[babc50] | 1 | /* emacs edit mode for this file is -*- C++ -*- */ |
---|
| 2 | |
---|
[b52d27] | 3 | /** |
---|
| 4 | * |
---|
[a34bee4] | 5 | * @file cf_inline.cc |
---|
| 6 | * |
---|
| 7 | * definition of configurable inline |
---|
[b52d27] | 8 | * `CanonicalForm' methods. |
---|
| 9 | * |
---|
| 10 | * Hierarchy: canonicalform |
---|
| 11 | * |
---|
| 12 | * Header file: canonicalform.h |
---|
| 13 | * |
---|
| 14 | * Developers note: |
---|
| 15 | * ---------------- |
---|
| 16 | * The central class in Factory is, of course, `CanonicalForm'. |
---|
| 17 | * Hence it is a quiet reasonable to assume that inlining its |
---|
| 18 | * most important methods will improve execution speed. The same |
---|
| 19 | * holds for some methods of the `CFIterator' class. Everything |
---|
| 20 | * on configurable inline `CanonicalForm' methods explained here |
---|
| 21 | * applies mutatis mutandis to the `CFIterator' methods. |
---|
| 22 | * |
---|
| 23 | * However, inlining `CanonicalForm' methods has two major |
---|
| 24 | * drawbacks: |
---|
| 25 | * |
---|
| 26 | * o If `CanonicalForm' methods simply would have been declared |
---|
| 27 | * `inline' it would have been necessary to include the |
---|
| 28 | * definition of `InternalCF' in `factory.h'. This would have |
---|
| 29 | * been quite a contradiction to the internal nature of the |
---|
| 30 | * class. |
---|
| 31 | * Hence it seemed desirable to introduce a mechanism to have |
---|
| 32 | * both the inlined versions for internal use and compiled |
---|
| 33 | * versions for the library. |
---|
| 34 | * |
---|
| 35 | * o Second, inlining in most cases leads to larger object code. |
---|
| 36 | * E.g., inlining `CanonicalForm::~CanonicalForm()' increases the |
---|
| 37 | * object code by approx. 15% without any effect on computation |
---|
| 38 | * speed. |
---|
| 39 | * Thus another design aim was to keep things configurable. |
---|
| 40 | * That is why the methods defined here are called |
---|
| 41 | * "configurable inline methods". |
---|
| 42 | * |
---|
| 43 | * The low level solution to both problems is the macro |
---|
| 44 | * `CF_INLINE' which either expands to `inline' or nothing. The |
---|
| 45 | * counterpart `CF_NO_INLINE' exists only for convenience, it |
---|
| 46 | * always expands to nothing. `CF_INLINE' is set immediately |
---|
| 47 | * before defining resp. declaring the methods to exclude any |
---|
| 48 | * esoteric influences from included files. |
---|
| 49 | * |
---|
| 50 | * The high level interface is the macro `CF_USE_INLINE'. If it |
---|
| 51 | * is defined any header file that uses configurable inline |
---|
| 52 | * methods defines them to be `inline', otherwise they are |
---|
| 53 | * defined as ordinary methods. `CF_USE_INLINE' is defined in |
---|
| 54 | * `config.h' only. |
---|
| 55 | * |
---|
| 56 | * To switch on (off) all configurable inline methods, it is |
---|
| 57 | * sufficient to define (undefine) `CF_USE_INLINE' in `config.h'. |
---|
| 58 | * To switch off separate configurable inline methods it is |
---|
| 59 | * necessary to prefix their declaration in `canonicalform.h' by |
---|
| 60 | * `CF_NO_INLINE' instead of `CF_INLINE'. Furthermore, to avoid |
---|
| 61 | * duplicate symbols at link time, their definition in this file |
---|
| 62 | * has to be wrapped by an `#ifndef INCL_CF_INLINE_CC'. |
