<a href="quad_float.txt">[more details]</a>
<li>
Added an <tt>ifdef</tt> in <tt>tools.h</tt> that allows
one to suppress the declaration of <tt>min</tt> and <tt>max</tt>
functions in NTL client programs;
these were causing problems when writing 'Windows applications'.
<li>
Implemented a faster algorithm for initializing the
<tt>ZZ_p</tt> auxilliary data structures.
<li>
Polished up a few other minor things in the code and documentation.
</ul>

<p> <hr> <p>

<p>
<h3>
Changes between NTL 4.0a and 4.1a
</h3>
<p>

This is backward compatible with previous versions.

<p>
<ul>
<li>
Made some changes that should make NTL compile smoothly
using any variation of the <tt>C++</tt> language between traditional and 
ISO Standard.
These changes do not affect the documented NTL interface or the
behaviour of NTL.

<li>
Added a flag <tt>NTL_STD_CXX</tt> in the <tt>config.h</tt> file.
Setting this flag causes all of NTL to be "wrapped" in namespace <tt>NTL</tt>,
and that part of the standard library used by NTL is "wrapped"
in namespace <tt>std</tt>.
This should greatly help with the <i>namespace pollution</i> problem.
<a href="tour-stdcxx.html">Go here</a> for more details.

</ul>



<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.9b and 4.0a
</h3>
<p>

This is backward compatible with previous version.

<p>
<ul>
<li>
Attached the GNU General Public License to NTL.

<li>
Fixed two bugs:
<ul>
<li>
one in <tt>ReconstructRational</tt> which resulted in a crash on some inputs;
<li>
one in <tt>exp(RR)</tt> (and by implication in <tt>pow(RR,RR)</tt>),
which led to wrong answers on 64-bit machines when computing <tt>exp(x)</tt>
for <tt>x > 2^53</tt>.
</ul>

<li>
Increased some inconvenient limiting bounds, including a restriction on the 
FFT.

</ul>


<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.9a and 3.9b
</h3>
<p>

This is a minor revision of 3.9a.

<ul>
<li>
Improved time and space efficiency of the HNF routine
(see <a href="HNF.txt"><tt>HNF.txt</tt></a>).
The old version was based on the description in Henri Cohen's book,
which was not really properly optimized.
</ul>



<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.8b and 3.9a
</h3>
<p>

This is backward compatible with previous versions.

<ul>
<li>
Modified the installation script somewhat, adding
a <i>configuration wizard</i> that sets the flags in
<tt>config.h</tt> "automagically".
This works for the <a href="tour-unix.html">Unix version</a> only.

<li>
Improved the <tt>xdouble</tt> input/output and ascii to <tt>xdouble</tt>
conversion.
The old version could be a bit flaky when reading/writing
very large numbers.
The new I/O routines also attain better accuracy.

<li>
Improved conversion routines between <tt>xdouble</tt>
and <tt>ZZ</tt>/<tt>RR</tt>. 

<li>
Improved the <tt>RR</tt> output routine.
The new version should be more accurate and also 
completely platform independent.

<li>
Added the following routines to the <tt>RR</tt> package:
<pre>
   {Trunc,Floor,Ceil,Round}ToZZ, round
   RoundToPrecision, MakeRR
   random
</pre>
See <a href="RR.txt"><tt>RR.txt</tt></a> for details.

<li>
Improved the accuracy of <tt>quad_float</tt> input/output,
and the accuracy of conversion between <tt>quad_float</tt> and <tt>RR</tt>.

<li>
Made the timing function somewhat more robust.

<li>
Hacked the Unix installation script so that it works 
more smoothly with Cygnus tools under Windows.

<li>
Fixed a few other, small problems.
</ul>

<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.8a and 3.8b
</h3>
<p>

This is a minor revision of 3.8a.

