Least common denominator (LCD) and corresponding numerators for the comparison of a pair of rational numbers. More...

#include <common-denom.hpp>

Public Types
enum	{ LCD_BITS = clamp64(DB1 + DB2), N1_BITS = clamp64(NB1 + DB2), N2_BITS = clamp64(NB2 + DB1), NMR_BITS = (N1_BITS > N2_BITS ? N1_BITS : N2_BITS) }
	Number of bits required for storage of various items. More...

using	lcd_t = typename int_types< LCD_BITS >::UF
	Type of LCD. More...

using	n1_t = typename int_types< N1_BITS >::SF
	Type of first numerator. More...

using	n2_t = typename int_types< N2_BITS >::SF
	Type of secnd numerator. More...

Static Public Member Functions
static constexpr unsigned	clamp64 (unsigned n)
	Clamp an unsigned number at the maximum value of 64. More...

Public Attributes
lcd_t const	lcd
	LCD. More...

n1_t const	n1
	First numerator. More...

n2_t const	n2
	Second numerator. More...

Private Types
using	rat1 = rational< NB1, DB1 >
	Type of first rational. More...

using	rat2 = rational< NB2, DB2 >
	Type of second rational. More...

Private Member Functions
constexpr	common_denom_params (lcd_t ll, n1_t nn1, n2_t nn2)
	Construct from list of initializers. More...

Friends
constexpr friend common_denom_params	common_denom (rat1 r1, rat2 r2)
	Allow common_denom() to call private constructor. More...

Detailed Description

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>
struct vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >

Least common denominator (LCD) and corresponding numerators for the comparison of a pair of rational numbers.

An instance of common_denom_params is returned by common_denom().

Template Parameters

NB1	Number of bits for numerator of first rational.
DB1	Number of bits for denominator of first rational.
NB2	Number of bits for numerator of second rational.
DB2	Number of bits for denominator of second rational.

Definition at line 20 of file common-denom.hpp.

Member Typedef Documentation

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

using vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::lcd_t = typename int_types<LCD_BITS>::UF

Type of LCD.

Definition at line 72 of file common-denom.hpp.

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

using vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::n1_t = typename int_types<N1_BITS>::SF

Type of first numerator.

Definition at line 73 of file common-denom.hpp.

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

using vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::n2_t = typename int_types<N2_BITS>::SF

Type of secnd numerator.

Definition at line 74 of file common-denom.hpp.

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

using vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::rat1 = rational<NB1, DB1>

private

Type of first rational.

Definition at line 81 of file common-denom.hpp.

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

using vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::rat2 = rational<NB2, DB2>

private

Type of second rational.

Definition at line 82 of file common-denom.hpp.

Member Enumeration Documentation

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

anonymous enum

Number of bits required for storage of various items.

Enumerator
LCD_BITS	For storage of LCD.
N1_BITS	For storage of first numerator.
N2_BITS	For storage of second numerator.
NMR_BITS	For use by client for storage of sum of numerators.

Definition at line 64 of file common-denom.hpp.

        {
     LCD_BITS = clamp64(DB1 + DB2), 
     N1_BITS  = clamp64(NB1 + DB2), 
     N2_BITS  = clamp64(NB2 + DB1), 
     NMR_BITS = (N1_BITS > N2_BITS ? N1_BITS : N2_BITS)
   };

Constructor & Destructor Documentation

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

constexpr vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::common_denom_params	(	lcd_t	ll,
		n1_t	nn1,
		n2_t	nn2
	)

inlineprivate

Construct from list of initializers.

Parameters

ll	Least common denominator.
nn1	First numerator.
nn2	Second numerator.

Definition at line 92 of file common-denom.hpp.

93 : lcd(ll), n1(nn1), n2(nn2) {}

vnix::rat::common_denom_params::n1

n1_t const n1

First numerator.

Definition: common-denom.hpp:77

vnix::rat::common_denom_params::n2

n2_t const n2

Second numerator.

Definition: common-denom.hpp:78

vnix::rat::common_denom_params::lcd

lcd_t const lcd

LCD.

Definition: common-denom.hpp:76

Member Function Documentation

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

static constexpr unsigned vnix::rat::common_denom_params< NB1, DB1, NB2, DB2 >::clamp64 ( unsigned n )

inlinestatic

Clamp an unsigned number at the maximum value of 64.

Parameters

n	Unsigned input.

Returns: Clamped output.

Definition at line 61 of file common-denom.hpp.

61 { return n > 64 ? 64 : n; }

Friends And Related Function Documentation

template<unsigned NB1, unsigned DB1, unsigned NB2, unsigned DB2>

constexpr friend common_denom_params common_denom	(	rat1	r1,
		rat2	r2
	)

friend

Allow common_denom() to call private constructor.

Template Parameters

NB1	Number of bits for numerator of first rational.
DB1	Number of bits for denominator of first rational.
NB2	Number of bits for numerator of second rational.
DB2	Number of bits for denominator of second rational.

Parameters

r1	First input rational number.
r2	Second input rational number.

Returns: Instance of common_denom_pairs.

Definition at line 35 of file common-denom.hpp.

                                                            {
   using cdp       = common_denom_params<NB1, DB1, NB2, DB2>;
   using UF1       = typename int_types<DB1>::UF;
   using UF2       = typename int_types<DB2>::UF;
   using gcd_t     = gcd_promoted<UF1, UF2>;
   gcd_t const g   = gcd(r1.d(), r2.d()); // GCD of input denominators.
   UF1 const   d1g = r1.d() / g; // First input denominator divided by g.
   UF2 const   d2g = r2.d() / g; // Second input denominator divided by g.
   return cdp(d1g * r2.d(), r1.n() * d2g, r2.n() * d1g);
 };