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      from  3adc3e6   releasing package libmath-prime-util-perl version 0.50-1
      adds  7d7ae7a   Initial commit
      adds  db6e278   Implementation
      adds  173374e   Add MemFree object for better memory control
      adds  b918b92   Add factoring
      adds  d9467f3   text cleanup
      adds  b7d0e69   Add some items to do
      adds  1bfc4ea   Updates for 32-bit behavior
      adds  504099f   prime_count uses segmented sieve
      adds  40b1a2a   Updates for next release
      adds  c54cd40   Speed up factoring a smidgeon, prep for 0.03
      adds  39f6ea1   Make squfof recurse, and fix some issues with it
      adds  f7deef1   Miller-Rabin and prob_prime
      adds  7e66d0d   New tests and benchmarks
      adds  5c160e0   factoring benchmarks
      adds  f761e56   Split out bitarray and type header files
      adds  7d6012c   Redo factor loop
      adds  52935e2   Factoring is isprime updates
      adds  a740090   More factoring changes
      adds  15e84bd   pedantic cleanup
      adds  62a9793   Next prime overflow, HOLF factoring, compare with Pari
      adds  04af4ab   Fix next_prime
      adds  f9b9193   Factoring updates
      adds  0e4fe85   random primes, and no asserts
      adds  8ebc5ae   Try another 64-bit detection method
      adds  f4de011   Rename some test files
      adds  18c272d   Changes for v0.04
      adds  e0ab486   Tweak to mulmod use
      adds  b7796c8   Add pseudoprime test for MR
      adds  c882d45   Note need for more pseudoprime testing
      adds  eafd373   Make asm x64 only
      adds  85685bc   More pseudoprime testing
      adds  8f4796d   Add perfect square discriminator
      adds  f7169a1   Overflow for nth_prime, segment prime_count
      adds  92269f6   Add math functions
      adds  cd97a86   Rewrite prime_count for segments
      adds  4afae2b   Updates from testing, make nth_prime_approx more accurate 
for large values
      adds  2c3cc18   Allow random_prime to use overridden rand
      adds  c62ab6f   Fix issue with sqrt rounding
      adds  a17975b   Small fixes
      adds  be45b08   Many more tests
      adds  e8a0765   Move from mallloc/free to New/Safefree
      adds  852bd58   Update for 0.06
      adds  5ceba17   Move Test::More to build vs. prereq; comment changes
      adds  3f327f7   Update for 0.07
      adds  fd0d5e5   Initial scaffolding for threads
      adds  fd61c4c   Accuracy for math functions
      adds  f900788   Remove simple sieve
      adds  ed6a752   7/11/13 presieve added
      adds  1be2ec9   7/11/13 presieve added
      adds  4df9619   Add add_factors
      adds  4f1ca63   Add rational Chebyshev approx for Ei
      adds  fc1e8c6   Thread safety
      adds  10fba38   improve threading
      adds  e5857a6   Improve threading
      adds  78d5bed   Add tests for all_factors
      adds  f3fd04e   Segments were in MB instead of KB.  Waaaaay too much 
      adds  1bcf403   Add PrimeArray tied array
      adds  9334951   Fiddle with Makefile.PL
      adds  b2e0c52   Add tests for primearray, move MemFree, prepare for 0.08 
      adds  863fed3   Get ready for 0.08 release
      adds  ef43b9b   Start work on PP code
      adds  cc71cd2   Pure Perl working on all tests
      adds  57028c6   Big speedups for pure perl code, though still too slow
      adds  bfcdbea   threading and PP changes
      adds  2e93053   Wasn't correctly selecting win32
      adds  f1ac8f0   Documentation
      adds  a2f9630   Add documentation
      adds  8c1a02c   PP sieve benchmark, update tests, MR always returns 0 for 
even input
      adds  2f3e8ce   Update timings, fix test plan
      adds  b728d6b   Add some more implementations
      adds  3fedfb5   Add simple SoA (along with rant)
      adds  1362a6b   Add some PP benchmarks
      adds  1670eb8   Style change for is_prime -- no performance difference
      adds  5c2f083   Speedup for PP is_prime and factor
      adds  b4d8c78   Speedup for powmod/mulmod (helps factor, isprime, etc.)
      adds  e6ac88e   Cleanup random_prime a little
      adds  cc7c8a4   Speed up random_ndigit_prime a little for 9+ digits
      adds  4c0490e   Adjust comments
      adds  bd31f9a   Remove old renamed file
      adds  eda96a0   Forgot prototype -- could be cause of test failure
      adds  fc21970   Turn on bignum support for PP code
      adds  d94fc11   Lots of bignum support
      adds  8e22367   Do a mod before power operations -- avoids fp exception 
for very large bases on small n
      adds  3e23f1f   Many changes for bignum support
      adds  a940cb0   Test euler_phi for small values
      adds  d33cde5   Note some bignum things that should be done
      adds  2188da0   Lots of bignum changes, new tests, update version number
      adds  50222df   More bignum fun
      adds  fff06a5   Benchmark both XS and front end
      adds  61e1c65   Add BPSW primality test, hooray
      adds  0c0f910   Miller Rabin returns 0 or 1 only.  Export strong Lucas 
pseudoprime function
      adds  fb04008   Add missing test file to MANIFEST
      adds  3e3b780   Bigint enhancements
      adds  9271a62   Doc updates
      adds  8c46868   Full bigint support, add -bigint to import list to turn 
      adds  5f0ed78   Merge conflicts?
