vnix::rat::normalized_pair< NMR_BITS, DNM_BITS > Class Template Reference

Numerator and denominator of a rational number as separate numbers, not encoded into the same word. More...

#include <normalized-pair.hpp>

Public Member Functions
constexpr	normalized_pair (S nn, S dd)
	Initialize normalized numerator and denominator for encoding of rational number. More...
constexpr S	n () const
	Normalized numerator. More...
constexpr U	d () const
	Normalized denominator. More...

Private Types
using	types = int_types< NMR_BITS+DNM_BITS >
	Working integer-types. More...
using	S = typename types::SF
	Fastest large-enough signed type. More...
using	U = typename types::UF
	Fastest large-enough unsigned type. More...

Static Private Member Functions
static constexpr std::pair< S, U >	pair (S n, S d)
	Normalize numerator and denominator. More...

Private Attributes
std::pair< S, U >	pair_
	Normalized numerator and denominator. More...

Detailed Description

template<unsigned NMR_BITS, unsigned DNM_BITS>
class vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >

Numerator and denominator of a rational number as separate numbers, not encoded into the same word.

These separate numbers are guaranteed to be normalized so that they can be encoded into a word of type rational_base<NMR_BITS, DNM_BITS>::US.

Template Parameters

NMR_BITS	Number of bits for numerator.
DNM_BITS	Number of bits for denominator.

Definition at line 25 of file normalized-pair.hpp.

Member Typedef Documentation

template<unsigned NMR_BITS, unsigned DNM_BITS>

using vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::S = typename types::SF

private

Fastest large-enough signed type.

Definition at line 31 of file normalized-pair.hpp.

template<unsigned NMR_BITS, unsigned DNM_BITS>

using vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::types = int_types<NMR_BITS + DNM_BITS>

private

Working integer-types.

Definition at line 30 of file normalized-pair.hpp.

template<unsigned NMR_BITS, unsigned DNM_BITS>

using vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::U = typename types::UF

private

Fastest large-enough unsigned type.

Definition at line 32 of file normalized-pair.hpp.

Constructor & Destructor Documentation

template<unsigned NMR_BITS, unsigned DNM_BITS>

constexpr vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::normalized_pair ( S  nn, S  dd  )

inline

Initialize normalized numerator and denominator for encoding of rational number.

Normalization includes making sure that the denominator is positive, that the numerator and denominator are relatively prime, and that each fits in its allocation of bits within the word.

Parameters

nn	Initial numerator.
dd	Initial denominator.

Definition at line 56 of file normalized-pair.hpp.

                                        : pair_(pair(nn, dd)) {
    enum {
      NMAX = U(1) << (NMR_BITS - 1), // maximum magnitude of numerator
      DMAX = U(1) << (DNM_BITS)      // maximum value of denominator
    };
    if (dd == 0) { throw "null denominator (division by zero)"; }
    if (n() >= NMAX) { throw "numerator too large and positive"; }
    if (n() < -NMAX) { throw "numerator too large and negative"; }
    if (d() > +DMAX) { throw "denominator too large"; }
  }

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Member Function Documentation

template<unsigned NMR_BITS, unsigned DNM_BITS>

constexpr U vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::d ( ) const

inline

Normalized denominator.

Definition at line 68 of file normalized-pair.hpp.

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template<unsigned NMR_BITS, unsigned DNM_BITS>

constexpr S vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::n ( ) const

inline

Normalized numerator.

Definition at line 67 of file normalized-pair.hpp.

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template<unsigned NMR_BITS, unsigned DNM_BITS>

static constexpr std::pair<S, U> vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::pair ( S  n, S  d  )

inlinestaticprivate

Normalize numerator and denominator.

Parameters

n	Input numerator.
d	Input denominator.

Returns

Normalized numerator and denominator.

Definition at line 40 of file normalized-pair.hpp.

                                                {
    U const g = gcd(n, d);
    if (d < 0) { return {-n / g, -d / g}; }
    return {n / g, d / g};
  }

Member Data Documentation

template<unsigned NMR_BITS, unsigned DNM_BITS>

std::pair<S, U> vnix::rat::normalized_pair< NMR_BITS, DNM_BITS >::pair_

private

Normalized numerator and denominator.

Definition at line 34 of file normalized-pair.hpp.

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The documentation for this class was generated from the following file:

• vnix/rat/normalized-pair.hpp