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|---|---|---|---|
| 1 | /* | ||
| 2 | * Copyright (c) 2000-2022 Inria | ||
| 3 | * All rights reserved. | ||
| 4 | * | ||
| 5 | * Redistribution and use in source and binary forms, with or without | ||
| 6 | * modification, are permitted provided that the following conditions are met: | ||
| 7 | * | ||
| 8 | * * Redistributions of source code must retain the above copyright notice, | ||
| 9 | * this list of conditions and the following disclaimer. | ||
| 10 | * * Redistributions in binary form must reproduce the above copyright notice, | ||
| 11 | * this list of conditions and the following disclaimer in the documentation | ||
| 12 | * and/or other materials provided with the distribution. | ||
| 13 | * * Neither the name of the ALICE Project-Team nor the names of its | ||
| 14 | * contributors may be used to endorse or promote products derived from this | ||
| 15 | * software without specific prior written permission. | ||
| 16 | * | ||
| 17 | * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" | ||
| 18 | * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE | ||
| 19 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE | ||
| 20 | * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE | ||
| 21 | * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR | ||
| 22 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF | ||
| 23 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS | ||
| 24 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN | ||
| 25 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) | ||
| 26 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE | ||
| 27 | * POSSIBILITY OF SUCH DAMAGE. | ||
| 28 | * | ||
| 29 | * Contact: Bruno Levy | ||
| 30 | * | ||
| 31 | * https://www.inria.fr/fr/bruno-levy | ||
| 32 | * | ||
| 33 | * Inria, | ||
| 34 | * Domaine de Voluceau, | ||
| 35 | * 78150 Le Chesnay - Rocquencourt | ||
| 36 | * FRANCE | ||
| 37 | * | ||
| 38 | */ | ||
| 39 | |||
| 40 | #ifndef GEOGRAM_NUMERICS_EXPANSION_NT | ||
| 41 | #define GEOGRAM_NUMERICS_EXPANSION_NT | ||
| 42 | |||
| 43 | #include <geogram/basic/common.h> | ||
| 44 | #include <geogram/numerics/multi_precision.h> | ||
| 45 | #include <geogram/basic/matrix.h> | ||
| 46 | #include <geogram/basic/rationalg.h> | ||
| 47 | |||
| 48 | /** | ||
| 49 | * \file geogram/numerics/expansion_nt.h | ||
| 50 | * \brief High-level interface to multi-precision arithmetics | ||
| 51 | * \details | ||
| 52 | * This file provides a "number-type" that encapsulates a (low-level) | ||
| 53 | * GEO::expansion object. | ||
| 54 | */ | ||
| 55 | |||
| 56 | namespace GEO { | ||
| 57 | |||
| 58 | class expansion_nt; | ||
| 59 | |||
| 60 | /** | ||
| 61 | * \brief Expansion_nt (expansion Number Type) is used to compute the | ||
| 62 | * sign of polynoms exactly. | ||
| 63 | * \details Expansion_nt can be used like float and double. It supports | ||
| 64 | * three arithmetic operations (+,-,*), comparisons (>,>=,<,<=,==,!=) | ||
| 65 | * and exact sign computation. expansion_nt is a wrapper around | ||
| 66 | * an \ref expansion allocated on the heap. When | ||
| 67 | * performance is a concern, the lower-level expansion class may be | ||
| 68 | * used instead. | ||
| 69 | */ | ||
| 70 | class GEOGRAM_API expansion_nt { | ||
| 71 | public: | ||
| 72 | |||
| 73 | /** | ||
| 74 | * \brief This type is used by the constructor that | ||
| 75 | * takes two expansion%s. | ||
| 76 | */ | ||
| 77 | enum Operation { | ||
| 78 | SUM, DIFF, PRODUCT | ||
| 79 | }; | ||
| 80 | |||
| 81 | /** | ||
| 82 | * \brief Constructs an uninitialized expansion_nt. | ||
| 83 | */ | ||
| 84 |
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298020 | expansion_nt() : rep_(nullptr) { |
| 85 | } | ||
| 86 | |||
| 87 | /** | ||
| 88 | * \brief Constructs a new expansion_nt from a double. | ||
| 89 | * \param[in] x the value to initialize this expansion. | ||
| 90 | */ | ||
| 91 |
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3551 | explicit expansion_nt(double x) { |
| 92 | 908671 | rep_ = expansion::new_expansion_on_heap(1); | |
| 93 |
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3551 | rep()[0] = x; |
| 94 | rep().set_length(1); | ||
| 95 | } | ||
| 96 | |||
| 97 | /** | ||
| 98 | * \brief Constructs a new expansion_nt from an expansion | ||
| 99 | * \details A new expansion is created on the heap and its | ||
| 100 | * content is initialized from \p rhs | ||
| 101 | * \param[in] rhs the expansion to be copied | ||
| 102 | */ | ||
| 103 | 222801 | explicit expansion_nt(const expansion& rhs) { | |
| 104 | 222801 | rep_ = expansion::new_expansion_on_heap(rhs.length()); | |
| 105 | rep().assign(rhs); | ||
| 106 | 222801 | } | |
| 107 | |||
| 108 | /** | ||
| 109 | * \brief Constructs a new expansion_nt from two expansions | ||
| 110 | * \details A new expansion is created on the heap and its | ||
| 111 | * content is initialized from \p x \p op \p y. This function | ||
| 112 | * is used by code that combines the low-level API (expansion) | ||
| 113 | * with the high-level number type (expansion_nt). When returning | ||
| 114 | * the result of operations that combine expansion as an expansion_nt, | ||
| 115 | * it makes it possible to avoid copying the result of the | ||
| 116 | * last operation by directly assigning it to an expansion_nt. | ||
| 117 | * \param[in] x , y the two operands | ||
| 118 | * \param[in] op one of | ||
| 119 | * expansion_nt::SUM, expansion_nt::DIFF, expansion_nt::PRODUCT | ||
| 120 | */ | ||
| 121 | 668403 | explicit expansion_nt( | |
| 122 | Operation op, const expansion& x, const expansion& y | ||
| 123 | 668403 | ) { | |
| 124 |