      adds  2187c92   Restore from $&^&$ up merge
      adds  c1a3e12   Update for older Perls and bigint
      adds  da62a64   Add tests for strong lucas pseudoprimes
      adds  695c937   3x speedup for bigint factor and primality
      adds  a5842dc   Redo random primes, add Maurer's algorithm.  
random_ndigit_prime needs work.
      adds  b72adcd   Updates for portable bigints and random primes
      adds  40cb80d   More random prime work
      adds  c4219ab   More random prime changes
      adds  c05f032   Minor updates
      adds  23d03cd   Tests for random primes, fix for random primes on 5.6.2
      adds  d65f872   Recommend Math::BigInt::GMP and try to use in tests
      adds  330a0a1   more fun with bigints and random primes
      adds  3d981b4   Use the MPU:GMP module if we can
      adds  15cfc51   Fix an issue with random primes
      adds  084e79e   Minor GMP related change for performance and doc
      adds  d569ae0   GMP and bigint stuff
      adds  533650a   fix POD issue
      adds  8347ffa   Work on factoring a little
      adds  2d1025e   Factoring speedups
      adds  4828d2f   Change %lu to use unsigned long
      adds  097995b   Use GMP primes function.  Doc tweaks
      adds  60d5b63   Update TODO, add Math::Big to performance
      adds  dfde14f   Update performance number with Math::Primality estimate
      adds  9736a13   Merge branch 'master' of
      adds  e7ecf6f   Strip out the prime_count and nth_prime bounds and approx 
from C code
      adds  b7a24d3   Minor updates for release
      adds  b37e2ba   Tweak native precision factoring sequence
      adds  c48ac70   Tweaks, Dusart 2010 bounds, documentation overhaul
      adds  0fcc6dc   Big documentation update for PP
      adds  1424210   Check main::rand() existance at runtime
      adds  5b2c0f6   Turn off threading tests for Cygwin
      adds  f440ed1   Change exp2 to pow, and incorporate inverse into exponent
      adds  7b8aa40   Wrap inverse into exponent in Riemann Zeta evaluation
      adds  ca6fc7b   Bump version number
      adds  22003b3   Compile issues, especially MSC
      adds  a6ece61   Add a prototype, remove an unused variable
      adds  77b5fcf   rearrange math to keep precision in some cases
      adds  6915076   Change tests for next/prev 0..3572 to do 2 tests instead 
of 7146.  Speeds up a lot, and in theory should give us the same debug info
      adds  1d54e81   bigint / bignum changes
      adds  7677b7b   Note the changes for today
      adds  ed1a67a   Add racing SQUFOF
      adds  e885753   Racing SQUFOF & other UV factoring changes
      adds  0cb4b42   Turn off racing squfof in main routine
      adds  585537d   Export RiemannZeta function
      adds  bea44fd   Update versions for next release
      adds  105da77   Call GMP prime_count if available
      adds  9c52e2d   Add prime_set_config, add assume_rh, use Schoenfeld bounds
      adds  e9d3a41   Remove done_testing()
      adds  f32a6de   Some changes for valgrind -- nothing big
      adds  78e0015   Add primorial and pn_primorial
      adds  d8acf40   Use long doubles for possible better precision
      adds  45767df   Fix issue with string input just a little larger than ~0
      adds  a9e3611   Allow trial_primes to be more intelligent instead of 
always forcing true trial division
      adds  158b8ba   Better switch between segment and trial methods for very 
large end values
      adds  0ba452d   If using the GMP module for primes(), convert the result 
to BigInts
      adds  303c044   Initial implementation
      adds  480b5a2   Add script
      adds  b725603   Add Lucas, Fibonacci, and Palindromic primes, plus 
      adds  48e0e70   Test harness for script, comparing to OEIS data
      adds  bbcbdb6   Fix up primorial and pn_primorial for bigints
      adds  1a3ce7e   Major rewrite of, and add more filters
      adds  3531db8   Small speedups
      adds  6c850f8   Next round of mods
      adds  050e185   More changes, and script test does multiple 
      adds  af5cecc   Recommend Math::BigInt::GMP -- it can speed things up a 
LOT with big numbers
      adds  a892e8f   Enhancements to tests
      adds  32c0cf3   Minor issues with huge inputs
      adds  badbbc5   Add Lucky primes, make Cuban primes via a generator 
instead of filter (hugely faster)
      adds  b3e35fa   Speed up powmod a tiny bit
      adds  de88bbc   Use 2 MR bases for more numbers
      adds  7b380c2   Rewrite p-1 factoring, enhance racing SQUFOF, switch to 
racing SQUFOF in factor
      adds  f11f5ef   Simple primality proving added (the GMP code is much 
      adds  62f61f8   Add option to ensure all output has gone through 
primality proving
      adds  baf304f   Fix compiler warnings
      adds  d441297   Enable Travis CI
      adds  6f831a1   Changes for p-1 factoring
      adds  a23c8b7   Add and enhance examples, add bin/
      adds  7a63deb   Add documentation for prime_set_config
      adds  c4013aa   Fix prime_count bug (added to test suite), add Lehmer 
prime count
      adds  2b002b0   Use Lehmer method for big prime counts
      adds  3b88409   Comments and a small speedup for Lehmer
      adds  a7bc5c6   More Lehmer improvements (faster, lower memory)
      adds  3d48233   More Lehmer speedups and memory enhancements
      adds  eb3b3dd   Don't run the 64-bit edge case on broken 5.6.2
      adds  f8943f7   No timing messages from Lehmer, and reduce threshold 
since it's faster now
      adds  3fe998d   Relax constraint on bignum version.  It works fine with 
      adds  e440b5d   Add AKS primality test
      adds  b88fdb7   Update some examples
      adds  cbdd225   Skip the AKS tests on 32-bit machines.  They're way too 
slow in PP.
