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J.T. Conklin's latest version of the Sun math library. -- Begin comments from J.T. Conklin: The most significant improvement is the addition of "float" versions of the math functions that take float arguments, return floats, and do all operations in floating point. This doesn't help (performance) much on the i386, but they are still nice to have. The float versions were orginally done by Cygnus' Ian Taylor when fdlibm was integrated into the libm we support for embedded systems. I gave Ian a copy of my libm as a starting point since I had already fixed a lot of bugs & problems in Sun's original code. After he was done, I cleaned it up a bit and integrated the changes back into my libm. -- End comments Reviewed by: jkh Submitted by: jtc
1994-08-19 09:40:01 +00:00
.\" 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.
.\" 3. All advertising materials mentioning features or use of this software
.\" must display the following acknowledgement:
.\" This product includes software developed by the University of
.\" California, Berkeley and its contributors.
.\" 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
$Id$ -> $FreeBSD$
1999-08-28 00:22:10 +00:00
.\" $FreeBSD$
J.T. Conklin's latest version of the Sun math library. -- Begin comments from J.T. Conklin: The most significant improvement is the addition of "float" versions of the math functions that take float arguments, return floats, and do all operations in floating point. This doesn't help (performance) much on the i386, but they are still nice to have. The float versions were orginally done by Cygnus' Ian Taylor when fdlibm was integrated into the libm we support for embedded systems. I gave Ian a copy of my libm as a starting point since I had already fixed a lot of bugs & problems in Sun's original code. After he was done, I cleaned it up a bit and integrated the changes back into my libm. -- End comments Reviewed by: jkh Submitted by: jtc
1994-08-19 09:40:01 +00:00
.\"
Document [l]lrint[f]() and [l]lround[f]().
2005-01-11 23:12:17 +00:00
.Dd January 11, 2005
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.Dt MATH 3
.Os
Sanitize the markup, as prompted.
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.if n \{\
.char \[sr] "sqrt
.\}
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.Sh NAME
Sanitize the markup, as prompted.
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.Nm math
.Nd "floating-point mathematical library"
More updates for math(3): - Make some minor rearrangements in the introduction. - Mention the problem with argument reduction on i386. - Add recently-implemented functions to the table. - Un-document the error bounds that only apply to the old 4BSD math library, and fill in the correct values where I know them. No attempt has been made to document bounds lower than 1 ulp, although smaller bounds are usually achievable in round-to-nearest mode.
2004-10-11 20:13:52 +00:00
.Sh LIBRARY
.Lb libm
.Sh SYNOPSIS
.In math.h
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.Sh DESCRIPTION
More updates for math(3): - Make some minor rearrangements in the introduction. - Mention the problem with argument reduction on i386. - Add recently-implemented functions to the table. - Un-document the error bounds that only apply to the old 4BSD math library, and fill in the correct values where I know them. No attempt has been made to document bounds lower than 1 ulp, although smaller bounds are usually achievable in round-to-nearest mode.
2004-10-11 20:13:52 +00:00
These functions constitute the C math library.
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.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
Sanitize the markup, as prompted.
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.Vt "long double"
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
counterpart with an
.Ql l
appended.
As an example, the
.Vt float
and
Sanitize the markup, as prompted.
2005-01-11 20:16:03 +00:00
.Vt "long double"
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
counterparts of
.Ft double
.Fn acos "double x"
are
.Ft float
.Fn acosf "float x"
and
Sanitize the markup, as prompted.
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.Ft "long double"
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.Fn acosl "long double x" ,
respectively.
Many changes, including the following major ones: - Rearrange the list of functions into categories. - Remove the ulps column. It was appropriate for only some of the functions in the list, and correct for even fewer of them. - Add some new paragraphs, and remove some old ones about NaNs that may do more harm than good. - Document precisions other than double-precision.
2005-01-23 22:05:33 +00:00
.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 Functions
.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
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
.\" .Cl
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.\" nan return quiet \*(Na) 0
Many changes, including the following major ones: - Rearrange the list of functions into categories. - Remove the ulps column. It was appropriate for only some of the functions in the list, and correct for even fewer of them. - Add some new paragraphs, and remove some old ones about NaNs that may do more harm than good. - Document precisions other than double-precision.
2005-01-23 22:05:33 +00:00
.\" .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
Add nexttoward to the list of implemented functions, and explicitly list the four that are still missing.
2005-03-07 04:59:53 +00:00
nexttoward next representable value
Many changes, including the following major ones: - Rearrange the list of functions into categories. - Remove the ulps column. It was appropriate for only some of the functions in the list, and correct for even fewer of them. - Add some new paragraphs, and remove some old ones about NaNs that may do more harm than good. - Document precisions other than double-precision.
2005-01-23 22:05:33 +00:00
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
Sanitize the markup, as prompted.
2005-01-11 20:16:03 +00:00
.El
Many changes, including the following major ones: - Rearrange the list of functions into categories. - Remove the ulps column. It was appropriate for only some of the functions in the list, and correct for even fewer of them. - Add some new paragraphs, and remove some old ones about NaNs that may do more harm than good. - Document precisions other than double-precision.
2005-01-23 22:05:33 +00:00
.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
Unlike the algebraic functions listed earlier, the routines
in this section may not produce a result that is correctly rounded.
In general, an unbounded number of digits of a value taken by a
transcendental function may be needed to determine the correctly rounded
result.
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
.Sh SEE ALSO
.Xr fenv 3 ,
.Xr ieee 3
.Sh HISTORY
A math library with many of the present functions appeared in
Sanitize the markup, as prompted.
2005-01-11 20:16:03 +00:00
.At v7 .
The library was substantially rewritten for
.Bx 4.3
to provide
Memory's free, but all the world ain't a VAX anymore. Bring math.3 kicking and screaming into the 1980's. This change converts most of the markup from man(7) to mdoc(7) format, and I believe it removes or updates everything that was flat out wrong. However, much work is still needed to sanitize the markup, improve coverage, and reduce overlap with other manpages. Some of the sections would better belong in a philosophy_of_w_kahan.3 manpage, but they are informative and remain at least as reminders of topics to cover. Reviewed by: doc@, trhodes@
2004-06-19 03:25:28 +00:00
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 .
Many changes, including the following major ones: - Rearrange the list of functions into categories. - Remove the ulps column. It was appropriate for only some of the functions in the list, and correct for even fewer of them. - Add some new paragraphs, and remove some old ones about NaNs that may do more harm than good. - Document precisions other than double-precision.
2005-01-23 22:05:33 +00:00
Additional routines, including ones for
.Vt float
and
.Vt long double
values, were written for or imported into subsequent versions of FreeBSD.
Sort sections.
2005-01-20 09:17:07 +00:00
.Sh BUGS
Add nexttoward to the list of implemented functions, and explicitly list the four that are still missing.
2005-03-07 04:59:53 +00:00
The
.Fn exp2 ,
.Fn log2 ,
.Fn nan ,
and
.Fn remquo
functions are missing, and many functions are not available in their
Sort sections.
2005-01-20 09:17:07 +00:00
.Vt "long double"
variants.
.Pp
On some architectures, trigonometric argument reduction is not
performed accurately, resulting in errors greater than 1
.Em ulp
for large arguments to
.Fn cos ,
.Fn sin ,
and
.Fn tan .
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