1 | // Boost rational.hpp header file ------------------------------------------// |
2 | |
3 | // (C) Copyright Paul Moore 1999. Permission to copy, use, modify, sell and |
4 | // distribute this software is granted provided this copyright notice appears |
5 | // in all copies. This software is provided "as is" without express or |
6 | // implied warranty, and with no claim as to its suitability for any purpose. |
7 | |
8 | // boostinspect:nolicense (don't complain about the lack of a Boost license) |
9 | // (Paul Moore hasn't been in contact for years, so there's no way to change the |
10 | // license.) |
11 | |
12 | // See http://www.boost.org/libs/rational for documentation. |
13 | |
14 | // Credits: |
15 | // Thanks to the boost mailing list in general for useful comments. |
16 | // Particular contributions included: |
17 | // Andrew D Jewell, for reminding me to take care to avoid overflow |
18 | // Ed Brey, for many comments, including picking up on some dreadful typos |
19 | // Stephen Silver contributed the test suite and comments on user-defined |
20 | // IntType |
21 | // Nickolay Mladenov, for the implementation of operator+= |
22 | |
23 | // Revision History |
24 | // 02 Sep 13 Remove unneeded forward declarations; tweak private helper |
25 | // function (Daryle Walker) |
26 | // 30 Aug 13 Improve exception safety of "assign"; start modernizing I/O code |
27 | // (Daryle Walker) |
28 | // 27 Aug 13 Add cross-version constructor template, plus some private helper |
29 | // functions; add constructor to exception class to take custom |
30 | // messages (Daryle Walker) |
31 | // 25 Aug 13 Add constexpr qualification wherever possible (Daryle Walker) |
32 | // 05 May 12 Reduced use of implicit gcd (Mario Lang) |
33 | // 05 Nov 06 Change rational_cast to not depend on division between different |
34 | // types (Daryle Walker) |
35 | // 04 Nov 06 Off-load GCD and LCM to Boost.Math; add some invariant checks; |
36 | // add std::numeric_limits<> requirement to help GCD (Daryle Walker) |
37 | // 31 Oct 06 Recoded both operator< to use round-to-negative-infinity |
38 | // divisions; the rational-value version now uses continued fraction |
39 | // expansion to avoid overflows, for bug #798357 (Daryle Walker) |
40 | // 20 Oct 06 Fix operator bool_type for CW 8.3 (Joaquín M López Muñoz) |
41 | // 18 Oct 06 Use EXPLICIT_TEMPLATE_TYPE helper macros from Boost.Config |
42 | // (Joaquín M López Muñoz) |
43 | // 27 Dec 05 Add Boolean conversion operator (Daryle Walker) |
44 | // 28 Sep 02 Use _left versions of operators from operators.hpp |
45 | // 05 Jul 01 Recode gcd(), avoiding std::swap (Helmut Zeisel) |
46 | // 03 Mar 01 Workarounds for Intel C++ 5.0 (David Abrahams) |
47 | // 05 Feb 01 Update operator>> to tighten up input syntax |
48 | // 05 Feb 01 Final tidy up of gcd code prior to the new release |
49 | // 27 Jan 01 Recode abs() without relying on abs(IntType) |
50 | // 21 Jan 01 Include Nickolay Mladenov's operator+= algorithm, |
51 | // tidy up a number of areas, use newer features of operators.hpp |
52 | // (reduces space overhead to zero), add operator!, |
53 | // introduce explicit mixed-mode arithmetic operations |
54 | // 12 Jan 01 Include fixes to handle a user-defined IntType better |
55 | // 19 Nov 00 Throw on divide by zero in operator /= (John (EBo) David) |