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668403 | switch(op) { |
| 125 | case SUM: | ||
| 126 | 668403 | rep_ = expansion::new_expansion_on_heap( | |
| 127 | expansion::sum_capacity(x,y) | ||
| 128 | ); | ||
| 129 | 668403 | rep_->assign_sum(x,y); | |
| 130 | 668403 | break; | |
| 131 | case DIFF: | ||
| 132 | ✗ | rep_ = expansion::new_expansion_on_heap( | |
| 133 | expansion::diff_capacity(x,y) | ||
| 134 | ); | ||
| 135 | ✗ | rep_->assign_diff(x,y); | |
| 136 | ✗ | break; | |
| 137 | case PRODUCT: | ||
| 138 | ✗ | rep_ = expansion::new_expansion_on_heap( | |
| 139 | expansion::product_capacity(x,y) | ||
| 140 | ); | ||
| 141 | ✗ | rep_->assign_product(x,y); | |
| 142 | ✗ | break; | |
| 143 | } | ||
| 144 | 668403 | } | |
| 145 | |||
| 146 | /** | ||
| 147 | * \brief Constructs a new expansion_nt from three expansions | ||
| 148 | * \details A new expansion is created on the heap and its | ||
| 149 | * content is initialized from \p x \p op \p y \p op \p z. | ||
| 150 | * This function is used by code that combines the low-level | ||
| 151 | * API (expansion) with the high-level number type (expansion_nt). | ||
| 152 | * When returning the result of operations that combine expansion | ||
| 153 | * as an expansion_nt, it makes it possible to avoid copying | ||
| 154 | * the result of the last operation by directly assigning it | ||
| 155 | * to an expansion_nt. | ||
| 156 | * \param[in] x , y , z the three operands | ||
| 157 | * \param[in] op one of expansion_nt::SUM, expansion_nt::PRODUCT | ||
| 158 | */ | ||
| 159 | 197602 | explicit expansion_nt( | |
| 160 | Operation op, | ||
| 161 | const expansion& x, const expansion& y, const expansion& z | ||
| 162 | 197602 | ) { | |
| 163 |
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197602 | switch(op) { |
| 164 | case SUM: | ||
| 165 | 197602 | rep_ = expansion::new_expansion_on_heap( | |
| 166 | expansion::sum_capacity(x,y,z) | ||
| 167 | ); | ||
| 168 | 197602 | rep_->assign_sum(x,y,z); | |
| 169 | 197602 | break; | |
| 170 | case DIFF: | ||
| 171 | ✗ | geo_assert_not_reached; | |
| 172 | break; | ||
| 173 | case PRODUCT: | ||
| 174 | ✗ | rep_ = expansion::new_expansion_on_heap( | |
| 175 | expansion::product_capacity(x,y,z) | ||
| 176 | ); | ||
| 177 | ✗ | rep_->assign_product(x,y,z); | |
| 178 | ✗ | break; | |
| 179 | } | ||
| 180 | 197602 | } | |
| 181 | |||
| 182 | /** | ||
| 183 | * \brief Constructs a new expansion_nt from four expansions | ||
| 184 | * \details A new expansion is created on the heap and its | ||
| 185 | * content is initialized from \p x \p op \p y \p op \p z \p op \p t. | ||
| 186 | * This function is used by code that combines the | ||
| 187 | * low-level API (expansion) with the high-level number type | ||
| 188 | * (expansion_nt). When returning | ||
| 189 | * the result of operations that combine expansion as an expansion_nt, | ||
| 190 | * it makes it possible to avoid copying the result of the | ||
| 191 | * last operation by directly assigning it to an expansion_nt. | ||
| 192 | * \param[in] x , y , z , t the four operands | ||
| 193 | * \param[in] op one of expansion_nt::SUM, expansion_nt::PRODUCT | ||
| 194 | */ | ||
| 195 | explicit expansion_nt( | ||
| 196 | Operation op, | ||
| 197 | const expansion& x, const expansion& y, | ||
| 198 | const expansion& z, const expansion& t | ||
| 199 | ) { | ||
| 200 | switch(op) { | ||
| 201 | case SUM: | ||
| 202 | rep_ = expansion::new_expansion_on_heap( | ||
| 203 | expansion::sum_capacity(x,y,z,t) | ||
| 204 | ); | ||
| 205 | rep_->assign_sum(x,y,z,t); | ||
| 206 | break; | ||
| 207 | case DIFF: | ||
| 208 | geo_assert_not_reached; | ||
| 209 | break; | ||
| 210 | case PRODUCT: | ||
| 211 | // HERE: TODO CHECK SIZE | ||
| 212 | const expansion& p1 = expansion_product(x,y); | ||
| 213 | const expansion& p2 = expansion_product(z,t); | ||
| 214 | rep_ = expansion::new_expansion_on_heap( | ||
| 215 | expansion::product_capacity(p1,p2) | ||
| 216 | ); | ||
| 217 | rep_->assign_sum(p1,p2); | ||
| 218 | break; | ||
| 219 | } | ||
| 220 | } | ||
| 221 | |||
| 222 | /** | ||
| 223 | * \brief Constructs a new expansion_nt from two doubles | ||
| 224 | * \details A new expansion is created on the heap and its | ||
| 225 | * content is initialized from \p x \p op \p y. This function | ||
| 226 | * is used by code that combines the low-level API (expansion) | ||
| 227 | * with the high-level number type (expansion_nt). When returning | ||
| 228 | * the result of operations that combine expansion as an expansion_nt, | ||
| 229 | * it makes it possible to avoid copying the result of the | ||
| 230 | * last operation by directly assigning it to an expansion_nt. | ||
| 231 | * \param[in] x , y the two operands | ||
| 232 | * \param[in] op one of | ||
| 233 | * expansion_nt::SUM, expansion_nt::DIFF, expansion_nt::PRODUCT | ||
| 234 | */ | ||
| 235 | 3889407 | explicit expansion_nt(Operation op, double x, double y) { | |
| 236 |
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3889407 | switch(op) { |
| 237 | case SUM: | ||
| 238 | ✗ | rep_ = expansion::new_expansion_on_heap( | |
| 239 | expansion::sum_capacity(x,y) | ||
| 240 | ); | ||
| 241 | rep_->assign_sum(x,y); | ||
| 242 | break; | ||
| 243 | case DIFF: | ||
| 244 | 3889407 | rep_ = expansion::new_expansion_on_heap( | |
| 245 | expansion::diff_capacity(x,y) | ||
| 246 | ); | ||
| 247 | rep_->assign_diff(x,y); | ||
| 248 | break; | ||
| 249 | case PRODUCT: | ||
| 250 | ✗ | rep_ = expansion::new_expansion_on_heap( | |
| 251 | expansion::product_capacity(x,y) | ||
| 252 | ); | ||
| 253 | rep_->assign_product(x,y); | ||
| 254 | break; | ||
| 255 | } | ||
| 256 | 3889407 | } | |
| 257 | |||
| 258 | /** | ||
