1 | /*
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2 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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3 | *
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4 | * Licensed under the OpenSSL license (the "License"). You may not use
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5 | * this file except in compliance with the License. You can obtain a copy
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6 | * in the file LICENSE in the source distribution or at
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7 | * https://www.openssl.org/source/license.html
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8 | */
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9 |
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10 | #include <openssl/bn.h>
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11 | #include "internal/cryptlib.h"
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12 | #include "bn_lcl.h"
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13 |
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14 | /* The old slow way */
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15 | #if 0
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16 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
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17 | BN_CTX *ctx)
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18 | {
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19 | int i, nm, nd;
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20 | int ret = 0;
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21 | BIGNUM *D;
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22 |
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23 | bn_check_top(m);
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24 | bn_check_top(d);
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25 | if (BN_is_zero(d)) {
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26 | BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
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27 | return (0);
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28 | }
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29 |
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30 | if (BN_ucmp(m, d) < 0) {
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31 | if (rem != NULL) {
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32 | if (BN_copy(rem, m) == NULL)
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33 | return (0);
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34 | }
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35 | if (dv != NULL)
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36 | BN_zero(dv);
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37 | return (1);
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38 | }
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39 |
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40 | BN_CTX_start(ctx);
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41 | D = BN_CTX_get(ctx);
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42 | if (dv == NULL)
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43 | dv = BN_CTX_get(ctx);
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44 | if (rem == NULL)
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45 | rem = BN_CTX_get(ctx);
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46 | if (D == NULL || dv == NULL || rem == NULL)
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47 | goto end;
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48 |
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49 | nd = BN_num_bits(d);
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50 | nm = BN_num_bits(m);
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51 | if (BN_copy(D, d) == NULL)
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52 | goto end;
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53 | if (BN_copy(rem, m) == NULL)
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54 | goto end;
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55 |
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56 | /*
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57 | * The next 2 are needed so we can do a dv->d[0]|=1 later since
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58 | * BN_lshift1 will only work once there is a value :-)
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59 | */
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60 | BN_zero(dv);
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61 | if (bn_wexpand(dv, 1) == NULL)
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62 | goto end;
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63 | dv->top = 1;
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64 |
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65 | if (!BN_lshift(D, D, nm - nd))
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66 | goto end;
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67 | for (i = nm - nd; i >= 0; i--) {
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68 | if (!BN_lshift1(dv, dv))
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69 | goto end;
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70 | if (BN_ucmp(rem, D) >= 0) {
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71 | dv->d[0] |= 1;
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72 | if (!BN_usub(rem, rem, D))
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73 | goto end;
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74 | }
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75 | /* CAN IMPROVE (and have now :=) */
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76 | if (!BN_rshift1(D, D))
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77 | goto end;
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78 | }
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79 | rem->neg = BN_is_zero(rem) ? 0 : m->neg;
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80 | dv->neg = m->neg ^ d->neg;
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81 | ret = 1;
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82 | end:
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83 | BN_CTX_end(ctx);
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84 | return (ret);
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85 | }
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86 |
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87 | #else
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88 |
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89 | # if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
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90 | && !defined(PEDANTIC) && !defined(BN_DIV3W)
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91 | # if defined(__GNUC__) && __GNUC__>=2
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92 | # if defined(__i386) || defined (__i386__)
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93 | /*-
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94 | * There were two reasons for implementing this template:
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95 | * - GNU C generates a call to a function (__udivdi3 to be exact)
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96 | * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
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97 | * understand why...);
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98 | * - divl doesn't only calculate quotient, but also leaves
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99 | * remainder in %edx which we can definitely use here:-)
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100 | *
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101 | * <appro@fy.chalmers.se>
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102 | */
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103 | # undef bn_div_words
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104 | # define bn_div_words(n0,n1,d0) \
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105 | ({ asm volatile ( \
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106 | "divl %4" \
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107 | : "=a"(q), "=d"(rem) \
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108 | : "a"(n1), "d"(n0), "r"(d0) \
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109 | : "cc"); \
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110 | q; \
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111 | })
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112 | # define REMAINDER_IS_ALREADY_CALCULATED
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113 | # elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
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114 | /*
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115 | * Same story here, but it's 128-bit by 64-bit division. Wow!
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116 | * <appro@fy.chalmers.se>
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117 | */
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118 | # undef bn_div_words
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119 | # define bn_div_words(n0,n1,d0) \
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120 | ({ asm volatile ( \
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121 | "divq %4" \
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122 | : "=a"(q), "=d"(rem) \
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123 | : "a"(n1), "d"(n0), "r"(d0) \
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124 | : "cc"); \
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125 | q; \
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126 | })
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127 | # define REMAINDER_IS_ALREADY_CALCULATED
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128 | # endif /* __<cpu> */
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129 | # endif /* __GNUC__ */
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130 | # endif /* OPENSSL_NO_ASM */
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131 |
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132 | /*-
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133 | * BN_div computes dv := num / divisor, rounding towards
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134 | * zero, and sets up rm such that dv*divisor + rm = num holds.