56 | // 23 Jun 00 Incorporate changes from Mark Rodgers for Borland C++ |
57 | // 22 Jun 00 Change _MSC_VER to BOOST_MSVC so other compilers are not |
58 | // affected (Beman Dawes) |
59 | // 6 Mar 00 Fix operator-= normalization, #include <string> (Jens Maurer) |
60 | // 14 Dec 99 Modifications based on comments from the boost list |
61 | // 09 Dec 99 Initial Version (Paul Moore) |
62 | |
63 | #ifndef BOOST_RATIONAL_HPP |
64 | #define BOOST_RATIONAL_HPP |
65 | |
66 | #include <boost/config.hpp> // for BOOST_NO_STDC_NAMESPACE, BOOST_MSVC, etc |
67 | #ifndef BOOST_NO_IOSTREAM |
68 | #include <iomanip> // for std::setw |
69 | #include <ios> // for std::noskipws, streamsize |
70 | #include <istream> // for std::istream |
71 | #include <ostream> // for std::ostream |
72 | #include <sstream> // for std::ostringstream |
73 | #endif |
74 | #include <cstddef> // for NULL |
75 | #include <stdexcept> // for std::domain_error |
76 | #include <string> // for std::string implicit constructor |
77 | #include <boost/operators.hpp> // for boost::addable etc |
78 | #include <cstdlib> // for std::abs |
79 | #include <boost/call_traits.hpp> // for boost::call_traits |
80 | #include <boost/detail/workaround.hpp> // for BOOST_WORKAROUND |
81 | #include <boost/assert.hpp> // for BOOST_ASSERT |
82 | #include <boost/integer/common_factor_rt.hpp> // for boost::integer::gcd, lcm |
83 | #include <limits> // for std::numeric_limits |
84 | #include <boost/static_assert.hpp> // for BOOST_STATIC_ASSERT |
85 | #include <boost/throw_exception.hpp> |
86 | |
87 | // Control whether depreciated GCD and LCM functions are included (default: yes) |
88 | #ifndef BOOST_CONTROL_RATIONAL_HAS_GCD |
89 | #define BOOST_CONTROL_RATIONAL_HAS_GCD 1 |
90 | #endif |
91 | |
92 | namespace boost { |
93 | |
94 | #if BOOST_CONTROL_RATIONAL_HAS_GCD |
95 | template <typename IntType> |
96 | IntType gcd(IntType n, IntType m) |
97 | { |
98 | // Defer to the version in Boost.Math |
99 | return integer::gcd( n, m ); |
100 | } |
101 | |
102 | template <typename IntType> |
103 | IntType lcm(IntType n, IntType m) |
104 | { |
105 | // Defer to the version in Boost.Math |
106 | return integer::lcm( n, m ); |
107 | } |
108 | #endif // BOOST_CONTROL_RATIONAL_HAS_GCD |
109 | |
110 | class bad_rational : public std::domain_error |
111 | { |
112 | public: |
113 | explicit bad_rational() : std::domain_error("bad rational: zero denominator" ) {} |
114 | explicit bad_rational( char const *what ) : std::domain_error( what ) {} |
115 | }; |
116 | |
117 | template <typename IntType> |
118 | class rational : |
119 | less_than_comparable < rational<IntType>, |
120 | equality_comparable < rational<IntType>, |
121 | less_than_comparable2 < rational<IntType>, IntType, |
122 | equality_comparable2 < rational<IntType>, IntType, |
123 | addable < rational<IntType>, |
124 | subtractable < rational<IntType>, |
125 | multipliable < rational<IntType>, |
126 | dividable < rational<IntType>, |
127 | addable2 < rational<IntType>, IntType, |
128 | subtractable2 < rational<IntType>, IntType, |
129 | subtractable2_left < rational<IntType>, IntType, |
130 | multipliable2 < rational<IntType>, IntType, |
131 | dividable2 < rational<IntType>, IntType, |
132 | dividable2_left < rational<IntType>, IntType, |
133 | incrementable < rational<IntType>, |
134 | decrementable < rational<IntType> |
135 | > > > > > > > > > > > > > > > > |
