1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* $Id: rmodulo2m.cc,v 1.6 2006-12-06 17:43:32 Singular Exp $ */ |
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5 | /* |
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6 | * ABSTRACT: numbers modulo 2^m |
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7 | */ |
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8 | |
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9 | #include <string.h> |
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10 | #include "mod2.h" |
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11 | #include <mylimits.h> |
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12 | #include "structs.h" |
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13 | #include "febase.h" |
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14 | #include "omalloc.h" |
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15 | #include "numbers.h" |
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16 | #include "longrat.h" |
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17 | #include "mpr_complex.h" |
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18 | #include "ring.h" |
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19 | #include "rmodulo2m.h" |
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20 | |
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21 | #ifdef HAVE_RING2TOM |
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22 | int nr2mExp; |
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23 | long nr2mModul; |
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24 | |
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25 | /* |
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26 | * Multiply two numbers |
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27 | */ |
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28 | number nr2mMult (number a,number b) |
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29 | { |
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30 | if (((long)a == 0) || ((long)b == 0)) |
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31 | return (number)0; |
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32 | else |
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33 | return nr2mMultM(a,b); |
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34 | } |
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35 | |
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36 | /* |
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37 | * Give the smallest non unit k, such that a * x = k = b * y has a solution |
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38 | */ |
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39 | number nr2mLcm (number a,number b,ring r) |
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40 | { |
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41 | long res = 0; |
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42 | if ((long) a == 0) a = (number) 1; |
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43 | if ((long) b == 0) b = (number) 1; |
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44 | while ((long) a % 2 == 0) |
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45 | { |
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46 | a = (number) ((long) a / 2); |
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47 | if ((long) b % 2 == 0) b = (number) ((long) b / 2); |
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48 | res++; |
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49 | } |
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50 | while ((long) b % 2 == 0) |
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51 | { |
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52 | b = (number) ((long) b / 2); |
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53 | res++; |
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54 | } |
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55 | return (number) (1L << res); // (2**res) |
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56 | } |
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57 | |
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58 | /* |
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59 | * Give the largest non unit k, such that a = x * k, b = y * k has |
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60 | * a solution. |
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61 | */ |
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62 | number nr2mGcd (number a,number b,ring r) |
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63 | { |
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64 | long res = 0; |
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65 | if ((long) a == 0 && (long) b == 0) return (number) 1; |
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66 | while ((long) a % 2 == 0 && (long) b % 2 == 0) |
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67 | { |
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68 | a = (number) ((long) a / 2); |
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69 | b = (number) ((long) b / 2); |
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70 | res++; |
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71 | } |
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72 | if ((long) b % 2 == 0) |
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73 | { |
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74 | return (number) ((1L << res));// * (long) a); // (2**res)*a a ist Einheit |
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75 | } |
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76 | else |
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77 | { |
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78 | return (number) ((1L << res));// * (long) b); // (2**res)*b b ist Einheit |
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79 | } |
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80 | } |
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81 | |
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82 | void nr2mPower (number a, int i, number * result) |
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83 | { |
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84 | if (i==0) |
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85 | { |
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86 | //npInit(1,result); |
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87 | *(long *)result = 1; |
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88 | } |
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89 | else if (i==1) |
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90 | { |
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91 | *result = a; |
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92 | } |
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93 | else |
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94 | { |
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95 | nr2mPower(a,i-1,result); |
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96 | *result = nr2mMultM(a,*result); |
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97 | } |
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98 | } |
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99 | |
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100 | /* |
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101 | * create a number from int |
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102 | */ |
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103 | number nr2mInit (int i) |
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104 | { |
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105 | long ii = i; |
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106 | while (ii < 0) ii += nr2mModul; |
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107 | while ((ii>1) && (ii >= nr2mModul)) ii -= nr2mModul; |
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108 | return (number) ii; |
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109 | } |
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110 | |
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111 | /* |
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112 | * convert a number to int (-p/2 .. p/2) |
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113 | */ |
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114 | int nr2mInt(number &n) |
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115 | { |
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116 | if ((long)n > (nr2mModul >>1)) return (int)((long)n - nr2mModul); |
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117 | else return (int)((long)n); |
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118 | } |
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119 | |
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120 | number nr2mAdd (number a, number b) |
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121 | { |
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122 | return nr2mAddM(a,b); |
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123 | } |
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124 | |
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125 | number nr2mSub (number a, number b) |
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126 | { |
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127 | return nr2mSubM(a,b); |
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128 | } |
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129 | |
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130 | BOOLEAN nr2mIsZero (number a) |
