Brick Math

https://github.com/brick/math
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Brick Math is a PHP library for arbitrary-precision arithmetic operations with support for large...
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### Catching all MathException with try-catch

Source: https://github.com/brick/math/blob/main/README.md

Shows how to catch all exceptions thrown by the library using the MathException interface. The example attempts to divide by 3 and catches any MathException, including DivisionByZeroException and others.

```php
use Brick\Math\BigInteger;
use Brick\Math\Exception\MathException;

try {
    $number = BigInteger::of(1)->dividedBy(3);
} catch (MathException $e) {
    // ...
}
```

--------------------------------

### Create a BigInteger with of()

Source: https://github.com/brick/math/blob/main/README.md

Creates a BigInteger instance from an integer value. This is the base example for the parameter types section.

```php
$integer = BigInteger::of(123);
```

--------------------------------

### Install Brick\Math via Composer

Source: https://github.com/brick/math/blob/main/README.md

Use this command to install the brick/math package with Composer. Requires PHP 8.2 or later. GMP or BCMath extensions are recommended for faster calculations.

```bash
composer require brick/math
```

--------------------------------

### toString()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to its string representation.

```APIDOC
## toString()

### Description
Converts the number to its string representation.

### Method
toString()

### Return Value
- **string** - The string representation

### Examples
```php
echo BigInteger::of(-123)->toString(); // -123
echo BigDecimal::of('1.0')->toString(); // 1.0
echo BigDecimal::of('1')->toString(); // 1
echo BigRational::of('2/3')->toString(); // 2/3
echo BigRational::of('1/1')->toString(); // 1
```

```

--------------------------------

### min()

Source: https://github.com/brick/math/blob/main/README.md

Returns the minimum of this number and another number.

```APIDOC
## min()

### Description
Returns the minimum of this number and the given number.

### Method
min()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **BigNumber** - The smaller of the two numbers

```

--------------------------------

### BigInteger::fromBytes()

Source: https://github.com/brick/math/blob/main/README.md

Converts a byte string to a BigInteger.

```APIDOC
## [PHP] BigInteger::fromBytes()

### Description
Converts a byte string to a BigInteger.

### Method
Static method

### Signature
`public static function fromBytes(string $bytes): BigInteger`

### Parameters
- **$bytes** (string) - Required - The byte string to convert.

### Return Value
- **BigInteger** - The resulting BigInteger.

### Example
```php
$bigInteger = BigInteger::fromBytes("\x01\x02");
```
```

--------------------------------

### isZero()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether the number is equal to zero.

```APIDOC
## isZero()

### Description
Returns true if the number is zero, false otherwise.

### Method
isZero()

### Return Value
- **bool** - true if zero, false otherwise

```

--------------------------------

### BigInteger::power

Source: https://github.com/brick/math/blob/main/README.md

Raises a BigInteger to a power. Returns a new BigInteger.

```APIDOC
## [BigInteger::power]

### Description
Raises a BigInteger to a power. Returns a new BigInteger.

### Method
power

### Parameters
- **exponent** (int) - Required - The exponent.

### Request Example
```php
BigInteger::of(2)->power(10)
```

### Response
#### Success Response
- **result** (BigInteger) - The result of the exponentiation.

#### Response Example
```php
1024
```
```

--------------------------------

### clamp()

Source: https://github.com/brick/math/blob/main/README.md

Clamps this number to a range defined by a minimum and maximum value.

```APIDOC
## clamp()

### Description
Clamps this number to the range [min, max].

### Method
clamp()

### Parameters
- **min** (BigNumber) - Required - The lower bound
- **max** (BigNumber) - Required - The upper bound

### Return Value
- **BigNumber** - The clamped value

```

--------------------------------

### BigInteger::toBytes()

Source: https://github.com/brick/math/blob/main/README.md

Converts a BigInteger to a byte string.

```APIDOC
## [PHP] BigInteger::toBytes()

### Description
Converts a BigInteger to a byte string.

### Method
Instance method

### Signature
`public function toBytes(): string`

### Return Value
- **string** - The byte string representation of the BigInteger.

### Example
```php
$bytes = BigInteger::of(258)->toBytes();
```
```

--------------------------------

### isPositiveOrZero()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether the number is positive or zero.

```APIDOC
## isPositiveOrZero()

### Description
Returns true if the number is greater than or equal to zero, false otherwise.

### Method
isPositiveOrZero()

### Return Value
- **bool** - true if positive or zero, false otherwise

```

--------------------------------

### toBigRational()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to a BigRational. Always returns an exact result.

```APIDOC
## toBigRational()

### Description
Converts the number to a BigRational. Always returns an exact result.

### Method
toBigRational()

### Return Value
- **BigRational** - The converted value

```

--------------------------------

### max()

Source: https://github.com/brick/math/blob/main/README.md

Returns the maximum of this number and another number.

```APIDOC
## max()

### Description
Returns the maximum of this number and the given number.

### Method
max()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **BigNumber** - The larger of the two numbers

