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      Projects are examples
      on the usage of interval containers that go beyond small toy snippets of code.
      The code presented here addresses more serious applications that approach the
      quality of real world programming. At the same time it aims to guide the reader
      more deeply into various aspects of the library. In order not to overburden
      the reader with implementation details, the code in projects
      tries to be minimal.
      It has a focus on the main aspects of the projects and is not intended to be
      complete and mature like the library code itself. Cause it's minimal, project
      code lives in namespace mini.
    
        Bitsets are just sets. Sets of unsigned integrals, to be more precise. The
        prefix bit usually
        only indicates, that the representation of those sets is organized in a compressed
        form that exploits the fact, that we can switch on an off single bits in
        machine words. Bitsets are therefore known to be very small and thus efficient.
        The efficiency of bitsets is usually coupled to the precondition that the
        range of values of elements is relatively small, like [0..32) or [0..64),
        values that can be typically represented in single or a small number of machine
        words. If we wanted to represent a set containing two values {1, 1000000},
        we would be much better off using other sets like e.g. an std::set.
      
        Bitsets compress well, if elements spread over narrow ranges only. Interval
        sets compress well, if many elements are clustered over intervals. They can
        span large sets very efficiently then. In project Large
        Bitset we want to combine
        the bit compression and the interval compression to
        achieve a set implementation, that is capable of spanning large chunks of
        contiguous elements using intervals and also to represent more narrow nests
        of varying bit sequences using bitset compression. As we will see, this can
        be achieved using only a small amount of code because most of the properties
        we need are provided by an interval_map
        of bitsets:
      
typedef interval_map<IntegralT, SomeBitSet<N>, partial_absorber, std::less, inplace_bit_add, inplace_bit_and> IntervalBitmap;
        Such an IntervalBitmap represents
        k*N bits for every segment.
[a, a+k)->'1111....1111' // N bits associated: Represents a total of k*N bits.
        For the interval [a, a+k) above
        all bits are set. But we can also have individual nests
        or clusters of bitsequences.
      
[b, b+1)->'01001011...1' [b+1,b+2)->'11010001...0' . . .
and we can span intervals of equal bit sequences that represent periodic patterns.
[c,d)->'010101....01' // Every second bit is set in range [c,d) [d,e)->'001100..0011' // Every two bits alterate in range [d,e) [e,f)->'bit-sequence' // 'bit-sequence' reoccurs every N bits in range [e,f)
        An IntervalBitmap can represent
        N*(2^M) elements, if M
        is the number of bits of the integral type IntegralT.
        Unlike bitsets, that usually represent unsigned
        integral numbers, large_bitset may range over negative numbers as well. There
        are fields where such large bitsets implementations are needed. E.g. for
        the compact representation of large file allocation tables. What remains
        to be done for project Large Bitset is to
        code a wrapper class large_bitset
        around IntervalBitmap so
        that large_bitset looks and
        feels like a usual set class.
      
          To quicken your appetite for a look at the implementation here are a few
          use cases first. Within the examples that follow, we will use natk
          for unsigned integrals and bitsk
          for bitsets containing k bits.
        
Let's start large. In the first example . . .
void test_large() { const nat64 much = 0xffffffffffffffffull; large_bitset<> venti; // ... the largest, I can think of ;) venti += discrete_interval<nat64>(0, much); cout << "----- Test function test_large() -----------------------------------------------\n"; cout << "We have just turned on the awesome amount of 18,446,744,073,709,551,616 bits ;-)\n"; venti.show_segments();
. . . we are testing the limits. First we set all bits and then we switch off the very last bit.
cout << "---- Let's swich off the very last bit -----------------------------------------\n"; venti -= much; venti.show_segments(); cout << "---- Venti is plenty ... let's do something small: A tall ----------------------\n\n"; }
Program output (a little beautified):
----- Test function test_large() ----------------------------------------------- We have just turned on the awesome amount of 18,446,744,073,709,551,616 bits ;-) [ 0, 288230376151711744) -> 1111111111111111111111111111111111111111111111111111111111111111 ---- Let's swich off the very last bit ----------------------------------------- [ 0, 288230376151711743) -> 1111111111111111111111111111111111111111111111111111111111111111 [288230376151711743, 288230376151711744) -> 1111111111111111111111111111111111111111111111111111111111111110 ---- Venti is plenty ... let's do something small: A tall ----------------------
          More readable is a smaller version of large_bitset.
          In function test_small() we apply a few more operations . . .
        
