---|
1223 | _ntl_gzero(rres); |
---|
1224 | else |
---|
1225 | _ntl_grshift(n, -k, rres); |
---|
1226 | return; |
---|
1227 | } |
---|
1228 | |
---|
1229 | GET_SIZE_NEG(sn, nneg, n); |
---|
1230 | |
---|
1231 | limb_cnt = k/NTL_ZZ_NBITS; |
---|
1232 | sres = sn + limb_cnt + 1; |
---|
1233 | |
---|
1234 | if (MustAlloc(res, sres)) { |
---|
1235 | _ntl_gsetlength(&res, sres); |
---|
1236 | if (n_alias) n = res; |
---|
1237 | *rres = res; |
---|
1238 | } |
---|
1239 | |
---|
1240 | ndata = DATA(n); |
---|
1241 | resdata = DATA(res); |
---|
1242 | resdata1 = resdata + limb_cnt; |
---|
1243 | k %= NTL_ZZ_NBITS; |
---|
1244 | sres--; |
---|
1245 | |
---|
1246 | if (k != 0) { |
---|
1247 | mp_limb_t t = mpn_lshift(resdata1, ndata, sn, k); |
---|
1248 | if (t != 0) { |
---|
1249 | resdata[sres] = t; |
---|
1250 | sres++; |
---|
1251 | } |
---|
1252 | } |
---|
1253 | else { |
---|
1254 | for (i = sn-1; i >= 0; i--) |
---|
1255 | resdata1[i] = ndata[i]; |
---|
1256 | } |
---|
1257 | |
---|
1258 | for (i = 0; i < limb_cnt; i++) |
---|
1259 | resdata[i] = 0; |
---|
1260 | |
---|
1261 | if (nneg) sres = -sres; |
---|
1262 | SIZE(res) = sres; |
---|
1263 | } |
---|
1264 | |
---|
1265 | void _ntl_grshift(_ntl_gbigint n, long k, _ntl_gbigint *rres) |
---|
1266 | { |
---|
1267 | _ntl_gbigint res; |
---|
1268 | mp_limb_t *ndata, *resdata, *ndata1; |
---|
1269 | long limb_cnt, i, sn, nneg, sres; |
---|
1270 | |
---|
1271 | if (ZEROP(n)) { |
---|
1272 | _ntl_gzero(rres); |
---|
1273 | return; |
---|
1274 | } |
---|
1275 | |
---|
1276 | if (!k) { |
---|
1277 | if (n != *rres) |
---|
1278 | _ntl_gcopy(n, rres); |
---|
1279 | return; |
---|
1280 | } |
---|
1281 | |
---|
1282 | if (k < 0) { |
---|
1283 | if (k < -NTL_MAX_LONG) ghalt("overflow in _ntl_glshift"); |
---|
1284 | _ntl_glshift(n, -k, rres); |
---|
1285 | return; |
---|
1286 | } |
---|
1287 | |
---|
1288 | GET_SIZE_NEG(sn, nneg, n); |
---|
1289 | |
---|
1290 | limb_cnt = k/NTL_ZZ_NBITS; |
---|
1291 | |
---|
1292 | sres = sn - limb_cnt; |
---|
1293 | |
---|
1294 | if (sres <= 0) { |
---|
1295 | _ntl_gzero(rres); |
---|
1296 | return; |
---|
1297 | } |
---|
1298 | |
---|
1299 | res = *rres; |
---|
1300 | if (MustAlloc(res, sres)) { |
---|
1301 | /* n won't move if res aliases n */ |
---|
1302 | _ntl_gsetlength(&res, sres); |
---|
1303 | *rres = res; |
---|
1304 | } |
---|
1305 | |
---|
1306 | ndata = DATA(n); |
---|
1307 | resdata = DATA(res); |
---|
1308 | ndata1 = ndata + limb_cnt; |
---|
1309 | k %= NTL_ZZ_NBITS; |
---|
1310 | |
---|
1311 | if (k != 0) { |
---|
1312 | mpn_rshift(resdata, ndata1, sres, k); |
---|
1313 | if (resdata[sres-1] == 0) |
---|
1314 | sres--; |
---|
1315 | } |
---|
1316 | else { |
---|
1317 | for (i = 0; i < sres; i++) |
---|
1318 | resdata[i] = ndata1[i]; |
---|
1319 | } |
---|
1320 | |
---|
1321 | if (nneg) sres = -sres; |
---|
1322 | SIZE(res) = sres; |
---|
1323 | } |
---|
1324 | |
---|
1325 | |
---|
1326 | |
---|
1327 | void |
---|
1328 | _ntl_gadd(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
1329 | { |
---|
1330 | long sa, aneg, sb, bneg, sc, cmp; |
---|
1331 | mp_limb_t *adata, *bdata, *cdata, carry; |
---|
1332 | _ntl_gbigint c; |
---|
1333 | long a_alias, b_alias; |
---|
1334 | |
---|
1335 | if (ZEROP(a)) { |
---|
1336 | _ntl_gcopy(b, cc); |
---|
1337 | return; |
---|
1338 | } |
---|
1339 | |
---|
1340 | if (ZEROP(b)) { |
---|
1341 | _ntl_gcopy(a, cc); |
---|
1342 | return; |
---|
1343 | } |
---|
1344 | |
---|
1345 | GET_SIZE_NEG(sa, aneg, a); |
---|
1346 | GET_SIZE_NEG(sb, bneg, b); |
---|
1347 | |
---|
1348 | if (sa < sb) { |
---|
1349 | SWAP_BIGINT(a, b); |
---|
1350 | SWAP_LONG(sa, sb); |
---|
1351 | SWAP_LONG(aneg, bneg); |
---|
1352 | } |
---|
1353 | |
---|
1354 | /* sa >= sb */ |
---|
1355 | |
---|
1356 | c = *cc; |
---|
1357 | a_alias = (a == c); |
---|
1358 | b_alias = (b == c); |
---|
1359 | |
---|
1360 | if (aneg == bneg) { |
---|
1361 | /* same sign => addition */ |
---|
1362 | |
---|
1363 | sc = sa + 1; |
---|
1364 | if (MustAlloc(c, sc)) { |
---|
1365 | _ntl_gsetlength(&c, sc); |
---|
1366 | if (a_alias) a = c; |
---|
1367 | if (b_alias) b = c; |
---|
1368 | *cc = c; |
---|
1369 | } |
---|
1370 | |
---|
1371 | adata = DATA(a); |
---|
1372 | bdata = DATA(b); |
---|
1373 | cdata = DATA(c); |
---|
1374 | |
---|
1375 | carry = mpn_add(cdata, adata, sa, bdata, sb); |
---|
1376 | if (carry) |
---|
1377 | cdata[sc-1] = carry; |
---|
1378 | else |
---|
1379 | sc--; |
---|
1380 | |
---|
1381 | if (aneg) sc = -sc; |
---|
1382 | SIZE(c) = sc; |
---|
1383 | } |
---|
1384 | else { |
---|
1385 | /* opposite sign => subtraction */ |
---|
1386 | |
---|
1387 | sc = sa; |
---|
1388 | if (MustAlloc(c, sc)) { |
---|
1389 | _ntl_gsetlength(&c, sc); |
---|
1390 | if (a_alias) a = c; |
---|
1391 | if (b_alias) b = c; |
---|
1392 | *cc = c; |
---|
1393 | } |
---|
1394 | |
---|
1395 | adata = DATA(a); |
---|
1396 | bdata = DATA(b); |
---|
1397 | cdata = DATA(c); |
---|
1398 | |
---|
1399 | if (sa > sb) |
---|
1400 | cmp = 1; |
---|
1401 | else |
---|
1402 | cmp = mpn_cmp(adata, bdata, sa); |
---|
1403 | |
---|
1404 | if (cmp == 0) { |
---|
1405 | SIZE(c) = 0; |
---|
1406 | } |
---|
1407 | else { |
---|
1408 | if (cmp < 0) cmp = 0; |
---|
1409 | if (cmp > 0) cmp = 1; |
---|
1410 | /* abs(a) != abs(b) && (abs(a) > abs(b) <=> cmp) */ |
---|
1411 | |
---|
1412 | if (cmp) |
---|
1413 | mpn_sub(cdata, adata, sa, bdata, sb); |
---|
1414 | else |
---|
1415 | mpn_sub(cdata, bdata, sb, adata, sa); /* sa == sb */ |
---|
1416 | |
---|
1417 | STRIP(sc, cdata); |
---|
1418 | if (aneg == cmp) sc = -sc; |
---|
1419 | SIZE(c) = sc; |
---|
1420 | } |
---|
1421 | } |
---|
1422 | } |
---|
1423 | |
---|
1424 | void |
---|
1425 | _ntl_gsadd(_ntl_gbigint a, long b, _ntl_gbigint *cc) |
---|
1426 | { |
---|
1427 | static _ntl_gbigint B = 0; |
---|
1428 | _ntl_gintoz(b, &B); |
---|
1429 | _ntl_gadd(a, B, cc); |
---|
1430 | } |
---|
1431 | |
---|
1432 | void |
---|
1433 | _ntl_gsub(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
1434 | { |
---|
1435 | long sa, aneg, sb, bneg, sc, cmp, rev; |
---|
1436 | mp_limb_t *adata, *bdata, *cdata, carry; |
---|
1437 | _ntl_gbigint c; |
---|
1438 | long a_alias, b_alias; |
---|
1439 | |
---|
1440 | if (ZEROP(a)) { |
---|
1441 | _ntl_gcopy(b, cc); |
---|
1442 | c = *cc; |
---|
1443 | if (c) SIZE(c) = -SIZE(c); |
---|
1444 | return; |
---|
1445 | } |
---|
1446 | |
---|
1447 | if (ZEROP(b)) { |
---|
1448 | _ntl_gcopy(a, cc); |
---|
1449 | return; |
---|
1450 | } |
---|
1451 | |
---|
1452 | GET_SIZE_NEG(sa, aneg, a); |
---|
1453 | GET_SIZE_NEG(sb, bneg, b); |
---|
1454 | |
---|
1455 | if (sa < sb) { |
---|
1456 | SWAP_BIGINT(a, b); |
---|
1457 | SWAP_LONG(sa, sb); |
---|
1458 | SWAP_LONG(aneg, bneg); |
---|
1459 | rev = 1; |
---|
1460 | } |
---|
1461 | else |
---|
1462 | rev = 0; |
---|
1463 | |
---|
1464 | /* sa >= sb */ |
---|
1465 | |
---|
1466 | c = *cc; |
---|
1467 | a_alias = (a == c); |
---|
1468 | b_alias = (b == c); |
---|
1469 | |
---|
1470 | if (aneg != bneg) { |
---|
1471 | /* opposite sign => addition */ |
---|
1472 | |
---|
1473 | sc = sa + 1; |
---|
1474 | if (MustAlloc(c, sc)) { |
---|
1475 | _ntl_gsetlength(&c, sc); |
---|
1476 | if (a_alias) a = c; |
---|
1477 | if (b_alias) b = c; |
---|
1478 | *cc = c; |
---|
1479 | } |
---|
1480 | |
---|
1481 | adata = DATA(a); |
---|
1482 | bdata = DATA(b); |
---|
1483 | cdata = DATA(c); |
---|
1484 | |
---|
1485 | carry = mpn_add(cdata, adata, sa, bdata, sb); |
---|
1486 | if (carry) |
---|
1487 | cdata[sc-1] = carry; |
---|
1488 | else |
---|
1489 | sc--; |
---|
1490 | |
---|
1491 | if (aneg ^ rev) sc = -sc; |
---|
1492 | SIZE(c) = sc; |
---|
1493 | } |
---|
1494 | else { |
---|
1495 | /* same sign => subtraction */ |
---|
1496 | |
---|
1497 | sc = sa; |
---|
1498 | if (MustAlloc(c, sc)) { |
---|
1499 | _ntl_gsetlength(&c, sc); |
---|
1500 | if (a_alias) a = c; |
---|
1501 | if (b_alias) b = c; |
---|
1502 | *cc = c; |
---|
1503 | } |
---|
1504 | |
---|
1505 | adata = DATA(a); |
---|
1506 | bdata = DATA(b); |
---|
1507 | cdata = DATA(c); |
---|
1508 | |
---|
1509 | if (sa > sb) |
---|
1510 | cmp = 1; |
---|
1511 | else |
---|
1512 | cmp = mpn_cmp(adata, bdata, sa); |
---|
1513 | |
---|
1514 | if (cmp == 0) { |
---|
1515 | SIZE(c) = 0; |
---|
1516 | } |
---|
1517 | else { |
---|
1518 | if (cmp < 0) cmp = 0; |
---|
1519 | if (cmp > 0) cmp = 1; |
---|
1520 | /* abs(a) != abs(b) && (abs(a) > abs(b) <=> cmp) */ |
---|
1521 | |
---|
1522 | if (cmp) |
---|
1523 | mpn_sub(cdata, adata, sa, bdata, sb); |
---|
1524 | else |
---|
1525 | mpn_sub(cdata, bdata, sb, adata, sa); /* sa == sb */ |
---|
1526 | |
---|
1527 | STRIP(sc, cdata); |
---|
1528 | if ((aneg == cmp) ^ rev) sc = -sc; |
---|
1529 | SIZE(c) = sc; |
---|
1530 | } |
---|
1531 | } |
---|
1532 | } |
---|
1533 | |
---|
1534 | void |
---|
1535 | _ntl_gsubpos(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
1536 | { |
---|
1537 | long sa, sb, sc; |
---|
1538 | mp_limb_t *adata, *bdata, *cdata; |
---|
1539 | _ntl_gbigint c; |
---|
1540 | long a_alias, b_alias; |
---|
1541 | |
---|
1542 | if (ZEROP(a)) { |
---|
1543 | _ntl_gzero(cc); |
---|
1544 | return; |
---|
1545 | } |
---|
1546 | |
---|
1547 | if (ZEROP(b)) { |
---|
1548 | _ntl_gcopy(a, cc); |
---|
1549 | return; |
---|
1550 | } |
---|
1551 | |
---|
1552 | sa = SIZE(a); |
---|
1553 | sb = SIZE(b); |
---|
1554 | |
---|
1555 | c = *cc; |
---|
1556 | a_alias = (a == c); |
---|
1557 | b_alias = (b == c); |
---|
1558 | |
---|
1559 | sc = sa; |
---|
1560 | if (MustAlloc(c, sc)) { |
---|
1561 | _ntl_gsetlength(&c, sc); |
---|
1562 | if (a_alias) a = c; |
---|
1563 | if (b_alias) b = c; |
---|
1564 | *cc = c; |
---|
1565 | } |
---|
1566 | |
---|
1567 | adata = DATA(a); |
---|
1568 | bdata = DATA(b); |
---|
1569 | cdata = DATA(c); |
---|
1570 | |
---|
1571 | mpn_sub(cdata, adata, sa, bdata, sb); |
---|
1572 | |
---|
1573 | STRIP(sc, cdata); |
---|
1574 | SIZE(c) = sc; |
---|
1575 | } |
---|
1576 | |
---|
1577 | void _ntl_gmul(_ntl_gbigint a, _ntl_gbigint b, _ntl_gbigint *cc) |
---|
1578 | { |
---|
1579 | static _ntl_gbigint mem = 0; |
---|
1580 | |
---|
1581 | long sa, aneg, sb, bneg, alias, sc; |
---|
1582 | mp_limb_t *adata, *bdata, *cdata, msl; |
---|
1583 | _ntl_gbigint c; |
---|
1584 | |
---|
1585 | if (ZEROP(a) || ZEROP(b)) { |
---|
1586 | _ntl_gzero(cc); |
---|
1587 | return; |
---|
1588 | } |
---|
1589 | |
---|
1590 | GET_SIZE_NEG(sa, aneg, a); |
---|
1591 | GET_SIZE_NEG(sb, bneg, b); |
---|
1592 | |
---|
1593 | if (a == *cc || b == *cc) { |
---|
1594 | c = mem; |
---|
1595 | alias = 1; |
---|
1596 | } |
---|
1597 | else { |
---|
1598 | c = *cc; |
---|
1599 | alias = 0; |
---|
1600 | } |
---|
1601 | |
---|
1602 | sc = sa + sb; |
---|
1603 | if (MustAlloc(c, sc)) |
---|
1604 | _ntl_gsetlength(&c, sc); |
---|
1605 | |
---|
1606 | if (alias) |
---|
1607 | mem = c; |
---|
1608 | else |
---|
1609 | *cc = c; |
---|
1610 | |
---|
1611 | adata = DATA(a); |
---|
1612 | bdata = DATA(b); |
---|
1613 | cdata = DATA(c); |
---|
1614 | |
---|
1615 | if (sa >= sb) |
---|
1616 | msl = mpn_mul(cdata, adata, sa, bdata, sb); |
---|
1617 | else |
---|
1618 | msl = mpn_mul(cdata, bdata, sb, adata, sa); |
---|
1619 | |
---|
1620 | if (!msl) sc--; |
---|
1621 | if (aneg != bneg) sc = -sc; |
---|
1622 | SIZE(c) = sc; |
---|
1623 | |
---|
1624 | if (alias) _ntl_gcopy(mem, cc); |
---|
1625 | } |
---|
1626 | |
---|
1627 | void _ntl_gsq(_ntl_gbigint a, _ntl_gbigint *cc) |
---|
1628 | { |
---|
1629 | _ntl_gmul(a, a, cc); |
---|
1630 | /* this is good enough...eventually, mpn_sqr_n will be called */ |
---|
1631 | } |
---|
1632 | |
---|
1633 | |
---|
1634 | /* |
---|
1635 | * DIRT: this implementation of _ntl_gsmul relies crucially |
---|
1636 | * on the assumption that the number of bits per limb_t is at least |
---|
1637 | * equal to the number of bits per long. |
---|
1638 | */ |
---|
1639 | |
---|
1640 | void |
---|
1641 | _ntl_gsmul(_ntl_gbigint a, long d, _ntl_gbigint *bb) |
---|
1642 | { |
---|
1643 | long sa, sb; |
---|
1644 | long anegative, bnegative; |
---|
1645 | _ntl_gbigint b; |
---|
1646 | mp_limb_t *adata, *bdata; |
---|
1647 | mp_limb_t dd, carry; |
---|
1648 | long a_alias; |
---|
1649 | |
---|
1650 | if (ZEROP(a) || !d) { |
---|
1651 | _ntl_gzero(bb); |
---|
1652 | return; |
---|
1653 | } |
---|
1654 | |
---|
1655 | GET_SIZE_NEG(sa, anegative, a); |
---|
1656 | |
---|
1657 | if (d < 0) { |
---|
1658 | dd = - ((mp_limb_t) d); /* careful ! */ |
---|
1659 | bnegative = 1-anegative; |
---|
1660 | } |
---|
1661 | else { |
---|
1662 | dd = (mp_limb_t) d; |
---|
1663 | bnegative = anegative; |
---|
1664 | } |
---|
1665 | |
---|
1666 | sb = sa + 1; |
---|
1667 | |
---|
1668 | b = *bb; |
---|
1669 | a_alias = (a == b); |
---|
1670 | |
---|
1671 | if (MustAlloc(b, sb)) { |
---|
1672 | _ntl_gsetlength(&b, sb); |
---|
1673 | if (a_alias) a = b; |
---|
1674 | *bb = b; |
---|
1675 | } |
---|
1676 | |
---|
1677 | adata = DATA(a); |
---|
1678 | bdata = DATA(b); |
---|
1679 | |
---|
1680 | if (dd == 2) |
---|
1681 | carry = mpn_lshift(bdata, adata, sa, 1); |
---|
1682 | else |
---|
1683 | carry = mpn_mul_1(bdata, adata, sa, dd); |
---|
1684 | |
---|
1685 | if (carry) |
---|
1686 | bdata[sa] = carry; |
---|
1687 | else |
---|
1688 | sb--; |
---|
1689 | |
---|
1690 | if (bnegative) sb = -sb; |
---|
1691 | SIZE(b) = sb; |
---|
1692 | } |
---|
1693 | |
---|
1694 | /* |
---|
1695 | * DIRT: this implementation of _ntl_gsdiv relies crucially |
---|
1696 | * on the assumption that the number of bits per limb_t is at least |
---|
1697 | * equal to the number of bits per long. |
---|
1698 | */ |
---|
1699 | |
---|
1700 | long _ntl_gsdiv(_ntl_gbigint a, long d, _ntl_gbigint *bb) |
---|
1701 | { |
---|
1702 | long sa, aneg, sb, dneg; |
---|
1703 | _ntl_gbigint b; |
---|
1704 | mp_limb_t dd, *adata, *bdata; |
---|
1705 | long r; |
---|
1706 | |
---|
1707 | if (!d) { |
---|
1708 | ghalt("division by zero in _ntl_gsdiv"); |
---|
1709 | } |
---|
1710 | |
---|
1711 | if (ZEROP(a)) { |
---|
