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1 /* glplib02.c (64-bit arithmetic) */ |
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2 |
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3 /*********************************************************************** |
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4 * This code is part of GLPK (GNU Linear Programming Kit). |
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5 * |
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6 * Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, |
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7 * 2009, 2010 Andrew Makhorin, Department for Applied Informatics, |
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8 * Moscow Aviation Institute, Moscow, Russia. All rights reserved. |
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9 * E-mail: <mao@gnu.org>. |
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10 * |
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11 * GLPK is free software: you can redistribute it and/or modify it |
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12 * under the terms of the GNU General Public License as published by |
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13 * the Free Software Foundation, either version 3 of the License, or |
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14 * (at your option) any later version. |
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15 * |
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16 * GLPK is distributed in the hope that it will be useful, but WITHOUT |
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17 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
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18 * or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public |
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19 * License for more details. |
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20 * |
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21 * You should have received a copy of the GNU General Public License |
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22 * along with GLPK. If not, see <http://www.gnu.org/licenses/>. |
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23 ***********************************************************************/ |
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24 |
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25 #include "glpenv.h" |
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26 #include "glplib.h" |
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27 |
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28 /*********************************************************************** |
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29 * NAME |
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30 * |
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31 * xlset - expand integer to long integer |
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32 * |
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33 * SYNOPSIS |
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34 * |
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35 * #include "glplib.h" |
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36 * glp_long xlset(int x); |
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37 * |
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38 * RETURNS |
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39 * |
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40 * The routine xlset returns x expanded to long integer. */ |
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41 |
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42 glp_long xlset(int x) |
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43 { glp_long t; |
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44 t.lo = x, t.hi = (x >= 0 ? 0 : -1); |
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45 return t; |
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46 } |
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47 |
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48 /*********************************************************************** |
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49 * NAME |
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50 * |
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51 * xlneg - negate long integer |
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52 * |
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53 * SYNOPSIS |
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54 * |
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55 * #include "glplib.h" |
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56 * glp_long xlneg(glp_long x); |
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57 * |
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58 * RETURNS |
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59 * |
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60 * The routine xlneg returns the difference 0 - x. */ |
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61 |
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62 glp_long xlneg(glp_long x) |
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63 { if (x.lo) |
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64 x.lo = - x.lo, x.hi = ~x.hi; |
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65 else |
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66 x.hi = - x.hi; |
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67 return x; |
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68 } |
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69 |
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70 /*********************************************************************** |
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71 * NAME |
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72 * |
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73 * xladd - add long integers |
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74 * |
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75 * SYNOPSIS |
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76 * |
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77 * #include "glplib.h" |
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78 * glp_long xladd(glp_long x, glp_long y); |
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79 * |
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80 * RETURNS |
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81 * |
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82 * The routine xladd returns the sum x + y. */ |
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83 |
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84 glp_long xladd(glp_long x, glp_long y) |
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85 { if ((unsigned int)x.lo <= 0xFFFFFFFF - (unsigned int)y.lo) |
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86 x.lo += y.lo, x.hi += y.hi; |
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87 else |
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88 x.lo += y.lo, x.hi += y.hi + 1; |
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89 return x; |
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90 } |
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91 |
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92 /*********************************************************************** |
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93 * NAME |
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94 * |
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95 * xlsub - subtract long integers |
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96 * |
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97 * SYNOPSIS |
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98 * |
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99 * #include "glplib.h" |
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100 * glp_long xlsub(glp_long x, glp_long y); |
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101 * |
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102 * RETURNS |
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103 * |
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104 * The routine xlsub returns the difference x - y. */ |
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105 |
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106 glp_long xlsub(glp_long x, glp_long y) |
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107 { return |
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108 xladd(x, xlneg(y)); |
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109 } |
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110 |
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111 /*********************************************************************** |
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112 * NAME |
