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Rational.h
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Rational.h
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/* Copyright (c) 1997-2007
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.math.tu-berlin.de/polymake, mailto:polymake@math.tu-berlin.de
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
*/
#ifndef _POLYMAKE_GMP_RATIONAL_H
#define _POLYMAKE_GMP_RATIONAL_H "$Project: polymake $$Id: Rational.h 7565 2007-01-16 16:29:43Z gawrilow $"
#include <Integer.h>
#include <string.h>
#if __GNU_MP_VERSION < 4
#define _tmp_little_Integer(x) \
mpz_t x; \
mp_limb_t x##_limb; \
x[0]._mp_alloc=1; \
x[0]._mp_d=&x##_limb
#endif
class temp_Rational : public MP_RAT {
protected:
/// never instantiate this class: it is a pure masquerade
temp_Rational();
~temp_Rational();
};
Rational inv(const Rational& a);
/** Arbitrary precision rational number.
It is a wrapper around GMP (GNU Multiple Precision Library) type \\mpq_t\\.
Developed and tested with GMP Version 3.1 and higher.
See the GMP Home Pages at `http://www.swox.com/gmp/'.
@index main
*/
class Rational {
private:
/// GMP's representation
mpq_t rep;
static void zero_division() __attribute__((noreturn));
void canonicalize()
{
if (!mpz_sgn(mpq_denref(rep))) zero_division();
mpq_canonicalize(rep);
}
public:
#if defined(__GMP_PLUSPLUS__)
//constructs from gmp's mpz_class as numerator and denominator
Rational(const mpz_class& num, const mpz_class& den)
{
mpz_init_set(mpq_numref(rep), num.get_mpz_t());
mpz_init_set(mpq_denref(rep), den.get_mpz_t());
canonicalize();
}
#endif
/// Initializes to 0.
Rational() { mpq_init(rep); }
Rational(const Rational& a)
{
mpz_init_set(mpq_numref(rep), mpq_numref(a.rep));
mpz_init_set(mpq_denref(rep), mpq_denref(a.rep));
}
Rational(const Integer& num)
{
mpz_init_set(mpq_numref(rep), num.rep);
mpz_init_set_ui(mpq_denref(rep), 1);
}
Rational(long num)
{
mpz_init_set_si(mpq_numref(rep), num);
mpz_init_set_ui(mpq_denref(rep), 1);
}
Rational(int num)
{
mpz_init_set_si(mpq_numref(rep), num);
mpz_init_set_ui(mpq_denref(rep), 1);
}
Rational(const Integer& num, const Integer& den)
{
mpz_init_set(mpq_numref(rep), num.rep);
mpz_init_set(mpq_denref(rep), den.rep);
canonicalize();
}
Rational(long num, long den)
{
mpz_init_set_si(mpq_numref(rep), num);
mpz_init_set_si(mpq_denref(rep), den);
canonicalize();
}
Rational(const Integer& num, long den)
{
mpz_init_set(mpq_numref(rep), num.rep);
mpz_init_set_si(mpq_denref(rep), den);
canonicalize();
}
Rational(long num, const Integer& den)
{
mpz_init_set_si(mpq_numref(rep), num);
mpz_init_set(mpq_denref(rep), den.rep);
canonicalize();
}
Rational(const double& b)
{
mpq_init(rep);
mpq_set_d(rep,b);
}
explicit Rational(const char* s)
{
mpq_init(rep);
try {
set(s);
}
catch (const gmp_error&) {
mpq_clear(rep);
throw;
}
}
explicit Rational(mpq_srcptr src)
{
mpz_init_set(mpq_numref(rep), mpq_numref(src));
mpz_init_set(mpq_denref(rep), mpq_denref(src));
canonicalize();
}
explicit Rational(mpz_srcptr num_src)
{
