[Cfp-interest 1641] Re: C++ floating-point work

[Paul Zimmermann]

       Dear Mike,

> From: "Mike Cowlishaw" <mfc at speleotrove.com>
> Date: Mon, 15 Jun 2020 19:47:19 +0100
> 
> Hi David, thanks for posting this!   I just took a quick skim through 
> P1467R4.html ; one sentence caught my eye:
>  
>     When an implementation supports both binary and decimal floating-point,
> the conversion ranks of a binary type and a decimal type will always be
> unordered, because neither type’s set of values will be a subset of the other
> due to the different radixes. 
>  
> This is not right; binary floating-point types can always be a subset of
> appropriate decimal floating-point types because the latter have a base of
> 5*2 (in C/C++ notation), so you can make an exact conversion using the same
> number of digits.  Decimal floating-point-types, however, cannot be converted
> exactly to binary types (in general) because of that power of five.  
> 
> See http://speleotrove.com/decimal/decifaq1.html for some of the background,
> rationale, etc.

maybe the sentence was only considering numbers representable in the
corresponding format. For example 10^16+2 is representable in binary64 but
not in decimal64. For two formats of the same bit-width I guess a counting
argument can prove that you cannot have inclusion, except if the sets of
representable numbers are the same (modulo the number of encodings of NaN).

Best regards,
Paul