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annotate liboctave/Range.cc @ 8920:eb63fbe60fab
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Sat, 07 Mar 2009 10:41:27 -0500 |
| parents | d2b06871afac |
| children | 967a692ddfe2 |
| rev | line source |
|---|---|
| 3 | 1 /* |
| 2 | |
| 7017 | 3 Copyright (C) 1993, 1994, 1995, 1996, 1997, 2000, 2001, 2002, 2004, |
| 8920 | 4 2005, 2007, 2008, 2009 John W. Eaton |
| 3 | 5 |
| 6 This file is part of Octave. | |
| 7 | |
| 8 Octave is free software; you can redistribute it and/or modify it | |
| 9 under the terms of the GNU General Public License as published by the | |
| 7016 | 10 Free Software Foundation; either version 3 of the License, or (at your |
| 11 option) any later version. | |
| 3 | 12 |
| 13 Octave is distributed in the hope that it will be useful, but WITHOUT | |
| 14 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or | |
| 15 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License | |
| 16 for more details. | |
| 17 | |
| 18 You should have received a copy of the GNU General Public License | |
| 7016 | 19 along with Octave; see the file COPYING. If not, see |
| 20 <http://www.gnu.org/licenses/>. | |
| 3 | 21 |
| 22 */ | |
| 23 | |
| 238 | 24 #ifdef HAVE_CONFIG_H |
| 1192 | 25 #include <config.h> |
| 3 | 26 #endif |
| 27 | |
| 1546 | 28 #include <cfloat> |
| 1367 | 29 |
| 3503 | 30 #include <iostream> |
| 6490 | 31 #include <limits> |
| 3 | 32 |
| 33 #include "Range.h" | |
| 7458 | 34 #include "lo-error.h" |
| 2383 | 35 #include "lo-mappers.h" |
| 7231 | 36 #include "lo-math.h" |
| 2383 | 37 #include "lo-utils.h" |
| 38 | |
| 39 bool | |
| 40 Range::all_elements_are_ints (void) const | |
| 41 { | |
| 42 // If the base and increment are ints, the final value in the range | |
| 6457 | 43 // will also be an integer, even if the limit is not. If there is one |
| 44 // or fewer elements only the base needs to be an integer | |
| 2383 | 45 |
| 46 return (! (xisnan (rng_base) || xisnan (rng_inc)) | |
| 6457 | 47 && (NINTbig (rng_base) == rng_base || rng_nelem < 1) |
| 48 && (NINTbig (rng_inc) == rng_inc || rng_nelem <= 1)); | |
| 2383 | 49 } |
| 645 | 50 |
| 51 Matrix | |
| 52 Range::matrix_value (void) const | |
| 53 { | |
| 4811 | 54 if (rng_nelem > 0 && cache.rows () == 0) |
| 645 | 55 { |
| 4810 | 56 cache.resize (1, rng_nelem); |
| 645 | 57 double b = rng_base; |
| 58 double increment = rng_inc; | |
| 5275 | 59 for (octave_idx_type i = 0; i < rng_nelem; i++) |
| 4810 | 60 cache(i) = b + i * increment; |
| 4791 | 61 |
| 62 // On some machines (x86 with extended precision floating point | |
| 63 // arithmetic, for example) it is possible that we can overshoot | |
| 64 // the limit by approximately the machine precision even though | |
| 65 // we were very careful in our calculation of the number of | |
| 66 // elements. | |
| 67 | |
| 4810 | 68 if ((rng_inc > 0 && cache(rng_nelem-1) > rng_limit) |
| 69 || (rng_inc < 0 && cache(rng_nelem-1) < rng_limit)) | |
| 70 cache(rng_nelem-1) = rng_limit; | |
| 645 | 71 } |
| 72 | |
| 4810 | 73 return cache; |
| 645 | 74 } |
| 3 | 75 |
| 4810 | 76 |
| 208 | 77 // NOTE: max and min only return useful values if nelem > 0. |
| 78 | |
| 79 double | |
| 80 Range::min (void) const | |
| 81 { | |
| 82 double retval = 0.0; | |
| 83 if (rng_nelem > 0) | |
| 84 { | |
| 85 if (rng_inc > 0) | |
| 86 retval = rng_base; | |
| 87 else | |
| 4791 | 88 { |
| 89 retval = rng_base + (rng_nelem - 1) * rng_inc; | |
| 90 | |
| 91 // See the note in the matrix_value method above. | |
| 92 | |
| 93 if (retval < rng_limit) | |
| 94 retval = rng_limit; | |
| 95 } | |
| 96 | |
| 208 | 97 } |
| 98 return retval; | |
| 99 } | |
| 100 | |
| 101 double | |
| 102 Range::max (void) const | |
| 103 { | |
| 104 double retval = 0.0; | |
| 105 if (rng_nelem > 0) | |
| 106 { | |
| 107 if (rng_inc > 0) | |
| 4791 | 108 { |
| 109 retval = rng_base + (rng_nelem - 1) * rng_inc; | |
