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<p>Updated webrev:
<a class="moz-txt-link-freetext" href="http://cr.openjdk.java.net/~apetcher/8208648/webrev.01/">http://cr.openjdk.java.net/~apetcher/8208648/webrev.01/</a><br>
</p>
<p>Thanks for looking at this. See below.<br>
</p>
<div class="moz-cite-prefix">On 12/6/2018 8:03 PM, Jamil Nimeh
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:102ad6c6-30b6-bdb8-9ef4-725315319f79@oracle.com">
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Hi Adam, comments/questions below (mostly simple stuff, nothing
major):<br>
<ul>
<li>IntegerPolynomial.java</li>
<ul>
<li>The comment block for multByInt should reflect your
changes you made, namely the removal of "r" from the
signature.</li>
</ul>
</ul>
</blockquote>
<p>Fixed.<br>
</p>
<blockquote type="cite"
cite="mid:102ad6c6-30b6-bdb8-9ef4-725315319f79@oracle.com">
<ul>
<ul>
<li>88: In the case of multiplying two very large long values
would we ever see those cause an overflow. If so, is it OK
to have them overflow before the reduce operation?<br>
</li>
</ul>
</ul>
</blockquote>
<p>The potential for overflow is the hardest part of all this, and
any overflow will cause serious problems. You can do some
calculations to ensure that overflow doesn't happen. For the
multiplication, these calculations are pretty simple and can be
done manually. For an n-bit representation, each limb has a
maximum magnitude of 2^(n + 1) going into the multiplication. If
there are k limbs, then the maximum magnitude of any limb after
the multiplication is 2^(2n + 2 + log k). There is no overflow
during multiplication as long as this maximum is strictly less
than 2^63. For example, the P-521 field uses 19 limbs with 28 bits
each. So the maximum limb magnitude after multiplication is
2^(2*28 + 2 + log 19) =~ 2^(62.25).</p>
<p>Doing these sorts of calculations to ensure that there is no
overflow during the carry/reduce sequence is much more tedious. I
have a model of this arithmetic that does all this calculation for
me, and that is what I used to ensure there is no overflow. Also,
the unit test (TestIntegerModuloP.java) does a large number of
random operations, and I suspect that it would be very unlikely
for an accidental overflow to get past that test. <br>
</p>
<blockquote type="cite"
cite="mid:102ad6c6-30b6-bdb8-9ef4-725315319f79@oracle.com">
<ul>
<ul>
<li> <br>
</li>
<li>420-425: Looks like this was a copy of the comment block
from conditionalSwap(). Maybe needs to be tailored to what
the conditionalAssign method does?</li>
</ul>
</ul>
</blockquote>
Fixed. <br>
<blockquote type="cite"
cite="mid:102ad6c6-30b6-bdb8-9ef4-725315319f79@oracle.com">
<ul>
<ul>
<li>IntegerPolynomialP256.java, IntegerPolynomialP384.java,
IntegerPolynomialP521.java</li>
<ul>
<li>In the carryReduce0 and carryReduce methods, you have
many uses of an integer literal (33554432 for P256,
134217728 for P384/521). Should these be made as private
static final long values?</li>
</ul>
<li>P256OrderField.java, P384OrderField.java,
P521OrderField.java</li>
<ul>
<li>Similar question about using a static final long vs.
repeated int literal values in the carryReduce* methods.</li>
</ul>
<li>With respect to the last two main bullet items: Would
conversion to a static final value be difficult due to the
fact that they are generated from Fieldgen.jsh?<br>
</li>
</ul>
</ul>
</blockquote>
<p>I changed the literal that was used during the carry operations
to a class constant called CARRY_ADD, and made it more clear what
it is (it is 1 << n for some n). The only literals remaining
are the coefficients that are used in reduction. Making these
constants is a bit more complicated, because there are several
cases to consider, and there are optimizations for each of these
cases to make the code more clear. For example, if the coefficient
is 1, then don't bother multiplying by it. I can make these class
constants, too, but I'm not sure it is worth the trouble. Let me
know what you think. <br>
</p>
<p>Changing the generator to produce better generated code is no
problem, so please let me know if you find more opportunities to
make this code more clear. <br>
</p>
<br>
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