mpz_init_set(mpq_numref(rep), num_src);
mpz_init_set_ui(mpq_denref(rep), 1);
}
Rational(mpz_srcptr num_src, mpz_srcptr den_src)
{
mpz_init_set(mpq_numref(rep), num_src);
mpz_init_set(mpq_denref(rep), den_src);
canonicalize();
}
explicit Rational(temp_Rational& tmp)
{
rep[0]=tmp;
canonicalize();
}
explicit Rational(temp_Integer& tmp_num)
{
*mpq_numref(rep)=tmp_num;
mpz_init_set_ui(mpq_denref(rep), 1);
}
Rational(temp_Integer& tmp_num, temp_Integer& tmp_den)
{
*mpq_numref(rep)=tmp_num;
*mpq_denref(rep)=tmp_den;
canonicalize();
}
Rational(void (*f)(mpq_ptr,mpq_srcptr), mpq_srcptr a)
{
mpq_init(rep);
f(rep,a);
}
template <class Arg>
Rational(void (*f)(mpq_ptr,mpq_srcptr,Arg), mpq_srcptr a, Arg b)
{
mpq_init(rep);
f(rep,a,b);
}
template <class Arg>
Rational(void (*numf)(mpz_ptr,Arg), Arg a, mpz_srcptr den)
{
mpz_init(mpq_numref(rep));
numf(mpq_numref(rep),a);
mpz_init_set(mpq_denref(rep),den);
}
template <class Arg>
Rational(mpz_srcptr num, void (*denf)(mpz_ptr,Arg), Arg a)
{
mpz_init_set(mpq_numref(rep),num);
mpz_init(mpq_denref(rep));
denf(mpq_denref(rep),a);
}
template <class Arg1, class Arg2>
Rational(void (*numf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b, mpz_srcptr den)
{
mpz_init(mpq_numref(rep));
numf(mpq_numref(rep),a,b);
mpz_init_set(mpq_denref(rep),den);
}
template <class Arg1, class Arg2>
Rational(mpz_srcptr num, void (*denf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b)
{
mpz_init_set(mpq_numref(rep),num);
mpz_init(mpq_denref(rep));
denf(mpq_denref(rep),a,b);
}
template <class Arg1, class Arg2>
Rational(void (*numf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b, unsigned long den)
{
mpz_init(mpq_numref(rep));
numf(mpq_numref(rep),a,b);
mpz_init_set_ui(mpq_denref(rep),den);
}
template <class Arg1, class Arg2>
Rational(unsigned long num, void (*denf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b)
{
mpz_init_set_ui(mpq_numref(rep),num);
mpz_init(mpq_denref(rep));
denf(mpq_denref(rep),a,b);
}
template <class Arg1, class Arg2>
Rational(void (*numf)(mpz_ptr,Arg1,Arg2), mpz_srcptr num, Arg1 a, Arg2 b, mpz_srcptr den)
{
mpz_init_set(mpq_numref(rep),num);
numf(mpq_numref(rep),a,b);
mpz_init_set(mpq_denref(rep),den);
}
template <class Arg1, class Arg2>
Rational(mpz_srcptr num, void (*denf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b, mpz_srcptr den)
{
mpz_init_set(mpq_numref(rep),num);
mpz_init_set(mpq_denref(rep),den);
denf(mpq_denref(rep),a,b);
}
template <class Arg1, class Arg2, class Arg3, class Arg4>
Rational(void (*numf)(mpz_ptr,Arg1,Arg2), Arg1 a, Arg2 b,
void (*denf)(mpz_ptr,Arg3,Arg4), Arg3 c, Arg4 d)
{
mpq_init(rep);
numf(mpq_numref(rep),a,b);
denf(mpq_denref(rep),c,d);
}
friend Integer::Integer(const Rational& r);
friend Integer& Integer::operator= (const Rational& r);
~Rational() { mpq_clear(rep); }
protected:
enum proxy_kind { num, den };
template <proxy_kind kind, bool _canonicalize=true>
class proxy : public Integer {
private:
void canonicalize() {
if (!_canonicalize) return;
// The constant 8 is arbitrarily chosen.
