mirror of https://github.com/mkerrisk/man-pages
267 lines
7.1 KiB
Groff
267 lines
7.1 KiB
Groff
.\" Copyright (c) 2008, Linux Foundation, written by Michael Kerrisk
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.\" <mtk.manpages@gmail.com>
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.\"
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.\" %%%LICENSE_START(VERBATIM)
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.\" Permission is granted to make and distribute verbatim copies of this
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.\" manual provided the copyright notice and this permission notice are
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.\" preserved on all copies.
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.\"
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.\" Permission is granted to copy and distribute modified versions of this
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.\" manual under the conditions for verbatim copying, provided that the
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.\" entire resulting derived work is distributed under the terms of a
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.\" permission notice identical to this one.
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.\"
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.\" Since the Linux kernel and libraries are constantly changing, this
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.\" manual page may be incorrect or out-of-date. The author(s) assume no
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.\" responsibility for errors or omissions, or for damages resulting from
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.\" the use of the information contained herein. The author(s) may not
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.\" have taken the same level of care in the production of this manual,
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.\" which is licensed free of charge, as they might when working
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.\" professionally.
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.\"
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.\" Formatted or processed versions of this manual, if unaccompanied by
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.\" the source, must acknowledge the copyright and authors of this work.
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.\" %%%LICENSE_END
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.\"
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.TH MATH_ERROR 7 2008-08-11 "Linux" "Linux Programmer's Manual"
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.SH NAME
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math_error \- detecting errors from mathematical functions
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.SH SYNOPSIS
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.nf
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.B #include <math.h>
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.B #include <errno.h>
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.B #include <fenv.h>
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.fi
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.SH DESCRIPTION
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When an error occurs,
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most library functions indicate this fact by returning a special value
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(e.g., \-1 or NULL).
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Because they typically return a floating-point number,
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the mathematical functions declared in
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.IR <math.h>
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indicate an error using other mechanisms.
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There are two error-reporting mechanisms:
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the older one sets
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.IR errno ;
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the newer one uses the floating-point exception mechanism (the use of
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.BR feclearexcept (3)
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and
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.BR fetestexcept (3),
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as outlined below)
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described in
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.BR fenv (3).
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A portable program that needs to check for an error from a mathematical
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function should set
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.I errno
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to zero, and make the following call
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.in +4n
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.nf
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feclearexcept(FE_ALL_EXCEPT);
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.fi
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.in
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before calling a mathematical function.
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Upon return from the mathematical function, if
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.I errno
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is nonzero, or the following call (see
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.BR fenv (3))
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returns nonzero
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.in +4n
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.nf
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fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
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FE_UNDERFLOW);
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.fi
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.in
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.\" enum
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.\" {
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.\" FE_INVALID = 0x01,
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.\" __FE_DENORM = 0x02,
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.\" FE_DIVBYZERO = 0x04,
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.\" FE_OVERFLOW = 0x08,
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.\" FE_UNDERFLOW = 0x10,
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.\" FE_INEXACT = 0x20
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.\" };
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then an error occurred in the mathematical function.
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The error conditions that can occur for mathematical functions
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are described below.
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.SS Domain error
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A
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.I domain error
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occurs when a mathematical function is supplied with an argument whose
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value falls outside the domain for which the function
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is defined (e.g., giving a negative argument to
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.BR log (3)).
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When a domain error occurs,
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math functions commonly return a NaN
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(though some functions return a different value in this case);
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.I errno
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is set to
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.BR EDOM ,
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and an "invalid"
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.RB ( FE_INVALID )
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floating-point exception is raised.
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.SS Pole error
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A
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.I pole error
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occurs when the mathematical result of a function is an exact infinity
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(e.g., the logarithm of 0 is negative infinity).
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When a pole error occurs,
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the function returns the (signed) value
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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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depending on whether the function result type is
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.IR double ,
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.IR float ,
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or
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.IR "long double" .
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The sign of the result is that which is mathematically correct for
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the function.