void test_small() { large_bitset<nat32, bits8> tall; // small is tall ... // ... because even this 'small' large_bitset // can represent up to 2^32 == 4,294,967,296 bits. cout << "----- Test function test_small() -----------\n"; cout << "-- Switch on all bits in range [0,64] ------\n"; tall += discrete_interval<nat>(0, 64); tall.show_segments(); cout << "--------------------------------------------\n"; cout << "-- Turn off bits: 25,27,28 -----------------\n"; (((tall -= 25) -= 27) -= 28) ; tall.show_segments(); cout << "--------------------------------------------\n"; cout << "-- Flip bits in range [24,30) --------------\n"; tall ^= discrete_interval<nat>::right_open(24,30); tall.show_segments(); cout << "--------------------------------------------\n"; cout << "-- Remove the first 10 bits ----------------\n"; tall -= discrete_interval<nat>::right_open(0,10); tall.show_segments(); cout << "-- Remove even bits in range [0,72) --------\n"; int bit; for(bit=0; bit<72; bit++) if(!(bit%2)) tall -= bit; tall.show_segments(); cout << "-- Set odd bits in range [0,72) --------\n"; for(bit=0; bit<72; bit++) if(bit%2) tall += bit; tall.show_segments(); cout << "--------------------------------------------\n\n"; }
. . . producing this output:
----- Test function test_small() ----------- -- Switch on all bits in range [0,64] ------ [0,8)->11111111 [8,9)->10000000 -------------------------------------------- -- Turn off bits: 25,27,28 ----------------- [0,3)->11111111 [3,4)->10100111 [4,8)->11111111 [8,9)->10000000 -------------------------------------------- -- Flip bits in range [24,30) -------------- [0,3)->11111111 [3,4)->01011011 [4,8)->11111111 [8,9)->10000000 -------------------------------------------- -- Remove the first 10 bits ---------------- [1,2)->00111111 [2,3)->11111111 [3,4)->01011011 [4,8)->11111111 [8,9)->10000000 -- Remove even bits in range [0,72) -------- [1,2)->00010101 [2,3)->01010101 [3,4)->01010001 [4,8)->01010101 -- Set odd bits in range [0,72) -------- [0,9)->01010101 --------------------------------------------
          Finally, we present a little picturesque example,
          that demonstrates that large_bitset
          can also serve as a self compressing bitmap, that we can 'paint' with.
        
void test_picturesque() { typedef large_bitset<nat, bits8> Bit8Set; Bit8Set square, stare; square += discrete_interval<nat>(0,8); for(int i=1; i<5; i++) { square += 8*i; square += 8*i+7; } square += discrete_interval<nat>(41,47); cout << "----- Test function test_picturesque() -----\n"; cout << "-------- empty face: " << square.interval_count() << " intervals -----\n"; square.show_matrix(" *"); stare += 18; stare += 21; stare += discrete_interval<nat>(34,38); cout << "-------- compressed smile: " << stare.interval_count() << " intervals -----\n"; stare.show_matrix(" *"); cout << "-------- staring bitset: " << (square + stare).interval_count() << " intervals -----\n"; (square + stare).show_matrix(" *"); cout << "--------------------------------------------\n"; }
          Note that we have two large_bitsets
          for the outline and the interior.
          Both parts are compressed but we can compose both by operator
          +, because the right positions
          are provided. This is the program output:
        
----- Test function test_picturesque() ----- -------- empty face: 3 intervals ----- ******** * * * * * * * * ****** -------- compressed smile: 2 intervals ----- * * **** -------- staring bitset: 6 intervals ----- ******** * * * * * * * * * **** * ****** --------------------------------------------
          So, may be you are curious how this class template is coded on top of
          interval_map using
          only about 250 lines of code. This is shown in the sections that follow.
        