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131 | { |
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132 | return 0 == (long)a; |
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133 | } |
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134 | |
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135 | BOOLEAN nr2mIsOne (number a) |
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136 | { |
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137 | return 1 == (long)a; |
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138 | } |
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139 | |
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140 | BOOLEAN nr2mIsMOne (number a) |
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141 | { |
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142 | return nr2mModul == (long)a + 1; |
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143 | } |
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144 | |
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145 | BOOLEAN nr2mEqual (number a,number b) |
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146 | { |
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147 | return nr2mEqualM(a,b); |
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148 | } |
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149 | |
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150 | BOOLEAN nr2mGreater (number a,number b) |
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151 | { |
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152 | if ((long) a == 0) return TRUE; |
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153 | if ((long) b == 0) return FALSE; |
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154 | while ((long) a % 2 == 0 && (long) b % 2 == 0) |
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155 | { |
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156 | a = (number) ((long) a / 2); |
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157 | b = (number) ((long) b / 2); |
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158 | } |
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159 | return ((long) b % 2 == 1); |
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160 | } |
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161 | |
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162 | BOOLEAN nr2mGreaterZero (number k) |
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163 | { |
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164 | int h = (int)((long) k); |
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165 | return ((int)h !=0) && (h <= (nr2mModul>>1)); |
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166 | } |
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167 | |
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168 | //#ifdef HAVE_DIV_MOD |
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169 | #if 1 //ifdef HAVE_NTL // in ntl.a |
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170 | //extern void XGCD(long& d, long& s, long& t, long a, long b); |
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171 | #include <NTL/ZZ.h> |
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172 | #ifdef NTL_CLIENT |
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173 | NTL_CLIENT |
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174 | #endif |
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175 | #else |
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176 | void XGCD(long& d, long& s, long& t, long a, long b) |
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177 | { |
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178 | long u, v, u0, v0, u1, v1, u2, v2, q, r; |
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179 | |
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180 | long aneg = 0, bneg = 0; |
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181 | |
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182 | if (a < 0) { |
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183 | a = -a; |
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184 | aneg = 1; |
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185 | } |
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186 | |
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187 | if (b < 0) { |
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188 | b = -b; |
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189 | bneg = 1; |
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190 | } |
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191 | |
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192 | u1=1; v1=0; |
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193 | u2=0; v2=1; |
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194 | u = a; v = b; |
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195 | |
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196 | while (v != 0) { |
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197 | q = u / v; |
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198 | r = u % v; |
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199 | u = v; |
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200 | v = r; |
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201 | u0 = u2; |
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202 | v0 = v2; |
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203 | u2 = u1 - q*u2; |
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204 | v2 = v1- q*v2; |
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205 | u1 = u0; |
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206 | v1 = v0; |
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207 | } |
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208 | |
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209 | if (aneg) |
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210 | u1 = -u1; |
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211 | |
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212 | if (bneg) |
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213 | v1 = -v1; |
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214 | |
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215 | d = u; |
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216 | s = u1; |
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217 | t = v1; |
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218 | } |
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219 | #endif |
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220 | |
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221 | long InvMod(long a) |
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222 | { |
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223 | long d, s, t; |
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224 | |
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225 | XGCD(d, s, t, a, nr2mModul); |
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226 | assume (d == 1); |
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227 | if (s < 0) |
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228 | return s + nr2mModul; |
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229 | else |
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230 | return s; |
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231 | } |
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232 | //#endif |
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233 | |
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234 | inline number nr2mInversM (number c) |
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235 | { |
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236 | // Table !!! |
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237 | long inv; |
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238 | inv = InvMod((long)c); |
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239 | return (number) inv; |
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240 | } |
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241 | |
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242 | number nr2mDiv (number a,number b) |
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243 | { |
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244 | if ((long)a==0) |
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245 | return (number)0; |
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246 | else if ((long)b%2==0) |
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247 | { |
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248 | if ((long)b != 0) |
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249 | { |
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250 | while ((long) b%2 == 0 && (long) a%2 == 0) |
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251 | { |
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252 | a = (number) ((long) a / 2); |
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253 | b = (number) ((long) b / 2); |
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254 | } |
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255 | } |
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256 | if ((long) b%2 == 0) |
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257 | { |
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258 | WerrorS("div by zero divisor"); |
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259 | return (number)0; |
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260 | } |
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261 | } |
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262 | return (number) nr2mMult(a, nr2mInversM(b)); |
