Fwd: math_error.7 draft 3, for review

[Michael Kerrisk]

Andreas,

The latest version of the page is below.

===

Hi Andreas,

(Andries suggested that you probably have the background knowledge to
help here.)

The math man pages in man-pages are in a somewhat sorry state, with
respect to the following:

* Few of the pages properly describe the special cases for Inf, -Inf,
NaN arguments (e.g., compare "man 3 log" with the POSIX.1 page "man 3p
log").

* There isn't a clear discussion of error cases, and how to determine
if an error occurrred using errno and/or fetestexcept(3).

I'm planning to fix each of the math man pages to address these
issues, and use a new page, math_error.7, as an anchor page referenced
by all of the math pages for discussion of how to handle errors.

Would you be willing to review this new page (below) to see whether it
correctly describes the glibc details?  Might you also be willing to
look at a sampling of the changed math page pages that I'll make later
this week/early next week in order to let me know I'm on the right
track in terms of the changes I'm making?

Cheers,

Michael


.\" Copyright (c) 2008, Linux Foundation, written by Michael Kerrisk
.\"     <mtk.manpages@xxxxxxxxx>
.\"
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.\" manual provided the copyright notice and this permission notice are
.\" preserved on all copies.
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.\" manual under the conditions for verbatim copying, provided that the
.\" entire resulting derived work is distributed under the terms of a
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.\"
.\" Since the Linux kernel and libraries are constantly changing, this
.\" manual page may be incorrect or out-of-date.  The author(s) assume no
.\" responsibility for errors or omissions, or for damages resulting from
.\" the use of the information contained herein.  The author(s) may not
.\" have taken the same level of care in the production of this manual,
.\" which is licensed free of charge, as they might when working
.\" professionally.
.\"
.\" Formatted or processed versions of this manual, if unaccompanied by
.\" the source, must acknowledge the copyright and authors of this work.
.\"
.TH MATH_ERROR 7 2008-07-21 "Linux" "Linux Programmer's Manual"
.SH SYNOPSIS
.nf
.B #include <math.h>
.B #include <errno.h>
.B #include <fenv.h>
.fi
.SH NAME
math_error \- detecting errors from mathematical functions
.SH DESCRIPTION
On error, many of the mathematical functions declared in
.IR <math.h>
return a NaN (not a number).
However, rather than looking at the return value
(which is not always possible)
one can also check whether an error was signaled.
There are two signaling mechanisms:
the older one sets
.IR errno ;
the newer one uses the floating-point exception mechanism (the use of
.BR feclearexcept (3)
and
.BR fetestexcept (3),
as outlined below)
described in
.BR fenv (3).

C99 and POSIX.1-2001 specify a
.I math_errhandling
identifier,
which is supposed to indicate which of these two mechanisms is in use;
the standards require that at least one be in use,
but permit both to be available.
Although glibc does not support this identifier,
in practice it supports both mechanisms.

A portable program that needs to check for an error from a mathematical
function should set
.I errno
to zero, and make the following call
.in +4n
.nf

feclearexcept(FE_ALL_EXCEPT);

.fi
.in
before calling a mathematical function.

Upon return from the mathematical function, if
.I errno
is non-zero, or the following call (see
.BR fenv (3))
returns non-zero
.in +4n
.nf

fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW |
             FE_UNDERFLOW);

.fi
.in
.\" enum
.\" {
.\" FE_INVALID = 0x01,
.\" __FE_DENORM = 0x02,
.\" FE_DIVBYZERO = 0x04,
.\" FE_OVERFLOW = 0x08,
.\" FE_UNDERFLOW = 0x10,
.\" FE_INEXACT = 0x20
.\" };
then an error occurred in the mathematical function.

The error conditions that can occur for mathematical functions
are described below.
.SS Domain Error
A
.I domain error
occurs when a mathematical function is supplied with an argument whose
value falls outside the domain for which the function
is defined (e.g., giving a negative argument to
.BR log (3)).
When a domain error occurs,
.I errno
is set to
.BR EDOM ,
and an "invalid"
.RB ( FE_INVALID )
floating-point exception is raised.
.SS Pole Error
A
.I pole error
occurs when the mathematical result of a function is an exact infinity
(e.g., the logarithm of 0 is negative infinity).
When a pole error occurs,
the function returns the (signed) value
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
depending on whether the function result type is
.IR double ,
.IR float ,
or
.IR "long double" .
The sign of the result is that which is mathematically correct for
the function.
.I errno
is set to
.BR ERANGE ,
and a "divide-by-zero"
.RB ( FE_DIVBYZERO )
floating-point exception is raised.
.SS Range Error
A
.I range error
occurs when the magnitude of the function result means that it
cannot be represented in the result type of the function.
The return value of the function depends on whether the range error
was an overflow or an underflow.

A floating result
.I overflows
if the  result is finite,
but is too large to represented in the result type.
When an overflow occurs,
the function returns the value
.BR HUGE_VAL ,
.BR HUGE_VALF ,
or
.BR HUGE_VALL ,
depending on whether the function result type is
.IR double ,
.IR float ,
or
.IR "long double" .
.I errno
is set to
.BR ERANGE ,
and an "overflow"
.RB ( FE_OVERFLOW )
floating-point exception is raised.

A floating result
.I underflows
if the result is too small to be represented in the result type.
If an underflow occurs,
a mathematical function typically returns 0.0
(C99 says a function shall return "an implementation-defined value
whose magnitude is no greater than the smallest normalized
positive number in the specified type").
.\" FIXME(mtk) POSIX.1 says "may" for the following two cases; need to
.\" investigate this further for specific functions.
.I errno
may be set to
.BR ERANGE ,
and an "overflow"
.RB ( FE_UNDERFLOW )
floating-point exception may be raised.

Some functions deliver a range error if the supplied argument value,
or the correct function result, would be
.IR subnormal .
A subnormal value is one that is non-zero,
but with a magnitude that is so small that
it can't be presented in normalized form
(i.e., with a 1 in the most significant bit of the significand).
The representation of a subnormal number will contain one
or more leading zeros in the significand.
.SH NOTES
The
.I math_errhandling
identifier specified by C99 and POSIX.1-2001 is not supported.
.\" See CONFORMANCE in the glibc 2.8 (and earlier) source.

To avoid the complexities of using
.I errno
and
.BR fetestexcept (3)
for error checking,
it is often advised that one should instead check for bad argument
values before each call.
.\" http://www.securecoding.cert.org/confluence/display/seccode/FLP32-C.+Prevent+or+detect+domain+and+range+errors+in+math+functions
For example, the following code ensures that
.BR log (3)'s
argument is not a NaN and is not zero (a pole error) or
less than zero (a domain error):
.in +4n
.nf

double x, r;

if (isnan(x) || islessequal(x, 0)) {
    /* Deal with NaN / pole error / domain error */
}

r = log(x);

.fi
.in
The discussion on this page does not apply to the complex
mathematical functions (i.e., those declared by
.IR <complex.h> ),
which in general are not required to return errors by C99
and POSIX.1-2001.

The
.BR gcc (1)
.I "-fno-math-errno"
option causes the executable to employ implementations of some
mathematical functions that are faster than the standard
implementations, but do not set
.I errno
on error.
(The
.BR gcc (1)
.I "-ffast-math"
option also enables
.IR "-fno-math-errno" .)
An error can still be tested for using
.BR fetestexcept (3).
.fi
.in
.SH SEE ALSO
.BR gcc (1),
.BR errno (3),
.BR fenv (3),
.BR fpclassify (3),
.BR INFINITY (3),
.BR isgreater (3),
.BR matherr (3),
.BR nan (3)
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