To begin, let's look at the basic data type again, that will be providing the major functionality:
typedef interval_map<DomainT, BitSetT, partial_absorber, std::less, inplace_bit_add, inplace_bit_and> IntervalBitmap;
          DomainT is supposed to
          be an integral type, the bitset type BitSetT
          will be a wrapper class around an unsigned integral type. BitSetT has to implement bitwise operators
          that will be called by the functors inplace_bit_add<BitSetT> and inplace_bit_and<BitSetT>. The type trait of interval_map is
          partial_absorber, which
          means that it is partial and that empty BitSetTs are not stored in the map. This
          is desired and keeps the interval_map
          minimal, storing only bitsets, that contain at least one bit switched on.
          Functor template inplace_bit_add
          for parameter Combine indicates
          that we do not expect operator += as addition but the bitwise operator
          |=. For template parameter
          Section which is instaniated
          by inplace_bit_and we expect
          the bitwise &= operator.
        
          The code of the project is enclosed in a namespace
          mini. The name indicates, that
          the implementation is a minimal example implementation.
          The name of the bitset class will be bits
          or mini::bits if qualified.
        
          To be used as a codomain parameter of class template interval_map,
          mini::bits has to implement all the functions
          that are required for a codomain_type in general, which are the default
          constructor bits()
          and an equality operator==.
          Moreover mini::bits has to implement operators required
          by the instantiations for parameter Combine
          and Section which are
          inplace_bit_add and inplace_bit_and. From functors inplace_bit_add and inplace_bit_and
          there are inverse functors inplace_bit_subtract
          and inplace_bit_xor. Those
          functors use operators |= &= ^=
          and ~. Finally if we want
          to apply lexicographical and subset comparison on large_bitset, we also
          need an operator <.
          All the operators that we need can be implemented for mini::bits
          on a few lines:
        
template<class NaturalT> class bits { public: typedef NaturalT word_type; static const int digits = std::numeric_limits<NaturalT>::digits; static const word_type w1 = static_cast<NaturalT>(1) ; bits():_bits(){} explicit bits(word_type value):_bits(value){} word_type word()const{ return _bits; } bits& operator |= (const bits& value){_bits |= value._bits; return *this;} bits& operator &= (const bits& value){_bits &= value._bits; return *this;} bits& operator ^= (const bits& value){_bits ^= value._bits; return *this;} bits operator ~ ()const { return bits(~_bits); } bool operator < (const bits& value)const{return _bits < value._bits;} bool operator == (const bits& value)const{return _bits == value._bits;} bool contains(word_type element)const{ return ((w1 << element) & _bits) != 0; } std::string as_string(const char off_on[2] = " 1")const; private: word_type _bits; };
          Finally there is one important piece of meta information, we have to provide:
          mini::bits has to be recognized as a Set by the icl code. Otherwise we can
          not exploit the fact that a map of sets is model of Set
          and the resulting large_bitset would not behave like a set. So we have
          to say that mini::bits shall be sets:
        
namespace boost { namespace icl { template<class NaturalT> struct is_set<mini::bits<NaturalT> > { typedef is_set<mini::bits<NaturalT> > type; BOOST_STATIC_CONSTANT(bool, value = true); }; template<class NaturalT> struct has_set_semantics<mini::bits<NaturalT> > { typedef has_set_semantics<mini::bits<NaturalT> > type; BOOST_STATIC_CONSTANT(bool, value = true); }; }}
          This is done by adding a partial template specialization to the type trait
          template icl::is_set. For the extension of this type
          trait template and the result values of inclusion_compare we need these
          #includes for the implementation
          of mini::bits:
        
// These includes are needed ... #include <string> // for conversion to output and to #include <boost/icl/type_traits/has_set_semantics.hpp>//declare that bits has the // behavior of a set.
          Having finished our mini::bits
          implementation, we can start to code the wrapper class that hides the efficient
          interval map of mini::bits and exposes a simple and convenient set behavior
          to the world of users.
        
          Let's start with the required #includes
          this time:
        
#include <iostream> // to organize output #include <limits> // limits and associated constants #include <boost/operators.hpp> // to define operators with minimal effort #include "meta_log.hpp" // a meta logarithm #include "bits.hpp" // a minimal bitset implementation #include <boost/icl/interval_map.hpp> // base of large bitsets namespace mini // minimal implementations for example projects {
          Besides boost/icl/interval_map.hpp and bits.hpp
          the most important include here is boost/operators.hpp.
          We use this library in order to further minimize the code and to provide
          pretty extensive operator functionality using very little code.
        