| 259 | * \brief Copy-constructor. | ||
| 260 | * \param[in] rhs the expansion to be copied | ||
| 261 | */ | ||
| 262 | 14260385 | expansion_nt(const expansion_nt& rhs) { | |
| 263 | 5677870 | copy(rhs); | |
| 264 | } | ||
| 265 | |||
| 266 | /** | ||
| 267 | * \brief Move-constructor. | ||
| 268 | * \details Steals the expansion from \p rhs | ||
| 269 | * \param[in] rhs the victim expansion_nt | ||
| 270 | */ | ||
| 271 | 24896 | expansion_nt(expansion_nt&& rhs) { | |
| 272 | rep_ = nullptr; | ||
| 273 | std::swap(rep_, rhs.rep_); | ||
| 274 | } | ||
| 275 | |||
| 276 | /** | ||
| 277 | * \brief Assignment operator. | ||
| 278 | * \param[in] rhs the expansion to be copied | ||
| 279 | * \return the new value of this expansion (rhs) | ||
| 280 | */ | ||
| 281 | 1169344 | expansion_nt& operator= (const expansion_nt& rhs) { | |
| 282 |
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1169344 | if(&rhs != this) { |
| 283 | cleanup(); | ||
| 284 | 1169344 | copy(rhs); | |
| 285 | } | ||
| 286 | 1169344 | return *this; | |
| 287 | } | ||
| 288 | |||
| 289 | /** | ||
| 290 | * \brief Assignment operator with move semantics | ||
| 291 | * \param[in] rhs the expansion to be copied | ||
| 292 | * \return the new value of this expansion (rhs) | ||
| 293 | */ | ||
| 294 | expansion_nt& operator= (expansion_nt&& rhs) { | ||
| 295 |
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28736 | if(&rhs != this) { |
| 296 | cleanup(); | ||
| 297 | std::swap(rep_, rhs.rep_); | ||
| 298 | } | ||
| 299 | return *this; | ||
| 300 | } | ||
| 301 | |||
| 302 | /** | ||
| 303 | * \brief Expansion_nt destructor. | ||
| 304 | * \details The stored expansion is deallocated whenever | ||
| 305 | * reference counting reaches 0. | ||
| 306 | */ | ||
| 307 | ~expansion_nt() { | ||
| 308 | cleanup(); | ||
| 309 |
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9054557 | } |
| 310 | |||
| 311 | /** | ||
| 312 | * \brief Optimizes the internal representation without changing the | ||
| 313 | * represented value | ||
| 314 | * \details this function can reduce the length of an expansion | ||
| 315 | */ | ||
| 316 | void optimize() { | ||
| 317 | 1844677 | rep().optimize(); | |
| 318 | 254583 | } | |
| 319 | |||
| 320 | /** | ||
| 321 | * \brief Flips the sign of an expansion. | ||
| 322 | */ | ||
| 323 | void negate() { | ||
| 324 | rep().negate(); | ||
| 325 | } | ||
| 326 | |||
| 327 | /********************************************************************/ | ||
| 328 | |||
| 329 | /** | ||
| 330 | * \brief Adds an expansion_nt to this expansion_nt | ||
| 331 | * \param[in] rhs the expansion_nt to be added to this expansion_nt | ||
| 332 | * \return the new value of this expansion_nt | ||
| 333 | */ | ||
| 334 | expansion_nt& operator+= (const expansion_nt& rhs); | ||
| 335 | |||
| 336 | /** | ||
| 337 | * \brief Subtracts an expansion_nt to this expansion_nt | ||
| 338 | * \param[in] rhs the expansion_nt to be subtracted | ||
| 339 | * \return the new value of this expansion_nt | ||
| 340 | */ | ||
| 341 | expansion_nt& operator-= (const expansion_nt& rhs); | ||
| 342 | |||
| 343 | /** | ||
| 344 | * \brief Multiplies this expansion_nt by an expansion_nt | ||
| 345 | * \param[in] rhs the expansion_nt to multiply this expansion_nt by | ||
| 346 | * \return the new value of this expansion_nt | ||
| 347 | */ | ||
| 348 | expansion_nt& operator*= (const expansion_nt& rhs); | ||
| 349 | |||
| 350 | /** | ||
| 351 | * \brief Adds a double to this expansion_nt | ||
| 352 | * \param[in] rhs the double to be added to this expansion_nt | ||
| 353 | * \return the new value of this expansion_nt | ||
| 354 | */ | ||
| 355 | expansion_nt& operator+= (double rhs); | ||
| 356 | |||
| 357 | /** | ||
| 358 | * \brief Subtracts a double from this expansion_nt | ||
| 359 | * \param[in] rhs the double to be subtracted from this expansion_nt | ||
| 360 | * \return the new value of this expansion_nt | ||
| 361 | */ | ||
| 362 | expansion_nt& operator-= (double rhs); | ||
| 363 | |||
| 364 | /** | ||
| 365 | * \brief Multiplies this expansion_nt by a double | ||
| 366 | * \details If the double is a constant (possibly negative) power of | ||
| 367 | * two (e.g. 0.125, 0.5, 2.0, 4.0 ...), one may use | ||
| 368 | * scale_fast() instead. | ||
| 369 | * \param[in] rhs the double to multiply this expansion_nt with | ||
| 370 | * \return the new value of this expansion_nt | ||
| 371 | */ | ||
| 372 | expansion_nt& operator*= (double rhs); | ||
| 373 | |||
| 374 | /********************************************************************/ | ||
| 375 | |||
| 376 | /** | ||
| 377 | * \brief Computes the sum of two expansion_nt%s | ||
| 378 | * \param[in] rhs the expansion_nt to be added to this expansion_nt | ||
| 379 | * \return the sum of this expansion_nt and \p rhs | ||
| 380 | */ | ||
| 381 | expansion_nt operator+ (const expansion_nt& rhs) const; | ||
| 382 | |||
| 383 | /** | ||
| 384 | * \brief Computes the difference between two expansion_nt%s | ||
| 385 | * \param[in] rhs the expansion_nt to be subtracted from | ||
| 386 | * this expansion_nt | ||
| 387 | * \return the difference between this expansion_nt and \p rhs | ||
| 388 | */ | ||
| 389 | expansion_nt operator- (const expansion_nt& rhs) const; | ||
| 390 | |||
| 391 | /** | ||
| 392 | * \brief Computes the product between two expansion_nt%s | ||
| 393 | * \param[in] rhs the expansion_nt to be multiplied by | ||
| 394 | * this expansion_nt | ||
| 395 | * \return the product between this expansion_nt and \p rhs | ||
| 396 | */ | ||
| 397 | expansion_nt operator* (const expansion_nt& rhs) const; | ||
| 398 | |||
| 399 | /** | ||
| 400 | * \brief Computes the sum of an expansion_nt and a double. | ||
