# Common mathematical functions

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< c‎ | numeric

### 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)

### Constants

Defined in header ``<math.h>``
HUGE_VALFHUGE_VALHUGE_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_FMAFFP_FAST_FMAFP_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_ILOGB0FP_ILOGBNAN (C99)(C99) | evaluates to ilogb (x) if x is zero or NaN, respectively (macro constant)
math_errhandlingMATH_ERRNOMATH_ERREXCEPT (C99)(C99)(C99) | defines the error handling mechanism used by the common mathematical functions (macro constant)

##### Classification

FP_NORMALFP_SUBNORMALFP_ZEROFP_INFINITEFP_NAN (C99)(C99)(C99)(C99)(C99) | indicates a floating-point category (macro constant)

### Functions

Defined in header ``<stdlib.h>``
abslabsllabs (C99) | computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
divldivlldiv (C99) | computes quotient and remainder of integer division (function)
Defined in header ``<inttypes.h>``
imaxabs (C99) | computes absolute value of an integral value (\(\small{|x|}\)|x|) (function)
imaxdiv (C99) | computes quotient and remainder of integer division (function)
Defined in header ``<math.h>``

##### Basic operations

fabsfabsffabsl (C99)(C99) | computes absolute value of a floating-point value (\(\small{|x|}\)|x|) (function)
fmodfmodffmodl (C99)(C99) | computes remainder of the floating-point division operation (function)
remainderremainderfremainderl (C99)(C99)(C99) | computes signed remainder of the floating-point division operation (function)
remquoremquofremquol (C99)(C99)(C99) | computes signed remainder as well as the three last bits of the division operation (function)
fmafmaffmal (C99)(C99)(C99) | computes fused multiply-add operation (function)
fmaxfmaxffmaxl (C99)(C99)(C99) | determines larger of two floating-point values (function)
fminfminffminl (C99)(C99)(C99) | determines smaller of two floating-point values (function)
fdimfdimffdiml (C99)(C99)(C99) | determines positive difference of two floating-point values (\({\small\max{(0, x-y)} }\)max(0, x-y)) (function)
nannanfnanl (C99)(C99)(C99) | returns a NaN (not-a-number) (function)

##### Exponential functions

expexpfexpl (C99)(C99) | computes e raised to the given power (\({\small e^x}\)ex) (function)
exp2exp2fexp2l (C99)(C99)(C99) | computes 2 raised to the given power (\({\small 2^x}\)2x) (function)
expm1expm1fexpm1l (C99)(C99)(C99) | computes e raised to the given power, minus one (\({\small e^x-1}\)ex-1) (function)
loglogflogl (C99)(C99) | computes natural (base-e) logarithm (\({\small \ln{x} }\)ln(x)) (function)
log10log10flog10l (C99)(C99) | computes common (base-10) logarithm (\({\small \log_{10}{x} }\)log10(x)) (function)
log2log2flog2l (C99)(C99)(C99) | computes base-2 logarithm (\({\small \log_{2}{x} }\)log2(x)) (function)
log1plog1pflog1pl (C99)(C99)(C99) | computes natural (base-e) logarithm of 1 plus the given number (\({\small \ln{(1+x)} }\)ln(1+x)) (function)

##### Power functions

powpowfpowl (C99)(C99) | computes a number raised to the given power (\(\small{x^y}\)xy) (function)
sqrtsqrtfsqrtl (C99)(C99) | computes square root (\(\small{\sqrt{x} }\)√x) (function)
cbrtcbrtfcbrtl (C99)(C99)(C99) | computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypothypotfhypotl (C99)(C99)(C99) | computes square root of the sum of the squares of two given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ) (function)

##### Trigonometric functions

sinsinfsinl (C99)(C99) | computes sine (\({\small\sin{x} }\)sin(x)) (function)
coscosfcosl (C99)(C99) | computes cosine (\({\small\cos{x} }\)cos(x)) (function)
tantanftanl (C99)(C99) | computes tangent (\({\small\tan{x} }\)tan(x)) (function)
asinasinfasinl (C99)(C99) | computes arc sine (\({\small\arcsin{x} }\)arcsin(x)) (function)
acosacosfacosl (C99)(C99) | computes arc cosine (\({\small\arccos{x} }\)arccos(x)) (function)
atanatanfatanl (C99)(C99) | computes arc tangent (\({\small\arctan{x} }\)arctan(x)) (function)
atan2atan2fatan2l (C99)(C99) | computes arc tangent, using signs to determine quadrants (function)

