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m (→‎Bit manipulation: Add anchor to section name without "since C++20" tag.)
 
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The C++ numerics library includes common mathematical functions and types, as well as optimized numeric arrays and support for random number generation.
 
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==
  
 
===[[cpp/numeric/math|Common mathematical functions]]===
 
===[[cpp/numeric/math|Common mathematical functions]]===
 +
The header {{header|cmath}} provides [[cpp/numeric/math|standard C library mathematical functions]] such as {{lc|std::fabs}}, {{lc|std::sqrt}}, and {{lc|std::sin}}.
  
−
The header {{tt|cmath}} provides [[cpp/numeric/math|standard C library mathematical functions]] such as {{lc|std::fabs}}, {{lc|std::sqrt}}, and {{lc|std::sin}}.
+
===[[cpp/numeric/special_functions|Mathematical special functions]] {{mark since c++17}}===
 +
The header {{header|cmath}} also provides several mathematical special functions such as {{lc|std::beta}}, {{lc|std::hermite}}, and {{lc|std::cyl_bessel_i}}.
  
−
===Complex numbers===
+
===[[cpp/numeric/constants|Mathematical constants]] {{mark since c++20}}===
 +
The header {{header|numbers}} provides several mathematical constants, such as {{lc|std::numbers::pi}} or {{lc|std::numbers::sqrt2}}
  
 +
===[[cpp/numeric/linalg|Basic linear algebra algorithms]] {{mark since c++26}}===
 +
The header {{header|linalg}} provides basic linear algebra algorithms which are based on BLAS.
 +
 +
===Complex number arithmetic===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc header | complex}}
+
{{dsc header|complex}}
−
{{dsc tclass | cpp/numeric/complex | a complex number type }}
+
{{dsc tclass|cpp/numeric/complex|a complex number type}}
 
{{dsc end}}
 
{{dsc end}}
  
 
===Numeric arrays===
 
===Numeric arrays===
 +
{{dsc begin}}
 +
{{dsc header|valarray}}
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{{dsc tclass|cpp/numeric/valarray|numeric arrays, array masks and array slices}}
 +
{{dsc end}}
  
 +
==Numeric algorithms==
 +
 +
The header {{header|numeric}} provides numeric algorithms below:
 +
 +
===Factor operations===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc header | valarray}}
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{{dsc header|numeric}}
−
{{dsc tclass | cpp/numeric/valarray | numeric arrays and array slices }}
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{{dsc inc|cpp/numeric/dsc gcd}}
 +
{{dsc inc|cpp/numeric/dsc lcm}}
 
{{dsc end}}
 
{{dsc end}}
  
−
===Generic numeric operations===
+
===Interpolation operations===
 +
{{dsc begin}}
 +
{{dsc header|numeric}}
 +
{{dsc inc|cpp/numeric/dsc midpoint}}
 +
{{dsc header|cmath}}
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{{dsc inc|cpp/numeric/dsc lerp}}
 +
{{dsc end}}
  
 +
===Saturation arithmetic {{mark since c++26}}===
 
{{dsc begin}}
 
{{dsc begin}}
−
{{dsc header | numeric}}
+
{{dsc header|numeric}}
−
{{dsc inc | cpp/algorithm/dcl list iota}}
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{{dsc inc|cpp/numeric/dsc add_sat}}
−
{{dsc inc | cpp/algorithm/dcl list accumulate}}
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{{dsc inc|cpp/numeric/dsc sub_sat}}
−
{{dsc inc | cpp/algorithm/dcl list inner_product}}
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{{dsc inc|cpp/numeric/dsc mul_sat}}
−
{{dsc inc | cpp/algorithm/dcl list adjacent_difference}}
+
{{dsc inc|cpp/numeric/dsc div_sat}}
−
{{dsc inc | cpp/algorithm/dcl list partial_sum}}
+
{{dsc inc|cpp/numeric/dsc saturate_cast}}
 