| 401 | * \param[in] rhs the double to be added to this expansion_nt | ||
| 402 | * \return the sum of this expansion_nt and \p rhs | ||
| 403 | */ | ||
| 404 | expansion_nt operator+ (double rhs) const; | ||
| 405 | |||
| 406 | /** | ||
| 407 | * \brief Computes the difference between an expansion_nt and a double. | ||
| 408 | * \param[in] rhs the double to be subtracted from this expansion_nt | ||
| 409 | * \return the difference between this expansion_nt and \p rhs | ||
| 410 | */ | ||
| 411 | expansion_nt operator- (double rhs) const; | ||
| 412 | |||
| 413 | /** | ||
| 414 | * \brief Computes the product between an expansion_nt and a double. | ||
| 415 | * \param[in] rhs the double to be multiplied by this expansion_nt | ||
| 416 | * \return the product between this expansion_nt and \p rhs | ||
| 417 | */ | ||
| 418 | expansion_nt operator* (double rhs) const; | ||
| 419 | |||
| 420 | /********************************************************************/ | ||
| 421 | |||
| 422 | /** | ||
| 423 | * \brief Computes the opposite of this expansion_nt. | ||
| 424 | * \return the opposite of this expansion_nt | ||
| 425 | */ | ||
| 426 | expansion_nt operator- () const; | ||
| 427 | |||
| 428 | /********************************************************************/ | ||
| 429 | |||
| 430 | /** | ||
| 431 | * \brief Compares two expansion_nt | ||
| 432 | * \return the sign of this expansion minus rhs | ||
| 433 | */ | ||
| 434 | Sign compare(const expansion_nt& rhs) const { | ||
| 435 | ✗ | return rep().compare(rhs.rep()); | |
| 436 | } | ||
| 437 | |||
| 438 | /** | ||
| 439 | * \brief Compares an expansion_nt with a double | ||
| 440 | * \return the sign of this expansion minus rhs | ||
| 441 | */ | ||
| 442 | Sign compare(double rhs) const { | ||
| 443 | return rep().compare(rhs); | ||
| 444 | } | ||
| 445 | |||
| 446 | /** | ||
| 447 | * \brief Compares this expansion_nt with another one. | ||
| 448 | * \details Internally computes the sign of the difference | ||
| 449 | * between this expansion_nt and \p rhs. | ||
| 450 | * \return true if this expansion_nt is greater than \p rhs, | ||
| 451 | * false otherwise | ||
| 452 | */ | ||
| 453 | bool operator> (const expansion_nt& rhs) const { | ||
| 454 | ✗ | return (int(compare(rhs))>0); | |
| 455 | } | ||
| 456 | |||
| 457 | /** | ||
| 458 | * \brief Compares this expansion_nt with another one. | ||
| 459 | * \details Internally computes the sign of the difference | ||
| 460 | * between this expansion_nt and \p rhs. | ||
| 461 | * \return true if this expansion_nt is greater or equal than \p rhs, | ||
| 462 | * false otherwise | ||
| 463 | */ | ||
| 464 | bool operator>= (const expansion_nt& rhs) const { | ||
| 465 | return (int(compare(rhs))>=0); | ||
| 466 | } | ||
| 467 | |||
| 468 | /** | ||
| 469 | * \brief Compares this expansion_nt with another one. | ||
| 470 | * \details Internally computes the sign of the difference | ||
| 471 | * between this expansion_nt and \p rhs. | ||
| 472 | * \return true if this expansion_nt is smaller than \p rhs, | ||
| 473 | * false otherwise | ||
| 474 | */ | ||
| 475 | bool operator< (const expansion_nt& rhs) const { | ||
| 476 | return (int(compare(rhs))<0); | ||
| 477 | } | ||
| 478 | |||
| 479 | /** | ||
| 480 | * \brief Compares this expansion_nt with another one. | ||
| 481 | * \details Internally computes the sign of the difference | ||
| 482 | * between this expansion_nt and \p rhs. | ||
| 483 | * \return true if this expansion_nt is smaller or equal than \p rhs, | ||
| 484 | * false otherwise | ||
| 485 | */ | ||
| 486 | bool operator<= (const expansion_nt& rhs) const { | ||
| 487 | return (int(compare(rhs))<=0); | ||
| 488 | } | ||
| 489 | |||
| 490 | /** | ||
| 491 | * \brief Compares this expansion_nt with another one. | ||
| 492 | * \details Internally computes the sign of the difference | ||
| 493 | * between this expansion_nt and \p rhs. | ||
| 494 | * \return true if this expansion_nt is greater than \p rhs, | ||
| 495 | * false otherwise | ||
| 496 | */ | ||
| 497 | bool operator> (double rhs) const { | ||
| 498 | return (int(compare(rhs))>0); | ||
| 499 | } | ||
| 500 | |||
| 501 | /** | ||
| 502 | * \brief Compares this expansion_nt with another one. | ||
| 503 | * \details Internally computes the sign of the difference | ||
| 504 | * between this expansion_nt and \p rhs. | ||
| 505 | * \return true if this expansion_nt is greater or equal than \p rhs, | ||
| 506 | * false otherwise | ||
| 507 | */ | ||
| 508 | bool operator>= (double rhs) const { | ||
| 509 | return (int(compare(rhs))>=0); | ||
| 510 | } | ||
| 511 | |||
| 512 | /** | ||
| 513 | * \brief Compares this expansion_nt with another one. | ||
| 514 | * \details Internally computes the sign of the difference | ||
| 515 | * between this expansion_nt and \p rhs. | ||
| 516 | * \return true if this expansion_nt is smaller than \p rhs, | ||
| 517 | * false otherwise | ||
| 518 | */ | ||
| 519 | bool operator< (double rhs) const { | ||
| 520 | return (int(compare(rhs))<0); | ||
| 521 | } | ||
| 522 | |||
| 523 | /** | ||
| 524 | * \brief Compares this expansion_nt with another one. | ||
| 525 | * \details Internally computes the sign of the difference | ||
| 526 | * between this expansion_nt and \p rhs. | ||
| 527 | * \return true if this expansion_nt is smaller or equal than \p rhs, | ||
| 528 | * false otherwise | ||
| 529 | */ | ||
| 530 | bool operator<= (double rhs) const { | ||
| 531 | return (int(compare(rhs))<=0); | ||
| 532 | } | ||
| 533 | |||
| 534 | /********************************************************************/ | ||
| 535 | |||
| 536 | /** | ||
| 537 | * \brief Computes an approximation of the stored | ||
