DGtal 1.3.0
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approximation.cpp
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1
50#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
60using namespace DGtal;
61
63
64void 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
73int 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
Aim: The Stern-Brocot tree is the tree of irreducible fractions. This class allows to construct it pr...
Point::Coordinate Integer
DGtal is the top-level namespace which contains all DGtal functions and types.
boost::int64_t int64_t
signed 94-bit integer.
Definition: BasicTypes.h:74
Aim: The traits class for all models of Cinteger.
Definition: NumberTraits.h:564
int main()
Definition: testBits.cpp:56