      adds  9e13087   Have nth_prime use Lehmer prime count on lower bound.  
100x speedup for big numbers.
      adds  08dbf56   Update documentation
      adds  b205114   Fix prime count issue and make standalone.  Add Meissel 
      adds  c1a2755   Ready for next release
      adds  b9dde29   Add 'verbose' config option
      adds  e9a1984   Have verbose option set GMP verbosity also
      adds  d574abd   Increased precision for bignum zeta and R
      adds  7f8f395   Update MR bases for deterministic tests
      adds  e3521a5   Use references in for performance.  Lucky 
primes take less memory.
      adds  73b3a6e   Move mulmod, powmod, etc. to separate file.  A few 
      adds  b1c0afc   Let AKS in XS work with larger inputs.
      adds  29d4faa   Split AKS out of isprime tests.  Extend AKS from halfword 
to fullword.
      adds  433250b   Add jordan_totient, divisor_sum.  Slight speedup for 
euler_phi and moebius.
      adds  1f19230   Streamline random prime test, add more testing for nbit 
and maurer random primes
      adds  e0e6f21   Streamline some expensive tests, move bignum Zeta/R to 
separate file
      adds  d003539   Changes file has test and zeta changes mentioned
      adds  9b97f8a   Skip 15+ digit tests on broken 5.6.2.  Workaround bug in 
Math::BigInt in extra tests.
      adds  0a75888   Fixup 5.6.2, and some li and Ei range cases
      adds  3e5a8b2   Tweak MR test, add environment variables to disable XS 
and GMP
      adds  a49ae24   Add PP Lehmer prime count, including nth_prime speedup.  
Fix some no-XS-with-GMP issues.
      adds  2ffb217   Speed up PP Lehmer by 10-100x at the expense of memory
      adds  6695c65   Fixes for various compile / test issues
      adds  d719bbe   Update for release, and standardize infinity processing
      adds  d0834cb   Modify tests to handle Win32 infinity also
      adds  49b7d03   Missed an inf
      adds  44aef7d   Fix 32-bit issue with lehmer
      adds  d6f41a6   Work around broken 64-bit Perl 5.6.2
      adds  e04d2d3   Use Math::MPFR if possible for Ei/li/Zeta/R functions.  
Huge speedup and accuracy gains for BigFloats.
      adds  f5ca1e0   Tests for primorial, jordan_totient, divisor_sum
      adds  7943a7b   Make random_*_prime do bignums when passed Math::BigInt 
      adds  855ad8c   Random prime updates
      adds  315d5e2   Major changes to random primes.  Return BigInts for big 
results on primorial and random primes.
      adds  6e7e3bf   Update tests for new functions, and Perl 5.6.2 workarounds
      adds  43b09d3   Revamp internal rand system for random primes
      adds  a35c107   Swap system/user rand
      adds  d588c12   Fix issue with Math::BigInt::GMP on 32-bit Win32
      adds  25b940c   Fix some horrible breakage on 32-bit
      adds  5eef916   Better R accuracy with multiple calls
      adds  82af23f   Remove an extra loop from PP M-R
      adds  7119f8e   Work around randbits >= 32 on 32-bit system
      adds  e48f2f9   Perl 5.8.2 gets 12345**4 wrong, change to 
      adds  113f735   Don't use last bit of drand48
      adds  11c1903   MSC doesn't use inline.  In theory __inline should work.
      adds  85b5552   Update timings for prime_count
      adds  0ead230   Make sure we don't try to use really old versions of MPFR
      adds  e865e45   Very small optimization for PrimeArray.
      adds  c5533dc   Lighten threads testing for normal case (helps some 
slower machines), add more for release testing
      adds  5711de7   Allow turning off MPFR.  Run travis tests on dynamic 
dependency variations.