          For a short and concise naming of the most important unsigned integer types
          and the corresponding mini::bits
          we define this:
        
typedef unsigned char nat8; // nati i: number bits typedef unsigned short nat16; typedef unsigned long nat32; typedef unsigned long long nat64; typedef unsigned long nat; typedef bits<nat8> bits8; typedef bits<nat16> bits16; typedef bits<nat32> bits32; typedef bits<nat64> bits64;
            And now let's code large_bitset.
          
template < typename DomainT = nat64, typename BitSetT = bits64, ICL_COMPARE Compare = ICL_COMPARE_INSTANCE(std::less, DomainT), ICL_INTERVAL(ICL_COMPARE) Interval = ICL_INTERVAL_INSTANCE(ICL_INTERVAL_DEFAULT, DomainT, Compare), ICL_ALLOC Alloc = std::allocator > class large_bitset : boost::equality_comparable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::less_than_comparable< large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::addable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::orable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::subtractable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::andable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::xorable < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc> , boost::addable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, DomainT , boost::orable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, DomainT , boost::subtractable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, DomainT , boost::andable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, DomainT , boost::xorable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, DomainT , boost::addable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, ICL_INTERVAL_TYPE(Interval,DomainT,Compare) , boost::orable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, ICL_INTERVAL_TYPE(Interval,DomainT,Compare) , boost::subtractable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, ICL_INTERVAL_TYPE(Interval,DomainT,Compare) , boost::andable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, ICL_INTERVAL_TYPE(Interval,DomainT,Compare) , boost::xorable2 < large_bitset<DomainT,BitSetT,Compare,Interval,Alloc>, ICL_INTERVAL_TYPE(Interval,DomainT,Compare) > > > > > > > > > > > > > > > > > //^ & - | + ^ & - | + ^ & - | + < == //segment element container
            The first template parameter DomainT
            will be instantiated with an integral type that defines the kind of numbers
            that can be elements of the set. Since we want to go for a large set
            we use nat64 as default
            which is a 64 bit unsigned integer ranging from 0
            to 2^64-1.
            As bitset parameter we also choose a 64-bit default. Parameters Combine and Interval
            are necessary to be passed to dependent type expressions. An allocator
            can be chosen, if desired.
          
            The nested list of private inheritance contains groups of template instantiations
            from Boost.Operator,
            that provides derivable operators from more fundamental once. Implementing
            the fundamental operators, we get the derivable ones for free.
            Below is a short overview of what we get using Boost.Operator, where
            S
            stands for large_bitset,
            i
            for it's interval_type
            and e
            for it's domain_type
            or element_type.
          
| Group | fundamental | derivable | 
|---|---|---|
| Equality, ordering | 
                       | 
                       | 
| 
                       | 
                       | |
| 
                       | 
                       | |
| 
                       | 
                       | |
| 
                       | 
                       | 
There is a number of associated types
typedef boost::icl::interval_map <DomainT, BitSetT, boost::icl::partial_absorber, std::less, boost::icl::inplace_bit_add, boost::icl::inplace_bit_and> interval_bitmap_type; typedef DomainT domain_type; typedef DomainT element_type; typedef BitSetT bitset_type; typedef typename BitSetT::word_type word_type; typedef typename interval_bitmap_type::interval_type interval_type; typedef typename interval_bitmap_type::value_type value_type;
            most importantly the implementing interval_bitmap_type
            that is used for the implementing container.
          
private: interval_bitmap_type _map;
In order to use Boost.Operator we have to implement the fundamental operators as class members. This can be done quite schematically.
public: bool operator ==(const large_bitset& rhs)const { return _map == rhs._map; } bool operator < (const large_bitset& rhs)const { return _map < rhs._map; } large_bitset& operator +=(const large_bitset& rhs) {_map += rhs._map; return *this;} large_bitset& operator |=(const large_bitset& rhs) {_map |= rhs._map; return *this;} large_bitset& operator -=(const large_bitset& rhs) {_map -= rhs._map; return *this;} large_bitset& operator &=(const large_bitset& rhs) {_map &= rhs._map; return *this;} large_bitset& operator ^=(const large_bitset& rhs) {_map ^= rhs._map; return *this;} large_bitset& operator +=(const element_type& rhs) {return add(interval_type(rhs)); } large_bitset& operator |=(const element_type& rhs) {return add(interval_type(rhs)); } large_bitset& operator -=(const element_type& rhs) {return subtract(interval_type(rhs)); } large_bitset& operator &=(const element_type& rhs) {return intersect(interval_type(rhs));} large_bitset& operator ^=(const element_type& rhs) {return flip(interval_type(rhs)); } large_bitset& operator +=(const interval_type& rhs){return add(rhs); } large_bitset& operator |=(const interval_type& rhs){return add(rhs); } large_bitset& operator -=(const interval_type& rhs){return subtract(rhs); } large_bitset& operator &=(const interval_type& rhs){return intersect(rhs);} large_bitset& operator ^=(const interval_type& rhs){return flip(rhs); }
            As we can see, the seven most important operators that work on the class
            type large_bitset can
            be directly implemented by propagating the operation to the implementing
            _map of type interval_bitmap_type. For the operators
            that work on segment and element types, we use member functions add, subtract,
            intersect and flip. As we will see only a small amount
            of adaper code is needed to couple those functions with the functionality
            of the implementing container.
          