```

--------------------------------

### BigRational::power

Source: https://github.com/brick/math/blob/main/README.md

Raises a BigRational to a power. Returns a new BigRational.

```APIDOC
## [BigRational::power]

### Description
Raises a BigRational to a power. Returns a new BigRational.

### Method
power

### Parameters
- **exponent** (int) - Required - The exponent.

### Request Example
```php
BigRational::of('2/3')->power(2)
```

### Response
#### Success Response
- **result** (BigRational) - The result of the exponentiation.

#### Response Example
```php
4/9
```
```

--------------------------------

### dividedBy() usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Usage examples for division with different rounding modes. Unnecessary throws RoundingNecessaryException for non-exact division; Down truncates toward zero; Up rounds away from zero.

```php
use Brick\Math\BigInteger;
use Brick\Math\RoundingMode;

BigInteger::of(999)->dividedBy(3);                       // 333
BigInteger::of(1000)->dividedBy(3);                      // RoundingNecessaryException
BigInteger::of(1000)->dividedBy(3, RoundingMode::Down);  // 333
BigInteger::of(1000)->dividedBy(3, RoundingMode::Up);    // 334
```

--------------------------------

### plus(), minus(), multipliedBy() usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Usage examples for addition, subtraction, and multiplication. Note that '5.0' converts exactly to 5, while '2.5' causes a RoundingNecessaryException because it is not an integer.

```php
use Brick\Math\BigInteger;

BigInteger::of(10)->plus(5);              // 15
BigInteger::of(10)->minus('5.0');         // 5  ('5.0' converts exactly)
BigInteger::of(10)->multipliedBy('2.5');  // RoundingNecessaryException
```

--------------------------------

### BigInteger::and()

Source: https://github.com/brick/math/blob/main/README.md

Performs a bitwise AND operation between two BigIntegers.

```APIDOC
## [PHP] BigInteger::and()

### Description
Performs a bitwise AND operation between two BigIntegers.

### Method
Instance method

### Signature
`public function and(BigInteger|int|string $that): BigInteger`

### Parameters
- **$that** (BigInteger|int|string) - Required - The other operand.

### Return Value
- **BigInteger** - The result of the bitwise AND operation.

### Example
```php
$result = BigInteger::of(12)->and(10); // 8
```
```

--------------------------------

### isPositive()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether the number is positive.

```APIDOC
## isPositive()

### Description
Returns true if the number is greater than zero, false otherwise.

### Method
isPositive()

### Return Value
- **bool** - true if positive, false otherwise

```

--------------------------------

### power() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Usage example for exponentiation: 2^10 equals 1024.

```php
BigInteger::of(2)->power(10);   // 1024
```

--------------------------------

### isNegativeOrZero()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether the number is negative or zero.

```APIDOC
## isNegativeOrZero()

### Description
Returns true if the number is less than or equal to zero, false otherwise.

### Method
isNegativeOrZero()

### Return Value
- **bool** - true if negative or zero, false otherwise

```

--------------------------------

### toFloat()

Source: https://github.com/brick/math/blob/main/README.md

Returns an approximation of the number as a float. This is the only method that returns an approximation.

```APIDOC
## toFloat()

### Description
Returns an approximation of the number as a float. This is the only method that returns an approximation.

### Method
toFloat()

### Return Value
- **float** - The approximate value

### Warning
This method may return an infinite value.

```

--------------------------------

### BigDecimal::power

Source: https://github.com/brick/math/blob/main/README.md

Raises a BigDecimal to a power. Returns a new BigDecimal.

```APIDOC
## [BigDecimal::power]

### Description
Raises a BigDecimal to a power. Returns a new BigDecimal.

### Method
power

### Parameters
- **exponent** (int) - Required - The exponent.

### Request Example
```php
BigDecimal::of('1.2')->power(2)
```

### Response
#### Success Response
- **result** (BigDecimal) - The result of the exponentiation.

#### Response Example
```php
1.44
```
```

--------------------------------

### Converting floats to BigDecimal with fromFloatExact and fromFloatShortest

Source: https://github.com/brick/math/blob/main/README.md

The of() method does not accept float values because casting a float to string can be lossy. Use fromFloatExact to get the exact IEEE-754 representation, or fromFloatShortest for the shortest decimal that round-trips back to the same float.

```php
// Exact IEEE-754 representation — the value the float actually holds:
BigDecimal::fromFloatExact(0.1); // 0.1000000000000000055511151231257827021181583404541015625

// Shortest decimal that round-trips back to the same float:
BigDecimal::fromFloatShortest(0.1); // 0.1
```

--------------------------------

### abs()

Source: https://github.com/brick/math/blob/main/README.md

Returns the absolute value of the number.

```APIDOC
## abs()

### Description
Returns the absolute value of the number.

### Method
abs()

### Return Value
- **BigNumber** - The absolute value

```

--------------------------------

### isNegative()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether the number is negative.

```APIDOC
## isNegative()

### Description
Returns true if the number is less than zero, false otherwise.

### Method
isNegative()

### Return Value
- **bool** - true if negative, false otherwise

```

--------------------------------

### isEqualTo()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether this number is equal to another number.

```APIDOC
## isEqualTo()

### Description
Returns true if this number is equal to the given number, false otherwise.

### Method
isEqualTo()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **bool** - true if equal, false otherwise

