Setting the Rounding Precision (cont'd)

We may keep it double precision
(supposing the store-reload applies).

[Q]   If the precision is kept double,
         the result of an operation is rounded twice.
to double prec. (53 bits) when stored in a register
to single prec. (24 bits) when stored in memory

         Can the double-rounded result be differentiated
         from the true result ?

[A]   No problem.
         The double-rounded result cannot be different from the true result.

Results of single-precision addition and subtraction
         reaches only 25 bits at most.
The product reaches 48 bits at most.
The quotient cannot take the form which suffers double rounding.