| 538 | * value in this expansion. | ||
| 539 | * \return an approximation of the stored value. | ||
| 540 | */ | ||
| 541 | double estimate() const { | ||
| 542 | return rep().estimate(); | ||
| 543 | } | ||
| 544 | |||
| 545 | /** | ||
| 546 | * \brief Gets the sign of this expansion_nt. | ||
| 547 | * \return the sign of this expansion_nt, computed exactly. | ||
| 548 | */ | ||
| 549 | Sign sign() const { | ||
| 550 | return rep().sign(); | ||
| 551 | } | ||
| 552 | |||
| 553 | /** | ||
| 554 | * \brief Gets the length of this expansion. | ||
| 555 | * \return the number of components used internally | ||
| 556 | * to represend this expansion | ||
| 557 | * \note most client code will not need to use this | ||
| 558 | * (advanced use only). | ||
| 559 | */ | ||
| 560 | index_t length() const { | ||
| 561 | return rep().length(); | ||
| 562 | } | ||
| 563 | |||
| 564 | /** | ||
| 565 | * \brief Gets the i-th component of this expansion. | ||
| 566 | * \param i index of the component | ||
| 567 | * \return the i-th component of this expansion | ||
| 568 | * \pre i < length() | ||
| 569 | * \note most client code will not need to use this | ||
| 570 | * (advanced use only). | ||
| 571 | */ | ||
| 572 | double component(index_t i) const { | ||
| 573 | geo_debug_assert(i < length()); | ||
| 574 |
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82975314 | return rep()[i]; |
| 575 | } | ||
| 576 | |||
| 577 | /** | ||
| 578 | * \brief Constructs a new expansion_nt from an expansion. | ||
| 579 | * \details Used internally | ||
| 580 | * \param[in] rep should be a reference-counted expansion, created | ||
| 581 | * by new_expansion_on_heap(). Its reference counter is incremented. | ||
| 582 | * \note most client code will not need to use this | ||
| 583 | * (advanced use only). | ||
| 584 | */ | ||
| 585 | 17052 | expansion_nt(expansion* rep) : | |
| 586 | 5895422 | rep_(rep) { | |
| 587 | } | ||
| 588 | |||
| 589 | /** | ||
| 590 | * \brief Gets the internal expansion that represents this | ||
| 591 | * expansion_nt. | ||
| 592 | * \return a reference to the expansion that represents | ||
| 593 | * this expansion_nt | ||
| 594 | * \note most client code will not need to use this | ||
| 595 | * (advanced use only). | ||
| 596 | */ | ||
| 597 | expansion& rep() { | ||
| 598 |
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777212 | return *rep_; |
| 599 | } | ||
| 600 | |||
| 601 | /** | ||
| 602 | * \brief Gets the internal expansion that represents | ||
| 603 | * this expansion_nt. | ||
| 604 | * \return a const reference to the expansion that represents | ||
| 605 | * this expansion_nt | ||
| 606 | * \note most client code will not need to use this | ||
| 607 | * (advanced use only). | ||
| 608 | */ | ||
| 609 | const expansion& rep() const { | ||
| 610 |
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87054765 | return *rep_; |
| 611 | } | ||
| 612 | |||
| 613 | /** | ||
| 614 | * \brief Gets a string representation of this expansion | ||
| 615 | * \return a string with the length and components or "null" | ||
| 616 | * if this expansion_nt was explicitely set to uninitialized. | ||
| 617 | */ | ||
| 618 | std::string to_string() const { | ||
| 619 | return (rep_ == nullptr) ? | ||
| 620 | std::string("null") : | ||
| 621 | rep_->to_string() ; | ||
| 622 | } | ||
| 623 | |||
| 624 | /** | ||
| 625 | * \brief Tests whether an expansion_nt is equal to one. | ||
| 626 | * \details Optimized using the low-level API | ||
| 627 | * \retval true if \p x is equal to one | ||
| 628 | * \retval false otherwise | ||
| 629 | */ | ||
| 630 | bool is_one() const { | ||
| 631 | return rep().equals(1.0); | ||
| 632 | } | ||
| 633 | |||
| 634 | /** | ||
| 635 | * \brief Tests whether an expansion_nt is equal to zero | ||
| 636 | * \details Optimized using the low-level API | ||
| 637 | * \retval true if \p x is equal to zero | ||
| 638 | * \retval false otherwise | ||
| 639 | */ | ||
| 640 | bool is_zero() const { | ||
| 641 | return sign() == ZERO; | ||
| 642 | } | ||
| 643 | |||
| 644 | protected: | ||
| 645 | |||
| 646 | /** | ||
| 647 | * \brief Copies an expansion into this one. | ||
| 648 | * \details current rep_ pointer is supposed to be | ||
| 649 | * uninitialized or freed before calling this function. | ||
| 650 | * \param[in] rhs a const reference to the expansion to be copied | ||
| 651 | */ | ||
| 652 | 16428745 | void copy(const expansion_nt& rhs) { | |
| 653 |
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16428745 | if(rhs.rep_ == nullptr) { |
| 654 | ✗ | rep_ = nullptr; | |
| 655 | } else { | ||
| 656 | 16428745 | rep_ = expansion::new_expansion_on_heap(rhs.rep().capacity()); | |
| 657 | rep_->set_length(rhs.rep().length()); | ||
| 658 |
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54425027 | for(index_t i=0; i<rep_->length(); ++i) { |
| 659 | 37996282 | (*rep_)[i] = rhs.rep()[i]; | |
| 660 | } | ||
| 661 | } | ||
| 662 | 16428745 | } | |
| 663 | |||
| 664 | /** | ||
| 665 | * \brief Cleanups the memory associated with this expansion_nt. | ||
| 666 | */ | ||
| 667 | void cleanup() { | ||
| 668 |
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|
13151113 | if(rep_ != nullptr) { |
| 669 | expansion::delete_expansion_on_heap(rep_); | ||
| 670 | 15779 | rep_ = nullptr; | |
| 671 | } | ||
| 672 | } | ||
| 673 | |||
| 674 | private: | ||
| 675 | expansion* rep_; | ||
| 676 | friend expansion_nt operator- (double a, const expansion_nt& b); | ||
| 677 | |||
| 678 | friend expansion_nt expansion_nt_sq_dist( | ||
| 679 | const double* a, const double* b, coord_index_t dim | ||
| 680 | ); | ||
| 681 | |||
| 682 | friend expansion_nt expansion_nt_dot_at( | ||