```

--------------------------------

### BigInteger::or()

Source: https://github.com/brick/math/blob/main/README.md

Performs a bitwise OR operation between two BigIntegers.

```APIDOC
## [PHP] BigInteger::or()

### Description
Performs a bitwise OR operation between two BigIntegers.

### Method
Instance method

### Signature
`public function or(BigInteger|int|string $that): BigInteger`

### Parameters
- **$that** (BigInteger|int|string) - Required - The other operand.

### Return Value
- **BigInteger** - The result of the bitwise OR operation.

### Example
```php
$result = BigInteger::of(12)->or(10); // 14
```
```

--------------------------------

### quotient(), remainder(), quotientAndRemainder() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigDecimal.md

Example usage of division methods. quotient(3) returns 2, remainder(3) returns 1.5, and quotientAndRemainder('3') returns [2, 1.5]. Remainder, when non-zero, has the same sign as the dividend.

```php
use Brick\Math\BigDecimal;

BigDecimal::of('7.5')->quotient(3);        // 2
BigDecimal::of('7.5')->remainder(3);       // 1.5
[$q, $r] = BigDecimal::of('7.5')->quotientAndRemainder('3');   // [2, 1.5]
```

--------------------------------

### toInt()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to a native int if possible, throwing an exception otherwise.

```APIDOC
## toInt()

### Description
Converts the number to a native int if possible, throwing an exception otherwise.

### Method
toInt()

### Return Value
- **int** - The converted value

### Exceptions
- **Exception** - If the conversion is not possible

```

--------------------------------

### BigInteger::isBitSet()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether a specific bit in the BigInteger is set.

```APIDOC
## [PHP] BigInteger::isBitSet()

### Description
Checks whether a specific bit in the BigInteger is set.

### Method
Instance method

### Signature
`public function isBitSet(int $index): bool`

### Parameters
- **$index** (int) - Required - The bit index to check.

### Return Value
- **bool** - True if the bit is set, false otherwise.

### Example
```php
$isSet = BigInteger::of(12)->isBitSet(2); // true
```
```

--------------------------------

### negated()

Source: https://github.com/brick/math/blob/main/README.md

Returns the opposite value of the number.

```APIDOC
## negated()

### Description
Returns the negated value of the number.

### Method
negated()

### Return Value
- **BigNumber** - The opposite value

```

--------------------------------

### BigInteger::toArbitraryBase()

Source: https://github.com/brick/math/blob/main/README.md

Converts a BigInteger to a string representation using a custom single-byte alphabet.

```APIDOC
## [PHP] BigInteger::toArbitraryBase()

### Description
Converts a BigInteger to a string representation using a custom single-byte alphabet.

### Method
Instance method

### Signature
`public function toArbitraryBase(string $alphabet): string`

### Parameters
- **$alphabet** (string) - Required - The custom alphabet used for the base.

### Return Value
- **string** - The string representation of the BigInteger in the given alphabet.

### Example
```php
$string = BigInteger::of(5)->toArbitraryBase('ab'); // 'bab'
```
```

--------------------------------

### String conversion with toString and cast

Source: https://github.com/brick/math/blob/main/README.md

Shows that toString() and (string) cast are equivalent for converting a BigInteger to string.

```php
echo BigInteger::of(123)->toString();
echo (string) BigInteger::of(123);
```

--------------------------------

### BigInteger::remainder

Source: https://github.com/brick/math/blob/main/README.md

Computes the remainder of a BigInteger division.

```APIDOC
## [BigInteger::remainder]

### Description
Computes the remainder of a BigInteger division.

### Method
remainder

### Parameters
- **operand** (mixed) - Required - The divisor.

### Request Example
```php
BigInteger::of(1000)->remainder(3)
```

### Response
#### Success Response
- **result** (BigInteger) - The remainder.

#### Response Example
```php
1
```
```

--------------------------------

### BigInteger::quotient

Source: https://github.com/brick/math/blob/main/README.md

Computes the quotient of a BigInteger division, discarding the remainder.

```APIDOC
## [BigInteger::quotient]

### Description
Computes the quotient of a BigInteger division, discarding the remainder.

### Method
quotient

### Parameters
- **operand** (mixed) - Required - The divisor.

### Request Example
```php
BigInteger::of(1000)->quotient(3)
```

### Response
#### Success Response
- **result** (BigInteger) - The quotient.

#### Response Example
```php
333
```
```

--------------------------------

### BigInteger::xor()

Source: https://github.com/brick/math/blob/main/README.md

Performs a bitwise XOR operation between two BigIntegers.

```APIDOC
## [PHP] BigInteger::xor()

### Description
Performs a bitwise XOR operation between two BigIntegers.

### Method
Instance method

### Signature
`public function xor(BigInteger|int|string $that): BigInteger`

### Parameters
- **$that** (BigInteger|int|string) - Required - The other operand.

### Return Value
- **BigInteger** - The result of the bitwise XOR operation.

### Example
```php
$result = BigInteger::of(12)->xor(10); // 6
```
```

--------------------------------

### BigInteger::nthRoot

Source: https://github.com/brick/math/blob/main/README.md

Computes the nth root of a BigInteger. Returns a new BigInteger.

```APIDOC
## [BigInteger::nthRoot]

### Description
Computes the nth root of a BigInteger. Returns a new BigInteger.

### Method
nthRoot

### Parameters
- **n** (int) - Required - The root degree.

### Request Example
```php
BigInteger::of(27)->nthRoot(3)
```

### Response
#### Success Response
- **result** (BigInteger) - The nth root.

#### Response Example
```php
3
```
```

