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Common mathematical functions

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< cpp‎ | numeric

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Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Basic linear algebra algorithms (C++26)

Data-parallel types (SIMD) (C++26)

Floating-point environment (C++11)

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Numeric array (valarray)

Pseudo-random number generation

Bit manipulation (C++20)

Saturation arithmetic (C++26)

Factor operations

(C++17)

(C++17)

(C++20)

(C++20)

Generic numeric operations

(C++11)

(C++23)

adjacent_difference

(C++17)

transform_reduce

(C++17)

(C++17)

(C++17)

transform_inclusive_scan

(C++17)

transform_exclusive_scan

(C++17)

C-style checked integer arithmetic

(C++26)

(C++26)

(C++26)

Common mathematical functions

Basic operations

abs(int)labsllabsimaxabs

(C++11)

divldivlldivimaxdiv

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)(C++11)(C++11)

Exponential functions

(C++11)

(C++11)

(C++11)

(C++11)

Power functions

(C++11)

(C++11)

Trigonometric and
hyperbolic functions

(C++11)

(C++11)

(C++11)

Error and gamma functions

(C++11)

(C++11)

(C++11)

(C++11)

Nearest integer floating point operations

roundlroundllround

(C++11)(C++11)(C++11)

(C++11)

(C++11)

rintlrintllrint

(C++11)(C++11)(C++11)

Floating point manipulation functions

(C++11)(C++11)

(C++11)

(C++11)

nextafternexttoward

(C++11)(C++11)

(C++11)

Classification and comparison

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

(C++11)

Macro constants

HUGE_VALFHUGE_VALHUGE_VALL

(C++11)(C++11)

math_errhandlingMATH_ERRNOMATH_ERREXCEPT

(C++11)

(C++11)

(C++11)

FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN

(C++11)(C++11)(C++11)(C++11)(C++11)

Contents

[edit] Functions

Defined in header <cstdlib>

abs(int)labsllabs

(C++11)

computes absolute value of an integral value (\(\small{|x|}\)|x|)
(function) [edit]

div(int)ldivlldiv

(C++11)

computes quotient and remainder of integer division
(function) [edit]

Defined in header <cinttypes>

abs(std::intmax_t)imaxabs

(C++11)(C++11)

computes absolute value of an integral value (\(\small{|x|}\)|x|)
(function) [edit]

div(std::intmax_t)imaxdiv

(C++11)(C++11)

computes quotient and remainder of integer division
(function) [edit]

Defined in header <cmath>

Basic operations

abs(float)fabsfabsffabsl

(C++11)(C++11)

absolute value of a floating point value (\(\small{|x|}\)|x|)
(function) [edit]

(C++11)(C++11)

remainder of the floating point division operation
(function) [edit]

remainderremainderfremainderl

(C++11)(C++11)(C++11)

signed remainder of the division operation
(function) [edit]

remquoremquofremquol

(C++11)(C++11)(C++11)

signed remainder as well as the three last bits of the division operation
(function) [edit]

(C++11)(C++11)(C++11)

fused multiply-add operation
(function) [edit]

(C++11)(C++11)(C++11)

larger of two floating-point values
(function) [edit]

(C++11)(C++11)(C++11)

smaller of two floating point values
(function) [edit]

(C++11)(C++11)(C++11)

positive difference of two floating point values (\({\small\max{(0, x-y)}}\)max(0, x-y))
(function) [edit]

(C++11)(C++11)(C++11)

not-a-number (NaN)
(function) [edit]

Exponential functions

(C++11)(C++11)

returns e raised to the given power (\({\small e^x}\)e^x)
(function) [edit]

(C++11)(C++11)(C++11)

returns 2 raised to the given power (\({\small 2^x}\)2^x)
(function) [edit]

expm1expm1fexpm1l

(C++11)(C++11)(C++11)

returns e raised to the given power, minus 1 (\({\small e^x-1}\)e^x-1)
(function) [edit]