---|
| 63 | * |
---|
| 64 | * It turned out that inlining the following methods (and only |
---|
| 65 | * them) results in the best time to size ratio on Linux and HP |
---|
| 66 | * machines: |
---|
| 67 | * o all `CanonicalForm' constructors |
---|
| 68 | * o the binary `CanonicalForm' operators `+' and `*' |
---|
| 69 | * |
---|
| 70 | **/ |
---|
[babc50] | 71 | |
---|
| 72 | // check whether we are included or translated and |
---|
| 73 | // define `INCL_CF_INLINE_CC' if we are included |
---|
| 74 | #ifdef INCL_CANONICALFORM_H |
---|
| 75 | #define INCL_CF_INLINE_CC |
---|
| 76 | #endif |
---|
| 77 | |
---|
[9f7665] | 78 | |
---|
[e4fe2b] | 79 | #include "config.h" |
---|
[9f7665] | 80 | |
---|
[babc50] | 81 | |
---|
[650f2d8] | 82 | #include "cf_assert.h" |
---|
[babc50] | 83 | |
---|
| 84 | // temporarily switch off `CF_USE_INLINE' and include |
---|
| 85 | // `canonicalform.h' if we are being translated. |
---|
| 86 | // `CF_USE_INLINE_SAVE' is used to save the state of |
---|
| 87 | // `CF_USE_INLINE'. It is unset after use. |
---|
| 88 | #ifndef INCL_CF_INLINE_CC |
---|
| 89 | #ifdef CF_USE_INLINE |
---|
| 90 | #define CF_USE_INLINE_SAVE |
---|
| 91 | #undef CF_USE_INLINE |
---|
| 92 | #endif |
---|
| 93 | #include "canonicalform.h" |
---|
| 94 | #ifdef CF_USE_INLINE_SAVE |
---|
| 95 | #define CF_USE_INLINE |
---|
| 96 | #undef CF_USE_INLINE_SAVE |
---|
| 97 | #endif |
---|
| 98 | #endif /* ! INCL_CF_INLINE_CC */ |
---|
| 99 | |
---|
| 100 | // regular include files |
---|
| 101 | #include "int_cf.h" |
---|
| 102 | #include "imm.h" |
---|
| 103 | #include "cf_factory.h" |
---|
| 104 | |
---|
| 105 | // set the value of `CF_INLINE' for the following methods and |
---|
| 106 | // functions |
---|
| 107 | #if defined( CF_USE_INLINE ) && defined( INCL_CF_INLINE_CC ) |
---|
| 108 | #undef CF_INLINE |
---|
| 109 | #define CF_INLINE inline |
---|
| 110 | #else |
---|
| 111 | #undef CF_INLINE |
---|
| 112 | #define CF_INLINE |
---|
| 113 | #endif /* ! defined( CF_USE_INLINE ) && defined( INCL_CF_INLINE_CC ) */ |
---|
| 114 | |
---|
| 115 | // constructors, destructors, assignment |
---|
[b52d27] | 116 | /** CF_INLINE CanonicalForm::CanonicalForm () |
---|
| 117 | * |
---|
| 118 | * |
---|
| 119 | * CanonicalForm() - create the default canonical form. |
---|
| 120 | * |
---|
| 121 | * The canonical form is initialized to zero from the current |
---|
| 122 | * domain. |
---|
| 123 | * |
---|
| 124 | **/ |
---|
[babc50] | 125 | CF_INLINE |
---|
| 126 | CanonicalForm::CanonicalForm () |
---|
[9b88e6] | 127 | : value( CFFactory::basic( 0L ) ) |
---|
[babc50] | 128 | { |
---|
| 129 | } |
---|
[b52d27] | 130 | |
---|
| 131 | /** CF_INLINE CanonicalForm::CanonicalForm ( const int i ) |
---|
| 132 | * |
---|
| 133 | * |
---|
| 134 | * CanonicalForm() - create a canonical form from an integer. |
---|
| 135 | * |
---|
| 136 | * The canonical form is initialized to the "canonical image" of |
---|
| 137 | * `i' in the current domain. This is `i' itself for |
---|
| 138 | * characteristic zero, `i' mod p for finite fields of |
---|
| 139 | * characteristic p, and `i' mod p^n for prime power domains with |
---|
| 140 | * p^n elements. |
---|
| 141 | * |
---|
| 142 | **/ |
---|
[babc50] | 143 | CF_INLINE |
---|
| 144 | CanonicalForm::CanonicalForm ( const int i ) |
---|
[be587d] | 145 | : value( CFFactory::basic( (long)i ) ) |
