Mercurial > hg > octave-nkf
annotate liboctave/Range.cc @ 14026:3781981be535 ss-3-5-90
snapshot 3.5.90
* configure.ac (AC_INIT): Version is now 3.5.90.
(OCTAVE_API_VERSION_NUMBER): Now 46.
(OCTAVE_RELEASE_DATE): Now 2011-12-11.
| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sun, 11 Dec 2011 23:18:31 -0500 |
| parents | 731a0b589cab |
| children | 72c96de7a403 |
| rev | line source |
|---|---|
| 3 | 1 /* |
| 2 | |
| 11523 | 3 Copyright (C) 1993-2011 John W. Eaton |
| 3 | 4 |
| 5 This file is part of Octave. | |
| 6 | |
| 7 Octave is free software; you can redistribute it and/or modify it | |
| 8 under the terms of the GNU General Public License as published by the | |
| 7016 | 9 Free Software Foundation; either version 3 of the License, or (at your |
| 10 option) any later version. | |
| 3 | 11 |
| 12 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 13 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 14 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 15 for more details. | |
| 16 | |
| 17 You should have received a copy of the GNU General Public License | |
| 7016 | 18 along with Octave; see the file COPYING. If not, see |
| 19 <http://www.gnu.org/licenses/>. | |
| 3 | 20 |
| 21 */ | |
| 22 | |
| 238 | 23 #ifdef HAVE_CONFIG_H |
| 1192 | 24 #include <config.h> |
| 3 | 25 #endif |
| 26 | |
| 1546 | 27 #include <cfloat> |
| 1367 | 28 |
| 3503 | 29 #include <iostream> |
| 6490 | 30 #include <limits> |
| 3 | 31 |
| 32 #include "Range.h" | |
| 7458 | 33 #include "lo-error.h" |
| 2383 | 34 #include "lo-mappers.h" |
| 7231 | 35 #include "lo-math.h" |
| 2383 | 36 #include "lo-utils.h" |
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37 #include "Array-util.h" |
| 2383 | 38 |
| 8971 | 39 Range::Range (double b, double i, octave_idx_type n) |
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40 : rng_base (b), rng_limit (b + (n-1) * i), rng_inc (i), |
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41 rng_nelem (n), cache () |
| 8971 | 42 { |
| 43 if (! xfinite (b) || ! xfinite (i)) | |
| 44 rng_nelem = -2; | |
| 45 } | |
| 46 | |
| 2383 | 47 bool |
| 48 Range::all_elements_are_ints (void) const | |
| 49 { | |
| 50 // If the base and increment are ints, the final value in the range | |
| 6457 | 51 // will also be an integer, even if the limit is not. If there is one |
| 52 // or fewer elements only the base needs to be an integer | |
| 2383 | 53 |
| 54 return (! (xisnan (rng_base) || xisnan (rng_inc)) | |
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55 && (NINTbig (rng_base) == rng_base || rng_nelem < 1) |
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56 && (NINTbig (rng_inc) == rng_inc || rng_nelem <= 1)); |
| 2383 | 57 } |
| 645 | 58 |
| 59 Matrix | |
| 60 Range::matrix_value (void) const | |
| 61 { | |
| 8971 | 62 if (rng_nelem > 0 && cache.nelem () == 0) |
| 645 | 63 { |
| 4810 | 64 cache.resize (1, rng_nelem); |
| 645 | 65 double b = rng_base; |
| 66 double increment = rng_inc; | |
| 5275 | 67 for (octave_idx_type i = 0; i < rng_nelem; i++) |
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68 cache(i) = b + i * increment; |
| 4791 | 69 |
| 70 // On some machines (x86 with extended precision floating point | |
| 71 // arithmetic, for example) it is possible that we can overshoot | |
| 72 // the limit by approximately the machine precision even though | |
| 73 // we were very careful in our calculation of the number of | |
| 74 // elements. | |
| 75 | |
| 4810 | 76 if ((rng_inc > 0 && cache(rng_nelem-1) > rng_limit) |
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77 || (rng_inc < 0 && cache(rng_nelem-1) < rng_limit)) |
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78 cache(rng_nelem-1) = rng_limit; |
| 645 | 79 } |
| 80 | |
| 4810 | 81 return cache; |
| 645 | 82 } |
| 3 | 83 |
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84 double |
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85 Range::checkelem (octave_idx_type i) const |
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86 { |
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87 if (i < 0 || i >= rng_nelem) |
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88 gripe_index_out_of_range (1, 1, i+1, rng_nelem); |
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89 |
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90 return rng_base + rng_inc * i; |
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91 } |
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92 |
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93 struct _rangeidx_helper |
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94 { |
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95 double *array, base, inc; |
