1 | /**************************************** |
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2 | * Computer Algebra System SINGULAR * |
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3 | ****************************************/ |
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4 | /* |
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5 | * ABSTRACT: computations with GMP floating-point numbers |
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6 | * |
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7 | * ngf == number gnu floats |
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8 | */ |
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9 | |
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10 | #include <misc/auxiliary.h> |
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11 | #include <omalloc/omalloc.h> |
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12 | |
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13 | #include <reporter/reporter.h> |
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14 | |
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15 | #include "coeffs.h" |
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16 | #include "numbers.h" |
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17 | #include "mpr_complex.h" |
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18 | |
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19 | #include "longrat.h" |
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20 | #include "shortfl.h" |
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21 | #include "gnumpfl.h" |
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22 | #include "modulop.h" |
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23 | |
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24 | //ring ngfMapRing; // to be used also in gnumpc.cc |
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25 | |
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26 | /// Get a mapping function from src into the domain of this type: |
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27 | nMapFunc ngfSetMap(const coeffs src, const coeffs dst); |
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28 | |
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29 | const char * ngfRead (const char *s, number *a, const coeffs r); |
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30 | |
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31 | // Private interface should be hidden!!! |
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32 | /// Note: MAY NOT WORK AS EXPECTED! |
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33 | BOOLEAN ngfGreaterZero(number za, const coeffs r); |
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34 | BOOLEAN ngfGreater(number a, number b, const coeffs r); |
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35 | BOOLEAN ngfEqual(number a, number b, const coeffs r); |
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36 | BOOLEAN ngfIsOne(number a, const coeffs r); |
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37 | BOOLEAN ngfIsMOne(number a, const coeffs r); |
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38 | BOOLEAN ngfIsZero(number za, const coeffs r); |
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39 | number ngfInit(long i, const coeffs r); |
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40 | long ngfInt(number &n, const coeffs r); |
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41 | number ngfNeg(number za, const coeffs r); |
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42 | number ngfInvers(number a, const coeffs r); |
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43 | number ngfAdd(number la, number li, const coeffs r); |
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44 | number ngfSub(number la, number li, const coeffs r); |
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45 | number ngfMult(number a, number b, const coeffs r); |
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46 | number ngfDiv(number a, number b, const coeffs r); |
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47 | void ngfPower(number x, int exp, number *lu, const coeffs r); |
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48 | number ngfCopy(number a, const coeffs r); |
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49 | number ngf_Copy(number a, coeffs r); |
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50 | void ngfWrite(number a, const coeffs r); |
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51 | void ngfCoeffWrite(const coeffs r, BOOLEAN details); |
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52 | |
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53 | void ngfDelete(number *a, const coeffs r); |
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54 | |
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55 | number ngfMapQ(number from, const coeffs src, const coeffs r); |
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56 | |
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57 | union nf |
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58 | { |
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59 | float _f; |
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60 | number _n; |
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61 | nf(float f) {_f = f;} |
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62 | nf(number n) {_n = n;} |
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63 | float F() const {return _f;} |
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64 | number N() const {return _n;} |
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65 | }; |
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66 | |
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67 | /*2 |
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68 | * n := i |
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69 | */ |
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70 | number ngfInit (long i, const coeffs r) |
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71 | { |
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72 | assume( getCoeffType(r) == n_long_R ); |
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73 | |
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74 | gmp_float* n= new gmp_float( (double)i ); |
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75 | return (number)n; |
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76 | } |
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77 | |
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78 | /*2 |
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79 | * convert number to int |
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80 | */ |
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81 | long ngfInt(number &i, const coeffs r) |
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82 | { |
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83 | assume( getCoeffType(r) == n_long_R ); |
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84 | |
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85 | double d=(double)*(gmp_float*)i; |
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86 | if (d<0.0) |
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87 | return (long)(d-0.5); |
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88 | else |
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89 | return (long)(d+0.5); |
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90 | } |
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91 | |
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92 | int ngfSize(number n, const coeffs r) |
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93 | { |
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94 | long i = ngfInt(n, r); |
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95 | /* basically return the largest integer in n; |
