C mathematical functions

C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions. Most of the functions involve the use of floating point numbers. 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++.

Overview of functions

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.

In C89, all functions accept only the type double for the floating-point arguments. In C99, this limitation was fixed by introducing new sets of functions with f and l suffixes that work on float and long double arguments respectively.

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

Exponential functions

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

Power functions

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

Trigonometric functions

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

Hyperbolic functions

• sinh - computes hyperbolic sine
• cosh - computes hyperbolic cosine
• tanh - computes hyperbolic tangent
• asinh - computes hyperbolic arc sine
• acosh - computes hyperbolic arc cosine
• atanh - computes hyperbolic arc tangent

Error and gamma functions

• erf - computes error function
• erfc - computes complementary error function
• lgamma - computes natural logarithm of the gamma function
• tgamma - computes gamma function

Nearest integer floating point operations

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

Floating point manipulation functions

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

Classification

• fpclassify - categorizes the given floating point value
• isfinite - checks if the given number has finite value
• isinf - checks if the given number is infinite
• isnan - checks if the given number is NaN
• isnormal - checks if the given number is normal
• signbit - 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 - computes absolute value
• carg - computes argument of a complex number
• cimag - computes imaginary part of a complex number
• creal - computes real part of a complex number
• conj - computes complex conjugate
• cproj - computes complex projection into the Riemann sphere

Exponentiation operations

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

Trigonometric operations

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

Hyperbolic operations

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

External links

• math.h: mathematical declarations – Base Definitions Reference, The Single UNIX Specification, Version 4 from The Open Group
• Dinkumware math.h reference, a reference of all math.h functions
• C++ reference for math functions inherited from C