// Every non-zero double word aligned address would do as well.
enum { fict_addr=8 };
reinterpret_cast<Rational*>
(// address of the num/den field
reinterpret_cast<char*>(this)
- (// offset from the begin of a mpq_t to appropriate mpz_t
reinterpret_cast<char*>(kind==num ? mpq_numref(reinterpret_cast<Rational*>(fict_addr)->rep)
: mpq_denref(reinterpret_cast<Rational*>(fict_addr)->rep))
-reinterpret_cast<char*>(fict_addr)))
->canonicalize();
}
/// both undefined
proxy(const proxy&);
proxy();
friend class Rational;
public:
template <class T>
proxy& operator= (const T& b)
{
Integer::operator=(b);
canonicalize();
return *this;
}
proxy& operator++()
{
Integer::operator++();
canonicalize();
return *this;
}
proxy& operator--()
{
Integer::operator--();
canonicalize();
return *this;
}
template <class T>
proxy& operator+= (const T& b)
{
Integer::operator+=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator-= (const T& b)
{
Integer::operator-=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator*= (const T& b)
{
Integer::operator*=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator/= (const T& b)
{
Integer::operator/=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator%= (const T& b)
{
Integer::operator%=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator<<= (const T& b)
{
Integer::operator<<=(b);
canonicalize();
return *this;
}
template <class T>
proxy& operator>>= (const T& b)
{
Integer::operator>>=(b);
canonicalize();
return *this;
}
};
public:
friend const proxy<num>& numerator(const Rational& a)
{
return *reinterpret_cast<const proxy<num>*>(mpq_numref(a.rep));
}
friend proxy<num>& numerator(Rational& a)
{
return *reinterpret_cast<proxy<num>*>(mpq_numref(a.rep));
}
friend const proxy<den>& denominator(const Rational& a)
{
return *reinterpret_cast<const proxy<den>*>(mpq_denref(a.rep));
}
friend proxy<den>& denominator(Rational& a)
{
return *reinterpret_cast<proxy<den>*>(mpq_denref(a.rep));
}
friend proxy<num,false>& numerator_nocanon(Rational& a)
{
return *reinterpret_cast<proxy<num,false>*>(mpq_numref(a.rep));
}
void set(const Integer& num, const Integer& den)
{
set(num.rep, den.rep);
}
void set(long num, long den)
{
mpz_set_si(mpq_numref(rep),num);
mpz_set_si(mpq_denref(rep),den);
canonicalize();
}
/** Conversion from a printable representation.
Numerator and denominator are expected delimited by `/'.
Omitted denominator assumed equal to 1.
*/
Rational& set(const char *s);
Rational& operator= (const Rational& b)
{
mpq_set(rep, b.rep);
return *this;
}
/// for the seldom case of unwrapped GMP objects coexisting with us
Rational& set(mpz_srcptr num_src, mpz_srcptr den_src)
{
mpq_set_num(rep, num_src);
mpq_set_den(rep, den_src);
canonicalize();
return *this;
}
Rational& set(mpq_srcptr src)
{
mpq_set(rep, src);
return *this;
}
Rational& operator= (const Integer& b)
{
mpq_set_z(rep, b.rep);
return *this;
}
Rational& operator= (long b)
{
mpq_set_si(rep, b, 1);
return *this;
}
Rational& operator= (int b) { return operator=(long(b)); }
Rational& operator= (const double& b)
{
mpq_set_d(rep, b);
return *this;
}
operator double() const
{
return mpq_get_d(rep);
}
operator long() const
{
return static_cast<Integer>(*this);
}
operator int() const
{
return static_cast<Integer>(*this);
}
/// Convert rational to string.
std::string to_string(int base=10) const;
/// Swaps the values.
void swap(Rational& b) { mpq_swap(rep, b.rep); }
/** Accelerated combination of copy constructor and destructor.
