**1. Overview**

In this article, we will see some useful Mathematical Operations available in the Guava Library.

There are four maths utility classes available with Guava:

*IntMath* – operation on int values
*LongMath* – operations on long values
*BigIntegerMath* – operations on *BigIntegers*
*DoubleMath* – operations on double values

**2. ***IntMath* Utility

*IntMath* is used to perform mathematical operations on Integer values. We'll go through the available method list explaining each of their behavior.

**2.1. ***binomial(int n, int k)*

This function calculates the binomial coefficient of n and k. It makes sure that the result is within the integer range. Otherwise, it gives the *Integer.MAX_VALUE*. The answer can be derived using the formula n/k(n-k):

```
@Test
public void whenBinomialOnTwoInt_shouldReturnResultIfUnderInt() {
int result = IntMath.binomial(6, 3);
assertEquals(20, result);
}
@Test
public void whenBinomialOnTwoInt_shouldReturnIntMaxIfOVerflowInt() {
int result = IntMath.binomial(Integer.MAX_VALUE, 3);
assertEquals(Integer.MAX_VALUE, result);
}
```

**2.2. ***ceilingPowerOfTwo(int x)*

This calculates the value of the smallest power of two which is greater than or equal to x. The result n is such that 2^(n-1) < x < 2 ^n:

```
@Test
public void whenCeilPowOfTwoInt_shouldReturnResult() {
int result = IntMath.ceilingPowerOfTwo(20);
assertEquals(32, result);
}
```

**2.3. ***checkedAdd(int a, int b) *and Others

This function calculates the sum of the two parameters. This one provides an additional check which Throws *ArithmeticException* if the result overflows:

```
@Test
public void whenAddTwoInt_shouldReturnTheSumIfNotOverflow() {
int result = IntMath.checkedAdd(1, 2);
assertEquals(3, result);
}
@Test(expected = ArithmeticException.class)
public void whenAddTwoInt_shouldThrowArithmeticExceptionIfOverflow() {
IntMath.checkedAdd(Integer.MAX_VALUE, 100);
}
```

Guava has checked methods for three other operators which can overflow: *checkedMultiply*, *checkedPow, *and *checkedSubtract*.

**2.4. ***divide(int p, int q, RoundingMode mode)*

This is a simple divide but allows us to define a rounding mode:

```
@Test
public void whenDivideTwoInt_shouldReturnTheResultForCeilingRounding() {
int result = IntMath.divide(10, 3, RoundingMode.CEILING);
assertEquals(4, result);
}
@Test(expected = ArithmeticException.class)
public void whenDivideTwoInt_shouldThrowArithmeticExIfRoundNotDefinedButNeeded() {
IntMath.divide(10, 3, RoundingMode.UNNECESSARY);
}
```

**2.5. ***factorial(int n)*

Calculates the factorial value of n. i.e the product of the first n positive integers. Returns 1 if n = 0 and returns *Integer.MAX_VALUE* if the result does not fit in for int range. The result can be obtained by n x (n-1) x (n-2) x ….. x 2 x 1:

```
@Test
public void whenFactorialInt_shouldReturnTheResultIfInIntRange() {
int result = IntMath.factorial(5);
assertEquals(120, result);
}
@Test
public void whenFactorialInt_shouldReturnIntMaxIfNotInIntRange() {
int result = IntMath.factorial(Integer.MAX_VALUE);
assertEquals(Integer.MAX_VALUE, result);
}
```

**2.6. ***floorPowerOfTwo(int x)*

Returns the largest power of two, of which the results is less than or equal to x. The result n is such that 2^n < x < 2 ^(n+1):

```
@Test
public void whenFloorPowerOfInt_shouldReturnValue() {
int result = IntMath.floorPowerOfTwo(30);
assertEquals(16, result);
}
```

**2.7. ***gcd(int a, int b)*

This function gives us the greatest common divisor of a and b:

```
@Test
public void whenGcdOfTwoInt_shouldReturnValue() {
int result = IntMath.gcd(30, 40);
assertEquals(10, result);
}
```

**2.8. ***isPowerOfTwo(int x)*

Returns whether x is a power of two or not. Returns true if the value is a power of two and false otherwise:

```
@Test
public void givenIntOfPowerTwo_whenIsPowOfTwo_shouldReturnTrue() {
boolean result = IntMath.isPowerOfTwo(16);
assertTrue(result);
}
@Test
public void givenIntNotOfPowerTwo_whenIsPowOfTwo_shouldReturnFalse() {
boolean result = IntMath.isPowerOfTwo(20);
assertFalse(result);
}
```

**2.9. ***isPrime(int n)*

This function will tell us if the number passed is prime or not:

```
@Test
public void givenNonPrimeInt_whenIsPrime_shouldReturnFalse() {
boolean result = IntMath.isPrime(20);
assertFalse(result);
}
```

