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*From*: Joseph Myers <joseph at codesourcery dot com>*To*: <libc-alpha at sourceware dot org>*Date*: Tue, 17 Feb 2015 23:42:32 +0000*Subject*: Refine documentation of libm exceptions goals [committed]*Authentication-results*: sourceware.org; auth=none

This patch refines the math.texi documentation of the goals for when libm function raise the inexact and underflow exceptions. The previous text was problematic in some cases around the underflow threshold. * Strictly, it would have meant that if the mathematical result of pow was very slightly below DBL_MIN, for example, it was required to raise the underflow exception; although normally a few ulps error would be OK, if that error meant the computed value was slightly above DBL_MIN it would fail the previously described underflow exception goal. * Similarly, strict IEEE semantics would imply that sin (DBL_MIN), in round-to-nearest mode, underflows on before-rounding but not after-rounding architectures, while returning DBL_MIN; the previous wording would have required an underflow exception, so preventing checks for a result with absolute value below DBL_MIN from being sufficient checks to determine whether the exception is required. (Under the previous wording, checks for a result with absolute value <= DBL_MIN wouldn't have been sufficient either, because in FE_TOWARDZERO mode a result of DBL_MIN definitely does not result from an underflowing infinite-precision result.) * The previous wording about rounding infinite-precision values could be taken to mean all exceptions including "inexact" must be consistent with some such value. That would mean that a result of DBL_MIN in FE_UPWARD mode with "inexact" raised must also have "underflow" raised on before-rounding architectures. Again, that would cause problems for computing a result (possibly with spurious "inexact" exceptions) and then using a rounding-mode-independent test for results with absolute value below DBL_MIN to determine whether an underflow exception must be forced in case the underflows from intermediate computations happened to be exact. By refining the documentation, this patch avoids stating goals for accuracy close to the underflow threshold that were stricter than applied anywhere else, and allows the implementation strategy of: compute a result within a few ulps, taking care to avoid underflows in intermediate computations, then force an underflow exception if that result was subnormal. Only fully-defined functions such as fma need to take greater care about the exact underflow threshold (including its dependence on whether the architecture is before-rounding or after-rounding, and on the rounding mode on after-rounding architectures). (If the rounding mode is changed as part of the computation, it's still necessary to ensure that not just intermediate computations, but the final computation of the result to be returned, do not raise underflow if that result is the least normal value and underflow would be inconsistent with the original rounding mode. Since such code can readily discard exceptions as part of saving and restoring the rounding mode - SET_RESTORE_ROUND_NOEX etc. - I don't think that should be a problem in practice.) Committed. 2015-02-17 Joseph Myers <joseph@codesourcery.com> * manual/math.texi (Errors in Math Functions): Clarify goals regarding inexact and underflow exceptions. diff --git a/manual/math.texi b/manual/math.texi index 206021c..72f3fda 100644 --- a/manual/math.texi +++ b/manual/math.texi @@ -1313,7 +1313,9 @@ exact value passed as the input. Exceptions are raised appropriately for this value and in accordance with IEEE 754 / ISO C / POSIX semantics, and it is then rounded according to the current rounding direction to the result that is returned to the user. @code{errno} -may also be set (@pxref{Math Error Reporting}). +may also be set (@pxref{Math Error Reporting}). (The ``inexact'' +exception may be raised, or not raised, even if this is inconsistent +with the infinite-precision value.) @item For the IBM @code{long double} format, as used on PowerPC GNU/Linux, @@ -1344,11 +1346,16 @@ subnormal (in each case, with the correct sign), according to the current rounding direction and with the underflow exception raised. @item -Where the mathematical result underflows and is not exactly -representable as a floating-point value, the underflow exception is -raised (so there may be spurious underflow exceptions in cases where -the underflowing result is exact, but not missing underflow exceptions -in cases where it is inexact). +Where the mathematical result underflows (before rounding) and is not +exactly representable as a floating-point value, the function does not +behave as if the computed infinite-precision result is an exact value +in the subnormal range. This means that the underflow exception is +raised other than possibly for cases where the mathematical result is +very close to the underflow threshold and the function behaves as if +it computes an infinite-precision result that does not underflow. (So +there may be spurious underflow exceptions in cases where the +underflowing result is exact, but not missing underflow exceptions in +cases where it is inexact.) @item @Theglibc{} does not aim for functions to satisfy other properties of -- Joseph S. Myers joseph@codesourcery.com

**Follow-Ups**:**Re: Refine documentation of libm exceptions goals [committed]***From:*Szabolcs Nagy

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