1712 | _ntl_gzero(bb); |
---|
1713 | return (0); |
---|
1714 | } |
---|
1715 | |
---|
1716 | GET_SIZE_NEG(sa, aneg, a); |
---|
1717 | |
---|
1718 | if (d < 0) { |
---|
1719 | dd = - ((mp_limb_t) d); /* careful ! */ |
---|
1720 | dneg = 1; |
---|
1721 | } |
---|
1722 | else { |
---|
1723 | dd = (mp_limb_t) d; |
---|
1724 | dneg = 0; |
---|
1725 | } |
---|
1726 | |
---|
1727 | sb = sa; |
---|
1728 | b = *bb; |
---|
1729 | if (MustAlloc(b, sb)) { |
---|
1730 | /* if b aliases a, then b won't move */ |
---|
1731 | _ntl_gsetlength(&b, sb); |
---|
1732 | *bb = b; |
---|
1733 | } |
---|
1734 | |
---|
1735 | adata = DATA(a); |
---|
1736 | bdata = DATA(b); |
---|
1737 | |
---|
1738 | if (dd == 2) |
---|
1739 | r = mpn_rshift(bdata, adata, sa, 1) >> (NTL_ZZ_NBITS - 1); |
---|
1740 | else |
---|
1741 | r = mpn_divmod_1(bdata, adata, sa, dd); |
---|
1742 | |
---|
1743 | if (bdata[sb-1] == 0) |
---|
1744 | sb--; |
---|
1745 | |
---|
1746 | SIZE(b) = sb; |
---|
1747 | |
---|
1748 | if (aneg || dneg) { |
---|
1749 | if (aneg != dneg) { |
---|
1750 | if (!r) { |
---|
1751 | SIZE(b) = -SIZE(b); |
---|
1752 | } |
---|
1753 | else { |
---|
1754 | _ntl_gsadd(b, 1, &b); |
---|
1755 | SIZE(b) = -SIZE(b); |
---|
1756 | if (dneg) |
---|
1757 | r = r + d; |
---|
1758 | else |
---|
1759 | r = d - r; |
---|
1760 | *bb = b; |
---|
1761 | } |
---|
1762 | } |
---|
1763 | else |
---|
1764 | r = -r; |
---|
1765 | } |
---|
1766 | |
---|
1767 | return r; |
---|
1768 | } |
---|
1769 | |
---|
1770 | /* |
---|
1771 | * DIRT: this implementation of _ntl_gsmod relies crucially |
---|
1772 | * on the assumption that the number of bits per limb_t is at least |
---|
1773 | * equal to the number of bits per long. |
---|
1774 | */ |
---|
1775 | |
---|
1776 | long _ntl_gsmod(_ntl_gbigint a, long d) |
---|
1777 | { |
---|
1778 | long sa, aneg, dneg; |
---|
1779 | mp_limb_t dd, *adata; |
---|
1780 | long r; |
---|
1781 | |
---|
1782 | if (!d) { |
---|
1783 | ghalt("division by zero in _ntl_gsmod"); |
---|
1784 | } |
---|
1785 | |
---|
1786 | if (ZEROP(a)) { |
---|
1787 | return (0); |
---|
1788 | } |
---|
1789 | |
---|
1790 | GET_SIZE_NEG(sa, aneg, a); |
---|
1791 | |
---|
1792 | if (d < 0) { |
---|
1793 | dd = - ((mp_limb_t) d); /* careful ! */ |
---|
1794 | dneg = 1; |
---|
1795 | } |
---|
1796 | else { |
---|
1797 | dd = (mp_limb_t) d; |
---|
1798 | dneg = 0; |
---|
1799 | } |
---|
1800 | |
---|
1801 | adata = DATA(a); |
---|
1802 | |
---|
1803 | if (dd == 2) |
---|
1804 | r = adata[0] & 1; |
---|
1805 | else |
---|
1806 | r = mpn_mod_1(adata, sa, dd); |
---|
1807 | |
---|
1808 | if (aneg || dneg) { |
---|
1809 | if (aneg != dneg) { |
---|
1810 | if (r) { |
---|
1811 | if (dneg) |
---|
1812 | r = r + d; |
---|
1813 | else |
---|
1814 | r = d - r; |
---|
1815 | } |
---|
1816 | } |
---|
1817 | else |
---|
1818 | r = -r; |
---|
1819 | } |
---|
1820 | |
---|
1821 | return r; |
---|
1822 | } |
---|
1823 | |
---|
1824 | |
---|
1825 | void _ntl_gdiv(_ntl_gbigint a, _ntl_gbigint d, |
---|
1826 | _ntl_gbigint *bb, _ntl_gbigint *rr) |
---|
1827 | { |
---|
1828 | static _ntl_gbigint b = 0, rmem = 0; |
---|
1829 | |
---|
1830 | _ntl_gbigint r; |
---|
1831 | |
---|
1832 | long sa, aneg, sb, sd, dneg, sr, in_place; |
---|
1833 | mp_limb_t *adata, *ddata, *bdata, *rdata; |
---|
1834 | |
---|
1835 | if (ZEROP(d)) { |
---|
1836 | ghalt("division by zero in _ntl_gdiv"); |
---|
1837 | } |
---|
1838 | |
---|
1839 | if (ZEROP(a)) { |
---|
1840 | if (bb) _ntl_gzero(bb); |
---|
1841 | if (rr) _ntl_gzero(rr); |
---|
1842 | return; |
---|
1843 | } |
---|
1844 | |
---|
1845 | GET_SIZE_NEG(sa, aneg, a); |
---|
1846 | GET_SIZE_NEG(sd, dneg, d); |
---|
1847 | |
---|
1848 | if (!aneg && !dneg && rr && *rr != a && *rr != d) { |
---|
1849 | in_place = 1; |
---|
1850 | r = *rr; |
---|
1851 | } |
---|
1852 | else { |
---|
1853 | in_place = 0; |
---|
1854 | r = rmem; |
---|
1855 | } |
---|
1856 | |
---|
1857 | if (sa < sd) { |
---|
1858 | _ntl_gzero(&b); |
---|
1859 | _ntl_gcopy(a, &r); |
---|
1860 | if (aneg) SIZE(r) = -SIZE(r); |
---|
1861 | goto done; |
---|
1862 | } |
---|
1863 | |
---|
1864 | sb = sa-sd+1; |
---|
1865 | if (MustAlloc(b, sb)) |
---|
1866 | _ntl_gsetlength(&b, sb); |
---|
1867 | |
---|
1868 | sr = sd; |
---|
1869 | if (MustAlloc(r, sr)) |
---|
1870 | _ntl_gsetlength(&r, sr); |
---|
1871 | |
---|
1872 | adata = DATA(a); |
---|
1873 | ddata = DATA(d); |
---|
1874 | bdata = DATA(b); |
---|
1875 | rdata = DATA(r); |
---|
1876 | |
---|
1877 | mpn_tdiv_qr(bdata, rdata, 0, adata, sa, ddata, sd); |
---|
1878 | |
---|
1879 | if (bdata[sb-1] == 0) |
---|
1880 | sb--; |
---|
1881 | SIZE(b) = sb; |
---|
1882 | |
---|
1883 | STRIP(sr, rdata); |
---|
1884 | SIZE(r) = sr; |
---|
1885 | |
---|
1886 | done: |
---|
1887 | |
---|
1888 | if (aneg || dneg) { |
---|
1889 | if (aneg != dneg) { |
---|
1890 | if (ZEROP(r)) { |
---|
1891 | SIZE(b) = -SIZE(b); |
---|
1892 | } |
---|
1893 | else { |
---|
1894 | if (bb) { |
---|
1895 | _ntl_gsadd(b, 1, &b); |
---|
1896 | SIZE(b) = -SIZE(b); |
---|
1897 | } |
---|
1898 | if (rr) { |
---|
1899 | if (dneg) |
---|
1900 | _ntl_gadd(r, d, &r); |
---|
1901 | else |
---|
1902 | _ntl_gsub(d, r, &r); |
---|
1903 | } |
---|
1904 | } |
---|
1905 | } |
---|
1906 | else |
---|
1907 | SIZE(r) = -SIZE(r); |
---|
1908 | } |
---|
1909 | |
---|
1910 | if (bb) _ntl_gcopy(b, bb); |
---|
1911 | |
---|
1912 | if (in_place) |
---|
1913 | *rr = r; |
---|
1914 | else { |
---|
1915 | if (rr) _ntl_gcopy(r, rr); |
---|
1916 | rmem = r; |
---|
1917 | } |
---|
1918 | } |
---|
1919 | |
---|
1920 | |
---|
1921 | /* a simplified mod operation: assumes a >= 0, d > 0 are non-negative, |
---|
1922 | * that space for the result has already been allocated, |
---|
1923 | * and that inputs do not alias output. */ |
---|
1924 | |
---|
1925 | static |
---|
1926 | void gmod_simple(_ntl_gbigint a, _ntl_gbigint d, _ntl_gbigint *rr) |
---|
1927 | { |
---|
1928 | static _ntl_gbigint b = 0; |
---|
1929 | |
---|
1930 | long sa, sb, sd, sr; |
---|
1931 | mp_limb_t *adata, *ddata, *bdata, *rdata; |
---|
1932 | _ntl_gbigint r; |
---|
1933 | |
---|
1934 | if (ZEROP(a)) { |
---|
1935 | _ntl_gzero(rr); |
---|
1936 | return; |
---|
1937 | } |
---|
1938 | |
---|
1939 | sa = SIZE(a); |
---|
1940 | sd = SIZE(d); |
---|
1941 | |
---|
1942 | if (sa < sd) { |
---|
1943 | _ntl_gcopy(a, rr); |
---|
1944 | return; |
---|
1945 | } |
---|
1946 | |
---|
1947 | sb = sa-sd+1; |
---|
1948 | if (MustAlloc(b, sb)) |
---|
1949 | _ntl_gsetlength(&b, sb); |
---|
1950 | |
---|
1951 | sr = sd; |
---|
1952 | r = *rr; |
---|
1953 | |
---|
1954 | adata = DATA(a); |
---|
1955 | ddata = DATA(d); |
---|
1956 | bdata = DATA(b); |
---|
1957 | rdata = DATA(r); |
---|
1958 | |
---|
1959 | mpn_tdiv_qr(bdata, rdata, 0, adata, sa, ddata, sd); |
---|
1960 | |
---|
1961 | STRIP(sr, rdata); |
---|
1962 | SIZE(r) = sr; |
---|
1963 | } |
---|
1964 | |
---|
1965 | |
---|
1966 | void _ntl_gmod(_ntl_gbigint a, _ntl_gbigint d, _ntl_gbigint *rr) |
---|
1967 | { |
---|
1968 | _ntl_gdiv(a, d, 0, rr); |
---|
1969 | } |
---|
1970 | |
---|
1971 | void _ntl_gquickmod(_ntl_gbigint *rr, _ntl_gbigint d) |
---|
1972 | { |
---|
1973 | _ntl_gdiv(*rr, d, 0, rr); |
---|
1974 | } |
---|
1975 | |
---|
1976 | void _ntl_gsqrt(_ntl_gbigint n, _ntl_gbigint *rr) |
---|
1977 | { |
---|
1978 | static _ntl_gbigint r = 0; |
---|
1979 | |
---|
1980 | long sn, sr; |
---|
1981 | mp_limb_t *ndata, *rdata; |
---|
1982 | |
---|
1983 | if (ZEROP(n)) { |
---|
1984 | _ntl_gzero(rr); |
---|
1985 | return; |
---|
1986 | } |
---|
1987 | |
---|
1988 | sn = SIZE(n); |
---|
1989 | if (sn < 0) ghalt("negative argument to _ntl_sqrt"); |
---|
1990 | |
---|
1991 | sr = (sn+1)/2; |
---|
1992 | _ntl_gsetlength(&r, sr); |
---|
1993 | |
---|
1994 | ndata = DATA(n); |
---|
1995 | rdata = DATA(r); |
---|
1996 | |
---|
1997 | mpn_sqrtrem(rdata, 0, ndata, sn); |
---|
1998 | |
---|
1999 | STRIP(sr, rdata); |
---|
2000 | SIZE(r) = sr; |
---|
2001 | |
---|
2002 | _ntl_gcopy(r, rr); |
---|
2003 | } |
---|
2004 | |
---|
2005 | /* |
---|
2006 | * DIRT: this implementation of _ntl_gsqrts relies crucially |
---|
2007 | * on the assumption that the number of bits per limb_t is at least |
---|
2008 | * equal to the number of bits per long. |
---|
2009 | */ |
---|
2010 | |
---|
2011 | long _ntl_gsqrts(long n) |
---|
2012 | { |
---|
2013 | mp_limb_t ndata, rdata; |
---|
2014 | |
---|
2015 | if (n == 0) { |
---|
2016 | return 0; |
---|
2017 | } |
---|
2018 | |
---|
2019 | if (n < 0) ghalt("negative argument to _ntl_sqrts"); |
---|
2020 | |
---|
2021 | ndata = n; |
---|
2022 | |
---|
2023 | mpn_sqrtrem(&rdata, 0, &ndata, 1); |
---|
2024 | |
---|
2025 | return rdata; |
---|
2026 | } |
---|
2027 | |
---|
2028 | |
---|
2029 | void _ntl_ggcd(_ntl_gbigint m1, _ntl_gbigint m2, _ntl_gbigint *r) |
---|
2030 | { |
---|
2031 | static _ntl_gbigint s1 = 0, s2 = 0, res = 0; |
---|
2032 | |
---|
2033 | long k1, k2, k_min, l1, l2, ss1, ss2, sres; |
---|
2034 | |
---|
2035 | _ntl_gcopy(m1, &s1); |
---|
2036 | _ntl_gabs(&s1); |
---|
2037 | |
---|
2038 | _ntl_gcopy(m2, &s2); |
---|
2039 | _ntl_gabs(&s2); |
---|
2040 | |
---|
2041 | if (ZEROP(s1)) { |
---|
2042 | _ntl_gcopy(s2, r); |
---|
2043 | return; |
---|
2044 | } |
---|
2045 | |
---|
2046 | if (ZEROP(s2)) { |
---|
2047 | _ntl_gcopy(s1, r); |
---|
2048 | return; |
---|
2049 | } |
---|
2050 | |
---|
2051 | k1 = _ntl_gmakeodd(&s1); |
---|
2052 | k2 = _ntl_gmakeodd(&s2); |
---|
2053 | |
---|
2054 | if (k1 <= k2) |
---|
2055 | k_min = k1; |
---|
2056 | else |
---|
2057 | k_min = k2; |
---|
2058 | |
---|
2059 | l1 = _ntl_g2log(s1); |
---|
2060 | l2 = _ntl_g2log(s2); |
---|
2061 | |
---|
2062 | ss1 = SIZE(s1); |
---|
2063 | ss2 = SIZE(s2); |
---|
2064 | |
---|
2065 | if (ss1 >= ss2) |
---|
2066 | sres = ss1; |
---|
2067 | else |
---|
2068 | sres = ss2; |
---|
2069 | |
---|
2070 | /* set to max: gmp documentation is unclear on this point */ |
---|
2071 | |
---|
2072 | _ntl_gsetlength(&res, sres); |
---|
2073 | |
---|
2074 | if (l1 >= l2) |
---|
2075 | SIZE(res) = mpn_gcd(DATA(res), DATA(s1), ss1, DATA(s2), ss2); |
---|
2076 | else |
---|
2077 | SIZE(res) = mpn_gcd(DATA(res), DATA(s2), ss2, DATA(s1), ss1); |
---|
2078 | |
---|
2079 | _ntl_glshift(res, k_min, &res); |
---|
2080 | |
---|
2081 | _ntl_gcopy(res, r); |
---|
2082 | } |
---|
2083 | |
---|
2084 | static long |
---|
2085 | gxxeucl( |
---|
2086 | _ntl_gbigint ain, |
---|
2087 | _ntl_gbigint nin, |
---|
2088 | _ntl_gbigint *invv, |
---|
2089 | _ntl_gbigint *uu |
---|
2090 | ) |
---|
2091 | { |
---|
2092 | static _ntl_gbigint a = 0; |
---|
2093 | static _ntl_gbigint n = 0; |
---|
2094 | static _ntl_gbigint q = 0; |
---|
2095 | static _ntl_gbigint w = 0; |
---|
2096 | static _ntl_gbigint x = 0; |
---|
2097 | static _ntl_gbigint y = 0; |
---|
2098 | static _ntl_gbigint z = 0; |
---|
2099 | _ntl_gbigint inv = *invv; |
---|
2100 | _ntl_gbigint u = *uu; |
---|
2101 | long diff; |
---|
2102 | long ilo; |
---|
2103 | long sa; |
---|
2104 | long sn; |
---|
2105 | long temp; |
---|
2106 | long e; |
---|
2107 | long fast; |
---|
2108 | long parity; |
---|
2109 | long gotthem; |
---|
2110 | mp_limb_t *p; |
---|
2111 | long try11; |
---|
2112 | long try12; |
---|
2113 | long try21; |
---|
2114 | long try22; |
---|
2115 | long got11; |
---|
2116 | long got12; |
---|
2117 | long got21; |
---|
2118 | long got22; |
---|
2119 | double hi; |
---|
2120 | double lo; |
---|
2121 | double dt; |
---|
2122 | double fhi, fhi1; |
---|
2123 | double flo, flo1; |
---|
2124 | double num; |
---|
2125 | double den; |
---|
2126 | double dirt; |
---|
2127 | |
---|
2128 | _ntl_gsetlength(&a, (e = (SIZE(ain) > SIZE(nin) ? SIZE(ain) : SIZE(nin)))); |
---|
2129 | _ntl_gsetlength(&n, e); |
---|
2130 | _ntl_gsetlength(&q, e); |
---|
2131 | _ntl_gsetlength(&w, e); |
---|
2132 | _ntl_gsetlength(&x, e); |
---|
2133 | _ntl_gsetlength(&y, e); |
---|
2134 | _ntl_gsetlength(&z, e); |
---|
2135 | _ntl_gsetlength(&inv, e); |
---|
2136 | *invv = inv; |
---|
2137 | _ntl_gsetlength(&u, e); |
---|
2138 | *uu = u; |
---|
2139 | |
---|
2140 | fhi1 = 1.0 + ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
2141 | flo1 = 1.0 - ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
2142 | |
---|
2143 | fhi = 1.0 + ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
2144 | flo = 1.0 - ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
2145 | |
---|
2146 | _ntl_gcopy(ain, &a); |
---|
2147 | _ntl_gcopy(nin, &n); |
---|
2148 | |
---|
2149 | _ntl_gone(&inv); |
---|
2150 | _ntl_gzero(&w); |
---|
2151 | |
---|
2152 | while (SIZE(n) > 0) |
---|
2153 | { |
---|
2154 | gotthem = 0; |
---|
2155 | sa = SIZE(a); |
---|
2156 | sn = SIZE(n); |
---|
2157 | diff = sa - sn; |
---|
2158 | if (!diff || diff == 1) |
---|
2159 | { |
---|
2160 | sa = SIZE(a); |
---|
2161 | p = DATA(a) + (sa-1); |
---|
2162 | num = (double) (*p) * NTL_ZZ_FRADIX; |
---|
2163 | if (sa > 1) |
---|
2164 | num += (*(--p)); |
---|
2165 | num *= NTL_ZZ_FRADIX; |
---|
2166 | if (sa > 2) |
---|
2167 | num += (*(p - 1)); |
---|
2168 | |
---|
2169 | sn = SIZE(n); |
---|
2170 | p = DATA(n) + (sn-1); |
---|
2171 | den = (double) (*p) * NTL_ZZ_FRADIX; |
---|
2172 | if (sn > 1) |
---|
2173 | den += (*(--p)); |
---|
2174 | den *= NTL_ZZ_FRADIX; |
---|
2175 | if (sn > 2) |
---|
2176 | den += (*(p - 1)); |
---|
2177 | |
---|
2178 | hi = fhi1 * (num + 1.0) / den; |
---|
2179 | lo = flo1 * num / (den + 1.0); |
---|
2180 | if (diff > 0) |
---|
2181 | { |
---|
2182 | hi *= NTL_ZZ_FRADIX; |
---|
2183 | lo *= NTL_ZZ_FRADIX; |
---|
2184 | } |
---|
2185 | try11 = 1; |
---|
2186 | try12 = 0; |
---|
2187 | try21 = 0; |
---|
2188 | try22 = 1; |
---|
2189 | parity = 1; |
---|
2190 | fast = 1; |
---|
2191 | while (fast > 0) |
---|
2192 | { |
---|
2193 | parity = 1 - parity; |
---|
2194 | if (hi >= NTL_SP_BOUND) |
---|
2195 | fast = 0; |
---|
2196 | else |
---|
2197 | { |
---|
2198 | ilo = (long)lo; |
---|
2199 | dirt = hi - ilo; |
---|
2200 | if (dirt < 1.0/NTL_FDOUBLE_PRECISION || !ilo || ilo < (long)hi) |
---|
2201 | fast = 0; |
