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The standard defines the following FP types:

**Single Precision.** (4 consecutive bytes/ number).

Useful for most short calculations.
**Double Precision.** (8 consecutive bytes/number)

Most often used with scientific and engineering numerical computations.
**Extended Precision.** (10 consecutive bytes/number).

Useful for
temporary storage of intermediate results in long calculations.
(e.g. compute a long inner product
in extended precision then convert the result back to double)
There is a single-extended format also. The standard suggests that
implementations should support the extended format corresponding to
the widest basic format supported (since all processors today allow for double
precision, the double-extended format is the only one we discuss here).
Extended precision enables libraries to efficiently compute quantities within
0.5 `ulp`. For example, the result of `x*y` is correct within
0.5 `ulp`, and so is the result of `log(x)`. Clearly,
computing the logarithm is a more involved operation than multiplication;
the log library function performs all the intermediate computations in
extended precision, then rounds the result to single or double precision,
thus avoiding the corruption of more digits and achieving a 0.5 `ulp`
accuracy.
From the user point of view this is transparent, the log function returns a
result correct within 0.5 `ulp`, the same accuracy as simple multiplication
has.

** Next:** Detailed IEEE representation
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Adrian Sandu
2001-08-26