7e6cabd06e
Renumber cluase 4 to 3, per what everybody else did when BSD granted them permission to remove clause 3. My insistance on keeping the same numbering for legal reasons is too pedantic, so give up on that point. Submitted by: Jan Schaumann <jschauma@stevens.edu> Pull Request: https://github.com/freebsd/freebsd/pull/96
255 lines
7.0 KiB
Groff
255 lines
7.0 KiB
Groff
.\" Copyright (c) 1985 Regents of the University of California.
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.\" All rights reserved.
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.\"
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.\" Redistribution and use in source and binary forms, with or without
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.\" modification, are permitted provided that the following conditions
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.\" are met:
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.\" 1. Redistributions of source code must retain the above copyright
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.\" notice, this list of conditions and the following disclaimer.
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.\" 2. Redistributions in binary form must reproduce the above copyright
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.\" notice, this list of conditions and the following disclaimer in the
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.\" documentation and/or other materials provided with the distribution.
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.\" 3. Neither the name of the University nor the names of its contributors
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.\" may be used to endorse or promote products derived from this software
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.\" without specific prior written permission.
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.\"
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.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
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.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
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.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
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.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
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.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
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.\" SUCH DAMAGE.
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.\"
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.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91
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.\" $FreeBSD$
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.\"
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.Dd December 5, 2010
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.Dt MATH 3
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.Os
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.Sh NAME
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.Nm math
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.Nd "floating-point mathematical library"
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In math.h
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.Sh DESCRIPTION
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The math library includes the following components:
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.Bl -column "<complex.h>" "polymorphic (type-generic) versions of functions" -compact -offset indent
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.In math.h Ta basic routines and real-valued functions
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.In complex.h Ta complex number support
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.In tgmath.h Ta polymorphic (type-generic) versions of functions
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.In fenv.h Ta routines to control rounding and exceptions
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.El
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The rest of this manual page describes the functions provided by
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.In math.h .
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Please consult
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.Xr complex 3 ,
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.Xr tgmath 3 ,
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and
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.Xr fenv 3
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for information on the other components.
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.Sh "LIST OF FUNCTIONS"
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Each of the following
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.Vt double
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functions has a
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.Vt float
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counterpart with an
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.Ql f
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appended to the name and a
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.Vt "long double"
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counterpart with an
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.Ql l
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appended.
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As an example, the
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.Vt float
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and
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.Vt "long double"
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counterparts of
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.Ft double
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.Fn acos "double x"
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are
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.Ft float
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.Fn acosf "float x"
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and
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.Ft "long double"
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.Fn acosl "long double x" ,
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respectively.
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The classification macros and silent order predicates are type generic and
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should not be suffixed with
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.Ql f
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or
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.Ql l .
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.de Cl
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.Bl -column "isgreaterequal" "bessel function of the second kind of the order 0"
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.Em "Name Description"
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..
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.Ss Algebraic Functions
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.Cl
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cbrt cube root
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fma fused multiply-add
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hypot Euclidean distance
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sqrt square root
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.El
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.Ss Classification Macros
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.Cl
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fpclassify classify a floating-point value
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isfinite determine whether a value is finite
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isinf determine whether a value is infinite
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isnan determine whether a value is \*(Na
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isnormal determine whether a value is normalized
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.El
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.Ss Exponent Manipulation Functions
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.Cl
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frexp extract exponent and mantissa
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ilogb extract exponent
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ldexp multiply by power of 2
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logb extract exponent
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scalbln adjust exponent
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scalbn adjust exponent
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.El
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.Ss Extremum- and Sign-Related Functions
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.Cl
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copysign copy sign bit
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fabs absolute value
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fdim positive difference
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fmax maximum function
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fmin minimum function
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signbit extract sign bit
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.El
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.Ss Not a Number Functions
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.Cl
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nan generate a quiet \*(Na
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.El
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.Ss Residue and Rounding Functions
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.Cl
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ceil integer no less than
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floor integer no greater than
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fmod positive remainder
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llrint round to integer in fixed-point format
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llround round to nearest integer in fixed-point format
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lrint round to integer in fixed-point format
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lround round to nearest integer in fixed-point format
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modf extract integer and fractional parts
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nearbyint round to integer (silent)
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nextafter next representable value
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nexttoward next representable value
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remainder remainder
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remquo remainder with partial quotient
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rint round to integer
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round round to nearest integer
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trunc integer no greater in magnitude than
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.El
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.Pp
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The
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.Fn ceil ,
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.Fn floor ,
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.Fn llround ,
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.Fn lround ,
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.Fn round ,
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and
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.Fn trunc
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functions round in predetermined directions, whereas
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.Fn llrint ,
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.Fn lrint ,
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and
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.Fn rint
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round according to the current (dynamic) rounding mode.
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For more information on controlling the dynamic rounding mode, see
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.Xr fenv 3
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and
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.Xr fesetround 3 .
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.Ss Silent Order Predicates
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.Cl
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isgreater greater than relation
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isgreaterequal greater than or equal to relation
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isless less than relation
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islessequal less than or equal to relation
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islessgreater less than or greater than relation
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isunordered unordered relation
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.El
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.Ss Transcendental Functions
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.Cl
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acos inverse cosine
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acosh inverse hyperbolic cosine
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asin inverse sine
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asinh inverse hyperbolic sine
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atan inverse tangent
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atanh inverse hyperbolic tangent
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atan2 atan(y/x); complex argument
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cos cosine
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cosh hyperbolic cosine
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erf error function
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erfc complementary error function
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exp exponential base e
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exp2 exponential base 2
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expm1 exp(x)\-1
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j0 Bessel function of the first kind of the order 0
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j1 Bessel function of the first kind of the order 1
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jn Bessel function of the first kind of the order n
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lgamma log gamma function
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log natural logarithm
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log10 logarithm to base 10
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log1p log(1+x)
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log2 base 2 logarithm
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pow exponential x**y
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sin trigonometric function
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sinh hyperbolic function
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tan trigonometric function
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tanh hyperbolic function
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tgamma gamma function
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y0 Bessel function of the second kind of the order 0
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y1 Bessel function of the second kind of the order 1
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yn Bessel function of the second kind of the order n
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.El
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.Pp
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The routines
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in this section might not produce a result that is correctly rounded,
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so reproducible results cannot be guaranteed across platforms.
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For most of these functions, however, incorrect rounding occurs
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rarely, and then only in very-close-to-halfway cases.
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.Sh SEE ALSO
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.Xr complex 3 ,
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.Xr fenv 3 ,
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.Xr ieee 3 ,
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.Xr tgmath 3
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.Sh HISTORY
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A math library with many of the present functions appeared in
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.At v7 .
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The library was substantially rewritten for
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.Bx 4.3
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to provide
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better accuracy and speed on machines supporting either VAX
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or IEEE 754 floating-point.
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Most of this library was replaced with FDLIBM, developed at Sun
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Microsystems, in
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.Fx 1.1.5 .
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Additional routines, including ones for
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.Vt float
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and
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.Vt long double
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values, were written for or imported into subsequent versions of FreeBSD.
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.Sh BUGS
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Some of the
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.Vt "long double"
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math functions in
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.St -isoC-99
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are not available.
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.Pp
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Many of the routines to compute transcendental functions produce
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inaccurate results in other than the default rounding mode.
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.Pp
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On the i386 platform, trigonometric argument reduction is not
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performed accurately for huge arguments, resulting in
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large errors
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for such arguments to
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.Fn cos ,
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.Fn sin ,
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and
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.Fn tan .
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