---|
2202 | else |
---|
2203 | { |
---|
2204 | dt = lo-ilo; |
---|
2205 | lo = flo / dirt; |
---|
2206 | if (dt > 1.0/NTL_FDOUBLE_PRECISION) |
---|
2207 | hi = fhi / dt; |
---|
2208 | else |
---|
2209 | hi = NTL_SP_BOUND; |
---|
2210 | temp = try11; |
---|
2211 | try11 = try21; |
---|
2212 | if ((NTL_WSP_BOUND - temp) / ilo < try21) |
---|
2213 | fast = 0; |
---|
2214 | else |
---|
2215 | try21 = temp + ilo * try21; |
---|
2216 | temp = try12; |
---|
2217 | try12 = try22; |
---|
2218 | if ((NTL_WSP_BOUND - temp) / ilo < try22) |
---|
2219 | fast = 0; |
---|
2220 | else |
---|
2221 | try22 = temp + ilo * try22; |
---|
2222 | if ((fast > 0) && (parity > 0)) |
---|
2223 | { |
---|
2224 | gotthem = 1; |
---|
2225 | got11 = try11; |
---|
2226 | got12 = try12; |
---|
2227 | got21 = try21; |
---|
2228 | got22 = try22; |
---|
2229 | } |
---|
2230 | } |
---|
2231 | } |
---|
2232 | } |
---|
2233 | } |
---|
2234 | if (gotthem) |
---|
2235 | { |
---|
2236 | _ntl_gsmul(inv, got11, &x); |
---|
2237 | _ntl_gsmul(w, got12, &y); |
---|
2238 | _ntl_gsmul(inv, got21, &z); |
---|
2239 | _ntl_gsmul(w, got22, &w); |
---|
2240 | _ntl_gadd(x, y, &inv); |
---|
2241 | _ntl_gadd(z, w, &w); |
---|
2242 | _ntl_gsmul(a, got11, &x); |
---|
2243 | _ntl_gsmul(n, got12, &y); |
---|
2244 | _ntl_gsmul(a, got21, &z); |
---|
2245 | _ntl_gsmul(n, got22, &n); |
---|
2246 | _ntl_gsub(x, y, &a); |
---|
2247 | _ntl_gsub(n, z, &n); |
---|
2248 | } |
---|
2249 | else |
---|
2250 | { |
---|
2251 | _ntl_gdiv(a, n, &q, &a); |
---|
2252 | _ntl_gmul(q, w, &x); |
---|
2253 | _ntl_gadd(inv, x, &inv); |
---|
2254 | if (!ZEROP(a)) |
---|
2255 | { |
---|
2256 | _ntl_gdiv(n, a, &q, &n); |
---|
2257 | _ntl_gmul(q, inv, &x); |
---|
2258 | _ntl_gadd(w, x, &w); |
---|
2259 | } |
---|
2260 | else |
---|
2261 | { |
---|
2262 | _ntl_gcopy(n, &a); |
---|
2263 | _ntl_gzero(&n); |
---|
2264 | _ntl_gcopy(w, &inv); |
---|
2265 | _ntl_gnegate(&inv); |
---|
2266 | } |
---|
2267 | } |
---|
2268 | } |
---|
2269 | |
---|
2270 | if (_ntl_gscompare(a, 1) == 0) |
---|
2271 | e = 0; |
---|
2272 | else |
---|
2273 | e = 1; |
---|
2274 | |
---|
2275 | _ntl_gcopy(a, &u); |
---|
2276 | |
---|
2277 | *invv = inv; |
---|
2278 | *uu = u; |
---|
2279 | |
---|
2280 | return (e); |
---|
2281 | } |
---|
2282 | |
---|
2283 | #if 0 |
---|
2284 | void |
---|
2285 | _ntl_gexteucl( |
---|
2286 | _ntl_gbigint aa, |
---|
2287 | _ntl_gbigint *xa, |
---|
2288 | _ntl_gbigint bb, |
---|
2289 | _ntl_gbigint *xb, |
---|
2290 | _ntl_gbigint *d |
---|
2291 | ) |
---|
2292 | { |
---|
2293 | static _ntl_gbigint modcon = 0; |
---|
2294 | static _ntl_gbigint a=0, b=0; |
---|
2295 | long anegative = 0; |
---|
2296 | long bnegative = 0; |
---|
2297 | |
---|
2298 | _ntl_gcopy(aa, &a); |
---|
2299 | _ntl_gcopy(bb, &b); |
---|
2300 | |
---|
2301 | if (a && SIZE(a) < 0) { |
---|
2302 | anegative = 1; |
---|
2303 | SIZE(a) = -SIZE(a); |
---|
2304 | } |
---|
2305 | else |
---|
2306 | anegative = 0; |
---|
2307 | |
---|
2308 | if (b && SIZE(b) < 0) { |
---|
2309 | bnegative = 1; |
---|
2310 | SIZE(b) = -SIZE(b); |
---|
2311 | } |
---|
2312 | else |
---|
2313 | bnegative = 0; |
---|
2314 | |
---|
2315 | |
---|
2316 | if (ZEROP(b)) |
---|
2317 | { |
---|
2318 | _ntl_gone(xa); |
---|
2319 | _ntl_gzero(xb); |
---|
2320 | _ntl_gcopy(a, d); |
---|
2321 | goto done; |
---|
2322 | } |
---|
2323 | |
---|
2324 | if (ZEROP(a)) |
---|
2325 | { |
---|
2326 | _ntl_gzero(xa); |
---|
2327 | _ntl_gone(xb); |
---|
2328 | _ntl_gcopy(b, d); |
---|
2329 | goto done; |
---|
2330 | } |
---|
2331 | |
---|
2332 | gxxeucl(a, b, xa, d); |
---|
2333 | _ntl_gmul(a, *xa, xb); |
---|
2334 | _ntl_gsub(*d, *xb, xb); |
---|
2335 | _ntl_gdiv(*xb, b, xb, &modcon); |
---|
2336 | |
---|
2337 | if (!ZEROP(modcon)) |
---|
2338 | { |
---|
2339 | ghalt("non-zero remainder in _ntl_gexteucl BUG"); |
---|
2340 | } |
---|
2341 | |
---|
2342 | |
---|
2343 | done: |
---|
2344 | if (anegative) |
---|
2345 | { |
---|
2346 | _ntl_gnegate(xa); |
---|
2347 | } |
---|
2348 | if (bnegative) |
---|
2349 | { |
---|
2350 | _ntl_gnegate(xb); |
---|
2351 | } |
---|
2352 | } |
---|
2353 | #endif |
---|
2354 | |
---|
2355 | void |
---|
2356 | _ntl_gexteucl( |
---|
2357 | _ntl_gbigint ain, |
---|
2358 | _ntl_gbigint *xap, |
---|
2359 | _ntl_gbigint bin, |
---|
2360 | _ntl_gbigint *xbp, |
---|
2361 | _ntl_gbigint *dp |
---|
2362 | ) |
---|
2363 | { |
---|
2364 | if (ZEROP(bin)) { |
---|
2365 | long asign = _ntl_gsign(ain); |
---|
2366 | |
---|
2367 | _ntl_gcopy(ain, dp); |
---|
2368 | _ntl_gabs(dp); |
---|
2369 | _ntl_gintoz( (asign >= 0 ? 1 : -1), xap); |
---|
2370 | _ntl_gzero(xbp); |
---|
2371 | } |
---|
2372 | else if (ZEROP(ain)) { |
---|
2373 | long bsign = _ntl_gsign(bin); |
---|
2374 | |
---|
2375 | _ntl_gcopy(bin, dp); |
---|
2376 | _ntl_gabs(dp); |
---|
2377 | _ntl_gzero(xap); |
---|
2378 | _ntl_gintoz(bsign, xbp); |
---|
2379 | } |
---|
2380 | else { |
---|
2381 | static _ntl_gbigint a = 0, b = 0, xa = 0, xb = 0, d = 0, tmp = 0; |
---|
2382 | |
---|
2383 | long sa, aneg, sb, bneg, rev; |
---|
2384 | mp_limb_t *adata, *bdata, *ddata, *xadata; |
---|
2385 | mp_size_t sxa, sd; |
---|
2386 | |
---|
2387 | GET_SIZE_NEG(sa, aneg, ain); |
---|
2388 | GET_SIZE_NEG(sb, bneg, bin); |
---|
2389 | |
---|
2390 | _ntl_gsetlength(&a, sa+1); /* +1 because mpn_gcdext may need it */ |
---|
2391 | _ntl_gcopy(ain, &a); |
---|
2392 | |
---|
2393 | _ntl_gsetlength(&b, sb+1); /* +1 because mpn_gcdext may need it */ |
---|
2394 | _ntl_gcopy(bin, &b); |
---|
2395 | |
---|
2396 | |
---|
2397 | adata = DATA(a); |
---|
2398 | bdata = DATA(b); |
---|
2399 | |
---|
2400 | if (sa < sb || (sa == sb && mpn_cmp(adata, bdata, sa) < 0)) { |
---|
2401 | SWAP_BIGINT(ain, bin); |
---|
2402 | SWAP_LONG(sa, sb); |
---|
2403 | SWAP_LONG(aneg, bneg); |
---|
2404 | SWAP_LIMB_PTR(adata, bdata); |
---|
2405 | rev = 1; |
---|
2406 | } |
---|
2407 | else |
---|
2408 | rev = 0; |
---|
2409 | |
---|
2410 | _ntl_gsetlength(&d, sa+1); /* +1 because mpn_gcdext may need it... |
---|
2411 | documentation is unclear, but this is |
---|
2412 | what is done in mpz_gcdext */ |
---|
2413 | _ntl_gsetlength(&xa, sa+1); /* ditto */ |
---|
2414 | |
---|
2415 | ddata = DATA(d); |
---|
2416 | xadata = DATA(xa); |
---|
2417 | |
---|
2418 | sd = mpn_gcdext(ddata, xadata, &sxa, adata, sa, bdata, sb); |
---|
2419 | |
---|
2420 | SIZE(d) = sd; |
---|
2421 | SIZE(xa) = sxa; |
---|
2422 | |
---|
2423 | if (aneg) _ntl_gnegate(&xa); |
---|
2424 | |
---|
2425 | _ntl_gmul(ain, xa, &tmp); |
---|
2426 | _ntl_gsub(d, tmp, &tmp); |
---|
2427 | _ntl_gdiv(tmp, bin, &xb, &tmp); |
---|
2428 | |
---|
2429 | if (!ZEROP(tmp)) ghalt("internal bug in _ntl_gexteucl"); |
---|
2430 | |
---|
2431 | if (rev) SWAP_BIGINT(xa, xb); |
---|
2432 | |
---|
2433 | _ntl_gcopy(xa, xap); |
---|
2434 | _ntl_gcopy(xb, xbp); |
---|
2435 | _ntl_gcopy(d, dp); |
---|
2436 | } |
---|
2437 | } |
---|
2438 | |
---|
2439 | |
---|
2440 | long _ntl_ginv(_ntl_gbigint ain, _ntl_gbigint nin, _ntl_gbigint *invv) |
---|
2441 | { |
---|
2442 | static _ntl_gbigint u = 0; |
---|
2443 | static _ntl_gbigint d = 0; |
---|
2444 | static _ntl_gbigint a = 0; |
---|
2445 | static _ntl_gbigint n = 0; |
---|
2446 | |
---|
2447 | long sz; |
---|
2448 | long sd; |
---|
2449 | mp_size_t su; |
---|
2450 | |
---|
2451 | if (_ntl_gscompare(nin, 1) <= 0) { |
---|
2452 | ghalt("InvMod: second input <= 1"); |
---|
2453 | } |
---|
2454 | |
---|
2455 | if (_ntl_gsign(ain) < 0) { |
---|
2456 | ghalt("InvMod: first input negative"); |
---|
2457 | } |
---|
2458 | |
---|
2459 | if (_ntl_gcompare(ain, nin) >= 0) { |
---|
2460 | ghalt("InvMod: first input too big"); |
---|
2461 | } |
---|
2462 | |
---|
2463 | sz = SIZE(nin) + 2; |
---|
2464 | |
---|
2465 | if (MustAlloc(a, sz)) |
---|
2466 | _ntl_gsetlength(&a, sz); |
---|
2467 | |
---|
2468 | |
---|
2469 | if (MustAlloc(n, sz)) |
---|
2470 | _ntl_gsetlength(&n, sz); |
---|
2471 | |
---|
2472 | |
---|
2473 | if (MustAlloc(d, sz)) |
---|
2474 | _ntl_gsetlength(&d, sz); |
---|
2475 | |
---|
2476 | if (MustAlloc(u, sz)) |
---|
2477 | _ntl_gsetlength(&u, sz); |
---|
2478 | |
---|
2479 | _ntl_gadd(ain, nin, &a); |
---|
2480 | _ntl_gcopy(nin, &n); |
---|
2481 | |
---|
2482 | /* We apply mpn_gcdext to (a, n) = (ain+nin, nin), because that function |
---|
2483 | * only computes the co-factor of the larger input. This way, we avoid |
---|
2484 | * a multiplication and a division. |
---|
2485 | */ |
---|
2486 | |
---|
2487 | sd = mpn_gcdext(DATA(d), DATA(u), &su, DATA(a), SIZE(a), DATA(n), SIZE(n)); |
---|
2488 | |
---|
2489 | SIZE(d) = sd; |
---|
2490 | SIZE(u) = su; |
---|
2491 | |
---|
2492 | if (ONEP(d)) { |
---|
2493 | |
---|
2494 | /* |
---|
2495 | * We make sure that u is in range 0..n-1, just in case |
---|
2496 | * GMP is sloppy. |
---|
2497 | */ |
---|
2498 | |
---|
2499 | while (_ntl_gsign(u) < 0) _ntl_gadd(u, nin, &u); |
---|
2500 | while (_ntl_gcompare(u, nin) >= 0) _ntl_gsub(u, nin, &u); |
---|
2501 | |
---|
2502 | _ntl_gcopy(u, invv); |
---|
2503 | return 0; |
---|
2504 | } |
---|
2505 | else { |
---|
2506 | _ntl_gcopy(d, invv); |
---|
2507 | return 1; |
---|
2508 | } |
---|
2509 | } |
---|
2510 | |
---|
2511 | |
---|
2512 | void |
---|
2513 | _ntl_ginvmod( |
---|
2514 | _ntl_gbigint a, |
---|
2515 | _ntl_gbigint n, |
---|
2516 | _ntl_gbigint *c |
---|
2517 | ) |
---|
2518 | { |
---|
2519 | if (_ntl_ginv(a, n, c)) |
---|
2520 | ghalt("undefined inverse in _ntl_ginvmod"); |
---|
2521 | } |
---|
2522 | |
---|
2523 | |
---|
2524 | void |
---|
2525 | _ntl_gaddmod( |
---|
2526 | _ntl_gbigint a, |
---|
2527 | _ntl_gbigint b, |
---|
2528 | _ntl_gbigint n, |
---|
2529 | _ntl_gbigint *c |
---|
2530 | ) |
---|
2531 | { |
---|
2532 | if (*c != n) { |
---|
2533 | _ntl_gadd(a, b, c); |
---|
2534 | if (_ntl_gcompare(*c, n) >= 0) |
---|
2535 | _ntl_gsubpos(*c, n, c); |
---|
2536 | } |
---|
2537 | else { |
---|
2538 | static _ntl_gbigint mem = 0; |
---|
2539 | |
---|
2540 | _ntl_gadd(a, b, &mem); |
---|
2541 | if (_ntl_gcompare(mem, n) >= 0) |
---|
2542 | _ntl_gsubpos(mem, n, c); |
---|
2543 | else |
---|
2544 | _ntl_gcopy(mem, c); |
---|
2545 | } |
---|
2546 | } |
---|
2547 | |
---|
2548 | |
---|
2549 | void |
---|
2550 | _ntl_gsubmod( |
---|
2551 | _ntl_gbigint a, |
---|
2552 | _ntl_gbigint b, |
---|
2553 | _ntl_gbigint n, |
---|
2554 | _ntl_gbigint *c |
---|
2555 | ) |
---|
2556 | { |
---|
2557 | static _ntl_gbigint mem = 0; |
---|
2558 | long cmp; |
---|
2559 | |
---|
2560 | if ((cmp=_ntl_gcompare(a, b)) < 0) { |
---|
2561 | _ntl_gadd(n, a, &mem); |
---|
2562 | _ntl_gsubpos(mem, b, c); |
---|
2563 | } else if (!cmp) |
---|
2564 | _ntl_gzero(c); |
---|
2565 | else |
---|
2566 | _ntl_gsubpos(a, b, c); |
---|
2567 | } |
---|
2568 | |
---|
2569 | void |
---|
2570 | _ntl_gsmulmod( |
---|
2571 | _ntl_gbigint a, |
---|
2572 | long d, |
---|
2573 | _ntl_gbigint n, |
---|
2574 | _ntl_gbigint *c |
---|
2575 | ) |
---|
2576 | { |
---|
2577 | static _ntl_gbigint mem = 0; |
---|
2578 | |
---|
2579 | _ntl_gsmul(a, d, &mem); |
---|
2580 | _ntl_gmod(mem, n, c); |
---|
2581 | } |
---|
2582 | |
---|
2583 | |
---|
2584 | |
---|
2585 | void |
---|
2586 | _ntl_gmulmod( |
---|
2587 | _ntl_gbigint a, |
---|
2588 | _ntl_gbigint b, |
---|
2589 | _ntl_gbigint n, |
---|
2590 | _ntl_gbigint *c |
---|
2591 | ) |
---|
2592 | { |
---|
2593 | static _ntl_gbigint mem = 0; |
---|
2594 | |
---|
2595 | _ntl_gmul(a, b, &mem); |
---|
2596 | _ntl_gmod(mem, n, c); |
---|
2597 | } |
---|
2598 | |
---|
2599 | void |
---|
2600 | _ntl_gsqmod( |
---|
2601 | _ntl_gbigint a, |
---|
2602 | _ntl_gbigint n, |
---|
2603 | _ntl_gbigint *c |
---|
2604 | ) |
---|
2605 | { |
---|
2606 | _ntl_gmulmod(a, a, n, c); |
---|
2607 | } |
---|
2608 | |
---|
2609 | |
---|
2610 | double _ntl_gdoub_aux(_ntl_gbigint n) |
---|
2611 | { |
---|
2612 | double res; |
---|
2613 | mp_limb_t *ndata; |
---|
2614 | long i, sn, nneg; |
---|
2615 | |
---|
2616 | if (!n) |
---|
2617 | return ((double) 0); |
---|
2618 | |
---|
2619 | GET_SIZE_NEG(sn, nneg, n); |
---|
2620 | |
---|
2621 | ndata = DATA(n); |
---|
2622 | |
---|
2623 | res = 0; |
---|
2624 | for (i = sn-1; i >= 0; i--) |
---|
2625 | res = res * NTL_ZZ_FRADIX + ((double) ndata[i]); |
---|
2626 | |
---|
2627 | if (nneg) res = -res; |
---|
2628 | |
---|
2629 | return res; |
---|
2630 | } |
---|
2631 | |
---|
2632 | long _ntl_ground_correction(_ntl_gbigint a, long k, long residual) |
---|
2633 | { |
---|
2634 | long direction; |
---|
2635 | long p; |
---|
2636 | long sgn; |
---|
2637 | long bl; |
---|
2638 | mp_limb_t wh; |
---|
2639 | long i; |
---|
2640 | mp_limb_t *adata; |
---|
2641 | |
---|
2642 | if (SIZE(a) > 0) |
---|
2643 | sgn = 1; |
---|
2644 | else |
---|
2645 | sgn = -1; |
---|
2646 | |
---|
2647 | adata = DATA(a); |
---|
2648 | |
---|
2649 | p = k - 1; |
---|
2650 | bl = (p/NTL_ZZ_NBITS); |
---|
2651 | wh = ((mp_limb_t) 1) << (p - NTL_ZZ_NBITS*bl); |
---|
2652 | |
---|
2653 | if (adata[bl] & wh) { |
---|
2654 | /* bit is 1...we have to see if lower bits are all 0 |
---|
2655 | in order to implement "round to even" */ |
---|
2656 | |
---|
2657 | if (adata[bl] & (wh - ((mp_limb_t) 1))) |
---|
2658 | direction = 1; |
---|
2659 | else { |
---|
2660 | i = bl - 1; |
---|
2661 | while (i >= 0 && adata[i] == 0) i--; |
---|
2662 | if (i >= 0) |
---|
2663 | direction = 1; |
---|
2664 | else |
---|
2665 | direction = 0; |
---|
2666 | } |
---|
2667 | |
---|
2668 | /* use residual to break ties */ |
---|
2669 | |
---|
2670 | if (direction == 0 && residual != 0) { |
---|
2671 | if (residual == sgn) |
---|
2672 | direction = 1; |
---|
2673 | else |
---|
2674 | direction = -1; |
---|
2675 | } |
---|
2676 | |
---|
2677 | if (direction == 0) { |
---|
2678 | /* round to even */ |
---|
2679 | |
---|
2680 | wh = wh << 1; |
---|
2681 | |
---|
2682 | /* |
---|
2683 | * DIRT: if GMP has non-empty "nails", this won't work. |
---|
2684 | */ |
---|
2685 | |
---|
2686 | if (wh == 0) { |
---|
2687 | wh = 1; |
---|
2688 | bl++; |
---|
2689 | } |
---|
2690 | |
---|
2691 | if (adata[bl] & wh) |
---|
