Common mathematical functions

 

C++

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Feature test macros (C++20)

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Iterators library

Ranges library (C++20)

Algorithms library

Numerics library

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Filesystem library (C++17)

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External libraries

 

Numerics library

Common mathematical functions

Mathematical special functions (C++17)

Mathematical constants (C++20)

Floating-point environment (C++11)

Complex numbers

Numeric arrays

Pseudo-random number generation

Factor operations

gcd (C++17)

lcm (C++17)

Interpolations

midpoint (C++20)

lerp (C++20)

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

bit_cast (C++20)

byteswap (C++23)

has_single_bit (C++20)

bit_ceil (C++20)

bit_floor (C++20)

bit_width (C++20)

rotl (C++20)

rotr (C++20)

countl_zero (C++20)

countl_one (C++20)

countr_zero (C++20)

countr_one (C++20)

popcount (C++20)

endian (C++20)

 

Common mathematical functions

Functions
Basic operations
abs(int)labsllabsimaxabs (C++11) abs(float)fabs divldivlldivimaxdiv (C++11) fmod	remainder (C++11) remquo (C++11) fma (C++11) fmax (C++11) fmin (C++11) fdim (C++11) nannanfnanl (C++11)(C++11)(C++11)
Exponential functions
exp exp2 (C++11) expm1 (C++11)	log log10 log1p (C++11) log2 (C++11)
Power functions
sqrt cbrt (C++11)	hypot (C++11) pow
Trigonometric and hyperbolic functions
sin cos tan asin acos atan atan2	sinh cosh tanh asinh (C++11) acosh (C++11) atanh (C++11)

Error and gamma functions
erf (C++11) erfc (C++11)	lgamma (C++11) tgamma (C++11)
Nearest integer floating point operations
ceil floor roundlroundllround (C++11)(C++11)(C++11)	trunc (C++11) nearbyint (C++11) rintlrintllrint (C++11)(C++11)(C++11)
Floating point manipulation functions
ldexp scalbnscalbln (C++11)(C++11) ilogb (C++11) logb (C++11)	frexp modf nextafternexttoward (C++11)(C++11) copysign (C++11)
Classification/Comparison
fpclassify (C++11) isfinite (C++11) isinf (C++11) isnan (C++11) isnormal (C++11) signbit (C++11)	isgreater (C++11) isgreaterequal (C++11) isless (C++11) islessequal (C++11) islessgreater (C++11) isunordered (C++11)
Macro constants
HUGE_VALFHUGE_VALHUGE_VALL (C++11)(C++11) INFINITY (C++11) NAN (C++11) math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)	FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)

 