136 | { |
137 | // Class-wide pre-conditions |
138 | BOOST_STATIC_ASSERT( ::std::numeric_limits<IntType>::is_specialized ); |
139 | |
140 | // Helper types |
141 | typedef typename boost::call_traits<IntType>::param_type param_type; |
142 | |
143 | struct helper { IntType parts[2]; }; |
144 | typedef IntType (helper::* bool_type)[2]; |
145 | |
146 | public: |
147 | // Component type |
148 | typedef IntType int_type; |
149 | |
150 | BOOST_CONSTEXPR |
151 | rational() : num(0), den(1) {} |
152 | BOOST_CONSTEXPR |
153 | rational(param_type n) : num(n), den(1) {} |
154 | rational(param_type n, param_type d) : num(n), den(d) { normalize(); } |
155 | |
156 | #ifndef BOOST_NO_MEMBER_TEMPLATES |
157 | template < typename NewType > |
158 | BOOST_CONSTEXPR explicit |
159 | rational(rational<NewType> const &r) |
160 | : num(r.numerator()), den(is_normalized(n: int_type(r.numerator()), |
161 | d: int_type(r.denominator())) ? r.denominator() : |
162 | (BOOST_THROW_EXCEPTION(bad_rational("bad rational: denormalized conversion" )), 0)){} |
163 | #endif |
164 | |
165 | // Default copy constructor and assignment are fine |
166 | |
167 | // Add assignment from IntType |
168 | rational& operator=(param_type i) { num = i; den = 1; return *this; } |
169 | |
170 | // Assign in place |
171 | rational& assign(param_type n, param_type d); |
172 | |
173 | // Access to representation |
174 | BOOST_CONSTEXPR |
175 | const IntType& numerator() const { return num; } |
176 | BOOST_CONSTEXPR |
177 | const IntType& denominator() const { return den; } |
178 | |
179 | // Arithmetic assignment operators |
180 | rational& operator+= (const rational& r); |
181 | rational& operator-= (const rational& r); |
182 | rational& operator*= (const rational& r); |
183 | rational& operator/= (const rational& r); |
184 | |
185 | rational& operator+= (param_type i) { num += i * den; return *this; } |
186 | rational& operator-= (param_type i) { num -= i * den; return *this; } |
187 | rational& operator*= (param_type i); |
188 | rational& operator/= (param_type i); |
189 | |
190 | // Increment and decrement |
191 | const rational& operator++() { num += den; return *this; } |
192 | const rational& operator--() { num -= den; return *this; } |
193 | |
194 | // Operator not |
195 | BOOST_CONSTEXPR |
196 | bool operator!() const { return !num; } |
197 | |
198 | // Boolean conversion |
199 | |
200 | #if BOOST_WORKAROUND(__MWERKS__,<=0x3003) |
201 | // The "ISO C++ Template Parser" option in CW 8.3 chokes on the |
202 | // following, hence we selectively disable that option for the |
203 | // offending memfun. |
204 | #pragma parse_mfunc_templ off |
205 | #endif |
206 | |
207 | BOOST_CONSTEXPR |
208 | operator bool_type() const { return operator !() ? 0 : &helper::parts; } |
209 | |
210 | #if BOOST_WORKAROUND(__MWERKS__,<=0x3003) |
211 | #pragma parse_mfunc_templ reset |
212 | #endif |
213 | |
214 | // Comparison operators |
215 | bool operator< (const rational& r) const; |
216 | BOOST_CONSTEXPR |
217 | bool operator== (const rational& r) const; |
218 | |
219 | bool operator< (param_type i) const; |
220 | bool operator> (param_type i) const; |
221 | BOOST_CONSTEXPR |
222 | bool operator== (param_type i) const; |
223 | |
224 | private: |
225 | // Implementation - numerator and denominator (normalized). |
226 | // Other possibilities - separate whole-part, or sign, fields? |