      adds  f0c0c5f   Install mpfr before Math::MPFR
      adds  87f1585   Speed up Travis CI
      adds  a6339fa   Unroll inner loop of sieve for another 20% speedup
      adds  a9df352   Allow script to eval simple math expressions
      adds  028e761   Allow an expression to eval to 0
      adds  be6502f   Silence perl critic for expression eval
      adds  e6b826c   Revamp rand internals yet again.  Sadly also a rand API 
      adds  4e13e5d   Update rand function in test - Win32 32-bit needs mod 
instead of and
      adds  3419e58   Update versions and dates for release
      adds  0f25dde   Tweak rand setup a little
      adds  91a9d1c   Don't run the long AKS test on any 32-bit platform
      adds  664f102   Fix old Solaris compilation
      adds  4ec5c58   Log some more bignum info to get a clue why old 
ActiveState's BigInt::Calc barfs
      adds  8c4dfeb   Round the perfect power test, note its faults
      adds  a522f78   Add random_strong_prime, update to 0.18
      adds  df6e091   Travis test with all features as well as deselections
      adds  26f73ce   Update MR bases
      adds  8f56bbd   Fix bignum / Calc issues (things turning into BigFloats)
      adds  6c21795   Add tests for is_provable_prime
      adds  2990405   Fix more bignum issues
      adds  5687cb8   Better test coverage
      adds  86ac1d8   More bignum and 5.6 changes
      adds  7f2819e   Update MR bases
      adds  590d564   Update M-R bases
      adds  a635e5e   Modify validation to lower overhead
      adds  b77b1d8   Prepare for 0.19 release
      adds  cccb050   Speedup for PP AKS, turn off tests on 32-bit machines
      adds  dc5a392   Change PP perfect square test
      adds  e2794ed   New perfect power implementation
      adds  bdd3f15   Bump version for release
      adds  e2461d9   Add function def to example
      adds  5f02d79   Add circular primes to (OEIS 68652, also in 
Project Euler problem 35)
      adds  40cdc70   Speedups for Pillai primes
      adds  11034f8   Minor tweaks
      adds  96d0f6d   Spelling corrections in documentation
      adds  ccc7965   Add Euler totient range, speedup divisor_sum
      adds  308abdc   Switch to Bytes::Random::Secure
      adds  0862ac9   New M-R bases
      adds  f400625   Range Moebius function.  Fast Mertens function.
      adds  666d44f   Ranged mobius function
      adds  079e8b1   Update documentation to reflect the change to 
      adds  990011d   Faster Mertens
      adds  5c70045   Add Mangoldt function
      adds  9285897   Performance enhancements
      adds  f27df65   Testing changes for release
      adds  1adab04   Final changes for release
      adds  6cbd2cd   Remove Algorithm::Diff dependency, as it isn't used any 
      adds  49f6ec7   Totient and Mobius changes, move factor loop out of XS.xs
      adds  7c8fa21   Switch to pthreads condition variables
      adds  b7bf6f6   Squash some compiler warnings
      adds  7228a75   Compiler warnings and coverage
      adds  11422a5   Put segment mutex back
      adds  4b9d3f3   move scripts
      adds  0fada75   Turn thread tests on for Cygwin and NetBSD.  Add simple 
RiemannZeta test cases
      adds  c7d6fb0   Getting ready for release
      adds  3bf8b1e   Optimizations for von Mangoldt function
      adds  590b1e1   Merge Akron's fix to dates in Changes
      adds  3caff7c   Slight doc change for moebius/phi/lambda/M
      adds  4e81f05   Change XS Zeta code
      adds  1d1d03d   Update PP Zeta -- much better now
      adds  9393ea9   Add consec int lcm, documentation changes
      adds  ed4cf69   Fix return value with consec int lcm and MPU::GMP
      adds  0965fab   Add binary search for nth_prime, for inputs > 2e11
      adds  a48fe49   Minor updates
      adds  1e807e1   Add Chebyshev theta and psi functions
      adds  8aea368   10x speedup for divisor_sum
      adds  574e36e   Test coverage and small AKS speedup
      adds  705c924   Start to add LMO prime_count
      adds  7be91a6   Change type of mobius return.  Some different ranged 
algorithms in comments
      adds  4af6895   Move totient range to util.c, speed it up a little bit
      adds  fe9a34d   Fix divisor sum on bigints
      adds  52b8d85   New data structure for phi(x,a): faster prime_count
      adds  0901cc7   In-place phi(x,a) merge
      adds  b19757e   Minor updates for release
      adds  4562fd0   Fix 32-bit issues
      adds  6390df3   Fix segmented euler_phi
      adds  972b3da   Some more speedups
      adds  4b59f67   More lehmer tweaks
      adds  b9cab41   Set smaller preseive with standalone primesieve
      adds  adbc62b   Improvements for PP prime_count
      adds  30e22b8   Minor updates for release
      adds  58cd150   Move a test into xt directory
      adds  1bbbfaf   Add table sieve, fix off-by-one in Lehmer, change 
sieve/advanced transition in Lehmer
      adds  ec6de3b   Merge branch 'master' of
      adds  476d336   Newest M-R bases
      adds  49512f3   Change to unified method for small is_prime, next_prime, 
prev_prime, prime_count
      adds  5226574   Add xt test to do exhaustive small is/next/prev tests
      adds  0b76b7f   Update for release
      adds  21cd3c6   Documentation tweaks
      adds  49b8d46   Speed up p-1 stage 2
      adds  718c44d   New internal macro to loop a..b using primary sieve
      adds  bb1cc9e   Forgot to skip one of the tests with broken 5.6.2
      adds  184a688   Update for primesieve 4.2
      adds  3e69d09   Documentation update, including a giant SEE ALSO section
      adds  c72237b   Tweak factoring and factor tests based on coverage 
      adds  ccb111f   Documentation changes
      adds  4229dfe   Speed up rsqufof a little, use for 19 dig semiprimes
      adds  5a80aeb   Allow turning on/off gnufactor or pari
      adds  0f652e5   Travis-CI change in installation order
      adds  e6db57b   Add large bases to pseudoprime tests
      adds  6b2a185   Move the a=1 pbrent into XS.xs instead of factor.h
      adds  7150384   Move to next version number
      adds  0eef4fe   Documentation updates
      adds  e26a347   Fix: Was checking wrong BigInt variable and loading a 
second backend.