--------------------------------

### BigInteger::plus

Source: https://github.com/brick/math/blob/main/README.md

Adds a number to a BigInteger. Returns a new BigInteger with the sum.

```APIDOC
## [BigInteger::plus]

### Description
Adds a number to a BigInteger. Returns a new BigInteger with the sum.

### Method
plus

### Parameters
- **operand** (mixed) - Required - The number to add.

### Request Example
```php
BigInteger::of(1)->plus(2)
```

### Response
#### Success Response
- **result** (BigInteger) - The sum.

#### Response Example
```php
3
```
```

--------------------------------

### toBigInteger()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to a BigInteger. Throws a RoundingNecessaryException if the conversion is not exact.

```APIDOC
## toBigInteger()

### Description
Converts the number to a BigInteger. Throws a RoundingNecessaryException if the conversion is not exact.

### Method
toBigInteger()

### Return Value
- **BigInteger** - The converted value

### Exceptions
- **RoundingNecessaryException** - If the conversion is not exact

```

--------------------------------

### BigInteger::getBitLength()

Source: https://github.com/brick/math/blob/main/README.md

Returns the number of bits in the minimal two's-complement representation of the BigInteger.

```APIDOC
## [PHP] BigInteger::getBitLength()

### Description
Returns the number of bits in the minimal two's-complement representation of the BigInteger.

### Method
Instance method

### Signature
`public function getBitLength(): int`

### Return Value
- **int** - The bit length.

### Example
```php
$length = BigInteger::of(255)->getBitLength(); // 8
```
```

--------------------------------

### BigInteger::not()

Source: https://github.com/brick/math/blob/main/README.md

Performs a bitwise NOT operation on a BigInteger.

```APIDOC
## [PHP] BigInteger::not()

### Description
Performs a bitwise NOT operation on a BigInteger.

### Method
Instance method

### Signature
`public function not(): BigInteger`

### Return Value
- **BigInteger** - The result of the bitwise NOT operation.

### Example
```php
$result = BigInteger::of(12)->not(); // -13
```
```

--------------------------------

### toScale()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to a BigDecimal with a given scale, rounding if necessary.

```APIDOC
## toScale()

### Description
Converts the number to a BigDecimal with the specified scale, rounding the result if necessary.

### Method
toScale()

### Parameters
- **scale** (int) - Required - The number of decimal places
- **roundingMode** (RoundingMode) - Required - The rounding mode to use

### Return Value
- **BigDecimal** - The converted value with the specified scale

### Example
```php
echo BigRational::of('2/3')->toScale(5, RoundingMode::Up); // 0.66667
```

```

--------------------------------

### isGreaterThan()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether this number is greater than another number.

```APIDOC
## isGreaterThan()

### Description
Returns true if this number is greater than the given number, false otherwise.

### Method
isGreaterThan()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **bool** - true if greater than, false otherwise

```

--------------------------------

### BigInteger::modInverse

Source: https://github.com/brick/math/blob/main/README.md

Computes the modular inverse of a BigInteger. Returns a new BigInteger.

```APIDOC
## [BigInteger::modInverse]

### Description
Computes the modular inverse of a BigInteger. Returns a new BigInteger.

### Method
modInverse

### Parameters
- **modulus** (mixed) - Required - The modulus.

### Request Example
```php
BigInteger::of(3)->modInverse(11)
```

### Response
#### Success Response
- **result** (BigInteger) - The modular inverse.

#### Response Example
```php
4
```
```

--------------------------------

### BigInteger::quotientAndRemainder

Source: https://github.com/brick/math/blob/main/README.md

Computes both the quotient and remainder of a BigInteger division in one call.

```APIDOC
## [BigInteger::quotientAndRemainder]

### Description
Computes both the quotient and remainder of a BigInteger division in one call.

### Method
quotientAndRemainder

### Parameters
- **operand** (mixed) - Required - The divisor.

### Request Example
```php
[$quotient, $remainder] = BigInteger::of(1000)->quotientAndRemainder(3);
```

### Response
#### Success Response
- **quotient** (BigInteger) - The quotient.
- **remainder** (BigInteger) - The remainder.

#### Response Example
```php
[333, 1]
```
```

--------------------------------

### power() examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigRational.md

Shows positive and negative exponent results. Throws DivisionByZeroException when the base is zero and the exponent is negative.

```php
BigRational::of('2/3')->power(3);       // 8/27
BigRational::of('2/3')->power(-3);      // 27/8
BigRational::of(0)->power(-1);          // DivisionByZeroException
```

--------------------------------

### BigInteger::sqrt

Source: https://github.com/brick/math/blob/main/README.md

Computes the square root of a BigInteger. Returns a new BigInteger.

```APIDOC
## [BigInteger::sqrt]

### Description
Computes the square root of a BigInteger. Returns a new BigInteger.

### Method
sqrt

### Parameters
None

### Request Example
```php
BigInteger::of(16)->sqrt()
```

### Response
#### Success Response
- **result** (BigInteger) - The square root.

#### Response Example
```php
4
```
```