---|
[8710ff0] | 146 | { |
---|
| 147 | } |
---|
| 148 | |
---|
| 149 | CF_INLINE |
---|
| 150 | CanonicalForm::CanonicalForm ( const long i ) |
---|
[babc50] | 151 | : value( CFFactory::basic( i ) ) |
---|
| 152 | { |
---|
| 153 | } |
---|
[b52d27] | 154 | |
---|
| 155 | /** CF_INLINE CanonicalForm::CanonicalForm ( const CanonicalForm & cf ) |
---|
| 156 | * |
---|
| 157 | * |
---|
| 158 | * CanonicalForm() - create a copy of a canonical form. |
---|
| 159 | * |
---|
| 160 | * Type info: |
---|
| 161 | * ---------- |
---|
| 162 | * cf: Anything |
---|
| 163 | * |
---|
| 164 | **/ |
---|
[babc50] | 165 | CF_INLINE |
---|
| 166 | CanonicalForm::CanonicalForm ( const CanonicalForm & cf ) |
---|
| 167 | : value( is_imm( cf.value ) ? cf.value : cf.value->copyObject() ) |
---|
| 168 | { |
---|
| 169 | } |
---|
[b52d27] | 170 | |
---|
| 171 | /** CF_INLINE CanonicalForm::CanonicalForm ( InternalCF * cf ) |
---|
| 172 | * |
---|
| 173 | * |
---|
| 174 | * CanonicalForm() - create a canonical form from a pointer to an |
---|
| 175 | * internal canonical form. |
---|
| 176 | * |
---|
| 177 | * This constructor is reserved for internal usage. |
---|
| 178 | * |
---|
| 179 | * Developers note: |
---|
| 180 | * ---------------- |
---|
| 181 | * The canonical form gets its value immediately from `cf'. |
---|
| 182 | * `cf's reference counter is not incremented, so be careful with |
---|
| 183 | * this constructor. |
---|
| 184 | * |
---|
| 185 | **/ |
---|
[babc50] | 186 | CF_INLINE |
---|
| 187 | CanonicalForm::CanonicalForm ( InternalCF * cf ) |
---|
| 188 | : value( cf ) |
---|
| 189 | { |
---|
| 190 | } |
---|
[b52d27] | 191 | |
---|
| 192 | /** CF_INLINE CanonicalForm::CanonicalForm ( const Variable & v ) |
---|
| 193 | * |
---|
| 194 | * |
---|
| 195 | * CanonicalForm() - create a canonical form from a variable. |
---|
| 196 | * |
---|
| 197 | * If `v' is a polynomial variable or an algebraic element the |
---|
| 198 | * resulting polynomial (or algebraic element) is 1*`v'^1, the |
---|
| 199 | * one being from the current domain. |
---|
| 200 | * |
---|
| 201 | * Variables of level `LEVELBASE' are transformed to one from the |
---|
| 202 | * current domain. |
---|
| 203 | * |
---|
| 204 | * Type info: |
---|
| 205 | * ---------- |
---|
| 206 | * v: Anything |
---|
| 207 | * |
---|
| 208 | **/ |
---|
[babc50] | 209 | CF_INLINE |
---|
| 210 | CanonicalForm::CanonicalForm ( const Variable & v ) |
---|
| 211 | : value( CFFactory::poly( v ) ) |
---|
| 212 | { |
---|
| 213 | } |
---|
[b52d27] | 214 | |
---|
| 215 | /** CF_INLINE CanonicalForm::CanonicalForm ( const Variable & v, int e ) |
---|
| 216 | * |
---|
| 217 | * |
---|
| 218 | * CanonicalForm() - create a canonical form from a power of a |
---|
| 219 | * variable. |
---|
| 220 | * |
---|
| 221 | * If `v' is a polynomial variable or an algebraic element the |
---|
| 222 | * resulting polynomial (or algebraic element) is 1*`v'^`e', the |
---|
| 223 | * one being from the current domain. Algebraic elements are |
---|
| 224 | * reduced modulo their minimal polynomial. |
---|
| 225 | * |
---|
| 226 | * Variables of level `LEVELBASE' are transformed to one from the |
---|
| 227 | * current domain. |
---|
| 228 | * |
---|
| 229 | * Type info: |
---|
| 230 | * ---------- |
---|
| 231 | * v: Anything |
---|
| 232 | * |
---|
