C mathematical operations are a group of functions in thestandard library of theC programming language implementing basic mathematical functions.^[1][2] Different C standards provide different, albeit backwards-compatible, sets of functions. Most of these functions are also available in theC++ standard library, though in different headers (the C headers are included as well, but only as a deprecated compatibility feature).

Most of the mathematical functions, which usefloating-point numbers, are defined in<math.h> (<cmath> header in C++). The functions that operate onintegers, such asabs,labs,div, andldiv, are instead defined in the<stdlib.h> header (<cstdlib> header in C++).

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

Not all of these functions are available in theC89 version of the standard. For those that are, the functions accept only typedouble for the floating-point arguments, leading to expensive type conversions in code that otherwise used single-precisionfloat values. In C99, this shortcoming was fixed by introducing new sets of functions that work onfloat andlong double arguments. Those functions are identified byf andl suffixes respectively.^[3]

C99 adds several functions and types for fine-grained control of floating-point environment.^[3] These functions can be used to control a variety of settings that affect floating-point computations, for example, the rounding mode, on what conditions exceptions occur, when numbers are flushed to zero, etc. The floating-point environment functions and types are defined in<fenv.h> header (<cfenv> inC++).

C99 adds a new_Complex keyword (andcomplex convenience macro; only available if the<complex.h> header is included) that provides support for complex numbers. Any floating-point type can be modified withcomplex, and is then defined as a pair of floating-point numbers. Note that C99 and C++ do not implement complex numbers in a code-compatible way – the latter instead provides the classstd::complex.

All operations on complex numbers are defined in the<complex.h> header. As with the real-valued functions, anf orl suffix denotes thefloat complex orlong double complex variant of the function.

A few more complex functions are "reserved for future use in C99".^[5] Implementations are provided by open-source projects that are not part of the standard library.

The header<tgmath.h> defines a type-generic macro for each mathematical function defined in<math.h> and<complex.h>. This adds a limited support forfunction overloading of the mathematical functions: the same function name can be used with different types of parameters; the actual function will be selected at compile time according to the types of the parameters.

Each type-generic macro that corresponds to a function that is defined for both real and complex numbers encapsulates a total of 6 different functions:float,double andlong double, and theircomplex variants. The type-generic macros that correspond to a function that is defined for only real numbers encapsulates a total of 3 different functions:float,double andlong double variants of the function.

The C++ language includes native support for function overloading and thus does not provide the<tgmath.h> header even as a compatibility feature.

The header<stdlib.h> (<cstdlib> in C++) defines several functions that can be used for statistically random number generation.^[6]

Thearc4random family of random number functions are not defined in POSIX standard, but is found in some commonlibc implementations. It used to refer to the keystream generator of a leaked version ofRC4 cipher (hence "allegedRC4"), but different algorithms, usually from other ciphers likeChaCha20, have been implemented since using the same name.

The quality of randomness fromrand are usually too weak to be even considered statistically random, and it requires explicit seeding. It is usually advised to usearc4random instead ofrand when possible. Some C libraries implementrand usingarc4random_uniform internally.

UnderPOSIX systems likeLinux andBSD, the mathematical functions (as declared in<math.h>) are bundled separately in the mathematical librarylibm. Therefore, if any of those functions are used, the linker must be given the directive-lm. There are variouslibm implementations, including:

• GNU libc'slibm
• AMD'slibm,github, used almost as is by Windows
• Intel C++ Compiler libm
• Red Hat'slibm (Newlib)
• Sun'sFDLIBM, which was used as the basis forFreeBSD'smsun andOpenBSD'slibm, both of which in turn were the basis ofJulia'sOpenLibm
• musl'slibm, based on the BSDlibms and other projects like Arm
• LLVM's libm, which is correctly rounded (i.e. errors from the mathematically correct result are lower than 0.5unit in the last place)^[7]
• Arénaire project'sCRlibm (correctly rounded libm), and its successorMetaLibm, which usesRemez algorithm to automatically generate approximations that are formally proven.
• Rutger's RLIBM, which provides correctly rounded functions in single precision.^[8]

Implementations not necessarily under a name oflibm include:

• Arm'soptimized math routines
• GCE-Math is a version of C/C++ math functions written for C++constexpr (compile-time calculation)
• CORE-MATH, correctly rounded for single and double precision.
• SIMD (vectorized) math libraries includeSLEEF,Yeppp!Archived 2020-07-14 at theWayback Machine, andAgner Fog's VCL, plus a few closed-source ones like SVML and DirectXMath.^[9]

• C99 floating-point support

The WikibookC Programming has a page on the topic of:C Programming/C Reference

• math.h: mathematical declarations – Base Definitions Reference,The Single UNIX Specification, Version 5 fromThe Open Group
• C reference for math functions

• C standard library

• Articles with short description
• Short description matches Wikidata
• Articles with example C++ code
• Webarchive template wayback links