Aimed to be used in container classes only! */
friend void relocate(Rational* from, Rational* to)
{
to->rep[0] = from->rep[0];
}
/// Comparison with 0.
bool operator!() const { return !mpq_sgn(rep); }
/// Comparison with 0.
operator bool() const { return mpq_sgn(rep); }
Rational& operator++ ()
{
mpz_add(mpq_numref(rep), mpq_numref(rep), mpq_denref(rep));
return *this;
}
Rational& operator-- ()
{
mpz_sub(mpq_numref(rep), mpq_numref(rep), mpq_denref(rep));
return *this;
}
/// In-place negation.
Rational& negate()
{
mpq_neg(rep, rep);
return *this;
}
Rational& operator+= (const Rational& b)
{
mpq_add(rep, rep, b.rep);
return *this;
}
Rational& operator+= (const Integer& b)
{
#if __GNU_MP_VERSION >= 4
mpz_addmul(mpq_numref(rep), mpq_denref(rep), b.rep);
#else
Integer t=denominator(*this)*b;
mpz_add(mpq_numref(rep), mpq_numref(rep), t.rep);
#endif
return *this;
}
Rational& operator+= (long b)
{
#if __GNU_MP_VERSION >= 4
if (b>=0) mpz_addmul_ui(mpq_numref(rep), mpq_denref(rep), b);
else mpz_submul_ui(mpq_numref(rep), mpq_denref(rep), -b);
#else
if (b) {
mpz_t minus_den;
mpz_srcptr den= b>0 ? mpq_denref(rep)
: (b=-b, Integer::_tmp_negate(minus_den,mpq_denref(rep)));
mpz_addmul_ui(mpq_numref(rep), den, b);
}
#endif
return *this;
}
Rational& operator-= (const Rational& b)
{
mpq_sub(rep, rep, b.rep);
return *this;
}
Rational& operator-= (const Integer& b)
{
#if __GNU_MP_VERSION >= 4
mpz_submul(mpq_numref(rep), mpq_denref(rep), b.rep);
#else
Integer t=denominator(*this)*b;
mpz_sub(mpq_numref(rep), mpq_numref(rep), t.rep);
#endif
return *this;
}
Rational& operator-= (long b)
{
#if __GNU_MP_VERSION >= 4
if (b>=0) mpz_submul_ui(mpq_numref(rep), mpq_denref(rep), b);
else mpz_addmul_ui(mpq_numref(rep), mpq_denref(rep), -b);
#else
if (b) {
mpz_t minus_den;
mpz_srcptr den= b>0 ? Integer::_tmp_negate(minus_den,mpq_denref(rep))
: (b=-b, mpq_denref(rep));
mpz_addmul_ui(mpq_numref(rep), den, b);
}
#endif
return *this;
}
Rational& operator*= (const Rational& b)
{
mpq_mul(rep, rep, b.rep);
return *this;
}
Rational& operator*= (const Integer& b);
Rational& operator*= (long b)
{
if (!*this) return *this;
if (b) {
#if __GNU_MP_VERSION >= 4
unsigned long g=mpz_gcd_ui(0, mpq_denref(rep), b>=0 ? b : -b);
if (g==1) {
mpz_mul_si(mpq_numref(rep), mpq_numref(rep), b);
} else {
mpz_mul_si(mpq_numref(rep), mpq_numref(rep), b/g);
mpz_divexact_ui(mpq_denref(rep), mpq_denref(rep), g);
}
#else
_tmp_little_Integer(g);
if (mpz_gcd_ui(g, mpq_denref(rep), b>=0 ? b : -b) == 1) {
mpz_mul_si(mpq_numref(rep), mpq_numref(rep), b);
} else {
mpz_mul_si(mpq_numref(rep), mpq_numref(rep), b/g_limb);
mpz_divexact(mpq_denref(rep), mpq_denref(rep), g);
}
#endif
} else {
*this=0;
}
return *this;
}