<ul>
<li>
Fixed a bug, a memory leak in routine <tt>gauss</tt> for <tt>mat_ZZ_pE</tt>
and <tt>mat_zz_pE</tt>.
<li>
Fixed a minor problem in <tt>config.h</tt>.
<li>
Tightened up some size checks, so that now some nice "size invariants"
are guaranteed, e.g., for a <tt>ZZ</tt> <tt>n</tt>,
<pre>
   NumBits(NumBits(n)) &lt;= NTL_BITS_PER_LONG-4
</pre>
Similarly for the type <tt>GF2X</tt>.
Of course, on most platforms, one will run out of memory before
these bounds are exceeded, but they are nevertheless convenient.
</ul>


<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.7a and 3.8a
</h3>
<p>

This is backward compatible with previous versions.


<ul>
<li>
Added conversion routines from <tt>unsigned</tt> <tt>int</tt>
and <tt>unsigned</tt> <tt>long</tt> to 
<tt>ZZ</tt>, <tt>RR</tt>, <tt>xdouble</tt>, and <tt>quad_float</tt>.

<li>
Added routines <tt>GF2XFromBytes</tt> and <tt>BytesFromGF2X</tt>
for conversion between byte vectors and polynomials over <tt>GF(2)</tt>,
along with routines <tt>NumBits</tt> and <tt>NumBytes</tt>
for such polynomials.
See <a href="GF2X.txt"><tt>GF2X.txt</tt></a> for details.

<li>
Added a hack in the <tt>ZZX</tt> factorizer
to exploit polynomials of the form <tt>g(x^k)</tt>.
This can be disabled by setting the variable <tt>ZZXFac_PowerHack</tt>
to zero.
See <a href="ZZXFactoring.txt"><tt>ZZXFactoring.txt</tt></a>
for details.

<li>
Improved the hensel system solver <tt>solve1</tt>.
See <a href="mat_ZZ.txt"><tt>mat_ZZ.txt</tt></a> for details.

<li>
Changed documentation for <tt>RationalReconstruction</tt>
to reflect the Wang, Guy, Davenport bounds.
See <a href="ZZ.txt"><tt>ZZ.txt</tt></a> for details.

<li>
Improved the routine <tt>GenPrime</tt> a bit. 

<li>
Some other small tweaks here and there.
No real bug fixes.

<li>
Polished the documentation a bit, adding more examples.

</ul>

<p> <hr> <p>

<p>
<h3>
Changes between NTL 3.6b and 3.7a
</h3>
<p>

This is backward compatible with previous versions.

<ul>
<li>
Added a "rational reconstruction" routine. 
See the routine <tt>ReconstructRational</tt> in <a href="ZZ.txt">ZZ.txt</a>.
<li>
Added another routine for solving linear systems over <tt>ZZ</tt>
that is based on Hensel lifting, rather than Chinese Remaindering.
It can be significantly faster in some cases.
See the routine <tt>solve1</tt> in <a href="mat_ZZ.txt">mat_ZZ.txt</a>).
<li>
Some performace tuning, especially CRT and polynomial interpolation code.
<li>
Various documentation corrections.
<li>
Added more "overflow checks" here and there to ensure programs crash gracefully
when certain things get too big.
<li>
Fixed a "benign" bug (i.e., it would never get triggered on any of today's
machines).
<li>
Removed references to <tt>&lt;malloc.h&gt;</tt>, which were unnecessary,
non-standard, and caused problems on some platforms.
</ul>

<p>
<hr>

<p>
<h3>
Changes between NTL 3.6a and 3.6b
</h3>
<p>

Bug fixes.

<p>
<hr>

<p>
<h3>
Changes between NTL 3.5a and 3.6a
</h3>
<p>

This version is backward compatible with 3.5a.

<p>

<ul>

<li>
A few small bug fixes and performance enhancements.

<li>
Changes to the <tt>ZZX</tt> factoring routines that in some
cases yield dramatic performance improvements
(<a href="tour-time.html">more details</a>).

</ul>

<p>
<hr>


<p>
<h3>
Changes between NTL 3.1b and 3.5a
</h3>
<p>

<b>Please note.</b> This version is <b>NOT</b> completely backward compatible.

<p>

Summary of changes:

<ul>

<li>
Improved performance of the "all integer" LLL routine.