| 110 | |
| 111 // See the note in the matrix_value method above. | |
| 112 | |
| 113 if (retval > rng_limit) | |
| 114 retval = rng_limit; | |
| 115 } | |
| 208 | 116 else |
| 117 retval = rng_base; | |
| 118 } | |
| 119 return retval; | |
| 120 } | |
| 121 | |
| 122 void | |
| 7458 | 123 Range::sort_internal (bool ascending) |
| 208 | 124 { |
| 7458 | 125 if (ascending && rng_base > rng_limit && rng_inc < 0.0) |
| 208 | 126 { |
| 127 double tmp = rng_base; | |
| 128 rng_base = min (); | |
| 129 rng_limit = tmp; | |
| 130 rng_inc = -rng_inc; | |
| 4811 | 131 clear_cache (); |
| 208 | 132 } |
| 8565 | 133 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0) |
| 7458 | 134 { |
| 135 double tmp = rng_limit; | |
| 136 rng_limit = min (); | |
| 137 rng_base = tmp; | |
| 138 rng_inc = -rng_inc; | |
| 139 clear_cache (); | |
| 140 } | |
| 141 } | |
| 142 | |
| 143 void | |
| 144 Range::sort_internal (Array<octave_idx_type>& sidx, bool ascending) | |
| 145 { | |
| 146 octave_idx_type nel = nelem (); | |
| 147 | |
| 148 sidx.resize (dim_vector (1, nel)); | |
| 149 | |
| 150 octave_idx_type *psidx = sidx.fortran_vec (); | |
| 151 | |
| 152 bool reverse = false; | |
| 153 | |
| 154 if (ascending && rng_base > rng_limit && rng_inc < 0.0) | |
| 155 { | |
| 156 double tmp = rng_base; | |
| 157 rng_base = min (); | |
| 158 rng_limit = tmp; | |
| 159 rng_inc = -rng_inc; | |
| 160 clear_cache (); | |
| 161 reverse = true; | |
| 162 } | |
| 163 else if (! ascending && rng_base < rng_limit && rng_inc > 0.0) | |
| 164 { | |
| 165 double tmp = rng_limit; | |
| 166 rng_limit = min (); | |
| 167 rng_base = tmp; | |
| 168 rng_inc = -rng_inc; | |
| 169 clear_cache (); | |
| 170 reverse = true; | |
| 171 } | |
| 172 | |
| 173 octave_idx_type tmp = reverse ? nel - 1 : 0; | |
| 7467 | 174 octave_idx_type stp = reverse ? -1 : 1; |
| 7458 | 175 |
| 7467 | 176 for (octave_idx_type i = 0; i < nel; i++, tmp += stp) |
| 7458 | 177 psidx[i] = tmp; |
| 178 | |
| 179 } | |
| 180 | |
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181 Matrix |
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182 Range::diag (octave_idx_type k) const |
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183 { |
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184 octave_idx_type nnr = 1; |
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185 octave_idx_type nnc = nelem (); |
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186 Matrix d; |
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187 |
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188 if (nnr != 0) |
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189 { |
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190 octave_idx_type roff = 0; |
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191 octave_idx_type coff = 0; |
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192 if (k > 0) |
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193 { |
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194 roff = 0; |
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195 coff = k; |
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196 } |
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197 else if (k < 0) |
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198 { |
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199 roff = -k; |
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200 coff = 0; |
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201 } |
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202 |
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203 // Force cached matrix to be created |
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204 matrix_value (); |
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205 |
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206 octave_idx_type n = nnc + std::abs (k); |