--------------------------------

### fromBase() usage

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Examples of parsing numbers in bases 16, 2, and 36.

```php
use Brick\Math\BigInteger;

BigInteger::fromBase('ff', 16);    // 255
BigInteger::fromBase('-101', 2);   // -5
BigInteger::fromBase('zz', 36);    // 1295
```

--------------------------------

### BigInteger::multipliedBy

Source: https://github.com/brick/math/blob/main/README.md

Multiplies a BigInteger by a number. Returns a new BigInteger with the product.

```APIDOC
## [BigInteger::multipliedBy]

### Description
Multiplies a BigInteger by a number. Returns a new BigInteger with the product.

### Method
multipliedBy

### Parameters
- **operand** (mixed) - Required - The multiplier.

### Request Example
```php
BigInteger::of(1)->multipliedBy(3)
```

### Response
#### Success Response
- **result** (BigInteger) - The product.

#### Response Example
```php
3
```
```

--------------------------------

### isLessThan()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether this number is less than another number.

```APIDOC
## isLessThan()

### Description
Returns true if this number is less than the given number, false otherwise.

### Method
isLessThan()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **bool** - true if less than, false otherwise

```

--------------------------------

### toBigDecimal()

Source: https://github.com/brick/math/blob/main/README.md

Converts the number to a BigDecimal. Throws a RoundingNecessaryException if the conversion is not exact.

```APIDOC
## toBigDecimal()

### Description
Converts the number to a BigDecimal. Throws a RoundingNecessaryException if the conversion is not exact.

### Method
toBigDecimal()

### Return Value
- **BigDecimal** - The converted value

### Exceptions
- **RoundingNecessaryException** - If the conversion is not exact

```

--------------------------------

### BigInteger::toBase()

Source: https://github.com/brick/math/blob/main/README.md

Converts a BigInteger to a string representation in a given base (2 to 36). Output is lowercase for bases above 10.

```APIDOC
## [PHP] BigInteger::toBase()

### Description
Converts a BigInteger to a string representation in a given base (2 to 36). Output is lowercase for bases above 10.

### Method
Instance method

### Signature
`public function toBase(int $base): string`

### Parameters
- **$base** (int) - Required - The base to convert to, between 2 and 36.

### Return Value
- **string** - The string representation of the BigInteger in the given base.

### Example
```php
$string = BigInteger::of(255)->toBase(16); // 'ff'
```
```

--------------------------------

### toArbitraryBase() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Converts 5 using alphabet 'ab' to 'bab'.

```php
BigInteger::of(5)->toArbitraryBase('ab');   // bab
```

--------------------------------

### BigInteger::modPow

Source: https://github.com/brick/math/blob/main/README.md

Computes modular exponentiation of a BigInteger. Returns a new BigInteger.

```APIDOC
## [BigInteger::modPow]

### Description
Computes modular exponentiation of a BigInteger. Returns a new BigInteger.

### Method
modPow

### Parameters
- **exponent** (mixed) - Required - The exponent.
- **modulus** (mixed) - Required - The modulus.

### Request Example
```php
BigInteger::of(2)->modPow(10, 1000)
```

### Response
#### Success Response
- **result** (BigInteger) - The result of modular exponentiation.

#### Response Example
```php
24
```
```

--------------------------------

### BigRational::reciprocal

Source: https://github.com/brick/math/blob/main/README.md

Computes the reciprocal of a BigRational. Returns a new BigRational.

```APIDOC
## [BigRational::reciprocal]

### Description
Computes the reciprocal of a BigRational. Returns a new BigRational.

### Method
reciprocal

### Parameters
None

### Request Example
```php
BigRational::of('2/3')->reciprocal()
```

### Response
#### Success Response
- **result** (BigRational) - The reciprocal.

#### Response Example
```php
3/2
```
```

--------------------------------

### BigInteger::mod

Source: https://github.com/brick/math/blob/main/README.md

Computes the modulo of a BigInteger. Returns a new BigInteger.

```APIDOC
## [BigInteger::mod]

### Description
Computes the modulo of a BigInteger. Returns a new BigInteger.

### Method
mod

### Parameters
- **modulus** (mixed) - Required - The modulus.

### Request Example
```php
BigInteger::of(10)->mod(3)
```

### Response
#### Success Response
- **result** (BigInteger) - The remainder.

#### Response Example
```php
1
```
```

--------------------------------

### fromBytes() usage

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Examples of parsing byte strings with and without sign interpretation.

```php
use Brick\Math\BigInteger;

BigInteger::fromBytes("\x01\x00");        // 256
BigInteger::fromBytes("\xff", false);      // 255
BigInteger::fromBytes("\xff");             // -1 (two's complement)
```

--------------------------------

### BigInteger::plus()

Source: https://github.com/brick/math/blob/main/README.md

Adds a number to the current BigInteger and returns a new BigInteger. The parameter accepts the same types as of().

```APIDOC
## [METHOD] BigInteger::plus()

### Description
Adds a number to the current BigInteger and returns a new BigInteger. The parameter accepts the same types as of().

### Method
Instance method

### Parameters
- **value** (int|string|BigInteger) - Required - The number to add.

### Return Value
- **BigInteger** - A new BigInteger with the sum.

### Example
```php
echo $ten->plus(5); // 15
```
```