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96 _rangeidx_helper (double *a, double b, double i) |
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97 : array (a), base (b), inc (i) { } |
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98 void operator () (octave_idx_type i) |
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99 { *array++ = base + i * inc; } |
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100 }; |
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101 |
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102 Array<double> |
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103 Range::index (const idx_vector& i) const |
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104 { |
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105 Array<double> retval; |
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106 |
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107 octave_idx_type n = rng_nelem; |
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108 |
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109 if (i.is_colon ()) |
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110 { |
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111 retval = matrix_value ().reshape (dim_vector (rng_nelem, 1)); |
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112 } |
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113 else |
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114 { |
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115 if (i.extent (n) != n) |
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116 gripe_index_out_of_range (1, 1, i.extent (n), n); // throws |
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117 |
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118 dim_vector rd = i.orig_dimensions (); |
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119 octave_idx_type il = i.length (n); |
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120 |
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121 // taken from Array.cc. |
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122 |
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123 if (n != 1 && rd.is_vector ()) |
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124 rd = dim_vector (1, il); |
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125 |
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126 retval.clear (rd); |
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127 |
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128 i.loop (n, _rangeidx_helper (retval.fortran_vec (), rng_base, rng_inc)); |
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129 } |
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130 |
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131 return retval; |
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132 } |
| 4810 | 133 |
| 208 | 134 // NOTE: max and min only return useful values if nelem > 0. |
| 135 | |
| 136 double | |
| 137 Range::min (void) const | |
| 138 { | |
| 139 double retval = 0.0; | |
| 140 if (rng_nelem > 0) | |
| 141 { | |
| 142 if (rng_inc > 0) | |
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143 retval = rng_base; |
| 208 | 144 else |
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145 { |
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146 retval = rng_base + (rng_nelem - 1) * rng_inc; |
| 4791 | 147 |
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148 // See the note in the matrix_value method above. |
| 4791 | 149 |
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150 if (retval < rng_limit) |
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151 retval = rng_limit; |
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152 } |
| 4791 | 153 |
| 208 | 154 } |
| 155 return retval; | |
| 156 } | |
| 157 | |
| 158 double | |
| 159 Range::max (void) const | |
| 160 { | |
| 161 double retval = 0.0; | |
| 162 if (rng_nelem > 0) | |
| 163 { | |
| 164 if (rng_inc > 0) | |
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165 { |
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166 retval = rng_base + (rng_nelem - 1) * rng_inc; |
| 4791 | 167 |
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168 // See the note in the matrix_value method above. |
| 4791 | 169 |
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170 if (retval > rng_limit) |
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171 retval = rng_limit; |
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172 } |
| 208 | 173 else |
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174 retval = rng_base; |
| 208 | 175 } |
| 176 return retval; | |
| 177 } | |
| 178 | |
| 179 void | |