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96 | only if this happens to be zero although n != 0, |
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97 | return 1; |
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98 | (this code ensures that zero has the size zero) */ |
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99 | if ((i == 0) && (ngfIsZero(n,r) == FALSE)) i = 1; |
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100 | return i; |
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101 | } |
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102 | |
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103 | /*2 |
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104 | * delete a |
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105 | */ |
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106 | void ngfDelete (number * a, const coeffs r) |
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107 | { |
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108 | assume( getCoeffType(r) == n_long_R ); |
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109 | |
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110 | if ( *a != NULL ) |
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111 | { |
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112 | delete *(gmp_float**)a; |
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113 | *a=NULL; |
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114 | } |
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115 | } |
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116 | |
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117 | /*2 |
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118 | * copy a to b |
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119 | */ |
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120 | number ngfCopy(number a, const coeffs r) |
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121 | { |
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122 | assume( getCoeffType(r) == n_long_R ); |
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123 | |
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124 | gmp_float* b= new gmp_float( *(gmp_float*)a ); |
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125 | return (number)b; |
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126 | } |
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127 | |
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128 | #if 0 |
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129 | static number ngfCopyMap(number a, const coeffs r1, const coeffs r2) |
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130 | { |
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131 | assume( getCoeffType(r1) == n_long_R ); |
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132 | assume( getCoeffType(r2) == n_long_R ); |
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133 | |
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134 | gmp_float* b= NULL; |
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135 | if ( a != NULL ) |
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136 | { |
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137 | b= new gmp_float( *(gmp_float*)a ); |
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138 | } |
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139 | return (number)b; |
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140 | } |
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141 | #endif |
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142 | |
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143 | /*2 |
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144 | * za:= - za |
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145 | */ |
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146 | number ngfNeg (number a, const coeffs r) |
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147 | { |
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148 | assume( getCoeffType(r) == n_long_R ); |
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149 | |
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150 | *(gmp_float*)a= -(*(gmp_float*)a); |
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151 | return (number)a; |
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152 | } |
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153 | |
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154 | /* |
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155 | * 1/a |
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156 | */ |
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157 | number ngfInvers(number a, const coeffs r) |
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158 | { |
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159 | assume( getCoeffType(r) == n_long_R ); |
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160 | |
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161 | gmp_float* f= NULL; |
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162 | if (((gmp_float*)a)->isZero() ) |
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163 | { |
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164 | WerrorS(nDivBy0); |
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165 | } |
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166 | else |
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167 | { |
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168 | f= new gmp_float( gmp_float(1) / (*(gmp_float*)a) ); |
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169 | } |
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170 | return (number)f; |
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171 | } |
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172 | |
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173 | /*2 |
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174 | * u:= a + b |
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175 | */ |
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176 | number ngfAdd (number a, number b, const coeffs R) |
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177 | { |
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178 | assume( getCoeffType(R) == n_long_R ); |
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179 | |
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180 | gmp_float* r= new gmp_float( (*(gmp_float*)a) + (*(gmp_float*)b) ); |
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181 | return (number)r; |
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182 | } |
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183 | |
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184 | /*2 |
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185 | * u:= a - b |
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186 | */ |
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187 | number ngfSub (number a, number b, const coeffs R) |
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188 | { |
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189 | assume( getCoeffType(R) == n_long_R ); |
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190 | |
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191 | gmp_float* r= new gmp_float( (*(gmp_float*)a) - (*(gmp_float*)b) ); |
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192 | return (number)r; |
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193 | } |
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194 | |
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195 | /*2 |
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196 | * u := a * b |
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197 | */ |
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198 | number ngfMult (number a, number b, const coeffs R) |
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199 | { |
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200 | assume( getCoeffType(R) == n_long_R ); |
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201 | |
