gf256poly.js

/*
  Ported to JavaScript by Lazar Laszlo 2011 
  
  lazarsoft@gmail.com, www.lazarsoft.info
  
*/

/*
*
* Copyright 2007 ZXing authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
*      http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/


function GF256Poly(field,  coefficients)
{
	if (coefficients == null || coefficients.length == 0)
	{
		throw "System.ArgumentException";
	}
	this.field = field;
	var coefficientsLength = coefficients.length;
	if (coefficientsLength > 1 && coefficients[0] == 0)
	{
		// Leading term must be non-zero for anything except the constant polynomial "0"
		var firstNonZero = 1;
		while (firstNonZero < coefficientsLength && coefficients[firstNonZero] == 0)
		{
			firstNonZero++;
		}
		if (firstNonZero == coefficientsLength)
		{
			this.coefficients = field.Zero.coefficients;
		}
		else
		{
			this.coefficients = new Array(coefficientsLength - firstNonZero);
			for(var i=0;i<this.coefficients.length;i++)this.coefficients[i]=0;
			//Array.Copy(coefficients, firstNonZero, this.coefficients, 0, this.coefficients.length);
			for(var ci=0;ci<this.coefficients.length;ci++)this.coefficients[ci]=coefficients[firstNonZero+ci];
		}
	}
	else
	{
		this.coefficients = coefficients;
	}
	
	this.__defineGetter__("Zero", function()
	{
		return this.coefficients[0] == 0;
	});
	this.__defineGetter__("Degree", function()
	{
		return this.coefficients.length - 1;
	});
	this.__defineGetter__("Coefficients", function()
	{
		return this.coefficients;
	});
	
	this.getCoefficient=function( degree)
	{
		return this.coefficients[this.coefficients.length - 1 - degree];
	}
	
	this.evaluateAt=function( a)
	{
		if (a == 0)
		{
			// Just return the x^0 coefficient
			return this.getCoefficient(0);
		}
		var size = this.coefficients.length;
		if (a == 1)
		{
			// Just the sum of the coefficients
			var result = 0;
			for (var i = 0; i < size; i++)
			{
				result = GF256.addOrSubtract(result, this.coefficients[i]);
			}
			return result;
		}
		var result2 = this.coefficients[0];
		for (var i = 1; i < size; i++)
		{
			result2 = GF256.addOrSubtract(this.field.multiply(a, result2), this.coefficients[i]);
		}
		return result2;
	}
	
	this.addOrSubtract=function( other)
		{
			if (this.field != other.field)
			{
				throw "GF256Polys do not have same GF256 field";
			}
			if (this.Zero)
			{
				return other;
			}
			if (other.Zero)
			{
				return this;
			}
			
			var smallerCoefficients = this.coefficients;
			var largerCoefficients = other.coefficients;
			if (smallerCoefficients.length > largerCoefficients.length)
			{
				var temp = smallerCoefficients;
				smallerCoefficients = largerCoefficients;
				largerCoefficients = temp;
			}
			var sumDiff = new Array(largerCoefficients.length);
			var lengthDiff = largerCoefficients.length - smallerCoefficients.length;
			// Copy high-order terms only found in higher-degree polynomial's coefficients
			//Array.Copy(largerCoefficients, 0, sumDiff, 0, lengthDiff);
			for(var ci=0;ci<lengthDiff;ci++)sumDiff[ci]=largerCoefficients[ci];
			
			for (var i = lengthDiff; i < largerCoefficients.length; i++)
			{
				sumDiff[i] = GF256.addOrSubtract(smallerCoefficients[i - lengthDiff], largerCoefficients[i]);
			}
			
			return new GF256Poly(field, sumDiff);
	}
	this.multiply1=function( other)
		{
			if (this.field!=other.field)
			{
				throw "GF256Polys do not have same GF256 field";
			}
			if (this.Zero || other.Zero)
			{
				return this.field.Zero;
			}
			var aCoefficients = this.coefficients;
			var aLength = aCoefficients.length;
			var bCoefficients = other.coefficients;
			var bLength = bCoefficients.length;
			var product = new Array(aLength + bLength - 1);
			for (var i = 0; i < aLength; i++)
			{
				var aCoeff = aCoefficients[i];
				for (var j = 0; j < bLength; j++)
				{
					product[i + j] = GF256.addOrSubtract(product[i + j], this.field.multiply(aCoeff, bCoefficients[j]));
				}
			}
			return new GF256Poly(this.field, product);
		}
	this.multiply2=function( scalar)
		{
			if (scalar == 0)
			{
				return this.field.Zero;
			}
			if (scalar == 1)
			{
				return this;
			}
			var size = this.coefficients.length;
			var product = new Array(size);
			for (var i = 0; i < size; i++)
			{
				product[i] = this.field.multiply(this.coefficients[i], scalar);
			}
			return new GF256Poly(this.field, product);
		}
	this.multiplyByMonomial=function( degree,  coefficient)
		{
			if (degree < 0)
			{
				throw "System.ArgumentException";
			}
			if (coefficient == 0)
			{
				return this.field.Zero;
			}
			var size = this.coefficients.length;
			var product = new Array(size + degree);
			for(var i=0;i<product.length;i++)product[i]=0;
			for (var i = 0; i < size; i++)
			{
				product[i] = this.field.multiply(this.coefficients[i], coefficient);
			}
			return new GF256Poly(this.field, product);
		}
	this.divide=function( other)
		{
			if (this.field!=other.field)
			{
				throw "GF256Polys do not have same GF256 field";
			}
			if (other.Zero)
			{
				throw "Divide by 0";
			}
			
			var quotient = this.field.Zero;
			var remainder = this;
			
			var denominatorLeadingTerm = other.getCoefficient(other.Degree);
			var inverseDenominatorLeadingTerm = this.field.inverse(denominatorLeadingTerm);
			
			while (remainder.Degree >= other.Degree && !remainder.Zero)
			{
				var degreeDifference = remainder.Degree - other.Degree;
				var scale = this.field.multiply(remainder.getCoefficient(remainder.Degree), inverseDenominatorLeadingTerm);
				var term = other.multiplyByMonomial(degreeDifference, scale);
				var iterationQuotient = this.field.buildMonomial(degreeDifference, scale);
				quotient = quotient.addOrSubtract(iterationQuotient);
				remainder = remainder.addOrSubtract(term);
			}
			
			return new Array(quotient, remainder);
		}
}