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135 | * Thus:
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136 | * dv->neg == num->neg ^ divisor->neg (unless the result is zero)
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137 | * rm->neg == num->neg (unless the remainder is zero)
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138 | * If 'dv' or 'rm' is NULL, the respective value is not returned.
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139 | */
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140 | int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
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141 | BN_CTX *ctx)
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142 | {
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143 | int norm_shift, i, loop;
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144 | BIGNUM *tmp, wnum, *snum, *sdiv, *res;
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145 | BN_ULONG *resp, *wnump;
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146 | BN_ULONG d0, d1;
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147 | int num_n, div_n;
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148 | int no_branch = 0;
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149 |
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150 | /*
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151 | * Invalid zero-padding would have particularly bad consequences so don't
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152 | * just rely on bn_check_top() here (bn_check_top() works only for
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153 | * BN_DEBUG builds)
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154 | */
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155 | if ((num->top > 0 && num->d[num->top - 1] == 0) ||
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156 | (divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
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157 | BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
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158 | return 0;
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159 | }
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160 |
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161 | bn_check_top(num);
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162 | bn_check_top(divisor);
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163 |
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164 | if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
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165 | || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
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166 | no_branch = 1;
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167 | }
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168 |
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169 | bn_check_top(dv);
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170 | bn_check_top(rm);
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171 | /*- bn_check_top(num); *//*
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172 | * 'num' has been checked already
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173 | */
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174 | /*- bn_check_top(divisor); *//*
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175 | * 'divisor' has been checked already
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176 | */
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177 |
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178 | if (BN_is_zero(divisor)) {
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179 | BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
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180 | return (0);
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181 | }
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182 |
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183 | if (!no_branch && BN_ucmp(num, divisor) < 0) {
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184 | if (rm != NULL) {
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185 | if (BN_copy(rm, num) == NULL)
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186 | return (0);
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187 | }
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188 | if (dv != NULL)
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189 | BN_zero(dv);
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190 | return (1);
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191 | }
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192 |
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193 | BN_CTX_start(ctx);
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194 | tmp = BN_CTX_get(ctx);
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195 | snum = BN_CTX_get(ctx);
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196 | sdiv = BN_CTX_get(ctx);
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197 | if (dv == NULL)
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198 | res = BN_CTX_get(ctx);
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199 | else
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200 | res = dv;
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201 | if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
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202 | goto err;
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203 |
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204 | /* First we normalise the numbers */
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205 | norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
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206 | if (!(BN_lshift(sdiv, divisor, norm_shift)))
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207 | goto err;
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208 | sdiv->neg = 0;
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209 | norm_shift += BN_BITS2;
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210 | if (!(BN_lshift(snum, num, norm_shift)))
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211 | goto err;
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212 | snum->neg = 0;
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213 |
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214 | if (no_branch) {
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215 | /*
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216 | * Since we don't know whether snum is larger than sdiv, we pad snum
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217 | * with enough zeroes without changing its value.
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218 | */
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219 | if (snum->top <= sdiv->top + 1) {
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220 | if (bn_wexpand(snum, sdiv->top + 2) == NULL)
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221 | goto err;
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222 | for (i = snum->top; i < sdiv->top + 2; i++)
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223 | snum->d[i] = 0;
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224 | snum->top = sdiv->top + 2;
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225 | } else {
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226 | if (bn_wexpand(snum, snum->top + 1) == NULL)
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227 | goto err;
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228 | snum->d[snum->top] = 0;
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229 | snum->top++;
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230 | }
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231 | }
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232 |
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233 | div_n = sdiv->top;
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234 | num_n = snum->top;
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235 | loop = num_n - div_n;
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236 | /*
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237 | * Lets setup a 'window' into snum This is the part that corresponds to
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238 | * the current 'area' being divided
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239 | */
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240 | wnum.neg = 0;
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241 | wnum.d = &(snum->d[loop]);
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242 | wnum.top = div_n;
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243 | /*
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244 | * only needed when BN_ucmp messes up the values between top and max
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245 | */
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246 | wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
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247 |
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248 | /* Get the top 2 words of sdiv */
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249 | /* div_n=sdiv->top; */
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250 | d0 = sdiv->d[div_n - 1];
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251 | d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
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252 |
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253 | /* pointer to the 'top' of snum */
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254 | wnump = &(snum->d[num_n - 1]);
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255 |
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256 | /* Setup to 'res' */
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257 | if (!bn_wexpand(res, (loop + 1)))
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258 | goto err;
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259 | res->neg = (num->neg ^ divisor->neg);
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260 | res->top = loop - no_branch;
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261 | resp = &(res->d[loop - 1]);
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262 |
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263 | /* space for temp */
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264 | if (!bn_wexpand(tmp, (div_n + 1)))
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265 | goto err;
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266 |
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267 | if (!no_branch) {
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268 | if (BN_ucmp(&wnum, sdiv) >= 0) {
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269 | /*
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270 | * If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
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271 | * the const bignum arguments => clean the values between top and
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272 | * max again
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273 | */
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274 | bn_clear_top2max(&wnum);
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275 | bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
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276 | *resp = 1;
