ocrm.bsky.social
the game where you go into mines and start crafting! but for consoles (forked directly from smartcmd's github)
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// 05 Nov 06 Change rational_cast to not depend on division between different
25// types (Daryle Walker)
26// 04 Nov 06 Off-load GCD and LCM to Boost.Math; add some invariant checks;
27// add std::numeric_limits<> requirement to help GCD (Daryle Walker)
28// 31 Oct 06 Recoded both operator< to use round-to-negative-infinity
29// divisions; the rational-value version now uses continued fraction
30// expansion to avoid overflows, for bug #798357 (Daryle Walker)
31// 20 Oct 06 Fix operator bool_type for CW 8.3 (Joaqu�n M L�pez Mu�oz)
32// 18 Oct 06 Use EXPLICIT_TEMPLATE_TYPE helper macros from Boost.Config
33// (Joaqu�n M L�pez Mu�oz)
34// 27 Dec 05 Add Boolean conversion operator (Daryle Walker)
35// 28 Sep 02 Use _left versions of operators from operators.hpp
36// 05 Jul 01 Recode gcd(), avoiding std::swap (Helmut Zeisel)
37// 03 Mar 01 Workarounds for Intel C++ 5.0 (David Abrahams)
38// 05 Feb 01 Update operator>> to tighten up input syntax
39// 05 Feb 01 Final tidy up of gcd code prior to the new release
40// 27 Jan 01 Recode abs() without relying on abs(IntType)
41// 21 Jan 01 Include Nickolay Mladenov's operator+= algorithm,
42// tidy up a number of areas, use newer features of operators.hpp
43// (reduces space overhead to zero), add operator!,
44// introduce explicit mixed-mode arithmetic operations
45// 12 Jan 01 Include fixes to handle a user-defined IntType better
46// 19 Nov 00 Throw on divide by zero in operator /= (John (EBo) David)
47// 23 Jun 00 Incorporate changes from Mark Rodgers for Borland C++
48// 22 Jun 00 Change _MSC_VER to BOOST_MSVC so other compilers are not
49// affected (Beman Dawes)
50// 6 Mar 00 Fix operator-= normalization, #include <string> (Jens Maurer)
51// 14 Dec 99 Modifications based on comments from the boost list
52// 09 Dec 99 Initial Version (Paul Moore)
53
54#ifndef BOOST_RATIONAL_HPP
55#define BOOST_RATIONAL_HPP
56
57#include <iostream> // for std::istream and std::ostream
58#include <ios> // for std::noskipws
59#include <stdexcept> // for std::domain_error
60#include <string> // for std::string implicit constructor
61#include <boost/operators.hpp> // for boost::addable etc
62#include <cstdlib> // for std::abs
63#include <boost/call_traits.hpp> // for boost::call_traits
64#include <boost/config.hpp> // for BOOST_NO_STDC_NAMESPACE, BOOST_MSVC
65#include <boost/detail/workaround.hpp> // for BOOST_WORKAROUND
66#include <boost/assert.hpp> // for BOOST_ASSERT
67#include <boost/math/common_factor_rt.hpp> // for boost::math::gcd, lcm
68#include <limits> // for std::numeric_limits
69#include <boost/static_assert.hpp> // for BOOST_STATIC_ASSERT
70
71// Control whether depreciated GCD and LCM functions are included (default: yes)
72#ifndef BOOST_CONTROL_RATIONAL_HAS_GCD
73#define BOOST_CONTROL_RATIONAL_HAS_GCD 1
74#endif
75
76namespace boost {
77
78#if BOOST_CONTROL_RATIONAL_HAS_GCD
79template <typename IntType>
80IntType gcd(IntType n, IntType m)
81{
82 // Defer to the version in Boost.Math
83 return math::gcd( n, m );
84}
85
86template <typename IntType>
87IntType lcm(IntType n, IntType m)
88{
89 // Defer to the version in Boost.Math
90 return math::lcm( n, m );
91}
92#endif // BOOST_CONTROL_RATIONAL_HAS_GCD
93
94class bad_rational : public std::domain_error
95{
96public:
97 explicit bad_rational() : std::domain_error("bad rational: zero denominator") {}
98};
99
100template <typename IntType>
101class rational;
102
103template <typename IntType>
104rational<IntType> abs(const rational<IntType>& r);
105
106template <typename IntType>
107class rational :
108 less_than_comparable < rational<IntType>,
109 equality_comparable < rational<IntType>,
110 less_than_comparable2 < rational<IntType>, IntType,
111 equality_comparable2 < rational<IntType>, IntType,
112 addable < rational<IntType>,
113 subtractable < rational<IntType>,
