# Common mathematical functions

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< cpp‎ | numeric

### Functions

Defined in header `<cstdlib>`
abs(int)labs llabs (C++11) | computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
div(int)ldiv lldiv (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)fabs fabsf fabsl (C++11)(C++11) | absolute value of a floating point value (\(\small{|x|}\)|x|) (function)
fmod fmodf fmodl (C++11)(C++11) | remainder of the floating point division operation (function)
remainder remainderf remainderl (C++11)(C++11)(C++11) | signed remainder of the division operation (function)
remquo remquof remquol (C++11)(C++11)(C++11) | signed remainder as well as the three last bits of the division operation (function)
fma fmaf fmal (C++11)(C++11)(C++11) | fused multiply-add operation (function)
fmax fmaxf fmaxl (C++11)(C++11)(C++11) | larger of two floating-point values (function)
fmin fminf fminl (C++11)(C++11)(C++11) | smaller of two floating point values (function)
fdim fdimf fdiml (C++11)(C++11)(C++11) | positive difference of two floating point values (\({\small\max{(0, x-y)} }\)max(0, x-y)) (function)
nan nanf nanl (C++11)(C++11)(C++11) | not-a-number (NaN) (function)
##### Exponential functions
exp expf expl (C++11)(C++11) | returns e raised to the given power (\({\small e^x}\)ex) (function)
exp2 exp2f exp2l (C++11)(C++11)(C++11) | returns 2 raised to the given power (\({\small 2^x}\)2x) (function)
expm1 expm1f expm1l (C++11)(C++11)(C++11) | returns e raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function)
log logf logl (C++11)(C++11) | computes natural (base e) logarithm (\({\small \ln{x} }\)ln(x)) (function)
log10 log10f log10l (C++11)(C++11) | computes common (base 10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)
log2 log2f log2l (C++11)(C++11)(C++11) | base 2 logarithm of the given number (\({\small \log_{2}{x} }\)log2(x)) (function)
log1p log1pf log1pl (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
pow powf powl (C++11)(C++11) | raises a number to the given power (\(\small{x^y}\)xy) (function)
sqrt sqrtf sqrtl (C++11)(C++11) | computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrt cbrtf cbrtl (C++11)(C++11)(C++11) | computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypot hypotf hypotl (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
sin sinf sinl (C++11)(C++11) | computes sine (\({\small\sin{x} }\)sin(x)) (function)
cos cosf cosl (C++11)(C++11) | computes cosine (\({\small\cos{x} }\)cos(x)) (function)
tan tanf tanl (C++11)(C++11) | computes tangent (\({\small\tan{x} }\)tan(x)) (function)
asin asinf asinl (C++11)(C++11) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
acos acosf acosl (C++11)(C++11) | computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
atan atanf atanl (C++11)(C++11) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
atan2 atan2f atan2l (C++11)(C++11) | arc tangent, using signs to determine quadrants (function)
##### Hyperbolic functions
sinh sinhf sinhl (C++11)(C++11) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
cosh coshf coshl (C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function)
tanh tanhf tanhl (C++11)(C++11) | computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function)
asinh asinhf asinhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x)) (function)
acosh acoshf acoshl (C++11)(C++11)(C++11) | computes the inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
atanh atanhf atanhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)
##### Error and gamma functions
erf erff erfl (C++11)(C++11)(C++11) | error function (function)
erfc erfcf erfcl (C++11)(C++11)(C++11) | complementary error function (function)
tgamma tgammaf tgammal (C++11)(C++11)(C++11) | gamma function (function)
lgamma lgammaf lgammal (C++11)(C++11)(C++11) | natural logarithm of the gamma function (function)
##### Nearest integer floating point operations
ceil ceilf ceill (C++11)(C++11) | nearest integer not less than the given value (function)
floor floorf floorl (C++11)(C++11) | nearest integer not greater than the given value (function)
trunc truncf truncl (C++11)(C++11)(C++11) | nearest integer not greater in magnitude than the given value (function)
round roundf roundl lround lroundf lroundl llround llroundf llroundl (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)
nearbyint nearbyintf nearbyintl (C++11)(C++11)(C++11) | nearest integer using current rounding mode (function)
rint rintf rintl lrint lrintf lrintl llrint llrintf llrintl (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
frexp frexpf frexpl (C++11)(C++11) | decomposes a number into significand and a power of 2 (function)
ldexp ldexpf ldexpl (C++11)(C++11) | multiplies a number by 2 raised to a power (function)
modf modff modfl (C++11)(C++11) | decomposes a number into integer and fractional parts (function)
scalbn scalbnf scalbnl scalbln scalblnf scalblnl (C++11)(C++11)(C++11)(C++11)(C++11)(C++11) | multiplies a number by FLT_RADIX raised to a power (function)
ilogb ilogbf ilogbl (C++11)(C++11)(C++11) | extracts exponent of the number (function)
logb logbf logbl (C++11)(C++11)(C++11) | extracts exponent of the number (function)
nextafter nextafterf nextafterl nexttoward nexttowardf nexttowardl (C++11)(C++11) (C++11)(C++11)(C++11)(C++11) | next representable floating point value towards the given value (function)
copysign copysignf copysignl (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_VALF HUGE_VAL HUGE_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_errhandling MATH_ERRNO MATH_ERREXCEPT (C++11)(C++11)(C++11) | defines the error handling mechanism used by the common mathematical functions (macro constant)
##### Classification
FP_NORMAL FP_SUBNORMAL FP_ZERO FP_INFINITE FP_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

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