[Boost-bugs] [Boost C++ Libraries] #12527: cpp_bin_float: Anal fixation. Part 3. Double rounding when result of convert_to<double>() is a subnormal

Subject: [Boost-bugs] [Boost C++ Libraries] #12527: cpp_bin_float: Anal fixation. Part 3. Double rounding when result of convert_to<double>() is a subnormal
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2016-10-13 23:46:52

#12527: cpp_bin_float: Anal fixation. Part 3. Double rounding when result of
convert_to<double>() is a subnormal
------------------------------+----------------------------
 Reporter:  Michael Shatz     |      Owner:  johnmaddock
     Type:  Bugs              |     Status:  new
Milestone:  To Be Determined  |  Component:  multiprecision
  Version:  Boost 1.62.0      |   Severity:  Problem
 Keywords:                    |
------------------------------+----------------------------
 When convert_to<double>() applied to numbers in subnormal range the value
 is initially rounded to 53-bit precision and then
 rounded again, by ldexp() routine, to the target precision which is lower
 than 53 bits.
 The problem is exactly the same as the well-known problem that makes it
 virtually impossible to produce 100% IEEE-754 compliant results with Intel
 x87 FPU.

 Because of double rounding, resulting subnormals are not always the
 closest representable double-precision numbers to the original value
 or, in case of tie, they are not always even.

 Exactly the same problem applies to convert_to<float>()

 The attached files demonstrate the problem and one possible workaround,
 not necessarily that fastest, but likely the simplest.

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/12527>
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