| 7458 | 180 Range::sort_internal (bool ascending) |
| 208 | 181 { |
| 7458 | 182 if (ascending && rng_base > rng_limit && rng_inc < 0.0) |
| 208 | 183 { |
| 184 double tmp = rng_base; | |
| 185 rng_base = min (); | |
| 186 rng_limit = tmp; | |
| 187 rng_inc = -rng_inc; | |
| 4811 | 188 clear_cache (); |
| 208 | 189 } |
| 8565 | 190 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0) |
| 7458 | 191 { |
| 192 double tmp = rng_limit; | |
| 193 rng_limit = min (); | |
| 194 rng_base = tmp; | |
| 195 rng_inc = -rng_inc; | |
| 196 clear_cache (); | |
| 197 } | |
| 198 } | |
| 199 | |
| 200 void | |
| 201 Range::sort_internal (Array<octave_idx_type>& sidx, bool ascending) | |
| 202 { | |
| 203 octave_idx_type nel = nelem (); | |
| 204 | |
| 205 sidx.resize (dim_vector (1, nel)); | |
| 206 | |
| 207 octave_idx_type *psidx = sidx.fortran_vec (); | |
| 208 | |
| 209 bool reverse = false; | |
| 210 | |
| 211 if (ascending && rng_base > rng_limit && rng_inc < 0.0) | |
| 212 { | |
| 213 double tmp = rng_base; | |
| 214 rng_base = min (); | |
| 215 rng_limit = tmp; | |
| 216 rng_inc = -rng_inc; | |
| 217 clear_cache (); | |
| 218 reverse = true; | |
| 219 } | |
| 220 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0) | |
| 221 { | |
| 222 double tmp = rng_limit; | |
| 223 rng_limit = min (); | |
| 224 rng_base = tmp; | |
| 225 rng_inc = -rng_inc; | |
| 226 clear_cache (); | |
| 227 reverse = true; | |
| 228 } | |
| 229 | |
| 230 octave_idx_type tmp = reverse ? nel - 1 : 0; | |
| 7467 | 231 octave_idx_type stp = reverse ? -1 : 1; |
| 7458 | 232 |
| 7467 | 233 for (octave_idx_type i = 0; i < nel; i++, tmp += stp) |
| 7458 | 234 psidx[i] = tmp; |
| 235 | |
| 236 } | |
| 237 | |
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238 Matrix |
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239 Range::diag (octave_idx_type k) const |
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240 { |
| 8971 | 241 return matrix_value ().diag (k); |
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242 } |
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243 |
| 7458 | 244 Range |
| 245 Range::sort (octave_idx_type dim, sortmode mode) const | |
| 246 { | |
| 247 Range retval = *this; | |
| 248 | |
| 249 if (dim == 1) | |
| 250 { | |
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251 if (mode == ASCENDING) |
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252 retval.sort_internal (true); |
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253 else if (mode == DESCENDING) |
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254 retval.sort_internal (false); |
| 7458 | 255 } |
| 256 else if (dim != 0) | |
| 257 (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); | |
| 258 | |
| 259 return retval; | |
| 260 } | |
| 261 | |
| 262 Range | |
| 263 Range::sort (Array<octave_idx_type>& sidx, octave_idx_type dim, | |
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264 sortmode mode) const |
| 7458 | 265 { |
| 266 Range retval = *this; | |
| 267 | |
| 268 if (dim == 1) | |
| 269 { | |
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270 if (mode == ASCENDING) |
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271 retval.sort_internal (sidx, true); |
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272 else if (mode == DESCENDING) |
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273 retval.sort_internal (sidx, false); |
| 7458 | 274 } |
| 275 else if (dim != 0) | |
| 276 (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); | |
| 277 | |
| 278 return retval; | |
| 208 | 279 } |
| 280 | |
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281 sortmode |
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282 Range::is_sorted (sortmode mode) const |
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283 { |
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284 if (rng_nelem > 1 && rng_inc < 0) |
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285 mode = (mode == ASCENDING) ? UNSORTED : DESCENDING; |
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286 else if (rng_nelem > 1 && rng_inc > 0) |
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287 mode = (mode == DESCENDING) ? UNSORTED : ASCENDING; |
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288 else |
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289 mode = mode ? mode : ASCENDING; |
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290 |
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291 return mode; |
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292 } |
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293 |
| 3504 | 294 std::ostream& |
| 295 operator << (std::ostream& os, const Range& a) | |
| 3 | 296 { |