114 multipliable < rational<IntType>,
115 dividable < rational<IntType>,
116 addable2 < rational<IntType>, IntType,
117 subtractable2 < rational<IntType>, IntType,
118 subtractable2_left < rational<IntType>, IntType,
119 multipliable2 < rational<IntType>, IntType,
120 dividable2 < rational<IntType>, IntType,
121 dividable2_left < rational<IntType>, IntType,
122 incrementable < rational<IntType>,
123 decrementable < rational<IntType>
124 > > > > > > > > > > > > > > > >
125{
126 // Class-wide pre-conditions
127 BOOST_STATIC_ASSERT( ::std::numeric_limits<IntType>::is_specialized );
128
129 // Helper types
130 typedef typename boost::call_traits<IntType>::param_type param_type;
131
132 struct helper { IntType parts[2]; };
133 typedef IntType (helper::* bool_type)[2];
134
135public:
136 typedef IntType int_type;
137 rational() : num(0), den(1) {}
138 rational(param_type n) : num(n), den(1) {}
139 rational(param_type n, param_type d) : num(n), den(d) { normalize(); }
140
141 // Default copy constructor and assignment are fine
142
143 // Add assignment from IntType
144 rational& operator=(param_type n) { return assign(n, 1); }
145
146 // Assign in place
147 rational& assign(param_type n, param_type d);
148
149 // Access to representation
150 IntType numerator() const { return num; }
151 IntType denominator() const { return den; }
152
153 // Arithmetic assignment operators
154 rational& operator+= (const rational& r);
155 rational& operator-= (const rational& r);
156 rational& operator*= (const rational& r);
157 rational& operator/= (const rational& r);
158
159 rational& operator+= (param_type i);
160 rational& operator-= (param_type i);
161 rational& operator*= (param_type i);
162 rational& operator/= (param_type i);
163
164 // Increment and decrement
165 const rational& operator++();
166 const rational& operator--();
167
168 // Operator not
169 bool operator!() const { return !num; }
170
171 // Boolean conversion
172
173#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
174 // The "ISO C++ Template Parser" option in CW 8.3 chokes on the
175 // following, hence we selectively disable that option for the
176 // offending memfun.
177#pragma parse_mfunc_templ off
178#endif
179
180 operator bool_type() const { return operator !() ? 0 : &helper::parts; }
181
182#if BOOST_WORKAROUND(__MWERKS__,<=0x3003)
183#pragma parse_mfunc_templ reset
184#endif
185
186 // Comparison operators
187 bool operator< (const rational& r) const;
188 bool operator== (const rational& r) const;
189
190 bool operator< (param_type i) const;
191 bool operator> (param_type i) const;
192 bool operator== (param_type i) const;
193
194private:
195 // Implementation - numerator and denominator (normalized).
196 // Other possibilities - separate whole-part, or sign, fields?
197 IntType num;
198 IntType den;
199
200 // Representation note: Fractions are kept in normalized form at all
201 // times. normalized form is defined as gcd(num,den) == 1 and den > 0.
202 // In particular, note that the implementation of abs() below relies
203 // on den always being positive.
204 bool test_invariant() const;
205 void normalize();
206};
207
208// Assign in place
209template <typename IntType>
210inline rational<IntType>& rational<IntType>::assign(param_type n, param_type d)
211{
212 num = n;
213 den = d;
214 normalize();
215 return *this;
216}
217
218// Unary plus and minus
219template <typename IntType>
220inline rational<IntType> operator+ (const rational<IntType>& r)
221{
222 return r;
223}
224
225template <typename IntType>
226inline rational<IntType> operator- (const rational<IntType>& r)
227{
228 return rational<IntType>(-r.numerator(), r.denominator());
229}
230
231// Arithmetic assignment operators
232template <typename IntType>
233rational<IntType>& rational<IntType>::operator+= (const rational<IntType>& r)
234{
235 // This calculation avoids overflow, and minimises the number of expensive
236 // calculations. Thanks to Nickolay Mladenov for this algorithm.