##### Hyperbolic functions

sinhsinhfsinhl (C99)(C99) | computes hyperbolic sine (\({\small\sinh{x} }\)sinh(x)) (function)
coshcoshfcoshl (C99)(C99) | computes hyperbolic cosine (\({\small\cosh{x} }\)cosh(x)) (function)
tanhtanhftanhl (C99)(C99) | computes hyperbolic tangent (\({\small\tanh{x} }\)tanh(x)) (function)
asinhasinhfasinhl (C99)(C99)(C99) | computes inverse hyperbolic sine (\({\small\operatorname{arsinh}{x} }\)arsinh(x)) (function)
acoshacoshfacoshl (C99)(C99)(C99) | computes inverse hyperbolic cosine (\({\small\operatorname{arcosh}{x} }\)arcosh(x)) (function)
atanhatanhfatanhl (C99)(C99)(C99) | computes inverse hyperbolic tangent (\({\small\operatorname{artanh}{x} }\)artanh(x)) (function)

##### Error and gamma functions

erferfferfl (C99)(C99)(C99) | computes error function (function)
erfcerfcferfcl (C99)(C99)(C99) | computes complementary error function (function)
tgammatgammaftgammal (C99)(C99)(C99) | computes gamma function (function)
lgammalgammaflgammal (C99)(C99)(C99) | computes natural (base-e) logarithm of the gamma function (function)

##### Nearest integer floating-point operations

ceilceilfceill (C99)(C99) | computes smallest integer not less than the given value (function)
floorfloorffloorl (C99)(C99) | computes largest integer not greater than the given value (function)
trunctruncftruncl (C99)(C99)(C99) | rounds to nearest integer not greater in magnitude than the given value (function)
roundroundfroundllroundlroundflroundlllroundllroundfllroundl (C99)(C99)(C99)(C99)(C99)(C99)(C99)(C99)(C99) | rounds to nearest integer, rounding away from zero in halfway cases (function)
nearbyintnearbyintfnearbyintl (C99)(C99)(C99) | rounds to an integer using current rounding mode (function)
rintrintfrintllrintlrintflrintlllrintllrintfllrintl (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

frexpfrexpffrexpl (C99)(C99) | breaks a number into significand and a power of 2 (function)
ldexpldexpfldexpl (C99)(C99) | multiplies a number by 2 raised to a power (function)
modfmodffmodfl (C99)(C99) | breaks a number into integer and fractional parts (function)
scalbnscalbnfscalbnlscalblnscalblnfscalblnl (C99)(C99)(C99)(C99)(C99)(C99) | computes efficiently a number times FLT_RADIX raised to a power (function)
ilogbilogbfilogbl (C99)(C99)(C99) | extracts exponent of the given number (function)
logblogbflogbl (C99)(C99)(C99) | extracts exponent of the given number (function)
nextafternextafterfnextafterlnexttowardnexttowardfnexttowardl (C99)(C99)(C99)(C99)(C99)(C99) | determines next representable floating-point value towards the given value (function)
copysigncopysignfcopysignl (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 macro)
isfinite (C99) | checks if the given number has finite value (function macro)
isinf (C99) | checks if the given number is infinite (function macro)
isnan (C99) | checks if the given number is NaN (function macro)
isnormal (C99) | checks if the given number is normal (function macro)
signbit (C99) | checks if the given number is negative (function macro)
isgreater (C99) | checks if the first floating-point argument is greater than the second (function macro)
isgreaterequal (C99) | checks if the first floating-point argument is greater or equal than the second (function macro)
isless (C99) | checks if the first floating-point argument is less than the second (function macro)
islessequal (C99) | checks if the first floating-point argument is less or equal than the second (function macro)
islessgreater (C99) | checks if the first floating-point argument is less or greater than the second (function macro)
isunordered (C99) | checks if two floating-point values are unordered (function macro)

### References

- C23 standard (ISO/IEC 9899:2024):

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

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

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

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

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

- C17 standard (ISO/IEC 9899:2018):

  - 7.8 Format conversion of integer types <inttypes.h> (p: 158-160)

  - 7.12 Mathematics <math.h> (p: 169-190)

  - 7.22 General utilities <stdlib.h> (p: 248-262)

  - 7.31.5 Format conversion of integer types <inttypes.h> (p: 332)

  - 7.31.12 General utilities <stdlib.h> (p: 333)

- 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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