1 | /* crypto/bn/bn_lcl.h */
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2 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
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3 | * All rights reserved.
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4 | *
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5 | * This package is an SSL implementation written
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6 | * by Eric Young (eay@cryptsoft.com).
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7 | * The implementation was written so as to conform with Netscapes SSL.
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8 | *
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9 | * This library is free for commercial and non-commercial use as long as
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10 | * the following conditions are aheared to. The following conditions
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11 | * apply to all code found in this distribution, be it the RC4, RSA,
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12 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation
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13 | * included with this distribution is covered by the same copyright terms
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14 | * except that the holder is Tim Hudson (tjh@cryptsoft.com).
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15 | *
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16 | * Copyright remains Eric Young's, and as such any Copyright notices in
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17 | * the code are not to be removed.
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18 | * If this package is used in a product, Eric Young should be given attribution
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19 | * as the author of the parts of the library used.
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20 | * This can be in the form of a textual message at program startup or
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21 | * in documentation (online or textual) provided with the package.
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22 | *
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23 | * Redistribution and use in source and binary forms, with or without
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24 | * modification, are permitted provided that the following conditions
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25 | * are met:
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26 | * 1. Redistributions of source code must retain the copyright
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27 | * notice, this list of conditions and the following disclaimer.
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28 | * 2. Redistributions in binary form must reproduce the above copyright
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29 | * notice, this list of conditions and the following disclaimer in the
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30 | * documentation and/or other materials provided with the distribution.
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31 | * 3. All advertising materials mentioning features or use of this software
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32 | * must display the following acknowledgement:
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33 | * "This product includes cryptographic software written by
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34 | * Eric Young (eay@cryptsoft.com)"
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35 | * The word 'cryptographic' can be left out if the rouines from the library
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36 | * being used are not cryptographic related :-).
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37 | * 4. If you include any Windows specific code (or a derivative thereof) from
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38 | * the apps directory (application code) you must include an acknowledgement:
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39 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
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40 | *
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41 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
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42 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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43 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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44 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
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45 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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46 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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47 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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48 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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49 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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50 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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51 | * SUCH DAMAGE.
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52 | *
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53 | * The licence and distribution terms for any publically available version or
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54 | * derivative of this code cannot be changed. i.e. this code cannot simply be
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55 | * copied and put under another distribution licence
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56 | * [including the GNU Public Licence.]
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57 | */
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58 | /* ====================================================================
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59 | * Copyright (c) 1998-2000 The OpenSSL Project. All rights reserved.
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60 | *
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61 | * Redistribution and use in source and binary forms, with or without
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62 | * modification, are permitted provided that the following conditions
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63 | * are met:
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64 | *
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65 | * 1. Redistributions of source code must retain the above copyright
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66 | * notice, this list of conditions and the following disclaimer.
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67 | *
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68 | * 2. Redistributions in binary form must reproduce the above copyright
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69 | * notice, this list of conditions and the following disclaimer in
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70 | * the documentation and/or other materials provided with the
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71 | * distribution.
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72 | *
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73 | * 3. All advertising materials mentioning features or use of this
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74 | * software must display the following acknowledgment:
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75 | * "This product includes software developed by the OpenSSL Project
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76 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)"
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77 | *
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78 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to
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79 | * endorse or promote products derived from this software without
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80 | * prior written permission. For written permission, please contact
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81 | * openssl-core@openssl.org.
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82 | *
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83 | * 5. Products derived from this software may not be called "OpenSSL"
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84 | * nor may "OpenSSL" appear in their names without prior written
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85 | * permission of the OpenSSL Project.
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86 | *
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87 | * 6. Redistributions of any form whatsoever must retain the following
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88 | * acknowledgment:
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89 | * "This product includes software developed by the OpenSSL Project
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90 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)"
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91 | *
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92 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY
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93 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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94 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
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95 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR
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96 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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97 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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98 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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99 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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100 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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101 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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102 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED
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103 | * OF THE POSSIBILITY OF SUCH DAMAGE.
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104 | * ====================================================================
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105 | *
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106 | * This product includes cryptographic software written by Eric Young
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107 | * (eay@cryptsoft.com). This product includes software written by Tim
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108 | * Hudson (tjh@cryptsoft.com).
