Potenciación con división y conquista.

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

diff --git a/src/number.h b/src/number.h
index 2c2d281b1e7a1c8947ce3654c3e69b5d6415494a..43ed0b9f28fdaa2a1d8ec037e30e1fc2dc1670b5 100644 (file)
--- a/src/number.h
+++ b/src/number.h
@@ -297,8 +297,12 @@ template < typename N, typename E >
 std::ostream& operator<< (std::ostream& os, const number< N, E >& n)
 {
        // FIXME sacar una salida bonita en ASCII =)
-       for (typename number< N, E >::const_iterator i = n.chunk.begin();
-                       i != n.chunk.end(); ++i)
+       if (n.sign == positive)
+               os << "+ ";
+       else
+               os << "- ";
+       for (typename number< N, E >::const_reverse_iterator i = n.chunk.rbegin();
+                       i != n.chunk.rend(); ++i)
                os << std::setfill('0') << std::setw(sizeof(N) * 2) << std::hex
                        << *i << " ";
        return os;
@@ -460,4 +464,70 @@ number < N, E > naif(const number< N, E > &u, const number< N, E > &v)
 }
 
 
+/* Algoritmo de multiplicacion de Karatsuba-Ofman
+ * Ver los comentarios del algoritmo naif, es practicamente identico salvo en
+ * los calculos numericos que se especifican debajo.
+ */
+template < typename N, typename E >
+number < N, E > karatsuba(const number< N, E > &u, const number< N, E > &v)
+{
+       typedef number< N, E > num_type;
+
+       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;
+       }
+
+       if (chunk_size == 1) {
+               E tmp;
+               tmp = static_cast< E >(u.chunk[0]) * static_cast< E >(v.chunk[0]);
+               num_type tnum = num_type(static_cast< N* >(&tmp), 2, sign);
+               return tnum;
+       }
+
+       std::pair< num_type, num_type > u12 = u.split();
+       std::pair< num_type, num_type > v12 = v.split();
+
+       // Los nombres M, D y H los puso Rosita en clase, cambiar si se les
+       // ocurren algunos mejores!
+       // m = u1*v1
+       // d = u2*v2
+       // h = (u1+v1)*(u2+v2) = u1*u2+u1*v2+u2*v1+u2*v2
+       num_type m = karastuba(u12.second, v12.second);
+       num_type d = karastuba(u12.first, v12.first);
+       num_type h = karastuba(u12.second + v12.second,
+                       u12.first + v12.first);
+
+       // H-D-M = u1*u2+u1*v2+u2*v1+u2*v2 - u2*v2 - u1*v1 = u1*v2+u2*v1
+       // u1*v1 << base^N + u1*v2+u2*v1 << base^N/2 + u2*v2
+       num_type res;
+       res = (m << chunk_size) + ((h - d - m) << (chunk_size / 2) ) + h;
+       res.sign = sign;
+       return res;
+}
+
+
+/* Potenciacion usando multiplicaciones sucesivas.
+ * Toma dos parametros u y v, devuelve u^v; asume v positivo.
+ */
+template < typename N, typename E >
+number < N, E > pot_ko(const number< N, E > &u, const number< N, E > &v)
+{
+       number< N, E > res, i;
+
+       res = u;
+       res.sign = u.sign;
+
+       for (i = 1; i < v; i += 1) {
+               res *= u;
+       }
+
+       return res;
+}