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.I errno
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is set to
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.BR ERANGE ,
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and a "divide-by-zero"
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.RB ( FE_DIVBYZERO )
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floating-point exception is raised.
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.SS Range error
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A
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.I range error
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occurs when the magnitude of the function result means that it
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cannot be represented in the result type of the function.
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The return value of the function depends on whether the range error
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was an overflow or an underflow.
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A floating result
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.I overflows
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if the result is finite,
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but is too large to represented in the result type.
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When an overflow occurs,
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the function returns the value
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.BR HUGE_VAL ,
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.BR HUGE_VALF ,
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or
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.BR HUGE_VALL ,
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depending on whether the function result type is
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.IR double ,
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.IR float ,
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or
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.IR "long double" .
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.I errno
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is set to
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.BR ERANGE ,
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and an "overflow"
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.RB ( FE_OVERFLOW )
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floating-point exception is raised.
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A floating result
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.I underflows
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if the result is too small to be represented in the result type.
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If an underflow occurs,
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a mathematical function typically returns 0.0
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(C99 says a function shall return "an implementation-defined value
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whose magnitude is no greater than the smallest normalized
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positive number in the specified type").
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.I errno
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may be set to
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.BR ERANGE ,
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and an "overflow"
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.RB ( FE_UNDERFLOW )
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floating-point exception may be raised.
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Some functions deliver a range error if the supplied argument value,
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or the correct function result, would be
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.IR subnormal .
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A subnormal value is one that is nonzero,
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but with a magnitude that is so small that
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it can't be presented in normalized form
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(i.e., with a 1 in the most significant bit of the significand).
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The representation of a subnormal number will contain one
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or more leading zeros in the significand.
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.SH NOTES
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The
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.I math_errhandling
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identifier specified by C99 and POSIX.1-2001 is not supported by glibc.
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.\" See CONFORMANCE in the glibc 2.8 (and earlier) source.
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This identifier is supposed to indicate which of the two
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error-notification mechanisms
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.RI ( errno ,
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exceptions retrievable via
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.BR fettestexcept (3))
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is in use.
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The standards require that at least one be in use,
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but permit both to be available.
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The current (version 2.8) situation under glibc is messy.
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Most (but not all) functions raise exceptions on errors.
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Some also set
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.IR errno .
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A few functions set
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.IR errno ,
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but don't raise an exception.
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A very few functions do neither.
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See the individual manual pages for details.
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To avoid the complexities of using
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.I errno
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and
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.BR fetestexcept (3)
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for error checking,
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it is often advised that one should instead check for bad argument
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values before each call.
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.\" http://www.securecoding.cert.org/confluence/display/seccode/FLP32-C.+Prevent+or+detect+domain+and+range+errors+in+math+functions
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For example, the following code ensures that
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.BR log (3)'s
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argument is not a NaN and is not zero (a pole error) or
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less than zero (a domain error):
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.in +4n
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.nf
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double x, r;
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if (isnan(x) || islessequal(x, 0)) {
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/* Deal with NaN / pole error / domain error */
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}
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r = log(x);
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.fi
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.in
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The discussion on this page does not apply to the complex
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mathematical functions (i.e., those declared by
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.IR <complex.h> ),
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which in general are not required to return errors by C99
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and POSIX.1-2001.
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The
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.BR gcc (1)
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.I "-fno-math-errno"
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option causes the executable to employ implementations of some
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mathematical functions that are faster than the standard
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implementations, but do not set
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.I errno
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on error.
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(The
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.BR gcc (1)
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.I "-ffast-math"
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option also enables
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.IR "-fno-math-errno" .)
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An error can still be tested for using
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.BR fetestexcept (3).
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.SH SEE ALSO
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.BR gcc (1),
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.BR errno (3),
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.BR fenv (3),
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.BR fpclassify (3),
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.BR INFINITY (3),
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.BR isgreater (3),
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.BR matherr (3),
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.BR nan (3)
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.I "info libc"
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