id	summary	reporter	owner	description	type	status	milestone	component	version	severity	resolution	keywords	cc
12527	cpp_bin_float: Anal fixation. Part 3. Double rounding when result of convert_to<double>() is a subnormal	Michael Shatz	John Maddock	"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.

"	Bugs	reopened	To Be Determined	multiprecision	Boost 1.62.0	Problem