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207 d = Matrix (n, n, Matrix::resize_fill_value ()); |
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208 for (octave_idx_type i = 0; i < nnc; i++) |
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209 d.xelem (i+roff, i+coff) = cache.xelem (i); |
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210 } |
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211 |
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212 return d; |
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213 } |
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214 |
| 7458 | 215 Range |
| 216 Range::sort (octave_idx_type dim, sortmode mode) const | |
| 217 { | |
| 218 Range retval = *this; | |
| 219 | |
| 220 if (dim == 1) | |
| 221 { | |
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222 if (mode == ASCENDING) |
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223 retval.sort_internal (true); |
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224 else if (mode == DESCENDING) |
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225 retval.sort_internal (false); |
| 7458 | 226 } |
| 227 else if (dim != 0) | |
| 228 (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); | |
| 229 | |
| 230 return retval; | |
| 231 } | |
| 232 | |
| 233 Range | |
| 234 Range::sort (Array<octave_idx_type>& sidx, octave_idx_type dim, | |
| 235 sortmode mode) const | |
| 236 { | |
| 237 Range retval = *this; | |
| 238 | |
| 239 if (dim == 1) | |
| 240 { | |
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241 if (mode == ASCENDING) |
| 7458 | 242 retval.sort_internal (sidx, true); |
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243 else if (mode == DESCENDING) |
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244 retval.sort_internal (sidx, false); |
| 7458 | 245 } |
| 246 else if (dim != 0) | |
| 247 (*current_liboctave_error_handler) ("Range::sort: invalid dimension"); | |
| 248 | |
| 249 return retval; | |
| 208 | 250 } |
| 251 | |
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252 sortmode |
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253 Range::is_sorted (sortmode mode) const |
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254 { |
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255 if (rng_nelem > 1 && rng_inc < 0) |
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256 mode = (mode == ASCENDING) ? UNSORTED : DESCENDING; |
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257 else if (rng_nelem > 1 && rng_inc > 0) |
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258 mode = (mode == DESCENDING) ? UNSORTED : ASCENDING; |
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259 else |
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260 mode = mode ? mode : ASCENDING; |
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261 |
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262 return mode; |
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263 } |
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264 |
| 3504 | 265 std::ostream& |
| 266 operator << (std::ostream& os, const Range& a) | |
| 3 | 267 { |
| 268 double b = a.base (); | |
| 269 double increment = a.inc (); | |
| 5275 | 270 octave_idx_type num_elem = a.nelem (); |
| 3 | 271 |
| 5275 | 272 for (octave_idx_type i = 0; i < num_elem-1; i++) |
| 3 | 273 os << b + i * increment << " "; |
| 274 | |
| 4791 | 275 // Prevent overshoot. See comment in the matrix_value method |
| 276 // above. | |
| 277 | |
| 278 os << (increment > 0 ? a.max () : a.min ()) << "\n"; | |
| 3 | 279 |
| 280 return os; | |
| 281 } | |
| 282 | |
| 3504 | 283 std::istream& |
| 284 operator >> (std::istream& is, Range& a) | |
| 3 | 285 { |
| 208 | 286 is >> a.rng_base; |
| 3 | 287 if (is) |
| 288 { | |
| 208 | 289 is >> a.rng_limit; |
| 3 | 290 if (is) |
| 291 { | |
| 208 | 292 is >> a.rng_inc; |
