# Numerics library

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< cpp

The C++ numerics library includes common mathematical functions and types, as well as optimized numeric arrays and support for random number generation.

## Mathematical functions and types

### Common mathematical functions

The header `<cmath>` provides standard C library mathematical functions such as std::fabs, std::sqrt, and std::sin.

### Mathematical special functions (since C++17)

The header `<cmath>` also provides several mathematical special functions such as std::beta, std::hermite, and std::cyl_bessel_i.

### Mathematical constants (since C++20)

The header `<numbers>` provides several mathematical constants, such as std::numbers::pi or std::numbers::sqrt2

### Complex number arithmetic

Defined in header `<complex>`
complex | a complex number type (class template)

### Numeric arrays

Defined in header `<valarray>`
valarray | numeric arrays, array masks and array slices (class template)

## Numeric algorithms

The header `<numeric>` provides numeric algorithms below:

### Factor operations

Defined in header `<numeric>`
gcd (C++17) | `constexpr` function template returning the greatest common divisor of two integers (function template)
lcm (C++17) | `constexpr` function template returning the least common multiple of two integers (function template)

### Interpolation operations

Defined in header `<numeric>`
midpoint (C++20) | midpoint between two numbers or pointers (function template)
Defined in header `<cmath>`
lerp (C++20) | linear interpolation function (function)

### Numeric operations

Defined in header `<numeric>`
iota (C++11) | fills a range with successive increments of the starting value (function template)
ranges::iota (C++23) | fills a range with successive increments of the starting value (niebloid)
accumulate | sums up or folds a range of elements (function template)
reduce (C++17) | similar to std::accumulate, except out of order (function template)
transform_reduce (C++17) | applies an invocable, then reduces out of order (function template)
inner_product | computes the inner product of two ranges of elements (function template)
adjacent_difference | computes the differences between adjacent elements in a range (function template)
partial_sum | computes the partial sum of a range of elements (function template)
inclusive_scan (C++17) | similar to std::partial_sum, includes the ith input element in the ith sum (function template)
exclusive_scan (C++17) | similar to std::partial_sum, excludes the ith input element from the ith sum (function template)
transform_inclusive_scan (C++17) | applies an invocable, then calculates inclusive scan (function template)
transform_exclusive_scan (C++17) | applies an invocable, then calculates exclusive scan (function template)

## Miscellanous

### Pseudo-random number generation

The header `<random>` defines pseudo-random number generators and numerical distributions. The header `<cstdlib>` also includes C-style random number generation via std::srand and std::rand.

### Floating-point environment (since C++11)

The header `<cfenv>` defines flags and functions related to exceptional floating-point state, such as overflow and division by zero.

### Bit manipulation (since C++20)

The header `<bit>` provides several function templates to access, manipulate, and process individual bits and bit sequences.

Defined in header `<bit>`
Defined in namespace `std`
bit_cast (C++20) | reinterpret the object representation of one type as that of another (function template)
byteswap (C++23) | reverses the bytes in the given integer value (function template)
has_single_bit (C++20) | checks if a number is an integral power of two (function template)
bit_ceil (C++20) | finds the smallest integral power of two not less than the given value (function template)
bit_floor (C++20) | finds the largest integral power of two not greater than the given value (function template)
bit_width (C++20) | finds the smallest number of bits needed to represent the given value (function template)
rotl (C++20) | computes the result of bitwise left-rotation (function template)
rotr (C++20) | computes the result of bitwise right-rotation (function template)
countl_zero (C++20) | counts the number of consecutive 0 bits, starting from the most significant bit (function template)
countl_one (C++20) | counts the number of consecutive 1 bits, starting from the most significant bit (function template)
countr_zero (C++20) | counts the number of consecutive 0 bits, starting from the least significant bit (function template)
countr_one (C++20) | counts the number of consecutive 1 bits, starting from the least significant bit (function template)
popcount (C++20) | counts the number of 1 bits in an unsigned integer (function template)
endian (C++20) | indicates the endianness of scalar types (enum)

### See also

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