| 233 | **/ |
---|
[babc50] | 234 | CF_INLINE |
---|
| 235 | CanonicalForm::CanonicalForm ( const Variable & v, int e ) |
---|
| 236 | : value( CFFactory::poly( v, e ) ) |
---|
| 237 | { |
---|
[57daf8] | 238 | //ASSERT( e > 0, "math error: exponent has to be positive" ); |
---|
[babc50] | 239 | } |
---|
| 240 | |
---|
| 241 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 242 | /** CF_INLINE CanonicalForm::~CanonicalForm () |
---|
| 243 | * |
---|
| 244 | * |
---|
| 245 | * ~CanonicalForm() - delete CO. |
---|
| 246 | * |
---|
| 247 | * Type info: |
---|
| 248 | * ---------- |
---|
| 249 | * CO: Anything |
---|
| 250 | * |
---|
| 251 | **/ |
---|
[babc50] | 252 | CF_INLINE |
---|
| 253 | CanonicalForm::~CanonicalForm () |
---|
| 254 | { |
---|
| 255 | if ( (! is_imm( value )) && value->deleteObject() ) |
---|
[806c18] | 256 | delete value; |
---|
[babc50] | 257 | } |
---|
| 258 | #endif |
---|
| 259 | |
---|
| 260 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 261 | /** CF_INLINE CanonicalForm & CanonicalForm::operator = ( const CanonicalForm & cf ) |
---|
| 262 | * |
---|
| 263 | * |
---|
| 264 | * operator =() - assign `cf' to CO. |
---|
| 265 | * |
---|
| 266 | * Type info: |
---|
| 267 | * ---------- |
---|
| 268 | * CO, cf: Anything |
---|
| 269 | * |
---|
| 270 | **/ |
---|
[babc50] | 271 | CF_INLINE CanonicalForm & |
---|
| 272 | CanonicalForm::operator = ( const CanonicalForm & cf ) |
---|
| 273 | { |
---|
| 274 | if ( this != &cf ) { |
---|
[806c18] | 275 | if ( (! is_imm( value )) && value->deleteObject() ) |
---|
| 276 | delete value; |
---|
| 277 | value = (is_imm( cf.value )) ? cf.value : cf.value->copyObject(); |
---|
[babc50] | 278 | } |
---|
| 279 | return *this; |
---|
| 280 | } |
---|
[b52d27] | 281 | |
---|
| 282 | /** |
---|
| 283 | * |
---|
| 284 | * operator =() - assign long `cf' to CO. |
---|
| 285 | * |
---|
| 286 | * `cf' converted to a canonical form as described in the |
---|
| 287 | * canonical form constructor which creates a canonical form from |
---|
| 288 | * an integer. |
---|
| 289 | * |
---|
| 290 | * Type info: |
---|
| 291 | * ---------- |
---|
| 292 | * CO: Anything |
---|
| 293 | * |
---|
| 294 | * Developers note: |
---|
| 295 | * ---------------- |
---|
| 296 | * Strictly speaking, this operator is superfluous. The ordinary |
---|
| 297 | * assignment operator together with automatic conversion from |
---|
| 298 | * `int' to `CanonicalForm' would do the job, too. But this way |
---|
| 299 | * the common operation of assigning an integer is faster. |
---|
| 300 | * |
---|
| 301 | **/ |
---|
[babc50] | 302 | CF_INLINE CanonicalForm & |
---|
[8710ff0] | 303 | CanonicalForm::operator = ( const long cf ) |
---|
[babc50] | 304 | { |
---|
| 305 | if ( (! is_imm( value )) && value->deleteObject() ) |
---|
[806c18] | 306 | delete value; |
---|
[babc50] | 307 | value = CFFactory::basic( cf ); |
---|
| 308 | return *this; |
---|
| 309 | } |
---|
| 310 | #endif |
---|
| 311 | |
---|
| 312 | // predicates |
---|
| 313 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 314 | /** CF_INLINE bool CanonicalForm::isOne, isZero () const |
---|
| 315 | * |
---|
| 316 | * |
---|
| 317 | * isOne(), isZero() - test whether a `CanonicalForm' equals one |
---|
| 318 | * or zero, resp. |
---|
| 319 | * |
---|
| 320 | * The predicates `isOne()' and `isZero()' are much faster than |