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113 * |
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114 * xlcmp - compare long integers |
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115 * |
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116 * SYNOPSIS |
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117 * |
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118 * #include "glplib.h" |
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119 * int xlcmp(glp_long x, glp_long y); |
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120 * |
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121 * RETURNS |
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122 * |
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123 * The routine xlcmp returns the sign of the difference x - y. */ |
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124 |
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125 int xlcmp(glp_long x, glp_long y) |
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126 { if (x.hi >= 0 && y.hi < 0) return +1; |
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127 if (x.hi < 0 && y.hi >= 0) return -1; |
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128 if ((unsigned int)x.hi < (unsigned int)y.hi) return -1; |
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129 if ((unsigned int)x.hi > (unsigned int)y.hi) return +1; |
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130 if ((unsigned int)x.lo < (unsigned int)y.lo) return -1; |
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131 if ((unsigned int)x.lo > (unsigned int)y.lo) return +1; |
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132 return 0; |
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133 } |
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134 |
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135 /*********************************************************************** |
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136 * NAME |
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137 * |
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138 * xlmul - multiply long integers |
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139 * |
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140 * SYNOPSIS |
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141 * |
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142 * #include "glplib.h" |
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143 * glp_long xlmul(glp_long x, glp_long y); |
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144 * |
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145 * RETURNS |
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146 * |
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147 * The routine xlmul returns the product x * y. */ |
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148 |
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149 glp_long xlmul(glp_long x, glp_long y) |
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150 { unsigned short xx[8], yy[4]; |
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151 xx[4] = (unsigned short)x.lo; |
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152 xx[5] = (unsigned short)(x.lo >> 16); |
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153 xx[6] = (unsigned short)x.hi; |
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154 xx[7] = (unsigned short)(x.hi >> 16); |
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155 yy[0] = (unsigned short)y.lo; |
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156 yy[1] = (unsigned short)(y.lo >> 16); |
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157 yy[2] = (unsigned short)y.hi; |
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158 yy[3] = (unsigned short)(y.hi >> 16); |
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159 bigmul(4, 4, xx, yy); |
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160 x.lo = (unsigned int)xx[0] | ((unsigned int)xx[1] << 16); |
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161 x.hi = (unsigned int)xx[2] | ((unsigned int)xx[3] << 16); |
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162 return x; |
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163 } |
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164 |
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165 /*********************************************************************** |
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166 * NAME |
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167 * |
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168 * xldiv - divide long integers |
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169 * |
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170 * SYNOPSIS |
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171 * |
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172 * #include "glplib.h" |
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173 * glp_ldiv xldiv(glp_long x, glp_long y); |
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174 * |
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175 * RETURNS |
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176 * |
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177 * The routine xldiv returns a structure of type glp_ldiv containing |
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178 * members quot (the quotient) and rem (the remainder), both of type |
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179 * glp_long. */ |
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180 |
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181 glp_ldiv xldiv(glp_long x, glp_long y) |
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182 { glp_ldiv t; |
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183 int m, sx, sy; |
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184 unsigned short xx[8], yy[4]; |
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185 /* sx := sign(x) */ |
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186 sx = (x.hi < 0); |
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187 /* sy := sign(y) */ |
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188 sy = (y.hi < 0); |
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189 /* x := |x| */ |
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190 if (sx) x = xlneg(x); |
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191 /* y := |y| */ |
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192 if (sy) y = xlneg(y); |
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193 /* compute x div y and x mod y */ |
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194 xx[0] = (unsigned short)x.lo; |
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195 xx[1] = (unsigned short)(x.lo >> 16); |
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196 xx[2] = (unsigned short)x.hi; |
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197 xx[3] = (unsigned short)(x.hi >> 16); |
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198 yy[0] = (unsigned short)y.lo; |
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199 yy[1] = (unsigned short)(y.lo >> 16); |
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200 yy[2] = (unsigned short)y.hi; |
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201 yy[3] = (unsigned short)(y.hi >> 16); |
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202 if (yy[3]) |
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203 m = 4; |
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204 else if (yy[2]) |
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205 m = 3; |
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206 else if (yy[1]) |
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207 m = 2; |
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208 else if (yy[0]) |
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209 m = 1; |
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210 else |
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211 xerror("xldiv: divide by zero\n"); |
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212 bigdiv(4 - m, m, xx, yy); |
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213 /* remainder in x[0], x[1], ..., x[m-1] */ |
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214 t.rem.lo = (unsigned int)xx[0], t.rem.hi = 0; |
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215 if (m >= 2) t.rem.lo |= (unsigned int)xx[1] << 16; |
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216 if (m >= 3) t.rem.hi = (unsigned int)xx[2]; |
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217 if (m >= 4) t.rem.hi |= (unsigned int)xx[3] << 16; |
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218 if (sx) t.rem = xlneg(t.rem); |
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219 /* quotient in x[m], x[m+1], ..., x[4] */ |
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220 t.quot.lo = (unsigned int)xx[m], t.quot.hi = 0; |