2692 | direction = 1; |
---|
2693 | else |
---|
2694 | direction = -1; |
---|
2695 | } |
---|
2696 | } |
---|
2697 | else |
---|
2698 | direction = -1; |
---|
2699 | |
---|
2700 | if (direction == 1) |
---|
2701 | return sgn; |
---|
2702 | |
---|
2703 | return 0; |
---|
2704 | } |
---|
2705 | |
---|
2706 | |
---|
2707 | |
---|
2708 | |
---|
2709 | double _ntl_gdoub(_ntl_gbigint n) |
---|
2710 | { |
---|
2711 | static _ntl_gbigint tmp = 0; |
---|
2712 | |
---|
2713 | long s; |
---|
2714 | long shamt; |
---|
2715 | long correction; |
---|
2716 | double x; |
---|
2717 | |
---|
2718 | s = _ntl_g2log(n); |
---|
2719 | shamt = s - NTL_DOUBLE_PRECISION; |
---|
2720 | |
---|
2721 | if (shamt <= 0) |
---|
2722 | return _ntl_gdoub_aux(n); |
---|
2723 | |
---|
2724 | _ntl_grshift(n, shamt, &tmp); |
---|
2725 | |
---|
2726 | correction = _ntl_ground_correction(n, shamt, 0); |
---|
2727 | |
---|
2728 | if (correction) _ntl_gsadd(tmp, correction, &tmp); |
---|
2729 | |
---|
2730 | x = _ntl_gdoub_aux(tmp); |
---|
2731 | |
---|
2732 | x = _ntl_ldexp(x, shamt); |
---|
2733 | |
---|
2734 | return x; |
---|
2735 | } |
---|
2736 | |
---|
2737 | |
---|
2738 | double _ntl_glog(_ntl_gbigint n) |
---|
2739 | { |
---|
2740 | static _ntl_gbigint tmp = 0; |
---|
2741 | |
---|
2742 | static double log_2; |
---|
2743 | static long init = 0; |
---|
2744 | |
---|
2745 | long s; |
---|
2746 | long shamt; |
---|
2747 | long correction; |
---|
2748 | double x; |
---|
2749 | |
---|
2750 | if (!init) { |
---|
2751 | log_2 = log(2.0); |
---|
2752 | init = 1; |
---|
2753 | } |
---|
2754 | |
---|
2755 | if (_ntl_gsign(n) <= 0) |
---|
2756 | ghalt("log argument <= 0"); |
---|
2757 | |
---|
2758 | s = _ntl_g2log(n); |
---|
2759 | shamt = s - NTL_DOUBLE_PRECISION; |
---|
2760 | |
---|
2761 | if (shamt <= 0) |
---|
2762 | return log(_ntl_gdoub_aux(n)); |
---|
2763 | |
---|
2764 | _ntl_grshift(n, shamt, &tmp); |
---|
2765 | |
---|
2766 | correction = _ntl_ground_correction(n, shamt, 0); |
---|
2767 | |
---|
2768 | if (correction) _ntl_gsadd(tmp, correction, &tmp); |
---|
2769 | |
---|
2770 | x = _ntl_gdoub_aux(tmp); |
---|
2771 | |
---|
2772 | return log(x) + shamt*log_2; |
---|
2773 | } |
---|
2774 | |
---|
2775 | |
---|
2776 | |
---|
2777 | |
---|
2778 | |
---|
2779 | /* To implement _ntl_gdoubtoz, I've implemented essentially the |
---|
2780 | * same algorithm as in LIP, processing in blocks of |
---|
2781 | * NTL_SP_NBITS bits, rather than NTL_ZZ_NBITS. |
---|
2782 | * This is conversion is rather delicate, and I don't want to |
---|
2783 | * make any new assumptions about the underlying arithmetic. |
---|
2784 | * This implementation should be quite portable. */ |
---|
2785 | |
---|
2786 | void _ntl_gdoubtoz(double a, _ntl_gbigint *xx) |
---|
2787 | { |
---|
2788 | static _ntl_gbigint x = 0; |
---|
2789 | |
---|
2790 | long neg, i, t, sz; |
---|
2791 | |
---|
2792 | a = floor(a); |
---|
2793 | |
---|
2794 | if (!_ntl_IsFinite(&a)) |
---|
2795 | ghalt("_ntl_gdoubtoz: attempt to convert non-finite value"); |
---|
2796 | |
---|
2797 | if (a < 0) { |
---|
2798 | a = -a; |
---|
2799 | neg = 1; |
---|
2800 | } |
---|
2801 | else |
---|
2802 | neg = 0; |
---|
2803 | |
---|
2804 | if (a == 0) { |
---|
2805 | _ntl_gzero(xx); |
---|
2806 | return; |
---|
2807 | } |
---|
2808 | |
---|
2809 | sz = 0; |
---|
2810 | while (a >= 1) { |
---|
2811 | a = a*(1.0/NTL_SP_FBOUND); |
---|
2812 | sz++; |
---|
2813 | } |
---|
2814 | |
---|
2815 | i = 0; |
---|
2816 | _ntl_gzero(&x); |
---|
2817 | |
---|
2818 | while (a != 0) { |
---|
2819 | i++; |
---|
2820 | a = a*NTL_SP_FBOUND; |
---|
2821 | t = (long) a; |
---|
2822 | a = a - t; |
---|
2823 | |
---|
2824 | if (i == 1) { |
---|
2825 | _ntl_gintoz(t, &x); |
---|
2826 | } |
---|
2827 | else { |
---|
2828 | _ntl_glshift(x, NTL_SP_NBITS, &x); |
---|
2829 | _ntl_gsadd(x, t, &x); |
---|
2830 | } |
---|
2831 | } |
---|
2832 | |
---|
2833 | if (i > sz) ghalt("bug in _ntl_gdoubtoz"); |
---|
2834 | |
---|
2835 | _ntl_glshift(x, (sz-i)*NTL_SP_NBITS, xx); |
---|
2836 | if (neg) _ntl_gnegate(xx); |
---|
2837 | } |
---|
2838 | |
---|
2839 | |
---|
2840 | |
---|
2841 | /* I've adapted LIP's extended euclidean algorithm to |
---|
2842 | * do rational reconstruction. -- VJS. |
---|
2843 | */ |
---|
2844 | |
---|
2845 | |
---|
2846 | long |
---|
2847 | _ntl_gxxratrecon( |
---|
2848 | _ntl_gbigint ain, |
---|
2849 | _ntl_gbigint nin, |
---|
2850 | _ntl_gbigint num_bound, |
---|
2851 | _ntl_gbigint den_bound, |
---|
2852 | _ntl_gbigint *num_out, |
---|
2853 | _ntl_gbigint *den_out |
---|
2854 | ) |
---|
2855 | { |
---|
2856 | static _ntl_gbigint a = 0; |
---|
2857 | static _ntl_gbigint n = 0; |
---|
2858 | static _ntl_gbigint q = 0; |
---|
2859 | static _ntl_gbigint w = 0; |
---|
2860 | static _ntl_gbigint x = 0; |
---|
2861 | static _ntl_gbigint y = 0; |
---|
2862 | static _ntl_gbigint z = 0; |
---|
2863 | static _ntl_gbigint inv = 0; |
---|
2864 | static _ntl_gbigint u = 0; |
---|
2865 | static _ntl_gbigint a_bak = 0; |
---|
2866 | static _ntl_gbigint n_bak = 0; |
---|
2867 | static _ntl_gbigint inv_bak = 0; |
---|
2868 | static _ntl_gbigint w_bak = 0; |
---|
2869 | |
---|
2870 | mp_limb_t *p; |
---|
2871 | |
---|
2872 | long diff; |
---|
2873 | long ilo; |
---|
2874 | long sa; |
---|
2875 | long sn; |
---|
2876 | long snum; |
---|
2877 | long sden; |
---|
2878 | long e; |
---|
2879 | long fast; |
---|
2880 | long temp; |
---|
2881 | long parity; |
---|
2882 | long gotthem; |
---|
2883 | long try11; |
---|
2884 | long try12; |
---|
2885 | long try21; |
---|
2886 | long try22; |
---|
2887 | long got11; |
---|
2888 | long got12; |
---|
2889 | long got21; |
---|
2890 | long got22; |
---|
2891 | |
---|
2892 | double hi; |
---|
2893 | double lo; |
---|
2894 | double dt; |
---|
2895 | double fhi, fhi1; |
---|
2896 | double flo, flo1; |
---|
2897 | double num; |
---|
2898 | double den; |
---|
2899 | double dirt; |
---|
2900 | |
---|
2901 | if (_ntl_gsign(num_bound) < 0) |
---|
2902 | ghalt("rational reconstruction: bad numerator bound"); |
---|
2903 | |
---|
2904 | if (!num_bound) |
---|
2905 | snum = 0; |
---|
2906 | else |
---|
2907 | snum = SIZE(num_bound); |
---|
2908 | |
---|
2909 | if (_ntl_gsign(den_bound) <= 0) |
---|
2910 | ghalt("rational reconstruction: bad denominator bound"); |
---|
2911 | |
---|
2912 | sden = SIZE(den_bound); |
---|
2913 | |
---|
2914 | if (_ntl_gsign(nin) <= 0) |
---|
2915 | ghalt("rational reconstruction: bad modulus"); |
---|
2916 | |
---|
2917 | if (_ntl_gsign(ain) < 0 || _ntl_gcompare(ain, nin) >= 0) |
---|
2918 | ghalt("rational reconstruction: bad residue"); |
---|
2919 | |
---|
2920 | |
---|
2921 | e = SIZE(nin); |
---|
2922 | |
---|
2923 | _ntl_gsetlength(&a, e); |
---|
2924 | _ntl_gsetlength(&n, e); |
---|
2925 | _ntl_gsetlength(&q, e); |
---|
2926 | _ntl_gsetlength(&w, e); |
---|
2927 | _ntl_gsetlength(&x, e); |
---|
2928 | _ntl_gsetlength(&y, e); |
---|
2929 | _ntl_gsetlength(&z, e); |
---|
2930 | _ntl_gsetlength(&inv, e); |
---|
2931 | _ntl_gsetlength(&u, e); |
---|
2932 | _ntl_gsetlength(&a_bak, e); |
---|
2933 | _ntl_gsetlength(&n_bak, e); |
---|
2934 | _ntl_gsetlength(&inv_bak, e); |
---|
2935 | _ntl_gsetlength(&w_bak, e); |
---|
2936 | |
---|
2937 | fhi1 = 1.0 + ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
2938 | flo1 = 1.0 - ((double) 32.0)/NTL_FDOUBLE_PRECISION; |
---|
2939 | |
---|
2940 | fhi = 1.0 + ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
2941 | flo = 1.0 - ((double) 8.0)/NTL_FDOUBLE_PRECISION; |
---|
2942 | |
---|
2943 | _ntl_gcopy(ain, &a); |
---|
2944 | _ntl_gcopy(nin, &n); |
---|
2945 | |
---|
2946 | _ntl_gone(&inv); |
---|
2947 | _ntl_gzero(&w); |
---|
2948 | |
---|
2949 | while (1) |
---|
2950 | { |
---|
2951 | if (SIZE(w) >= sden && _ntl_gcompare(w, den_bound) > 0) break; |
---|
2952 | if (SIZE(n) <= snum && _ntl_gcompare(n, num_bound) <= 0) break; |
---|
2953 | |
---|
2954 | _ntl_gcopy(a, &a_bak); |
---|
2955 | _ntl_gcopy(n, &n_bak); |
---|
2956 | _ntl_gcopy(w, &w_bak); |
---|
2957 | _ntl_gcopy(inv, &inv_bak); |
---|
2958 | |
---|
2959 | gotthem = 0; |
---|
2960 | sa = SIZE(a); |
---|
2961 | sn = SIZE(n); |
---|
2962 | diff = sa - sn; |
---|
2963 | if (!diff || diff == 1) |
---|
2964 | { |
---|
2965 | sa = SIZE(a); |
---|
2966 | p = DATA(a) + (sa-1); |
---|
2967 | num = (double) (*p) * NTL_ZZ_FRADIX; |
---|
2968 | if (sa > 1) |
---|
2969 | num += (*(--p)); |
---|
2970 | num *= NTL_ZZ_FRADIX; |
---|
2971 | if (sa > 2) |
---|
2972 | num += (*(p - 1)); |
---|
2973 | |
---|
2974 | sn = SIZE(n); |
---|
2975 | p = DATA(n) + (sn-1); |
---|
2976 | den = (double) (*p) * NTL_ZZ_FRADIX; |
---|
2977 | if (sn > 1) |
---|
2978 | den += (*(--p)); |
---|
2979 | den *= NTL_ZZ_FRADIX; |
---|
2980 | if (sn > 2) |
---|
2981 | den += (*(p - 1)); |
---|
2982 | |
---|
2983 | hi = fhi1 * (num + 1.0) / den; |
---|
2984 | lo = flo1 * num / (den + 1.0); |
---|
2985 | if (diff > 0) |
---|
2986 | { |
---|
2987 | hi *= NTL_ZZ_FRADIX; |
---|
2988 | lo *= NTL_ZZ_FRADIX; |
---|
2989 | } |
---|
2990 | |
---|
2991 | try11 = 1; |
---|
2992 | try12 = 0; |
---|
2993 | try21 = 0; |
---|
2994 | try22 = 1; |
---|
2995 | parity = 1; |
---|
2996 | fast = 1; |
---|
2997 | while (fast > 0) |
---|
2998 | { |
---|
2999 | parity = 1 - parity; |
---|
3000 | if (hi >= NTL_SP_BOUND) |
---|
3001 | fast = 0; |
---|
3002 | else |
---|
3003 | { |
---|
3004 | ilo = (long)lo; |
---|
3005 | dirt = hi - ilo; |
---|
3006 | if (dirt < 1.0/NTL_FDOUBLE_PRECISION || !ilo || ilo < (long)hi) |
---|
3007 | fast = 0; |
---|
3008 | else |
---|
3009 | { |
---|
3010 | dt = lo-ilo; |
---|
3011 | lo = flo / dirt; |
---|
3012 | if (dt > 1.0/NTL_FDOUBLE_PRECISION) |
---|
3013 | hi = fhi / dt; |
---|
3014 | else |
---|
3015 | hi = NTL_SP_BOUND; |
---|
3016 | temp = try11; |
---|
3017 | try11 = try21; |
---|
3018 | if ((NTL_WSP_BOUND - temp) / ilo < try21) |
---|
3019 | fast = 0; |
---|
3020 | else |
---|
3021 | try21 = temp + ilo * try21; |
---|
3022 | temp = try12; |
---|
3023 | try12 = try22; |
---|
3024 | if ((NTL_WSP_BOUND - temp) / ilo < try22) |
---|
3025 | fast = 0; |
---|
3026 | else |
---|
3027 | try22 = temp + ilo * try22; |
---|
3028 | if ((fast > 0) && (parity > 0)) |
---|
3029 | { |
---|
3030 | gotthem = 1; |
---|
3031 | got11 = try11; |
---|
3032 | got12 = try12; |
---|
3033 | got21 = try21; |
---|
3034 | got22 = try22; |
---|
3035 | } |
---|
3036 | } |
---|
3037 | } |
---|
3038 | } |
---|
3039 | } |
---|
3040 | if (gotthem) |
---|
3041 | { |
---|
3042 | _ntl_gsmul(inv, got11, &x); |
---|
3043 | _ntl_gsmul(w, got12, &y); |
---|
3044 | _ntl_gsmul(inv, got21, &z); |
---|
3045 | _ntl_gsmul(w, got22, &w); |
---|
3046 | _ntl_gadd(x, y, &inv); |
---|
3047 | _ntl_gadd(z, w, &w); |
---|
3048 | _ntl_gsmul(a, got11, &x); |
---|
3049 | _ntl_gsmul(n, got12, &y); |
---|
3050 | _ntl_gsmul(a, got21, &z); |
---|
3051 | _ntl_gsmul(n, got22, &n); |
---|
3052 | _ntl_gsub(x, y, &a); |
---|
3053 | _ntl_gsub(n, z, &n); |
---|
3054 | } |
---|
3055 | else |
---|
3056 | { |
---|
3057 | _ntl_gdiv(a, n, &q, &a); |
---|
3058 | _ntl_gmul(q, w, &x); |
---|
3059 | _ntl_gadd(inv, x, &inv); |
---|
3060 | if (!ZEROP(a)) |
---|
3061 | { |
---|
3062 | _ntl_gdiv(n, a, &q, &n); |
---|
3063 | _ntl_gmul(q, inv, &x); |
---|
3064 | _ntl_gadd(w, x, &w); |
---|
3065 | } |
---|
3066 | else |
---|
3067 | { |
---|
3068 | break; |
---|
3069 | } |
---|
3070 | } |
---|
3071 | } |
---|
3072 | |
---|
3073 | _ntl_gcopy(a_bak, &a); |
---|
3074 | _ntl_gcopy(n_bak, &n); |
---|
3075 | _ntl_gcopy(w_bak, &w); |
---|
3076 | _ntl_gcopy(inv_bak, &inv); |
---|
3077 | |
---|
3078 | _ntl_gnegate(&w); |
---|
3079 | |
---|
3080 | while (1) |
---|
3081 | { |
---|
3082 | sa = SIZE(w); |
---|
3083 | if (sa < 0) SIZE(w) = -sa; |
---|
3084 | if (SIZE(w) >= sden && _ntl_gcompare(w, den_bound) > 0) return 0; |
---|
3085 | SIZE(w) = sa; |
---|
3086 | |
---|
3087 | if (SIZE(n) <= snum && _ntl_gcompare(n, num_bound) <= 0) break; |
---|
3088 | |
---|
3089 | fast = 0; |
---|
3090 | sa = SIZE(a); |
---|
3091 | sn = SIZE(n); |
---|
3092 | diff = sa - sn; |
---|
3093 | if (!diff || diff == 1) |
---|
3094 | { |
---|
3095 | sa = SIZE(a); |
---|
3096 | p = DATA(a) + (sa-1); |
---|
3097 | num = (double) (*p) * NTL_ZZ_FRADIX; |
---|
3098 | if (sa > 1) |
---|
3099 | num += (*(--p)); |
---|
3100 | num *= NTL_ZZ_FRADIX; |
---|
3101 | if (sa > 2) |
---|
3102 | num += (*(p - 1)); |
---|
3103 | |
---|
3104 | sn = SIZE(n); |
---|
3105 | p = DATA(n) + (sn-1); |
---|
3106 | den = (double) (*p) * NTL_ZZ_FRADIX; |
---|
3107 | if (sn > 1) |
---|
3108 | den += (*(--p)); |
---|
3109 | den *= NTL_ZZ_FRADIX; |
---|
3110 | if (sn > 2) |
---|
3111 | den += (*(p - 1)); |
---|
3112 | |
---|
3113 | hi = fhi1 * (num + 1.0) / den; |
---|
3114 | lo = flo1 * num / (den + 1.0); |
---|
3115 | if (diff > 0) |
---|
3116 | { |
---|
3117 | hi *= NTL_ZZ_FRADIX; |
---|
3118 | lo *= NTL_ZZ_FRADIX; |
---|
3119 | } |
---|
3120 | |
---|
3121 | if (hi < NTL_SP_BOUND) |
---|
3122 | { |
---|
3123 | ilo = (long)lo; |
---|
3124 | if (ilo == (long)hi) |
---|
3125 | fast = 1; |
---|
3126 | } |
---|
3127 | } |
---|
3128 | |
---|
3129 | if (fast) |
---|
3130 | { |
---|
3131 | if (ilo != 0) { |
---|
3132 | if (ilo == 1) { |
---|
3133 | _ntl_gsub(inv, w, &inv); |
---|
3134 | _ntl_gsubpos(a, n, &a); |
---|
3135 | } |
---|
3136 | else { |
---|
3137 | _ntl_gsmul(w, ilo, &x); |
---|
3138 | _ntl_gsub(inv, x, &inv); |
---|
3139 | _ntl_gsmul(n, ilo, &x); |
---|
3140 | _ntl_gsubpos(a, x, &a); |
---|
3141 | } |
---|
3142 | } |
---|
3143 | } |
---|
3144 | else { |
---|
3145 | _ntl_gdiv(a, n, &q, &a); |
---|
3146 | _ntl_gmul(q, w, &x); |
---|
3147 | _ntl_gsub(inv, x, &inv); |
---|
3148 | } |
---|
3149 | |
---|
3150 | _ntl_gswap(&a, &n); |
---|
3151 | _ntl_gswap(&inv, &w); |
---|
3152 | } |
---|
3153 | |
---|
3154 | if (_ntl_gsign(w) < 0) { |
---|
3155 | _ntl_gnegate(&w); |
---|
3156 | _ntl_gnegate(&n); |
---|
3157 | } |
---|
3158 | |
---|
3159 | _ntl_gcopy(n, num_out); |
---|
3160 | _ntl_gcopy(w, den_out); |
---|
3161 | |
---|
3162 | return 1; |