      adds  1bd6c49   Primality verification (needs documentation)
      adds  ec6c1ab   Remove Data::Dump used for debugging
      adds  43a7cb9   Add tests for verify_prime
      adds  46166a2   Work on pure perl factoring
      adds  592e6c3   Add primality certificates, elliptic curve start
      adds  63a2961   Fix misspelled proof name
      adds  b835662   PP: add simple ECM factoring and BLS75 primality proof
      adds  c9ce369   Documentation formatting
      adds  1b374a4   Projective ECM for pure Perl
      adds  aa43b9b   Primality proof updates
      adds  3e6ff85   Add GMP-ECPP verification example
      adds  34da9f2   Tweak projective EC point
      adds  a5e6994   Fixup for 5.6.2
      adds  72a23f4   Allow to parse many MPU functions
      adds  1cc788d   Move a couple of the bigger primality proofs to 
RELEASE_TESTING -- slow without GMP
      adds  80cb008   Fixes for final release
      adds  5a33c7f   Fix spelling error (RT 84782)
      adds  0540efd   Speedups for pure perl factoring of small numbers
      adds  f191905   Fix filename of ecpp verification, add sage version
      adds  6f543ae   Fix error with big aks inputs (order would roll over)
      adds  8af5f6b   Must compare n and q as bigints
      adds  ef46084   primality certificate edge cases
      adds  de8f5aa   Convenient primality proof random test
      adds  9a05632   Merge branch 'master' of
      adds  17559c6   Allow BLS75 theorem 7 n-1 proofs
      adds  62e3e90   pure perl factoring tweaks
      adds  ef0c961   Merge branch 'master' of
      adds  7cb7982   Small speedup for composites in is_prob_prime/is_prime
      adds  9015356   Increase coverage
      adds  b7d411e   Remove dead code
      adds  e9b0ca7   Add spelling test and do some spelling adjustments
      adds  cac18f0   Add more test coverage
      adds  376cab3   Let accept +N as a second argument
      adds  1660bcb   More test coverage
      adds  738a953   More verbose/error output consistency for verify_prime.  
      adds  35414dd   Use XS initial validator
      adds  1478d34   Make is_prime go to is_prob_prime after initial tests
      adds  6675937   New 3-base solution
      adds  b2b2191   Adjust tests to work around Perl 5.6.2 quirks
      adds  4bd921b   Push full primality test into PP from
      adds  3c13e38   Invert XS/Perl relation for is_prime, is_prob_prime, 
next_prime, prev_prime
      adds  c1bd445   Make sure test works on 32-bit platforms
      adds  8c499ee   Rewrite PP Lucas code.  About same speed, but simpler.
      adds  52430c9   Updates for release, including docuemntation and direct 
C->MPU:GMP calls
      adds  2ea2f7a   Minor updates for release
      adds  2f92c04   More efficient ranged Moebius code
      adds  5f42b95   Add forprimes multicall
      adds  76843d9   Backward compatibility changes around multicall
      adds  c803cae   Fix memory leak in forprimes.  Document it.
      adds  a217b6a   Fix Win32 threading breakage
      adds  ed60b06   Update primearray and add a simple iterator
      adds  efa7895   Document the prime iterator
      adds  b1a7215   tests for forprimes and iterator
      adds  67ba108   Update for release
      adds  d10f7b3   Fix some multicall portability issues (5.8.2)
      adds  8dd3c25   Add new files to MANIFEST
      adds  ae11792   ranged moebius was depending on char being signed.  Fix.  
Thanks Debian testers.
      adds  ede3138   segmented sieve infrastructure, and have forprimes use it.