{{dsc end}}
 
{{dsc end}}
 +
 +
===Numeric operations===
 +
{{dsc begin}}
 +
{{dsc header|numeric}}
 +
{{dsc inc|cpp/algorithm/dsc iota}}
 +
{{dsc inc|cpp/algorithm/ranges/dsc iota}}
 +
{{dsc inc|cpp/algorithm/dsc accumulate}}
 +
<!--{{dsc inc|cpp/algorithm/ranges/dsc accumulate}}-->
 +
{{dsc inc|cpp/algorithm/dsc reduce}}
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<!--{{dsc inc|cpp/algorithm/ranges/dsc reduce}}-->
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{{dsc inc|cpp/algorithm/dsc transform_reduce}}
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<!--{{dsc inc|cpp/algorithm/ranges/dsc transform_reduce}}-->
 +
{{dsc inc|cpp/algorithm/dsc inner_product}}
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<!--{{dsc inc|cpp/algorithm/ranges/dsc inner_product}}-->
 +
{{dsc inc|cpp/algorithm/dsc adjacent_difference}}
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<!--{{dsc inc|cpp/algorithm/ranges/dsc adjacent_difference}}-->
 +
{{dsc inc|cpp/algorithm/dsc partial_sum}}
 +
<!--{{dsc inc|cpp/algorithm/ranges/dsc partial_sum}}-->
 +
{{dsc inc|cpp/algorithm/dsc inclusive_scan}}
 +
<!--{{dsc inc|cpp/algorithm/ranges/dsc inclusive_scan}}-->
 +
{{dsc inc|cpp/algorithm/dsc exclusive_scan}}
 +
<!--{{dsc inc|cpp/algorithm/ranges/dsc exclusive_scan}}-->
 +
{{dsc inc|cpp/algorithm/dsc transform_inclusive_scan}}
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<!--{{dsc inc|cpp/algorithm/ranges/dsc transform_inclusive_scan}}-->
 +
{{dsc inc|cpp/algorithm/dsc transform_exclusive_scan}}
 +
<!--{{dsc inc|cpp/algorithm/ranges/dsc transform_exclusive_scan}}-->
 +
{{dsc end}}
 +
 +
==Miscellanous==
  
 
===[[cpp/numeric/random|Pseudo-random number generation]]===
 
===[[cpp/numeric/random|Pseudo-random number generation]]===
 +
The header {{header|random}} defines [[cpp/numeric/random|pseudo-random number generators and numerical distributions]]. The header {{header|cstdlib}} also includes C-style random number generation via {{lc|std::srand}} and {{lc|std::rand}}.
  
−
The header {{tt|random}} defines [[cpp/numeric/random|pseudo-random number generators and numerical distributions]].  The header {{tt|cstdlib}} also includes C-style random number generation via {{lc|std::srand}} and {{lc|std::rand}}.
+
===[[cpp/numeric/fenv|Floating-point environment]] {{mark since c++11}}===
 +
The header {{header|cfenv}} defines [[cpp/numeric/fenv|flags and functions related to exceptional floating-point state]], such as overflow and division by zero.
  
−
===[[cpp/numeric/ratio|Compile time rational arithmetic]] {{mark since c++11}}===
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{{anchor|Bit manipulation}}
 +
===Bit manipulation {{mark since c++20}}===
 +
The header {{header|bit}} provides several function templates to access, manipulate, and process individual bits and bit sequences.
  