---|
3163 | } |
---|
3164 | |
---|
3165 | |
---|
3166 | void |
---|
3167 | _ntl_gexp( |
---|
3168 | _ntl_gbigint a, |
---|
3169 | long e, |
---|
3170 | _ntl_gbigint *bb |
---|
3171 | ) |
---|
3172 | { |
---|
3173 | long k; |
---|
3174 | long len_a; |
---|
3175 | static _ntl_gbigint res = 0; |
---|
3176 | |
---|
3177 | if (!e) |
---|
3178 | { |
---|
3179 | _ntl_gone(bb); |
---|
3180 | return; |
---|
3181 | } |
---|
3182 | |
---|
3183 | if (e < 0) |
---|
3184 | ghalt("negative exponent in _ntl_gexp"); |
---|
3185 | |
---|
3186 | if (_ntl_giszero(a)) |
---|
3187 | { |
---|
3188 | _ntl_gzero(bb); |
---|
3189 | return; |
---|
3190 | } |
---|
3191 | |
---|
3192 | len_a = _ntl_g2log(a); |
---|
3193 | if (len_a > (NTL_MAX_LONG-(NTL_ZZ_NBITS-1))/e) |
---|
3194 | ghalt("overflow in _ntl_gexp"); |
---|
3195 | |
---|
3196 | _ntl_gsetlength(&res, (len_a*e+NTL_ZZ_NBITS-1)/NTL_ZZ_NBITS); |
---|
3197 | |
---|
3198 | _ntl_gcopy(a, &res); |
---|
3199 | k = 1; |
---|
3200 | while ((k << 1) <= e) |
---|
3201 | k <<= 1; |
---|
3202 | while (k >>= 1) { |
---|
3203 | _ntl_gsq(res, &res); |
---|
3204 | if (e & k) |
---|
3205 | _ntl_gmul(a, res, &res); |
---|
3206 | } |
---|
3207 | |
---|
3208 | _ntl_gcopy(res, bb); |
---|
3209 | } |
---|
3210 | |
---|
3211 | void |
---|
3212 | _ntl_gexps( |
---|
3213 | long a, |
---|
3214 | long e, |
---|
3215 | _ntl_gbigint *bb |
---|
3216 | ) |
---|
3217 | { |
---|
3218 | long k; |
---|
3219 | long len_a; |
---|
3220 | static _ntl_gbigint res = 0; |
---|
3221 | |
---|
3222 | if (!e) |
---|
3223 | { |
---|
3224 | _ntl_gone(bb); |
---|
3225 | return; |
---|
3226 | } |
---|
3227 | |
---|
3228 | if (e < 0) |
---|
3229 | ghalt("negative exponent in _ntl_zexps"); |
---|
3230 | |
---|
3231 | if (!a) |
---|
3232 | { |
---|
3233 | _ntl_gzero(bb); |
---|
3234 | return; |
---|
3235 | } |
---|
3236 | |
---|
3237 | len_a = _ntl_g2logs(a); |
---|
3238 | if (len_a > (NTL_MAX_LONG-(NTL_ZZ_NBITS-1))/e) |
---|
3239 | ghalt("overflow in _ntl_gexps"); |
---|
3240 | |
---|
3241 | _ntl_gsetlength(&res, (len_a*e+NTL_ZZ_NBITS-1)/NTL_ZZ_NBITS); |
---|
3242 | |
---|
3243 | _ntl_gintoz(a, &res); |
---|
3244 | k = 1; |
---|
3245 | while ((k << 1) <= e) |
---|
3246 | k <<= 1; |
---|
3247 | while (k >>= 1) { |
---|
3248 | _ntl_gsq(res, &res); |
---|
3249 | if (e & k) |
---|
3250 | _ntl_gsmul(res, a, &res); |
---|
3251 | } |
---|
3252 | |
---|
3253 | _ntl_gcopy(res, bb); |
---|
3254 | } |
---|
3255 | |
---|
3256 | |
---|
3257 | static |
---|
3258 | long OptWinSize(long n) |
---|
3259 | /* finds k that minimizes n/(k+1) + 2^{k-1} */ |
---|
3260 | |
---|
3261 | { |
---|
3262 | long k; |
---|
3263 | double v, v_new; |
---|
3264 | |
---|
3265 | |
---|
3266 | v = n/2.0 + 1.0; |
---|
3267 | k = 1; |
---|
3268 | |
---|
3269 | for (;;) { |
---|
3270 | v_new = n/((double)(k+2)) + ((double)(1L << k)); |
---|
3271 | if (v_new >= v) break; |
---|
3272 | v = v_new; |
---|
3273 | k++; |
---|
3274 | } |
---|
3275 | |
---|
3276 | return k; |
---|
3277 | } |
---|
3278 | |
---|
3279 | |
---|
3280 | |
---|
3281 | /* DIRT: will not work with non-empty "nails" */ |
---|
3282 | |
---|
3283 | static |
---|
3284 | mp_limb_t neg_inv_mod_limb(mp_limb_t m0) |
---|
3285 | { |
---|
3286 | mp_limb_t x; |
---|
3287 | long k; |
---|
3288 | |
---|
3289 | x = 1; |
---|
3290 | k = 1; |
---|
3291 | while (k < NTL_ZZ_NBITS) { |
---|
3292 | x += x * (1 - x * m0); |
---|
3293 | k <<= 1; |
---|
3294 | } |
---|
3295 | |
---|
3296 | |
---|
3297 | return - x; |
---|
3298 | } |
---|
3299 | |
---|
3300 | |
---|
3301 | /* Montgomery reduction: |
---|
3302 | * This computes res = T/b^m mod N, where b = 2^{NTL_ZZ_NBITS}. |
---|
3303 | * It is assumed that N has n limbs, and that T has at most n + m limbs. |
---|
3304 | * Also, inv should be set to -N^{-1} mod b. |
---|
3305 | * Finally, it is assumed that T has space allocated for n + m limbs, |
---|
3306 | * and that res has space allocated for n limbs. |
---|
3307 | * Note: res should not overlap any inputs, and T is destroyed. |
---|
3308 | * Note: res will have at most n limbs, but may not be fully reduced |
---|
3309 | * mod N. In general, we will have res < T/b^m + N. |
---|
3310 | */ |
---|
3311 | |
---|
3312 | /* DIRT: this routine may not work with non-empty "nails" */ |
---|
3313 | |
---|
3314 | static |
---|
3315 | void redc(_ntl_gbigint T, _ntl_gbigint N, long m, mp_limb_t inv, |
---|
3316 | _ntl_gbigint res) |
---|
3317 | { |
---|
3318 | long n, sT, i; |
---|
3319 | mp_limb_t *Ndata, *Tdata, *resdata, q, d, t, c; |
---|
3320 | |
---|
3321 | n = SIZE(N); |
---|
3322 | Ndata = DATA(N); |
---|
3323 | sT = SIZE(T); |
---|
3324 | Tdata = DATA(T); |
---|
3325 | resdata = DATA(res); |
---|
3326 | |
---|
3327 | for (i = sT; i < m+n; i++) |
---|
3328 | Tdata[i] = 0; |
---|
3329 | |
---|
3330 | c = 0; |
---|
3331 | for (i = 0; i < m; i++) { |
---|
3332 | q = Tdata[i]*inv; |
---|
3333 | d = mpn_addmul_1(Tdata+i, Ndata, n, q); |
---|
3334 | t = Tdata[i+n] + d; |
---|
3335 | Tdata[i+n] = t + c; |
---|
3336 | if (t < d || (c == 1 && t + c == 0)) |
---|
3337 | c = 1; |
---|
3338 | else |
---|
3339 | c = 0; |
---|
3340 | } |
---|
3341 | |
---|
3342 | if (c) { |
---|
3343 | mpn_sub_n(resdata, Tdata + m, Ndata, n); |
---|
3344 | } |
---|
3345 | else { |
---|
3346 | for (i = 0; i < n; i++) |
---|
3347 | resdata[i] = Tdata[m + i]; |
---|
3348 | } |
---|
3349 | |
---|
3350 | i = n; |
---|
3351 | STRIP(i, resdata); |
---|
3352 | |
---|
3353 | SIZE(res) = i; |
---|
3354 | SIZE(T) = 0; |
---|
3355 | } |
---|
3356 | |
---|
3357 | |
---|
3358 | |
---|
3359 | #define REDC_CROSS (32) |
---|
3360 | |
---|
3361 | void _ntl_gpowermod(_ntl_gbigint g, _ntl_gbigint e, _ntl_gbigint F, |
---|
3362 | _ntl_gbigint *h) |
---|
3363 | |
---|
3364 | /* h = g^e mod f using "sliding window" algorithm |
---|
3365 | |
---|
3366 | remark: the notation (h, g, e, F) is strange, because I |
---|
3367 | copied the code from BB.c. |
---|
3368 | */ |
---|
3369 | |
---|
3370 | { |
---|
3371 | _ntl_gbigint res, gg, *v, t; |
---|
3372 | long n, i, k, val, cnt, m; |
---|
3373 | long use_redc, sF; |
---|
3374 | mp_limb_t inv; |
---|
3375 | |
---|
3376 | if (_ntl_gsign(g) < 0 || _ntl_gcompare(g, F) >= 0 || |
---|
3377 | _ntl_gscompare(F, 1) <= 0) |
---|
3378 | ghalt("PowerMod: bad args"); |
---|
3379 | |
---|
3380 | if (_ntl_gscompare(e, 0) == 0) { |
---|
3381 | _ntl_gone(h); |
---|
3382 | return; |
---|
3383 | } |
---|
3384 | |
---|
3385 | if (_ntl_gscompare(e, 1) == 0) { |
---|
3386 | _ntl_gcopy(g, h); |
---|
3387 | return; |
---|
3388 | } |
---|
3389 | |
---|
3390 | if (_ntl_gscompare(e, -1) == 0) { |
---|
3391 | _ntl_ginvmod(g, F, h); |
---|
3392 | return; |
---|
3393 | } |
---|
3394 | |
---|
3395 | if (_ntl_gscompare(e, 2) == 0) { |
---|
3396 | _ntl_gsqmod(g, F, h); |
---|
3397 | return; |
---|
3398 | } |
---|
3399 | |
---|
3400 | if (_ntl_gscompare(e, -2) == 0) { |
---|
3401 | res = 0; |
---|
3402 | _ntl_gsqmod(g, F, &res); |
---|
3403 | _ntl_ginvmod(res, F, h); |
---|
3404 | _ntl_gfree(&res); |
---|
3405 | return; |
---|
3406 | } |
---|
3407 | |
---|
3408 | n = _ntl_g2log(e); |
---|
3409 | |
---|
3410 | sF = SIZE(F); |
---|
3411 | |
---|
3412 | res = 0; |
---|
3413 | _ntl_gsetlength(&res, sF*2); |
---|
3414 | |
---|
3415 | t = 0; |
---|
3416 | _ntl_gsetlength(&t, sF*2); |
---|
3417 | |
---|
3418 | use_redc = (DATA(F)[0] & 1) && sF < REDC_CROSS; |
---|
3419 | |
---|
3420 | gg = 0; |
---|
3421 | |
---|
3422 | if (use_redc) { |
---|
3423 | _ntl_glshift(g, sF*NTL_ZZ_NBITS, &res); |
---|
3424 | _ntl_gmod(res, F, &gg); |
---|
3425 | |
---|
3426 | inv = neg_inv_mod_limb(DATA(F)[0]); |
---|
3427 | } |
---|
3428 | else |
---|
3429 | _ntl_gcopy(g, &gg); |
---|
3430 | |
---|
3431 | |
---|
3432 | if (_ntl_gscompare(g, 2) == 0) { |
---|
3433 | /* plain square-and-multiply algorithm, optimized for g == 2 */ |
---|
3434 | |
---|
3435 | _ntl_gbigint F1 = 0; |
---|
3436 | |
---|
3437 | if (use_redc) { |
---|
3438 | long shamt; |
---|
3439 | |
---|
3440 | COUNT_BITS(shamt, DATA(F)[sF-1]); |
---|
3441 | shamt = NTL_ZZ_NBITS - shamt; |
---|
3442 | _ntl_glshift(F, shamt, &F1); |
---|
3443 | } |
---|
3444 | |
---|
3445 | _ntl_gcopy(gg, &res); |
---|
3446 | |
---|
3447 | for (i = n - 2; i >= 0; i--) { |
---|
3448 | _ntl_gsq(res, &t); |
---|
3449 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3450 | |
---|
3451 | if (_ntl_gbit(e, i)) { |
---|
3452 | _ntl_gadd(res, res, &res); |
---|
3453 | |
---|
3454 | if (use_redc) { |
---|
3455 | while (SIZE(res) > sF) { |
---|
3456 | _ntl_gsubpos(res, F1, &res); |
---|
3457 | } |
---|
3458 | } |
---|
3459 | else { |
---|
3460 | if (_ntl_gcompare(res, F) >= 0) |
---|
3461 | _ntl_gsubpos(res, F, &res); |
---|
3462 | } |
---|
3463 | } |
---|
3464 | } |
---|
3465 | |
---|
3466 | |
---|
3467 | if (use_redc) { |
---|
3468 | _ntl_gcopy(res, &t); |
---|
3469 | redc(t, F, sF, inv, res); |
---|
3470 | if (_ntl_gcompare(res, F) >= 0) { |
---|
3471 | _ntl_gsub(res, F, &res); |
---|
3472 | } |
---|
3473 | } |
---|
3474 | |
---|
3475 | if (_ntl_gsign(e) < 0) _ntl_ginvmod(res, F, &res); |
---|
3476 | |
---|
3477 | _ntl_gcopy(res, h); |
---|
3478 | _ntl_gfree(&res); |
---|
3479 | _ntl_gfree(&gg); |
---|
3480 | _ntl_gfree(&t); |
---|
3481 | _ntl_gfree(&F1); |
---|
3482 | return; |
---|
3483 | } |
---|
3484 | |
---|
3485 | |
---|
3486 | if (n < 16) { |
---|
3487 | /* plain square-and-multiply algorithm */ |
---|
3488 | |
---|
3489 | _ntl_gcopy(gg, &res); |
---|
3490 | |
---|
3491 | for (i = n - 2; i >= 0; i--) { |
---|
3492 | _ntl_gsq(res, &t); |
---|
3493 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3494 | |
---|
3495 | if (_ntl_gbit(e, i)) { |
---|
3496 | _ntl_gmul(res, gg, &t); |
---|
3497 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3498 | } |
---|
3499 | } |
---|
3500 | |
---|
3501 | |
---|
3502 | if (use_redc) { |
---|
3503 | _ntl_gcopy(res, &t); |
---|
3504 | redc(t, F, sF, inv, res); |
---|
3505 | if (_ntl_gcompare(res, F) >= 0) { |
---|
3506 | _ntl_gsub(res, F, &res); |
---|
3507 | } |
---|
3508 | } |
---|
3509 | |
---|
3510 | if (_ntl_gsign(e) < 0) _ntl_ginvmod(res, F, &res); |
---|
3511 | |
---|
3512 | _ntl_gcopy(res, h); |
---|
3513 | _ntl_gfree(&res); |
---|
3514 | _ntl_gfree(&gg); |
---|
3515 | _ntl_gfree(&t); |
---|
3516 | return; |
---|
3517 | } |
---|
3518 | |
---|
3519 | k = OptWinSize(n); |
---|
3520 | |
---|
3521 | if (k > 5) k = 5; |
---|
3522 | |
---|
3523 | v = (_ntl_gbigint *) NTL_MALLOC((1L << (k-1)), sizeof(_ntl_gbigint), 0); |
---|
3524 | if (!v) ghalt("out of memory"); |
---|
3525 | for (i = 0; i < (1L << (k-1)); i++) { |
---|
3526 | v[i] = 0; |
---|
3527 | _ntl_gsetlength(&v[i], sF); |
---|
3528 | } |
---|
3529 | |
---|
3530 | _ntl_gcopy(gg, &v[0]); |
---|
3531 | |
---|
3532 | if (k > 1) { |
---|
3533 | _ntl_gsq(gg, &t); |
---|
3534 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3535 | |
---|
3536 | for (i = 1; i < (1L << (k-1)); i++) { |
---|
3537 | _ntl_gmul(v[i-1], res, &t); |
---|
3538 | if (use_redc) redc(t, F, sF, inv, v[i]); else _ntl_gmod(t, F, &v[i]); |
---|
3539 | } |
---|
3540 | } |
---|
3541 | |
---|
3542 | _ntl_gcopy(gg, &res); |
---|
3543 | |
---|
3544 | val = 0; |
---|
3545 | for (i = n-2; i >= 0; i--) { |
---|
3546 | val = (val << 1) | _ntl_gbit(e, i); |
---|
3547 | if (val == 0) { |
---|
3548 | _ntl_gsq(res, &t); |
---|
3549 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3550 | } |
---|
3551 | else if (val >= (1L << (k-1)) || i == 0) { |
---|
3552 | cnt = 0; |
---|
3553 | while ((val & 1) == 0) { |
---|
3554 | val = val >> 1; |
---|
3555 | cnt++; |
---|
3556 | } |
---|
3557 | |
---|
3558 | m = val; |
---|
3559 | while (m > 0) { |
---|
3560 | _ntl_gsq(res, &t); |
---|
3561 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3562 | m = m >> 1; |
---|
3563 | } |
---|
3564 | |
---|
3565 | _ntl_gmul(res, v[val >> 1], &t); |
---|
3566 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3567 | |
---|
3568 | while (cnt > 0) { |
---|
3569 | _ntl_gsq(res, &t); |
---|
3570 | if (use_redc) redc(t, F, sF, inv, res); else _ntl_gmod(t, F, &res); |
---|
3571 | cnt--; |
---|
3572 | } |
---|
3573 | |
---|
3574 | val = 0; |
---|
3575 | } |
---|
3576 | } |
---|
3577 | |
---|
3578 | if (use_redc) { |
---|
3579 | _ntl_gcopy(res, &t); |
---|
3580 | redc(t, F, sF, inv, res); |
---|
3581 | if (_ntl_gcompare(res, F) >= 0) { |
---|
3582 | _ntl_gsub(res, F, &res); |
---|
3583 | } |
---|
3584 | } |
---|
3585 | |
---|
3586 | if (_ntl_gsign(e) < 0) _ntl_ginvmod(res, F, &res); |
---|
3587 | |
---|
3588 | _ntl_gcopy(res, h); |
---|
3589 | |
---|
3590 | _ntl_gfree(&res); |
---|
3591 | _ntl_gfree(&gg); |
---|
3592 | _ntl_gfree(&t); |
---|
3593 | for (i = 0; i < (1L << (k-1)); i++) |
---|
3594 | _ntl_gfree(&v[i]); |
---|
3595 | free(v); |
---|
3596 | } |
---|
3597 | |
---|
3598 | long _ntl_gsize(_ntl_gbigint rep) |
---|
3599 | { |
---|
3600 | if (!rep) |
---|
3601 | return 0; |
---|
3602 | else if (SIZE(rep) < 0) |
---|
3603 | return -SIZE(rep); |
---|
3604 | else |
---|
3605 | return SIZE(rep); |
---|
3606 | } |
---|
3607 | |
---|
3608 | long _ntl_gisone(_ntl_gbigint rep) |
---|
3609 | { |
---|
3610 | return rep != 0 && SIZE(rep) == 1 && DATA(rep)[0] == 1; |
---|
3611 | } |
---|
3612 | |
---|
3613 | long _ntl_gsptest(_ntl_gbigint rep) |
---|
3614 | { |
---|
3615 | return !rep || SIZE(rep) == 0 || |
---|
3616 | ((SIZE(rep) == 1 || SIZE(rep) == -1) && |
---|
3617 | DATA(rep)[0] < ((mp_limb_t) NTL_SP_BOUND)); |
---|
3618 | } |
---|
3619 | |
---|
3620 | long _ntl_gwsptest(_ntl_gbigint rep) |
---|
3621 | { |
---|
3622 | return !rep || SIZE(rep) == 0 || |
---|
3623 | ((SIZE(rep) == 1 || SIZE(rep) == -1) && |
---|
3624 | DATA(rep)[0] < ((mp_limb_t) NTL_WSP_BOUND)); |
---|
3625 | } |
---|
3626 | |
---|
3627 | |
---|
3628 | |
---|
3629 | long _ntl_gcrtinrange(_ntl_gbigint g, _ntl_gbigint a) |
---|
3630 | { |
---|
3631 | long sa, sg, i; |
---|
3632 | mp_limb_t carry, u, v; |
---|
3633 | mp_limb_t *adata, *gdata; |
---|
3634 | |
---|
3635 | if (!a || SIZE(a) <= 0) return 0; |
---|
3636 | |
---|
3637 | sa = SIZE(a); |