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221 if (m <= 3) t.quot.lo |= (unsigned int)xx[m+1] << 16; |
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222 if (m <= 2) t.quot.hi = (unsigned int)xx[m+2]; |
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223 if (m <= 1) t.quot.hi |= (unsigned int)xx[m+3] << 16; |
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224 if (sx ^ sy) t.quot = xlneg(t.quot); |
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225 return t; |
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226 } |
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227 |
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228 /*********************************************************************** |
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229 * NAME |
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230 * |
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231 * xltod - convert long integer to double |
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232 * |
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233 * SYNOPSIS |
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234 * |
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235 * #include "glplib.h" |
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236 * double xltod(glp_long x); |
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237 * |
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238 * RETURNS |
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239 * |
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240 * The routine xltod returns x converted to double. */ |
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241 |
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242 double xltod(glp_long x) |
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243 { double s, z; |
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244 if (x.hi >= 0) |
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245 s = +1.0; |
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246 else |
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247 s = -1.0, x = xlneg(x); |
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248 if (x.hi >= 0) |
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249 z = 4294967296.0 * (double)x.hi + (double)(unsigned int)x.lo; |
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250 else |
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251 { xassert(x.hi == 0x80000000 && x.lo == 0x00000000); |
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252 z = 9223372036854775808.0; /* 2^63 */ |
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253 } |
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254 return s * z; |
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255 } |
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256 |
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257 char *xltoa(glp_long x, char *s) |
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258 { /* convert long integer to character string */ |
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259 static const char *d = "0123456789"; |
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260 glp_ldiv t; |
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261 int neg, len; |
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262 if (x.hi >= 0) |
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263 neg = 0; |
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264 else |
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265 neg = 1, x = xlneg(x); |
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266 if (x.hi >= 0) |
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267 { len = 0; |
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268 while (!(x.hi == 0 && x.lo == 0)) |
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269 { t = xldiv(x, xlset(10)); |
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270 xassert(0 <= t.rem.lo && t.rem.lo <= 9); |
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271 s[len++] = d[t.rem.lo]; |
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272 x = t.quot; |
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273 } |
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274 if (len == 0) s[len++] = d[0]; |
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275 if (neg) s[len++] = '-'; |
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276 s[len] = '\0'; |
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277 strrev(s); |
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278 } |
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279 else |
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280 strcpy(s, "-9223372036854775808"); /* -2^63 */ |
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281 return s; |
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282 } |
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283 |
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284 /**********************************************************************/ |
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285 |
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286 #if 0 |
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287 #include "glprng.h" |
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288 |
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289 #define N_TEST 1000000 |
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290 /* number of tests */ |
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291 |
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292 static glp_long myrand(RNG *rand) |
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293 { glp_long x; |
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294 int k; |
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295 k = rng_unif_rand(rand, 4); |
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296 xassert(0 <= k && k <= 3); |
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297 x.lo = rng_unif_rand(rand, 65536); |
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298 if (k == 1 || k == 3) |
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299 { x.lo <<= 16; |
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300 x.lo += rng_unif_rand(rand, 65536); |
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301 } |
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302 if (k <= 1) |
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303 x.hi = 0; |
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304 else |
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305 x.hi = rng_unif_rand(rand, 65536); |
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306 if (k == 3) |
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307 { x.hi <<= 16; |
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308 x.hi += rng_unif_rand(rand, 65536); |
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309 } |
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310 if (rng_unif_rand(rand, 2)) x = xlneg(x); |
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311 return x; |
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312 } |
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313 |
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314 int main(void) |
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315 { RNG *rand; |
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316 glp_long x, y; |
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317 glp_ldiv z; |
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318 int test; |
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319 rand = rng_create_rand(); |
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320 for (test = 1; test <= N_TEST; test++) |
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321 { x = myrand(rand); |
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322 y = myrand(rand); |
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323 if (y.lo == 0 && y.hi == 0) y.lo = 1; |
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324 /* z.quot := x div y, z.rem := x mod y */ |
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325 z = xldiv(x, y); |
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326 /* x must be equal to y * z.quot + z.rem */ |
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327 xassert(xlcmp(x, xladd(xlmul(y, z.quot), z.rem)) == 0); |
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328 } |
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329 xprintf("%d tests successfully passed\n", N_TEST); |
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330 rng_delete_rand(rand); |
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331 return 0; |
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332 } |
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333 #endif |
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334 |
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335 /* eof */ |