| 293 a.rng_nelem = a.nelem_internal (); | |
| 3 | 294 } |
| 295 } | |
| 296 | |
| 297 return is; | |
| 298 } | |
| 299 | |
| 2599 | 300 Range |
| 301 operator - (const Range& r) | |
| 302 { | |
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303 return Range (-r.base (), -r.inc (), r.nelem ()); |
| 2599 | 304 } |
| 305 | |
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306 Range operator + (double x, const Range& r) |
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307 { |
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308 return Range (x + r.base (), r.inc (), r.nelem ()); |
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309 } |
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310 |
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311 Range operator + (const Range& r, double x) |
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312 { |
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313 return Range (r.base () + x, r.inc (), r.nelem ()); |
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314 } |
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315 |
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316 Range operator - (double x, const Range& r) |
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317 { |
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318 return Range (x - r.base (), -r.inc (), r.nelem ()); |
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319 } |
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320 |
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321 Range operator - (const Range& r, double x) |
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322 { |
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323 return Range (r.base () - x, r.inc (), r.nelem ()); |
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324 } |
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325 |
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326 Range operator * (double x, const Range& r) |
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327 { |
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328 return Range (x * r.base (), x * r.inc (), r.nelem ()); |
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329 } |
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330 |
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331 Range operator * (const Range& r, double x) |
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332 { |
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333 return Range (r.base () * x, r.inc () * x, r.nelem ()); |
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334 } |
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335 |
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336 |
| 1546 | 337 // C See Knuth, Art Of Computer Programming, Vol. 1, Problem 1.2.4-5. |
| 338 // C | |
| 339 // C===Tolerant FLOOR function. | |
| 340 // C | |
| 341 // C X - is given as a Double Precision argument to be operated on. | |
| 342 // C It is assumed that X is represented with M mantissa bits. | |
| 343 // C CT - is given as a Comparison Tolerance such that | |
| 344 // C 0.LT.CT.LE.3-SQRT(5)/2. If the relative difference between | |
| 345 // C X and A whole number is less than CT, then TFLOOR is | |
| 346 // C returned as this whole number. By treating the | |
| 347 // C floating-point numbers as a finite ordered set note that | |
| 348 // C the heuristic EPS=2.**(-(M-1)) and CT=3*EPS causes | |
| 349 // C arguments of TFLOOR/TCEIL to be treated as whole numbers | |
| 350 // C if they are exactly whole numbers or are immediately | |
| 351 // C adjacent to whole number representations. Since EPS, the | |
| 352 // C "distance" between floating-point numbers on the unit | |
| 353 // C interval, and M, the number of bits in X'S mantissa, exist | |
| 354 // C on every floating-point computer, TFLOOR/TCEIL are | |
