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1 /* |
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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, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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20 |
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21 */ |
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22 |
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23 #if defined (__GNUG__) |
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24 #pragma implementation |
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25 #endif |
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26 |
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27 #ifdef HAVE_CONFIG_H |
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28 #include <config.h> |
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29 #endif |
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30 |
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31 #include <cfloat> |
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32 #include <climits> |
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33 #include <cmath> |
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34 |
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35 #include <iostream> |
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36 |
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37 #include "Range.h" |
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38 #include "dMatrix.h" |
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39 #include "lo-mappers.h" |
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40 #include "lo-utils.h" |
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41 |
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42 bool |
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43 Range::all_elements_are_ints (void) const |
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44 { |
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45 // If the base and increment are ints, the final value in the range |
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46 // will also be an integer, even if the limit is not. |
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47 |
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48 return (! (xisnan (rng_base) || xisnan (rng_inc)) |
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49 && NINT (rng_base) == rng_base |
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50 && NINT (rng_inc) == rng_inc); |
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51 } |
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52 |
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53 Matrix |
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54 Range::matrix_value (void) const |
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55 { |
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56 Matrix retval; |
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57 |
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58 if (rng_nelem > 0) |
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59 { |
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60 retval.resize (1, rng_nelem); |
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61 double b = rng_base; |
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62 double increment = rng_inc; |
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63 for (int i = 0; i < rng_nelem; i++) |
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64 retval.elem (0, i) = b + i * increment; |
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65 } |
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66 |
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67 return retval; |
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68 } |
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69 |
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70 // NOTE: max and min only return useful values if nelem > 0. |
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71 |
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72 double |
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73 Range::min (void) const |
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74 { |
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75 double retval = 0.0; |
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76 if (rng_nelem > 0) |
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77 { |
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78 if (rng_inc > 0) |
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79 retval = rng_base; |
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80 else |
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81 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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82 } |
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83 return retval; |
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84 } |
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85 |
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86 double |
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87 Range::max (void) const |
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88 { |
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89 double retval = 0.0; |
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90 if (rng_nelem > 0) |
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91 { |
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92 if (rng_inc > 0) |
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93 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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94 else |
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95 retval = rng_base; |
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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 void |
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101 Range::sort (void) |
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102 { |
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103 if (rng_base > rng_limit && rng_inc < 0.0) |
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104 { |
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105 double tmp = rng_base; |
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106 rng_base = min (); |
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107 rng_limit = tmp; |
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108 rng_inc = -rng_inc; |
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109 } |
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110 } |
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111 |
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112 void |
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113 Range::print_range (void) |
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114 { |
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115 std::cerr << "Range: rng_base = " << rng_base |
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116 << " rng_limit " << rng_limit |
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117 << " rng_inc " << rng_inc |
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118 << " rng_nelem " << rng_nelem << "\n"; |
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119 } |
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120 |
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121 std::ostream& |
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122 operator << (std::ostream& os, const Range& a) |
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123 { |
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124 double b = a.base (); |
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125 double increment = a.inc (); |
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126 int num_elem = a.nelem (); |
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127 |
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128 for (int i = 0; i < num_elem; i++) |
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129 os << b + i * increment << " "; |
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130 |
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131 os << "\n"; |
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132 |
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133 return os; |
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134 } |
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135 |
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136 std::istream& |
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137 operator >> (std::istream& is, Range& a) |
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138 { |
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139 is >> a.rng_base; |
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140 if (is) |
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141 { |
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142 is >> a.rng_limit; |
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143 if (is) |
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144 { |
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145 is >> a.rng_inc; |
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146 a.rng_nelem = a.nelem_internal (); |
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147 } |
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148 } |
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149 |
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150 return is; |
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151 } |
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152 |
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153 Range |
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154 operator - (const Range& r) |
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155 { |
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156 return Range (-r.base (), -r.limit (), -r.inc ()); |
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157 } |
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158 |
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159 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. |
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160 // C |
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161 // C===Tolerant FLOOR function. |
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162 // C |
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163 // C X - is given as a Double Precision argument to be operated on. |
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164 // C It is assumed that X is represented with M mantissa bits. |
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165 // C CT - is given as a Comparison Tolerance such that |
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166 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between |
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167 // C X and A whole number is less than CT, then TFLOOR is |
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168 // C returned as this whole number. By treating the |
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169 // C floating-point numbers as a finite ordered set note that |
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170 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes |
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171 // C arguments of TFLOOR/TCEIL to be treated as whole numbers |
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172 // C if they are exactly whole numbers or are immediately |
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173 // C adjacent to whole number representations. Since EPS, the |
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174 // C "distance" between floating-point numbers on the unit |
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175 // C interval, and M, the number of bits in X'S mantissa, exist |
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176 // C on every floating-point computer, TFLOOR/TCEIL are |
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177 // C consistently definable on every floating-point computer. |
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178 // C |
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179 // C For more information see the following references: |
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180 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE |
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181 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. |
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182 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL |
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183 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through |
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184 // C FL5, the history of five years of evolutionary development of |
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185 // C FL5 - the seven lines of code below - by open collaboration |
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186 // C and corroboration of the mathematical-computing community. |
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187 // C |
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188 // C Penn State University Center for Academic Computing |
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189 // C H. D. Knoble - August, 1978. |
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190 |
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191 static inline double |
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192 tfloor (double x, double ct) |
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193 { |
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194 // C---------FLOOR(X) is the largest integer algebraically less than |
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195 // C or equal to X; that is, the unfuzzy FLOOR function. |
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196 |
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197 // DINT (X) = X - DMOD (X, 1.0); |
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198 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); |
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199 |
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200 // C---------Hagerty's FL5 function follows... |
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201 |
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202 double q = 1.0; |
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203 |
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204 if (x < 0.0) |
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205 q = 1.0 - ct; |
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206 |
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207 double rmax = q / (2.0 - ct); |
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208 |
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209 double t1 = 1.0 + floor (x); |
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210 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); |
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211 t1 = rmax < t1 ? rmax : t1; |
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212 t1 = ct > t1 ? ct : t1; |
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213 t1 = floor (x + t1); |
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214 |
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215 if (x <= 0.0 || (t1 - x) < rmax) |
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216 return t1; |
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217 else |
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218 return t1 - 1.0; |
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219 } |
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220 |
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221 static inline double |
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222 tceil (double x, double ct) |
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223 { |
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224 return -tfloor (-x, ct); |
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225 } |
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226 |
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227 static inline double |
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228 round (double x, double ct) |
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229 { |
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230 return tfloor (x+0.5, ct); |
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231 } |
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232 |
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233 int |
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234 Range::nelem_internal (void) const |
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235 { |
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236 double ct = 3.0 * DBL_EPSILON; |
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237 |
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238 double tmp = round ((rng_limit - rng_base + rng_inc) / rng_inc, ct); |
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239 |
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240 int n_elt = (tmp > 0.0 ? static_cast<int> (tmp) : 0); |
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241 |
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242 return (n_elt >= INT_MAX - 1) ? -1 : n_elt; |
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243 } |
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244 |
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245 /* |
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246 ;;; Local Variables: *** |
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247 ;;; mode: C++ *** |
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248 ;;; End: *** |
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249 */ |
