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C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical operations.^[1] Most of the functions involve the use of floating point numbers. Different C standards provide different albeit backwards-compatible, sets of functions. C mathematical functions are inherited in C++.

Function overview

Most of the mathematical functions are placed in math.h header (cmath header in C++). The functions that operate on integers, such as abs, labs, div, and ldiv, are instead specified in the stdlib.h header (cstdlib header in C++).

Any functions that operate on angles use radians as the unit of angle.^[1]

In original C, all functions accept only double for the floating-point arguments. In C99, this limitation was fixed by introducing a new set of functions with f or l suffix that work on float and long double arguments respectively.

Basic operations

• abs, labs, llabs - C/C++ - computes absolute value of an integral value
• fabs - C/C++ - computes absolute value of a floating point value
• div, ldiv, lldiv - C/C++ - computes the quotient and remainder of integer division
• fmod- C/C++ - remainder of the floating point division operation
• remainder - C99/C++11 - signed remainder of the division operation
• remquo - C99/C++11 - signed remainder as well as the three last bits of the division operation
• fma - C99/C++11 - fused multiply-add operation
• fmax - C99/C++11 - larger of two floating point values
• fmin - C99/C++11 - smaller of two floating point values
• fdim - C99/C++11 - positive difference of two floating point values
• nan, nanf, nanl - C99/C++11 - returns a not-a-number (NaN)

Exponential functions

• exp - C/C++ - returns e raised to the given power
• exp2 - C99/C++11 - returns 2 raised to the given power
• expm1 - C99/C++11 - returns e raised to the given power, minus one
• log - C/C++ - computes natural (base e) logarithm (to base e)
• log10 - C/C++ - computes common (base 10) logarithm
• log1p - C99/C++11 - computes natural logarithm (to base e) of 1 plus the given number
• ilogb - C99/C++11 - extracts exponent of the number
• logb - C99/C++11 - extracts exponent of the number

Power functions

• sqrt - C/C++ - computes square root
• cbrt - C99/C++11 - computes cubic root
• hypot - C99/C++11 - computes square root of the sum of the squares of two given numbers
• pow - C/C++ - raises a number to the given power

Trigonometric functions

• sin - C/C++ - computes sine
• cos - C/C++ - computes cosine
• tan - C/C++ - computes tangent
• asin - C/C++ - computes arc sine
• acos - C/C++ - computes arc cosine
• atan - C/C++ - computes arc tangent
• atan2 - C/C++ - computes arc tangent, using signs to determine quadrants

Hyperbolic functions

• sinh - C/C++ - computes hyperbolic sine
• cosh - C/C++ - computes hyperbolic cosine
• tanh - C/C++ - computes hyperbolic tangent
• asinh - C99/C++11 - computes hyperbolic arc sine
• acosh - C99/C++11 - computes hyperbolic arc cosine
• atanh - C99/C++11 - computes hyperbolic arc tangent

Error and gamma functions

• erf - C99/C++11 - computes error function
• erfc - C99/C++11 - computes complementary error function
• lgamma - C99/C++11 - computes natural logarithm of the gamma function
• tgamma - C99/C++11 - computes gamma function

Nearest integer floating point operations

• ceil - C/C++ - returns the nearest integer not less than the given value
• floor - C/C++ - returns the nearest integer not greater than the given value
• trunc - C99/C++11 - returns the nearest integer not greater in magnitude than the given value
• round, lround, llround - C99/C++11 - returns the nearest integer, rounding away from zero in halfway cases
• nearbyint - C99/C++11 - returns the nearest integer using current rounding mode
• rint, lrint, llrint - C99/C++11 - returns the nearest integer using current rounding mode with exception if the result differs

Floating point manipulation functions

• frexp - C/C++ - decomposes a number into significand and a power of 2
• ldexp - C/C++ - multiplies a number by 2 raised to a power
• modf - C/C++ - decomposes a number into integer and fractional parts
• scalbn, scalbln - C99/C++11 - multiplies a number by FLT_RADIX raised to a power
• nextafter, nexttoward - C99/C++11 - returns next representable floating point value towards the given value
• copysign - C/C++ - copies the sign of a floating point value

Classification

• fpclassify - C99/C++11 - categorizes the given floating point value
• isfinite - C99/C++11 - checks if the given number has finite value
• isinf - C99/C++11 - checks if the given number is infinite
• isnan - C99/C++11 - checks if the given number is NaN
• isnormal - C99/C++11 - checks if the given number is normal
• signbit - C99/C++11 - checks if the given number is negative

Floating point environment

Declaration	Description
int feclearexcept(int excepts);	clear exceptions specified by excepts
int fegetenv(fenv_t *penv);	store current floating-point environment in penv
int fegetexceptflag(fexcept_t *pflag, int excepts);	store current status flags in pflags
int fegetround(void);	retrieve current rounding direction
int feholdexcept(fenv_t *penv);	save current floating-point environment to penv and clear all exceptions
int feraiseexcept(int excepts);	raise floating-point exceptions
int fesetenv(const fenv_t *penv);	set current floating-point environment to penv
int fesetexceptflag(const fexcept_t *pflags, int excepts);	set current status flags to those stored in pflags
int fesetround(int round);	set current rounding direction to round
int fetestexcept(int excepts);	test whether certain exceptions have been raised
int feupdateenv(const fenv_t *penv);	restore floating-point environment penv, but keep current exceptions
int fesetprec(int prec)	Sets the precision mode to the value specified by prec.

Complex numbers

C99 adds a new _Complex keyword that provides support for complex numbers. Any floating point type can be modified with _Complex. In that case, a variable of such type contains a pair of floating point numbers and in such a way defines a complex number. C++ does not provide complex numbers in backwards compatible way. As an alternative, std::complex can be used.

All operations on complex numbers are defined in complex.h header.

Basic operations

• cabs- C99 - computes absolute value
• carg- C99 - computes argument of a complex number
• cimag- C99 - computes imaginary part of a complex number
• creal- C99 - computes real part of a complex number
• conj- C99 - computes complex conjugate
• cproj- C99 - computes complex projection into the Riemann sphere

Exponentiation operations

• cexp- C99 - computes complex exponential
• clog- C99 - computes complex logarithm
• csqrt- C99 - computes complex square root
• cpow- C99 - computes complex power

Trigonometric operations

• csin- C99 - computes complex sine
• ccos- C99 - computes complex cosine
• ctan- C99 - computes complex tangent
• casin- C99 - computes complex arc sine
• cacos- C99 - computes complex arc cosine
• catan- C99 - computes complex arc tangent

Hyperbolic operations

• csinh- C99 - computes complex hyperbolic sine
• ccosh- C99 - computes complex hyperbolic cosine
• ctanh- C99 - computes complex hyperbolic tangent
• casinh- C99 - computes complex hyperbolic arc sine
• cacosh- C99 - computes complex hyperbolic arc cosine
• catanh- C99 - computes complex hyperbolic arc tangent

Type-generic functions

The header tgmath.h defines a type-generic macro for each mathematical function, so that the same function name can be used to call functions accepting different types of the arguments.

References

External links