Question: van Vliet: real_width and exp_width

[chris hermansen]

Good afternoon everyone,

The RR pp 162-163 defines two integral values L real width and L exp width
as follows:

int L real width =
      { the smallest integral value such that different strings are
      produced by conversion of '1.0' and of '1.0 + L small real' using
      the pattern d. n(L real width - L 1)d }
   1 - S entier(L ln (L small real) / L ln (L 10));
int L exp width=
      { the smallest integral value such that 'L max real' may be
      converted without error using the pattern
      d. n(L real width - l)d e n(L exp width)d }
   1 + S entler (L ln (L ln (L max real) / L ln (L 10)) / L in (L 10));

We could restate these as

int L real width = 1 - S entier (L log10(L small real));
int L exp width = 1 + S entier (L log10(L log10(L max real)));
proc log10 = (L real x) L real:
    L ln(x) / L ln(L 10.0);

Conversely, van Vliet defines them as follows:

INT {<} xlx real width =
  INT(pseudo49) { the smallest integral value such that different
    values yield different strings using the pattern
    d.n(xlx real width - 1)d } {>};

INT {<} xlx exp width =
  INT(pseudo50) { the smallest integral value such that 'xlx max real'
    may be converted without error using the pattern
    d.n(xlx real width - 1)d e n(xlx exp width)d } {>};

Two things bother me about van Vliet's version of L real width and L exp
width:

   1. he leaves out "produced by conversion of '1.0' and of '1.0 + L small
   real'
   2. why doesn't he just use the formulas of the RR here?

Anyone have any thoughts?

-- 
Chris Hermansen · clhermansen "at" gmail "dot" com

C'est ma façon de parler.
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