<s>
The	O
level-index	B-Algorithm
(	O
LI	O
)	O
representation	O
of	O
numbers	O
,	O
and	O
its	O
algorithms	O
for	O
arithmetic	B-Algorithm
operations	O
,	O
were	O
introduced	O
by	O
Charles	O
Clenshaw	O
and	O
Frank	O
Olver	O
in	O
1984	O
.	O
</s>
<s>
The	O
symmetric	O
form	O
of	O
the	O
LI	B-Algorithm
system	I-Algorithm
and	O
its	O
arithmetic	B-Algorithm
operations	O
were	O
presented	O
by	O
Clenshaw	O
and	O
Peter	O
Turner	O
in	O
1987	O
.	O
</s>
<s>
Michael	O
Anuta	O
,	O
Daniel	O
Lozier	O
,	O
Nicolas	O
Schabanel	O
and	O
Turner	O
developed	O
the	O
algorithm	O
for	O
symmetric	B-Algorithm
level-index	I-Algorithm
(	O
SLI	O
)	O
arithmetic	B-Algorithm
,	O
and	O
a	O
parallel	O
implementation	O
of	O
it	O
.	O
</s>
<s>
There	O
has	O
been	O
extensive	O
work	O
on	O
developing	O
the	O
SLI	B-Algorithm
arithmetic	I-Algorithm
algorithms	O
and	O
extending	O
them	O
to	O
complex	O
and	O
vector	O
arithmetic	B-Algorithm
operations	O
.	O
</s>
<s>
A	O
sign	B-Algorithm
bit	I-Algorithm
may	O
also	O
be	O
used	O
to	O
allow	O
negative	O
numbers	O
.	O
</s>
<s>
The	O
mapping	O
function	O
is	O
called	O
the	O
generalized	B-Algorithm
logarithm	I-Algorithm
function	I-Algorithm
.	O
</s>
<s>
The	O
generalized	B-Algorithm
logarithm	I-Algorithm
function	I-Algorithm
is	O
closely	O
related	O
to	O
the	O
iterated	O
logarithm	O
used	O
in	O
computer	O
science	O
analysis	O
of	O
algorithms	O
.	O
</s>