237 //
238 // Proof:
239 // We have to compute a/b + c/d, where gcd(a,b)=1 and gcd(b,c)=1.
240 // Let g = gcd(b,d), and b = b1*g, d=d1*g. Then gcd(b1,d1)=1
241 //
242 // The result is (a*d1 + c*b1) / (b1*d1*g).
243 // Now we have to normalize this ratio.
244 // Let's assume h | gcd((a*d1 + c*b1), (b1*d1*g)), and h > 1
245 // If h | b1 then gcd(h,d1)=1 and hence h|(a*d1+c*b1) => h|a.
246 // But since gcd(a,b1)=1 we have h=1.
247 // Similarly h|d1 leads to h=1.
248 // So we have that h | gcd((a*d1 + c*b1) , (b1*d1*g)) => h|g
249 // Finally we have gcd((a*d1 + c*b1), (b1*d1*g)) = gcd((a*d1 + c*b1), g)
250 // Which proves that instead of normalizing the result, it is better to
251 // divide num and den by gcd((a*d1 + c*b1), g)
252
253 // Protect against self-modification
254 IntType r_num = r.num;
255 IntType r_den = r.den;
256
257 IntType g = math::gcd(den, r_den);
258 den /= g; // = b1 from the calculations above
259 num = num * (r_den / g) + r_num * den;
260 g = math::gcd(num, g);
261 num /= g;
262 den *= r_den/g;
263
264 return *this;
265}
266
267template <typename IntType>
268rational<IntType>& rational<IntType>::operator-= (const rational<IntType>& r)
269{
270 // Protect against self-modification
271 IntType r_num = r.num;
272 IntType r_den = r.den;
273
274 // This calculation avoids overflow, and minimises the number of expensive
275 // calculations. It corresponds exactly to the += case above
276 IntType g = math::gcd(den, r_den);
277 den /= g;
278 num = num * (r_den / g) - r_num * den;
279 g = math::gcd(num, g);
280 num /= g;
281 den *= r_den/g;
282
283 return *this;
284}
285
286template <typename IntType>
287rational<IntType>& rational<IntType>::operator*= (const rational<IntType>& r)
288{
289 // Protect against self-modification
290 IntType r_num = r.num;
291 IntType r_den = r.den;
292
293 // Avoid overflow and preserve normalization
294 IntType gcd1 = math::gcd(num, r_den);
295 IntType gcd2 = math::gcd(r_num, den);
296 num = (num/gcd1) * (r_num/gcd2);
297 den = (den/gcd2) * (r_den/gcd1);
298 return *this;
299}
300
301template <typename IntType>
302rational<IntType>& rational<IntType>::operator/= (const rational<IntType>& r)
303{
304 // Protect against self-modification
305 IntType r_num = r.num;
306 IntType r_den = r.den;
307
308 // Avoid repeated construction
309 IntType zero(0);
310
311 // Trap division by zero
312 if (r_num == zero)
313 throw bad_rational();
314 if (num == zero)
315 return *this;
316
317 // Avoid overflow and preserve normalization
318 IntType gcd1 = math::gcd(num, r_num);
319 IntType gcd2 = math::gcd(r_den, den);
320 num = (num/gcd1) * (r_den/gcd2);
321 den = (den/gcd2) * (r_num/gcd1);
322
323 if (den < zero) {
324 num = -num;
325 den = -den;
326 }
327 return *this;
328}
329
330// Mixed-mode operators
331template <typename IntType>
332inline rational<IntType>&
333rational<IntType>::operator+= (param_type i)
334{
335 return operator+= (rational<IntType>(i));
336}
337
338template <typename IntType>
339inline rational<IntType>&
340rational<IntType>::operator-= (param_type i)
341{
342 return operator-= (rational<IntType>(i));
343}
344
345template <typename IntType>
346inline rational<IntType>&
347rational<IntType>::operator*= (param_type i)
348{
349 return operator*= (rational<IntType>(i));
350}
351
352template <typename IntType>
353inline rational<IntType>&
354rational<IntType>::operator/= (param_type i)
355{
356 return operator/= (rational<IntType>(i));
357}
358
359// Increment and decrement
360template <typename IntType>
361inline const rational<IntType>& rational<IntType>::operator++()
362{
363 // This can never denormalise the fraction
364 num += den;
365 return *this;
366}
367
368template <typename IntType>
369inline const rational<IntType>& rational<IntType>::operator--()
370{
371 // This can never denormalise the fraction
372 num -= den;
373 return *this;
374}
375
376// Comparison operators
377template <typename IntType>
378bool rational<IntType>::operator< (const rational<IntType>& r) const
379{
380 // Avoid repeated construction
381 int_type const zero( 0 );
382
383 // This should really be a class-wide invariant. The reason for these
384 // checks is that for 2's complement systems, INT_MIN has no corresponding
385 // positive, so negating it during normalization keeps it INT_MIN, which
386 // is bad for later calculations that assume a positive denominator.