---|
3638 | |
---|
3639 | if (!g) return 1; |
---|
3640 | |
---|
3641 | sg = SIZE(g); |
---|
3642 | |
---|
3643 | if (sg == 0) return 1; |
---|
3644 | |
---|
3645 | if (sg < 0) sg = -sg; |
---|
3646 | |
---|
3647 | if (sa-sg > 1) return 1; |
---|
3648 | |
---|
3649 | if (sa-sg < 0) return 0; |
---|
3650 | |
---|
3651 | adata = DATA(a); |
---|
3652 | gdata = DATA(g); |
---|
3653 | |
---|
3654 | carry=0; |
---|
3655 | |
---|
3656 | if (sa-sg == 1) { |
---|
3657 | if (adata[sa-1] > ((mp_limb_t) 1)) return 1; |
---|
3658 | carry = 1; |
---|
3659 | } |
---|
3660 | |
---|
3661 | i = sg-1; |
---|
3662 | u = 0; |
---|
3663 | v = 0; |
---|
3664 | while (i >= 0 && u == v) { |
---|
3665 | u = (carry << (NTL_ZZ_NBITS-1)) + (adata[i] >> 1); |
---|
3666 | v = gdata[i]; |
---|
3667 | carry = (adata[i] & 1); |
---|
3668 | i--; |
---|
3669 | } |
---|
3670 | |
---|
3671 | if (u == v) { |
---|
3672 | if (carry) return 1; |
---|
3673 | return (SIZE(g) > 0); |
---|
3674 | } |
---|
3675 | else |
---|
3676 | return (u > v); |
---|
3677 | } |
---|
3678 | |
---|
3679 | |
---|
3680 | |
---|
3681 | /* DIRT: this routine will not work with non-empty "nails" */ |
---|
3682 | |
---|
3683 | void _ntl_gfrombytes(_ntl_gbigint *x, const unsigned char *p, long n) |
---|
3684 | { |
---|
3685 | long BytesPerLimb; |
---|
3686 | long lw, r, i, j; |
---|
3687 | mp_limb_t *xp, t; |
---|
3688 | |
---|
3689 | if (n <= 0) { |
---|
3690 | x = 0; |
---|
3691 | return; |
---|
3692 | } |
---|
3693 | |
---|
3694 | BytesPerLimb = NTL_ZZ_NBITS/8; |
---|
3695 | |
---|
3696 | |
---|
3697 | lw = n/BytesPerLimb; |
---|
3698 | r = n - lw*BytesPerLimb; |
---|
3699 | |
---|
3700 | if (r != 0) |
---|
3701 | lw++; |
---|
3702 | else |
---|
3703 | r = BytesPerLimb; |
---|
3704 | |
---|
3705 | _ntl_gsetlength(x, lw); |
---|
3706 | xp = DATA(*x); |
---|
3707 | |
---|
3708 | for (i = 0; i < lw-1; i++) { |
---|
3709 | t = 0; |
---|
3710 | for (j = 0; j < BytesPerLimb; j++) { |
---|
3711 | t >>= 8; |
---|
3712 | t += (((mp_limb_t)(*p)) & ((mp_limb_t) 255)) << ((BytesPerLimb-1)*8); |
---|
3713 | p++; |
---|
3714 | } |
---|
3715 | xp[i] = t; |
---|
3716 | } |
---|
3717 | |
---|
3718 | t = 0; |
---|
3719 | for (j = 0; j < r; j++) { |
---|
3720 | t >>= 8; |
---|
3721 | t += (((mp_limb_t)(*p)) & ((mp_limb_t) 255)) << ((BytesPerLimb-1)*8); |
---|
3722 | p++; |
---|
3723 | } |
---|
3724 | |
---|
3725 | t >>= (BytesPerLimb-r)*8; |
---|
3726 | xp[lw-1] = t; |
---|
3727 | |
---|
3728 | STRIP(lw, xp); |
---|
3729 | SIZE(*x) = lw; |
---|
3730 | } |
---|
3731 | |
---|
3732 | |
---|
3733 | |
---|
3734 | /* DIRT: this routine will not work with non-empty "nails" */ |
---|
3735 | |
---|
3736 | void _ntl_gbytesfromz(unsigned char *p, _ntl_gbigint a, long n) |
---|
3737 | { |
---|
3738 | long BytesPerLimb; |
---|
3739 | long lbits, lbytes, min_bytes, min_words, r; |
---|
3740 | long i, j; |
---|
3741 | mp_limb_t *ap, t; |
---|
3742 | |
---|
3743 | if (n < 0) n = 0; |
---|
3744 | |
---|
3745 | BytesPerLimb = NTL_ZZ_NBITS/8; |
---|
3746 | |
---|
3747 | lbits = _ntl_g2log(a); |
---|
3748 | lbytes = (lbits+7)/8; |
---|
3749 | |
---|
3750 | min_bytes = (lbytes < n) ? lbytes : n; |
---|
3751 | |
---|
3752 | min_words = min_bytes/BytesPerLimb; |
---|
3753 | |
---|
3754 | r = min_bytes - min_words*BytesPerLimb; |
---|
3755 | if (r != 0) |
---|
3756 | min_words++; |
---|
3757 | else |
---|
3758 | r = BytesPerLimb; |
---|
3759 | |
---|
3760 | if (a) |
---|
3761 | ap = DATA(a); |
---|
3762 | else |
---|
3763 | ap = 0; |
---|
3764 | |
---|
3765 | |
---|
3766 | for (i = 0; i < min_words-1; i++) { |
---|
3767 | t = ap[i]; |
---|
3768 | for (j = 0; j < BytesPerLimb; j++) { |
---|
3769 | *p = t & ((mp_limb_t) 255); |
---|
3770 | t >>= 8; |
---|
3771 | p++; |
---|
3772 | } |
---|
3773 | } |
---|
3774 | |
---|
3775 | if (min_words > 0) { |
---|
3776 | t = ap[min_words-1]; |
---|
3777 | for (j = 0; j < r; j++) { |
---|
3778 | *p = t & ((mp_limb_t) 255); |
---|
3779 | t >>= 8; |
---|
3780 | p++; |
---|
3781 | } |
---|
3782 | } |
---|
3783 | |
---|
3784 | for (j = min_bytes; j < n; j++) { |
---|
3785 | *p = 0; |
---|
3786 | p++; |
---|
3787 | } |
---|
3788 | } |
---|
3789 | |
---|
3790 | |
---|
3791 | |
---|
3792 | |
---|
3793 | long _ntl_gblock_construct_alloc(_ntl_gbigint *x, long d, long n) |
---|
3794 | { |
---|
3795 | long d1, sz, AllocAmt, m, j, alloc; |
---|
3796 | char *p; |
---|
3797 | _ntl_gbigint t; |
---|
3798 | |
---|
3799 | |
---|
3800 | /* check n value */ |
---|
3801 | |
---|
3802 | if (n <= 0) |
---|
3803 | ghalt("block construct: n must be positive"); |
---|
3804 | |
---|
3805 | |
---|
3806 | |
---|
3807 | /* check d value */ |
---|
3808 | |
---|
3809 | if (d <= 0) |
---|
3810 | ghalt("block construct: d must be positive"); |
---|
3811 | |
---|
3812 | if (NTL_OVERFLOW(d, NTL_ZZ_NBITS, NTL_ZZ_NBITS)) |
---|
3813 | ghalt("block construct: d too large"); |
---|
3814 | |
---|
3815 | #ifdef NTL_SMALL_MP_SIZE_T |
---|
3816 | /* this makes sure that numbers don't get too big for GMP */ |
---|
3817 | if (d >= (1L << (NTL_BITS_PER_INT-4))) |
---|
3818 | ghalt("size too big for GMP"); |
---|
3819 | #endif |
---|
3820 | |
---|
3821 | d1 = d + 1; |
---|
3822 | |
---|
3823 | if (STORAGE_OVF(d1)) |
---|
3824 | ghalt("block construct: d too large"); |
---|
3825 | |
---|
3826 | |
---|
3827 | |
---|
3828 | sz = STORAGE(d1); |
---|
3829 | |
---|
3830 | AllocAmt = NTL_MAX_ALLOC_BLOCK/sz; |
---|
3831 | if (AllocAmt == 0) AllocAmt = 1; |
---|
3832 | |
---|
3833 | if (AllocAmt < n) |
---|
3834 | m = AllocAmt; |
---|
3835 | else |
---|
3836 | m = n; |
---|
3837 | |
---|
3838 | p = (char *) NTL_MALLOC(m, sz, 0); |
---|
3839 | if (!p) ghalt("out of memory in _ntl_gblock_construct"); |
---|
3840 | |
---|
3841 | *x = (_ntl_gbigint) p; |
---|
3842 | |
---|
3843 | for (j = 0; j < m; j++) { |
---|
3844 | t = (_ntl_gbigint) p; |
---|
3845 | alloc = (d1 << 2) | 1; |
---|
3846 | if (j < m-1) alloc |= 2; |
---|
3847 | ALLOC(t) = alloc; |
---|
3848 | SIZE(t) = 0; |
---|
3849 | p += sz; |
---|
3850 | } |
---|
3851 | |
---|
3852 | return m; |
---|
3853 | } |
---|
3854 | |
---|
3855 | |
---|
3856 | void _ntl_gblock_construct_set(_ntl_gbigint x, _ntl_gbigint *y, long i) |
---|
3857 | { |
---|
3858 | long d1, sz; |
---|
3859 | |
---|
3860 | |
---|
3861 | d1 = ALLOC(x) >> 2; |
---|
3862 | sz = STORAGE(d1); |
---|
3863 | |
---|
3864 | *y = (_ntl_gbigint) (((char *) x) + i*sz); |
---|
3865 | } |
---|
3866 | |
---|
3867 | |
---|
3868 | long _ntl_gblock_destroy(_ntl_gbigint x) |
---|
3869 | { |
---|
3870 | long d1, sz, alloc, m; |
---|
3871 | char *p; |
---|
3872 | _ntl_gbigint t; |
---|
3873 | |
---|
3874 | |
---|
3875 | d1 = ALLOC(x) >> 2; |
---|
3876 | sz = STORAGE(d1); |
---|
3877 | |
---|
3878 | p = (char *) x; |
---|
3879 | |
---|
3880 | m = 1; |
---|
3881 | |
---|
3882 | for (;;) { |
---|
3883 | t = (_ntl_gbigint) p; |
---|
3884 | alloc = ALLOC(t); |
---|
3885 | if ((alloc & 1) == 0) |
---|
3886 | ghalt("corrupted memory detected in _ntl_gblock_destroy"); |
---|
3887 | if ((alloc & 2) == 0) break; |
---|
3888 | m++; |
---|
3889 | p += sz; |
---|
3890 | } |
---|
3891 | |
---|
3892 | free(x); |
---|
3893 | return m; |
---|
3894 | } |
---|
3895 | |
---|
3896 | |
---|
3897 | long _ntl_gblock_storage(long d) |
---|
3898 | { |
---|
3899 | long d1, sz; |
---|
3900 | |
---|
3901 | d1 = d + 1; |
---|
3902 | sz = STORAGE(d1) + sizeof(_ntl_gbigint); |
---|
3903 | |
---|
3904 | return sz; |
---|
3905 | } |
---|
3906 | |
---|
3907 | |
---|
3908 | /* |
---|
3909 | * This is a completely portable MulMod routine. |
---|
3910 | */ |
---|
3911 | |
---|
3912 | #define SP_MUL_MOD(r, a, b, n) \ |
---|
3913 | { \ |
---|
3914 | long l__a = (a); \ |
---|
3915 | long l__b = (b); \ |
---|
3916 | long l__n = (n); \ |
---|
3917 | long l__q; \ |
---|
3918 | unsigned long l__res; \ |
---|
3919 | \ |
---|
3920 | l__q = (long) ((((double) l__a) * ((double) l__b)) / ((double) l__n)); \ |
---|
3921 | l__res = ((unsigned long) l__a)*((unsigned long) l__b) - \ |
---|
3922 | ((unsigned long) l__q)*((unsigned long) l__n); \ |
---|
3923 | if (l__res >> (NTL_BITS_PER_LONG-1)) \ |
---|
3924 | l__res += l__n; \ |
---|
3925 | else if (((long) l__res) >= l__n) \ |
---|
3926 | l__res -= l__n; \ |
---|
3927 | \ |
---|
3928 | r = (long) l__res; \ |
---|
3929 | } |
---|
3930 | |
---|
3931 | |
---|
3932 | |
---|
3933 | |
---|
3934 | #if (NTL_ARITH_RIGHT_SHIFT && defined(NTL_AVOID_BRANCHING) && !defined(NTL_CLEAN_INT)) |
---|
3935 | |
---|
3936 | #define SP_MUL_MOD2(res, a, b, n, bninv) \ |
---|
3937 | do { \ |
---|
3938 | long _a = (a); \ |
---|
3939 | long _b = (b); \ |
---|
3940 | long _n = (n); \ |
---|
3941 | double _bninv = (bninv); \ |
---|
3942 | long _q, _res; \ |
---|
3943 | \ |
---|
3944 | _q = (long) (((double) _a) * _bninv); \ |
---|
3945 | _res = _a*_b - _q*_n; \ |
---|
3946 | \ |
---|
3947 | _res += (_res >> (NTL_BITS_PER_LONG-1)) & _n; \ |
---|
3948 | _res -= _n; \ |
---|
3949 | _res += (_res >> (NTL_BITS_PER_LONG-1)) & _n; \ |
---|
3950 | \ |
---|
3951 | res = _res; \ |
---|
3952 | } while (0) |
---|
3953 | |
---|
3954 | #else |
---|
3955 | |
---|
3956 | /* |
---|
3957 | * This is a completely portable MulMod routine. |
---|
3958 | */ |
---|
3959 | |
---|
3960 | #define SP_MUL_MOD2(res, a, b, n, bninv) \ |
---|
3961 | do { \ |
---|
3962 | long _a = (a); \ |
---|
3963 | long _b = (b); \ |
---|
3964 | long _n = (n); \ |
---|
3965 | double _bninv = (bninv); \ |
---|
3966 | long _q; \ |
---|
3967 | unsigned long _res; \ |
---|
3968 | \ |
---|
3969 | _q = (long) (((double) _a) * _bninv); \ |
---|
3970 | _res = ((unsigned long) _a)*((unsigned long) _b) - \ |
---|
3971 | ((unsigned long) _q)*((unsigned long) _n); \ |
---|
3972 | \ |
---|
3973 | if (_res >> (NTL_BITS_PER_LONG-1)) \ |
---|
3974 | _res += _n; \ |
---|
3975 | else if (((long) _res) >= _n) \ |
---|
3976 | _res -= _n; \ |
---|
3977 | \ |
---|
3978 | res = (long) _res; \ |
---|
3979 | } while (0) |
---|
3980 | |
---|
3981 | #endif |
---|
3982 | |
---|
3983 | |
---|
3984 | static |
---|
3985 | long SpecialPower(long e, long p) |
---|
3986 | { |
---|
3987 | long a; |
---|
3988 | long x, y; |
---|
3989 | |
---|
3990 | a = (long) ((((mp_limb_t) 1) << (NTL_ZZ_NBITS-2)) % ((mp_limb_t) p)); |
---|
3991 | SP_MUL_MOD(a, a, 2, p); |
---|
3992 | SP_MUL_MOD(a, a, 2, p); |
---|
3993 | |
---|
3994 | x = 1; |
---|
3995 | y = a; |
---|
3996 | while (e) { |
---|
3997 | if (e & 1) SP_MUL_MOD(x, x, y, p); |
---|
3998 | SP_MUL_MOD(y, y, y, p); |
---|
3999 | e = e >> 1; |
---|
4000 | } |
---|
4001 | |
---|
4002 | return x; |
---|
4003 | } |
---|
4004 | |
---|
4005 | |
---|
4006 | static |
---|
4007 | void sp_ext_eucl(long *dd, long *ss, long *tt, long a, long b) |
---|
4008 | { |
---|
4009 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
---|
4010 | |
---|
4011 | long aneg = 0, bneg = 0; |
---|
4012 | |
---|
4013 | if (a < 0) { |
---|
4014 | if (a < -NTL_MAX_LONG) ghalt("integer overflow"); |
---|
4015 | a = -a; |
---|
4016 | aneg = 1; |
---|
4017 | } |
---|
4018 | |
---|
4019 | if (b < 0) { |
---|
4020 | if (b < -NTL_MAX_LONG) ghalt("integer overflow"); |
---|
4021 | b = -b; |
---|
4022 | bneg = 1; |
---|
4023 | } |
---|
4024 | |
---|
4025 | u1=1; v1=0; |
---|
4026 | u2=0; v2=1; |
---|
4027 | u = a; v = b; |
---|
4028 | |
---|
4029 | while (v != 0) { |
---|
4030 | q = u / v; |
---|
4031 | r = u % v; |
---|
4032 | u = v; |
---|
4033 | v = r; |
---|
4034 | u0 = u2; |
---|
4035 | v0 = v2; |
---|
4036 | u2 = u1 - q*u2; |
---|
4037 | v2 = v1- q*v2; |
---|
4038 | u1 = u0; |
---|
4039 | v1 = v0; |
---|
4040 | } |
---|
4041 | |
---|
4042 | if (aneg) |
---|
4043 | u1 = -u1; |
---|
4044 | |
---|
4045 | if (bneg) |
---|
4046 | v1 = -v1; |
---|
4047 | |
---|
4048 | *dd = u; |
---|
4049 | *ss = u1; |
---|
4050 | *tt = v1; |
---|
4051 | } |
---|
4052 | |
---|
4053 | static |
---|
4054 | long sp_inv_mod(long a, long n) |
---|
4055 | { |
---|
4056 | long d, s, t; |
---|
4057 | |
---|
4058 | sp_ext_eucl(&d, &s, &t, a, n); |
---|
4059 | if (d != 1) ghalt("inverse undefined"); |
---|
4060 | if (s < 0) |
---|
4061 | return s + n; |
---|
4062 | else |
---|
4063 | return s; |
---|
4064 | } |
---|
4065 | |
---|
4066 | /* ------ HERE ------ */ |
---|
4067 | |
---|
4068 | |
---|
4069 | |
---|
4070 | struct crt_body_gmp { |
---|
4071 | _ntl_gbigint *v; |
---|
4072 | long sbuf; |
---|
4073 | long n; |
---|
4074 | _ntl_gbigint buf; |
---|
4075 | }; |
---|
4076 | |
---|
4077 | struct crt_body_gmp1 { |
---|
4078 | long n; |
---|
4079 | long levels; |
---|
4080 | long *primes; |
---|
4081 | long *inv_vec; |
---|
4082 | long *val_vec; |
---|
4083 | long *index_vec; |
---|
4084 | _ntl_gbigint *prod_vec; |
---|
4085 | _ntl_gbigint *rem_vec; |
---|
4086 | _ntl_gbigint *coeff_vec; |
---|
4087 | _ntl_gbigint temps[2]; |
---|
4088 | _ntl_gbigint modulus; |
---|
4089 | }; |
---|
4090 | |
---|
4091 | |
---|
4092 | struct crt_body { |
---|
4093 | long strategy; |
---|
4094 | |
---|
4095 | union { |
---|
4096 | struct crt_body_gmp G; |
---|
4097 | struct crt_body_gmp1 G1; |
---|
4098 | } U; |
---|
4099 | }; |
---|
4100 | |
---|
4101 | |
---|
4102 | |
---|
4103 | |
---|
4104 | void _ntl_gcrt_struct_init(void **crt_struct, long n, _ntl_gbigint p, |
---|
4105 | const long *primes) |
---|
4106 | { |
---|
4107 | struct crt_body *c; |
---|
4108 | |
---|
4109 | c = (struct crt_body *) NTL_MALLOC(1, sizeof(struct crt_body), 0); |
---|
4110 | if (!c) ghalt("out of memory"); |
---|
4111 | |
---|
4112 | if (n >= 600) { |
---|
4113 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
4114 | long *q; |
---|
4115 | long i, j; |
---|
4116 | long levels, vec_len; |
---|
4117 | long *val_vec, *inv_vec; |
---|
4118 | long *index_vec; |
---|
4119 | _ntl_gbigint *prod_vec, *rem_vec, *coeff_vec; |
---|
4120 | _ntl_gbigint *temps; |
---|
4121 | |
---|
4122 | C->modulus = 0; |
---|
4123 | _ntl_gcopy(p, &C->modulus); |
---|
4124 | |
---|
4125 | temps = &C->temps[0]; |
---|
4126 | |
---|
4127 | temps[0] = 0; |
---|
4128 | temps[1] = 0; |
---|
4129 | |
---|