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202 | gmp_float* r= new gmp_float( (*(gmp_float*)a) * (*(gmp_float*)b) ); |
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203 | return (number)r; |
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204 | } |
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205 | |
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206 | /*2 |
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207 | * u := a / b |
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208 | */ |
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209 | number ngfDiv (number a, number b, const coeffs r) |
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210 | { |
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211 | assume( getCoeffType(r) == n_long_R ); |
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212 | |
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213 | if ( ((gmp_float*)b)->isZero() ) |
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214 | { |
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215 | // a/0 = error |
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216 | WerrorS(nDivBy0); |
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217 | return NULL; |
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218 | } |
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219 | gmp_float* f= new gmp_float( (*(gmp_float*)a) / (*(gmp_float*)b) ); |
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220 | return (number)f; |
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221 | } |
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222 | |
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223 | /*2 |
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224 | * u:= x ^ exp |
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225 | */ |
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226 | number ngfPower (number x, int exp, const coeffs r) |
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227 | { |
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228 | assume( getCoeffType(r) == n_long_R ); |
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229 | |
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230 | if ( exp == 0 ) |
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231 | { |
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232 | gmp_float* n = new gmp_float(1); |
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233 | return (number)n; |
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234 | } |
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235 | else if ( ngfIsZero(x, r) ) // 0^e, e>0 |
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236 | { |
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237 | return ngfInit(0, r); |
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238 | } |
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239 | else if ( exp == 1 ) |
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240 | { |
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241 | return ngfCopy(x,r); |
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242 | } |
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243 | return (number) ( new gmp_float( (*(gmp_float*)x)^exp ) ); |
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244 | } |
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245 | |
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246 | /* kept for compatibility reasons, to be deleted */ |
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247 | void ngfPower ( number x, int exp, number * u, const coeffs r ) |
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248 | { |
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249 | *u = ngfPower(x, exp, r); |
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250 | } |
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251 | |
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252 | BOOLEAN ngfIsZero (number a, const coeffs r) |
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253 | { |
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254 | assume( getCoeffType(r) == n_long_R ); |
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255 | |
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256 | return ( ((gmp_float*)a)->isZero() ); |
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257 | } |
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258 | |
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259 | /*2 |
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260 | * za > 0 ? |
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261 | */ |
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262 | BOOLEAN ngfGreaterZero (number a, const coeffs r) |
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263 | { |
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264 | assume( getCoeffType(r) == n_long_R ); |
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265 | |
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266 | return (((gmp_float*)a)->sign() > 0); |
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267 | } |
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268 | |
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269 | /*2 |
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270 | * a > b ? |
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271 | */ |
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272 | BOOLEAN ngfGreater (number a, number b, const coeffs r) |
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273 | { |
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274 | assume( getCoeffType(r) == n_long_R ); |
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275 | |
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276 | return ( (*(gmp_float*)a) > (*(gmp_float*)b) ); |
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277 | } |
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278 | |
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279 | /*2 |
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280 | * a = b ? |
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281 | */ |
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282 | BOOLEAN ngfEqual (number a, number b, const coeffs r) |
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283 | { |
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284 | assume( getCoeffType(r) == n_long_R ); |
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285 | |
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286 | return ( (*(gmp_float*)a) == (*(gmp_float*)b) ); |
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287 | } |
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288 | |
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289 | /*2 |
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290 | * a == 1 ? |
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291 | */ |
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292 | BOOLEAN ngfIsOne (number a, const coeffs r) |
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293 | { |
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294 | assume( getCoeffType(r) == n_long_R ); |
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295 | |
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296 | return ((gmp_float*)a)->isOne(); |
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297 | } |
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298 | |
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299 | /*2 |
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300 | * a == -1 ? |
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301 | */ |
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302 | BOOLEAN ngfIsMOne (number a, const coeffs r) |
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303 | { |
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304 | assume( getCoeffType(r) == n_long_R ); |
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305 | |