      adds  8d11397   Speed up primality proof tests on non-64-bit machines
      adds  c50f380   Speed up primality proof tests on non-64-bit machines
      adds  c7223a5   Add strong Lucas test
      adds  70ba979   Don't use MULTICALL yet -- memory leak
      adds  61ad7e5   Add two more probable prime tests
      adds  f4e33b7   Add standard Lucas test
      adds  615c375   Transition some functions to forprimes
      adds  7b239a7   Fixes for 5.6 (sigh)
      adds  eca9e7d   Make sure non-XS can use forprimes properly
      adds  83472c0   Update some benchmarks and examples
      adds  7c4d65c   Code comments about primality testing and the 
non-exported F-U test
      adds  c22623d   Fix prime_count_approx being really slow for > 10^36 
without Math::MPFR
      adds  a8d928e   Workaround for MSVC compiler
      adds  d0ba63c   Try to work around old Activestate crud
      adds  aa85624   Add Lucas sequence and have all 3 Lucas tests use it
      adds  c4c27ca   Change to submod and mulsubmod for better portability
      adds  b7e26bd   Fix a refcount GMP callback issue, and add test for it
      adds  472e956   Remove unused variables, set reproducible random results 
in a benchmark
      adds  6281c5a   Add F-U compositeness test, and tighted ECPP certificate 
      adds  3671c32   Use Data::Dump::dumpf
      adds  4ebadd5   Add lucas_sequence
      adds  ea22a6b   Add PP code and simple test for frobenius_underwood 
probable prime test
      adds  be92b20   Documentation updates
      adds  1fa0cbe   Add braindead p+1 factoring
      adds  ea68447   Speedup for P=1,Q=-1 Lucas sequence, which is half the 
standard/Strong Lucas test cases
      adds  83b385f   Make sure n is odd to get exact results from 
      adds  69f6a75   Update Lucas tests
      adds  0c66a38   Almost extra strong lucas prps
      adds  371f900   Cleanup is_prob_prime
      adds  d4c1bd6   Rewrite some performance comparison text
      adds  7ace5fb   Turn on gcc's uint128 types if we have a new enough 
      adds  6bf74f6   Update some benchmarks
      adds  68151cb   Update todo list
      adds  d584e6a   Update p+1 factoring, add to tests
      adds  937450c   Combine lots of functions with common signatures
      adds  d0d1afa   fixup AES Lucas test
      adds  fcd36c1   typo fix
      adds  7e5b796   typo fixes
      adds  7b4558a   Merge pull request #2 from dsteinbrunner/patch-1
      adds  8dffb63   Clean up Lucas, update PP is_prime, remove an test func 
that got put in XS.xs, add documentation
      adds  77fe0d7   Changes file follows CPAN::Changes::Spec format
      adds  1a75d71   Not all gcc targets support uint128, e.g. Atom
      adds  829acaf   Fix case of forprimes with begin = 6 returning 5, and add 
      adds  3ca27cd   signed chars fix for defined-out LMO function
      adds  3eded31   Tested multicall with 5.8, 5.10, 5.16, 5.17s, 5.18 -- 
looks good so just use it.
      adds  74fec80   Add cpanfile
      adds  88d4390   is_prime is faster now, so SophieGermain is over 2x faster
      adds  046c5a9   INCOMPLETE BROKEN : Switching to new text proofs, part 1
      adds  16b1986   Add primality proving submodule
      adds  f282fde   Switch to new text proofs, part 2
      adds  1aad573   Add standalone verifier (from MPU::GMP)
      adds  745317b   Small grammar updates
      adds  4ba8d59   Add x86_64 asm for addmod from Kruppa
      adds  b2f8022   Add more limitations on __int128 use
      adds  a407ea9   Add proof documentation to TODO list
      adds  0bdb38c   Update primality certificate documentation
      adds  a7281dc   10-15% speedup for ranged totient internals
      adds  5d5534c   Patch up silly MPU::GMP cert mistake
      adds  829338f   Updates for random_nbit_prime and documentation
      adds  6a96229   Add random_proven_prime, modify random_nbit_prime
      adds  1ef154a   Add carmichael_lambda; use F&T A2 for random_nbit_prime
      adds  7791b3c   Turn off F&T A2, need to make sure top bit is set
      adds  66b60c1   Update for new M-R base from Panasiuk and Izykowski
      adds  67ce456   Remove code for F&T A2 -- needs fundamental change to 
have nth bit set
      adds  5b245c9   Add BLS75 paper to references list
      adds  a341eef   Add a couple more CPAN mirrors, as the Travis-CI one has 
lost data
      adds  11b8a1f   Redo mirrors
      adds  23c1a98   Small updates for prime array
      adds  65ea92e   Add output comments to primesarray bench
      adds  25809f6   Update a couple examples
      adds  0799f43   Speedup Maurer slightly by going straight to 
is_prob_prime with GMP
      adds  cb1eb7a   Add ifs to powmod initial mod; add verbose to
      adds  19d92dd   Use MPU::GMP::pn_primorial if possible
      adds  e1244e2   Merge branch 'master' of
      adds  c24f6f6   Allow parallel phi sum by using critical section around 
      adds  c2a0056   Add speedup for divisor count
      adds  83190bf   Revised mulmod x86_64 asm, work with Wojciech Izykowski
      adds  040a785   Add Pk_2 function, simplify some code
      adds  2cb9452   Merge branch 'master' of
      adds  f64020b   Merge branch 'master' of
      adds  f246f75   Move primality functions to new file.  Use Monty routines
      adds  9749d8c   Primorial primes print a bit faster
      adds  2b32586   standardize variable names
      adds  3c14ce7   Add znorder function for multiplicative order