4130 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4131 | if (!q) ghalt("out of memory"); |
---|
4132 | |
---|
4133 | val_vec = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4134 | if (!val_vec) ghalt("out of memory"); |
---|
4135 | |
---|
4136 | inv_vec = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4137 | if (!inv_vec) ghalt("out of memory"); |
---|
4138 | |
---|
4139 | for (i = 0; i < n; i++) |
---|
4140 | q[i] = primes[i]; |
---|
4141 | |
---|
4142 | levels = 0; |
---|
4143 | while ((n >> levels) >= 16) levels++; |
---|
4144 | |
---|
4145 | vec_len = (1L << levels) - 1; |
---|
4146 | |
---|
4147 | index_vec = (long *) NTL_MALLOC((vec_len+1), sizeof(long), 0); |
---|
4148 | if (!index_vec) ghalt("out of memory"); |
---|
4149 | |
---|
4150 | prod_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4151 | if (!prod_vec) ghalt("out of memory"); |
---|
4152 | |
---|
4153 | rem_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4154 | if (!rem_vec) ghalt("out of memory"); |
---|
4155 | |
---|
4156 | coeff_vec = (_ntl_gbigint *) NTL_MALLOC(n, sizeof(_ntl_gbigint), 0); |
---|
4157 | if (!coeff_vec) ghalt("out of memory"); |
---|
4158 | |
---|
4159 | for (i = 0; i < vec_len; i++) |
---|
4160 | prod_vec[i] = 0; |
---|
4161 | |
---|
4162 | for (i = 0; i < vec_len; i++) |
---|
4163 | rem_vec[i] = 0; |
---|
4164 | |
---|
4165 | for (i = 0; i < n; i++) |
---|
4166 | coeff_vec[i] = 0; |
---|
4167 | |
---|
4168 | index_vec[0] = 0; |
---|
4169 | index_vec[1] = n; |
---|
4170 | |
---|
4171 | for (i = 0; i <= levels-2; i++) { |
---|
4172 | long start = (1L << i) - 1; |
---|
4173 | long finish = (1L << (i+1)) - 2; |
---|
4174 | for (j = finish; j >= start; j--) { |
---|
4175 | index_vec[2*j+2] = index_vec[j] + (index_vec[j+1] - index_vec[j])/2; |
---|
4176 | index_vec[2*j+1] = index_vec[j]; |
---|
4177 | } |
---|
4178 | index_vec[2*finish+3] = n; |
---|
4179 | } |
---|
4180 | |
---|
4181 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4182 | /* multiply primes index_vec[i]..index_vec[i+1]-1 into |
---|
4183 | * prod_vec[i] |
---|
4184 | */ |
---|
4185 | |
---|
4186 | _ntl_gone(&prod_vec[i]); |
---|
4187 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
4188 | _ntl_gsmul(prod_vec[i], q[j], &prod_vec[i]); |
---|
4189 | } |
---|
4190 | |
---|
4191 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4192 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
4193 | _ntl_gsdiv(prod_vec[i], q[j], &coeff_vec[j]); |
---|
4194 | } |
---|
4195 | |
---|
4196 | for (i = (1L << (levels-1)) - 2; i >= 0; i--) |
---|
4197 | _ntl_gmul(prod_vec[2*i+1], prod_vec[2*i+2], &prod_vec[i]); |
---|
4198 | |
---|
4199 | |
---|
4200 | /* the following is asymptotically the bottleneck...but it |
---|
4201 | * it probably doesn't matter. */ |
---|
4202 | |
---|
4203 | for (i = 0; i < n; i++) { |
---|
4204 | long tt; |
---|
4205 | _ntl_gsdiv(prod_vec[0], q[i], &temps[0]); |
---|
4206 | tt = mpn_mod_1(DATA(temps[0]), SIZE(temps[0]), q[i]); |
---|
4207 | inv_vec[i] = sp_inv_mod(tt, q[i]); |
---|
4208 | } |
---|
4209 | |
---|
4210 | c->strategy = 2; |
---|
4211 | C->n = n; |
---|
4212 | C->primes = q; |
---|
4213 | C->val_vec = val_vec; |
---|
4214 | C->inv_vec = inv_vec; |
---|
4215 | C->levels = levels; |
---|
4216 | C->index_vec = index_vec; |
---|
4217 | C->prod_vec = prod_vec; |
---|
4218 | C->rem_vec = rem_vec; |
---|
4219 | C->coeff_vec = coeff_vec; |
---|
4220 | |
---|
4221 | *crt_struct = (void *) c; |
---|
4222 | return; |
---|
4223 | } |
---|
4224 | |
---|
4225 | { |
---|
4226 | struct crt_body_gmp *C = &c->U.G; |
---|
4227 | long i; |
---|
4228 | c->strategy = 1; |
---|
4229 | |
---|
4230 | C->n = n; |
---|
4231 | C->v = (_ntl_gbigint *) NTL_MALLOC(n, sizeof(_ntl_gbigint), 0); |
---|
4232 | if (!C->v) ghalt("out of memory"); |
---|
4233 | |
---|
4234 | for (i = 0; i < n; i++) |
---|
4235 | C->v[i] = 0; |
---|
4236 | |
---|
4237 | C->sbuf = SIZE(p)+2; |
---|
4238 | |
---|
4239 | C->buf = 0; |
---|
4240 | _ntl_gsetlength(&C->buf, C->sbuf); |
---|
4241 | |
---|
4242 | *crt_struct = (void *) c; |
---|
4243 | return; |
---|
4244 | } |
---|
4245 | } |
---|
4246 | |
---|
4247 | void _ntl_gcrt_struct_insert(void *crt_struct, long i, _ntl_gbigint m) |
---|
4248 | { |
---|
4249 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
4250 | |
---|
4251 | switch (c->strategy) { |
---|
4252 | case 1: { |
---|
4253 | _ntl_gcopy(m, &c->U.G.v[i]); |
---|
4254 | break; |
---|
4255 | } |
---|
4256 | |
---|
4257 | default: |
---|
4258 | ghalt("_ntl_gcrt_struct_insert: inconsistent strategy"); |
---|
4259 | |
---|
4260 | } /* end switch */ |
---|
4261 | } |
---|
4262 | |
---|
4263 | |
---|
4264 | void _ntl_gcrt_struct_free(void *crt_struct) |
---|
4265 | { |
---|
4266 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
4267 | |
---|
4268 | switch (c->strategy) { |
---|
4269 | case 1: { |
---|
4270 | struct crt_body_gmp *C = &c->U.G; |
---|
4271 | long i, n; |
---|
4272 | |
---|
4273 | n = C->n; |
---|
4274 | |
---|
4275 | for (i = 0; i < n; i++) |
---|
4276 | _ntl_gfree(&C->v[i]); |
---|
4277 | |
---|
4278 | _ntl_gfree(&C->buf); |
---|
4279 | |
---|
4280 | free(C->v); |
---|
4281 | |
---|
4282 | free(c); |
---|
4283 | break; |
---|
4284 | } |
---|
4285 | |
---|
4286 | case 2: { |
---|
4287 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
4288 | long n = C->n; |
---|
4289 | long levels = C->levels; |
---|
4290 | long *primes = C->primes; |
---|
4291 | long *inv_vec = C->inv_vec; |
---|
4292 | long *val_vec = C->val_vec; |
---|
4293 | long *index_vec = C->index_vec; |
---|
4294 | _ntl_gbigint *prod_vec = C->prod_vec; |
---|
4295 | _ntl_gbigint *rem_vec = C->rem_vec; |
---|
4296 | _ntl_gbigint *coeff_vec = C->coeff_vec; |
---|
4297 | _ntl_gbigint *temps = C->temps; |
---|
4298 | _ntl_gbigint modulus = C->modulus; |
---|
4299 | long vec_len = (1L << levels) - 1; |
---|
4300 | |
---|
4301 | long i; |
---|
4302 | |
---|
4303 | for (i = 0; i < vec_len; i++) |
---|
4304 | _ntl_gfree(&prod_vec[i]); |
---|
4305 | |
---|
4306 | for (i = 0; i < vec_len; i++) |
---|
4307 | _ntl_gfree(&rem_vec[i]); |
---|
4308 | |
---|
4309 | for (i = 0; i < n; i++) |
---|
4310 | _ntl_gfree(&coeff_vec[i]); |
---|
4311 | |
---|
4312 | _ntl_gfree(&temps[0]); |
---|
4313 | _ntl_gfree(&temps[1]); |
---|
4314 | |
---|
4315 | _ntl_gfree(&modulus); |
---|
4316 | |
---|
4317 | free(primes); |
---|
4318 | free(inv_vec); |
---|
4319 | free(val_vec); |
---|
4320 | free(index_vec); |
---|
4321 | free(prod_vec); |
---|
4322 | free(rem_vec); |
---|
4323 | free(coeff_vec); |
---|
4324 | |
---|
4325 | free(c); |
---|
4326 | break; |
---|
4327 | } |
---|
4328 | |
---|
4329 | default: |
---|
4330 | |
---|
4331 | ghalt("_ntl_gcrt_struct_free: inconsistent strategy"); |
---|
4332 | |
---|
4333 | } /* end case */ |
---|
4334 | } |
---|
4335 | |
---|
4336 | static |
---|
4337 | void gadd_mul_many(_ntl_gbigint *res, _ntl_gbigint *a, long *b, |
---|
4338 | long n, long sz) |
---|
4339 | |
---|
4340 | { |
---|
4341 | mp_limb_t *xx, *yy; |
---|
4342 | long i, sx; |
---|
4343 | long sy; |
---|
4344 | mp_limb_t carry; |
---|
4345 | |
---|
4346 | sx = sz + 2; |
---|
4347 | if (MustAlloc(*res, sx)) |
---|
4348 | _ntl_gsetlength(res, sx); |
---|
4349 | |
---|
4350 | xx = DATA(*res); |
---|
4351 | |
---|
4352 | for (i = 0; i < sx; i++) |
---|
4353 | xx[i] = 0; |
---|
4354 | |
---|
4355 | for (i = 0; i < n; i++) { |
---|
4356 | if (!a[i]) continue; |
---|
4357 | |
---|
4358 | yy = DATA(a[i]); |
---|
4359 | sy = SIZE(a[i]); |
---|
4360 | |
---|
4361 | if (!sy || !b[i]) continue; |
---|
4362 | |
---|
4363 | carry = mpn_addmul_1(xx, yy, sy, b[i]); |
---|
4364 | yy = xx + sy; |
---|
4365 | *yy += carry; |
---|
4366 | |
---|
4367 | if (*yy < carry) { /* unsigned comparison! */ |
---|
4368 | do { |
---|
4369 | yy++; |
---|
4370 | *yy += 1; |
---|
4371 | } while (*yy == 0); |
---|
4372 | } |
---|
4373 | } |
---|
4374 | |
---|
4375 | while (sx > 0 && xx[sx-1] == 0) sx--; |
---|
4376 | SIZE(*res) = sx; |
---|
4377 | } |
---|
4378 | |
---|
4379 | void _ntl_gcrt_struct_eval(void *crt_struct, _ntl_gbigint *x, const long *b) |
---|
4380 | { |
---|
4381 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
4382 | |
---|
4383 | switch (c->strategy) { |
---|
4384 | |
---|
4385 | case 1: { |
---|
4386 | struct crt_body_gmp *C = &c->U.G; |
---|
4387 | |
---|
4388 | mp_limb_t *xx, *yy; |
---|
4389 | _ntl_gbigint *a; |
---|
4390 | long i, sx, n; |
---|
4391 | long sy; |
---|
4392 | mp_limb_t carry; |
---|
4393 | |
---|
4394 | n = C->n; |
---|
4395 | sx = C->sbuf; |
---|
4396 | |
---|
4397 | xx = DATA(C->buf); |
---|
4398 | |
---|
4399 | for (i = 0; i < sx; i++) |
---|
4400 | xx[i] = 0; |
---|
4401 | |
---|
4402 | a = C->v; |
---|
4403 | |
---|
4404 | for (i = 0; i < n; i++) { |
---|
4405 | if (!a[i]) continue; |
---|
4406 | |
---|
4407 | yy = DATA(a[i]); |
---|
4408 | sy = SIZE(a[i]); |
---|
4409 | |
---|
4410 | if (!sy || !b[i]) continue; |
---|
4411 | |
---|
4412 | carry = mpn_addmul_1(xx, yy, sy, b[i]); |
---|
4413 | yy = xx + sy; |
---|
4414 | *yy += carry; |
---|
4415 | |
---|
4416 | if (*yy < carry) { /* unsigned comparison! */ |
---|
4417 | do { |
---|
4418 | yy++; |
---|
4419 | *yy += 1; |
---|
4420 | } while (*yy == 0); |
---|
4421 | } |
---|
4422 | } |
---|
4423 | |
---|
4424 | while (sx > 0 && xx[sx-1] == 0) sx--; |
---|
4425 | SIZE(C->buf) = sx; |
---|
4426 | _ntl_gcopy(C->buf, x); |
---|
4427 | break; |
---|
4428 | } |
---|
4429 | |
---|
4430 | case 2: { |
---|
4431 | struct crt_body_gmp1 *C = &c->U.G1; |
---|
4432 | |
---|
4433 | long n = C->n; |
---|
4434 | long levels = C->levels; |
---|
4435 | long *primes = C->primes; |
---|
4436 | long *inv_vec = C->inv_vec; |
---|
4437 | long *val_vec = C->val_vec; |
---|
4438 | long *index_vec = C->index_vec; |
---|
4439 | _ntl_gbigint *prod_vec = C->prod_vec; |
---|
4440 | _ntl_gbigint *rem_vec = C->rem_vec; |
---|
4441 | _ntl_gbigint *coeff_vec = C->coeff_vec; |
---|
4442 | _ntl_gbigint *temps = C->temps; |
---|
4443 | long vec_len = (1L << levels) - 1; |
---|
4444 | |
---|
4445 | long i, j; |
---|
4446 | |
---|
4447 | for (i = 0; i < n; i++) { |
---|
4448 | SP_MUL_MOD(val_vec[i], b[i], inv_vec[i], primes[i]); |
---|
4449 | } |
---|
4450 | |
---|
4451 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4452 | long j1 = index_vec[i]; |
---|
4453 | long j2 = index_vec[i+1]; |
---|
4454 | gadd_mul_many(&rem_vec[i], &coeff_vec[j1], &val_vec[j1], j2-j1, |
---|
4455 | SIZE(prod_vec[i])); |
---|
4456 | } |
---|
4457 | |
---|
4458 | for (i = (1L << (levels-1)) - 2; i >= 0; i--) { |
---|
4459 | _ntl_gmul(prod_vec[2*i+1], rem_vec[2*i+2], &temps[0]); |
---|
4460 | _ntl_gmul(rem_vec[2*i+1], prod_vec[2*i+2], &temps[1]); |
---|
4461 | _ntl_gadd(temps[0], temps[1], &rem_vec[i]); |
---|
4462 | } |
---|
4463 | |
---|
4464 | /* temps[0] = rem_vec[0] mod prod_vec[0] (least absolute residue) */ |
---|
4465 | _ntl_gmod(rem_vec[0], prod_vec[0], &temps[0]); |
---|
4466 | _ntl_gsub(temps[0], prod_vec[0], &temps[1]); |
---|
4467 | _ntl_gnegate(&temps[1]); |
---|
4468 | if (_ntl_gcompare(temps[0], temps[1]) > 0) { |
---|
4469 | _ntl_gnegate(&temps[1]); |
---|
4470 | _ntl_gcopy(temps[1], &temps[0]); |
---|
4471 | } |
---|
4472 | |
---|
4473 | _ntl_gmod(temps[0], C->modulus, &temps[1]); |
---|
4474 | _ntl_gcopy(temps[1], x); |
---|
4475 | |
---|
4476 | break; |
---|
4477 | } |
---|
4478 | |
---|
4479 | default: |
---|
4480 | |
---|
4481 | ghalt("_crt_gstruct_eval: inconsistent strategy"); |
---|
4482 | |
---|
4483 | } /* end case */ |
---|
4484 | |
---|
4485 | } |
---|
4486 | |
---|
4487 | |
---|
4488 | long _ntl_gcrt_struct_special(void *crt_struct) |
---|
4489 | { |
---|
4490 | struct crt_body *c = (struct crt_body *) crt_struct; |
---|
4491 | return (c->strategy == 2); |
---|
4492 | } |
---|
4493 | |
---|
4494 | |
---|
4495 | struct rem_body_lip { |
---|
4496 | long n; |
---|
4497 | long *primes; |
---|
4498 | }; |
---|
4499 | |
---|
4500 | struct rem_body_gmp { |
---|
4501 | long n; |
---|
4502 | long levels; |
---|
4503 | long *primes; |
---|
4504 | long *index_vec; |
---|
4505 | _ntl_gbigint *prod_vec; |
---|
4506 | _ntl_gbigint *rem_vec; |
---|
4507 | }; |
---|
4508 | |
---|
4509 | |
---|
4510 | struct rem_body_gmp1 { |
---|
4511 | long n; |
---|
4512 | long levels; |
---|
4513 | long *primes; |
---|
4514 | long *index_vec; |
---|
4515 | long *len_vec; |
---|
4516 | mp_limb_t *inv_vec; |
---|
4517 | long *corr_vec; |
---|
4518 | double *corraux_vec; |
---|
4519 | _ntl_gbigint *prod_vec; |
---|
4520 | _ntl_gbigint *rem_vec; |
---|
4521 | }; |
---|
4522 | |
---|
4523 | |
---|
4524 | struct rem_body { |
---|
4525 | long strategy; |
---|
4526 | |
---|
4527 | union { |
---|
4528 | struct rem_body_lip L; |
---|
4529 | struct rem_body_gmp G; |
---|
4530 | struct rem_body_gmp1 G1; |
---|
4531 | } U; |
---|
4532 | }; |
---|
4533 | |
---|
4534 | |
---|
4535 | |
---|
4536 | |
---|
4537 | void _ntl_grem_struct_init(void **rem_struct, long n, _ntl_gbigint modulus, |
---|
4538 | const long *p) |
---|
4539 | { |
---|
4540 | struct rem_body *r; |
---|
4541 | |
---|
4542 | r = (struct rem_body *) NTL_MALLOC(1, sizeof(struct rem_body), 0); |
---|
4543 | if (!r) ghalt("out of memory"); |
---|
4544 | |
---|
4545 | if (n >= 32 && n <= 256) { |
---|
4546 | struct rem_body_gmp1 *R = &r->U.G1; |
---|
4547 | |
---|
4548 | long *q; |
---|
4549 | long i, j; |
---|
4550 | long levels, vec_len; |
---|
4551 | long *index_vec; |
---|
4552 | long *len_vec, *corr_vec; |
---|
4553 | double *corraux_vec; |
---|
4554 | mp_limb_t *inv_vec; |
---|
4555 | _ntl_gbigint *prod_vec, *rem_vec; |
---|
4556 | |
---|
4557 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4558 | if (!q) ghalt("out of memory"); |
---|
4559 | |
---|
4560 | for (i = 0; i < n; i++) |
---|
4561 | q[i] = p[i]; |
---|
4562 | |
---|
4563 | levels = 0; |
---|
4564 | while ((n >> levels) >= 4) levels++; |
---|
4565 | |
---|
4566 | vec_len = (1L << levels) - 1; |
---|
4567 | |
---|
4568 | index_vec = (long *) NTL_MALLOC((vec_len+1), sizeof(long), 0); |