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306 | return ((gmp_float*)a)->isMOne(); |
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307 | } |
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308 | |
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309 | static char * ngfEatFloatNExp(char * s ) |
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310 | { |
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311 | char *start= s; |
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312 | |
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313 | // eat floats (mantissa) like: |
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314 | // 0.394394993, 102.203003008, .300303032, pssibly starting with - |
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315 | if (*s == '-') s++; |
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316 | while ((*s >= '0' && *s <= '9')||(*s == '.')) s++; |
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317 | |
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318 | // eat the exponent, starts with 'e' followed by '+', '-' |
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319 | // and digits, like: |
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320 | // e-202, e+393, accept also E7 |
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321 | if ( (s != start) && ((*s == 'e')||(*s=='E'))) |
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322 | { |
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323 | if (*s=='E') *s='e'; |
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324 | s++; // skip 'e'/'E' |
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325 | if ((*s == '+') || (*s == '-')) s++; |
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326 | while ((*s >= '0' && *s <= '9')) s++; |
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327 | } |
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328 | |
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329 | return s; |
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330 | } |
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331 | |
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332 | /*2 |
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333 | * extracts the number a from s, returns the rest |
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334 | * |
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335 | * This is also called to print components of complex coefficients. |
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336 | * Handle with care! |
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337 | */ |
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338 | const char * ngfRead (const char * start, number * a, const coeffs r) |
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339 | { |
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340 | assume( getCoeffType(r) == n_long_R or getCoeffType(r) == n_long_C); |
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341 | |
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342 | char *s= (char *)start; |
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343 | |
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344 | //Print("%s\n",s); |
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345 | |
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346 | s= ngfEatFloatNExp( s ); |
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347 | |
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348 | if (*s=='\0') // 0 |
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349 | { |
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350 | if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float(); |
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351 | (*(gmp_float**)a)->setFromStr(start); |
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352 | } |
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353 | else if (s==start) // 1 |
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354 | { |
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355 | if ( *(gmp_float**)a != NULL ) delete (*(gmp_float**)a); |
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356 | (*(gmp_float**)a)= new gmp_float(1); |
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357 | } |
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358 | else |
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359 | { |
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360 | gmp_float divisor(1.0); |
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361 | char *start2=s; |
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362 | if ( *s == '/' ) |
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363 | { |
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364 | s++; |
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365 | s= ngfEatFloatNExp( (char *)s ); |
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366 | if (s!= start2+1) |
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367 | { |
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368 | char tmp_c=*s; |
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369 | *s='\0'; |
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370 | divisor.setFromStr(start2+1); |
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371 | *s=tmp_c; |
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372 | } |
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373 | else |
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374 | { |
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375 | Werror("wrong long real format: %s",start2); |
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376 | } |
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377 | } |
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378 | char c=*start2; |
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379 | *start2='\0'; |
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380 | if ( *(gmp_float**)a == NULL ) (*(gmp_float**)a)= new gmp_float(); |
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381 | (*(gmp_float**)a)->setFromStr(start); |
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382 | *start2=c; |
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383 | if (divisor.isZero()) |
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384 | { |
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385 | WerrorS(nDivBy0); |
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386 | } |
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387 | else |
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388 | (**(gmp_float**)a) /= divisor; |
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389 | } |
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390 | |
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391 | return s; |
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392 | } |
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393 | |
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394 | /*2 |
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395 | * write a floating point number |
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396 | */ |
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397 | void ngfWrite (number a, const coeffs r) |
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398 | { |
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399 | assume( getCoeffType(r) == n_long_R ); |
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400 | |
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401 | char *out; |
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402 | if ( a != NULL ) |
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403 | { |
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404 | out= floatToStr(*(gmp_float*)a, r->float_len); |
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405 | StringAppendS(out); |
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406 | //omFreeSize((void *)out, (strlen(out)+1)* sizeof(char) ); |