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109 | *
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110 | */
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111 |
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112 | #ifndef HEADER_BN_LCL_H
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113 | #define HEADER_BN_LCL_H
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114 |
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115 | #include "bn.h"
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116 |
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117 | #ifdef __cplusplus
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118 | extern "C" {
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119 | #endif
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120 |
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121 |
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122 | /*
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123 | * BN_window_bits_for_exponent_size -- macro for sliding window mod_exp functions
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124 | *
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125 | *
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126 | * For window size 'w' (w >= 2) and a random 'b' bits exponent,
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127 | * the number of multiplications is a constant plus on average
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128 | *
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129 | * 2^(w-1) + (b-w)/(w+1);
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130 | *
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131 | * here 2^(w-1) is for precomputing the table (we actually need
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132 | * entries only for windows that have the lowest bit set), and
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133 | * (b-w)/(w+1) is an approximation for the expected number of
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134 | * w-bit windows, not counting the first one.
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135 | *
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136 | * Thus we should use
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137 | *
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138 | * w >= 6 if b > 671
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139 | * w = 5 if 671 > b > 239
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140 | * w = 4 if 239 > b > 79
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141 | * w = 3 if 79 > b > 23
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142 | * w <= 2 if 23 > b
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143 | *
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144 | * (with draws in between). Very small exponents are often selected
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145 | * with low Hamming weight, so we use w = 1 for b <= 23.
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146 | */
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147 | #if 1
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148 | #define BN_window_bits_for_exponent_size(b) \
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149 | ((b) > 671 ? 6 : \
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150 | (b) > 239 ? 5 : \
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151 | (b) > 79 ? 4 : \
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152 | (b) > 23 ? 3 : 1)
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153 | #else
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154 | /* Old SSLeay/OpenSSL table.
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155 | * Maximum window size was 5, so this table differs for b==1024;
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156 | * but it coincides for other interesting values (b==160, b==512).
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157 | */
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158 | #define BN_window_bits_for_exponent_size(b) \
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159 | ((b) > 255 ? 5 : \
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160 | (b) > 127 ? 4 : \
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161 | (b) > 17 ? 3 : 1)
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162 | #endif
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163 |
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164 |
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165 |
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166 | /* Pentium pro 16,16,16,32,64 */
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167 | /* Alpha 16,16,16,16.64 */
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168 | #define BN_MULL_SIZE_NORMAL (16) /* 32 */
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169 | #define BN_MUL_RECURSIVE_SIZE_NORMAL (16) /* 32 less than */
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170 | #define BN_SQR_RECURSIVE_SIZE_NORMAL (16) /* 32 */
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171 | #define BN_MUL_LOW_RECURSIVE_SIZE_NORMAL (32) /* 32 */
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172 | #define BN_MONT_CTX_SET_SIZE_WORD (64) /* 32 */
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173 |
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174 | #if !defined(NO_ASM) && !defined(NO_INLINE_ASM) && !defined(PEDANTIC)
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175 | /*
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176 | * BN_UMULT_HIGH section.
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177 | *
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178 | * No, I'm not trying to overwhelm you when stating that the
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179 | * product of N-bit numbers is 2*N bits wide:-) No, I don't expect
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180 | * you to be impressed when I say that if the compiler doesn't
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181 | * support 2*N integer type, then you have to replace every N*N
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182 | * multiplication with 4 (N/2)*(N/2) accompanied by some shifts
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183 | * and additions which unavoidably results in severe performance
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184 | * penalties. Of course provided that the hardware is capable of
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185 | * producing 2*N result... That's when you normally start
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186 | * considering assembler implementation. However! It should be
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187 | * pointed out that some CPUs (most notably Alpha, PowerPC and
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188 | * upcoming IA-64 family:-) provide *separate* instruction
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189 | * calculating the upper half of the product placing the result
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190 | * into a general purpose register. Now *if* the compiler supports
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191 | * inline assembler, then it's not impossible to implement the
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192 | * "bignum" routines (and have the compiler optimize 'em)
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193 | * exhibiting "native" performance in C. That's what BN_UMULT_HIGH
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194 | * macro is about:-)
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195 | *
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196 | * <appro@fy.chalmers.se>
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197 | */
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198 | # if defined(__alpha) && (defined(SIXTY_FOUR_BIT_LONG) || defined(SIXTY_FOUR_BIT))
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199 | # if defined(__DECC)
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200 | # include <c_asm.h>
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201 | # define BN_UMULT_HIGH(a,b) (BN_ULONG)asm("umulh %a0,%a1,%v0",(a),(b))
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202 | # elif defined(__GNUC__)
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203 | # define BN_UMULT_HIGH(a,b) ({ \
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204 | register BN_ULONG ret; \
