MATH(3) | Library Functions Manual | MATH(3) |
math
—
mathematical library functions
#include
<math.h>
The header file math.h provides function prototypes and macros for working with floating point values.
Each math.h function is provided in three variants: single, double and extended precision. The single and double precision variants operate on IEEE-754 single and double precision values, which correspond to the C types float and double, respectively.
On Intel Macs, the C type long double corresponds to 80-bit IEEE-754 double extended precision. On iOS devices using ARM processors, long double is mapped to double, as there is no hardware-supported wider type.
Details of the floating point formats can be found via "man float".
Users who need to repeatedly perform the same calculation on a large set of data will probably find that the vector math library (composed of vMathLib and vForce) yields better performance for their needs than sequential calls to the libm.
Users who need to perform mathematical operations on complex floating-point numbers should consult the man pages for the complex portion of the math library, via "man complex".
Each of the functions that use floating-point values are provided in single, double, and extended precision; the double precision prototypes are listed here. The man pages for the individual functions provide more details on their use, special cases, and prototypes for their single and extended precision versions.
int
fpclassify
(double)
int
isfinite
(double)
int
isinf
(double)
int
isnan
(double)
int
isnormal
(double)
int
signbit
(double)
These function-like macros are used to classify a single floating-point argument.
double
copysign
(double,
double)
double
nextafter
(double,
double)
copysign
(x,
y) returns the value equal in magnitude to x
with the sign of y.
nextafter
(x,
y) returns the next floating-point number after
x in the direction of y. Both
are correctly-rounded.
double
nan
(const
char *tag)
The
nan
()
function returns a quiet NaN, without raising the invalid flag.
double
ceil
(double)
double
floor
(double)
double
nearbyint
(double)
double
rint
(double)
double
round
(double)
long int
lrint
(double)
long int
lround
(double)
long long int
llrint
(double)
long long int
llround
(double)
double
trunc
(double)
These functions provide various means to round floating-point values to integral values. They are correctly rounded.
double
fmod
(double,
double)
double
remainder
(double,
double)
double
remquo
(double x, double y, int
*)
These return a remainder of the division of x by y
with an integral quotient.
remquo
()
additionally provides access to a few lower bits of the quotient. They are
correctly rounded.
double
fdim
(double,
double)
double
fmax
(double, double)
double
fmin
(double, double)
fmax
(x,
y) and
fmin
(x,
y) return the maximum and minimum of x and
y, respectively.
fdim
(x, y) returns the
positive difference of x and y.
All are correctly rounded.
double
fma
(double
x, double y, double z)
fma
(x,
y, z) computes the value (x*y) + z as though without intermediate
rounding. It is correctly rounded.
double
fabs
(double)
double
sqrt
(double)
double
cbrt
(double)
double
hypot
(double,
double)
fabs
(x),
sqrt
(x),
and
cbrt
(x)
return the absolute value, square root, and cube root of
x, respectively.
hypot
(x,
y) returns sqrt(x*x + y*y). fabs
() and
sqrt
() are correctly rounded.
double
exp
(double)
double
exp2
(double)
double
__exp10
(double)
double
expm1
(double)
exp
(x),
exp2
(x),
__exp10
(x),
and
expm1
(x)
return e**x, 2**x, 10**x, and e**x - 1, respectively.
double
log
(double)
double
log2
(double)
double
log10
(double)
double
log1p
(double)
log
(x),
log2
(x),
and
log10
(x)
return the natural, base-2, and base-10 logarithms of
x, respectively.
log1p
(x)
returns the natural log of 1+x.
double
logb
(double)
int
ilogb
(double)
logb
(x)
and
ilogb
(x)
return the exponent of x.
double
modf
(double,
double *)
double
frexp
(double,
int *)
modf
(x,
&y) returns the fractional part of x and
stores the integral part in y.
frexp
(x,
&n) returns the mantissa of x and stores the
exponent in n. They are correctly
rounded.
double
ldexp
(double,
int)
double
scalbn
(double,
int)
double
scalbln
(double,
long int)
ldexp
(x,
n),
scalbn
(x,
n), and
scalbln
(x,
n) return x*2**n. They are correctly rounded.
double
pow
(double,
double)
pow
(x,y)
returns x raised to the power y.
double
cos
(double)
double
sin
(double)
double
tan
(double)
cos
(x),
sin
(x),
and
tan
(x)
return the cosine, sine and tangent of x,
respectively. Note that x is interpreted as specifying
an angle in radians.
double
cosh
(double)
double
sinh
(double)
double
tanh
(double)
cosh
(x),
sinh
(x),
and
tanh
(x)
return the hyperbolic cosine, hyperbolic sine and hyperbolic tangent of
x, respectively.
double
acos
(double)
double
asin
(double)
double
atan
(double)
double
atan2
(double,
double)
acos
(x),
asin
(x),
and
atan
(x)
return the inverse cosine, inverse sine and inverse tangent of
x, respectively. Note that the result is an angle in
radians.
atan2
(y,
x) returns the inverse tangent of y/x in radians, with sign chosen
according to the quadrant of (x,y).
double
acosh
(double)
double
asinh
(double)
double
atanh
(double)
acosh
(x),
asinh
(x),
and
atanh
(x)
return the inverse hyperbolic cosine, inverse hyperbolic sine and inverse
hyperbolic tangent of x, respectively.
double
tgamma
(double)
double
lgamma
(double)
tgamma
(x)
and
lgamma
(x)
return the values of the gamma function and its logarithm evalutated at
x, respectively.
double
j0
(double)
double
j1
(double)
double
jn
(int,
double)
double
y0
(double)
double
y1
(double)
double
yn
(int,
double)
j0
(x),
j1
(x),
and
jn
(x)
return the values of the zeroth, first, and nth Bessel function of the first
kind evaluated at x, respectively.
y0
(x),
y1
(x),
and
yn
(x)
return the values of the zeroth, first, and nth Bessel function of the
second kind evaluated at x, respectively.
double
erf
(double)
double
erfc
(double)
erf
(x)
and
erfc
(x)
return the values of the error function and the complementary error function
evaluated at x, respectively.
In addition to the functions listed above, math.h defines a number of useful constants, listed below.
CONSTANT VALUE M_E base of natural logarithm, e M_LOG2E log2(e) M_LOG10E log10(e) M_LN2 ln(2) M_LN10 ln(10) M_PI pi M_PI_2 pi / 2 M_PI_4 pi / 4 M_1_PI 1 / pi M_2_PI 2 / pi M_2_SQRTPI 2 / sqrt(pi) M_SQRT2 sqrt(2) M_SQRT1_2 sqrt(1/2)
The libm functions declared in math.h provide mathematical library functions in single-, double-, and extended-precision IEEE-754 floating-point formats on Intel macs, and in single- and double-precision IEEE-754 floating-point formats on PowerPC macs.
The <math.h> functions conform to the ISO/IEC 9899:2011 standard.
August 16, 2012 | macOS 14.6 |