Numerics library

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.

Data-parallel types (since C++26)

The header <simd> provides portable types for explicitly stating data-parallelism and structuring data for more efficient SIMD access.

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 (since C++17)

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 (C++20)

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>
saturating_add (C++26)	saturating addition operation on two integers (function template)
saturating_sub (C++26)	saturating subtraction operation on two integers (function template)
saturating_mul (C++26)	saturating multiplication operation on two integers (function template)
saturating_div (C++26)	saturating division operation on two integers (function template)
saturating_cast (C++26)	returns an integer value clamped to the range of 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 & algorithm function object)
ranges::iota (C++23)
ranges::iota (C++23)	fills a range with successive increments of the starting value (algorithm function object)
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)

Miscellaneous

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. The byte ordering (endianness) of scalar types can be inspected via std::endian facility.

Checked integer arithmetic (since C++26)

The C compatibility header <stdckdint.h> provides several function templates for checked integer arithmetic.

Defined in header <stdckdint.h>
ckd_add (C++26)	checked addition operation on two integers (function template)
ckd_sub (C++26)	checked subtraction operation on two integers (function template)
ckd_mul (C++26)	checked multiplication operation on two integers (function template)

See also

C documentation for Numerics