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1 /* |
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2 |
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3 Copyright (C) 1996, 1997 John W. Eaton |
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4 |
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5 This file is part of Octave. |
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6 |
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7 Octave is free software; you can redistribute it and/or modify it |
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8 under the terms of the GNU General Public License as published by the |
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9 Free Software Foundation; either version 2, or (at your option) any |
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10 later version. |
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11 |
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12 Octave is distributed in the hope that it will be useful, but WITHOUT |
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13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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15 for more details. |
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16 |
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17 You should have received a copy of the GNU General Public License |
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18 along with Octave; see the file COPYING. If not, write to the Free |
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19 Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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20 02110-1301, USA. |
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21 |
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22 */ |
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23 |
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24 #ifdef HAVE_CONFIG_H |
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25 #include <config.h> |
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26 #endif |
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27 |
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28 #include <cfloat> |
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29 #include <cmath> |
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30 |
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31 #include <iostream> |
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32 #include <limits> |
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33 |
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34 #include "Range.h" |
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35 #include "lo-mappers.h" |
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36 #include "lo-utils.h" |
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37 |
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38 bool |
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39 Range::all_elements_are_ints (void) const |
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40 { |
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41 // If the base and increment are ints, the final value in the range |
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42 // will also be an integer, even if the limit is not. If there is one |
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43 // or fewer elements only the base needs to be an integer |
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44 |
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45 return (! (xisnan (rng_base) || xisnan (rng_inc)) |
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46 && (NINTbig (rng_base) == rng_base || rng_nelem < 1) |
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47 && (NINTbig (rng_inc) == rng_inc || rng_nelem <= 1)); |
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48 } |
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49 |
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50 Matrix |
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51 Range::matrix_value (void) const |
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52 { |
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53 if (rng_nelem > 0 && cache.rows () == 0) |
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645
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54 { |
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55 cache.resize (1, rng_nelem); |
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56 double b = rng_base; |
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57 double increment = rng_inc; |
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58 for (octave_idx_type i = 0; i < rng_nelem; i++) |
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59 cache(i) = b + i * increment; |
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60 |
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61 // On some machines (x86 with extended precision floating point |
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62 // arithmetic, for example) it is possible that we can overshoot |
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63 // the limit by approximately the machine precision even though |
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64 // we were very careful in our calculation of the number of |
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65 // elements. |
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66 |
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67 if ((rng_inc > 0 && cache(rng_nelem-1) > rng_limit) |
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68 || (rng_inc < 0 && cache(rng_nelem-1) < rng_limit)) |
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69 cache(rng_nelem-1) = rng_limit; |
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70 } |
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71 |
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72 return cache; |
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73 } |
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74 |
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75 |
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76 // NOTE: max and min only return useful values if nelem > 0. |
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77 |
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78 double |
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79 Range::min (void) const |
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80 { |
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81 double retval = 0.0; |
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82 if (rng_nelem > 0) |
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83 { |
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84 if (rng_inc > 0) |
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85 retval = rng_base; |
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86 else |
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87 { |
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88 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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89 |
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90 // See the note in the matrix_value method above. |
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91 |
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92 if (retval < rng_limit) |
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93 retval = rng_limit; |
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94 } |
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95 |
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96 } |
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97 return retval; |
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98 } |
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99 |
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100 double |
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101 Range::max (void) const |
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102 { |
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103 double retval = 0.0; |
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104 if (rng_nelem > 0) |
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105 { |
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106 if (rng_inc > 0) |
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107 { |
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108 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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109 |
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110 // See the note in the matrix_value method above. |
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111 |
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112 if (retval > rng_limit) |
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113 retval = rng_limit; |
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114 } |
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115 else |
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116 retval = rng_base; |
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117 } |
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118 return retval; |
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119 } |
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120 |
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121 void |
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122 Range::sort (void) |
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123 { |
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124 if (rng_base > rng_limit && rng_inc < 0.0) |
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125 { |
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126 double tmp = rng_base; |
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127 rng_base = min (); |
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128 rng_limit = tmp; |
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129 rng_inc = -rng_inc; |
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130 clear_cache (); |
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131 } |
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132 } |
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133 |
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134 std::ostream& |
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135 operator << (std::ostream& os, const Range& a) |
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136 { |
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137 double b = a.base (); |
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138 double increment = a.inc (); |
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139 octave_idx_type num_elem = a.nelem (); |
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140 |
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141 for (octave_idx_type i = 0; i < num_elem-1; i++) |
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142 os << b + i * increment << " "; |
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143 |
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144 // Prevent overshoot. See comment in the matrix_value method |
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145 // above. |
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146 |
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147 os << (increment > 0 ? a.max () : a.min ()) << "\n"; |
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148 |
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149 return os; |
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150 } |
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151 |
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152 std::istream& |
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153 operator >> (std::istream& is, Range& a) |
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154 { |
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155 is >> a.rng_base; |
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156 if (is) |
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157 { |