Rational& operator/= (const Rational& b)
{
mpq_div(rep, rep, b.rep);
return *this;
}
Rational& operator/= (const Integer& b);
Rational& operator/= (long b)
{
if (!b) zero_division();
if (*this) {
const long babs=b>0 ? b : -b;
#if __GNU_MP_VERSION >= 4
unsigned long g=mpz_gcd_ui(0, mpq_numref(rep), babs);
if (g==1) {
mpz_mul_ui(mpq_denref(rep), mpq_denref(rep), babs);
} else {
mpz_mul_ui(mpq_denref(rep), mpq_denref(rep), babs/g);
mpz_divexact_ui(mpq_numref(rep), mpq_numref(rep), g);
}
#else
_tmp_little_Integer(g);
if (mpz_gcd_ui(g, mpq_numref(rep), babs) == 1) {
mpz_mul_ui(mpq_denref(rep), mpq_denref(rep), babs);
} else {
mpz_mul_ui(mpq_denref(rep), mpq_denref(rep), babs/g_limb);
mpz_divexact(mpq_numref(rep), mpq_numref(rep), g);
}
#endif
if (b<0) mpz_neg(mpq_numref(rep), mpq_numref(rep));
}
return *this;
}
/// Multiply with $2^k$.
Rational& operator<<= (unsigned long k)
{
#if __GNU_MP_VERSION >= 4
mpq_mul_2exp(rep, rep, k);
#else
if (mpq_sgn(rep)) {
unsigned long den0s=mpz_scan1(mpq_denref(rep), 0);
if (k<=den0s) {
mpz_tdiv_q_2exp(mpq_denref(rep), mpq_denref(rep), k);
} else {
mpz_tdiv_q_2exp(mpq_denref(rep), mpq_denref(rep), den0s);
mpz_mul_2exp(mpq_numref(rep), mpq_numref(rep), k-den0s);
}
}
#endif
return *this;
}
/// Divide thru $2^k$.
Rational& operator>>= (unsigned long k)
{
#if __GNU_MP_VERSION >= 4
mpq_div_2exp(rep, rep, k);
#else
if (mpz_sgn(mpq_numref(rep))) {
unsigned long num0s=mpz_scan1(mpq_numref(rep), 0);
if (k<=num0s) {
mpz_tdiv_q_2exp(mpq_numref(rep), mpq_numref(rep), k);
} else {
mpz_tdiv_q_2exp(mpq_numref(rep), mpq_numref(rep), num0s);
mpz_mul_2exp(mpq_denref(rep), mpq_denref(rep), k-num0s);
}
}
#endif
return *this;
}
friend Rational operator+ (const Rational& a, const Rational& b)
{
return Rational(mpq_add, a.rep, b.get_rep());
}
friend Rational operator+ (const Rational& a, const Integer& b)
{
#if __GNU_MP_VERSION >= 4
return Rational(mpz_addmul, mpq_numref(a.rep), mpq_denref(a.rep), b.get_rep(), mpq_denref(a.rep));
#else
Integer t=denominator(a)*b;
return Rational(mpz_add, mpq_numref(a.rep), t.get_rep(), mpq_denref(a.rep));
#endif
}
friend Rational operator+ (const Rational& a, long b)
{
#if __GNU_MP_VERSION >= 4
if (b>=0) return Rational(mpz_addmul_ui, mpq_numref(a.rep), mpq_denref(a.rep), (unsigned long)b,
mpq_denref(a.rep));
return Rational(mpz_submul_ui, mpq_numref(a.rep), mpq_denref(a.rep), (unsigned long)(-b),
mpq_denref(a.rep));
#else
mpz_t minus_den;
mpz_srcptr den= b>=0 ? mpq_denref(a.rep)
: (b=-b, Integer::_tmp_negate(minus_den,mpq_denref(a.rep)));
return Rational(mpz_addmul_ui, mpq_numref(a.rep), den, (unsigned long)b, mpq_denref(a.rep));
#endif
}
friend Rational operator- (const Rational& a, const Rational& b)
{
return Rational(mpq_sub, a.rep, b.rep);