---|
| 321 | * the comparison operators. Furthermore, a test `f.isZero()' is |
---|
| 322 | * independent from the current domain, whereas an expression |
---|
| 323 | * `f == 0' is not. |
---|
| 324 | * |
---|
| 325 | * Type info: |
---|
| 326 | * ---------- |
---|
| 327 | * CO: Anything |
---|
| 328 | * |
---|
| 329 | * Internal implementation: |
---|
| 330 | * ------------------------ |
---|
| 331 | * Note that only immediate objects and objects of class |
---|
| 332 | * `InternalPrimePower' may equal one or zero, resp. |
---|
| 333 | * |
---|
| 334 | * imm_isone(), imm_iszero() |
---|
| 335 | * Trivial. |
---|
| 336 | * |
---|
| 337 | * imm_isone_p(), imm_iszero_p() |
---|
| 338 | * Trivial. |
---|
| 339 | * |
---|
| 340 | * imm_isone_gf(), imm_iszero_gf() |
---|
| 341 | * Use `gf_isone()' and `gf_iszero()', resp., to test whether CO |
---|
| 342 | * equals zero or one, resp. |
---|
| 343 | * |
---|
| 344 | * InternalCF::isOne(), isZero() |
---|
| 345 | * Always return false. |
---|
| 346 | * |
---|
| 347 | * InternalPrimePower::isOne(), isZero() |
---|
| 348 | * Use `mpz_cpm_ui()' resp. `mpz_sgn()' to check the underlying |
---|
| 349 | * mpi. |
---|
| 350 | * |
---|
| 351 | * @sa CanonicalForm::isZero() |
---|
| 352 | **/ |
---|
[babc50] | 353 | CF_INLINE bool |
---|
| 354 | CanonicalForm::isOne () const |
---|
| 355 | { |
---|
| 356 | int what = is_imm( value ); |
---|
| 357 | |
---|
| 358 | if ( ! what ) |
---|
[806c18] | 359 | return value->isOne(); |
---|
[babc50] | 360 | else if ( what == INTMARK ) |
---|
[806c18] | 361 | return imm_isone( value ); |
---|
[babc50] | 362 | else if ( what == FFMARK ) |
---|
[806c18] | 363 | return imm_isone_p( value ); |
---|
[babc50] | 364 | else |
---|
[806c18] | 365 | return imm_isone_gf( value ); |
---|
[babc50] | 366 | } |
---|
| 367 | |
---|
[b52d27] | 368 | /** |
---|
| 369 | * @sa CanonicalForm::isOne() |
---|
| 370 | **/ |
---|
[babc50] | 371 | CF_INLINE bool |
---|
| 372 | CanonicalForm::isZero () const |
---|
| 373 | { |
---|
| 374 | int what = is_imm( value ); |
---|
| 375 | |
---|
[aa5055] | 376 | if ( what == 0 ) |
---|
[806c18] | 377 | return value->isZero(); |
---|
[babc50] | 378 | else if ( what == INTMARK ) |
---|
[806c18] | 379 | return imm_iszero( value ); |
---|
[babc50] | 380 | else if ( what == FFMARK ) |
---|
[806c18] | 381 | return imm_iszero_p( value ); |
---|
[babc50] | 382 | else |
---|
[806c18] | 383 | return imm_iszero_gf( value ); |
---|
[babc50] | 384 | } |
---|
| 385 | #endif |
---|
| 386 | |
---|
| 387 | // arithmetic operators |
---|
| 388 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 389 | /** CF_INLINE CanonicalForm operator - ( const CanonicalForm & cf ) |
---|
| 390 | * |
---|
| 391 | * |
---|
| 392 | * operator -() - return additive inverse of `cf'. |
---|
| 393 | * |
---|
| 394 | * Returns the additive inverse of `cf'. One should keep in mind |
---|
| 395 | * that to negate a canonical form a complete (deep) copy of it |
---|
| 396 | * has to be created. |
---|
| 397 | * |
---|
| 398 | * Type info: |
---|
| 399 | * ---------- |
---|
| 400 | * cf: CurrentPP |
---|
| 401 | * |
---|
| 402 | * In fact, the type is almost `Anything', but it is, e.g., not |
---|
| 403 | * possible to invert an element from a finite field when the |
---|
| 404 | * characteristic of the current domain has changed. |
