dce5f3abed
Both IEEE-754 2008 and ISO/IEC TS 18661-4 define the half-cycle
trignometric functions cospi, sinpi, and tanpi. The attached
patch implements cospi[fl], sinpi[fl], and tanpi[fl]. Limited
testing on the cospi and sinpi reveal a max ULP less than 0.89;
while tanpi is more problematic with a max ULP less than 2.01
in the interval [0,0.5]. The algorithms used in these functions
are documented in {ks}_cospi.c, {ks}_sinpi.c, and s_tanpi.c.
Note. I no longer have access to a system with ld128 and
adequate support to compile and test the ld128 implementations
of these functions. Given the almost complete lack of input from
others on improvements to libm, I doubt that anyone cares. If
someone does care, the ld128 files contain a number of FIXME comments,
and in particular, while the polynomial coefficients are given
I did not update the polynomial algorithms to properly use the
coefficients.
PR: 218514
MFC after: 2 weeks
107 lines
2.9 KiB
Groff
107 lines
2.9 KiB
Groff
.\" Copyright (c) 2017 Steven G. Kargl <kargl@FreeBSD.org>
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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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.\"
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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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.\" $FreeBSD$
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.\"
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.Dd April 1, 2017
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.Dt TANPI 3
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.Os
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.Sh NAME
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.Nm tanpi ,
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.Nm tanpif ,
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.Nm tanpil
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.Nd half\(encycle tangent functions
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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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.Ft double
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.Fn tanpi "double x"
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.Ft float
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.Fn tanpif "float x"
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.Ft long double
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.Fn tanpil "long double x"
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.Sh DESCRIPTION
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The
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.Fn tanpi ,
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.Fn tanpif ,
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and
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.Fn tanpil
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functions compute the tangent of
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.Fa "\(*p \(mu x"
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and measure angles in half-cycles.
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.Sh RETURN VALUES
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The
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.Fn tanpi ,
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.Fn tanpif ,
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and
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.Fn tanpil
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functions returns
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.Fn tan "\(*p \(mu x" .
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If \*(Bax\*(Ba \*(Ge 2^(p - 1)
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where p is the floating\(enpoint precision of
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.Ar x ,
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then the returned value is \*(Pm0 and it has no significance.
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.Sh SPECIAL VALUES
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.Bl -tag
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.It
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.Fn tanpi \*(Pm0
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returns \*(Pm0.
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.It
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.Fn tanpi \*(Pmn
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returns \*(Pm0 for positive integers
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.Ar n .
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.It
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.Fn tanpi \*(Pmn/2
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returns \*(Na for n > 0 and raises an FE_INVALID exception.
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.It
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.Fn tanpi \*(Pm\(if
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return an \*(Na and raises an FE_INVALID exception.
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.It
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.Fn tanpi \*(Na
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return an \*(Na and raises an FE_INVALID exception.
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.El
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.Sh SEE ALSO
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.Xr cos 3 ,
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.Xr cospi 3 ,
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.Xr fenv 3 ,
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.Xr math 3 ,
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.Xr sin 3 ,
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.Xr sinpi 3 ,
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.Xr tan 3 ,
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.Sh AUTHORS
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The half\(encycle trignometric functions were written by
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.An Steven G. Kargl Aq Mt kargl@FreeBSD.org .
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.Sh STANDARDS
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These functions conform to
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IEEE Std 754\(tm\(en2008 ,
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\(dqIEEE Standard for Floating-Point Arithmetic\(dq
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and to
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ISO/IEC TS 18661-4 ,
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\(dqInformation technology \(em Programming languages, their environments,
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and system software interfaces \(em Floating\(enpoint extensions for
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C\(dq \(em Part 4: Supplementary functions.
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