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Document some libm error handling intents

This patch documents certain intents regarding libm error handling
that have previously been mentioned on this list without getting any
objections as far as I can tell:

* When matherr is used, exceptions may not be raised (because the
  matherr mechanism predates exceptions).  See
  <>.  This
  makes bugs 6805 and 6806 INVALID.  (Actually, I expect exceptions
  would in fact get raised in all except those particular Bessel
  function TLOSS cases.)  Note that this patch doesn't document the
  need to set _LIB_VERSION to use matherr - it leaves that
  undocumented.  And of course it doesn't rule out deprecating the
  whole matherr / _LIB_VERSION mechanism so new binaries can't use it
  (subject to finding a new solution for -lieee, probably no-errno
  versions of functions used when compiling with -fno-math-errno).

* The intent for setting errno on overflow and underflow is only for
  overflow to infinity and underflow to zero, not for other overflow
  cases (in non-default rounding modes) and underflow to subnormals
  (or, in corner cases, to the least normal).  See
  <>.  This
  makes bugs 6785 and 6795 INVALID, as erf and hypot can never
  underflow to zero.

2013-11-28  Joseph Myers  <>

	* manual/arith.texi (FP Exceptions): Document that exceptions may
	not be raised when matherr is used.
	(Math Error Reporting): Document overflow in directed rounding
	modes.  Document that errno may not be set when finite values are
	returned on overflow.  Document intent to set errno on underflow
	only for underflow to zero.

diff --git a/manual/arith.texi b/manual/arith.texi
index 85aa197..9cd6127 100644
--- a/manual/arith.texi
+++ b/manual/arith.texi
@@ -497,7 +497,8 @@ In the System V math library, the user-defined function @code{matherr}
 is called when certain exceptions occur inside math library functions.
 However, the Unix98 standard deprecates this interface.  We support it
 for historical compatibility, but recommend that you do not use it in
-new programs.
+new programs.  When this interface is used, exceptions may not be
 The exceptions defined in @w{IEEE 754} are:
@@ -806,7 +807,8 @@ an integer.  Do not attempt to modify an @code{fexcept_t} variable.
 Many of the math functions are defined only over a subset of the real or
 complex numbers.  Even if they are mathematically defined, their result
 may be larger or smaller than the range representable by their return
-type.  These are known as @dfn{domain errors}, @dfn{overflows}, and
+type without loss of accuracy.  These are known as @dfn{domain errors},
+@dfn{overflows}, and
 @dfn{underflows}, respectively.  Math functions do several things when
 one of these errors occurs.  In this manual we will refer to the
 complete response as @dfn{signalling} a domain error, overflow, or
@@ -816,11 +818,20 @@ When a math function suffers a domain error, it raises the invalid
 exception and returns NaN.  It also sets @var{errno} to @code{EDOM};
 this is for compatibility with old systems that do not support @w{IEEE
 754} exception handling.  Likewise, when overflow occurs, math
-functions raise the overflow exception and return @math{@infinity{}} or
-@math{-@infinity{}} as appropriate.  They also set @var{errno} to
-@code{ERANGE}.  When underflow occurs, the underflow exception is
-raised, and zero (appropriately signed) is returned.  @var{errno} may be
-set to @code{ERANGE}, but this is not guaranteed.
+functions raise the overflow exception and, in the default rounding
+mode, return @math{@infinity{}} or @math{-@infinity{}} as appropriate
+(in other rounding modes, the largest finite value of the appropriate
+sign is returned when appropriate for that rounding mode).  They also
+set @var{errno} to @code{ERANGE} if returning @math{@infinity{}} or
+@math{-@infinity{}}; @var{errno} may or may not be set to
+@code{ERANGE} when a finite value is returned on overflow.  When
+underflow occurs, the underflow exception is raised, and zero
+(appropriately signed) or a subnormal value, as appropriate for the
+mathematical result of the function and the rounding mode, is
+returned.  @var{errno} may be set to @code{ERANGE}, but this is not
+guaranteed; it is intended that @theglibc{} should set it when the
+underflow is to an appropriately signed zero, but not necessarily for
+other underflows.
 Some of the math functions are defined mathematically to result in a
 complex value over parts of their domains.  The most familiar example of

Joseph S. Myers

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