# Common mathematical functions

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< c‎ | numeric

### Functions

Defined in header `<stdlib.h>`
abs labs llabs (C99) | computes absolute value of an integral value (|x|) (function)
div ldiv lldiv (C99) | computes quotient and remainder of integer division (function)
Defined in header `<inttypes.h>`
imaxabs (C99) | computes absolute value of an integral value (|x|) (function)
imaxdiv (C99) | computes quotient and remainder of integer division (function)
Defined in header `<math.h>`

##### Basic operations

fabs fabsf fabsl (C99)(C99) | computes absolute value of a floating-point value (|x|) (function)
fmod fmodf fmodl (C99)(C99) | computes remainder of the floating-point division operation (function)
remainder remainderf remainderl (C99)(C99)(C99) | computes signed remainder of the floating-point division operation (function)
remquo remquof remquol (C99)(C99)(C99) | computes signed remainder as well as the three last bits of the division operation (function)
fma fmaf fmal (C99)(C99)(C99) | computes fused multiply-add operation (function)
fmax fmaxf fmaxl (C99)(C99)(C99) | determines larger of two floating-point values (function)
fmin fminf fminl (C99)(C99)(C99) | determines smaller of two floating-point values (function)
fdim fdimf fdiml (C99)(C99)(C99) | determines positive difference of two floating-point values (max(0, x-y)) (function)
nan nanf nanl (C99)(C99)(C99) | returns a NaN (not-a-number) (function)

##### Exponential functions

exp expf expl (C99)(C99) | computes e raised to the given power (ex) (function)
exp2 exp2f exp2l (C99)(C99)(C99) | computes 2 raised to the given power (2x) (function)
expm1 expm1f expm1l (C99)(C99)(C99) | computes e raised to the given power, minus one (ex-1) (function)
log logf logl (C99)(C99) | computes natural (base-e) logarithm (ln(x)) (function)
log10 log10f log10l (C99)(C99) | computes common (base-10) logarithm (log10(x)) (function)
log2 log2f log2l (C99)(C99)(C99) | computes base-2 logarithm (log2(x)) (function)
log1p log1pf log1pl (C99)(C99)(C99) | computes natural (base-e) logarithm of 1 plus the given number (ln(1+x)) (function)

##### Power functions

pow powf powl (C99)(C99) | computes a number raised to the given power (xy) (function)
sqrt sqrtf sqrtl (C99)(C99) | computes square root (√x) (function)
cbrt cbrtf cbrtl (C99)(C99)(C99) | computes cubic root (3√x) (function)
hypot hypotf hypotl (C99)(C99)(C99) | computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function)

##### Trigonometric functions

sin sinf sinl (C99)(C99) | computes sine (sin(x)) (function)
cos cosf cosl (C99)(C99) | computes cosine (cos(x)) (function)
tan tanf tanl (C99)(C99) | computes tangent (tan(x)) (function)
asin asinf asinl (C99)(C99) | computes arc sine (arcsin(x)) (function)
acos acosf acosl (C99)(C99) | computes arc cosine (arccos(x)) (function)
atan atanf atanl (C99)(C99) | computes arc tangent (arctan(x)) (function)
atan2 atan2f atan2l (C99)(C99) | computes arc tangent, using signs to determine quadrants (function)

##### Hyperbolic functions

sinh sinhf sinhl (C99)(C99) | computes hyperbolic sine (sh(x)) (function)
cosh coshf coshl (C99)(C99) | computes hyperbolic cosine (ch(x)) (function)
tanh tanhf tanhl (C99)(C99) | computes hyperbolic tangent (function)
asinh asinhf asinhl (C99)(C99)(C99) | computes inverse hyperbolic sine (arsinh(x)) (function)
acosh acoshf acoshl (C99)(C99)(C99) | computes inverse hyperbolic cosine (arcosh(x)) (function)
atanh atanhf atanhl (C99)(C99)(C99) | computes inverse hyperbolic tangent (artanh(x)) (function)

##### Error and gamma functions

erf erff erfl (C99)(C99)(C99) | computes error function (function)
erfc erfcf erfcl (C99)(C99)(C99) | computes complementary error function (function)
tgamma tgammaf tgammal (C99)(C99)(C99) | computes gamma function (function)
lgamma lgammaf lgammal (C99)(C99)(C99) | computes natural (base-e) logarithm of the gamma function (function)

##### Nearest integer floating-point operations

ceil ceilf ceill (C99)(C99) | computes smallest integer not less than the given value (function)
floor floorf floorl (C99)(C99) | computes largest integer not greater than the given value (function)
trunc truncf truncl (C99)(C99)(C99) | rounds to nearest integer not greater in magnitude than the given value (function)
round lround llround (C99)(C99)(C99) | rounds to nearest integer, rounding away from zero in halfway cases (function)
nearbyint nearbyintf nearbyintl (C99)(C99)(C99) | rounds to an integer using current rounding mode (function)
rint rintf rintl lrint lrintf lrintl llrint llrintf llrintl (C99)(C99)(C99)(C99)(C99)(C99)(C99)(C99)(C99) | rounds to an integer using current rounding mode with exception if the result differs (function)