227 | IntType num; |
228 | IntType den; |
229 | |
230 | // Helper functions |
231 | static BOOST_CONSTEXPR |
232 | int_type inner_gcd( param_type a, param_type b, int_type const &zero = |
233 | int_type(0) ) |
234 | { return b == zero ? a : inner_gcd(a: b, b: a % b, zero); } |
235 | |
236 | static BOOST_CONSTEXPR |
237 | int_type inner_abs( param_type x, int_type const &zero = int_type(0) ) |
238 | { return x < zero ? -x : +x; } |
239 | |
240 | // Representation note: Fractions are kept in normalized form at all |
241 | // times. normalized form is defined as gcd(num,den) == 1 and den > 0. |
242 | // In particular, note that the implementation of abs() below relies |
243 | // on den always being positive. |
244 | bool test_invariant() const; |
245 | void normalize(); |
246 | |
247 | static BOOST_CONSTEXPR |
248 | bool is_normalized( param_type n, param_type d, int_type const &zero = |
249 | int_type(0), int_type const &one = int_type(1) ) |
250 | { |
251 | return d > zero && ( n != zero || d == one ) && inner_abs( x: inner_gcd(a: n, |
252 | b: d, zero), zero ) == one; |
253 | } |
254 | }; |
255 | |
256 | // Assign in place |
257 | template <typename IntType> |
258 | inline rational<IntType>& rational<IntType>::assign(param_type n, param_type d) |
259 | { |
260 | return *this = rational( n, d ); |
261 | } |
262 | |
263 | // Unary plus and minus |
264 | template <typename IntType> |
265 | BOOST_CONSTEXPR |
266 | inline rational<IntType> operator+ (const rational<IntType>& r) |
267 | { |
268 | return r; |
269 | } |
270 | |
271 | template <typename IntType> |
272 | inline rational<IntType> operator- (const rational<IntType>& r) |
273 | { |
274 | return rational<IntType>(-r.numerator(), r.denominator()); |
275 | } |
276 | |
277 | // Arithmetic assignment operators |
278 | template <typename IntType> |
279 | rational<IntType>& rational<IntType>::operator+= (const rational<IntType>& r) |
280 | { |
281 | // This calculation avoids overflow, and minimises the number of expensive |
282 | // calculations. Thanks to Nickolay Mladenov for this algorithm. |
283 | // |
284 | // Proof: |
285 | // We have to compute a/b + c/d, where gcd(a,b)=1 and gcd(b,c)=1. |
286 | // Let g = gcd(b,d), and b = b1*g, d=d1*g. Then gcd(b1,d1)=1 |
287 | // |
288 | // The result is (a*d1 + c*b1) / (b1*d1*g). |
289 | // Now we have to normalize this ratio. |
290 | // Let's assume h | gcd((a*d1 + c*b1), (b1*d1*g)), and h > 1 |
291 | // If h | b1 then gcd(h,d1)=1 and hence h|(a*d1+c*b1) => h|a. |
292 | // But since gcd(a,b1)=1 we have h=1. |
293 | // Similarly h|d1 leads to h=1. |
294 | // So we have that h | gcd((a*d1 + c*b1) , (b1*d1*g)) => h|g |
295 | // Finally we have gcd((a*d1 + c*b1), (b1*d1*g)) = gcd((a*d1 + c*b1), g) |
296 | // Which proves that instead of normalizing the result, it is better to |
297 | // divide num and den by gcd((a*d1 + c*b1), g) |
298 | |
299 | // Protect against self-modification |
300 | IntType r_num = r.num; |
301 | IntType r_den = r.den; |
302 | |
303 | IntType g = integer::gcd(den, r_den); |
304 | den /= g; // = b1 from the calculations above |
305 | num = num * (r_den / g) + r_num * den; |
306 | g = integer::gcd(num, g); |
307 | num /= g; |
308 | den *= r_den/g; |
309 | |
310 | return *this; |
311 | } |
312 | |
313 | template <typename IntType> |
