From 57edd8276b149ac99cc685e4691294bec413f0cb Mon Sep 17 00:00:00 2001
From: Alberto Bertogli <albertogli@telpin.com.ar>
Date: Tue, 4 Oct 2005 04:32:59 +0000
Subject: [PATCH] Agregar karatsuba() y pot_ko(). En este patch se reintroduce
 karatsuba() (todavia no probado porque falta la resta, pero no deberia distar
 mucho de su implementacion final) y pot_ko(), tampoco probada. Soy un loco
 barbaro.

---
 src/number.h | 66 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 66 insertions(+)

diff --git a/src/number.h b/src/number.h
index 2c2d281..3d64955 100644
--- a/src/number.h
+++ b/src/number.h
@@ -460,4 +460,70 @@ 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++) {
+		res *= u;
+	}
+
+	return res;
+}
 
-- 
2.43.0