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158 is >> a.rng_limit; |
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159 if (is) |
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160 { |
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161 is >> a.rng_inc; |
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162 a.rng_nelem = a.nelem_internal (); |
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163 } |
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164 } |
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165 |
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166 return is; |
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167 } |
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168 |
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169 Range |
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170 operator - (const Range& r) |
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171 { |
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172 return Range (-r.base (), -r.limit (), -r.inc ()); |
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173 } |
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174 |
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175 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. |
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176 // C |
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177 // C===Tolerant FLOOR function. |
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178 // C |
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179 // C X - is given as a Double Precision argument to be operated on. |
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180 // C It is assumed that X is represented with M mantissa bits. |
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181 // C CT - is given as a Comparison Tolerance such that |
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182 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between |
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183 // C X and A whole number is less than CT, then TFLOOR is |
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184 // C returned as this whole number. By treating the |
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185 // C floating-point numbers as a finite ordered set note that |
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186 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes |
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187 // C arguments of TFLOOR/TCEIL to be treated as whole numbers |
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188 // C if they are exactly whole numbers or are immediately |
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189 // C adjacent to whole number representations. Since EPS, the |
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190 // C "distance" between floating-point numbers on the unit |
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191 // C interval, and M, the number of bits in X'S mantissa, exist |
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192 // C on every floating-point computer, TFLOOR/TCEIL are |
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193 // C consistently definable on every floating-point computer. |
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194 // C |
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195 // C For more information see the following references: |
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196 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE |
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197 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. |
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198 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL |
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199 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through |
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200 // C FL5, the history of five years of evolutionary development of |
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201 // C FL5 - the seven lines of code below - by open collaboration |
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202 // C and corroboration of the mathematical-computing community. |
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203 // C |
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204 // C Penn State University Center for Academic Computing |
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205 // C H. D. Knoble - August, 1978. |
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206 |
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207 static inline double |
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208 tfloor (double x, double ct) |
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209 { |
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210 // C---------FLOOR(X) is the largest integer algebraically less than |
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211 // C or equal to X; that is, the unfuzzy FLOOR function. |
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212 |
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213 // DINT (X) = X - DMOD (X, 1.0); |
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214 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); |
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215 |
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216 // C---------Hagerty's FL5 function follows... |
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217 |
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218 double q = 1.0; |
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219 |
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220 if (x < 0.0) |
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221 q = 1.0 - ct; |
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222 |
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223 double rmax = q / (2.0 - ct); |
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224 |
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225 double t1 = 1.0 + floor (x); |
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226 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); |
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227 t1 = rmax < t1 ? rmax : t1; |
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228 t1 = ct > t1 ? ct : t1; |
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229 t1 = floor (x + t1); |
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230 |
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231 if (x <= 0.0 || (t1 - x) < rmax) |
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232 return t1; |
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233 else |
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234 return t1 - 1.0; |
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235 } |
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236 |
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237 static inline double |
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238 tceil (double x, double ct) |
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239 { |
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240 return -tfloor (-x, ct); |
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241 } |
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242 |
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243 static inline bool |
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244 teq (double u, double v, double ct = 3.0 * DBL_EPSILON) |
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245 { |
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246 double tu = fabs (u); |
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247 double tv = fabs (v); |
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248 |
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249 return fabs (u - v) < ((tu > tv ? tu : tv) * ct); |
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250 } |
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251 |
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252 octave_idx_type |
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253 Range::nelem_internal (void) const |
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254 { |
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255 octave_idx_type retval = -1; |
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256 |
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257 if (rng_inc == 0 |
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258 || (rng_limit > rng_base && rng_inc < 0) |
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259 || (rng_limit < rng_base && rng_inc > 0)) |
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260 { |
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261 retval = 0; |
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262 } |
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263 else |
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264 { |
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265 double ct = 3.0 * DBL_EPSILON; |
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266 |
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267 double tmp = tfloor ((rng_limit - rng_base + rng_inc) / rng_inc, ct); |
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268 |
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269 octave_idx_type n_elt = (tmp > 0.0 ? static_cast<octave_idx_type> (tmp) : 0); |
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270 |
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271 // If the final element that we would compute for the range is |
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272 // equal to the limit of the range, or is an adjacent floating |
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273 // point number, accept it. Otherwise, try a range with one |
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274 // fewer element. If that fails, try again with one more |
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275 // element. |
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276 // |
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277 // I'm not sure this is very good, but it seems to work better than |
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278 // just using tfloor as above. For example, without it, the |
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279 // expression 1.8:0.05:1.9 fails to produce the expected result of |
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280 // [1.8, 1.85, 1.9]. |
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281 |
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282 if (! teq (rng_base + (n_elt - 1) * rng_inc, rng_limit)) |
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283 { |
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284 if (teq (rng_base + (n_elt - 2) * rng_inc, rng_limit)) |
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285 n_elt--; |
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286 else if (teq (rng_base + n_elt * rng_inc, rng_limit)) |
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287 n_elt++; |
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288 } |
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289 |
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290 retval = (n_elt >= std::numeric_limits<octave_idx_type>::max () - 1) ? -1 : n_elt; |
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291 } |
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292 |
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293 return retval; |
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294 } |
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295 |
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296 /* |
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297 ;;; Local Variables: *** |
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298 ;;; mode: C++ *** |
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299 ;;; End: *** |
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300 */ |