--------------------------------

### BigInteger quotient and remainder separately

Source: https://github.com/brick/math/blob/main/README.md

quotient() returns the integer quotient, remainder() returns the remainder of the division.

```php
echo BigInteger::of(1000)->quotient(3); // 333
echo BigInteger::of(1000)->remainder(3); // 1
```

--------------------------------

### BigDecimal::parse() with maxDigits and allowedSyntax examples

Source: https://github.com/brick/math/blob/main/README.md

Shows parse() behavior: valid decimal input returns the number; exponent notation is rejected when not allowed by NumberSyntax::DECIMAL; scientific notation with too many digits is rejected before expansion.

```php
BigDecimal::parse('123.45', allowedSyntax: NumberSyntax::DECIMAL, maxDigits: 20); // 123.45
BigDecimal::parse('1.2e3', allowedSyntax: NumberSyntax::DECIMAL, maxDigits: 20); // NumberFormatException (exponent not allowed)
BigDecimal::parse('1e1000000000', allowedSyntax: NumberSyntax::SCIENTIFIC, maxDigits: 20); // NumberFormatException (too many digits)
```

--------------------------------

### isGreaterThanOrEqualTo()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether this number is greater than or equal to another number.

```APIDOC
## isGreaterThanOrEqualTo()

### Description
Returns true if this number is greater than or equal to the given number, false otherwise.

### Method
isGreaterThanOrEqualTo()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **bool** - true if greater than or equal, false otherwise

```

--------------------------------

### BigDecimal::nthRoot

Source: https://github.com/brick/math/blob/main/README.md

Computes the nth root of a BigDecimal. Returns a new BigDecimal.

```APIDOC
## [BigDecimal::nthRoot]

### Description
Computes the nth root of a BigDecimal. Returns a new BigDecimal.

### Method
nthRoot

### Parameters
- **n** (int) - Required - The root degree.

### Request Example
```php
BigDecimal::of('27')->nthRoot(3)
```

### Response
#### Success Response
- **result** (BigDecimal) - The nth root.

#### Response Example
```php
3
```
```

--------------------------------

### reciprocal() examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigRational.md

Shows reciprocal of 2/3 is 3/2. Throws DivisionByZeroException when the number is zero.

```php
BigRational::of('2/3')->reciprocal();   // 3/2
BigRational::of(0)->reciprocal();        // DivisionByZeroException
```

--------------------------------

### BigInteger::gcdAll

Source: https://github.com/brick/math/blob/main/README.md

Computes the greatest common divisor of multiple BigIntegers. Returns a new BigInteger.

```APIDOC
## [BigInteger::gcdAll]

### Description
Computes the greatest common divisor of multiple BigIntegers. Returns a new BigInteger.

### Method
gcdAll

### Parameters
- **operands** (mixed[]) - Required - The numbers.

### Request Example
```php
BigInteger::of(12)->gcdAll(18, 24)
```

### Response
#### Success Response
- **result** (BigInteger) - The greatest common divisor.

#### Response Example
```php
6
```
```

--------------------------------

### Conversion method usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigNumber.md

Demonstrates conversion behavior: toBigInteger() throws RoundingNecessaryException for non-integer rationals, while toBigRational() converts exactly.

```php
use Brick\Math\BigDecimal;
use Brick\Math\BigRational;

BigRational::of('2/3')->toBigInteger();   // RoundingNecessaryException
BigDecimal::of('2.5')->toBigRational();    // 5/2
```

--------------------------------

### BigInteger::lcmAll

Source: https://github.com/brick/math/blob/main/README.md

Computes the least common multiple of multiple BigIntegers. Returns a new BigInteger.

```APIDOC
## [BigInteger::lcmAll]

### Description
Computes the least common multiple of multiple BigIntegers. Returns a new BigInteger.

### Method
lcmAll

### Parameters
- **operands** (mixed[]) - Required - The numbers.

### Request Example
```php
BigInteger::of(4)->lcmAll(6, 8)
```

### Response
#### Success Response
- **result** (BigInteger) - The least common multiple.

#### Response Example
```php
24
```
```

--------------------------------

### strippedOfTrailingZeros() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigDecimal.md

Example usage of strippedOfTrailingZeros(). BigDecimal::of('1.200')->strippedOfTrailingZeros() returns 1.2.

```php
BigDecimal::of('1.200')->strippedOfTrailingZeros();   // 1.2
```

--------------------------------

### Base conversion with fromBase, toBase, fromArbitraryBase, toArbitraryBase

Source: https://github.com/brick/math/blob/main/README.md

Shows how to parse and format numbers in bases 2 to 36 using fromBase()/toBase(), and custom single-byte alphabets using fromArbitraryBase()/toArbitraryBase(). Input is case-insensitive, output is lowercase above base 10.

```php
echo BigInteger::fromBase('ff', 16); // 255
echo BigInteger::of(255)->toBase(16); // ff

echo BigInteger::fromArbitraryBase('bab', 'ab'); // 5
echo BigInteger::of(5)->toArbitraryBase('ab'); // bab
```