314 | rational<IntType>& rational<IntType>::operator-= (const rational<IntType>& r) |
315 | { |
316 | // Protect against self-modification |
317 | IntType r_num = r.num; |
318 | IntType r_den = r.den; |
319 | |
320 | // This calculation avoids overflow, and minimises the number of expensive |
321 | // calculations. It corresponds exactly to the += case above |
322 | IntType g = integer::gcd(den, r_den); |
323 | den /= g; |
324 | num = num * (r_den / g) - r_num * den; |
325 | g = integer::gcd(num, g); |
326 | num /= g; |
327 | den *= r_den/g; |
328 | |
329 | return *this; |
330 | } |
331 | |
332 | template <typename IntType> |
333 | rational<IntType>& rational<IntType>::operator*= (const rational<IntType>& r) |
334 | { |
335 | // Protect against self-modification |
336 | IntType r_num = r.num; |
337 | IntType r_den = r.den; |
338 | |
339 | // Avoid overflow and preserve normalization |
340 | IntType gcd1 = integer::gcd(num, r_den); |
341 | IntType gcd2 = integer::gcd(r_num, den); |
342 | num = (num/gcd1) * (r_num/gcd2); |
343 | den = (den/gcd2) * (r_den/gcd1); |
344 | return *this; |
345 | } |
346 | |
347 | template <typename IntType> |
348 | rational<IntType>& rational<IntType>::operator/= (const rational<IntType>& r) |
349 | { |
350 | // Protect against self-modification |
351 | IntType r_num = r.num; |
352 | IntType r_den = r.den; |
353 | |
354 | // Avoid repeated construction |
355 | IntType zero(0); |
356 | |
357 | // Trap division by zero |
358 | if (r_num == zero) |
359 | BOOST_THROW_EXCEPTION(bad_rational()); |
360 | if (num == zero) |
361 | return *this; |
362 | |
363 | // Avoid overflow and preserve normalization |
364 | IntType gcd1 = integer::gcd(num, r_num); |
365 | IntType gcd2 = integer::gcd(r_den, den); |
366 | num = (num/gcd1) * (r_den/gcd2); |
367 | den = (den/gcd2) * (r_num/gcd1); |
368 | |
369 | if (den < zero) { |
370 | num = -num; |
371 | den = -den; |
372 | } |
373 | return *this; |
374 | } |
375 | |
376 | // Mixed-mode operators |
377 | template <typename IntType> |
378 | inline rational<IntType>& |
379 | rational<IntType>::operator*= (param_type i) |
380 | { |
381 | // Avoid overflow and preserve normalization |
382 | IntType gcd = integer::gcd(i, den); |
383 | num *= i / gcd; |
384 | den /= gcd; |
385 | |
386 | return *this; |
387 | } |
388 | |
389 | template <typename IntType> |
390 | rational<IntType>& |
391 | rational<IntType>::operator/= (param_type i) |
392 | { |
393 | // Avoid repeated construction |
394 | IntType const zero(0); |
395 | |
396 | if(i == zero) BOOST_THROW_EXCEPTION(bad_rational()); |
397 | if (num == zero) return *this; |
398 | |
399 | // Avoid overflow and preserve normalization |
400 | IntType const gcd = integer::gcd(num, i); |
401 | num /= gcd; |
402 | den *= i / gcd; |
403 | |
404 | if (den < zero) { |
405 | num = -num; |
406 | den = -den; |
407 | } |
408 | |
409 | return *this; |
410 | } |
411 | |
412 | // Comparison operators |
413 | template <typename IntType> |
414 | bool rational<IntType>::operator< (const rational<IntType>& r) const |
415 | { |
416 | // Avoid repeated construction |
417 | int_type const zero( 0 ); |
418 | |
419 | // This should really be a class-wide invariant. The reason for these |
420 | // checks is that for 2's complement systems, INT_MIN has no corresponding |
421 | // positive, so negating it during normalization keeps it INT_MIN, which |