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205 | asm ("umulh %1,%2,%0" \
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206 | : "=r"(ret) \
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207 | : "r"(a), "r"(b)); \
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208 | ret; })
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209 | # endif /* compiler */
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210 | # elif defined(_ARCH_PPC) && defined(__64BIT__) && defined(SIXTY_FOUR_BIT_LONG)
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211 | # if defined(__GNUC__)
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212 | # define BN_UMULT_HIGH(a,b) ({ \
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213 | register BN_ULONG ret; \
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214 | asm ("mulhdu %0,%1,%2" \
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215 | : "=r"(ret) \
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216 | : "r"(a), "r"(b)); \
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217 | ret; })
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218 | # endif /* compiler */
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219 | # endif /* cpu */
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220 | #endif /* NO_ASM */
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221 |
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222 | /*************************************************************
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223 | * Using the long long type
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224 | */
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225 | #define Lw(t) (((BN_ULONG)(t))&BN_MASK2)
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226 | #define Hw(t) (((BN_ULONG)((t)>>BN_BITS2))&BN_MASK2)
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227 |
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228 | /* This is used for internal error checking and is not normally used */
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229 | #ifdef BN_DEBUG
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230 | # include <assert.h>
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231 | # define bn_check_top(a) assert ((a)->top >= 0 && (a)->top <= (a)->dmax);
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232 | #else
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233 | # define bn_check_top(a)
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234 | #endif
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235 |
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236 | /* This macro is to add extra stuff for development checking */
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237 | #ifdef BN_DEBUG
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238 | #define bn_set_max(r) ((r)->max=(r)->top,BN_set_flags((r),BN_FLG_STATIC_DATA))
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239 | #else
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240 | #define bn_set_max(r)
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241 | #endif
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242 |
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243 | /* These macros are used to 'take' a section of a bignum for read only use */
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244 | #define bn_set_low(r,a,n) \
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245 | { \
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246 | (r)->top=((a)->top > (n))?(n):(a)->top; \
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247 | (r)->d=(a)->d; \
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248 | (r)->neg=(a)->neg; \
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249 | (r)->flags|=BN_FLG_STATIC_DATA; \
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250 | bn_set_max(r); \
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251 | }
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252 |
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253 | #define bn_set_high(r,a,n) \
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254 | { \
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255 | if ((a)->top > (n)) \
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256 | { \
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257 | (r)->top=(a)->top-n; \
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258 | (r)->d= &((a)->d[n]); \
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259 | } \
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260 | else \
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261 | (r)->top=0; \
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262 | (r)->neg=(a)->neg; \
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263 | (r)->flags|=BN_FLG_STATIC_DATA; \
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264 | bn_set_max(r); \
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265 | }
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266 |
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267 | #ifdef BN_LLONG
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268 | #define mul_add(r,a,w,c) { \
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269 | BN_ULLONG t; \
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270 | t=(BN_ULLONG)w * (a) + (r) + (c); \
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271 | (r)= Lw(t); \
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272 | (c)= Hw(t); \
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273 | }
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274 |
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275 | #define mul(r,a,w,c) { \
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276 | BN_ULLONG t; \
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277 | t=(BN_ULLONG)w * (a) + (c); \
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278 | (r)= Lw(t); \
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279 | (c)= Hw(t); \
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280 | }
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281 |
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282 | #define sqr(r0,r1,a) { \
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283 | BN_ULLONG t; \
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284 | t=(BN_ULLONG)(a)*(a); \
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285 | (r0)=Lw(t); \
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286 | (r1)=Hw(t); \
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287 | }
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288 |
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289 | #elif defined(BN_UMULT_HIGH)
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290 | #define mul_add(r,a,w,c) { \
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291 | BN_ULONG high,low,ret,tmp=(a); \
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292 | ret = (r); \
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293 | high= BN_UMULT_HIGH(w,tmp); \
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294 | ret += (c); \
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295 | low = (w) * tmp; \
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296 | (c) = (ret<(c))?1:0; \
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297 | (c) += high; \
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298 | ret += low; \
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299 | (c) += (ret<low)?1:0; \
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300 | (r) = ret; \
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301 | }
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302 |
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303 | #define mul(r,a,w,c) { \
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304 | BN_ULONG high,low,ret,ta=(a); \
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305 | low = (w) * ta; \
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306 | high= BN_UMULT_HIGH(w,ta); \
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307 | ret = low + (c); \
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308 | (c) = high; \
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309 | (c) += (ret<low)?1:0; \
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310 | (r) = ret; \
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311 | }
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312 |
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313 | #define sqr(r0,r1,a) { \
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314 | BN_ULONG tmp=(a); \
