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11 Dec 2014: v14.1 released. Again thanks to Mike Vang for doing independent-
build and QA work. This release features significant performance and accuracy
improvements for all recent x86 platforms, and especial gains for Intel
Haswell (and soon, Broadwell) users.

First, a note on version numbering: After many years frozen at 3.0x (since my
x86 code was until recently wildly uncompetitive with Prime95), now that I'm
< 2x slower (on Haswell+), resumed version numbering according to the scheme:

Major index = year - 2000
Minor index = release # of that year, zero-indexed.

As before, a patch suffix of x, y, or z following the numeric index indicates
an [alpha,beta,gamma] (experimental,unstable) code. Since I consider this
release stable and it's the 2nd release of the year
, thus 14.1 = [20]14.[--2][no xyz suffix].

What's new/improved:

	1. Self-test now has prestored residues for 10000 iterations
	(at least though FFT length 18432K), in addition to the previously-
	supported 100 and 1000. As before, to use a non-default #iters
	(default is 100) for a given self-test range
	, add '-iters [1000 | 10000]' to the command line.

	2. One no longer needs any special flags like DFT_V* for any FMA-
	using routines - just DUSE_THREADS to enable multithreading
	and DUSE_[SSE2 | AVX | AVX2] to select an x86 SIMD-vector-instruction
	target.

	3. Propagated Fused multiply-add optimizations to all key discrete
	Fourier transform (DFT) and related arithmetic macros. "FMA everywhere"
	means Haswell users should see at least a 10% speedup for their AVX2
	builds, compared to plain AVX.

	4. Overall accuracy should be appreciably better, meaning users should
	see very few roundoff warnings, even for 10Kiter self-tests.

	5. The program now only reports roundoff warnings if it encounters a
	fractional part > 0.40625 (previous was >= 0.4) during the carry step.
	Some self-tests (meaning exponents right at the upper limit for the
	given FFT length, by definition) were emitting slews of 0.40625
	warnings, but as this error level is nearly always benign
	, I've silenced the warnings for it.
	Larger errors will still emit warnings as before.

	6. The accuracy-problematic radix-11 DFTs (used to build composite
	leading radices such as 44 and 176) have improved accuracy in SSE2
	and AVX modes, but will still emit a few roundoff warnings in longer
	self-tests for certain radix combos in those build types. In AVX2 mode
	, however, the fact that "multiplies are free" (assuming we can fuse
	them with adds, which we can to a very large extent in this case)
	allowed me implement an entirely different radix-11 algorithm which is
	much more multiply-heavy, but has significantly better roundoff
	properties. Thus AVX2 builders will see dramatically lower roundoff
	errors for FFT lengths using the aforementioned leading radices 44
	and 176.

	7. I added large-stride prefetching to all the carry routines, since
	the 2 DFTs (specifically the final-radix-pass of the inverse FFT
	, followed by the normalize/carry step, followed by the initial-
	radix-pass of the subsequent iteration's forward FFT) bookending the
	carry step in those access data in large strides and are thus
	problematic for the kinds of default data prefetching done by most x86
	hardware. That "manual assist" prefetch should provide a nice boost (5-
	10% for me at FFT lengths in the Mdoubles range) for all build modes.


18 Sep 2014: Special thanks to Mike Vang for doing significant amounts of QA
work and making numerous feature-related suggestions for this version.
This release features mostly modest changes:

	Restoration of 32-bit USE_SSE2 build mode (GCC/clang only - no Visual
	Studio). But see the comments in the build section regarding the need
	to build some files using GCC
	(i.e. no pure-Clang builds in 32-bit mode).

	A new initial-FFT-pass/final-iFFT-pass radices 288, which should
	provide a decent (~5%%) speedup for folks doing 100Mdigit-range
	assignments (FFT length 18Mdoubles = 18432K).