--------------------------------

### isLessThanOrEqualTo()

Source: https://github.com/brick/math/blob/main/README.md

Checks whether this number is less than or equal to another number.

```APIDOC
## isLessThanOrEqualTo()

### Description
Returns true if this number is less than or equal to the given number, false otherwise.

### Method
isLessThanOrEqualTo()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **bool** - true if less than or equal, false otherwise

```

--------------------------------

### BigInteger::of()

Source: https://github.com/brick/math/blob/main/README.md

Creates a BigInteger instance from a number, string, or another BigInteger. The value must be safely convertible to an integer.

```APIDOC
## [STATIC] BigInteger::of()

### Description
Creates a BigInteger instance from a number, string, or another BigInteger. The value must be safely convertible to an integer.

### Method
Static factory method

### Parameters
- **value** (int|string|BigInteger) - Required - The value to convert to a BigInteger.

### Return Value
- **BigInteger** - A new BigInteger instance.

### Example
```php
$integer = BigInteger::of(123);
```
```

--------------------------------

### BigInteger::fromArbitraryBase()

Source: https://github.com/brick/math/blob/main/README.md

Parses a string representation of a number using a custom single-byte alphabet and returns a BigInteger.

```APIDOC
## [PHP] BigInteger::fromArbitraryBase()

### Description
Parses a string representation of a number using a custom single-byte alphabet and returns a BigInteger.

### Method
Static method

### Signature
`public static function fromArbitraryBase(string $number, string $alphabet): BigInteger`

### Parameters
- **$number** (string) - Required - The string representation of the number.
- **$alphabet** (string) - Required - The custom alphabet used for the base.

### Return Value
- **BigInteger** - The parsed BigInteger.

### Example
```php
$bigInteger = BigInteger::fromArbitraryBase('bab', 'ab'); // 5
```
```

--------------------------------

### BigDecimal::sqrt

Source: https://github.com/brick/math/blob/main/README.md

Computes the square root of a BigDecimal. Returns a new BigDecimal.

```APIDOC
## [BigDecimal::sqrt]

### Description
Computes the square root of a BigDecimal. Returns a new BigDecimal.

### Method
sqrt

### Parameters
None

### Request Example
```php
BigDecimal::of('2')->sqrt()
```

### Response
#### Success Response
- **result** (BigDecimal) - The square root.

#### Response Example
```php
1.4142135623730951
```
```

--------------------------------

### isEven() and isOdd() usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Shows parity checks: 4 is even and not odd.

```php
BigInteger::of(4)->isEven();   // true
BigInteger::of(4)->isOdd();    // false
```

--------------------------------

### quotient(), remainder(), quotientAndRemainder() usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigInteger.md

Usage examples for division operations. quotient truncates toward zero; remainder has the same sign as the dividend. quotientAndRemainder returns an array [quotient, remainder].

```php
use Brick\Math\BigInteger;

BigInteger::of(7)->quotient(3);              // 2
BigInteger::of(-7)->remainder(3);            // -1
[$q, $r] = BigInteger::of(1000)->quotientAndRemainder(3);   // [333, 1]
```

--------------------------------

### BigInteger quotient and remainder in one call

Source: https://github.com/brick/math/blob/main/README.md

quotientAndRemainder() returns an array with the quotient and remainder.

```php
[$quotient, $remainder] = BigInteger::of(1000)->quotientAndRemainder(3);
```

--------------------------------

### withPointMovedLeft() / withPointMovedRight() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigDecimal.md

Example usage of point movement methods. withPointMovedLeft(2) returns 0.0123, withPointMovedRight(2) returns 123, and withPointMovedRight(-1) returns 0.123 (reverses direction).

```php
BigDecimal::of('1.23')->withPointMovedLeft(2);     // 0.0123
BigDecimal::of('1.23')->withPointMovedRight(2);    // 123
BigDecimal::of('1.23')->withPointMovedRight(-1);    // 0.123 (reverses)
```

--------------------------------

### BigNumber overrides usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigDecimal.md

Examples of toBigInteger(), toScale(), toString(), and toBigRational(). toBigInteger() throws RoundingNecessaryException when the fractional part is non-zero. toScale() with RoundingMode::Down rounds down. toString() preserves scale. toBigRational() returns a simplified fraction.

```php
use Brick\Math\BigDecimal;
use Brick\Math\RoundingMode;

BigDecimal::of('2.5')->toBigInteger();                       // RoundingNecessaryException
BigDecimal::of('2.50')->toScale(1, RoundingMode::Down);     // 2.5
BigDecimal::of('1.0')->toString();                           // 1.0
BigDecimal::of('123.456')->toBigRational();                 // 15432/125
```

--------------------------------

### BigRational division

Source: https://github.com/brick/math/blob/main/README.md

Division of BigRational always yields an exact result, automatically reduced to lowest terms.

```php
echo BigRational::of('13/99')->dividedBy('7'); // 13/693
echo BigRational::of('13/99')->dividedBy('9/8'); // 104/891
```