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407 | omFree( (void *)out ); |
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408 | } |
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409 | else |
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410 | { |
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411 | StringAppendS("0"); |
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412 | } |
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413 | } |
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414 | |
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415 | BOOLEAN ngfCoeffIsEqual (const coeffs r, n_coeffType n, void * parameter) |
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416 | { |
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417 | if (n==n_long_R) |
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418 | { |
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419 | LongComplexInfo* p = (LongComplexInfo *)(parameter); |
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420 | if ((p!=NULL) |
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421 | && (p->float_len == r->float_len) |
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422 | && (p->float_len2 == r->float_len2)) |
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423 | return TRUE; |
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424 | } |
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425 | return FALSE; |
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426 | } |
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427 | |
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428 | void ngfSetChar(const coeffs r) |
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429 | { |
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430 | setGMPFloatDigits(r->float_len, r->float_len2); |
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431 | } |
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432 | |
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433 | static char* ngfCoeffString(const coeffs r) |
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434 | { |
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435 | char *s=(char*)omAlloc(27); |
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436 | snprintf(s,27,"real,%d,%d",r->float_len,r->float_len2); |
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437 | return s; |
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438 | } |
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439 | |
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440 | static char* ngfCoeffName(const coeffs r) |
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441 | { |
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442 | static char ngfCoeffName_buf[27]; |
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443 | snprintf(ngfCoeffName_buf,27,"RR(%d,%d)",r->float_len,r->float_len2); |
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444 | return ngfCoeffName_buf; |
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445 | } |
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446 | |
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447 | BOOLEAN ngfInitChar(coeffs n, void *parameter) |
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448 | { |
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449 | assume( getCoeffType(n) == n_long_R ); |
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450 | |
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451 | n->is_field=TRUE; |
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452 | n->is_domain=TRUE; |
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453 | n->rep=n_rep_gmp_float; |
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454 | |
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455 | //n->cfKillChar = ndKillChar; /* dummy */ |
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456 | |
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457 | n->cfSetChar = ngfSetChar; |
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458 | n->ch = 0; |
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459 | n->cfCoeffString=ngfCoeffString; |
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460 | n->cfCoeffName=ngfCoeffName; |
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461 | |
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462 | n->cfDelete = ngfDelete; |
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463 | //n->cfNormalize=ndNormalize; |
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464 | n->cfInit = ngfInit; |
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465 | n->cfInt = ngfInt; |
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466 | n->cfAdd = ngfAdd; |
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467 | n->cfSub = ngfSub; |
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468 | n->cfMult = ngfMult; |
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469 | n->cfDiv = ngfDiv; |
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470 | n->cfExactDiv= ngfDiv; |
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471 | n->cfInpNeg = ngfNeg; |
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472 | n->cfInvers = ngfInvers; |
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473 | n->cfCopy = ngfCopy; |
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474 | n->cfGreater = ngfGreater; |
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475 | n->cfEqual = ngfEqual; |
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476 | n->cfIsZero = ngfIsZero; |
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477 | n->cfIsOne = ngfIsOne; |
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478 | n->cfIsMOne = ngfIsMOne; |
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479 | n->cfGreaterZero = ngfGreaterZero; |
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480 | n->cfWriteLong = ngfWrite; |
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481 | n->cfRead = ngfRead; |
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482 | n->cfPower = ngfPower; |
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483 | n->cfSetMap = ngfSetMap; |
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484 | n->cfCoeffWrite = ngfCoeffWrite; |
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485 | #ifdef LDEBUG |
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486 | //n->cfDBTest = ndDBTest; // not yet implemented: ngfDBTest |
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487 | #endif |
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488 | |
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489 | n->nCoeffIsEqual = ngfCoeffIsEqual; |
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490 | |
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491 | if( parameter != NULL) |
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492 | { |
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493 | LongComplexInfo* p = (LongComplexInfo*)parameter; |
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494 | |
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495 | n->float_len = p->float_len; |
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496 | n->float_len2 = p->float_len2; |
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497 | } else // default values, just for testing! |
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498 | { |
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499 | n->float_len = SHORT_REAL_LENGTH; |
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500 | n->float_len2 = SHORT_REAL_LENGTH; |
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501 | } |
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502 | |
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503 | assume( n->float_len2 >= SHORT_REAL_LENGTH ); |
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504 | |
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505 | assume( n_NumberOfParameters(n) == 0 ); |
