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source/com/hurlant/math/MontgomeryReduction.as

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+package com.hurlant.math
+{
+	use namespace bi_internal;
+	/**
+	 * Montgomery reduction
+	 */
+	internal class MontgomeryReduction implements IReduction
+	{
+		private var m:BigInteger;
+		private var mp:int;
+		private var mpl:int;
+		private var mph:int;
+		private var um:int;
+		private var mt2:int;
+		public function MontgomeryReduction(m:BigInteger) {
+			this.m = m;
+			mp = m.invDigit();
+			mpl = mp & 0x7fff;
+			mph = mp>>15;
+			um = (1<<(BigInteger.DB-15))-1;
+			mt2 = 2*m.t;
+		}
+		/**
+		 * xR mod m
+		 */
+		public function convert(x:BigInteger):BigInteger {
+			var r:BigInteger = new BigInteger;
+		 	x.abs().dlShiftTo(m.t, r);
+		 	r.divRemTo(m, null, r);
+		 	if (x.s<0 && r.compareTo(BigInteger.ZERO)>0) {
+		 		m.subTo(r,r);
+		 	}
+		 	return r;
+		}
+		/**
+		 * x/R mod m
+		 */
+		public function revert(x:BigInteger):BigInteger {
+			var r:BigInteger = new BigInteger;
+			x.copyTo(r);
+			reduce(r);
+			return r;
+		}
+		/**
+		 * x = x/R mod m (HAC 14.32)
+		 */
+		public function reduce(x:BigInteger):void {
+			while (x.t<=mt2) {		// pad x so am has enough room later
+				x.a[x.t++] = 0;
+			}
+			for (var i:int=0; i<m.t; ++i) {
+				// faster way of calculating u0 = x[i]*mp mod DV
+				var j:int = x.a[i]&0x7fff;
+				var u0:int = (j*mpl+(((j*mph+(x.a[i]>>15)*mpl)&um)<<15))&BigInteger.DM;
+				// use am to combine the multiply-shift-add into one call
+				j = i+m.t;
+				x.a[j] += m.am(0, u0, x, i, 0, m.t);
+				// propagate carry
+				while (x.a[j]>=BigInteger.DV) {
+					x.a[j] -= BigInteger.DV;
+					x.a[++j]++;
+				}
+			}
+	 		x.clamp();
+		 	x.drShiftTo(m.t, x);
+	 		if (x.compareTo(m)>=0) {
+	 			x.subTo(m,x);
+	 		}
+		}
+		/**
+		 * r = "x^2/R mod m"; x != r
+		 */
+		public function sqrTo(x:BigInteger, r:BigInteger):void {
+			x.squareTo(r);
+			reduce(r);
+		}
+		/**
+		 * r = "xy/R mod m"; x,y != r
+		 */
+		public function mulTo(x:BigInteger, y:BigInteger, r:BigInteger):void {
+			x.multiplyTo(y,r);
+			reduce(r);
+		}
+	}
+}