##### Floating-point manipulation functions

frexp frexpf frexpl (C99)(C99) | breaks a number into significand and a power of 2 (function)
ldexp ldexpf ldexpl (C99)(C99) | multiplies a number by 2 raised to a power (function)
modf modff modfl (C99)(C99) | breaks a number into integer and fractional parts (function)
scalbn scalbnf scalbnl scalbln scalblnf scalblnl (C99)(C99)(C99)(C99)(C99)(C99) | computes efficiently a number times FLT_RADIX raised to a power (function)
ilogb ilogbf ilogbl (C99)(C99)(C99) | extracts exponent of the given number (function)
logb logbf logbl (C99)(C99)(C99) | extracts exponent of the given number (function)
nextafter nextafterf nextafterl nexttoward nexttowardf nexttowardl (C99)(C99)(C99)(C99)(C99)(C99) | determines next representable floating-point value towards the given value (function)
copysign copysignf copysignl (C99)(C99)(C99) | produces a value with the magnitude of a given value and the sign of another given value (function)

##### Classification and comparison

fpclassify (C99) | classifies the given floating-point value (function)
isfinite (C99) | checks if the given number has finite value (function)
isinf (C99) | checks if the given number is infinite (function)
isnan (C99) | checks if the given number is NaN (function)
isnormal (C99) | checks if the given number is normal (function)
signbit (C99) | checks if the given number is negative (function)
isgreater (C99) | checks if the first floating-point argument is greater than the second (function)
isgreaterequal (C99) | checks if the first floating-point argument is greater or equal than the second (function)
isless (C99) | checks if the first floating-point argument is less than the second (function)
islessequal (C99) | checks if the first floating-point argument is less or equal than the second (function)
islessgreater (C99) | checks if the first floating-point argument is less or greater than the second (function)
isunordered (C99) | checks if two floating-point values are unordered (function)

### Types

Defined in header `<stdlib.h>`
div_t | structure type, return of the div function (typedef)
ldiv_t | structure type, return of the ldiv function (typedef)
lldiv_t (C99) | structure type, return of the lldiv function (typedef)
Defined in header `<inttypes.h>`
imaxdiv_t (C99) | structure type, return of the imaxdiv function (typedef)
Defined in header `<math.h>`
float_t (C99) | most efficient floating-point type at least as wide as float (typedef)
double_t (C99) | most efficient floating-point type at least as wide as double (typedef)

### Macro constants

Defined in header `<math.h>`
HUGE_VALF HUGE_VAL HUGE_VALL (C99)(C99) | indicates value too big to be representable (infinity) by float, double and long double respectively (macro constant)
INFINITY (C99) | evaluates to positive infinity or the value guaranteed to overflow a float (macro constant)
NAN (C99) | evaluates to a quiet NaN of type float (macro constant)
FP_FAST_FMAF FP_FAST_FMA FP_FAST_FMAL (C99)(C99)(C99) | indicates that the fma function generally executes about as fast as, or faster than, a multiply and an add of double operands (macro constant)
FP_ILOGB0 FP_ILOGBNAN (C99)(C99) | evaluates to ilogb(x) if x is zero or NaN, respectively (macro constant)
math_errhandling MATH_ERRNO MATH_ERREXCEPT (C99)(C99)(C99) | defines the error handling mechanism used by the common mathematical functions (macro constant)

##### Classification

FP_NORMAL FP_SUBNORMAL FP_ZERO FP_INFINITE FP_NAN (C99)(C99)(C99)(C99)(C99) | indicates a floating-point category (macro constant)

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.8 Format conversion of integer types <inttypes.h> (p: 217-220)

  - 7.12 Mathematics <math.h> (p: 231-261)

  - 7.22 General utilities <stdlib.h> (p: 340-360)

  - 7.31.5 Format conversion of integer types <inttypes.h> (p: 455)

  - 7.31.12 General utilities <stdlib.h> (p: 456)

- C99 standard (ISO/IEC 9899:1999):

  - 7.8 Format conversion of integer types <inttypes.h> (p: 198-201)

  - 7.12 Mathematics <math.h> (p: 212-242)

  - 7.20 General utilities <stdlib.h> (p: 306-324)

  - 7.26.4 Format conversion of integer types <inttypes.h> (p: 401)

  - 7.26.10 General utilities <stdlib.h> (p: 402)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5 MATHEMATICS <math.h>

  - 4.10 GENERAL UTILITIES <stdlib.h>

  - 4.13.4 Mathematics <math.h>

  - 7.13.7 General utilities <stdlib.h>

### See also

C++ documentation for Common mathematical functions

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