      adds  ce2b9ec   Fix sluggish validation of AES increment for common cases
      adds  7061ccd   Add Monty math for Frob-Underwood, AES Lucas, and one 
case for standard Lucas
      adds  9cd55d3   Divisor sum with integer second arg
      adds  a7f63a0   Speedups for divisor_sum
      adds  8ce592a   Montgomery reduction for all Lucas tests
      adds  bb687ce   Perl 5.6 fixes
      adds  67f3d32   Revamp input processing to accept bigints
      adds  ae4f1d9   Cleanup
      adds  3508783   Tweak sieve to make more efficient for large bases
      adds  914ef7b   Make better comparisons for next/prev test
      adds  91d0a26   Add prime iterator object
      adds  14b421f   Test for edge cases, fix some near-maxuv issues
      adds  1401eeb   Use mpu method to get new oo iterator
      adds  7be347d   Minor cleanup
      adds  041e0c8   ECPP verification: floor(2*sqrt(n)) instead of 
      adds  15de5bb   Speedup for random_nbit_prime
      adds  5b0992f   Updates for release
      adds  9f816a8   Add stopword for newest spellchecker
      adds  468aacb   Remove trailing whitespace
      adds  6100612   Speedup lucas sequence => speedup BPSW test
      adds  92831b6   Dynamically load BRS; PP random_nbit_prime speedup
      adds  9556c43   Merge branch 'master' of
      adds  2b59342   Fix pure perl lucas sequence with Q=-1
      adds  a2ab7c9   Redo benchmark section
      adds  67979c3   Add miller_rabin_random; add primality testing opinions 
to documentation
      adds  99042b2   Make factor consistent in scalar context
      adds  86fae37   Merge branch 'master' of
      adds  156c807   Cache random function for less overhead
      adds  736a704   Adjust some benchmarks
      adds  8981c0a   Make sure strtoull is used for 64-bit when possible
      adds  9e68dad   Merge branch 'master' of
      adds  5279b32   Remove all mirrors from travis config
      adds  2d3483e   Only use TEST_REQUIRES with new enough MM
      adds  09ca3d5   Simplify some of the randomness loop code
      adds  fa70bdd   Make Test::Warn a suggested dependency -- no longer 
      adds  f737045   Merge branch 'master' of
      adds  997ec07   delete TEST_REQUIRES after merging
      adds  291efcd   Update Changes
      adds  4bb0db7   Example for abundant, deficient, perfect numbers
      adds  fa31f4e   Tiny PP factor speedup
      adds  722ec20   Iterator object tests and fixes for next/prev prime 
behavior near native boundary
      adds  396279f   Update iterator object value_to_i*
      adds  42d15b4   Documentation update
      adds  7e72cdd   Updated LMO and Lehmer internals, switch to LMO
      adds  fcbdc06   Silence compiler warnings on 32-bit
      adds  238db7e   Little updates before release
      adds  3af56a3   fix some prime count performance and openmp cases
      adds  ab0a869   Add XS routine for ([p1,p2,p3],[e1,e2,e3]) return from 
      adds  62d0d75   Lucas sequence should return a bigint if arg is a bigint
      adds  de789fa   Add liousville, factor_exp, partitions.  all_factor 
includes 1,n.  Internally use factor_exp in many places.
      adds  0886915   Fix tests for all_factor, add liouville stopword
      adds  82894f0   Update partitions function
      adds  0684fca   Document partitions, tweak implementation for a little 
more speed
      adds  6190da4   Tests for partition()
      adds  f8f9827   Add tests for liouville function
      adds  c170460   Add tests for factor_exp and liouville
      adds  03ee354   Update version numbers
      adds  9a74bb0   Comment changes for part
      adds  519f12f   Zeta updates
      adds  e104357   Zeta accuracy test in xt/
      adds  f4ffcaf   Keep BigInt accuracy for Riemann Zeta/R
      adds  ee69ab7   Speedups for pure perl testing
      adds  073d3a0   pondering pedantic perlcritic palaver
      adds  0ef064e   exp_mangoldt in XS by default
      adds  7bca588   Improve test coverage
      adds  b443c37   Fix PP is_pseudoprime; Fix test issues
      adds  126995b   Use Lehmer for small prime counts (below 8000 million), 
LMO for large
      adds  ffec917   Tweaks to LMO performance
      adds  10d63d3   Hash->Scalar.  Add peek() and __iter__()
      adds  ec94f13   Update with some more iterator examples
      adds  337f556   Segment chebyshev_theta/phi, slight performance for 
ranged totient
      adds  672bc12   Tiny efficiency for Mertens
      adds  0195347   Make sure large primorials don't overflow sigma_0
      adds  2f35ab9   Make sure we don't overflow large divisor counts on 
32-bit machines
      adds  e0cae15   Change C99 comments that snuck in
      adds  3117ccc   Quote 0 in two tests, 5.8.2 use bigint treats 0 = NaN
      adds  9fd83d7   Make all tests run with 5.6.2 (with lots of skipping)
      adds  ae32ca5   Remove unused feature requirement
      adds  7640a3e   Revise prime count table code, speedup 3.6M to 6M
      adds  90fe804   update for release
      adds  6a35028   Update for release
      adds  3228494   Remove 64-bit test for 32-bit machines
      adds  b1172a4   Update to next version number
      adds  5845699   Switch small primes and lpf arrays to uint32_t
      adds  6866e90   Wrap large constant in UVCONST
      adds  62f303b   Add the extended prime count test
      adds  c7908aa   For 64-bit, primei must be a UV instead of uint32_t
      adds  f3f8ce9   auto bigint, round 1
      adds  87fa96f   Tests hit by Math::BigInt::GMP bug.  Work around.
