C mathematical functions

Miscellaneous headers:

<assert.h>
<errno.h>
<iso646.h>
<setjmp.h>
<signal.h>
<stdarg.h>

C mathematical operations are a group of functions in the standard library of the C programming language implementing basic mathematical functions.^[1]^[2] 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++.

1 Overview of functions
2 References
3 External links

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.^[1]

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.^[3]

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

C99 adds several functions and types for fine-grained control of floating point computations.^[3] The additional functions and types are defined in fenv.h header (cfenv in C++).

feclearexcept - clears exceptions
fegetenv - stores current floating-point environment
fegetexceptflag - stores current status flags
fegetround - retrieves current rounding direction
feholdexcept - saves current floating-point environment and clears all exceptions
feraiseexcept - raises a floating-point exceptions
fesetenv - sets current floating-point environment
fesetexceptflag - sets current status flags
fesetround - sets current rounding direction
fetestexcept - tests whether certain exceptions have been raised
feupdateenv - restores floating-point environment, but keep current exceptions
fesetprec - 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, 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.

Random number generation

The header stdlib.h (cstdlib in C++) defines several functions that can be used for statistically random number generation^[4]

rand - generates a pseudo-random number
srand - initializes a pseudo-random number generator

References

^ ^a ^b ISO/IEC 9899:1999 specification. p. 212, § 7.12. http://www.open-std.org/jtc1/sc22/wg14/www/docs/n1124.pdf.
^ Prata, Stephen (2004). C primer plus. Sams Publishing. Appendix B, Section V: The Standard ANSI C Library with C99 Additions. ISBN 0-672-32696-5.
^ ^a ^b Prata, Stephen (2004). C primer plus. Sams Publishing. Appendix B, Section VIII: C99 Numeric Computational Enhancements. ISBN 0-672-32696-5.
^ "GNU C Library -- Mathematics". http://www.cs.utah.edu/dept/old/texinfo/glibc-manual-0.02/library_17.html. Retrieved 2 November 2011.

External links

math.h: mathematical declarations – Base Definitions Reference, The Single UNIX® Specification, Issue 7 from The Open Group
Dinkumware math.h reference, a reference of all math.h functions
C++ reference for math functions inherited from C