DGtal  0.9.4beta
approximation.cpp
1 
48 #include <cstdlib>
51 #include <cmath>
52 #include <iostream>
53 #include <iomanip>
54 #include "DGtal/arithmetic/LighterSternBrocot.h"
55 #include "DGtal/base/StdRebinders.h"
57 
59 
60 using namespace DGtal;
61 
63 
64 void usage( int, char** argv )
65 {
66  std::cerr << "Usage: " << argv[ 0 ] << " <floating point number>" << std::endl;
67  std::cerr << "\t - computes the successive rational approximation of this number, up to a precision of 1e-14." << std::endl;
68 }
69 
73 int main( int argc, char** argv )
74 {
75  if ( argc < 2 )
76  {
77  usage( argc, argv );
78  return 1;
79  }
80 
82  typedef DGtal::int64_t Integer;
83  typedef DGtal::int64_t Quotient;
84  typedef LighterSternBrocot<Integer, Quotient, StdMapRebinder> SB; // the type of the Stern-Brocot tree
85  typedef SB::Fraction Fraction; // the type for fractions
86  typedef std::back_insert_iterator< Fraction > OutputIterator;
88 
90  long double epsilon = 1e-14;
91  long double number0 = strtold( argv[ 1 ], 0 );
92  long double number = number0;
93  ASSERT( number >= 0.0 );
94  Fraction f;
95  OutputIterator itback = std::back_inserter( f );
96  Quotient i = 0;
97  while ( true )
98  {
99  long double int_part = floorl( number );
100  Quotient u = NumberTraits<long double>::castToInt64_t( int_part );
101  *itback++ = std::make_pair( u, i++ );
102  long double approx =
103  ( (long double) NumberTraits<Integer>::castToDouble( f.p() ) )
104  / ( (long double) NumberTraits<Integer>::castToDouble( f.q() ) );
105  std::cout << "z = " << f.p() << " / " << f.q()
106  << " =~ " << std::setprecision( 16 ) << approx << std::endl;
107  number -= int_part;
108  if ( ( (number0 - epsilon ) < approx )
109  && ( approx < (number0 + epsilon ) ) ) break;
110  number = 1.0 / number;
111  }
112  std::cout << "z = " << f.p() << " / " << f.q() << std::endl;
114  return 0;
115 }
116 
DGtal::int32_t Integer
Definition: StdDefs.h:74
Aim: The traits class for all models of Cinteger.
Definition: NumberTraits.h:69
static DGtal::int64_t castToInt64_t(const T &aT)
Definition: NumberTraits.h:146
DGtal is the top-level namespace which contains all DGtal functions and types.
Aim: The Stern-Brocot tree is the tree of irreducible fractions. This class allows to construct it pr...
boost::int64_t int64_t
signed 94-bit integer.
Definition: BasicTypes.h:74