| 683 | const double* a, const double* b, const double* c, | ||
| 684 | coord_index_t dim | ||
| 685 | ); | ||
| 686 | // friend class rational_nt; | ||
| 687 | }; | ||
| 688 | |||
| 689 | /** | ||
| 690 | * \brief Computes the sum of a double and an expansion_nt | ||
| 691 | * \param[in] a the double to be added | ||
| 692 | * \param[in] b the expansion_nt to be added | ||
| 693 | * \return an expansion_nt that represents \p a + \p b | ||
| 694 | * \relates expansion_nt | ||
| 695 | */ | ||
| 696 | inline expansion_nt operator+ (double a, const expansion_nt& b) { | ||
| 697 | return b + a; | ||
| 698 | } | ||
| 699 | |||
| 700 | /** | ||
| 701 | * \brief Computes the difference between a double and an expansion_nt | ||
| 702 | * \param[in] a the double | ||
| 703 | * \param[in] b the expansion_nt to be subtracted | ||
| 704 | * \return an expansion_nt that represents \p a - \p b | ||
| 705 | * \relates expansion_nt | ||
| 706 | */ | ||
| 707 | inline expansion_nt operator- (double a, const expansion_nt& b) { | ||
| 708 | expansion_nt result = b - a; | ||
| 709 | result.rep().negate(); | ||
| 710 | return result; | ||
| 711 | } | ||
| 712 | |||
| 713 | /** | ||
| 714 | * \brief Computes the product of a double and an expansion_nt | ||
| 715 | * \param[in] a the double | ||
| 716 | * \param[in] b the expansion_nt to be multiplied | ||
| 717 | * \return an expansion_nt that represents \p a * \p b | ||
| 718 | * \relates expansion_nt | ||
| 719 | */ | ||
| 720 | inline expansion_nt operator* (double a, const expansion_nt& b) { | ||
| 721 | return b * a; | ||
| 722 | } | ||
| 723 | |||
| 724 | /** | ||
| 725 | * \brief Tests equality between two expansion_nt%s. | ||
| 726 | * \details Implemented by testing whether the difference between | ||
| 727 | * \p a and \p b is 0. | ||
| 728 | * \return true if \p a and \p b represent exactly the same value, false | ||
| 729 | * otherwise | ||
| 730 | * \relates expansion_nt | ||
| 731 | */ | ||
| 732 | inline bool operator== (const expansion_nt& a, const expansion_nt& b) { | ||
| 733 | return a.rep().equals(b.rep()); | ||
| 734 | } | ||
| 735 | |||
| 736 | /** | ||
| 737 | * \brief Tests equality between an expansion_nt and a double. | ||
| 738 | * \details Implemented by testing whether the difference between | ||
| 739 | * \p a and \p b is 0. | ||
| 740 | * \return true if \p a and \p b represent exactly the same value, false | ||
| 741 | * otherwise | ||
| 742 | * \relates expansion_nt | ||
| 743 | */ | ||
| 744 | inline bool operator== (const expansion_nt& a, double b) { | ||
| 745 | return a.rep().equals(b); | ||
| 746 | } | ||
| 747 | |||
| 748 | /** | ||
| 749 | * \brief Tests equality between a double and an expansion_nt. | ||
| 750 | * \details Implemented by testing whether the difference between | ||
| 751 | * \p a and \p b is 0. | ||
| 752 | * \return true if \p a and \p b represent exactly the same value, false | ||
| 753 | * otherwise | ||
| 754 | * \relates expansion_nt | ||
| 755 | */ | ||
| 756 | inline bool operator== (double a, const expansion_nt& b) { | ||
| 757 | return b.rep().equals(a); | ||
| 758 | } | ||
| 759 | |||
| 760 | /** | ||
| 761 | * \brief Tests whether two expansion_nt%s differ. | ||
| 762 | * \details Implemented by testing whether the difference between | ||
| 763 | * \p a and \p b is different from 0. | ||
| 764 | * \return true if \p a and \p b do not represent the same exact value, | ||
| 765 | * false otherwise | ||
| 766 | * \relates expansion_nt | ||
| 767 | */ | ||
| 768 | inline bool operator!= (const expansion_nt& a, const expansion_nt& b) { | ||
| 769 | return !a.rep().equals(b.rep()); | ||
| 770 | } | ||
| 771 | |||
| 772 | /** | ||
| 773 | * \brief Tests whether an expansion_nt differs from a double. | ||
| 774 | * \details Implemented by testing whether the difference between | ||
| 775 | * \p a and \p b is different from 0. | ||
| 776 | * \return true if \p a and \p b do not represent the same exact value, | ||
| 777 | * false otherwise | ||
| 778 | * \relates expansion_nt | ||
| 779 | */ | ||
| 780 | inline bool operator!= (const expansion_nt& a, double b) { | ||
| 781 | return !a.rep().equals(b); | ||
| 782 | } | ||
| 783 | |||
| 784 | /** | ||
| 785 | * \brief Tests whether a double differs from an expansion_nt. | ||
| 786 | * \details Implemented by testing whether the difference between | ||
| 787 | * \p a and \p b is different from 0. | ||
| 788 | * \return true if \p a and \p b do not represent the same exact value, | ||
| 789 | * false otherwise | ||
| 790 | * \relates expansion_nt | ||
| 791 | */ | ||
| 792 | inline bool operator!= (double a, const expansion_nt& b) { | ||
| 793 | return !b.rep().equals(a); | ||
| 794 | } | ||
| 795 | |||
| 796 | /** | ||
| 797 | * \brief Computes an expansion that represents the square distance between | ||
| 798 | * two points. | ||
| 799 | * \param[in] a an array of \p dim doubles | ||
| 800 | * \param[in] b an array of \p dim doubles | ||
| 801 | * \param[in] dim the dimension of the points | ||
| 802 | * \return an expansion_nt that represent the exact squared | ||
| 803 | * distance between \p a and \p b | ||
| 804 | * \relates expansion_nt | ||
| 805 | */ | ||
| 806 | inline expansion_nt expansion_nt_sq_dist( | ||
| 807 | const double* a, const double* b, coord_index_t dim | ||
| 808 | ) { | ||
| 809 | expansion* result = expansion::new_expansion_on_heap( | ||
| 810 | expansion::sq_dist_capacity(dim) | ||
| 811 | ); | ||
| 812 | result->assign_sq_dist(a, b, dim); | ||
| 813 | return expansion_nt(result); | ||
| 814 | } | ||
| 815 | |||
| 816 | /** | ||
| 817 | * \brief Computes an expansion that represents the dot product of | ||
| 818 | * two vectors determined by three points. | ||