            Member functions add,
            subtract, intersect and flip,
            that allow to combine intervals
            to large_bitsets can
            be uniformly implemented using a private function segment_apply
            that applies addition, subtraction,
            intersection or symmetric difference,
            after having translated the interval's borders into the right bitset
            positions.
          
large_bitset& add (const interval_type& rhs){return segment_apply(&large_bitset::add_, rhs);} large_bitset& subtract (const interval_type& rhs){return segment_apply(&large_bitset::subtract_, rhs);} large_bitset& intersect(const interval_type& rhs){return segment_apply(&large_bitset::intersect_,rhs);} large_bitset& flip (const interval_type& rhs){return segment_apply(&large_bitset::flip_, rhs);}
            In the sample programs, that we will present to demonstrate the capabilities
            of large_bitset we will
            need a few additional functions specifically output functions in two
            different flavors.
          
size_t interval_count()const { return boost::icl::interval_count(_map); } void show_segments()const { for(typename interval_bitmap_type::const_iterator it_ = _map.begin(); it_ != _map.end(); ++it_) { interval_type itv = it_->first; bitset_type bits = it_->second; std::cout << itv << "->" << bits.as_string("01") << std::endl; } } void show_matrix(const char off_on[2] = " 1")const { using namespace boost; typename interval_bitmap_type::const_iterator iter = _map.begin(); while(iter != _map.end()) { element_type fst = icl::first(iter->first), lst = icl::last(iter->first); for(element_type chunk = fst; chunk <= lst; chunk++) std::cout << iter->second.as_string(off_on) << std::endl; ++iter; } }
show_segments() shows the container content as
                it is implemented, in the compressed form.
              show_matrix
                shows the complete matrix of bits that is represented by the container.
              
            In order to implement operations like the addition of an element say
            42 to the large bitset, we
            need to translate the value to the position
            of the associated bit representing
            42 in the interval container
            of bitsets. As an example, suppose we use a
large_bitset<nat, mini::bits8> lbs;
            that carries small bitsets of 8 bits only. The first four interval of
            lbs are assumed to be
            associated with some bitsets. Now we want to add the interval [a,b]==[5,27]. This
            will result in the following situation:
[0,1)-> [1,2)-> [2,3)-> [3,4)-> [00101100][11001011][11101001][11100000] + [111 11111111 11111111 1111] [5,27] as bitset a b => [0,1)-> [1,3)-> [3,4)-> [00101111][11111111][11110000]
So we have to convert values 5 and 27 into a part that points to the interval and a part that refers to the position within the interval, which is done by a division and a modulo computation. (In order to have a consistent representation of the bitsequences across the containers, within this project, bitsets are denoted with the least significant bit on the left!)
A = a/8 = 5/8 = 0 // refers to interval B = b/8 = 27/8 = 3 R = a%8 = 5%8 = 5 // refers to the position in the associated bitset. S = b%8 = 27%8 = 3
            All division and modulo operations
            needed here are always done using a divisor d
            that is a power of 2: d = 2^x.
            Therefore division and modulo can be expressed by bitset operations.
            The constants needed for those bitset computations are defined here:
          