| 297 double b = a.base (); | |
| 298 double increment = a.inc (); | |
| 5275 | 299 octave_idx_type num_elem = a.nelem (); |
| 3 | 300 |
| 5275 | 301 for (octave_idx_type i = 0; i < num_elem-1; i++) |
| 3 | 302 os << b + i * increment << " "; |
| 303 | |
| 4791 | 304 // Prevent overshoot. See comment in the matrix_value method |
| 305 // above. | |
| 306 | |
| 307 os << (increment > 0 ? a.max () : a.min ()) << "\n"; | |
| 3 | 308 |
| 309 return os; | |
| 310 } | |
| 311 | |
| 3504 | 312 std::istream& |
| 313 operator >> (std::istream& is, Range& a) | |
| 3 | 314 { |
| 208 | 315 is >> a.rng_base; |
| 3 | 316 if (is) |
| 317 { | |
| 208 | 318 is >> a.rng_limit; |
| 3 | 319 if (is) |
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320 { |
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321 is >> a.rng_inc; |
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322 a.rng_nelem = a.nelem_internal (); |
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323 } |
| 3 | 324 } |
| 325 | |
| 326 return is; | |
| 327 } | |
| 328 | |
| 2599 | 329 Range |
| 330 operator - (const Range& r) | |
| 331 { | |
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332 return Range (-r.base (), -r.inc (), r.nelem ()); |
| 2599 | 333 } |
| 334 | |
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335 Range operator + (double x, const Range& r) |
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336 { |
| 8971 | 337 Range result (x + r.base (), r.inc (), r.nelem ()); |
| 338 if (result.rng_nelem < 0) | |
| 339 result.cache = x + r.matrix_value (); | |
| 340 | |
| 341 return result; | |
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342 } |
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343 |
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344 Range operator + (const Range& r, double x) |
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345 { |
| 8971 | 346 Range result (r.base () + x, r.inc (), r.nelem ()); |
| 347 if (result.rng_nelem < 0) | |
| 348 result.cache = r.matrix_value () + x; | |
| 349 | |
| 350 return result; | |
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351 } |
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352 |
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353 Range operator - (double x, const Range& r) |
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354 { |
| 8971 | 355 Range result (x - r.base (), -r.inc (), r.nelem ()); |
| 356 if (result.rng_nelem < 0) | |
| 357 result.cache = x - r.matrix_value (); | |
| 358 | |
| 359 return result; | |
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360 } |
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361 |
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362 Range operator - (const Range& r, double x) |
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363 { |
| 8971 | 364 Range result (r.base () - x, r.inc (), r.nelem ()); |
| 365 if (result.rng_nelem < 0) | |
| 366 result.cache = r.matrix_value () - x; | |
| 367 | |
| 368 return result; | |
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369 } |
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370 |
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371 Range operator * (double x, const Range& r) |
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372 { |
| 8971 | 373 Range result (x * r.base (), x * r.inc (), r.nelem ()); |
| 374 if (result.rng_nelem < 0) | |
| 375 result.cache = x * r.matrix_value (); | |
| 376 | |
| 377 return result; | |
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378 } |
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379 |
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380 Range operator * (const Range& r, double x) |
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381 { |
| 8971 | 382 Range result (r.base () * x, r.inc () * x, r.nelem ()); |
| 383 if (result.rng_nelem < 0) | |
| 384 result.cache = r.matrix_value () * x; | |
| 385 | |
| 386 return result; | |
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387 } |
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388 |
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389 |
| 1546 | 390 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. |
| 391 // C | |
| 392 // C===Tolerant FLOOR function. | |
| 393 // C | |
| 394 // C X - is given as a Double Precision argument to be operated on. | |
| 395 // C It is assumed that X is represented with M mantissa bits. | |
| 396 // C CT - is given as a Comparison Tolerance such that | |
| 397 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between | |
| 398 // C X and A whole number is less than CT, then TFLOOR is | |
| 399 // C returned as this whole number. By treating the | |