| 355 // C consistently definable on every floating-point computer. | |
| 356 // C | |
| 357 // C For more information see the following references: | |
| 358 // C (1) P. E. Hagerty, "More On Fuzzy Floor And Ceiling," APL QUOTE | |
| 359 // C QUAD 8(4):20-24, June 1978. Note that TFLOOR=FL5. | |
| 360 // C (2) L. M. Breed, "Definitions For Fuzzy Floor And Ceiling", APL | |
| 361 // C QUOTE QUAD 8(3):16-23, March 1978. This paper cites FL1 through | |
| 362 // C FL5, the history of five years of evolutionary development of | |
| 363 // C FL5 - the seven lines of code below - by open collaboration | |
| 364 // C and corroboration of the mathematical-computing community. | |
| 365 // C | |
| 366 // C Penn State University Center for Academic Computing | |
| 367 // C H. D. Knoble - August, 1978. | |
| 368 | |
| 369 static inline double | |
| 370 tfloor (double x, double ct) | |
| 371 { | |
| 372 // C---------FLOOR(X) is the largest integer algebraically less than | |
| 373 // C or equal to X; that is, the unfuzzy FLOOR function. | |
| 374 | |
| 375 // DINT (X) = X - DMOD (X, 1.0); | |
| 376 // FLOOR (X) = DINT (X) - DMOD (2.0 + DSIGN (1.0, X), 3.0); | |
| 377 | |
| 378 // C---------Hagerty's FL5 function follows... | |
| 379 | |
| 380 double q = 1.0; | |
| 381 | |
| 382 if (x < 0.0) | |
| 383 q = 1.0 - ct; | |
| 384 | |
| 385 double rmax = q / (2.0 - ct); | |
| 386 | |
| 387 double t1 = 1.0 + floor (x); | |
| 388 t1 = (ct / q) * (t1 < 0.0 ? -t1 : t1); | |
| 389 t1 = rmax < t1 ? rmax : t1; | |
| 390 t1 = ct > t1 ? ct : t1; | |
| 391 t1 = floor (x + t1); | |
| 392 | |
| 1555 | 393 if (x <= 0.0 || (t1 - x) < rmax) |
| 1546 | 394 return t1; |
| 395 else | |
| 396 return t1 - 1.0; | |
| 397 } | |
| 398 | |
| 399 static inline double | |
| 400 tceil (double x, double ct) | |
| 401 { | |
| 402 return -tfloor (-x, ct); | |
| 403 } | |
| 404 | |
| 3753 | 405 static inline bool |
| 406 teq (double u, double v, double ct = 3.0 * DBL_EPSILON) | |
| 407 { | |
| 408 double tu = fabs (u); | |
| 409 double tv = fabs (v); | |
| 410 | |
| 411 return fabs (u - v) < ((tu > tv ? tu : tv) * ct); | |
| 412 } | |
| 413 | |
| 5275 | 414 octave_idx_type |
| 1360 | 415 Range::nelem_internal (void) const |
| 416 { | |
| 5275 | 417 octave_idx_type retval = -1; |
| 3 | 418 |
| 3858 | 419 if (rng_inc == 0 |
| 420 || (rng_limit > rng_base && rng_inc < 0) | |
| 421 || (rng_limit < rng_base && rng_inc > 0)) | |
| 422 { | |
| 423 retval = 0; | |
| 424 } | |
| 425 else | |
| 426 { | |
| 427 double ct = 3.0 * DBL_EPSILON; | |
| 3 | 428 |
| 3858 | 429 double tmp = tfloor ((rng_limit - rng_base + rng_inc) / rng_inc, ct); |
| 430 | |
| 5275 | 431 octave_idx_type n_elt = (tmp > 0.0 ? static_cast<octave_idx_type> (tmp) : 0); |
| 398 | 432 |
| 3858 | 433 // If the final element that we would compute for the range is |
| 434 // equal to the limit of the range, or is an adjacent floating | |
| 435 // point number, accept it. Otherwise, try a range with one | |
| 436 // fewer element. If that fails, try again with one more | |
| 437 // element. | |
| 438 // | |
| 439 // I'm not sure this is very good, but it seems to work better than | |
| 440 // just using tfloor as above. For example, without it, the | |
| 441 // expression 1.8:0.05:1.9 fails to produce the expected result of | |
| 442 // [1.8, 1.85, 1.9]. | |
| 3753 | 443 |
| 3858 | 444 if (! teq (rng_base + (n_elt - 1) * rng_inc, rng_limit)) |
| 445 { | |
| 446 if (teq (rng_base + (n_elt - 2) * rng_inc, rng_limit)) | |
| 447 n_elt--; | |
| 448 else if (teq (rng_base + n_elt * rng_inc, rng_limit)) | |
| 449 n_elt++; | |
| 450 } | |
| 451 | |
| 6490 | 452 retval = (n_elt >= std::numeric_limits<octave_idx_type>::max () - 1) ? -1 : n_elt; |
| 3753 | 453 } |
| 454 | |
| 3858 | 455 return retval; |
| 3 | 456 } |
| 457 | |
| 458 /* | |
| 459 ;;; Local Variables: *** | |
| 460 ;;; mode: C++ *** | |
| 461 ;;; End: *** | |
| 462 */ |