(C++11)(C++11)

computes natural (base e) logarithm (\({\small\ln{x}}\)ln(x))
(function) [edit]

log10log10flog10l

(C++11)(C++11)

computes common (base 10) logarithm (\({\small\log_{10}{x}}\)log₁₀(x))
(function) [edit]

(C++11)(C++11)(C++11)

base 2 logarithm of the given number (\({\small\log_{2}{x}}\)log₂(x))
(function) [edit]

log1plog1pflog1pl

(C++11)(C++11)(C++11)

natural logarithm (to base e) of 1 plus the given number (\({\small\ln{(1+x)}}\)ln(1+x))
(function) [edit]

Power functions

(C++11)(C++11)

raises a number to the given power (\(\small{x^y}\)x^y)
(function) [edit]

(C++11)(C++11)

computes square root (\(\small{\sqrt{x}}\)√x)
(function) [edit]

(C++11)(C++11)(C++11)

computes cube root (\(\small{\sqrt[3]{x}}\)3√x)
(function) [edit]

hypothypotfhypotl

(C++11)(C++11)(C++11)

computes hypotenuse \(\scriptsize{\sqrt{x^2+y^2}}\)√x2
+y2
and \(\scriptsize{\sqrt{x^2+y^2+z^2}}\)√x2
+y2
+z2
(since C++17)
(function) [edit]

Trigonometric functions

(C++11)(C++11)

computes sine (\({\small\sin{x}}\)sin(x))
(function) [edit]

(C++11)(C++11)

computes cosine (\({\small\cos{x}}\)cos(x))
(function) [edit]

(C++11)(C++11)

computes tangent (\({\small\tan{x}}\)tan(x))
(function) [edit]

(C++11)(C++11)

computes arc sine (\({\small\arcsin{x}}\)arcsin(x))
(function) [edit]

(C++11)(C++11)

computes arc cosine (\({\small\arccos{x}}\)arccos(x))
(function) [edit]

(C++11)(C++11)

computes arc tangent (\({\small\arctan{x}}\)arctan(x))
(function) [edit]

atan2atan2fatan2l

(C++11)(C++11)

arc tangent, using signs to determine quadrants
(function) [edit]

Hyperbolic functions

(C++11)(C++11)

computes hyperbolic sine (\({\small\sinh{x}}\)sinh(x))
(function) [edit]

(C++11)(C++11)

computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x))
(function) [edit]

(C++11)(C++11)

computes hyperbolic tangent (\({\small\tanh{x}}\)tanh(x))
(function) [edit]

asinhasinhfasinhl

(C++11)(C++11)(C++11)

computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x))
(function) [edit]

acoshacoshfacoshl

(C++11)(C++11)(C++11)

computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x}}\)arcosh(x))
(function) [edit]

atanhatanhfatanhl

(C++11)(C++11)(C++11)

computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)artanh(x))
(function) [edit]

Error and gamma functions

(C++11)(C++11)(C++11)

error function
(function) [edit]

(C++11)(C++11)(C++11)

complementary error function
(function) [edit]

tgammatgammaftgammal

(C++11)(C++11)(C++11)

gamma function
(function) [edit]

lgammalgammaflgammal

(C++11)(C++11)(C++11)

natural logarithm of the gamma function
(function) [edit]

Nearest integer floating point operations

(C++11)(C++11)

nearest integer not less than the given value
(function) [edit]

floorfloorffloorl

(C++11)(C++11)

nearest integer not greater than the given value
(function) [edit]

trunctruncftruncl

(C++11)(C++11)(C++11)

nearest integer not greater in magnitude than the given value
(function) [edit]

roundroundfroundllroundlroundflroundlllroundllroundfllroundl

(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)

nearest integer, rounding away from zero in halfway cases
(function) [edit]

nearbyintnearbyintfnearbyintl

(C++11)(C++11)(C++11)

nearest integer using current rounding mode
(function) [edit]

rintrintfrintllrintlrintflrintlllrintllrintfllrintl

(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)

nearest integer using current rounding mode with
exception if the result differs
(function) [edit]

