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1 // Range.cc -*- C++ -*- |
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2 /* |
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4 Copyright (C) 1992, 1993, 1994, 1995 John W. Eaton |
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5 |
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6 This file is part of Octave. |
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7 |
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8 Octave is free software; you can redistribute it and/or modify it |
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9 under the terms of the GNU General Public License as published by the |
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10 Free Software Foundation; either version 2, or (at your option) any |
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11 later version. |
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12 |
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13 Octave is distributed in the hope that it will be useful, but WITHOUT |
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14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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16 for more details. |
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17 |
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18 You should have received a copy of the GNU General Public License |
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19 along with Octave; see the file COPYING. If not, write to the Free |
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20 Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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21 |
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22 */ |
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23 |
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24 #if defined (__GNUG__) |
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25 #pragma implementation |
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26 #endif |
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27 |
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28 #ifdef HAVE_CONFIG_H |
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29 #include <config.h> |
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30 #endif |
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31 |
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32 #include <cfloat> |
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33 #include <climits> |
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34 #include <cmath> |
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35 |
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36 #include <iostream.h> |
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37 |
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38 #include "Range.h" |
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39 #include "dMatrix.h" |
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40 |
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41 Matrix |
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42 Range::matrix_value (void) const |
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43 { |
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44 Matrix retval; |
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45 |
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46 if (rng_nelem > 0) |
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47 { |
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48 retval.resize (1, rng_nelem); |
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49 double b = rng_base; |
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50 double increment = rng_inc; |
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51 for (int i = 0; i < rng_nelem; i++) |
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52 retval.elem (0, i) = b + i * increment; |
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53 } |
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54 |
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55 return retval; |
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56 } |
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57 |
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58 // NOTE: max and min only return useful values if nelem > 0. |
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59 |
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60 double |
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61 Range::min (void) const |
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62 { |
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63 double retval = 0.0; |
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64 if (rng_nelem > 0) |
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65 { |
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66 if (rng_inc > 0) |
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67 retval = rng_base; |
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68 else |
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69 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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70 } |
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71 return retval; |
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72 } |
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73 |
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74 double |
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75 Range::max (void) const |
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76 { |
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77 double retval = 0.0; |
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78 if (rng_nelem > 0) |
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79 { |
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80 if (rng_inc > 0) |
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81 retval = rng_base + (rng_nelem - 1) * rng_inc; |
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82 else |
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83 retval = rng_base; |
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84 } |
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85 return retval; |
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86 } |
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87 |
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88 void |
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89 Range::sort (void) |
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90 { |
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91 if (rng_base > rng_limit && rng_inc < 0.0) |
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92 { |
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93 double tmp = rng_base; |
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94 rng_base = min (); |
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95 rng_limit = tmp; |
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96 rng_inc = -rng_inc; |
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97 } |
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98 } |
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99 |
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100 void |
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101 Range::print_range (void) |
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102 { |
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103 cerr << "Range: rng_base = " << rng_base |
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104 << " rng_limit " << rng_limit |
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105 << " rng_inc " << rng_inc |
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106 << " rng_nelem " << rng_nelem << "\n"; |
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107 } |
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108 |
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109 ostream& |
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110 operator << (ostream& os, const Range& a) |
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111 { |
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112 double b = a.base (); |
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113 double increment = a.inc (); |
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114 int num_elem = a.nelem (); |
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115 |
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116 for (int i = 0; i < num_elem; i++) |
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117 os << b + i * increment << " "; |
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118 |
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119 os << "\n"; |
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120 |
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121 return os; |
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122 } |
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123 |
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124 istream& |
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125 operator >> (istream& is, Range& a) |
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126 { |
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127 is >> a.rng_base; |
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128 if (is) |
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129 { |
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130 is >> a.rng_limit; |
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131 if (is) |
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132 { |
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133 is >> a.rng_inc; |
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134 a.rng_nelem = a.nelem_internal (); |
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135 } |
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136 } |
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137 |
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138 return is; |
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139 } |
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140 |
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141 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. |
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142 // C |
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143 // C===Tolerant FLOOR function. |
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144 // C |
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145 // C X - is given as a Double Precision argument to be operated on. |
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146 // C It is assumed that X is represented with M mantissa bits. |
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147 // C CT - is given as a Comparison Tolerance such that |
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148 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between |
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149 // C X and A whole number is less than CT, then TFLOOR is |
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150 // C returned as this whole number. By treating the |
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151 // C floating-point numbers as a finite ordered set note that |
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152 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes |
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153 // C arguments of TFLOOR/TCEIL to be treated as whole numbers |
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154 // C if they are exactly whole numbers or are immediately |
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155 // C adjacent to whole number representations. Since EPS, the |
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156 // C "distance" between floating-point numbers on the unit |
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157 // C interval, and M, the number of bits in X'S mantissa, exist |
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158 // C on every floating-point computer, TFLOOR/TCEIL are |
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159 // C consistently definable on every floating-point computer. |
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160 // C |
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161 // C For more information see the following references: |
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162 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE |
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163 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. |
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164 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL |
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165 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through |
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166 // C FL5, the history of five years of evolutionary development of |
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167 // C FL5 - the seven lines of code below - by open collaboration |
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168 // C and corroboration of the mathematical-computing community. |
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169 // C |
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170 // C Penn State University Center for Academic Computing |
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171 // C H. D. Knoble - August, 1978. |
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172 |
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173 static inline double |
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174 tfloor (double x, double ct) |
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175 { |
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176 // C---------FLOOR(X) is the largest integer algebraically less than |
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177 // C or equal to X; that is, the unfuzzy FLOOR function. |
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178 |
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179 // DINT (X) = X - DMOD (X, 1.0); |
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180 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); |
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181 |
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182 // C---------Hagerty's FL5 function follows... |
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183 |
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184 double q = 1.0; |
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185 |
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186 if (x < 0.0) |
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187 q = 1.0 - ct; |
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188 |
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189 double rmax = q / (2.0 - ct); |
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190 |
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191 double t1 = 1.0 + floor (x); |
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192 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); |
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193 t1 = rmax < t1 ? rmax : t1; |
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194 t1 = ct > t1 ? ct : t1; |
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195 t1 = floor (x + t1); |
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196 |
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197 if (x <= 0.0 || (t1 - x) < rmax) |
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198 return t1; |
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199 else |
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200 return t1 - 1.0; |
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201 } |
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202 |
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203 static inline double |
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204 tceil (double x, double ct) |
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205 { |
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206 return -tfloor (-x, ct); |
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207 } |
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208 |
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209 static inline double |
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210 round (double x, double ct) |
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211 { |
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212 return tfloor (x+0.5, ct); |
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213 } |
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214 |
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215 int |
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216 Range::nelem_internal (void) const |
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217 { |
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218 double ct = 3.0 * DBL_EPSILON; |
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219 |
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220 double tmp = tfloor ((rng_limit - rng_base + rng_inc) / rng_inc, ct); |
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221 |
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222 int n_intervals = (int) (tmp > 0.0 ? tmp : 0); |
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223 |
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224 return (n_intervals >= INT_MAX - 1) ? -1 : n_intervals; |
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225 } |
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226 |
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227 /* |
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228 ;;; Local Variables: *** |
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229 ;;; mode: C++ *** |
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230 ;;; page-delimiter: "^/\\*" *** |
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231 ;;; End: *** |
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232 */ |
