diff --git a/c/qrcodegen.c b/c/qrcodegen.c
index a1466d0..45373e8 100644
--- a/c/qrcodegen.c
+++ b/c/qrcodegen.c
@@ -433,15 +433,15 @@ testable void calcReedSolomonGenerator(int degree, uint8_t result[]) {
 	// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
 	// drop the highest term, and store the rest of the coefficients in order of descending powers.
 	// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
-	int root = 1;
+	uint8_t root = 1;
 	for (int i = 0; i < degree; i++) {
 		// Multiply the current product by (x - r^i)
 		for (int j = 0; j < degree; j++) {
-			result[j] = finiteFieldMultiply(result[j], (uint8_t)root);
+			result[j] = finiteFieldMultiply(result[j], root);
 			if (j + 1 < degree)
 				result[j] ^= result[j + 1];
 		}
-		root = (root << 1) ^ ((root >> 7) * 0x11D);  // Multiply by 0x02 mod GF(2^8/0x11D)
+		root = finiteFieldMultiply(root, 0x02);
 	}
 }
 
diff --git a/cpp/QrCode.cpp b/cpp/QrCode.cpp
index 8448c14..579c30f 100644
--- a/cpp/QrCode.cpp
+++ b/cpp/QrCode.cpp
@@ -580,15 +580,15 @@ QrCode::ReedSolomonGenerator::ReedSolomonGenerator(int degree) :
 	// Compute the product polynomial (x - r^0) * (x - r^1) * (x - r^2) * ... * (x - r^{degree-1}),
 	// drop the highest term, and store the rest of the coefficients in order of descending powers.
 	// Note that r = 0x02, which is a generator element of this field GF(2^8/0x11D).
-	int root = 1;
+	uint8_t root = 1;
 	for (int i = 0; i < degree; i++) {
 		// Multiply the current product by (x - r^i)
 		for (size_t j = 0; j < coefficients.size(); j++) {
-			coefficients.at(j) = multiply(coefficients.at(j), static_cast<uint8_t>(root));
+			coefficients.at(j) = multiply(coefficients.at(j), root);
 			if (j + 1 < coefficients.size())
 				coefficients.at(j) ^= coefficients.at(j + 1);
 		}
-		root = (root << 1) ^ ((root >> 7) * 0x11D);  // Multiply by 0x02 mod GF(2^8/0x11D)
+		root = multiply(root, 0x02);
 	}
 }
 
diff --git a/java/io/nayuki/qrcodegen/QrCode.java b/java/io/nayuki/qrcodegen/QrCode.java
index 27befd5..0b8646c 100644
--- a/java/io/nayuki/qrcodegen/QrCode.java
+++ b/java/io/nayuki/qrcodegen/QrCode.java
@@ -811,7 +811,7 @@ public final class QrCode {
 					if (j + 1 < coefficients.length)
 						coefficients[j] ^= coefficients[j + 1];
 				}
-				root = (root << 1) ^ ((root >>> 7) * 0x11D);  // Multiply by 0x02 mod GF(2^8/0x11D)
+				root = multiply(root, 0x02);
 			}
 		}
 		
diff --git a/javascript/qrcodegen.js b/javascript/qrcodegen.js
index 405432e..09b7ad0 100644
--- a/javascript/qrcodegen.js
+++ b/javascript/qrcodegen.js
@@ -932,7 +932,7 @@ var qrcodegen = new function() {
 				if (j + 1 < coefficients.length)
 					coefficients[j] ^= coefficients[j + 1];
 			}
-			root = (root << 1) ^ ((root >>> 7) * 0x11D);  // Multiply by 0x02 mod GF(2^8/0x11D)
+			root = ReedSolomonGenerator.multiply(root, 0x02);
 		}
 		
 		// Computes and returns the Reed-Solomon error correction codewords for the given sequence of data codewords.
diff --git a/python/qrcodegen.py b/python/qrcodegen.py
index 7edb2b3..4a0c59a 100644
--- a/python/qrcodegen.py
+++ b/python/qrcodegen.py
@@ -779,7 +779,7 @@ class _ReedSolomonGenerator(object):
 				self.coefficients[j] = _ReedSolomonGenerator.multiply(self.coefficients[j], root)
 				if j + 1 < degree:
 					self.coefficients[j] ^= self.coefficients[j + 1]
-			root = (root << 1) ^ ((root >> 7) * 0x11D)  # Multiply by 0x02 mod GF(2^8/0x11D)
+			root = _ReedSolomonGenerator.multiply(root, 0x02)
 	
 	
 	def get_remainder(self, data):