---|
4569 | if (!index_vec) ghalt("out of memory"); |
---|
4570 | |
---|
4571 | len_vec = (long *) NTL_MALLOC(vec_len, sizeof(long), 0); |
---|
4572 | if (!len_vec) ghalt("out of memory"); |
---|
4573 | |
---|
4574 | inv_vec = (mp_limb_t *) NTL_MALLOC(vec_len, sizeof(mp_limb_t), 0); |
---|
4575 | if (!inv_vec) ghalt("out of memory"); |
---|
4576 | |
---|
4577 | corr_vec = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4578 | if (!corr_vec) ghalt("out of memory"); |
---|
4579 | |
---|
4580 | corraux_vec = (double *) NTL_MALLOC(n, sizeof(double), 0); |
---|
4581 | if (!corraux_vec) ghalt("out of memory"); |
---|
4582 | |
---|
4583 | prod_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4584 | if (!prod_vec) ghalt("out of memory"); |
---|
4585 | |
---|
4586 | rem_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4587 | if (!rem_vec) ghalt("out of memory"); |
---|
4588 | |
---|
4589 | for (i = 0; i < vec_len; i++) |
---|
4590 | prod_vec[i] = 0; |
---|
4591 | |
---|
4592 | for (i = 0; i < vec_len; i++) |
---|
4593 | rem_vec[i] = 0; |
---|
4594 | |
---|
4595 | index_vec[0] = 0; |
---|
4596 | index_vec[1] = n; |
---|
4597 | |
---|
4598 | for (i = 0; i <= levels-2; i++) { |
---|
4599 | long start = (1L << i) - 1; |
---|
4600 | long finish = (1L << (i+1)) - 2; |
---|
4601 | for (j = finish; j >= start; j--) { |
---|
4602 | index_vec[2*j+2] = index_vec[j] + (index_vec[j+1] - index_vec[j])/2; |
---|
4603 | index_vec[2*j+1] = index_vec[j]; |
---|
4604 | } |
---|
4605 | index_vec[2*finish+3] = n; |
---|
4606 | } |
---|
4607 | |
---|
4608 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4609 | /* multiply primes index_vec[i]..index_vec[i+1]-1 into |
---|
4610 | * prod_vec[i] |
---|
4611 | */ |
---|
4612 | |
---|
4613 | _ntl_gone(&prod_vec[i]); |
---|
4614 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
4615 | _ntl_gsmul(prod_vec[i], q[j], &prod_vec[i]); |
---|
4616 | } |
---|
4617 | |
---|
4618 | for (i = (1L << (levels-1)) - 2; i >= 3; i--) |
---|
4619 | _ntl_gmul(prod_vec[2*i+1], prod_vec[2*i+2], &prod_vec[i]); |
---|
4620 | |
---|
4621 | |
---|
4622 | for (i = 3; i < vec_len; i++) |
---|
4623 | len_vec[i] = _ntl_gsize(prod_vec[i]); |
---|
4624 | |
---|
4625 | /* Set len_vec[1] = len_vec[2] = |
---|
4626 | * max(_ntl_gsize(modulus), len_vec[3..6]). |
---|
4627 | * This is a bit paranoid, but it makes the code |
---|
4628 | * more robust. */ |
---|
4629 | |
---|
4630 | j = _ntl_gsize(modulus); |
---|
4631 | for (i = 3; i <= 6; i++) |
---|
4632 | if (len_vec[i] > j) j = len_vec[i]; |
---|
4633 | |
---|
4634 | len_vec[1] = len_vec[2] = j; |
---|
4635 | |
---|
4636 | for (i = 3; i < vec_len; i++) |
---|
4637 | inv_vec[i] = neg_inv_mod_limb(DATA(prod_vec[i])[0]); |
---|
4638 | |
---|
4639 | |
---|
4640 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4641 | for (j = index_vec[i]; j < index_vec[i+1]; j++) { |
---|
4642 | corr_vec[j] = SpecialPower(len_vec[1] - len_vec[i], q[j]); |
---|
4643 | corraux_vec[j] = ((double) corr_vec[j])/((double) q[j]); |
---|
4644 | } |
---|
4645 | } |
---|
4646 | |
---|
4647 | |
---|
4648 | /* allocate length in advance to streamline eval code */ |
---|
4649 | |
---|
4650 | _ntl_gsetlength(&rem_vec[0], len_vec[1]); /* a special temp */ |
---|
4651 | |
---|
4652 | for (i = 1; i < vec_len; i++) |
---|
4653 | _ntl_gsetlength(&rem_vec[i], len_vec[i]); |
---|
4654 | |
---|
4655 | |
---|
4656 | |
---|
4657 | |
---|
4658 | r->strategy = 2; |
---|
4659 | R->n = n; |
---|
4660 | R->primes = q; |
---|
4661 | R->levels = levels; |
---|
4662 | R->index_vec = index_vec; |
---|
4663 | R->len_vec = len_vec; |
---|
4664 | R->inv_vec = inv_vec; |
---|
4665 | R->corr_vec = corr_vec; |
---|
4666 | R->corraux_vec = corraux_vec; |
---|
4667 | R->prod_vec = prod_vec; |
---|
4668 | R->rem_vec = rem_vec; |
---|
4669 | |
---|
4670 | *rem_struct = (void *) r; |
---|
4671 | } |
---|
4672 | else if (n >= 32) { |
---|
4673 | struct rem_body_gmp *R = &r->U.G; |
---|
4674 | |
---|
4675 | long *q; |
---|
4676 | long i, j; |
---|
4677 | long levels, vec_len; |
---|
4678 | long *index_vec; |
---|
4679 | _ntl_gbigint *prod_vec, *rem_vec; |
---|
4680 | |
---|
4681 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4682 | if (!q) ghalt("out of memory"); |
---|
4683 | |
---|
4684 | for (i = 0; i < n; i++) |
---|
4685 | q[i] = p[i]; |
---|
4686 | |
---|
4687 | levels = 0; |
---|
4688 | while ((n >> levels) >= 4) levels++; |
---|
4689 | |
---|
4690 | vec_len = (1L << levels) - 1; |
---|
4691 | |
---|
4692 | index_vec = (long *) NTL_MALLOC((vec_len+1), sizeof(long), 0); |
---|
4693 | if (!index_vec) ghalt("out of memory"); |
---|
4694 | |
---|
4695 | prod_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4696 | if (!prod_vec) ghalt("out of memory"); |
---|
4697 | |
---|
4698 | rem_vec = (_ntl_gbigint *) NTL_MALLOC(vec_len, sizeof(_ntl_gbigint), 0); |
---|
4699 | if (!rem_vec) ghalt("out of memory"); |
---|
4700 | |
---|
4701 | for (i = 0; i < vec_len; i++) |
---|
4702 | prod_vec[i] = 0; |
---|
4703 | |
---|
4704 | for (i = 0; i < vec_len; i++) |
---|
4705 | rem_vec[i] = 0; |
---|
4706 | |
---|
4707 | index_vec[0] = 0; |
---|
4708 | index_vec[1] = n; |
---|
4709 | |
---|
4710 | for (i = 0; i <= levels-2; i++) { |
---|
4711 | long start = (1L << i) - 1; |
---|
4712 | long finish = (1L << (i+1)) - 2; |
---|
4713 | for (j = finish; j >= start; j--) { |
---|
4714 | index_vec[2*j+2] = index_vec[j] + (index_vec[j+1] - index_vec[j])/2; |
---|
4715 | index_vec[2*j+1] = index_vec[j]; |
---|
4716 | } |
---|
4717 | index_vec[2*finish+3] = n; |
---|
4718 | } |
---|
4719 | |
---|
4720 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4721 | /* multiply primes index_vec[i]..index_vec[i+1]-1 into |
---|
4722 | * prod_vec[i] |
---|
4723 | */ |
---|
4724 | |
---|
4725 | _ntl_gone(&prod_vec[i]); |
---|
4726 | for (j = index_vec[i]; j < index_vec[i+1]; j++) |
---|
4727 | _ntl_gsmul(prod_vec[i], q[j], &prod_vec[i]); |
---|
4728 | } |
---|
4729 | |
---|
4730 | for (i = (1L << (levels-1)) - 2; i >= 3; i--) |
---|
4731 | _ntl_gmul(prod_vec[2*i+1], prod_vec[2*i+2], &prod_vec[i]); |
---|
4732 | |
---|
4733 | |
---|
4734 | /* allocate length in advance to streamline eval code */ |
---|
4735 | |
---|
4736 | _ntl_gsetlength(&rem_vec[1], _ntl_gsize(modulus)); |
---|
4737 | _ntl_gsetlength(&rem_vec[2], _ntl_gsize(modulus)); |
---|
4738 | |
---|
4739 | for (i = 1; i < (1L << (levels-1)) - 1; i++) { |
---|
4740 | _ntl_gsetlength(&rem_vec[2*i+1], _ntl_gsize(prod_vec[2*i+1])); |
---|
4741 | _ntl_gsetlength(&rem_vec[2*i+2], _ntl_gsize(prod_vec[2*i+2])); |
---|
4742 | } |
---|
4743 | |
---|
4744 | r->strategy = 1; |
---|
4745 | R->n = n; |
---|
4746 | R->primes = q; |
---|
4747 | R->levels = levels; |
---|
4748 | R->index_vec = index_vec; |
---|
4749 | R->prod_vec = prod_vec; |
---|
4750 | R->rem_vec = rem_vec; |
---|
4751 | |
---|
4752 | *rem_struct = (void *) r; |
---|
4753 | } |
---|
4754 | else |
---|
4755 | { |
---|
4756 | struct rem_body_lip *R = &r->U.L; |
---|
4757 | |
---|
4758 | long *q; |
---|
4759 | long i; |
---|
4760 | |
---|
4761 | r->strategy = 0; |
---|
4762 | R->n = n; |
---|
4763 | q = (long *) NTL_MALLOC(n, sizeof(long), 0); |
---|
4764 | if (!q) ghalt("out of memory"); |
---|
4765 | R->primes = q; |
---|
4766 | |
---|
4767 | for (i = 0; i < n; i++) |
---|
4768 | q[i] = p[i]; |
---|
4769 | |
---|
4770 | *rem_struct = (void *) r; |
---|
4771 | } |
---|
4772 | |
---|
4773 | } |
---|
4774 | |
---|
4775 | |
---|
4776 | |
---|
4777 | void _ntl_grem_struct_free(void *rem_struct) |
---|
4778 | { |
---|
4779 | struct rem_body *r = (struct rem_body *) rem_struct; |
---|
4780 | |
---|
4781 | switch (r->strategy) { |
---|
4782 | |
---|
4783 | case 0: { |
---|
4784 | free(r->U.L.primes); |
---|
4785 | free(r); |
---|
4786 | break; |
---|
4787 | } |
---|
4788 | |
---|
4789 | case 1: { |
---|
4790 | struct rem_body_gmp *R = &r->U.G; |
---|
4791 | |
---|
4792 | long levels = R->levels; |
---|
4793 | long vec_len = (1L << levels) - 1; |
---|
4794 | long i; |
---|
4795 | |
---|
4796 | for (i = 0; i < vec_len; i++) |
---|
4797 | _ntl_gfree(&R->prod_vec[i]); |
---|
4798 | |
---|
4799 | for (i = 0; i < vec_len; i++) |
---|
4800 | _ntl_gfree(&R->rem_vec[i]); |
---|
4801 | |
---|
4802 | free(R->primes); |
---|
4803 | free(R->index_vec); |
---|
4804 | free(R->prod_vec); |
---|
4805 | free(R->rem_vec); |
---|
4806 | free(r); |
---|
4807 | break; |
---|
4808 | } |
---|
4809 | |
---|
4810 | case 2: { |
---|
4811 | struct rem_body_gmp1 *R = &r->U.G1; |
---|
4812 | |
---|
4813 | long levels = R->levels; |
---|
4814 | long vec_len = (1L << levels) - 1; |
---|
4815 | long i; |
---|
4816 | |
---|
4817 | for (i = 0; i < vec_len; i++) |
---|
4818 | _ntl_gfree(&R->prod_vec[i]); |
---|
4819 | |
---|
4820 | for (i = 0; i < vec_len; i++) |
---|
4821 | _ntl_gfree(&R->rem_vec[i]); |
---|
4822 | |
---|
4823 | free(R->primes); |
---|
4824 | free(R->index_vec); |
---|
4825 | free(R->len_vec); |
---|
4826 | free(R->corr_vec); |
---|
4827 | free(R->inv_vec); |
---|
4828 | free(R->corraux_vec); |
---|
4829 | free(R->prod_vec); |
---|
4830 | free(R->rem_vec); |
---|
4831 | free(r); |
---|
4832 | break; |
---|
4833 | } |
---|
4834 | |
---|
4835 | |
---|
4836 | default: |
---|
4837 | ghalt("_ntl_grem_struct_free: inconsistent strategy"); |
---|
4838 | |
---|
4839 | } /* end switch */ |
---|
4840 | } |
---|
4841 | |
---|
4842 | |
---|
4843 | |
---|
4844 | |
---|
4845 | void _ntl_grem_struct_eval(void *rem_struct, long *x, _ntl_gbigint a) |
---|
4846 | { |
---|
4847 | struct rem_body *r = (struct rem_body *) rem_struct; |
---|
4848 | |
---|
4849 | switch (r->strategy) { |
---|
4850 | |
---|
4851 | case 0: { |
---|
4852 | struct rem_body_lip *R = &r->U.L; |
---|
4853 | long n = R->n; |
---|
4854 | long *q = R->primes; |
---|
4855 | |
---|
4856 | long j; |
---|
4857 | mp_limb_t *adata; |
---|
4858 | long sa; |
---|
4859 | |
---|
4860 | if (!a) |
---|
4861 | sa = 0; |
---|
4862 | else |
---|
4863 | sa = SIZE(a); |
---|
4864 | |
---|
4865 | if (sa == 0) { |
---|
4866 | for (j = 0; j < n; j++) |
---|
4867 | x[j] = 0; |
---|
4868 | |
---|
4869 | break; |
---|
4870 | } |
---|
4871 | |
---|
4872 | adata = DATA(a); |
---|
4873 | |
---|
4874 | for (j = 0; j < n; j++) |
---|
4875 | x[j] = mpn_mod_1(adata, sa, q[j]); |
---|
4876 | |
---|
4877 | break; |
---|
4878 | } |
---|
4879 | |
---|
4880 | case 1: { |
---|
4881 | struct rem_body_gmp *R = &r->U.G; |
---|
4882 | |
---|
4883 | long n = R->n; |
---|
4884 | long levels = R->levels; |
---|
4885 | long *q = R->primes; |
---|
4886 | long *index_vec = R->index_vec; |
---|
4887 | _ntl_gbigint *prod_vec = R->prod_vec; |
---|
4888 | _ntl_gbigint *rem_vec = R->rem_vec; |
---|
4889 | long vec_len = (1L << levels) - 1; |
---|
4890 | |
---|
4891 | long i, j; |
---|
4892 | |
---|
4893 | if (ZEROP(a)) { |
---|
4894 | for (j = 0; j < n; j++) |
---|
4895 | x[j] = 0; |
---|
4896 | |
---|
4897 | break; |
---|
4898 | } |
---|
4899 | |
---|
4900 | _ntl_gcopy(a, &rem_vec[1]); |
---|
4901 | _ntl_gcopy(a, &rem_vec[2]); |
---|
4902 | |
---|
4903 | for (i = 1; i < (1L << (levels-1)) - 1; i++) { |
---|
4904 | gmod_simple(rem_vec[i], prod_vec[2*i+1], &rem_vec[2*i+1]); |
---|
4905 | gmod_simple(rem_vec[i], prod_vec[2*i+2], &rem_vec[2*i+2]); |
---|
4906 | } |
---|
4907 | |
---|
4908 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4909 | long lo = index_vec[i]; |
---|
4910 | long hi = index_vec[i+1]; |
---|
4911 | mp_limb_t *s1p = DATA(rem_vec[i]); |
---|
4912 | long s1size = SIZE(rem_vec[i]); |
---|
4913 | if (s1size == 0) { |
---|
4914 | for (j = lo; j <hi; j++) |
---|
4915 | x[j] = 0; |
---|
4916 | } |
---|
4917 | else { |
---|
4918 | for (j = lo; j < hi; j++) |
---|
4919 | x[j] = mpn_mod_1(s1p, s1size, q[j]); |
---|
4920 | } |
---|
4921 | } |
---|
4922 | |
---|
4923 | break; |
---|
4924 | } |
---|
4925 | |
---|
4926 | case 2: { |
---|
4927 | struct rem_body_gmp1 *R = &r->U.G1; |
---|
4928 | |
---|
4929 | long n = R->n; |
---|
4930 | long levels = R->levels; |
---|
4931 | long *q = R->primes; |
---|
4932 | long *index_vec = R->index_vec; |
---|
4933 | long *len_vec = R->len_vec; |
---|
4934 | long *corr_vec = R->corr_vec; |
---|
4935 | double *corraux_vec = R->corraux_vec; |
---|
4936 | mp_limb_t *inv_vec = R->inv_vec; |
---|
4937 | _ntl_gbigint *prod_vec = R->prod_vec; |
---|
4938 | _ntl_gbigint *rem_vec = R->rem_vec; |
---|
4939 | long vec_len = (1L << levels) - 1; |
---|
4940 | |
---|
4941 | long i, j; |
---|
4942 | |
---|
4943 | if (ZEROP(a)) { |
---|
4944 | for (j = 0; j < n; j++) |
---|
4945 | x[j] = 0; |
---|
4946 | |
---|
4947 | break; |
---|
4948 | } |
---|
4949 | |
---|
4950 | _ntl_gcopy(a, &rem_vec[1]); |
---|
4951 | _ntl_gcopy(a, &rem_vec[2]); |
---|
4952 | |
---|
4953 | for (i = 1; i < (1L << (levels-1)) - 1; i++) { |
---|
4954 | _ntl_gcopy(rem_vec[i], &rem_vec[0]); |
---|
4955 | redc(rem_vec[0], prod_vec[2*i+1], len_vec[i]-len_vec[2*i+1], |
---|
4956 | inv_vec[2*i+1], rem_vec[2*i+1]); |
---|
4957 | redc(rem_vec[i], prod_vec[2*i+2], len_vec[i]-len_vec[2*i+2], |
---|
4958 | inv_vec[2*i+2], rem_vec[2*i+2]); |
---|
4959 | } |
---|
4960 | |
---|
4961 | for (i = (1L << (levels-1)) - 1; i < vec_len; i++) { |
---|
4962 | long lo = index_vec[i]; |
---|
4963 | long hi = index_vec[i+1]; |
---|
4964 | mp_limb_t *s1p = DATA(rem_vec[i]); |
---|
4965 | long s1size = SIZE(rem_vec[i]); |
---|
4966 | if (s1size == 0) { |
---|
4967 | for (j = lo; j <hi; j++) |
---|
4968 | x[j] = 0; |
---|
4969 | } |
---|
4970 | else { |
---|
4971 | for (j = lo; j < hi; j++) { |
---|
4972 | long t = mpn_mod_1(s1p, s1size, q[j]); |
---|
4973 | SP_MUL_MOD2(x[j], t, corr_vec[j], q[j], corraux_vec[j]); |
---|
4974 | } |
---|
4975 | } |
---|
4976 | } |
---|
4977 | |
---|
4978 | break; |
---|
4979 | } |
---|
4980 | |
---|
4981 | default: |
---|
4982 | ghalt("_ntl_grem_struct_eval: inconsistent strategy"); |
---|
4983 | |
---|
4984 | |
---|
4985 | } /* end switch */ |
---|
4986 | |
---|
4987 | |
---|
4988 | } |
---|
4989 | |
---|
4990 | |
---|