math(3)

NAME

math – floating-point mathematical library

LIBRARY

Math Library (libm, -lm)

SYNOPSIS

#include <math.h>

DESCRIPTION

The math library includes the following components:

⟨math.h⟩ Ta basic routines and real-valued functions ⟨complex.h⟩ Ta complex number support ⟨tgmath.h⟩ Ta polymorphic (type-generic) versions of functions ⟨fenv.h⟩ Ta 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

Name Description cbrt cube root fma fused multiply-add hypot Euclidean distance sqrt square root

Classification Macros

Name Description 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

Name Description 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

Name Description copysign copy sign bit fabs absolute value fdim positive difference fmax maximum function (legacy) fmaximum maximum function (prefers ) fmaximum_num maximum function (avoids ) fmaximum_mag maximum magnitude (prefers ) fmaximum_mag_num maximum magnitude (avoids ) fmin minimum function (legacy) fminimum minimum function (prefers ) fminimum_num minimum function (avoids ) fminimum_mag minimum magnitude (prefers ) fminimum_mag_num minimum magnitude (avoids ) signbit extract sign bit

Not a Number Functions

Name Description nan generate a quiet

Residue and Rounding Functions

Name Description 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

Name Description 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

Name Description 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.

HISTORY

A math library with many of the present functions appeared in Version 7 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().