<li>
Put in a better pseudo-random number generator,
and added ZZ/byte array conversions.

<li>
Improved performance of primality test, and added a 
more convenient routine <tt>GenPrime</tt>.

<li>
Overloaded NTL's vector placement "new" operator in a different
way to avoid conflicts with standard <tt>C++</tt> library.

<li>
Renamed many macros.

<li>
Renamed header files.

<li>
Made some changes to the packaging
the installation procedure.

</ul>

<p>
<b>Renamed Macros.</b>
I renamed many macros defined in NTL header files.

<p>
The reason is that I want to minimize namespace pollution.
Someday, NTL will be wrapped in a namespace, and when that happens
the only remaining namespace pollution problems will be caused by macros.
Eliminating all macros from NTL is not feasible.
Instead, all NTL defined macros now begin with the prefix "NTL_",
which reduces the namespace pollution to an ecceptable level.
You will probably not be affected by this, unless you
do some low level hacking using a macro like <tt>ZZ_NBITS</tt>
(now called <tt>NTL_NBITS</tt>), or unless you create your
own NTL vectors using a macro like <tt>ntl_vector_decl</tt>
(now called <tt>NTL_vector_decl</tt>).

<p>
For a complete list of affected names, see <a href="names.txt">names.txt</a>.

<p>
Adapting to this name change should be painless, as there is a 
program to translate source files from the old naming convention to the new.
The file "newnames.c", 
can be compiled as either a <tt>C</tt> or <tt>C++</tt>
program. 
The program is a "filter" that copies its input to its output,
replacing all the old macro names by the new macro names.
<p>
In the WinNTL distribibution, "newnames.c" is called 
"newnames.cpp" and is located in the directory
"newnames".


<p>
<b>Renamed header files.</b>
The names of header files themeselves pollute another (extra-linguitsic) namespace.
To alleviate this problem, the header files have been renamed.
Instead of
<pre>
   #include "foo.h"
</pre>
one now should write
<pre>
   #include &lt;NTL/foo.h&gt;
</pre>
The only exceptions are the old header files "ntl_vector.h",
"ntl_matrix.h", and "ntl_pair.h", which are now called
<tt>&lt;NTL/vector.h&gt;</tt>, <tt>&lt;NTL/matrix.h&gt;</tt>, and 
<tt>&lt;NTL/pair.h&gt;</tt>.

<p>
<b>Installation procedure.</b>
Now all
NTL flags like NTL_LONG_LONG, NTL_AVOID_FLOAT, etc., can  now be set
by editing the special file "include/NTL/config.h".
See details in that file.
The reason for this change is that this allows all of these settings
to be made when NTL is configured and built.
Clients of NTL will then automatically use consistent settings.
One should not set these flags on the compiler command line as previously.


<p>
Pentium/Linux people should no longer have to worry
about the NTL_X86_FIX flag. NTL now psychically deduces
the "right thing to do", although if its psychic abilities fail,
you can override it with flags in "include/NTL/config.h".

<p>
The "packaging" in the Unix distribution is slightly
different, but hopefully nicer.
Among other things, the tar file now unpacks into a sub-directory of the current directory.
See <a href="tour-unix.html">the unix installation section</a>
for more details.
The Windows zip file now also 
unpacks into  sub-directory.


<p>
<b>My apologies.</b>
Although these changes are minor, they will cause some NTL
users some inconvenience.
I apologize for this.
I really, really hope there are no more changes like this
(see my <a href="tour-roadmap.html">roadmap</a> of NTL's future).

<p>
<hr>


<p>
<h3>
Changes between NTL 3.1a and 3.1b
</h3>
<p>

Defined functions <tt>div(GF2X,GF2X,GF2)</tt> and <tt>div(GF2X,GF2X,long)</tt>,
which had not been defined in earlier versions.
Affected file: <tt>GF2X.c</tt>.
Most programs never use this, and most linkers do not complain
if these are missing (but some do).

<p>
<hr>

<p>
<h3>
Changes between NTL 3.0f and 3.1a
</h3>
<p>

This version is backward compatible with previous versions.

<p>