--------------------------------

### Arithmetic operations example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigRational.md

Demonstrates plus, minus, multipliedBy, and dividedBy with sample operands. dividedBy throws DivisionByZeroException when the divisor is zero.

```php
use Brick\Math\BigRational;

BigRational::of('2/3')->plus('5/6');          // 3/2
BigRational::of('2/3')->minus('5/6');         // -1/6
BigRational::of('2/3')->multipliedBy('5/4');  // 5/6
BigRational::of('13/99')->dividedBy('9/8');   // 104/891
BigRational::of(1)->dividedBy(0);            // DivisionByZeroException
```

--------------------------------

### sqrt() usage example

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigDecimal.md

Example usage of sqrt(). BigDecimal::of(2)->sqrt(10) throws RoundingNecessaryException, with HalfEven returns 1.4142135624, of('1.21')->sqrt(0) returns 1.1, and of(-1)->sqrt(0) throws NegativeNumberException.

```php
use Brick\Math\BigDecimal;
use Brick\Math\RoundingMode;

BigDecimal::of(2)->sqrt(10);                               // RoundingNecessaryException
BigDecimal::of(2)->sqrt(10, RoundingMode::HalfEven);        // 1.4142135624
BigDecimal::of('1.21')->sqrt(0);                            // 1.1
BigDecimal::of(-1)->sqrt(0);                               // NegativeNumberException
```

--------------------------------

### Chaining BigInteger methods

Source: https://github.com/brick/math/blob/main/README.md

Demonstrates method chaining for readability: BigInteger::of(10)->plus(5)->multipliedBy(3) results in 45.

```php
echo BigInteger::of(10)->plus(5)->multipliedBy(3); // 45
```

--------------------------------

### Using getIntegralPart() and getFractionalPart()

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigRational.md

Examples showing the integral part of 7/3 is 2 and the fractional part of -7/3 is -1/3.

```php
BigRational::of('7/3')->getIntegralPart();      // 2
BigRational::of('-7/3')->getFractionalPart();   // -1/3
```

--------------------------------

### BigInteger::lcm

Source: https://github.com/brick/math/blob/main/README.md

Computes the least common multiple of two BigIntegers. Returns a new BigInteger.

```APIDOC
## [BigInteger::lcm]

### Description
Computes the least common multiple of two BigIntegers. Returns a new BigInteger.

### Method
lcm

### Parameters
- **operand** (mixed) - Required - The other number.

### Request Example
```php
BigInteger::of(4)->lcm(6)
```

### Response
#### Success Response
- **result** (BigInteger) - The least common multiple.

#### Response Example
```php
12
```
```

--------------------------------

### BigInteger::parse()

Source: https://github.com/brick/math/blob/main/README.md

Parses an untrusted string into a BigInteger. Use this method for untrusted input to ensure safe conversion.

```APIDOC
## [STATIC] BigInteger::parse()

### Description
Parses an untrusted string into a BigInteger. Use this method for untrusted input to ensure safe conversion.

### Method
Static factory method

### Parameters
- **value** (string) - Required - The untrusted string to parse.

### Return Value
- **BigInteger** - A new BigInteger instance.

### Example
```php
$integer = BigInteger::parse('123');
```
```

--------------------------------

### compareTo()

Source: https://github.com/brick/math/blob/main/README.md

Compares this number with another number, returning -1, 0, or 1 if this number is less than, equal to, or greater than the given number.

```APIDOC
## compareTo()

### Description
Compares this number with another number, returning -1, 0, or 1 if this number is less than, equal to, or greater than the given number.

### Method
compareTo()

### Parameters
- **other** (BigNumber) - Required - The number to compare against

### Return Value
- **int** - -1, 0, or 1

```

--------------------------------

### BigRational::plus

Source: https://github.com/brick/math/blob/main/README.md

Adds a number to a BigRational. Returns a new BigRational with the sum, reduced to lowest terms.

```APIDOC
## [BigRational::plus]

### Description
Adds a number to a BigRational. Returns a new BigRational with the sum, reduced to lowest terms.

### Method
plus

### Parameters
- **operand** (mixed) - Required - The number to add.

### Request Example
```php
BigRational::of('2/3')->plus('5/6')
```

### Response
#### Success Response
- **result** (BigRational) - The sum.

#### Response Example
```php
3/2
```
```

--------------------------------

### BigDecimal::plus()

Source: https://github.com/brick/math/blob/main/README.md

Adds a number to the current BigDecimal and returns a new BigDecimal. The parameter accepts the same types as of().

```APIDOC
## [METHOD] BigDecimal::plus()

### Description
Adds a number to the current BigDecimal and returns a new BigDecimal. The parameter accepts the same types as of().

### Method
Instance method

### Parameters
- **value** (int|float|string|BigDecimal) - Required - The number to add.

### Return Value
- **BigDecimal** - A new BigDecimal with the sum.

### Example
```php
echo $decimal->plus(5); // 7.5
```
```

--------------------------------

### toScale() usage examples

Source: https://github.com/brick/math/blob/main/_autodocs/api-reference/BigNumber.md

Shows rounding to a scale with RoundingMode::Up and the default Unnecessary mode which throws RoundingNecessaryException when rounding is required.

```php
use Brick\Math\BigRational;
use Brick\Math\RoundingMode;

BigRational::of('2/3')->toScale(5, RoundingMode::Up);   // 0.66667
BigRational::of('2/3')->toScale(5);                     // RoundingNecessaryException
```
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