	To allow for incremental rerun of testcases (e.g. ones which fail to
	match an independent test done by another user/machine, which is the
	standard matching-double-check requirement for "exponent retirement"
	by GIMPS, the program now saves a unique-named bytewise restart file
	every millionth iteration, i.e. if you are testing the Mersenne
	number M(XXX), in addition to the status (log) file pXXX.stat and the
	pair of redundant checkpoint files pXXX and qXXX, you will also see
	files pXXX.1M, pXXX.2M, etc, get deposited as those iteration
	milestones are passed. Note that in order to avoid an unneeded file-
	copy and to minimize the chances of a bad disk sector from corrupting
	a run, the way this works is that when it comes time to write the
	checkpoint files for (say) iteration 1010000 (1.01M), the code simply
	renames the current pXXX savefile (containing data for iteration 1M)
	to pXXX.1M, then creates a new pXXX file to write the new-checkpoint
	data to. (The redundant q-savefile is unaffected by this).
	Note also that as these files do pile up quickly on a fast machine
	, especially if disk space is constrained (for instance if you are
	using a smallish SSD rather than a big old-style moving-parts HD)
	, you will want to "offload" these Miteration files periodically to
	either a larger drive or backup media, and/or delete them if the
	result double-checks OK.)


23 Jun 2014: Special thanks to Stephen Searle for doing significant amounts of
analysis and debug of the code in this version.
This release features the following major enhancements and changes:

	Continuing the multithread optimizations described in the previous
	release below, new initial-FFT-pass/final-iFFT-pass radices
	128,144,160,176,192,208,224,240,256, as well as some larger
	experimental radices 768,960,1008 and 4032. The latter are not
	currently useful for LL testing (as the obligatory self-tests which
	create the mlucas.cfg file optimized for the user's machine will
	reveal, by way of absence of said radices in the best-radix-set data
	captured in the .cfg file), but the radices in the 128-256 range
	should provide a benefit for most users, especially for FFT lengths
	of roughly 2048 Kdoubles and larger.

	Fused-multiply-add (FMA) support for Intel Haswell (and beyond).
	Since Intel released their FMA support in the same chip generation they
	used to deploy the AVX2 instructions, use of FMA is triggered via
	-DUSE_AVX2 at compile time. Currently only a limited fraction of the
	key code macros use FMA, but this will continue to expand as I get a
	better sense of where use of FMA is most likely to yield a benefit.
	(This depends sensitively on the details of the particular FFT
	implementation, for example whether a pre-twiddles or post-twiddles
	complex-multiply scheme is used for the various passes of the inverse
	FFT; Mlucas uses the latter, which is nice from a dataflow-symmetry
	and auxiliary-data-indexing perspective, but is not favorable for an
	FMA-based code speedup.)

	A compact-object code scheme for all the carry-step-wrapping DFT
	radices >= 32. This yields a significant throughout boost for older
	and more bandwidth-limited processors such as Core2 and Sandy/Ivy
	Bridge. The speedups are more modest on Haswell, but even there the
	user will at least enjoy the slashed compile times for the larger-radix
	radix**_ditN_cy_dif1.c sourcefiles in question. Compile (and likely
	run-times) for non-SIMD (i.e. scalar-double C code) builds on non-x86
	hardware will benefit similarly.

	Multiple bugfixes, most related to self-testing and thread-safeness.

	The format for the per-iteration timing data written to mlucas.cfg file
	created by the running the automated self-tests is changed from seconds
	to milliseconds in this version, to provide finer-grained numbers.


02 Oct 2013 (Patched rev1 posted 09 May 2014): This features the following
major enhancements and changes:

	AVX-instructions-set inline assembly support for 64-bit Linux/GCC MacOS
	(both GCC and LLVM/clang). This yields nice speedups over the SSE2-
	based SIMD code on Intel chips supporting AVX (Sandy/Ivy Bridge and
	Haswell/Broadwell). Owners of AMD CPUs featuring AVX are welcome to try
	the code out, but should not get their hopes up too much, as AMD's
	implementation of AVX appears to be disappointing int terms of
	performance.

	Although the 32-bit Windows/MSVC and Linux/GCC inline assembler of the
	previous release is still all there, as of this version 32-bit support
	for x86 SIMD builds is officially discontinued. Builders using 64-bit
	Windows should use a *nix virtualization package such as mingw64.

	The previously-available-by-request-only threadpool code is now
	included in the release. See build instructions below for details.