private: // Example value static const word_type // 8-bit case digits = std::numeric_limits // -------------------------------------------------------------- <word_type>::digits , // 8 Size of the associated bitsets divisor = digits , // 8 Divisor to find intervals for values last = digits-1 , // 7 Last bit (0 based) shift = log2_<divisor>::value , // 3 To express the division as bit shift w1 = static_cast<word_type>(1) , // Helps to avoid static_casts for long long mask = divisor - w1 , // 7=11100000 Helps to express the modulo operation as bit_and all = ~static_cast<word_type>(0), // 255=11111111 Helps to express a complete associated bitset top = w1 << (digits-w1) ; // 128=00000001 Value of the most significant bit of associated bitsets // !> Note: Most signigicant bit on the right.
Looking at the example again, we can see that we have to identify the positions of the beginning and ending of the interval [5,27] that is to insert, and then subdivide that range of bitsets into three partitions.
combine interval [5,27] to large_bitset lbs w.r.t. some operation o [0,1)-> [1,2)-> [2,3)-> [3,4)-> [00101100][11001011][11101001][11100000] o [111 11111111 11111111 1111] a b subdivide: [first! ][mid_1] . . .[mid_n][ !last] [00000111][1...1] . . .[1...1][11110000]
            After subdividing, we perform the operation o
            as follows:
          
!) to the end of the bitset to 1. All other bits are 0. Then perform operation o: _map
                o=
                ([0,1)->00000111)
              !)
                to 1. All other bits
                are 0. Then perform operation
                o: _map o= ([3,4)->11110000)
              o: _map o= ([1,3)->11111111)
              
            The algorithm, that has been outlined and illustrated by the example,
            is implemented by the private member function segment_apply.
            To make the combiner operation a variable in this algorithm, we use a
            pointer to member function type
          
typedef void (large_bitset::*segment_combiner)(element_type, element_type, bitset_type);
            as first function argument. We will pass member functions combine_ here,
combine_(first_of_interval, end_of_interval, some_bitset);
            that take the beginning and ending of an interval and a bitset and combine
            them to the implementing interval_bitmap_type
            _map. Here are these functions:
          
void add_(DomainT lo, DomainT up, BitSetT bits){_map += value_type(interval_type::right_open(lo,up), bits);} void subtract_(DomainT lo, DomainT up, BitSetT bits){_map -= value_type(interval_type::right_open(lo,up), bits);} void intersect_(DomainT lo, DomainT up, BitSetT bits){_map &= value_type(interval_type::right_open(lo,up), bits);} void flip_(DomainT lo, DomainT up, BitSetT bits){_map ^= value_type(interval_type::right_open(lo,up), bits);}
            Finally we can code function segment_apply,
            that does the partitioning and subsequent combining:
          
large_bitset& segment_apply(segment_combiner combine, const interval_type& operand) { using namespace boost; if(icl::is_empty(operand)) return *this; // same as element_type base = icl::first(operand) >> shift, // icl::first(operand) / divisor ceil = icl::last (operand) >> shift; // icl::last (operand) / divisor word_type base_rest = icl::first(operand) & mask , // icl::first(operand) % divisor ceil_rest = icl::last (operand) & mask ; // icl::last (operand) % divisor if(base == ceil) // [first, last] are within one bitset (chunk) (this->*combine)(base, base+1, bitset_type( to_upper_from(base_rest) & from_lower_to(ceil_rest))); else // [first, last] spread over more than one bitset (chunk) { element_type mid_low = base_rest == 0 ? base : base+1, // first element of mid part mid_up = ceil_rest == all ? ceil+1 : ceil ; // last element of mid part if(base_rest > 0) // Bitset of base interval has to be filled from base_rest to last (this->*combine)(base, base+1, bitset_type(to_upper_from(base_rest))); if(ceil_rest < all) // Bitset of ceil interval has to be filled from first to ceil_rest (this->*combine)(ceil, ceil+1, bitset_type(from_lower_to(ceil_rest))); if(mid_low < mid_up) // For the middle part all bits have to set. (this->*combine)(mid_low, mid_up, bitset_type(all)); } return *this; }
The functions that help filling bitsets to and from a given bit are implemented here:
static word_type from_lower_to(word_type bit){return bit==last ? all : (w1<<(bit+w1))-w1;} static word_type to_upper_from(word_type bit){return bit==last ? top : ~((w1<<bit)-w1); }
            This completes the implementation of class template large_bitset.
            Using only a small amount of mostly schematic code, we have been able
            to provide a pretty powerful, self compressing and generally usable set
            type for all integral domain types.