C Programming/C Reference/math.h

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math.h is a header file in the standard library of the C programming language designed for basic mathematical operations. Most of the functions involve the use of floating point numbers. C++ also implements these functions for compatibility reasons and declares them in the header cmath (the C99 functions are not available in the current C++ standard, C++ 98).

All functions that take or return an angle work in radians.

All functions take doubles for floating-point arguments, unless otherwise specified. In C99, to work with floats or long doubles, append an f or an l to the name, respectively.

Mathematical library functions that operate on integers, such as abs, labs, div, and ldiv, are instead specified in the stdlib.h header.

Pre-C99 functions

Name	Description
`acos`	inverse cosine
`asin`	inverse sine
`atan`	one-parameter inverse tangent
`atan2`	two-parameter inverse tangent
`ceil`	ceiling, the smallest integer not less than parameter
`cos`	cosine
`cosh`	hyperbolic cosine
`exp`	exponential function
`fabs`	absolute value (of a floating-point number)
`floor`	floor, the largest integer not greater than parameter
`fmod`	floating-point remainder: `x - y*(int)(x/y)`
`frexp`	break floating-point number down into mantissa and exponent
`ldexp`	scale floating-point number by exponent (see article)
`log`	natural logarithm
`log10`	base-10 logarithm
`modf(x,p)`	returns fractional part of x and stores integral part where pointer p points to
`pow(x,y)`	raise x to the power of y, x^y
`sin`	sine
`sinh`	hyperbolic sine
`sqrt`	square root
`tan`	tangent
`tanh`	hyperbolic tangent

(For functions to convert strings to floating point numbers (atof(), strtod(), etc.), see C Programming/C Reference/stdlib.h.)

(For functions to convert floating point numbers to strings (snprintf(), itoa(), etc.), see C Programming/C Reference/stdio.h and C_Programming/C_Reference/stdlib.h#itoa.)

C99 functions

Name	Description
`acosh`	inverse hyperbolic cosine
`asinh`	inverse hyperbolic sine
`atanh`	inverse hyperbolic tangent
`cbrt`	cube root
`copysign(x,y)`	returns the value of x with the sign of y
`erf`	error function
`erfc`	complementary error function
`exp2(x)`	raise 2 to the power of x, 2^x
`expm1(x)`	one less than the exponential of x, e^x − 1
`fdim(x,y)`	positive difference between x and y, fmax(x−y, 0)
`fma(x,y,z)`	multiply and add, (x * y) + z
`fmax(x,y)`	largest value of x and y
`fmin(x,y)`	smallest value of x and y
`hypot(x,y)`	hypotenuse, sqrt(x² + y²)
`ilogb`	the exponent of a floating-point value, converted to an `int`
`lgamma`	natural log of the absolute value of the gamma function
`llrint`	round to integer (returns `long long`) using current rounding mode
`lrint`	round to integer (returns `long`) using current rounding mode
`llround`	round to integer (returns `long long`)
`lround`	round to integer (returns `long`)
`log1p(x)`	natural logarithm of 1 + x
`log2`	base-2 logarithm
`logb`	extract exponent from floating-point number
`nan(s)`	returns NaN, possibly using string argument
`nearbyint`	round floating-point number to nearest integer
`nextafter(x,y)`	returns next representable value after x (towards y)
`nexttoward(x,y)`	same as `nextafter`, except y is always a `long double`
`remainder(x,y)`	calculates remainder, as required by IEC 60559
`remquo(x,y,p)`	same as `remainder`, but store quotient (as `int`) at target of pointer p
`rint`	round to integer (returns `double`) using current rounding mode
`round`	round to integer (returns `double`), rounding halfway cases away from zero
`scalbln(x,n)`	x * `FLT_RADIX`ⁿ (n is `long`)
`scalbn(x,n)`	x * `FLT_RADIX`ⁿ (n is `int`)
`tgamma`	gamma function
`trunc`	truncate floating-point number

XSI Extensions

Extra functions may be available as X/Open System Interfaces Extensions. These are not present in any ANSI or ISO C standard.

Name	Description
`j0(x)`	Bessel function of x of the first kind of order 0
`j1(x)`	Bessel function of x of the first kind of order 1
`jn(n,x)`	Bessel function of x of the first kind of order n
`scalb(x,y)`	x * `FLT_RADIX`^y (x and y are `double`s)
`y0(x)`	Bessel function of x of the second kind of order 0
`y1(x)`	Bessel function of x of the second kind of order 1
`yn(n,x)`	Bessel function of x of the second kind of order n

The double-to-string conversion functions ecvt, fcvt and gcvt have been deprecated in favour of sprintf.

Mathematical constants (not standard)

Name	Description
`M_E`	The base of natural logarithms.
`M_LOG2E`	The logarithm to base 2 of M_E.
`M_LOG10E`	The logarithm to base 10 of M_E.
`M_LN2`	The natural logarithm of 2.
`M_LN10`	The natural logarithm of 10.
`M_PI`	Pi, the ratio of a circle's circumference to its diameter.
`M_PI_2`	Pi divided by two.
`M_PI_4`	Pi divided by four.
`M_1_PI`	The reciprocal of pi (1/pi).
`M_2_PI`	Two times the reciprocal of pi.
`M_2_SQRTPI`	Two times the reciprocal of the square root of pi.
`M_SQRT2`	The square root of two.
`M_SQRT1_2`	The reciprocal of the square root of two (also the square root of 1/2).

All values are of type double. As an extension, the GNU C library also defines these constants with type long double. The long double macros have a lowercase ‘l’ appended to their names: M_El, M_PIl, and so forth. These are only available if _GNU_SOURCE is defined.

Note: Some programs use a constant named PI which has the same value as M_PI. This constant is not standard; it may have appeared in some old AT&T headers, and is mentioned in Stroustrup's book on C++. It infringes on the user's name space, so the GNU C library does not define it. Fixing programs written to expect it is simple: replace PI with M_PI throughout, or put ‘-DPI=M_PI’ on the compiler command line.

While these constants are common, they are not part of the C standard, so most modern compilers require an explicit definition (such as _USE_MATH_DEFINES in Microsoft Visual C++ ^[1]) for them to be defined when including math.h.

External links

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

References

↑ Math Constants, MSDN.

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