	Several new carry-step-wrapping "initial FFT pass" DFT radices:
	48,56,64, all fully SIMD-capable. These are added to the existing
	SIMD-capable radix-16,20,24,28,32,36,40,44,52,60 carry-step-wrapping
	DFTs. The reason I added the new radices is related to ongoing
	experience with multithreaded performance: In particular
	, leading radices greater than 32 or so tend to perform quite poorly
	in unthreaded-build mode and for FFT lengths < 2048 Kdoubles
	(which guided most of the codebase evolution until quite recently)
	, but are standouts in multithreaded mode and for large FFT lengths.
	Since the parallelization strategy I use for my FFT means that
	"maximum number of independent thread-based work chunks" is directly
	related to the above leading-radix, the emerging manycore
	(GPU and similar) paradigm will be driving adoption of even larger DFT
	radices in future releases.

	Multithreaded (pthread/threadpool) support extended to the non-SIMD
	(i.e. scalar-double) code. This replaces the previous and only-
	partially-working threading model based on the OpenMP API, with its
	weird (and virtually-impossible-to-debug) performance issues and
	opaque interface. For code such as mine, opacity of the threading-
	interface is not advantageous, especially in terms of basic-
	development-and-debug work.


04 Feb 2013:

	Lots of SSE2-related enhancements, including inline assembler optimized
	for 64-bit OSes via use of the full 16-XMM-register set. New SSE2-
	supported carry-step-wrapping DFT radices, yielding SSE2-able radix-16
	,20,24,28,32,36,40,44,52,60 carry steps.

	Multithreaded (pthread/threadpool) SSE2 support! This code was used for
	the new-Mersenne-prime verification run described below. The threadpool
	code is not included in the default release; please contact the author
	if you wish to play with multithreaded builds of the code.

	Mlucas SSE2 used to verify the 48th known Mersenne prime. Note that the
	the author could have done the verification himself in around 11 days
	on his humble quad-core Sandy Bridge box, but since for new-prime
	verifies such as this wall-clock time is the overriding factor
	, it makes sense to run on the fastest hardware available, even if
	this is relatively less efficient than running on a fewer-core
	workstation. In the present case, Serge Batalov ran the verify in 6
	days on a 32-core Xeon cluster kindly made available by Novartis Inc.
	Due to poor scaling of the parallel code beyond 4 cores, this
	represents significantly more total cycles (and watt-hours) than a 4-
	core run would need, but we find new Mersenne primes rarely enough
	that such cycle-wastage is justified. (And Why hog all the fun, I say -
	Serge said he hadn't had this much computational fun in years.)


06 Nov 2009: Well, it took a full year longer than I had hoped, but a tarball
of the Mlucas v3.0 beta code described in the entry below is finally available.
This has SSE2 inline assembly support for 32-bit Windows and 32/64-bit Linux
, but no PrimeNet support (yet) ... the latter will come later this year, if
things go reasonably according to plan. A GUI will have to wait for at least
another year. But the code is sufficiently ready for early adopters to run on
their x86 machines (Win32, 32 and 64-bit Linux and MacOS ... code is most-
optimized for the latter) and for builders, profilers and assembler experts to
have a look and send me feedback and suggestions for improvement.


15 Sep 2008: Mlucas 3.0 used to verify 45th and 46th known Mersenne primes.
Note that the verify runs by Tom Duell and Rob Giltrap of Sun Microsystems used
a pre-beta version of Mlucas 3.0, scheduled for official release later this
Fall. Key new features of the upcoming release [besides a radically overhauled
header-file structure and many other code cleanups and bugfixes] include:

	SSE2 inline assembly support [at least for FFT lengths which are powers
	of 2 or divisible by the small odd primes 3, 5 and 7] - this will
	provide a roughly 2x speedup over the previous generic-C build on the
	newer x86 platforms [AMD64, Core2 and beyond]. Initial targets will be
	32-bit Windows and 32/64-bit Linux, as well as MacOS..

	Platform-independent compact bytewise savefile format - you can now
	transfer savefiles between any systems having a working 3.0 build
	, independently of the Endian-ness and 32-vs-64-bit-ness of the
	platform.

Copyright:
	 Copyright (C) 2015 Ernst W. Mayer.
	 Permission is granted to copy, distribute and/or modify
	 this document under the terms of the GNU Free Documentation License,
	 Version 1.3 or any later version published by
	 the Free Software Foundation; with no Invariant Sections,
	 no Front-Cover Texts, and no Back-Cover Texts.