181     rational() : num(0), den(1) {}  in rational()
186     >::type const* = 0) : num(n), den(1) {}  in rational()
191     >::type const* = 0) : num(n), den(d) {  in rational()
198        : num(r.numerator()), den(is_normalized(int_type(r.numerator()),  in rational()
205        : num(r.numerator()), den(is_normalized(int_type(r.numerator()),  in rational()
284     const IntType& denominator() const { return den; }  in denominator()
295        num += i * den;  in operator +=()
301        num -= i * den;  in operator -=()
308        IntType gcd = integer::gcd(static_cast<IntType>(i), den);  in operator *=()
310        den /= gcd;  in operator *=()
325        den *= i / gcd;  in operator /=()
327        if(den < zero) {  in operator /=()
329           den = -den;  in operator /=()
336     BOOST_CXX14_CONSTEXPR const rational& operator++() { num += den; return *this; }  in operator ++()
337     BOOST_CXX14_CONSTEXPR const rational& operator--() { num -= den; return *this; }  in operator --()
385        BOOST_ASSERT(this->den > zero);  in operator <()
386        int_type  q = this->num / this->den, r = this->num % this->den;  in operator <()
387        while(r < zero)  { r += this->den; --q; }  in operator <()
403        return ((den == IntType(1)) && (num == i));  in operator ==()
410     IntType den;  member in boost::rational
539     IntType r_den = r.den;  in operator +=()
541     IntType g = integer::gcd(den, r_den);  in operator +=()
542     den /= g;  // = b1 from the calculations above  in operator +=()
543     num = num * (r_den / g) + r_num * den;  in operator +=()
546     den *= r_den/g;  in operator +=()
556     IntType r_den = r.den;  in operator -=()
560     IntType g = integer::gcd(den, r_den);  in operator -=()
561     den /= g;  in operator -=()
562     num = num * (r_den / g) - r_num * den;  in operator -=()
565     den *= r_den/g;  in operator -=()
575     IntType r_den = r.den;  in operator *=()
579     IntType gcd2 = integer::gcd(r_num, den);  in operator *=()
581     den = (den/gcd2) * (r_den/gcd1);  in operator *=()
590     IntType r_den = r.den;  in operator /=()
603     IntType gcd2 = integer::gcd(r_den, den);  in operator /=()
605     den = (den/gcd2) * (r_num/gcd1);  in operator /=()
607     if (den < zero) {  in operator /=()
609         den = -den;  in operator /=()
794     BOOST_ASSERT( this->den > zero );  in operator <()
795     BOOST_ASSERT( r.den > zero );  in operator <()
800      ts = { this->num, this->den, static_cast<int_type>(this->num / this->den),  in operator <()
801      static_cast<int_type>(this->num % this->den) },  in operator <()
802      rs = { r.num, r.den, static_cast<int_type>(r.num / r.den),  in operator <()
803      static_cast<int_type>(r.num % r.den) };  in operator <()
872     return ((num == r.num) && (den == r.den));  in operator ==()
880     return ( this->den > int_type(0) ) && ( integer::gcd(this->num, this->den) ==  in test_invariant()
891     if (den == zero)  in normalize()
896         den = IntType(1);  in normalize()
900     IntType g = integer::gcd(num, den);  in normalize()
903     den /= g;  in normalize()
905     if (den < -(std::numeric_limits<IntType>::max)()) {  in normalize()
910     if (den < zero) {  in normalize()
912         den = -den;  in normalize()