422 | // is bad for later calculations that assume a positive denominator. |
423 | BOOST_ASSERT( this->den > zero ); |
424 | BOOST_ASSERT( r.den > zero ); |
425 | |
426 | // Determine relative order by expanding each value to its simple continued |
427 | // fraction representation using the Euclidian GCD algorithm. |
428 | struct { int_type n, d, q, r; } |
429 | ts = { this->num, this->den, static_cast<int_type>(this->num / this->den), |
430 | static_cast<int_type>(this->num % this->den) }, |
431 | rs = { r.num, r.den, static_cast<int_type>(r.num / r.den), |
432 | static_cast<int_type>(r.num % r.den) }; |
433 | unsigned reverse = 0u; |
434 | |
435 | // Normalize negative moduli by repeatedly adding the (positive) denominator |
436 | // and decrementing the quotient. Later cycles should have all positive |
437 | // values, so this only has to be done for the first cycle. (The rules of |
438 | // C++ require a nonnegative quotient & remainder for a nonnegative dividend |
439 | // & positive divisor.) |
440 | while ( ts.r < zero ) { ts.r += ts.d; --ts.q; } |
441 | while ( rs.r < zero ) { rs.r += rs.d; --rs.q; } |
442 | |
443 | // Loop through and compare each variable's continued-fraction components |
444 | for ( ;; ) |
445 | { |
446 | // The quotients of the current cycle are the continued-fraction |
447 | // components. Comparing two c.f. is comparing their sequences, |
448 | // stopping at the first difference. |
449 | if ( ts.q != rs.q ) |
450 | { |
451 | // Since reciprocation changes the relative order of two variables, |
452 | // and c.f. use reciprocals, the less/greater-than test reverses |
453 | // after each index. (Start w/ non-reversed @ whole-number place.) |
454 | return reverse ? ts.q > rs.q : ts.q < rs.q; |
455 | } |
456 | |
457 | // Prepare the next cycle |
458 | reverse ^= 1u; |
459 | |
460 | if ( (ts.r == zero) || (rs.r == zero) ) |
461 | { |
462 | // At least one variable's c.f. expansion has ended |
463 | break; |
464 | } |
465 | |
466 | ts.n = ts.d; ts.d = ts.r; |
467 | ts.q = ts.n / ts.d; ts.r = ts.n % ts.d; |
468 | rs.n = rs.d; rs.d = rs.r; |
469 | rs.q = rs.n / rs.d; rs.r = rs.n % rs.d; |
470 | } |
471 | |
472 | // Compare infinity-valued components for otherwise equal sequences |
473 | if ( ts.r == rs.r ) |
474 | { |
475 | // Both remainders are zero, so the next (and subsequent) c.f. |
476 | // components for both sequences are infinity. Therefore, the sequences |
477 | // and their corresponding values are equal. |
478 | return false; |
479 | } |
480 | else |
481 | { |
482 | #ifdef BOOST_MSVC |
483 | #pragma warning(push) |
484 | #pragma warning(disable:4800) |
485 | #endif |
486 | // Exactly one of the remainders is zero, so all following c.f. |
487 | // components of that variable are infinity, while the other variable |
488 | // has a finite next c.f. component. So that other variable has the |
489 | // lesser value (modulo the reversal flag!). |
490 | return ( ts.r != zero ) != static_cast<bool>( reverse ); |
491 | #ifdef BOOST_MSVC |
492 | #pragma warning(pop) |
493 | #endif |
494 | } |
495 | } |
496 | |
497 | template <typename IntType> |
498 | bool rational<IntType>::operator< (param_type i) const |
499 | { |
500 | // Avoid repeated construction |
501 | int_type const zero( 0 ); |
502 | |
503 | // Break value into mixed-fraction form, w/ always-nonnegative remainder |