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263 | } |
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264 | |
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265 | number nr2mIntDiv (number a,number b) |
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266 | { |
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267 | if ((long)a==0) |
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268 | { |
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269 | return (number) 0; |
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270 | } |
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271 | else |
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272 | { |
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273 | return (number) ((long) a / (long) b); |
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274 | } |
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275 | } |
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276 | |
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277 | number nr2mInvers (number c) |
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278 | { |
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279 | if ((long)c%2==0) |
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280 | { |
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281 | WerrorS("division by zero divisor"); |
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282 | return (number)0; |
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283 | } |
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284 | return nr2mInversM(c); |
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285 | } |
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286 | |
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287 | number nr2mNeg (number c) |
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288 | { |
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289 | if ((long)c==0) return c; |
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290 | return nr2mNegM(c); |
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291 | } |
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292 | |
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293 | nMapFunc nr2mSetMap(ring src, ring dst) |
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294 | { |
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295 | return NULL; /* default */ |
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296 | } |
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297 | |
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298 | |
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299 | /* |
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300 | * set the exponent (allocate and init tables) (TODO) |
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301 | */ |
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302 | |
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303 | void nr2mSetExp(int m, ring r) |
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304 | { |
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305 | if (m>1) |
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306 | { |
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307 | nr2mExp = m; |
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308 | nr2mModul = 2; |
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309 | for (int i = 1; i < m; i++) { |
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310 | nr2mModul = nr2mModul * 2; |
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311 | } |
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312 | } |
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313 | else |
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314 | { |
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315 | nr2mExp=0; |
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316 | nr2mModul=0; |
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317 | } |
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318 | // PrintS("Modul: "); |
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319 | // Print("%d\n", nr2mModul); |
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320 | } |
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321 | |
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322 | void nr2mInitExp(int m, ring r) |
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323 | { |
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324 | int i, w; |
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325 | |
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326 | if (m>1) |
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327 | { |
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328 | nr2mExp = m; |
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329 | nr2mModul = 2; |
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330 | for (int i = 1; i < m; i++) { |
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331 | nr2mModul = nr2mModul * 2; |
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332 | |
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333 | } |
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334 | } |
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335 | else |
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336 | { |
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337 | WarnS("nInitChar failed"); |
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338 | } |
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339 | } |
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340 | |
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341 | #ifdef LDEBUG |
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342 | BOOLEAN nr2mDBTest (number a, char *f, int l) |
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343 | { |
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344 | if (((long)a<0) || ((long)a>nr2mModul)) |
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345 | { |
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346 | return FALSE; |
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347 | } |
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348 | return TRUE; |
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349 | } |
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350 | #endif |
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351 | |
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352 | void nr2mWrite (number &a) |
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353 | { |
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354 | if ((long)a > (nr2mModul >>1)) StringAppend("-%d",(int)(nr2mModul-((long)a))); |
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355 | else StringAppend("%d",(int)((long)a)); |
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356 | } |
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357 | |
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358 | char* nr2mEati(char *s, int *i) |
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359 | { |
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360 | |
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361 | if (((*s) >= '0') && ((*s) <= '9')) |
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362 | { |
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363 | (*i) = 0; |
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364 | do |
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365 | { |
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366 | (*i) *= 10; |
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367 | (*i) += *s++ - '0'; |
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368 | if ((*i) >= (MAX_INT_VAL / 10)) (*i) = (*i) % nr2mModul; |
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369 | } |
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370 | while (((*s) >= '0') && ((*s) <= '9')); |
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371 | if ((*i) >= nr2mModul) (*i) = (*i) % nr2mModul; |
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372 | } |
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373 | else (*i) = 1; |
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374 | return s; |
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375 | } |
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376 | |
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377 | char * nr2mRead (char *s, number *a) |
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378 | { |
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379 | int z; |
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380 | int n=1; |
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381 | |
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382 | s = nr2mEati(s, &z); |
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383 | if ((*s) == '/') |
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384 | { |
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385 | s++; |
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386 | s = nr2mEati(s, &n); |
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387 | } |
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388 | if (n == 1) |
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389 | *a = (number)z; |
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390 | else |
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391 | *a = nr2mDiv((number)z,(number)n); |
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392 | return s; |
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393 | } |
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394 | #endif |
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