| 819 | * \param[in] a an array of \p dim doubles | ||
| 820 | * \param[in] b an array of \p dim doubles | ||
| 821 | * \param[in] c an array of \p dim doubles | ||
| 822 | * \param[in] dim the dimension of the points | ||
| 823 | * \return an expansion_nt that represents the exact | ||
| 824 | * dot product (\p a - \p c).(\p b - \p c) | ||
| 825 | * \relates expansion_nt | ||
| 826 | */ | ||
| 827 | inline expansion_nt expansion_nt_dot_at( | ||
| 828 | const double* a, const double* b, const double* c, coord_index_t dim | ||
| 829 | ) { | ||
| 830 | expansion* result = expansion::new_expansion_on_heap( | ||
| 831 | expansion::dot_at_capacity(dim) | ||
| 832 | ); | ||
| 833 | result->assign_dot_at(a, b, c, dim); | ||
| 834 | return expansion_nt(result); | ||
| 835 | } | ||
| 836 | |||
| 837 | /************************************************************************/ | ||
| 838 | |||
| 839 | /** | ||
| 840 | * \brief Specialization of geo_sgn() for expansion_nt. | ||
| 841 | * \param x a const reference to an expansion_nt | ||
| 842 | * \return the (exact) sign of x (one of POSITIVE, ZERO, NEGATIVE) | ||
| 843 | */ | ||
| 844 | template <> inline Sign geo_sgn(const expansion_nt& x) { | ||
| 845 | return x.sign(); | ||
| 846 | } | ||
| 847 | |||
| 848 | /** | ||
| 849 | * \brief Specialization of geo_cmp() for expansion_nt. | ||
| 850 | * \param x , y const references to two expansion_nt | ||
| 851 | * \retval POSITIVE if x > y | ||
| 852 | * \retval ZERO if x == y | ||
| 853 | * \retval NEGATIVE if x < y | ||
| 854 | */ | ||
| 855 | template <> inline Sign geo_cmp( | ||
| 856 | const expansion_nt& x, const expansion_nt& y | ||
| 857 | ) { | ||
| 858 | return x.compare(y); | ||
| 859 | } | ||
| 860 | |||
| 861 | /************************************************************************/ | ||
| 862 | |||
| 863 | /** | ||
| 864 | * \brief Tests whether an expansion_nt is zero. | ||
| 865 | * \details Optimized using the low-level API | ||
| 866 | * \param[in] x a const reference to the expansion_nt to be tested | ||
| 867 | * \retval true if \p x is equal to zero | ||
| 868 | * \retval false otherwise | ||
| 869 | */ | ||
| 870 | inline bool expansion_nt_is_zero(const expansion_nt& x) { | ||
| 871 | return (x.sign() == GEO::ZERO); | ||
| 872 | } | ||
| 873 | |||
| 874 | /** | ||
| 875 | * \brief Tests whether an expansion_nt is equal to one. | ||
| 876 | * \details Optimized using the low-level API | ||
| 877 | * \param[in] x a const reference to the expansion_nt to be tested | ||
| 878 | * \retval true if \p x is equal to one | ||
| 879 | * \retval false otherwise | ||
| 880 | */ | ||
| 881 | inline bool expansion_nt_is_one(const expansion_nt& x) { | ||
| 882 | return x.rep().equals(1.0); | ||
| 883 | } | ||
| 884 | |||
| 885 | |||
| 886 | /** | ||
| 887 | * \brief Compares two expansion_nt | ||
| 888 | * \details Optimized using the low-level API | ||
| 889 | * \param [in] x , y the two expansion_nt to compare | ||
| 890 | * \retval POSITIVE if \p x is greater than \p y | ||
| 891 | * \retval ZERO if \p x equals \p y | ||
| 892 | * \retval NEGATIVE if \p x is smaller than \p y | ||
| 893 | */ | ||
| 894 | inline Sign expansion_nt_compare( | ||
| 895 | const expansion_nt& x, const expansion_nt& y | ||
| 896 | ) { | ||
| 897 | const expansion& diff = expansion_diff(x.rep(), y.rep()); | ||
| 898 | return diff.sign(); | ||
| 899 | } | ||
| 900 | |||
| 901 | /** | ||
| 902 | * \brief Computes the square of an expansion_nt | ||
| 903 | * \details Optimized using the low-level API | ||
| 904 | * \param[in] x the expansion_nt to be squared | ||
| 905 | * \return \p x * \p x | ||
| 906 | */ | ||
| 907 | inline expansion_nt expansion_nt_square(const expansion_nt& x) { | ||
| 908 | expansion_nt result( | ||
| 909 | expansion::new_expansion_on_heap( | ||
| 910 | expansion::square_capacity(x.rep() | ||
| 911 | )) | ||
| 912 | ); | ||
| 913 | result.rep().assign_square(x.rep()); | ||
| 914 | return result; | ||
| 915 | } | ||
| 916 | |||
| 917 | |||
| 918 | /** | ||
| 919 | * \brief Computes a 2x2 determinant | ||
| 920 | * \details Specialization using the low-evel API for expansions. | ||
| 921 | * This gains some performance as compared to using CGAL's | ||
| 922 | * determinant template with expansion_nt. | ||
| 923 | */ | ||
| 924 | expansion_nt GEOGRAM_API expansion_nt_determinant( | ||
| 925 | const expansion_nt& a00,const expansion_nt& a01, | ||
| 926 | const expansion_nt& a10,const expansion_nt& a11 | ||
| 927 | ); | ||
| 928 | |||
| 929 | /** | ||
| 930 | * \brief Computes a 3x3 determinant | ||
| 931 | * \details Specialization using the low-evel API for expansions. | ||
| 932 | * This gains some performance as compared to using CGAL's determinant | ||
| 933 | * template with expansion_nt. | ||
| 934 | */ | ||
| 935 | expansion_nt GEOGRAM_API expansion_nt_determinant( | ||
| 936 | const expansion_nt& a00,const expansion_nt& a01,const expansion_nt& a02, | ||
| 937 | const expansion_nt& a10,const expansion_nt& a11,const expansion_nt& a12, | ||
| 938 | const expansion_nt& a20,const expansion_nt& a21,const expansion_nt& a22 | ||
| 939 | ); | ||
| 940 | |||
| 941 | /** | ||
| 942 | * \brief Computes a 4x4 determinant | ||
| 943 | * \details Specialization using the low-evel API for expansions. | ||
| 944 | * This gains some performance as compared to using CGAL's determinant | ||
| 945 | * template with expansion_nt. | ||
| 946 | */ | ||
| 947 | expansion_nt GEOGRAM_API expansion_nt_determinant( | ||
| 948 | const expansion_nt& a00,const expansion_nt& a01, | ||
| 949 | const expansion_nt& a02,const expansion_nt& a03, | ||
| 950 | const expansion_nt& a10,const expansion_nt& a11, | ||