504 | BOOST_ASSERT( this->den > zero ); |
505 | int_type q = this->num / this->den, r = this->num % this->den; |
506 | while ( r < zero ) { r += this->den; --q; } |
507 | |
508 | // Compare with just the quotient, since the remainder always bumps the |
509 | // value up. [Since q = floor(n/d), and if n/d < i then q < i, if n/d == i |
510 | // then q == i, if n/d == i + r/d then q == i, and if n/d >= i + 1 then |
511 | // q >= i + 1 > i; therefore n/d < i iff q < i.] |
512 | return q < i; |
513 | } |
514 | |
515 | template <typename IntType> |
516 | bool rational<IntType>::operator> (param_type i) const |
517 | { |
518 | return operator==(i)? false: !operator<(i); |
519 | } |
520 | |
521 | template <typename IntType> |
522 | BOOST_CONSTEXPR |
523 | inline bool rational<IntType>::operator== (const rational<IntType>& r) const |
524 | { |
525 | return ((num == r.num) && (den == r.den)); |
526 | } |
527 | |
528 | template <typename IntType> |
529 | BOOST_CONSTEXPR |
530 | inline bool rational<IntType>::operator== (param_type i) const |
531 | { |
532 | return ((den == IntType(1)) && (num == i)); |
533 | } |
534 | |
535 | // Invariant check |
536 | template <typename IntType> |
537 | inline bool rational<IntType>::test_invariant() const |
538 | { |
539 | return ( this->den > int_type(0) ) && ( integer::gcd(this->num, this->den) == |
540 | int_type(1) ); |
541 | } |
542 | |
543 | // Normalisation |
544 | template <typename IntType> |
545 | void rational<IntType>::normalize() |
546 | { |
547 | // Avoid repeated construction |
548 | IntType zero(0); |
549 | |
550 | if (den == zero) |
551 | BOOST_THROW_EXCEPTION(bad_rational()); |
552 | |
553 | // Handle the case of zero separately, to avoid division by zero |
554 | if (num == zero) { |
555 | den = IntType(1); |
556 | return; |
557 | } |
558 | |
559 | IntType g = integer::gcd(num, den); |
560 | |
561 | num /= g; |
562 | den /= g; |
563 | |
564 | // Ensure that the denominator is positive |
565 | if (den < zero) { |
566 | num = -num; |
567 | den = -den; |
568 | } |
569 | |
570 | // ...But acknowledge that the previous step doesn't always work. |
571 | // (Nominally, this should be done before the mutating steps, but this |
572 | // member function is only called during the constructor, so we never have |
573 | // to worry about zombie objects.) |
574 | if (den < zero) |
575 | BOOST_THROW_EXCEPTION(bad_rational("bad rational: non-zero singular denominator" )); |
576 | |
577 | BOOST_ASSERT( this->test_invariant() ); |
578 | } |
579 | |
580 | #ifndef BOOST_NO_IOSTREAM |
581 | namespace detail { |
582 | |
583 | // A utility class to reset the format flags for an istream at end |
584 | // of scope, even in case of exceptions |
585 | struct resetter { |
586 | resetter(std::istream& is) : is_(is), f_(is.flags()) {} |
587 | ~resetter() { is_.flags(fmtfl: f_); } |
588 | std::istream& is_; |
589 | std::istream::fmtflags f_; // old GNU c++ lib has no ios_base |
590 | }; |
591 | |
592 | } |
593 | |
594 | // Input and output |
595 | template <typename IntType> |
596 | std::istream& operator>> (std::istream& is, rational<IntType>& r) |
597 | { |
598 | using std::ios; |
599 | |
600 | IntType n = IntType(0), d = IntType(1); |
601 | char c = 0; |
602 | detail::resetter sentry(is); |
603 | |
604 | if ( is >> n ) |
605 | { |
606 | if ( is.get(c&: c) ) |
607 | { |