**2.10. ***log10(int x, RoundingMode mode)*

This API calculates the base-10 logarithm of the given number. The result is rounded using the provided rounding mode:

```
@Test
public void whenLog10Int_shouldReturnTheResultForCeilingRounding() {
int result = IntMath.log10(30, RoundingMode.CEILING);
assertEquals(2, result);
}
@Test(expected = ArithmeticException.class)
public void whenLog10Int_shouldThrowArithmeticExIfRoundNotDefinedButNeeded() {
IntMath.log10(30, RoundingMode.UNNECESSARY);
}
```

**2.11. ***log2(int x, RoundingMode mode)*

Returns the base-2 logarithm of the given number. The result is rounded using the provided rounding mode:

```
@Test
public void whenLog2Int_shouldReturnTheResultForCeilingRounding() {
int result = IntMath.log2(30, RoundingMode.CEILING);
assertEquals(5, result);
}
@Test(expected = ArithmeticException.class)
public void whenLog2Int_shouldThrowArithmeticExIfRoundNotDefinedButNeeded() {
IntMath.log2(30, RoundingMode.UNNECESSARY);
}
```

**2.12. ***mean(int x, int y)*

With this function we can calculate the mean of two values:

```
@Test
public void whenMeanTwoInt_shouldReturnTheResult() {
int result = IntMath.mean(30, 20);
assertEquals(25, result);
}
```

**2.13. ***mod(int x, int m)*

Returns the remainder of integer division of one number by the other:

```
@Test
public void whenModTwoInt_shouldReturnTheResult() {
int result = IntMath.mod(30, 4);
assertEquals(2, result);
}
```

**2.14. ***pow(int b, int k)*

Returns the value of b to the power of k:

```
@Test
public void whenPowTwoInt_shouldReturnTheResult() {
int result = IntMath.pow(6, 4);
assertEquals(1296, result);
}
```

**2.15. ***saturatedAdd(int a, int b)* and Others

A sum function with the benefit of controlling any overflows or underflows by returning the value *Integer.MAX_VALUE* or *Integer.MIN_VALUE* respectively when it occurs:

```
@Test:
public void whenSaturatedAddTwoInt_shouldReturnTheResult() {
int result = IntMath.saturatedAdd(6, 4);
assertEquals(10, result);
}
@Test
public void whenSaturatedAddTwoInt_shouldReturnIntMaxIfOverflow() {
int result = IntMath.saturatedAdd(Integer.MAX_VALUE, 1000);
assertEquals(Integer.MAX_VALUE, result);
}
```

There are three other saturated APIs: *saturatedMultiply*, *saturatedPow *and *saturatedSubtract*.

**2.16. ***sqrt(int x, RoundingMode mode)*

Returns the square root of the given number. The result is rounded using the provided rounding mode:

```
@Test
public void whenSqrtInt_shouldReturnTheResultForCeilingRounding() {
int result = IntMath.sqrt(30, RoundingMode.CEILING);
assertEquals(6, result);
}
@Test(expected = ArithmeticException.class)
public void whenSqrtInt_shouldThrowArithmeticExIfRoundNotDefinedButNeded() {
IntMath.sqrt(30, RoundingMode.UNNECESSARY);
}
```

**3. ***LongMath* Utility

*LongMath* has utilities for *Long* values. Most operations are similar to the *IntMath* utility, with an exceptional few described here.

**3.1. ***mod(long x, int m)* and *mod(long x, long m)*

Returns the x mod m. The remainder of integer division of x by m:

```
@Test
public void whenModLongAndInt_shouldModThemAndReturnTheResult() {
int result = LongMath.mod(30L, 4);
assertEquals(2, result);
}
```

```
@Test
public void whenModTwoLongValues_shouldModThemAndReturnTheResult() {
long result = LongMath.mod(30L, 4L);
assertEquals(2L, result);
}
```

**4. ***BigIntegerMath* Utility

*BigIntegerMath* is used to perform mathematical operations on type *BigInteger*.

This utility has some methods similar to the *IntMath.*

**5. DoubleMath Utility**

*DoubleMath* utility is used to perform an operation on double values.

Similar to the *BigInteger* utility, the number of available operations is limited and share similarity with *IntMath* utility. We will list some exceptional functions available only to this utility class.

**5.1. ***isMathematicalInteger(double x)*

Returns whether x is a mathematical integer. It checks if the number can be represented as an integer without a data loss:

```
@Test
public void givenInt_whenMathematicalDouble_shouldReturnTrue() {
boolean result = DoubleMath.isMathematicalInteger(5);
assertTrue(result);
}
@Test
public void givenDouble_whenMathematicalInt_shouldReturnFalse() {
boolean result = DoubleMath.isMathematicalInteger(5.2);
assertFalse(result);
}
```

**5.2. ***log2(double x)*

Calculates the base-2 logarithm of x:

```
@Test
public void whenLog2Double_shouldReturnResult() {
double result = DoubleMath.log2(4);
assertEquals(2, result, 0);
}
```

**6. Conclusion**

In this quick tutorial, we explored some useful Guava maths utility functions.

As always, the source code can be found over on GitHub.

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