| 951 | const expansion_nt& a12,const expansion_nt& a13, | ||
| 952 | const expansion_nt& a20,const expansion_nt& a21, | ||
| 953 | const expansion_nt& a22,const expansion_nt& a23, | ||
| 954 | const expansion_nt& a30,const expansion_nt& a31, | ||
| 955 | const expansion_nt& a32,const expansion_nt& a33 | ||
| 956 | ); | ||
| 957 | |||
| 958 | // Make things a bit faster if target OS has large stack size | ||
| 959 | #ifdef GEO_HAS_BIG_STACK | ||
| 960 | |||
| 961 | /** | ||
| 962 | * \brief Specialization of det2x2 | ||
| 963 | * \details Calls the optimized implementation for expansion_nt | ||
| 964 | */ | ||
| 965 | |||
| 966 | template <> inline expansion_nt det2x2( | ||
| 967 | const expansion_nt& a11, const expansion_nt& a12, | ||
| 968 | const expansion_nt& a21, const expansion_nt& a22 | ||
| 969 | ) { | ||
| 970 | return expansion_nt_determinant( | ||
| 971 | a11,a12, | ||
| 972 | a21,a22 | ||
| 973 |
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1010247 | ); |
| 974 | } | ||
| 975 | |||
| 976 | /** | ||
| 977 | * \brief Specialization of det3x3 | ||
| 978 | * \details Calls the optimized implementation for expansion_nt | ||
| 979 | */ | ||
| 980 | |||
| 981 | template <> inline expansion_nt det3x3( | ||
| 982 | const expansion_nt& a11, const expansion_nt& a12, | ||
| 983 | const expansion_nt& a13, | ||
| 984 | const expansion_nt& a21, const expansion_nt& a22, | ||
| 985 | const expansion_nt& a23, | ||
| 986 | const expansion_nt& a31, const expansion_nt& a32, | ||
| 987 | const expansion_nt& a33 | ||
| 988 | ) { | ||
| 989 | return expansion_nt_determinant( | ||
| 990 | a11,a12,a13, | ||
| 991 | a21,a22,a23, | ||
| 992 | a31,a32,a33 | ||
| 993 |
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17274 | ); |
| 994 | } | ||
| 995 | |||
| 996 | /** | ||
| 997 | * \brief Specialization of det4x4 | ||
| 998 | * \details Calls the optimized implementation for expansion_nt | ||
| 999 | */ | ||
| 1000 | |||
| 1001 | template <> inline expansion_nt det4x4( | ||
| 1002 | const expansion_nt& a11, const expansion_nt& a12, | ||
| 1003 | const expansion_nt& a13, const expansion_nt& a14, | ||
| 1004 | const expansion_nt& a21, const expansion_nt& a22, | ||
| 1005 | const expansion_nt& a23, const expansion_nt& a24, | ||
| 1006 | const expansion_nt& a31, const expansion_nt& a32, | ||
| 1007 | const expansion_nt& a33, const expansion_nt& a34, | ||
| 1008 | const expansion_nt& a41, const expansion_nt& a42, | ||
| 1009 | const expansion_nt& a43, const expansion_nt& a44 | ||
| 1010 | ) { | ||
| 1011 | return expansion_nt_determinant( | ||
| 1012 | a11,a12,a13,a14, | ||
| 1013 | a21,a22,a23,a24, | ||
| 1014 | a31,a32,a33,a34, | ||
| 1015 | a41,a42,a43,a44 | ||
| 1016 | ); | ||
| 1017 | } | ||
| 1018 | |||
| 1019 | #endif | ||
| 1020 | |||
| 1021 | /************************************************************************/ | ||
| 1022 | } | ||
| 1023 | |||
| 1024 | /** | ||
| 1025 | * \brief Displays the approximated value of an expansion_nt to a stream. | ||
| 1026 | * \param[out] os the stream | ||
| 1027 | * \param[in] a the expansion_nt to be sent to the stream | ||
| 1028 | * \return a reference to the stream | ||
| 1029 | */ | ||
| 1030 | inline std::ostream& operator<< ( | ||
| 1031 | std::ostream& os, const GEO::expansion_nt& a | ||
| 1032 | ) { | ||
| 1033 | return os << a.estimate(); | ||
| 1034 | } | ||
| 1035 | |||
| 1036 | /** | ||
| 1037 | * \brief Reads a double precision number from a stream and converts it to | ||
| 1038 | * an approximation. | ||
| 1039 | * \param[in] is the stream | ||
| 1040 | * \param[out] a the read expansion_nt | ||
| 1041 | * \return a reference to the stream | ||
| 1042 | */ | ||
| 1043 | inline std::istream& operator>> ( std::istream& is, GEO::expansion_nt& a) { | ||
| 1044 | double d; | ||
| 1045 | is >> d; | ||
| 1046 | if (is) { | ||
| 1047 | a = GEO::expansion_nt(d); | ||
| 1048 | } | ||
| 1049 | return is; | ||
| 1050 | } | ||
| 1051 | |||
| 1052 | /*****************************************************************************/ | ||
| 1053 | |||
| 1054 | namespace GEO { | ||
| 1055 | |||
| 1056 | /**************************************************************************/ | ||
| 1057 | |||
| 1058 | namespace Numeric { | ||
| 1059 | |||
| 1060 | template<> inline void optimize_number_representation(expansion_nt& x) { | ||
| 1061 | x.optimize(); | ||
| 1062 | } | ||
| 1063 | |||
| 1064 | /** | ||
| 1065 | * \brief Compares two rational numbers given as separate | ||
| 1066 | * numerators and denominators. Specialization for exact_nt. | ||
| 1067 | * \param[in] a_num , a_denom defines a = \p a_num / \p a_denom | ||
| 1068 | * \param[in] b_num , b_denom defines b = \p b_num / \p b_denom | ||
| 1069 | * \return the sign of a - b | ||
| 1070 | */ | ||
| 1071 | template<> Sign GEOGRAM_API ratio_compare( | ||
| 1072 | const expansion_nt& a_num, const expansion_nt& a_denom, | ||
| 1073 | const expansion_nt& b_num, const expansion_nt& b_denom | ||
| 1074 | ); | ||
| 1075 | } | ||
| 1076 | |||
| 1077 | /**************************************************************************/ | ||
| 1078 | |||
| 1079 | typedef rationalg<expansion_nt> rational_nt; | ||
| 1080 | |||
| 1081 | /**************************************************************************/ | ||
| 1082 | |||
| 1083 | /** \brief Specialization of GEO::is_scalar */ | ||
| 1084 | template <> struct is_scalar<expansion_nt> { | ||
| 1085 | typedef expansion_nt type; | ||
| 1086 | static constexpr bool value = true; | ||
| 1087 | }; | ||
| 1088 | |||
| 1089 | /**************************************************************************/ | ||
| 1090 | } | ||
| 1091 | |||
| 1092 | #endif | ||
| 1093 |