608 | if ( c == '/' ) |
609 | { |
610 | if ( is >> std::noskipws >> d ) |
611 | try { |
612 | r.assign( n, d ); |
613 | } catch ( bad_rational & ) { // normalization fail |
614 | try { is.setstate(ios::failbit); } |
615 | catch ( ... ) {} // don't throw ios_base::failure... |
616 | if ( is.exceptions() & ios::failbit ) |
617 | throw; // ...but the original exception instead |
618 | // ELSE: suppress the exception, use just error flags |
619 | } |
620 | } |
621 | else |
622 | is.setstate( ios::failbit ); |
623 | } |
624 | } |
625 | |
626 | return is; |
627 | } |
628 | |
629 | // Add manipulators for output format? |
630 | template <typename IntType> |
631 | std::ostream& operator<< (std::ostream& os, const rational<IntType>& r) |
632 | { |
633 | using namespace std; |
634 | |
635 | // The slash directly precedes the denominator, which has no prefixes. |
636 | ostringstream ss; |
637 | |
638 | ss.copyfmt( rhs: os ); |
639 | ss.tie( NULL ); |
640 | ss.exceptions( except: ios::goodbit ); |
641 | ss.width( wide: 0 ); |
642 | ss << noshowpos << noshowbase << '/' << r.denominator(); |
643 | |
644 | // The numerator holds the showpos, internal, and showbase flags. |
645 | string const tail = ss.str(); |
646 | streamsize const w = os.width() - static_cast<streamsize>( tail.size() ); |
647 | |
648 | ss.clear(); |
649 | ss.str( s: "" ); |
650 | ss.flags( fmtfl: os.flags() ); |
651 | ss << setw( w < 0 || (os.flags() & ios::adjustfield) != ios::internal ? 0 : |
652 | w ) << r.numerator(); |
653 | return os << ss.str() + tail; |
654 | } |
655 | #endif // BOOST_NO_IOSTREAM |
656 | |
657 | // Type conversion |
658 | template <typename T, typename IntType> |
659 | BOOST_CONSTEXPR |
660 | inline T rational_cast(const rational<IntType>& src) |
661 | { |
662 | return static_cast<T>(src.numerator())/static_cast<T>(src.denominator()); |
663 | } |
664 | |
665 | // Do not use any abs() defined on IntType - it isn't worth it, given the |
666 | // difficulties involved (Koenig lookup required, there may not *be* an abs() |
667 | // defined, etc etc). |
668 | template <typename IntType> |
669 | inline rational<IntType> abs(const rational<IntType>& r) |
670 | { |
671 | return r.numerator() >= IntType(0)? r: -r; |
672 | } |
673 | |
674 | namespace integer { |
675 | |
676 | template <typename IntType> |
677 | struct gcd_evaluator< rational<IntType> > |
678 | { |
679 | typedef rational<IntType> result_type, |
680 | first_argument_type, second_argument_type; |
681 | result_type operator() ( first_argument_type const &a |
682 | , second_argument_type const &b |
683 | ) const |
684 | { |
685 | return result_type(integer::gcd(a.numerator(), b.numerator()), |
686 | integer::lcm(a.denominator(), b.denominator())); |
687 | } |
688 | }; |
689 | |
690 | template <typename IntType> |
691 | struct lcm_evaluator< rational<IntType> > |
692 | { |
693 | typedef rational<IntType> result_type, |
694 | first_argument_type, second_argument_type; |
695 | result_type operator() ( first_argument_type const &a |
696 | , second_argument_type const &b |
697 | ) const |
698 | { |
699 | return result_type(integer::lcm(a.numerator(), b.numerator()), |
700 | integer::gcd(a.denominator(), b.denominator())); |
701 | } |
702 | }; |
703 | |
704 | } // namespace integer |
705 | |
706 | } // namespace boost |
707 | |
708 | #endif // BOOST_RATIONAL_HPP |
709 | |
710 | |