Floating point manipulation functions

frexpfrexpffrexpl

(C++11)(C++11)

decomposes a number into significand and base-2 exponent
(function) [edit]

ldexpldexpfldexpl

(C++11)(C++11)

multiplies a number by 2 raised to an integral power
(function) [edit]

(C++11)(C++11)

decomposes a number into integer and fractional parts
(function) [edit]

scalbnscalbnfscalbnlscalblnscalblnfscalblnl

(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)

multiplies a number by FLT_RADIX raised to a power
(function) [edit]

ilogbilogbfilogbl

(C++11)(C++11)(C++11)

extracts exponent of the number
(function) [edit]

(C++11)(C++11)(C++11)

extracts exponent of the number
(function) [edit]

nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl

(C++11)(C++11)(C++11)(C++11)(C++11)(C++11)

next representable floating-point value towards the given value
(function) [edit]

copysigncopysignfcopysignl

(C++11)(C++11)(C++11)

copies the sign of a floating point value
(function) [edit]

Classification and comparison

(C++11)

categorizes the given floating-point value
(function) [edit]

(C++11)

checks if the given number has finite value
(function) [edit]

(C++11)

checks if the given number is infinite
(function) [edit]

(C++11)

checks if the given number is NaN
(function) [edit]

(C++11)

checks if the given number is normal
(function) [edit]

(C++11)

checks if the given number is negative
(function) [edit]

(C++11)

checks if the first floating-point argument is greater than the second
(function) [edit]

(C++11)

checks if the first floating-point argument is greater or equal than the second
(function) [edit]

(C++11)

checks if the first floating-point argument is less than the second
(function) [edit]

(C++11)

checks if the first floating-point argument is less or equal than the second
(function) [edit]

(C++11)

checks if the first floating-point argument is less or greater than the second
(function) [edit]

(C++11)

checks if two floating-point values are unordered
(function) [edit]

[edit] Types

Defined in header <cstdlib>

structure type, returned by std::div
(typedef) [edit]

structure type, returned by std::ldiv
(typedef) [edit]

(C++11)

structure type, returned by std::lldiv
(typedef) [edit]

Defined in header <cinttypes>

(C++11)

structure type, returned by std::imaxdiv
(typedef) [edit]

Defined in header <cmath>

float_t

(C++11)

most efficient floating-point type at least as wide as float
(typedef) [edit]

double_t

(C++11)

most efficient floating-point type at least as wide as double
(typedef) [edit]

[edit] Macro constants

Defined in header <cmath>

HUGE_VALFHUGE_VALHUGE_VALL

(C++11)(C++11)

indicates the overflow value for float, double and long double respectively
(macro constant) [edit]

(C++11)

evaluates to positive infinity or the value guaranteed to overflow a float
(macro constant) [edit]

(C++11)

evaluates to a quiet NaN of type float
(macro constant) [edit]

math_errhandlingMATH_ERRNOMATH_ERREXCEPT

(C++11)(C++11)(C++11)

defines the error handling mechanism used by the common mathematical functions
(macro constant) [edit]

Classification

FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN

(C++11)(C++11)(C++11)(C++11)(C++11)

indicates a floating-point category
(macro constant) [edit]

[edit] Notes

Feature-test macro	Value	Std	Feature
`__cpp_lib_constexpr_cmath`	`202202L`	(C++23)	Constexpr for FP environment agnostic mathematical functions in `<cmath>` and `<cstdlib>`
`__cpp_lib_constexpr_cmath`	`202306L`	(C++26)	Constexpr for most mathematical functions in `<cmath>`

[edit] See also

Mathematical special functions

C documentation for Common mathematical functions

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