MATH(3)

NAME
math - floating-point mathematical library

LIBRARY
libm

SYNOPSIS
#include <math.h>

DESCRIPTION
The math library includes the following components:
<math.h> | basic routines and real-valued functions <complex.h> | complex number support <tgmath.h> | polymorphic (type-generic) versions of functions <fenv.h> | routines to control rounding and exceptions
The rest of this manual page describes the functions provided by <math.h>. Please consult complex(3), tgmath(3), and fenv(3) for information on the other components.

LIST OF FUNCTIONS
Each of the following double functions has a float counterpart with an ‘f’ appended to the name and a long double counterpart with an ‘l’ appended. As an example, the float and long double counterparts of double acos(double x) are float acosf(float x) and long double acosl(long double x), respectively. The classification macros and silent order predicates are type generic and should not be suffixed with ‘f’ or ‘l’.

  Algebraic Functions
cbrt cube root fma fused multiply-add hypot Euclidean distance sqrt square root

  Classification Macros
fpclassify classify a floating-point value isfinite determine whether a value is finite isinf determine whether a value is infinite isnan determine whether a value is isnormal determine whether a value is normalized

  Exponent Manipulation Functions
frexp extract exponent and mantissa ilogb extract exponent ldexp multiply by power of 2 logb extract exponent scalbln adjust exponent scalbn adjust exponent

  Extremum- and Sign-Related Functions
copysign copy sign bit fabs absolute value fdim positive difference fmax maximum function fmin minimum function signbit extract sign bit

  Not a Number Functions
nan generate a quiet

  Residue and Rounding Functions
ceil integer no less than floor integer no greater than fmod positive remainder llrint round to integer in fixed-point format llround round to nearest integer in fixed-point format lrint round to integer in fixed-point format lround round to nearest integer in fixed-point format modf extract integer and fractional parts nearbyint round to integer (silent) nextafter next representable value nexttoward next representable value remainder remainder remquo remainder with partial quotient rint round to integer round round to nearest integer trunc integer no greater in magnitude than

The ceil(), floor(), llround(), lround(), round(), and trunc() functions round in predetermined directions, whereas llrint(), lrint(), and rint() round according to the current (dynamic) rounding mode. For more information on controlling the dynamic rounding mode, see fenv(3) and fesetround(3).

  Silent Order Predicates
isgreater greater than relation isgreaterequal greater than or equal to relation isless less than relation islessequal less than or equal to relation islessgreater less than or greater than relation isunordered unordered relation

  Transcendental Functions
acos inverse cosine acosh inverse hyperbolic cosine asin inverse sine asinh inverse hyperbolic sine atan inverse tangent atanh inverse hyperbolic tangent atan2 atan(y/x); complex argument cos cosine cosh hyperbolic cosine erf error function erfc complementary error function exp exponential base e exp2 exponential base 2 expm1 exp(x)-1 j0 Bessel function of the first kind of the order 0 j1 Bessel function of the first kind of the order 1 jn Bessel function of the first kind of the order n lgamma log gamma function log natural logarithm log10 logarithm to base 10 log1p log(1+x) log2 base 2 logarithm pow exponential x**y sin trigonometric function sinh hyperbolic function tan trigonometric function tanh hyperbolic function tgamma gamma function y0 Bessel function of the second kind of the order 0 y1 Bessel function of the second kind of the order 1 yn Bessel function of the second kind of the order n

The routines in this section might not produce a result that is correctly rounded, so reproducible results cannot be guaranteed across platforms. For most of these functions, however, incorrect rounding occurs rarely, and then only in very-close-to-halfway cases.

SEE ALSO
complex(3), fenv(3), ieee(3), qmath(3), tgmath(3)

HISTORY
A math library with many of the present functions appeared in AT&T UNIX. The library was substantially rewritten for 4.3BSD to provide better accuracy and speed on machines supporting either VAX or IEEE 754 floating-point. Most of this library was replaced with FDLIBM, developed at Sun Microsystems, in FreeBSD 1.1.5. Additional routines, including ones for float and long double values, were written for or imported into subsequent versions of FreeBSD.

BUGS
Many of the routines to compute transcendental functions produce inaccurate results in other than the default rounding mode.

On the i386 platform, trigonometric argument reduction is not performed accurately for huge arguments, resulting in large errors for such arguments to cos(), sin(), and tan().