Numerics library

 

C++

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Freestanding and hosted

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Standard library headers

Named requirements

Feature test macros (C++20)

Language support library

Concepts library (C++20)

Metaprogramming library (C++11)

Diagnostics library

General utilities library

Strings library

Containers library

Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

Localizations library

Input/output library

Filesystem library (C++17)

Regular expressions library (C++11)

Concurrency support library (C++11)

Execution support library (C++26)

Technical specifications

Symbols index

External libraries

 

Numerics library

Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
Factor operations
gcd (C++17)	lcm (C++17)
Interpolations
midpoint (C++20)	lerp (C++20)
Saturation arithmetic
add_sat (C++26) sub_sat (C++26) saturate_cast (C++26)	mul_sat (C++26) div_sat (C++26)
Generic numeric operations
iota (C++11) ranges::iota (C++23) accumulate inner_product adjacent_difference partial_sum	reduce (C++17) transform_reduce (C++17) inclusive_scan (C++17) exclusive_scan (C++17) transform_inclusive_scan (C++17) transform_exclusive_scan (C++17)
Bit operations
has_single_bit (C++20)     bit_cast (C++20) bit_ceil (C++20) bit_floor (C++20) bit_width (C++20) rotl (C++20) rotr (C++20)	popcount (C++20) countl_zero (C++20) countl_one (C++20) countr_zero (C++20) countr_one (C++20) byteswap (C++23) endian (C++20)

 

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

Basic linear algebra algorithms (since C++26)

The header <linalg> provides basic linear algebra algorithms which are based on BLAS.

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)	computes the greatest common divisor of two integers (function template)
lcm (C++17)	computes 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)

Saturation arithmetic (since C++26)

Defined in header <numeric>
add_sat (C++26)	saturating addition operation on two integers (function template)
sub_sat (C++26)	saturating subtraction operation on two integers (function template)
mul_sat (C++26)	saturating multiplication operation on two integers (function template)
div_sat (C++26)	saturating division operation on two integers (function template)
saturate_cast (C++26)	returns an integer value clamped to the range of a another integer type (function template)

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 2 (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

C documentation for Numerics