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.\" Copyright (c) 1985 Regents of the University of California.
.\" All rights reserved.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\" 4. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91
.\" $FreeBSD$
.\"
.Dd December 5, 2010
.Dt MATH 3
.Os
.Sh NAME
.Nm math
.Nd "floating-point mathematical library"
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
.Sh DESCRIPTION
These functions constitute the C math library.
.Sh "LIST OF FUNCTIONS"
Each of the following
.Vt double
functions has a
.Vt float
counterpart with an
.Ql f
appended to the name and a
.Vt "long double"
counterpart with an
.Ql l
appended.
As an example, the
.Vt float
and
.Vt "long double"
counterparts of
.Ft double
.Fn acos "double x"
are
.Ft float
.Fn acosf "float x"
and
.Ft "long double"
.Fn acosl "long double x" ,
respectively.
The classification macros and silent order predicates are type generic and
should not be suffixed with
.Ql f
or
.Ql l .
.de Cl
.Bl -column "isgreaterequal" "bessel function of the second kind of the order 0"
.Em "Name Description"
..
.Ss Algebraic Functions
.Cl
cbrt cube root
fma fused multiply-add
hypot Euclidean distance
sqrt square root
.El
.Ss Classification Macros
.Cl
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 \*(Na
isnormal determine whether a value is normalized
.El
.Ss Exponent Manipulation Functions
.Cl
frexp extract exponent and mantissa
ilogb extract exponent
ldexp multiply by power of 2
logb extract exponent
scalbln adjust exponent
scalbn adjust exponent
.El
.Ss Extremum- and Sign-Related Functions
.Cl
copysign copy sign bit
fabs absolute value
fdim positive difference
fmax maximum function
fmin minimum function
signbit extract sign bit
.El
.Ss Not a Number Functions
.Cl
nan generate a quiet \*(Na
.El
.Ss Residue and Rounding Functions
.Cl
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
.El
.Pp
The
.Fn ceil ,
.Fn floor ,
.Fn llround ,
.Fn lround ,
.Fn round ,
and
.Fn trunc
functions round in predetermined directions, whereas
.Fn llrint ,
.Fn lrint ,
and
.Fn rint
round according to the current (dynamic) rounding mode.
For more information on controlling the dynamic rounding mode, see
.Xr fenv 3
and
.Xr fesetround 3 .
.Ss Silent Order Predicates
.Cl
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
.El
.Ss Transcendental Functions
.Cl
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
.El
.Pp
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.
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr ieee 3 ,
.Xr tgmath 3
.Sh HISTORY
A math library with many of the present functions appeared in
.At v7 .
The library was substantially rewritten for
.Bx 4.3
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
.Fx 1.1.5 .
Additional routines, including ones for
.Vt float
and
.Vt long double
values, were written for or imported into subsequent versions of FreeBSD.
.Sh BUGS
Some of the
.Vt "long double"
math functions in
.St -isoC-99
are not available.
.Pp
Many of the routines to compute transcendental functions produce
inaccurate results in other than the default rounding mode.
.Pp
On the i386 platform, trigonometric argument reduction is not
performed accurately for huge arguments, resulting in
large errors
for such arguments to
.Fn cos ,
.Fn sin ,
and
.Fn tan .
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