}
friend Rational operator- (const Rational& a, const Integer& b)
{
#if __GNU_MP_VERSION >= 4
return Rational(mpz_submul, mpq_numref(a.rep), mpq_denref(a.rep), b.get_rep(), mpq_denref(a.rep));
#else
Integer t=denominator(a)*b;
return Rational(mpz_sub, mpq_numref(a.rep), t.get_rep(), mpq_denref(a.rep));
#endif
}
friend Rational operator- (const Integer& a, const Rational& b)
{
#if __GNU_MP_VERSION >= 4
mpz_t minus_num;
return Rational(mpz_addmul, Integer::_tmp_negate(minus_num,mpq_numref(b.rep)), mpq_denref(b.rep), a.get_rep(),
mpq_denref(b.rep));
#else
Integer t=denominator(b)*a;
return Rational(mpz_sub, t.get_rep(), mpq_numref(b.rep), mpq_denref(b.rep));
#endif
}
friend Rational operator- (const Rational& a, long b)
{
#if __GNU_MP_VERSION >= 4
if (b>=0) return Rational(mpz_submul_ui, mpq_numref(a.rep), mpq_denref(a.rep), (unsigned long)b,
mpq_denref(a.rep));
return Rational(mpz_addmul_ui, mpq_numref(a.rep), mpq_denref(a.rep), (unsigned long)(-b),
mpq_denref(a.rep));
#else
mpz_t minus_den;
mpz_srcptr den= b>=0 ? Integer::_tmp_negate(minus_den,mpq_denref(a.rep))
: (b=-b, mpq_denref(a.rep));
return Rational(mpz_addmul_ui, mpq_numref(a.rep), den, (unsigned long)b, mpq_denref(a.rep));
#endif
}
friend Rational operator- (long a, const Rational& b)
{
mpz_t minus_num;
Integer::_tmp_negate(minus_num,mpq_numref(b.rep));
#if __GNU_MP_VERSION >= 4
if (a>=0) return Rational(mpz_addmul_ui, minus_num, mpq_denref(b.rep), (unsigned long)a, mpq_denref(b.rep));
return Rational(mpz_submul_ui, minus_num, mpq_denref(b.rep), (unsigned long)(-a), mpq_denref(b.rep));
#else
mpz_t minus_den;
mpz_srcptr den= a>=0 ? mpq_denref(b.rep)
: (a=-a, Integer::_tmp_negate(minus_den,mpq_denref(b.rep)));
return Rational(mpz_addmul_ui, minus_num, den, (unsigned long)a, mpq_denref(b.rep));
#endif
}
friend Rational operator- (const Rational& a)
{
return Rational(mpq_neg,a.rep);
}
friend Rational operator* (const Rational& a, const Rational& b)
{
return Rational(mpq_mul,a.rep,b.rep);
}
friend Rational operator* (const Rational& a, const Integer& b);
friend Rational operator* (const Rational& a, long b)
{
if (!b || !a) return Rational();
#if __GNU_MP_VERSION >= 4
unsigned long g=mpz_gcd_ui(0, mpq_denref(a.rep), b>=0 ? b : -b);
if (g==1)
return Rational(mpz_mul_si, mpq_numref(a.rep), b, mpq_denref(a.rep));
return Rational(mpz_mul_si, mpq_numref(a.rep), b/(long)g,
mpz_divexact_ui, mpq_denref(a.rep), g);
#else
_tmp_little_Integer(g);
if (mpz_gcd_ui(g, mpq_denref(a.rep), b>=0 ? b : -b) == 1)
return Rational(mpz_mul_si, mpq_numref(a.rep), b, mpq_denref(a.rep));
return Rational(mpz_mul_si, mpq_numref(a.rep), b/(long)g_limb,
mpz_divexact, mpq_denref(a.rep), const_cast<mpz_srcptr>(g));
#endif
}
