C mathematical operations are a group of functions in the standard library

C standard library

The C Standard Library is the standard library for the programming language C, as specified in the ANSI C standard.. It was developed at the same time as the C POSIX library, which is basically a superset of it...

 of the C programming language  implementing basic mathematical functions. Most of the functions involve the use of floating point

Floating point

In computing, floating point describes a method of representing real numbers in a way that can support a wide range of values. Numbers are, in general, represented approximately to a fixed number of significant digits and scaled using an exponent. The base for the scaling is normally 2, 10 or 16...

 numbers. Different C standards provide different albeit backwards-compatible, sets of functions. C mathematical functions are inherited in C++

C++

C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...

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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 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

Absolute value

In mathematics, the absolute value |a| of a real number a is the numerical value of a without regard to its sign. So, for example, the absolute value of 3 is 3, and the absolute value of -3 is also 3...

 of an integral valuefabs - computes absolute value of a floating point valuediv, ldiv, lldiv - computes the quotient and remainder of integer divisionfmod- remainder of the floating point division operationremainder - signed remainder of the division operationremquo - signed remainder as well as the three last bits of the division operationfma - fused multiply-add operationfmax - larger of two floating point valuesfmin - smaller of two floating point valuesfdim - positive difference of two floating point valuesnan, nanf, nanl - returns a not-a-number (NaN)

Exponential functionsexp - returns e raised to the given powerexp2 - returns 2 raised to the given powerexpm1 - returns e raised to the given power, minus onelog - computes natural (base e) logarithm (to base e)log10 - computes common (base 10) logarithmlog1p - computes natural logarithm (to base e) of 1 plus the given numberilogb - extracts exponent of the numberlogb - extracts exponent of the number

Power functionssqrt - computes square root

Square root

In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...

cbrt - computes cubic roothypot - computes square root of the sum of the squares of two given numberspow - raises a number to the given power

Trigonometric functionssin - computes sine

Sine

In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

cos - computes cosinetan - computes tangent

Tangent

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

asin - computes arc sine

Inverse hyperbolic function

The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they give the area of a sector of the unit hyperbola in the same way that the inverse trigonometric functions give the arc length of a sector on the unit circle...

acos - computes arc cosine

Inverse hyperbolic function

The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they give the area of a sector of the unit hyperbola in the same way that the inverse trigonometric functions give the arc length of a sector on the unit circle...

atan - computes arc tangent

Inverse hyperbolic function

The inverses of the hyperbolic functions are the area hyperbolic functions. The names hint at the fact that they give the area of a sector of the unit hyperbola in the same way that the inverse trigonometric functions give the arc length of a sector on the unit circle...

atan2 - computes arc tangent, using signs to determine quadrants

Hyperbolic functionssinh - computes hyperbolic sinecosh - computes hyperbolic cosinetanh - computes hyperbolic tangentasinh - computes hyperbolic arc sineacosh - computes hyperbolic arc cosineatanh - computes hyperbolic arc tangent

Error and gamma functionserf - computes error function

Error function

In mathematics, the error function is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations...

erfc - computes complementary error functionlgamma - computes natural logarithm of the gamma function

Gamma function

In mathematics, the gamma function is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers...

tgamma - computes gamma function

Nearest integer floating point operationsceil - returns the nearest integer not less than the given valuefloor - returns the nearest integer not greater than the given valuetrunc - returns the nearest integer not greater in magnitude than the given valueround, lround, llround - returns the nearest integer, rounding away from zero in halfway casesnearbyint - returns the nearest integer using current rounding moderint, lrint, llrint - returns the nearest integer using current rounding mode with exception if the result differs

Floating point manipulation functionsfrexp - decomposes a number into significand and a power of 2ldexp - multiplies a number by 2 raised to a powermodf - decomposes a number into integer and fractional partsscalbn, scalbln - multiplies a number by FLT_RADIX raised to a powernextafter, nexttoward - returns next representable floating point value towards the given valuecopysign - copies the sign of a floating point value

Classificationfpclassify - categorizes the given floating point valueisfinite - checks if the given number has finite valueisinf - checks if the given number is infiniteisnan - checks if the given number is NaNisnormal - checks if the given number is normalsignbit - checks if the given number is negative

Floating point environment

C99 adds several functions and types for fine-grained control of floating point computations. The additional functions and types are defined in fenv.h header (cfenv in C++

C++

C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...

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• - clears exceptions
• - stores current floating-point environment
• - stores current status flags
• - retrieves current rounding direction
• - saves current floating-point environment and clears all exceptions
• - raises a floating-point exceptions
• - sets current floating-point environment
• - sets current status flags
• - sets current rounding direction
• - tests whether certain exceptions have been raised
• - restores floating-point environment, but keep current exceptions
• - sets the precision mode

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, can be used.

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

Basic operations

• - computes absolute value
• - computes argument of a complex number
  Arg (mathematics)
  In mathematics, arg is a function operating on complex numbers . It gives the angle between the line joining the point to the origin and the positive real axis, shown as in figure 1 opposite, known as an argument of the point In mathematics, arg is a function operating on complex numbers...
  
  
• - computes imaginary part of a complex number
• - computes real part of a complex number - computes complex conjugate
  Complex conjugate
  In mathematics, complex conjugates are a pair of complex numbers, both having the same real part, but with imaginary parts of equal magnitude and opposite signs...
  
  
• - computes complex projection into the Riemann sphere
  Riemann sphere
  In mathematics, the Riemann sphere , named after the 19th century mathematician Bernhard Riemann, is the sphere obtained from the complex plane by adding a point at infinity...
  
  

Exponentiation operations

• - computes complex exponential
  Exponential function
  In mathematics, the exponential function is the function ex, where e is the number such that the function ex is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change In mathematics,...
  
  
• - computes complex logarithm
  Logarithm
  The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
  
  
• - computes complex square root
  Square root
  In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
  
  
• - computes complex power
  Exponentiation
  Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n...
  
  

Trigonometric operations

• - computes complex sine
  Sine
  In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....
  
  
• - computes complex cosine
• - computes complex tangent
• - computes complex arc sine
• - computes complex arc cosine
• - computes complex arc tangent

Hyperbolic operations

• - computes complex hyperbolic sine
• - computes complex hyperbolic cosine
• - computes complex hyperbolic tangent
• - computes complex hyperbolic arc sine
• - computes complex hyperbolic arc cosine
• - 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.

Random number generation

The header stdlib.h (cstdlib in C++) defines several functions that can be used for statistically random number generation
rand - generates a pseudo-random numbersrand - initializes a pseudo-random number generator

External links

• Dinkumware math.h reference, a reference of all math.h functions
• C++ reference for math functions inherited from C