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Add Sortix Math Library.
This work is based in part on code from NetBSD libm, libc and kernel. The library is partly public domain and partly BSD-style licensed.
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Jonas 'Sortie' Termansen
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475 changed files with 33962 additions and 92 deletions
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libm/man/fenv.3
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283
libm/man/fenv.3
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.\" $NetBSD: fenv.3,v 1.2 2010/08/04 18:58:28 wiz Exp $
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.\" Copyright (c) 2004 David Schultz <das@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 AUTHOR 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 AUTHOR 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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.Dd March 16, 2005
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.Dt FENV 3
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.Os
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.Sh NAME
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.Nm feclearexcept ,
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.Nm fegetexceptflag ,
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.Nm feraiseexcept ,
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.Nm fesetexceptflag ,
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.Nm fetestexcept ,
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.Nm fegetround ,
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.Nm fesetround ,
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.Nm fegetenv ,
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.Nm feholdexcept ,
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.Nm fesetenv ,
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.Nm feupdateenv ,
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.Nm feenableexcept ,
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.Nm fedisableexcept ,
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.Nm fegetexcept
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.Nd floating-point environment control
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.Sh LIBRARY
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.Lb libm
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.Sh SYNOPSIS
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.In fenv.h
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.Fd "#pragma STDC FENV_ACCESS ON"
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.Ft int
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.Fn feclearexcept "int excepts"
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.Ft int
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.Fn fegetexceptflag "fexcept_t *flagp" "int excepts"
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.Ft int
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.Fn feraiseexcept "int excepts"
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.Ft int
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.Fn fesetexceptflag "const fexcept_t *flagp" "int excepts"
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.Ft int
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.Fn fetestexcept "int excepts"
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.Ft int
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.Fn fegetround void
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.Ft int
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.Fn fesetround "int round"
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.Ft int
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.Fn fegetenv "fenv_t *envp"
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.Ft int
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.Fn feholdexcept "fenv_t *envp"
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.Ft int
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.Fn fesetenv "const fenv_t *envp"
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.Ft int
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.Fn feupdateenv "const fenv_t *envp"
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.Ft int
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.Fn feenableexcept "int excepts"
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.Ft int
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.Fn fedisableexcept "int excepts"
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.Ft int
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.Fn fegetexcept void
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.Sh DESCRIPTION
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The
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.In fenv.h
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routines manipulate the floating-point environment,
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which includes the exception flags and rounding modes defined in
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.St -ieee754 .
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.Ss Exceptions
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Exception flags are set as side-effects of floating-point arithmetic
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operations and math library routines, and they remain set until
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explicitly cleared.
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The following macros expand to bit flags of type
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.Vt int
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representing the five standard floating-point exceptions.
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.Bl -tag -width ".Dv FE_DIVBYZERO"
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.It Dv FE_DIVBYZERO
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A divide-by-zero exception occurs when the program attempts to
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divide a finite non-zero number by zero.
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.It Dv FE_INEXACT
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An inexact exception is raised whenever there is a loss of precision
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due to rounding.
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.It Dv FE_INVALID
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Invalid operation exceptions occur when a program attempts to
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perform calculations for which there is no reasonable representable
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answer.
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For instance, subtraction of infinities, division of zero by zero,
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ordered comparison involving \*(Nas, and taking the square root of a
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negative number are all invalid operations.
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.It Dv FE_OVERFLOW
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An overflow exception occurs when the magnitude of the result of a
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computation is too large to fit in the destination type.
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.It Dv FE_UNDERFLOW
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Underflow occurs when the result of a computation is too close to zero
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to be represented as a non-zero value in the destination type.
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.El
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.Pp
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Additionally, the
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.Dv FE_ALL_EXCEPT
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macro expands to the bitwise OR of the above flags and any
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architecture-specific flags.
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Combinations of these flags are passed to the
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.Fn feclearexcept ,
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.Fn fegetexceptflag ,
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.Fn feraiseexcept ,
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.Fn fesetexceptflag ,
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and
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.Fn fetestexcept
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functions to clear, save, raise, restore, and examine the
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processor's floating-point exception flags, respectively.
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.Pp
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Exceptions may be
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.Em unmasked
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with
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.Fn feenableexcept
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and masked with
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.Fn fedisableexcept .
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Unmasked exceptions cause a trap when they are produced, and
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all exceptions are masked by default.
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The current mask can be tested with
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.Fn fegetexcept .
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.Ss Rounding Modes
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.St -ieee754
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specifies four rounding modes.
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These modes control the direction in which results are rounded
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from their exact values in order to fit them into binary
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floating-point variables.
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The four modes correspond with the following symbolic constants.
