1. Overview
Sometimes, when programming in Java, we may need to work with integer values that exceed the limits of primitive types like the long type. The BigInteger class in allows us to do exactly that. For example, we need to use the BigInteger class to calculate the factorial of 100.
The BigInteger class provides two public multiplication methods, multiply and parallelMultiply. Although their usage is similar and they return the same mathematical result, one may be preferable to the other for certain cases.
In this tutorial, we’ll compare the multiply and parallelMultiply methods of the BigInteger class.
2. The multiply Method
The multiply method of the BigInteger class multiplies two BigInteger instances. Let’s look at an example that shows how to use this method:
BigInteger bigInteger1 = new BigInteger("131224324234234234234313");
BigInteger bigInteger2 = new BigInteger("13345663456346435648234313");
BigInteger result = bigInteger1.multiply(bigInteger2);
After creating two BigInteger instances, bigInteger1 and bigInteger2, we multiply them using the multiply() method. We assign the result of multiplication to the result variable, which is also of type BigInteger.
3. The parallelMultiply Method
The parallelMultiply method of the BigInteger class is another option for multiplying two BigInteger instances. Its usage is similar to the usage of the multiply method:
BigInteger bigInteger1 = new BigInteger("131224324234234234234313");
BigInteger bigInteger2 = new BigInteger("13345663456346435648234313");
BigInteger result = bigInteger1.parallelMultiply(bigInteger2);
This method has been available since Java 19.
4. Comparing the Implementations
Let’s start by comparing the implementation of the two methods. The public multiply method in BigInteger.java calls a private multiply method:
public BigInteger multiply(BigInteger val) {
return multiply(val, false, false, 0);
}
The parallelMultiply method also calls the same private multiply method:
public BigInteger parallelMultiply(BigInteger val) {
return multiply(val, false, true, 0);
}
The difference between them is the value of the third argument of multiply. It’s false in the first one while it’s true in the second one. Let’s check the signature of the private multiply method together with its return type:
private BigInteger multiply(BigInteger val, boolean isRecursion, boolean parallel, int depth)The name of the third parameter is parallel. This parameter specifies whether the multiplication operation is done in parallel.
Indeed, the multiply method speeds up the multiplication process by using different algorithms depending on the values of the multiplier and multiplicand. It uses the Karatsuba Algorithm for large numbers and the three-way Toom-Cook Algorithm for huge numbers consisting of several thousands of bits.
The three-way Toom Cook Algorithm can split two large integers into smaller integers and parallelize the multiplication of smaller integers. Therefore, it reduces the computational time complexity, leading to a faster calculation. So, we may prefer to use the parallelMultiply method while multiplying huge numbers. However, the parallelMultiply method might use more CPU and memory to compute the multiplication faster.
According to the reported test results, the calculation of the 100000000th Fibonacci number using parallelMultiply might be 2.75 times faster than using multiply.
5. Conclusion
In this article, we compared the multiply and parallelMultiply methods of the BigInteger class. First, we saw the usage of both methods. Their usage is the same.
Then, we briefly discussed their implementation details. We saw that they used the same private multiply method under the hood. However, the parallelMultiply method uses a parallel implementation of the three-way Toom-Cook method for huge integers. Therefore, it’s faster than the multiply method for integers consisting of several thousands of bits.