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277 | } else
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278 | res->top--;
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279 | }
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280 |
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281 | /* Increase the resp pointer so that we never create an invalid pointer. */
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282 | resp++;
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283 |
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284 | /*
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285 | * if res->top == 0 then clear the neg value otherwise decrease the resp
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286 | * pointer
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287 | */
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288 | if (res->top == 0)
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289 | res->neg = 0;
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290 | else
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291 | resp--;
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292 |
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293 | for (i = 0; i < loop - 1; i++, wnump--) {
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294 | BN_ULONG q, l0;
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295 | /*
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296 | * the first part of the loop uses the top two words of snum and sdiv
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297 | * to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
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298 | */
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299 | # if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
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300 | BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
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301 | q = bn_div_3_words(wnump, d1, d0);
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302 | # else
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303 | BN_ULONG n0, n1, rem = 0;
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304 |
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305 | n0 = wnump[0];
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306 | n1 = wnump[-1];
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307 | if (n0 == d0)
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308 | q = BN_MASK2;
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309 | else { /* n0 < d0 */
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310 |
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311 | # ifdef BN_LLONG
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312 | BN_ULLONG t2;
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313 |
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314 | # if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
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315 | q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
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316 | # else
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317 | q = bn_div_words(n0, n1, d0);
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318 | # endif
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319 |
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320 | # ifndef REMAINDER_IS_ALREADY_CALCULATED
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321 | /*
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322 | * rem doesn't have to be BN_ULLONG. The least we
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323 | * know it's less that d0, isn't it?
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324 | */
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325 | rem = (n1 - q * d0) & BN_MASK2;
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326 | # endif
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327 | t2 = (BN_ULLONG) d1 *q;
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328 |
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329 | for (;;) {
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330 | if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
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331 | break;
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332 | q--;
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333 | rem += d0;
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334 | if (rem < d0)
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335 | break; /* don't let rem overflow */
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336 | t2 -= d1;
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337 | }
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338 | # else /* !BN_LLONG */
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339 | BN_ULONG t2l, t2h;
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340 |
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341 | q = bn_div_words(n0, n1, d0);
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342 | # ifndef REMAINDER_IS_ALREADY_CALCULATED
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343 | rem = (n1 - q * d0) & BN_MASK2;
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344 | # endif
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345 |
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346 | # if defined(BN_UMULT_LOHI)
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347 | BN_UMULT_LOHI(t2l, t2h, d1, q);
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348 | # elif defined(BN_UMULT_HIGH)
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349 | t2l = d1 * q;
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350 | t2h = BN_UMULT_HIGH(d1, q);
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351 | # else
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352 | {
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353 | BN_ULONG ql, qh;
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354 | t2l = LBITS(d1);
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355 | t2h = HBITS(d1);
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356 | ql = LBITS(q);
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357 | qh = HBITS(q);
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358 | mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
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359 | }
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360 | # endif
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361 |
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362 | for (;;) {
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363 | if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
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364 | break;
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365 | q--;
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366 | rem += d0;
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367 | if (rem < d0)
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368 | break; /* don't let rem overflow */
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369 | if (t2l < d1)
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370 | t2h--;
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371 | t2l -= d1;
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372 | }
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373 | # endif /* !BN_LLONG */
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374 | }
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375 | # endif /* !BN_DIV3W */
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376 |
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377 | l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
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378 | tmp->d[div_n] = l0;
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379 | wnum.d--;
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380 | /*
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381 | * ingore top values of the bignums just sub the two BN_ULONG arrays
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382 | * with bn_sub_words
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383 | */
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384 | if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
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385 | /*
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386 | * Note: As we have considered only the leading two BN_ULONGs in
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387 | * the calculation of q, sdiv * q might be greater than wnum (but
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388 | * then (q-1) * sdiv is less or equal than wnum)
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389 | */
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390 | q--;
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391 | if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
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392 | /*
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393 | * we can't have an overflow here (assuming that q != 0, but
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394 | * if q == 0 then tmp is zero anyway)
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395 | */
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396 | (*wnump)++;
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397 | }
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398 | /* store part of the result */
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399 | resp--;
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400 | *resp = q;
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401 | }
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402 | bn_correct_top(snum);
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403 | if (rm != NULL) {
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404 | /*
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405 | * Keep a copy of the neg flag in num because if rm==num BN_rshift()
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406 | * will overwrite it.
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407 | */
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408 | int neg = num->neg;
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409 | BN_rshift(rm, snum, norm_shift);
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410 | if (!BN_is_zero(rm))
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411 | rm->neg = neg;
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412 | bn_check_top(rm);
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413 | }
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414 | if (no_branch)
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415 | bn_correct_top(res);
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416 | BN_CTX_end(ctx);
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417 | return (1);
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418 | err:
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419 | bn_check_top(rm);
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420 | BN_CTX_end(ctx);
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421 | return (0);
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422 | }
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423 | #endif
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