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.
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
cbrt
cube root
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, xy
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
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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, 2x
expm1(x)
one less than the exponential of x, ex − 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_RADIXn (n is long)
scalbn(x,n)
x * FLT_RADIXn (n is int)
tgamma
gamma function
trunc
truncate floating-point number
XSI Extensions
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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_RADIXy (x and y are doubles)
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)
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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.
