Thoth is a real-time operating system which is designed to be portable over a large set of machines. It is currently running on two minicomputers with quite different architectures. Both the system and application programs which use it are written in a high-level language. Because the system is implemented by the same software on different hardware, it has the same interface to user programs. Hence, application programs which use Thoth are highly portable. Thoth encourages structuring programs as networks of communicating processes by providing efficient interprocess communication primitives.
cumulation of floating-point sums is considered on a computer which performs
t
-digit base
β
floating-point addition with exponents in the range —
m
to
M
. An algorithm is given for accurately summing
n t
-digit floating-point numbers. Each of these
n
numbers is split into
q
parts, forming
q
·
n t
-digit floating-point numbers. Each of these is then added to the appropriate one of
η
auxiliary
t
-digit accumulators. Finally, the accumulators are added together to yield the computed sum. In all,
q
·
n
+
η
- 1
t
-digit floating-point additions are performed. Let
ν
= ⌈(
M
+
m
+ 1)/(
η
+ 1)⌉. If
n
≤ (1/
q
)
β
⌈((
q
-1)/
q
)
t
⌈-
ν
+1
(*), then the relative error in the computed sum is at most ⌈(
t
+ 1)/
ν
⌉
β
1-
t
. Further, with an additional
q
+
η
- 1
t
-digit additions, the computed sum can be corrected to full
t
-digit accuracy.
For example, for the IBM/360 (
β
= 16,
t
= 14,
M
= 63,
m
= 64), typical values for
q
and
η
are
q
= 2 and
η
= 32.
In this case, (*) becomes
n
≤ 1/2 × 16
4
= 32,768, and we have ⌈(
t
+ 1)/
ν
⌉
β
1-
t
= 4 × 16
-13
.
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