Functions

Defined in header <cstdlib>
abs(int)labsllabs (C++11)	computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
div(int)ldivlldiv (C++11)	computes quotient and remainder of integer division (function)
Defined in header <cinttypes>
abs(std::intmax_t)imaxabs (C++11)(C++11)	computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
div(std::intmax_t)imaxdiv (C++11)(C++11)	computes quotient and remainder of integer division (function)
Defined in header <cmath>
Basic operations
abs(float)fabsfabsffabsl (C++11)(C++11)	absolute value of a floating point value (\(\small{|x|}\)|x|) (function)
fmodfmodffmodl (C++11)(C++11)	remainder of the floating point division operation (function)
remainderremainderfremainderl (C++11)(C++11)(C++11)	signed remainder of the division operation (function)
remquoremquofremquol (C++11)(C++11)(C++11)	signed remainder as well as the three last bits of the division operation (function)
fmafmaffmal (C++11)(C++11)(C++11)	fused multiply-add operation (function)
fmaxfmaxffmaxl (C++11)(C++11)(C++11)	larger of two floating-point values (function)
fminfminffminl (C++11)(C++11)(C++11)	smaller of two floating point values (function)
fdimfdimffdiml (C++11)(C++11)(C++11)	positive difference of two floating point values (\({\small\max{(0, x-y)} }\)max(0, x-y)) (function)
nannanfnanl (C++11)(C++11)(C++11)	not-a-number (NaN) (function)
Exponential functions
expexpfexpl (C++11)(C++11)	returns e raised to the given power (\({\small e^x}\)ex) (function)
exp2exp2fexp2l (C++11)(C++11)(C++11)	returns 2 raised to the given power (\({\small 2^x}\)2x) (function)
expm1expm1fexpm1l (C++11)(C++11)(C++11)	returns e raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function)
loglogflogl (C++11)(C++11)	computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x)) (function)
log10log10flog10l (C++11)(C++11)	computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)
log2log2flog2l (C++11)(C++11)(C++11)	base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log2(x)) (function)
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)
Power functions
powpowfpowl (C++11)(C++11)	raises a number to the given power (\(\small{x^y}\)xy) (function)
sqrtsqrtfsqrtl (C++11)(C++11)	computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrtcbrtfcbrtl (C++11)(C++11)(C++11)	computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypothypotfhypotl (C++11)(C++11)(C++11)	computes square root of the sum of the squares of two or three (since C++17) given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ), (\(\scriptsize{\sqrt{x^2+y^2+z^2} }\)√x2 +y2 +z2 ) (since C++17) (function)
Trigonometric functions
sinsinfsinl (C++11)(C++11)	computes sine (\({\small\sin{x} }\)sin(x)) (function)
coscosfcosl (C++11)(C++11)	computes cosine (\({\small\cos{x} }\)cos(x)) (function)
tantanftanl (C++11)(C++11)	computes tangent (\({\small\tan{x} }\)tan(x)) (function)
asinasinfasinl (C++11)(C++11)	computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
acosacosfacosl (C++11)(C++11)	computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
atanatanfatanl (C++11)(C++11)	computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
atan2atan2fatan2l (C++11)(C++11)	arc tangent, using signs to determine quadrants (function)
Hyperbolic functions
sinhsinhfsinhl (C++11)(C++11)	computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
coshcoshfcoshl (C++11)(C++11)	computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function)
tanhtanhftanhl (C++11)(C++11)	computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function)
asinhasinhfasinhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x)) (function)
acoshacoshfacoshl (C++11)(C++11)(C++11)	computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11)	computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)
Error and gamma functions
erferfferfl (C++11)(C++11)(C++11)	error function (function)
erfcerfcferfcl (C++11)(C++11)(C++11)	complementary error function (function)
tgammatgammaftgammal (C++11)(C++11)(C++11)	gamma function (function)
lgammalgammaflgammal (C++11)(C++11)(C++11)	natural logarithm of the gamma function (function)
Nearest integer floating point operations
ceilceilfceill (C++11)(C++11)	nearest integer not less than the given value (function)
floorfloorffloorl (C++11)(C++11)	nearest integer not greater than the given value (function)
trunctruncftruncl (C++11)(C++11)(C++11)	nearest integer not greater in magnitude than the given value (function)
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)
nearbyintnearbyintfnearbyintl (C++11)(C++11)(C++11)	nearest integer using current rounding mode (function)
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)
Floating point manipulation functions
frexpfrexpffrexpl (C++11)(C++11)	decomposes a number into significand and a power of 2 (function)
ldexpldexpfldexpl (C++11)(C++11)	multiplies a number by 2 raised to a power (function)
modfmodffmodfl (C++11)(C++11)	decomposes a number into integer and fractional parts (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11)	multiplies a number by FLT_RADIX raised to a power (function)
ilogbilogbfilogbl (C++11)(C++11)(C++11)	extracts exponent of the number (function)
logblogbflogbl (C++11)(C++11)(C++11)	extracts exponent of the number (function)
nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (C++11)(C++11) (C++11)(C++11)(C++11)(C++11)	next representable floating point value towards the given value (function)
copysigncopysignfcopysignl (C++11)(C++11)(C++11)	copies the sign of a floating point value (function)
Classification and comparison
fpclassify (C++11)	categorizes the given floating-point value (function)
isfinite (C++11)	checks if the given number has finite value (function)
isinf (C++11)	checks if the given number is infinite (function)
isnan (C++11)	checks if the given number is NaN (function)
isnormal (C++11)	checks if the given number is normal (function)
signbit (C++11)	checks if the given number is negative (function)
isgreater (C++11)	checks if the first floating-point argument is greater than the second (function)
isgreaterequal (C++11)	checks if the first floating-point argument is greater or equal than the second (function)
isless (C++11)	checks if the first floating-point argument is less than the second (function)
islessequal (C++11)	checks if the first floating-point argument is less or equal than the second (function)
islessgreater (C++11)	checks if the first floating-point argument is less or greater than the second (function)
isunordered (C++11)	checks if two floating-point values are unordered (function)

Types

Defined in header <cstdlib>
div_t	structure type, returned by std::div (typedef)
ldiv_t	structure type, returned by std::ldiv (typedef)
lldiv_t (C++11)	structure type, returned by std::lldiv (typedef)
Defined in header <cinttypes>
imaxdiv_t (C++11)	structure type, returned by std::imaxdiv (typedef)
Defined in header <cmath>
float_t (C++11)	most efficient floating-point type at least as wide as float (typedef)
double_t (C++11)	most efficient floating-point type at least as wide as double (typedef)

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)
INFINITY (C++11)	evaluates to positive infinity or the value guaranteed to overflow a float (macro constant)
NAN (C++11)	evaluates to a quiet NaN of type float (macro constant)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C++11)(C++11)(C++11)	defines the error handling mechanism used by the common mathematical functions (macro constant)
Classification
FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C++11)(C++11)(C++11)(C++11)(C++11)	indicates a floating-point category (macro constant)

Notes

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

See also

Mathematical special functions