---|
| 405 | * |
---|
| 406 | * Internal implementation: |
---|
| 407 | * ------------------------ |
---|
| 408 | * All internal methods check whether the reference counter |
---|
| 409 | * equals one. If so CO is negated in-place. Otherwise, a new |
---|
| 410 | * copy of CO is created and negated. |
---|
| 411 | * |
---|
| 412 | * imm_neg() |
---|
| 413 | * Trivial. |
---|
| 414 | * |
---|
| 415 | * imm_neg_p() |
---|
| 416 | * Use `ff_neg()' to negate CO. |
---|
| 417 | * |
---|
| 418 | * imm_neg_gf() |
---|
| 419 | * Use `gf_neg()' to negate CO. |
---|
| 420 | * |
---|
| 421 | * InternalInteger::neg() |
---|
| 422 | * Use `mpz_neg()' to negate the underlying mpi. |
---|
| 423 | * |
---|
| 424 | * InternalRational::neg () |
---|
| 425 | * Use `mpz_neg()' to negate the denominator. |
---|
| 426 | * |
---|
| 427 | * InternalPrimePower::neg() |
---|
| 428 | * Subtract CO from `primepow' using `mpz_sub'. |
---|
| 429 | * |
---|
| 430 | * InternalPoly::neg() |
---|
| 431 | * If reference counter is one use `negateTermList()' to negate |
---|
| 432 | * the terms, otherwise create a negated copy using |
---|
| 433 | * `copyTermList()'. |
---|
| 434 | * |
---|
| 435 | * @sa CanonicalForm::operator -=() |
---|
| 436 | **/ |
---|
[babc50] | 437 | CF_INLINE CanonicalForm |
---|
| 438 | operator - ( const CanonicalForm & cf ) |
---|
| 439 | { |
---|
| 440 | CanonicalForm result( cf ); |
---|
| 441 | int what = is_imm( result.value ); |
---|
| 442 | |
---|
| 443 | if ( ! what ) |
---|
[806c18] | 444 | result.value = result.value->neg(); |
---|
[babc50] | 445 | else if ( what == INTMARK ) |
---|
[806c18] | 446 | result.value = imm_neg( result.value ); |
---|
[babc50] | 447 | else if ( what == FFMARK ) |
---|
[806c18] | 448 | result.value = imm_neg_p( result.value ); |
---|
[babc50] | 449 | else |
---|
[806c18] | 450 | result.value = imm_neg_gf( result.value ); |
---|
[babc50] | 451 | |
---|
| 452 | return result; |
---|
| 453 | } |
---|
| 454 | #endif |
---|
| 455 | |
---|
| 456 | // binary arithmetic operators and functions |
---|
[b52d27] | 457 | /** CF_INLINE CanonicalForm operator +, -, *, /, % ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 458 | * |
---|
| 459 | * |
---|
| 460 | * operators +, -, *, /, %(), div(), mod() - binary arithmetic |
---|
| 461 | * operators. |
---|
| 462 | * |
---|
| 463 | * The binary operators have their standard (mathematical) |
---|
| 464 | * semantics. As explained for the corresponding arithmetic |
---|
| 465 | * assignment operators, the operators `/' and `%' return the |
---|
| 466 | * quotient resp. remainder of (polynomial) division with |
---|
| 467 | * remainder, whereas `div()' and `mod()' may be used for exact |
---|
| 468 | * division and term-wise remaindering, resp. |
---|
| 469 | * |
---|
| 470 | * It is faster to use the arithmetic assignment operators (e.g., |
---|
| 471 | * `f += g;') instead of the binary operators (`f = f+g;' ). |
---|
| 472 | * |
---|
| 473 | * Type info: |
---|
| 474 | * ---------- |
---|
| 475 | * lhs, rhs: CurrentPP |
---|
| 476 | * |
---|
| 477 | * There are weaker preconditions for some cases (e.g., |
---|
| 478 | * arithmetic operations with elements from Q or Z work in any |
---|
| 479 | * domain), but type `CurrentPP' is the only one guaranteed to |
---|
| 480 | * work for all cases. |
---|
| 481 | * |
---|