−
The header {{tt|ratio}} provides [[cpp/numeric/ratio|types and functions for manipulating and storing compile-time ratios]].
+
{{dsc begin}}
 +
{{dsc header|bit}}
 +
{{dsc namespace|std}}
 +
{{dsc inc|cpp/numeric/dsc bit_cast}}
 +
{{dsc inc|cpp/numeric/dsc byteswap}}
 +
{{dsc inc|cpp/numeric/dsc has_single_bit}}
 +
{{dsc inc|cpp/numeric/dsc bit_ceil}}
 +
{{dsc inc|cpp/numeric/dsc bit_floor}}
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{{dsc inc|cpp/numeric/dsc bit_width}}
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{{dsc inc|cpp/numeric/dsc rotl}}
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{{dsc inc|cpp/numeric/dsc rotr}}
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{{dsc inc|cpp/numeric/dsc countl_zero}}
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{{dsc inc|cpp/numeric/dsc countl_one}}
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{{dsc inc|cpp/numeric/dsc countr_zero}}
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{{dsc inc|cpp/numeric/dsc countr_one}}
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{{dsc inc|cpp/numeric/dsc popcount}}
  
−
===[[cpp/numeric/fenv|Floating-point environment]]===
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{{dsc inc|cpp/types/dsc endian}}
 +
{{dsc end}}
  
−
The header {{tt|fenv}} defines [[cpp/numeric/fenv|flags and functions related to exceptional floating-point state]], such as overflow and division by zero.
+
===See also===
 +
{{dsc begin}}
 +
{{dsc see c|c/numeric|Numerics|nomono=true}}
 +
{{dsc end}}
  
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[[ar:cpp/numeric]]
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{{langlinks|ar|de|es|fr|it|ja|pt|ru|zh}}
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[[de:cpp/numeric]]
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[[es:cpp/numeric]]
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[[fr:cpp/numeric]]
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Latest revision as of 12:50, 1 January 2024

 
C++
 
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
(C++17)
(C++17)
Interpolations
(C++20)
(C++20)
Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 

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

Contents

[edit] Mathematical functions and types

[edit] Common mathematical functions

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

[edit] 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.

[edit] Mathematical constants (since C++20)

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

[edit] Basic linear algebra algorithms (since C++26)

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

[edit] Complex number arithmetic

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

[edit] Numeric arrays

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

[edit] Numeric algorithms

The header <numeric> provides numeric algorithms below:

[edit] Factor operations

Defined in header <numeric>
(C++17)
 computes the greatest common divisor of two integers
(function template) [edit]
(C++17)
 computes the least common multiple of two integers
(function template) [edit]

[edit] Interpolation operations

Defined in header <numeric>
(C++20)
 midpoint between two numbers or pointers
(function template) [edit]
Defined in header <cmath>
(C++20)
 linear interpolation function
(function) [edit]

[edit] Saturation arithmetic (since C++26)

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

[edit] Numeric operations

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

[edit] Miscellanous

[edit] 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.

[edit] 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.

[edit] 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
(C++20)
 reinterpret the object representation of one type as that of another
(function template) [edit]
(C++23)
 reverses the bytes in the given integer value
(function template) [edit]
(C++20)
 checks if a number is an integral power of 2
(function template) [edit]
(C++20)
 finds the smallest integral power of two not less than the given value
(function template) [edit]
(C++20)
 finds the largest integral power of two not greater than the given value
(function template) [edit]
(C++20)
 finds the smallest number of bits needed to represent the given value
(function template) [edit]
(C++20)
 computes the result of bitwise left-rotation
(function template) [edit]
(C++20)
 computes the result of bitwise right-rotation
(function template) [edit]
(C++20)
 counts the number of consecutive ​0​ bits, starting from the most significant bit
(function template) [edit]
(C++20)
 counts the number of consecutive 1 bits, starting from the most significant bit
(function template) [edit]
(C++20)
 counts the number of consecutive ​0​ bits, starting from the least significant bit
(function template) [edit]
(C++20)
 counts the number of consecutive 1 bits, starting from the least significant bit
(function template) [edit]
(C++20)
 counts the number of 1 bits in an unsigned integer
(function template) [edit]
(C++20)
 indicates the endianness of scalar types
(enum) [edit]

[edit] See also

C documentation for Numerics
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