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506 | assume( n_ParameterNames(n) == NULL ); |
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507 | |
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508 | return FALSE; |
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509 | } |
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510 | |
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511 | number ngfMapQ(number from, const coeffs src, const coeffs dst) |
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512 | { |
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513 | assume( getCoeffType(dst) == n_long_R ); |
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514 | assume( src->rep == n_rep_gap_rat ); |
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515 | |
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516 | gmp_float *res=new gmp_float(numberFieldToFloat(from,QTOF)); |
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517 | return (number)res; |
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518 | } |
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519 | number ngfMapZ(number from, const coeffs aRing, const coeffs r) |
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520 | { |
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521 | assume( getCoeffType(r) == n_long_R ); |
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522 | assume( aRing->rep == n_rep_gap_gmp); |
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523 | |
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524 | if ( from != NULL ) |
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525 | { |
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526 | if (SR_HDL(from) & SR_INT) |
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527 | { |
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528 | gmp_float f_i= gmp_float(SR_TO_INT(from)); |
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529 | gmp_float *res=new gmp_float(f_i); |
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530 | return (number)res; |
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531 | } |
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532 | gmp_float f_i=(mpz_ptr)from; |
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533 | gmp_float *res=new gmp_float(f_i); |
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534 | return (number)res; |
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535 | } |
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536 | else |
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537 | return NULL; |
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538 | } |
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539 | |
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540 | |
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541 | static number ngfMapR(number from, const coeffs src, const coeffs dst) |
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542 | { |
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543 | assume( getCoeffType(dst) == n_long_R ); |
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544 | assume( getCoeffType(src) == n_R ); |
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545 | |
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546 | gmp_float *res=new gmp_float((double)nf(from).F()); |
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547 | return (number)res; |
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548 | } |
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549 | |
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550 | static number ngfMapP(number from, const coeffs src, const coeffs dst) |
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551 | { |
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552 | assume( getCoeffType(dst) == n_long_R ); |
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553 | assume( getCoeffType(src) == n_Zp ); |
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554 | |
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555 | return ngfInit(npInt(from,src), dst); // FIXME? TODO? // extern int npInt (number &n, const coeffs r); |
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556 | } |
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557 | |
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558 | static number ngfMapC(number from, const coeffs src, const coeffs dst) |
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559 | { |
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560 | assume( getCoeffType(dst) == n_long_R ); |
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561 | assume( getCoeffType(src) == n_long_C ); |
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562 | |
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563 | gmp_float *res=new gmp_float(((gmp_complex*)from)->real()); |
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564 | return (number)res; |
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565 | } |
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566 | |
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567 | nMapFunc ngfSetMap(const coeffs src, const coeffs dst) |
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568 | { |
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569 | assume( getCoeffType(dst) == n_long_R ); |
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570 | |
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571 | if (src->rep==n_rep_gap_rat) /*Q, Z*/ |
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572 | { |
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573 | return ngfMapQ; |
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574 | } |
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575 | if (src->rep==n_rep_gap_gmp) /*Q, Z*/ |
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576 | { |
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577 | return ngfMapZ; |
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578 | } |
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579 | if ((src->rep==n_rep_gmp_float) && nCoeff_is_long_R(src)) |
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580 | { |
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581 | return ndCopyMap; //ngfCopyMap; |
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582 | } |
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583 | if ((src->rep==n_rep_float) && nCoeff_is_R(src)) |
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584 | { |
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585 | return ngfMapR; |
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586 | } |
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587 | if ((src->rep==n_rep_gmp_complex) && nCoeff_is_long_C(src)) |
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588 | { |
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589 | return ngfMapC; |
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590 | } |
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591 | if ((src->rep==n_rep_int) && nCoeff_is_Zp(src)) |
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592 | { |
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593 | return ngfMapP; |
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594 | } |
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595 | return NULL; |
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596 | } |
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597 | |
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598 | void ngfCoeffWrite (const coeffs r, BOOLEAN /*details*/) |
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599 | { |
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600 | Print("// characteristic : 0 (real:%d digits, additional %d digits)\n", |
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601 | r->float_len,r->float_len2); /* long R */ |
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602 | } |
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