Re: [boost] test_fp_comparisons and rounding errors

From: Beman Dawes (bdawes_at_[hidden])
Date: 2003-07-05 11:54:45

At 12:18 PM 7/5/2003, Guillaume Melquiond wrote:

 >On Sat, 5 Jul 2003, Beman Dawes wrote:
 >
 >> What is happening here? It seems to me that the error checking code
 >> itself that computes the values to be checked (d1 and d2) introduces 
one
 >> to four possible additional rounding errors. (The error checking code
 >> always does one subtraction, possibly one subtraction in an abs, 
possibly
 >> another subtraction in an abs, and possibly one division). That would
 >> account for the observed behavior.
 >
 >Sorry, I don't see all the substractions you are speaking about, I only
 >see these three floating-point operations in close_at_tolerance:
 >
 >  FPT diff = detail::fpt_abs( left - right );
 >  FPT d1   = detail::safe_fpt_division( diff, detail::fpt_abs( right ) );
 >  FPT d2   = detail::safe_fpt_division( diff, detail::fpt_abs( left ) );

fpt_abs may do a unary "-" operation. I'm assuming, perhaps incorrectly, 
that is essentially subtraction and subject to a possible rounding error.

--Beman