<s>
Mixed-precision	B-Algorithm
arithmetic	I-Algorithm
is	O
a	O
form	O
of	O
floating-point	B-Algorithm
arithmetic	I-Algorithm
that	O
uses	O
numbers	O
with	O
varying	O
widths	O
in	O
a	O
single	O
operation	O
.	O
</s>
<s>
A	O
common	O
usage	O
of	O
mixed-precision	B-Algorithm
arithmetic	I-Algorithm
is	O
for	O
operating	O
on	O
inaccurate	O
numbers	O
with	O
a	O
small	O
width	O
and	O
expanding	O
them	O
to	O
a	O
larger	O
,	O
more	O
accurate	O
representation	O
.	O
</s>
<s>
For	O
example	O
,	O
two	O
half-precision	O
or	O
bfloat16	O
(	O
16-bit	O
)	O
floating-point	B-Algorithm
numbers	I-Algorithm
may	O
be	O
multiplied	O
together	O
to	O
result	O
in	O
a	O
more	O
accurate	O
single-precision	O
(	O
32-bit	O
)	O
float	B-Algorithm
.	O
</s>
<s>
In	O
this	O
way	O
,	O
mixed-precision	B-Algorithm
arithmetic	I-Algorithm
approximates	O
arbitrary-precision	B-Algorithm
arithmetic	I-Algorithm
,	O
albeit	O
with	O
a	O
low	O
number	O
of	O
possible	O
precisions	O
.	O
</s>
<s>
Mixed-precision	B-Algorithm
arithmetic	I-Algorithm
is	O
touted	O
in	O
the	O
field	O
of	O
machine	O
learning	O
,	O
since	O
gradient	B-Algorithm
descent	I-Algorithm
algorithms	O
can	O
use	O
coarse	O
and	O
efficient	O
half-precision	O
floats	B-Algorithm
for	O
certain	O
tasks	O
,	O
but	O
can	O
be	O
more	O
accurate	O
if	O
they	O
use	O
more	O
precise	O
but	O
slower	O
single	O
-	O
or	O
double-precision	O
floats	B-Algorithm
.	O
</s>
<s>
Some	O
platforms	O
,	O
including	O
Nvidia	O
and	O
AMD	O
GPUs	O
,	O
provide	O
mixed-precision	B-Algorithm
arithmetic	I-Algorithm
for	O
this	O
purpose	O
,	O
using	O
coarse	O
floats	B-Algorithm
when	O
possible	O
,	O
but	O
expanding	O
them	O
to	O
higher	O
precision	O
when	O
necessary	O
.	O
</s>
<s>
Iterative	B-Algorithm
algorithms	I-Algorithm
(	O
like	O
gradient	B-Algorithm
descent	I-Algorithm
)	O
are	O
good	O
candidates	O
for	O
mixed-precision	B-Algorithm
arithmetic	I-Algorithm
.	O
</s>
<s>
In	O
an	O
iterative	B-Algorithm
algorithm	I-Algorithm
like	O
square	O
root	O
,	O
a	O
coarse	O
integral	O
guess	O
can	O
be	O
made	O
and	O
refined	O
over	O
many	O
iterations	O
until	O
the	O
error	O
in	O
precision	O
makes	O
it	O
such	O
that	O
the	O
smallest	O
addition	O
or	O
subtraction	O
to	O
the	O
guess	O
is	O
still	O
too	O
coarse	O
to	O
be	O
an	O
acceptable	O
answer	O
.	O
</s>
<s>
Supercomputers	B-Architecture
such	O
as	O
Summit	B-Device
utilize	O
mixed-precision	B-Algorithm
arithmetic	I-Algorithm
to	O
be	O
more	O
efficient	O
with	O
regards	O
to	O
memory	O
and	O
processing	O
time	O
,	O
as	O
well	O
as	O
power	O
consumption	O
.	O
</s>