| 400 // C floating-point numbers as a finite ordered set note that | |
| 401 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes | |
| 402 // C arguments of TFLOOR/TCEIL to be treated as whole numbers | |
| 403 // C if they are exactly whole numbers or are immediately | |
| 404 // C adjacent to whole number representations. Since EPS, the | |
| 405 // C "distance" between floating-point numbers on the unit | |
| 406 // C interval, and M, the number of bits in X'S mantissa, exist | |
| 407 // C on every floating-point computer, TFLOOR/TCEIL are | |
| 408 // C consistently definable on every floating-point computer. | |
| 409 // C | |
| 410 // C For more information see the following references: | |
| 411 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE | |
| 412 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. | |
| 413 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL | |
| 414 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through | |
| 415 // C FL5, the history of five years of evolutionary development of | |
| 416 // C FL5 - the seven lines of code below - by open collaboration | |
| 417 // C and corroboration of the mathematical-computing community. | |
| 418 // C | |
| 419 // C Penn State University Center for Academic Computing | |
| 420 // C H. D. Knoble - August, 1978. | |
| 421 | |
| 422 static inline double | |
| 423 tfloor (double x, double ct) | |
| 424 { | |
| 425 // C---------FLOOR(X) is the largest integer algebraically less than | |
| 426 // C or equal to X; that is, the unfuzzy FLOOR function. | |
| 427 | |
| 428 // DINT (X) = X - DMOD (X, 1.0); | |
| 429 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); | |
| 430 | |
| 431 // C---------Hagerty's FL5 function follows... | |
| 432 | |
| 433 double q = 1.0; | |
| 434 | |
| 435 if (x < 0.0) | |
| 436 q = 1.0 - ct; | |
| 437 | |
| 438 double rmax = q / (2.0 - ct); | |
| 439 | |
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440 double t1 = 1.0 + gnulib::floor (x); |
| 1546 | 441 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); |
| 442 t1 = rmax < t1 ? rmax : t1; | |
| 443 t1 = ct > t1 ? ct : t1; | |
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444 t1 = gnulib::floor (x + t1); |
| 1546 | 445 |
| 1555 | 446 if (x <= 0.0 || (t1 - x) < rmax) |
| 1546 | 447 return t1; |
| 448 else | |
| 449 return t1 - 1.0; | |
| 450 } | |
| 451 | |
| 452 static inline double | |
| 453 tceil (double x, double ct) | |
| 454 { | |
| 455 return -tfloor (-x, ct); | |
| 456 } | |
| 457 | |
| 3753 | 458 static inline bool |
| 459 teq (double u, double v, double ct = 3.0 * DBL_EPSILON) | |
| 460 { | |
| 461 double tu = fabs (u); | |
| 462 double tv = fabs (v); | |
| 463 | |
| 464 return fabs (u - v) < ((tu > tv ? tu : tv) * ct); | |
| 465 } | |
| 466 | |
| 5275 | 467 octave_idx_type |
| 1360 | 468 Range::nelem_internal (void) const |
| 469 { | |
| 5275 | 470 octave_idx_type retval = -1; |
| 3 | 471 |
| 3858 | 472 if (rng_inc == 0 |
| 473 || (rng_limit > rng_base && rng_inc < 0) | |
| 474 || (rng_limit < rng_base && rng_inc > 0)) | |
| 475 { | |
| 476 retval = 0; | |
| 477 } | |
| 478 else | |
| 479 { | |
| 480 double ct = 3.0 * DBL_EPSILON; | |
| 3 | 481 |
| 3858 | 482 double tmp = tfloor ((rng_limit - rng_base + rng_inc) / rng_inc, ct); |
| 483 | |
| 5275 | 484 octave_idx_type n_elt = (tmp > 0.0 ? static_cast<octave_idx_type> (tmp) : 0); |
| 398 | 485 |
| 3858 | 486 // If the final element that we would compute for the range is |
| 487 // equal to the limit of the range, or is an adjacent floating | |
| 488 // point number, accept it. Otherwise, try a range with one | |
| 489 // fewer element. If that fails, try again with one more | |
| 490 // element. | |
| 491 // | |
| 492 // I'm not sure this is very good, but it seems to work better than | |
| 493 // just using tfloor as above. For example, without it, the | |
| 494 // expression 1.8:0.05:1.9 fails to produce the expected result of | |
| 495 // [1.8, 1.85, 1.9]. | |
| 3753 | 496 |
| 3858 | 497 if (! teq (rng_base + (n_elt - 1) * rng_inc, rng_limit)) |
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498 { |
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499 if (teq (rng_base + (n_elt - 2) * rng_inc, rng_limit)) |
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500 n_elt--; |
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501 else if (teq (rng_base + n_elt * rng_inc, rng_limit)) |
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502 n_elt++; |
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503 } |
| 3858 | 504 |
| 6490 | 505 retval = (n_elt >= std::numeric_limits<octave_idx_type>::max () - 1) ? -1 : n_elt; |
| 3753 | 506 } |
| 507 | |
| 3858 | 508 return retval; |
| 3 | 509 } |