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315 | (r0) = tmp * tmp; \
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316 | (r1) = BN_UMULT_HIGH(tmp,tmp); \
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317 | }
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318 |
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319 | #else
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320 | /*************************************************************
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321 | * No long long type
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322 | */
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323 |
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324 | #define LBITS(a) ((a)&BN_MASK2l)
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325 | #define HBITS(a) (((a)>>BN_BITS4)&BN_MASK2l)
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326 | #define L2HBITS(a) ((BN_ULONG)((a)&BN_MASK2l)<<BN_BITS4)
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327 |
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328 | #define LLBITS(a) ((a)&BN_MASKl)
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329 | #define LHBITS(a) (((a)>>BN_BITS2)&BN_MASKl)
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330 | #define LL2HBITS(a) ((BN_ULLONG)((a)&BN_MASKl)<<BN_BITS2)
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331 |
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332 | #define mul64(l,h,bl,bh) \
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333 | { \
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334 | BN_ULONG m,m1,lt,ht; \
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335 | \
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336 | lt=l; \
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337 | ht=h; \
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338 | m =(bh)*(lt); \
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339 | lt=(bl)*(lt); \
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340 | m1=(bl)*(ht); \
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341 | ht =(bh)*(ht); \
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342 | m=(m+m1)&BN_MASK2; if (m < m1) ht+=L2HBITS(1L); \
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343 | ht+=HBITS(m); \
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344 | m1=L2HBITS(m); \
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345 | lt=(lt+m1)&BN_MASK2; if (lt < m1) ht++; \
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346 | (l)=lt; \
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347 | (h)=ht; \
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348 | }
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349 |
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350 | #define sqr64(lo,ho,in) \
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351 | { \
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352 | BN_ULONG l,h,m; \
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353 | \
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354 | h=(in); \
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355 | l=LBITS(h); \
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356 | h=HBITS(h); \
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357 | m =(l)*(h); \
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358 | l*=l; \
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359 | h*=h; \
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360 | h+=(m&BN_MASK2h1)>>(BN_BITS4-1); \
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361 | m =(m&BN_MASK2l)<<(BN_BITS4+1); \
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362 | l=(l+m)&BN_MASK2; if (l < m) h++; \
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363 | (lo)=l; \
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364 | (ho)=h; \
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365 | }
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366 |
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367 | #define mul_add(r,a,bl,bh,c) { \
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368 | BN_ULONG l,h; \
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369 | \
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370 | h= (a); \
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371 | l=LBITS(h); \
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372 | h=HBITS(h); \
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373 | mul64(l,h,(bl),(bh)); \
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374 | \
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375 | /* non-multiply part */ \
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376 | l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
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377 | (c)=(r); \
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378 | l=(l+(c))&BN_MASK2; if (l < (c)) h++; \
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379 | (c)=h&BN_MASK2; \
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380 | (r)=l; \
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381 | }
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382 |
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383 | #define mul(r,a,bl,bh,c) { \
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384 | BN_ULONG l,h; \
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385 | \
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386 | h= (a); \
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387 | l=LBITS(h); \
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388 | h=HBITS(h); \
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389 | mul64(l,h,(bl),(bh)); \
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390 | \
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391 | /* non-multiply part */ \
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392 | l+=(c); if ((l&BN_MASK2) < (c)) h++; \
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393 | (c)=h&BN_MASK2; \
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394 | (r)=l&BN_MASK2; \
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395 | }
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396 | #endif /* !BN_LLONG */
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397 |
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398 | void bn_mul_normal(BN_ULONG *r,BN_ULONG *a,int na,BN_ULONG *b,int nb);
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399 | void bn_mul_comba8(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
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400 | void bn_mul_comba4(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b);
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401 | void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp);
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402 | void bn_sqr_comba8(BN_ULONG *r,BN_ULONG *a);
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403 | void bn_sqr_comba4(BN_ULONG *r,BN_ULONG *a);
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404 | int bn_cmp_words(BN_ULONG *a,BN_ULONG *b,int n);
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405 | void bn_mul_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,BN_ULONG *t);
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406 | void bn_mul_part_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,
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407 | int tn, int n,BN_ULONG *t);
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408 | void bn_sqr_recursive(BN_ULONG *r,BN_ULONG *a, int n2, BN_ULONG *t);
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409 | void bn_mul_low_normal(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b, int n);
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410 | void bn_mul_low_recursive(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,int n2,
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411 | BN_ULONG *t);
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412 | void bn_mul_high(BN_ULONG *r,BN_ULONG *a,BN_ULONG *b,BN_ULONG *l,int n2,
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413 | BN_ULONG *t);
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414 |
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415 | #ifdef __cplusplus
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416 | }
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417 | #endif
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418 |
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419 | #endif
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