friend Rational operator/ (const Rational& a, const Rational& b)
{
return Rational(mpq_div,a.rep,b.rep);
}
friend Rational operator/ (const Rational& a, long b)
{
if (!b) zero_division();
if (!a) return Rational();
mpz_t minus_num;
mpz_srcptr num= b>0 ? mpq_numref(a.rep)
: (b=-b, Integer::_tmp_negate(minus_num,mpq_numref(a.rep)));
#if __GNU_MP_VERSION >= 4
unsigned long g=mpz_gcd_ui(0, mpq_numref(a.rep), b);
if (g==1)
return Rational(num, mpz_mul_ui, mpq_denref(a.rep), (unsigned long)b);
return Rational(mpz_divexact_ui, num, g,
mpz_mul_ui, mpq_denref(a.rep), b/g);
#else
_tmp_little_Integer(g);
if (mpz_gcd_ui(g, mpq_numref(a.rep), b) == 1)
return Rational(num, mpz_mul_ui, mpq_denref(a.rep), (unsigned long)b);
return Rational(mpz_divexact, num, const_cast<mpz_srcptr>(g),
mpz_mul_ui, mpq_denref(a.rep), b/g_limb);
#endif
}
friend Rational operator/ (long a, const Rational& b)
{
if (!b) zero_division();
if (!a) return Rational();
mpz_t num_abs;
mpz_srcptr num= mpz_sgn(mpq_numref(b.rep))>0 ? mpq_numref(b.rep)
: (a=-a, Integer::_tmp_negate(num_abs,mpq_numref(b.rep)));
#if __GNU_MP_VERSION >= 4
unsigned long g=mpz_gcd_ui(0, mpq_numref(b.rep), a>=0 ? a : -a);
if (g==1)
return Rational(mpz_mul_si, mpq_denref(b.rep), a, num);
return Rational(mpz_mul_si, mpq_denref(b.rep), a/(long)g,
mpz_divexact_ui, num, g);
#else
_tmp_little_Integer(g);
if (mpz_gcd_ui(g, mpq_numref(b.rep), a>=0 ? a : -a) == 1)
return Rational(mpz_mul_si, mpq_denref(b.rep), a, num);
return Rational(mpz_mul_si, mpq_denref(b.rep), a/(long)g_limb,
mpz_divexact, num, const_cast<mpz_srcptr>(g));
#endif
}
friend Rational operator/ (const Rational& a, const Integer& b)
{
if (!b) zero_division();
if (!a) return Rational();
const Integer g=gcd(numerator(a),b);
if (g==1)
return Rational(mpq_numref(a.rep), mpz_mul, mpq_denref(a.rep), b.get_rep());
const Integer t=div_exact(b,g);
return Rational(mpz_divexact, mpq_numref(a.rep), g.get_rep(),
mpz_mul, mpq_denref(a.rep), t.get_rep());
}
friend Rational operator/ (const Integer& a, const Rational& b)
{
if (!b) zero_division();
if (!a) return Rational();
const Integer g=gcd(a,numerator(b));
if (g==1)
return Rational(mpz_mul, mpq_denref(b.rep), a.get_rep(), mpq_numref(b.rep));
const Integer t=div_exact(a,g);
return Rational(mpz_mul, mpq_denref(b.rep), t.get_rep(),
mpz_divexact, mpq_numref(b.rep), g.get_rep());
}
friend Rational floor(const Rational& a)
{
return Rational(mpz_fdiv_q, mpq_numref(a.rep), mpq_denref(a.rep), 1);
}
friend Rational ceil(const Rational& a)
{
return Rational(mpz_cdiv_q, mpq_numref(a.rep), mpq_denref(a.rep), 1);
}
/// Multiply with $2^k$
friend Rational operator<< (const Rational& a, unsigned long k)
{
#if __GNU_MP_VERSION >= 4