| 482 | * Developers note: |
---|
| 483 | * ---------------- |
---|
| 484 | * All binary operators have their corresponding `CanonicalForm' |
---|
| 485 | * assignment operators (e.g., `operator +()' corresponds to |
---|
| 486 | * `CanonicalForm::operator +=()', `div()' corresponds to |
---|
| 487 | * `CanonicalForm::div()). |
---|
| 488 | * |
---|
| 489 | * And that is how they are implemented, too: Each of the binary |
---|
| 490 | * operators first creates a copy of `lhs', adds `rhs' to this |
---|
| 491 | * copy using the assignment operator, and returns the result. |
---|
| 492 | * |
---|
| 493 | * @sa CanonicalForm::operator +=() |
---|
| 494 | **/ |
---|
[babc50] | 495 | CF_INLINE CanonicalForm |
---|
| 496 | operator + ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 497 | { |
---|
| 498 | CanonicalForm result( lhs ); |
---|
| 499 | result += rhs; |
---|
| 500 | return result; |
---|
| 501 | } |
---|
| 502 | |
---|
| 503 | #ifndef INCL_CF_INLINE_CC |
---|
| 504 | CF_INLINE CanonicalForm |
---|
| 505 | operator - ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 506 | { |
---|
| 507 | CanonicalForm result( lhs ); |
---|
| 508 | result -= rhs; |
---|
| 509 | return result; |
---|
| 510 | } |
---|
| 511 | #endif |
---|
| 512 | |
---|
[b52d27] | 513 | /** |
---|
| 514 | * @sa CanonicalForm::operator *=() |
---|
| 515 | **/ |
---|
[babc50] | 516 | CF_INLINE CanonicalForm |
---|
| 517 | operator * ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 518 | { |
---|
| 519 | CanonicalForm result( lhs ); |
---|
| 520 | result *= rhs; |
---|
| 521 | return result; |
---|
| 522 | } |
---|
| 523 | |
---|
| 524 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 525 | /** |
---|
| 526 | * @sa CanonicalForm::operator /=() |
---|
| 527 | **/ |
---|
[babc50] | 528 | CF_INLINE CanonicalForm |
---|
| 529 | operator / ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 530 | { |
---|
| 531 | CanonicalForm result( lhs ); |
---|
| 532 | result /= rhs; |
---|
| 533 | return result; |
---|
| 534 | } |
---|
| 535 | |
---|
[b52d27] | 536 | /** |
---|
| 537 | * @sa CanonicalForm::operator %=() |
---|
| 538 | **/ |
---|
[babc50] | 539 | CF_INLINE CanonicalForm |
---|
| 540 | operator % ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 541 | { |
---|
| 542 | CanonicalForm result( lhs ); |
---|
| 543 | result %= rhs; |
---|
| 544 | return result; |
---|
| 545 | } |
---|
| 546 | #endif |
---|
| 547 | |
---|
| 548 | #ifndef INCL_CF_INLINE_CC |
---|
[b52d27] | 549 | /** CF_INLINE CanonicalForm div, mod ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 550 | * @sa mod(), operator/(), CanonicalForm::operator /=() |
---|
| 551 | **/ |
---|
[babc50] | 552 | CF_INLINE CanonicalForm |
---|
| 553 | div ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 554 | { |
---|
| 555 | CanonicalForm result( lhs ); |
---|
| 556 | result.div( rhs ); |
---|
| 557 | return result; |
---|
| 558 | } |
---|
| 559 | |
---|
[b52d27] | 560 | /** |
---|
| 561 | * @sa div(), operator%(), CanonicalForm::operator %=() |
---|
| 562 | **/ |
---|
[babc50] | 563 | CF_INLINE CanonicalForm |
---|
| 564 | mod ( const CanonicalForm & lhs, const CanonicalForm & rhs ) |
---|
| 565 | { |
---|
| 566 | CanonicalForm result( lhs ); |
---|
| 567 | result.mod( rhs ); |
---|
| 568 | return result; |
---|
| 569 | } |
---|
| 570 | #endif |
---|