387 BOOST_ASSERT( this->den > zero );
388 BOOST_ASSERT( r.den > zero );
389
390 // Determine relative order by expanding each value to its simple continued
391 // fraction representation using the Euclidian GCD algorithm.
392 struct { int_type n, d, q, r; } ts = { this->num, this->den, this->num /
393 this->den, this->num % this->den }, rs = { r.num, r.den, r.num / r.den,
394 r.num % r.den };
395 unsigned reverse = 0u;
396
397 // Normalize negative moduli by repeatedly adding the (positive) denominator
398 // and decrementing the quotient. Later cycles should have all positive
399 // values, so this only has to be done for the first cycle. (The rules of
400 // C++ require a nonnegative quotient & remainder for a nonnegative dividend
401 // & positive divisor.)
402 while ( ts.r < zero ) { ts.r += ts.d; --ts.q; }
403 while ( rs.r < zero ) { rs.r += rs.d; --rs.q; }
404
405 // Loop through and compare each variable's continued-fraction components
406 while ( true )
407 {
408 // The quotients of the current cycle are the continued-fraction
409 // components. Comparing two c.f. is comparing their sequences,
410 // stopping at the first difference.
411 if ( ts.q != rs.q )
412 {
413 // Since reciprocation changes the relative order of two variables,
414 // and c.f. use reciprocals, the less/greater-than test reverses
415 // after each index. (Start w/ non-reversed @ whole-number place.)
416 return reverse ? ts.q > rs.q : ts.q < rs.q;
417 }
418
419 // Prepare the next cycle
420 reverse ^= 1u;
421
422 if ( (ts.r == zero) || (rs.r == zero) )
423 {
424 // At least one variable's c.f. expansion has ended
425 break;
426 }
427
428 ts.n = ts.d; ts.d = ts.r;
429 ts.q = ts.n / ts.d; ts.r = ts.n % ts.d;
430 rs.n = rs.d; rs.d = rs.r;
431 rs.q = rs.n / rs.d; rs.r = rs.n % rs.d;
432 }
433
434 // Compare infinity-valued components for otherwise equal sequences
435 if ( ts.r == rs.r )
436 {
437 // Both remainders are zero, so the next (and subsequent) c.f.
438 // components for both sequences are infinity. Therefore, the sequences
439 // and their corresponding values are equal.
440 return false;
441 }
442 else
443 {
444#ifdef BOOST_MSVC
445#pragma warning(push)
446#pragma warning(disable:4800)
447#endif
448 // Exactly one of the remainders is zero, so all following c.f.
449 // components of that variable are infinity, while the other variable
450 // has a finite next c.f. component. So that other variable has the
451 // lesser value (modulo the reversal flag!).
