Implementar el algoritmo naif de multiplicacion.

[z.facultad/75.29/dale.git] / src / number.h

diff --git a/src/number.h b/src/number.h
index 3a42d7ee552f23735a0b021c4f7ad447a78a1085..dfd7934dd0d4b02bbeb47e03daee1267bc1eb008 100644 (file)
--- a/src/number.h
+++ b/src/number.h
@@ -7,12 +7,21 @@
 #include <deque>
 #include <utility>
 #include <algorithm>
 #include <deque>
 #include <utility>
 #include <algorithm>

-#include <iterator>
+#include <iomanip>

 #include <stdint.h>
 
 #include <stdint.h>
 

+enum sign_type { positive, negative };
+
+

 /* sizeof(E) tiene que ser 2*sizeof(N); y son los tipos nativos con los cuales
  * se haran las operaciones mas basicas. */
 
 /* sizeof(E) tiene que ser 2*sizeof(N); y son los tipos nativos con los cuales
  * se haran las operaciones mas basicas. */
 

+template < typename N, typename E >
+struct number;
+
+template < typename N, typename E >
+std::ostream& operator<< (std::ostream& os, const number< N, E >& n);
+

 template < typename N = uint32_t, typename E = uint64_t >
 struct number
 {
 template < typename N = uint32_t, typename E = uint64_t >
 struct number
 {


@@ -20,7 +29,6 @@ struct number
        // Tipos
        typedef N native_type;
        typedef E extended_type;
        // Tipos
        typedef N native_type;
        typedef E extended_type;

-       enum sign_type { positive, negative };

        typedef typename std::deque< native_type > chunk_type;
        typedef typename chunk_type::size_type size_type;
        typedef typename chunk_type::iterator iterator;
        typedef typename std::deque< native_type > chunk_type;
        typedef typename chunk_type::size_type size_type;
        typedef typename chunk_type::iterator iterator;


@@ -76,7 +84,10 @@ struct number
        const_reverse_iterator rbegin() const { return chunk.rbegin(); }
        const_reverse_iterator rend() const { return chunk.rend(); }
 
        const_reverse_iterator rbegin() const { return chunk.rbegin(); }
        const_reverse_iterator rend() const { return chunk.rend(); }
 

-       private:
+       // Friends
+       template < typename NN, typename EE >
+       friend std::ostream& operator<< (std::ostream& os, const number< NN, EE>& n);
+

        // Atributos
        chunk_type chunk;
        sign_type sign;
        // Atributos
        chunk_type chunk;
        sign_type sign;


@@ -206,7 +217,10 @@ template < typename N, typename E >
 std::ostream& operator<< (std::ostream& os, const number< N, E >& n)
 {
        // FIXME sacar una salida bonita en ASCII =)
 std::ostream& operator<< (std::ostream& os, const number< N, E >& n)
 {
        // FIXME sacar una salida bonita en ASCII =)

-       std::copy(n.begin(), n.end(), std::ostream_iterator< N >(os, " "));
+       for (typename number< N, E >::const_iterator i = n.chunk.begin();
+                       i != n.chunk.end(); ++i)
+               os << std::setfill('0') << std::setw(sizeof(N) * 2) << std::hex
+                       << *i << " ";

        return os;
 }
 
        return os;
 }
 


@@ -258,14 +272,16 @@ std::pair< number< N, E >, number< N, E > > number< N, E >::split() const
        std::pair< num_type, num_type > par;
 
        // la primera mitad va al pedazo inferior
        std::pair< num_type, num_type > par;
 
        // la primera mitad va al pedazo inferior

-       for (i = 0; i < halves_size; i++)
+       par.first.chunk[0] = chunk[0];
+       for (i = 1; i < halves_size; i++)

        {
                par.first.chunk.push_back(chunk[i]);
        }
 
        // la segunda mitad (si full_size es impar es 1 más que la primera
        // mitad) va al pedazo superior
        {
                par.first.chunk.push_back(chunk[i]);
        }
 
        // la segunda mitad (si full_size es impar es 1 más que la primera
        // mitad) va al pedazo superior

-       for ( ; i < full_size; i++)
+       par.second.chunk[0] = chunk[i];
+       for (i++ ; i < full_size; i++)

        {
                par.second.chunk.push_back(chunk[i]);
        }
        {
                par.second.chunk.push_back(chunk[i]);
        }


@@ -274,7 +290,7 @@ std::pair< number< N, E >, number< N, E > > number< N, E >::split() const
 
 // es el algoritmo de división y conquista, que se llama recursivamente
 template < typename N, typename E >
 
 // es el algoritmo de división y conquista, que se llama recursivamente
 template < typename N, typename E >