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.Bl -tag -width ".Dv FE_TOWARDZERO"
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.It Dv FE_TONEAREST
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Results are rounded to the closest representable value.
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If the exact result is exactly half way between two representable
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values, the value whose last binary digit is even (zero) is chosen.
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This is the default mode.
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.It Dv FE_DOWNWARD
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Results are rounded towards negative \*[If].
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.It Dv FE_UPWARD
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Results are rounded towards positive \*[If].
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.It Dv FE_TOWARDZERO
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Results are rounded towards zero.
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.El
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.Pp
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The
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.Fn fegetround
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and
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.Fn fesetround
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functions query and set the rounding mode.
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.Ss Environment Control
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The
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.Fn fegetenv
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and
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.Fn fesetenv
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functions save and restore the floating-point environment,
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which includes exception flags, the current exception mask,
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the rounding mode, and possibly other implementation-specific
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state.
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The
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.Fn feholdexcept
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function behaves like
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.Fn fegetenv ,
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but with the additional effect of clearing the exception flags and
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installing a
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.Em non-stop
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mode.
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In non-stop mode, floating-point operations will set exception flags
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as usual, but no
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.Dv SIGFPE
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signals will be generated as a result.
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Non-stop mode is the default, but it may be altered by
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non-standard mechanisms.
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.\" XXX Mention fe[gs]etmask() here after the interface is finalized
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.\" XXX and ready to be officially documented.
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The
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.Fn feupdateenv
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function restores a saved environment similarly to
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.Fn fesetenv ,
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but it also re-raises any floating-point exceptions from the old
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environment.
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.Pp
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The macro
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.Dv FE_DFL_ENV
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expands to a pointer to the default environment.
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.Sh EXAMPLES
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The following routine computes the square root function.
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It explicitly raises an invalid exception on appropriate inputs using
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.Fn feraiseexcept .
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It also defers inexact exceptions while it computes intermediate
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values, and then it allows an inexact exception to be raised only if
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the final answer is inexact.
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.Bd -literal -offset indent
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#pragma STDC FENV_ACCESS ON
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double sqrt(double n) {
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double x = 1.0;
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fenv_t env;
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if (isnan(n) || n \*[Lt] 0.0) {
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feraiseexcept(FE_INVALID);
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return (NAN);
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}
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if (isinf(n) || n == 0.0)
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return (n);
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feholdexcept(\*[Am]env);
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while (fabs((x * x) - n) \*[Gt] DBL_EPSILON * 2 * x)
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x = (x / 2) + (n / (2 * x));
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if (x * x == n)
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feclearexcept(FE_INEXACT);
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feupdateenv(\*[Am]env);
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return (x);
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}
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.Ed
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.Sh SEE ALSO
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.Xr c99 1 ,
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.Xr feclearexcept 3 ,
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.Xr fedisableexcept 3 ,
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.Xr feenableexcept 3 ,
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.Xr fegetenv 3 ,
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.Xr fegetexcept 3 ,
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.Xr fegetexceptflag 3 ,
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.Xr fegetround 3 ,
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.Xr feholdexcept 3 ,
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.Xr feraiseexcept 3 ,
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.Xr fesetenv 3 ,
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.Xr fesetexceptflag 3 ,
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.Xr fesetround 3 ,
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.Xr fetestexcept 3 ,
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.Xr feupdateenv 3
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.\"Xr fpgetprec 3 ,
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.\"Xr fpsetprec 3
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.Sh STANDARDS
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Except as noted below,
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.In fenv.h
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conforms to
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.St -isoC-99 .
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The
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.Fn feenableexcept ,
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.Fn fedisableexcept ,
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and
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.Fn fegetexcept
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routines are extensions.
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.Sh HISTORY
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The
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.In fenv.h
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header first appeared in
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.Fx 5.3
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and
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.Nx 6.0 .
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It supersedes the non-standard routines defined in
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.In ieeefp.h
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and documented in
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.Xr fpgetround 3 .
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.Sh CAVEATS
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The FENV_ACCESS pragma can be enabled with
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.Dl "#pragma STDC FENV_ACCESS ON"
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and disabled with the
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.Dl "#pragma STDC FENV_ACCESS OFF"
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directive.
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This lexically-scoped annotation tells the compiler that the program
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may access the floating-point environment, so optimizations that would
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violate strict IEEE-754 semantics are disabled.
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If execution reaches a block of code for which
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.Dv FENV_ACCESS
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is off, the floating-point environment will become undefined.
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.Sh BUGS
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The
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.Dv FENV_ACCESS
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pragma is unimplemented in the system compiler.
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However, non-constant expressions generally produce the correct
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side-effects at low optimization levels.
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