Ada decimal math, an example (or counterexample)

[NCOHEN@IBM.COM (Norman Cohen)]

Sam Harbaugh expects the addition in

  my_dime : dollar_type :=
  0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01;
--   1      2      3      4      5      6      7      8      9     10

to be performed using universal_real addition rather than dollar_type
addition.  Actually, it is performed using dollar_type addition:  Each
real literal is implicitly converted to dollar_type and the ten resulting
dollar_type values are summed.

If Sam had written

  my_dime : constant :=
    0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01 + 0.01;

then exact universal_real addition would have been performed.

The Ada rule is that conversion takes place only at the bottom of the
expression tree: Only numeric literals, named numbers, and attributes
with universal results are convertible.

The rule is given in RM paragraph 4.6(15).  Paragraph 4.6(20) provides
enlightening examples.

Norman Cohen
IBM Research