return Rational(mpq_mul_2exp, a.rep, k);
#else
if (!a) return Rational(0);
unsigned long den0s=mpz_scan1(mpq_denref(a.rep), 0);
if (k<=den0s)
return Rational(mpq_numref(a.rep), mpz_tdiv_q_2exp, mpq_denref(a.rep), k);
return Rational(mpz_mul_2exp, mpq_numref(a.rep), k-den0s,
mpz_tdiv_q_2exp, mpq_denref(a.rep), den0s);
#endif
}
/// Divide thru $2^k$
friend Rational operator>> (const Rational& a, unsigned long k)
{
#if __GNU_MP_VERSION >= 4
return Rational(mpq_div_2exp, a.rep, k);
#else
if (!a) return Rational(0);
unsigned long num0s=mpz_scan1(mpq_numref(a.rep), 0);
if (k<=num0s)
return Rational(mpz_tdiv_q_2exp, mpq_numref(a.rep), k, mpq_denref(a.rep));
return Rational(mpz_tdiv_q_2exp, mpq_numref(a.rep), num0s,
mpz_mul_2exp, mpq_denref(a.rep), k-num0s);
#endif
}
/// Comparison. The magnitude of the return value is arbitrary, only its sign is relevant.
int compare(const Rational& b) const
{
return mpq_cmp(rep, b.rep);
}
int compare(long b) const
{
return mpz_cmp_ui(mpq_denref(rep),1) ? numerator(*this).compare(b*denominator(*this))
: numerator(*this).compare(b);
}
int compare(const Integer& b) const
{
return mpz_cmp_ui(mpq_denref(rep),1) ? numerator(*this).compare(b*denominator(*this))
: numerator(*this).compare(b);
}
friend bool operator== (const Rational& a, const Rational& b)
{
#if __GNU_MP_VERSION >= 4
return mpq_equal(a.rep, b.rep);
#else
return !mpz_cmp(mpq_denref(a.rep), mpq_denref(b.rep)) &&
!mpz_cmp(mpq_numref(a.rep), mpq_numref(b.rep));
#endif
}
friend bool operator== (const Rational& a, const Integer& b)
{
return !mpz_cmp_ui(mpq_denref(a.rep),1) &&
!mpz_cmp(mpq_numref(a.rep), b.get_rep());
}
friend bool operator== (const Rational& a, long b)
{
return !mpz_cmp_ui(mpq_denref(a.rep),1) &&
mpz_fits_slong_p(mpq_numref(a.rep)) && mpz_get_si(mpq_numref(a.rep))==b;
}
friend bool abs_equal(const Rational& a, const Rational& b)
{
return !mpz_cmp(mpq_denref(a.rep), mpq_denref(b.rep)) &&
!mpz_cmpabs(mpq_numref(a.rep), mpq_numref(b.rep));
}
friend bool abs_equal(const Rational& a, const Integer& b)
{
return !mpz_cmp_ui(mpq_denref(a.rep),1) &&
!mpz_cmpabs(mpq_numref(a.rep), b.get_rep());
}
friend bool abs_equal(const Rational& a, long b)
{
return !mpz_cmp_ui(mpq_denref(a.rep),1) &&
mpz_fits_slong_p(mpq_numref(a.rep)) && mpz_get_si(mpq_numref(a.rep))==std::abs(b);
}
friend Rational std::abs(const Rational& a);
friend Rational inv(const Rational& a)
{
return Rational(mpq_inv, a.rep);
}
mpq_srcptr get_rep() const { return rep; }
template <typename Traits>
void read (std::basic_istream<char, Traits>& is)
{
numerator_nocanon(*this).read(is);
if (!is.eof() && is.peek() == '/') {
is.ignore();
denominator(*this).read(is,false);
canonicalize();
} else {
mpz_set_ui(mpq_denref(rep), 1);
}
}