X-Git-Url: https://git.llucax.com/z.facultad/75.29/dale.git/blobdiff_plain/c7567533704ad4178845ba1348bd6316a42da56d..4a91a736401518a4cfe3a7f5e814a2510fb39f40:/src/number.h?ds=sidebyside

diff --git a/src/number.h b/src/number.h
index 3a42d7e..dfd7934 100644
--- a/src/number.h
+++ b/src/number.h
@@ -7,12 +7,21 @@
 #include <deque>
 #include <utility>
 #include <algorithm>
-#include <iterator>
+#include <iomanip>
 #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. */
 
+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
 {
@@ -20,7 +29,6 @@ struct number
 	// 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;
@@ -76,7 +84,10 @@ struct number
 	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;
@@ -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::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;
 }
 
@@ -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
-	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
-	for ( ; i < full_size; i++)
+	par.second.chunk[0] = chunk[i];
+	for (i++ ; i < full_size; 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 >
-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;
 
@@ -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
-	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
@@ -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;
+}
+
+
+