452 return ( ts.r != zero ) != static_cast<bool>( reverse );
453#ifdef BOOST_MSVC
454#pragma warning(pop)
455#endif
456 }
457}
458
459template <typename IntType>
460bool rational<IntType>::operator< (param_type i) const
461{
462 // Avoid repeated construction
463 int_type const zero( 0 );
464
465 // Break value into mixed-fraction form, w/ always-nonnegative remainder
466 BOOST_ASSERT( this->den > zero );
467 int_type q = this->num / this->den, r = this->num % this->den;
468 while ( r < zero ) { r += this->den; --q; }
469
470 // Compare with just the quotient, since the remainder always bumps the
471 // value up. [Since q = floor(n/d), and if n/d < i then q < i, if n/d == i
472 // then q == i, if n/d == i + r/d then q == i, and if n/d >= i + 1 then
473 // q >= i + 1 > i; therefore n/d < i iff q < i.]
474 return q < i;
475}
476
477template <typename IntType>
478bool rational<IntType>::operator> (param_type i) const
479{
480 // Trap equality first
481 if (num == i && den == IntType(1))
482 return false;
483
484 // Otherwise, we can use operator<
485 return !operator<(i);
486}
487
488template <typename IntType>
489inline bool rational<IntType>::operator== (const rational<IntType>& r) const
490{
491 return ((num == r.num) && (den == r.den));
492}
493
494template <typename IntType>
495inline bool rational<IntType>::operator== (param_type i) const
496{
497 return ((den == IntType(1)) && (num == i));
498}
499
500// Invariant check
501template <typename IntType>
502inline bool rational<IntType>::test_invariant() const
503{
504 return ( this->den > int_type(0) ) && ( math::gcd(this->num, this->den) ==
505 int_type(1) );
506}
507
508// Normalisation
509template <typename IntType>
510void rational<IntType>::normalize()
511{
512 // Avoid repeated construction
513 IntType zero(0);
514
515 if (den == zero)
516 throw bad_rational();
517
518 // Handle the case of zero separately, to avoid division by zero
519 if (num == zero) {
520 den = IntType(1);
521 return;
522 }
523
524 IntType g = math::gcd(num, den);
525
526 num /= g;
527 den /= g;
528
529 // Ensure that the denominator is positive
530 if (den < zero) {
531 num = -num;
532 den = -den;
533 }
534
535 BOOST_ASSERT( this->test_invariant() );
536}
537
538namespace detail {
539
540 // A utility class to reset the format flags for an istream at end
541 // of scope, even in case of exceptions
542 struct resetter {
543 resetter(std::istream& is) : is_(is), f_(is.flags()) {}
544 ~resetter() { is_.flags(f_); }
545 std::istream& is_;
546 std::istream::fmtflags f_; // old GNU c++ lib has no ios_base
547 };
548
549}
550
551// Input and output
552template <typename IntType>
553std::istream& operator>> (std::istream& is, rational<IntType>& r)
554{
555 IntType n = IntType(0), d = IntType(1);
556 char c = 0;
557 detail::resetter sentry(is);
558
559 is >> n;
560 c = is.get();
561
562 if (c != '/')
563 is.clear(std::istream::badbit); // old GNU c++ lib has no ios_base
564
565#if !defined(__GNUC__) || (defined(__GNUC__) && (__GNUC__ >= 3)) || defined __SGI_STL_PORT
566 is >> std::noskipws;
567#else
568 is.unsetf(ios::skipws); // compiles, but seems to have no effect.
569#endif
570 is >> d;
571
572 if (is)
573 r.assign(n, d);
574
575 return is;
576}
577
578// Add manipulators for output format?
579template <typename IntType>
580std::ostream& operator<< (std::ostream& os, const rational<IntType>& r)
581{
582 os << r.numerator() << '/' << r.denominator();
583 return os;
584}
585
586// Type conversion
587template <typename T, typename IntType>
588inline T rational_cast(
589 const rational<IntType>& src BOOST_APPEND_EXPLICIT_TEMPLATE_TYPE(T))
590{
591 return static_cast<T>(src.numerator())/static_cast<T>(src.denominator());
592}
593
594// Do not use any abs() defined on IntType - it isn't worth it, given the
595// difficulties involved (Koenig lookup required, there may not *be* an abs()
596// defined, etc etc).
597template <typename IntType>
598inline rational<IntType> abs(const rational<IntType>& r)
599{
600 if (r.numerator() >= IntType(0))
601 return r;
602
603 return rational<IntType>(-r.numerator(), r.denominator());
604}
605
606} // namespace boost
607
608#endif // BOOST_RATIONAL_HPP
609