-number < N, E > divide_n_conquer(number< N, E > u, number< N, E > v)
+number < N, E > karatsuba(const number< N, E > &u, const number< N, E > &v)

 {
        typedef number< N, E > num_type;
 
 {
        typedef number< N, E > num_type;
 


@@ -297,9 +313,9 @@ number < N, E > divide_n_conquer(number< N, E > u, number< N, E > v)
        // m = u1*v1
        // d = u2*v2
        // h = (u1+v1)*(u2+v2) = u1*u2+u1*v2+u2*v1+u2*v2
        // m = u1*v1
        // d = u2*v2
        // h = (u1+v1)*(u2+v2) = u1*u2+u1*v2+u2*v1+u2*v2

-       num_type m = divide_n_conquer(u12.first, v12.first);
-       num_type d = divide_n_conquer(u12.second, v12.second);
-       num_type h = divide_n_conquer(u12.first + v12.first,
+       num_type m = karastuba(u12.first, v12.first);
+       num_type d = karastuba(u12.second, v12.second);
+       num_type h = karastuba(u12.first + v12.first,

                        u12.second + v12.second);
 
        // H-D-M = u1*u2+u1*v2+u2*v1+u2*v2 - u2*v2 - u1*v1 = u1*v2+u2*v1
                        u12.second + v12.second);
 
        // H-D-M = u1*u2+u1*v2+u2*v1+u2*v2 - u2*v2 - u1*v1 = u1*v2+u2*v1


@@ -308,3 +324,83 @@ number < N, E > divide_n_conquer(number< N, E > u, number< N, E > v)
 
 }
 
 
 }
 

+
+/* Algoritmo "naif" (por no decir "cabeza" o "bruto") de multiplicacion. */
+template < typename N, typename E >
+number < N, E > naif(const number< N, E > &u, const number< N, E > &v)
+{
+       typedef number< N, E > num_type;
+
+       // tomo el chunk size de u (el de v DEBE ser el mismo)
+       typename num_type::size_type chunk_size = u.chunk.size();
+
+       sign_type sign;
+
+       if ( (u.sign == positive && v.sign == positive) ||
+                       (u.sign == negative && v.sign == negative) ) {
+               sign = positive;
+       } else {
+               sign = negative;
+       }
+
+       //printf("naif %d %d\n", u.chunk.size(), v.chunk.size() );
+
+       if (chunk_size == 1)
+       {
+               /* Si llegamos a multiplicar dos de tamaño 1, lo que hacemos
+                * es usar la multiplicacion nativa del tipo N, guardando el
+                * resultado en el tipo E (que sabemos es del doble de tamaño
+                * de N, ni mas ni menos).
+                * Luego, armamos un objeto number usando al resultado como
+                * buffer. Si, es feo.
+                */
+               E tmp;
+               tmp = (E) u.chunk[0] * (E) v.chunk[0];
+               num_type tnum = num_type((N *) &tmp, 2, sign);
+               //std::cout << "T:" << tnum << " " << tmp << "\n";
+               //printf("1: %lu %lu %llu\n", u.chunk[0], v.chunk[0], tmp);
+               return tnum;
+       }
+
+       std::pair< num_type, num_type > u12 = u.split();
+       std::pair< num_type, num_type > v12 = v.split();
+
+       //std::cout << "u:" << u12.first << " - " << u12.second << "\n";
+       //std::cout << "v:" << v12.first << " - " << v12.second << "\n";
+
+       /* m11 = u1*v1
+        * m12 = u1*v2
+        * m21 = u2*v1
+        * m22 = u2*v2
+        */
+       num_type m11 = naif(u12.first, v12.first);
+       num_type m12 = naif(u12.first, v12.second);
+       num_type m21 = naif(u12.second, v12.first);
+       num_type m22 = naif(u12.second, v12.second);
+
+       /*
+       printf("csize: %d\n", chunk_size);
+       std::cout << "11 " << m11 << "\n";
+       std::cout << "12 " << m12 << "\n";
+       std::cout << "21 " << m21 << "\n";
+       std::cout << "22 " << m22 << "\n";
+       */
+
+       /* u*v = (u1*v1) * 2^n + (u1*v2 + u2*v1) * 2^(n/2) + u2*v2
+        * PERO! Como los numeros estan "al reves" nos queda:
+        *     = m22 * 2^n + (m12 + m21) * 2^(n/2) + m11
+        */
+       num_type res;
+       res = m22 << chunk_size;
+       res = res + ((m12 + m21) << (chunk_size / 2));
+       res = res + m11;
+       res.sign = sign;
+       /*
+       std::cout << "r: " << res << "\n";
+       std::cout << "\n";
+       */
+       return res;
+}
+
+
+