      adds  be8f98d   Next try at consistent type upgrades for 
      adds  622fa8f   Add commentary to measure_zeta_accuracy test
      adds  1cd370b   Use XS prime count for small approx/lower/upper
      adds  ab066b2   Changes for 32-bit
      adds  e706275   32-bit fixes
      adds  69f65ed   Extended LMO algorithm
      adds  6b63be2   Put icbrt in util.h
      adds  8056725   Move phi_total to sieve struct
      adds  200a6d5   Adjust M factor: save a little memory, gain a bit of 
      adds  8a308f6   Update version number
      adds  934f639   Just skip 64-bit testing on 5.6.2
      adds  7953a90   Remove two tests obsoleted by new BigInt behavior
      adds  7c25dcf   Add nth prime extra test
      adds  6d0b318   Give the M adjustment a steeper slope
      adds  dd2d4d7   Change nth_prime to use inverse Li+Corr instead of 
inverse R
      adds  1ff0a21   Restructure step 7 phi summation to streamline inner loop
      adds  1b6c179   Protect against overflow
      adds  31afb1b   Documentation updates
      adds  95e0280   Back off expensive PP prime count testing unless extended 
      adds  b9c24be   Thanks TravisCI -- need to count for the extra test when 
      adds  4d95539   Final updates for release
      adds  f5dc9dd   Add some missing files to manifest
      adds  bd7929c   Microsoft VC isn't C99, sigh
      adds  8b96e19   fix LMO previous prime (sieve) when very near 32-bit limit
      adds  89d9bc6   Measured mu+lpf methods, adjusted comments
      adds  535d480   A fix for prime counts > 18446744056529682436
      adds  f25d223   Comment changes
      adds  30e430d   Ensure M=alpha*n3 doesn't underflow
      adds  478e828   Documentation change
      adds  e0742a9   Add some 5.6.2 workarounds
      adds  dc95551   Microsoft compiler workarounds
      adds  599f366   32-bit fixes, documentation updates
      adds  78db558   Speedup for Legendre Pi (use small phi)
      adds  3662953   LMO phi sieve is UV-word based instead of 32-bit-word 
      adds  db3e43a   Documentation updates; popcnt updates for LMO
      adds  53ae236   Remove trailing white space
      adds  40e5b5f   Have 32-bit use parallel bit count instead of 8-bit table
      adds  8254d6d   Documentation updates
      adds  c6a1930   _divisor_list in XS, use it.  Add simple forcomposites.
      adds  68a0877   first round of changes for factor(1)
      adds  9a56656   Second round of factor(0),factor(1) changes
      adds  a5358ed   typo in all_factors alias
      adds  6e901e6   Add fordivisors, forcomposites
      adds  8a0928d   forcomposites using sieve
      adds  eac8b27   Fix some compiler warnings
      adds  9cffea5   forcomposites UVMAX edge cases
      adds  fa9264c   Mapes => table for small phi
      adds  c7e2b5a   Revert back to SvREFCNT_inc for old Perls
      adds  9535910   Lehmer update cache settings
      adds  0d64350   New sieve code for finding segment composite inc/masks
      adds  fd38afe   Performance changes for prime sieve
      adds  0716c2d   Fix spelling error (RT 91562)
      adds  0b97c03   Fix macro comparison, new benchmarks
      adds  426ffa6   Line too long in synopsis
      adds  c6349fb   Try to do fast word counts on 64-bit machines
      adds  034e128   Some performance tweaks
      adds  7125927   Remove dead code; convert count to segment start/next/end
      adds  11685f6   Convert segment_primes to segment start/next/end
      adds  f3f5fc7   Speedup for basic sieve walking
      adds  8f2edbd   Fixup for earlier sieve count change
      adds  620503e   Switch to primesieve 5.0
      adds  7dd02e2   Add sign multiply to caching phi for a=0,1
      adds  ea60ec1   Don't use GCC's builting popcount unless we have asm.  It 
can generate awful code.
      adds  18302e1   Small comment changes
      adds  fe1f92c   Use faster bit counting for sieve part of nth prime
      adds  e3def2d   Fix _XS_legendre_phi for new table phi
      adds  0b3812f   Use presieve/test for large segment bases.  Much faster 
and less memory.
      adds  98d0e8e   Wrap isqrt in #define so only included when needed
      adds  c07ebde   Switch znorder to factoring Carmichael Lambda
      adds  690a97f   New factor_exp function
      adds  272b948   Add kronecker, totient, carmichael_lambda, znprimroot
      adds  0371266   Updated validate_int; znprimroot, carmichael_lambda, 
      adds  47af0e2   Add kronecker, znprimroot; XSify carmichael_lambda
      adds  ba82ffc   Move znorder to XS; add tests for znprimroot
      adds  08a2f59   Fix PP test issues
      adds  7033eec   Huge speedup for znprimroot with non-cyclic input
      adds  94dd052   Allow string numbers to have a leading + sign
      adds  a193d10   Make sure PP znprimroot handles non-cyclic nputs quickly
      adds  0150346   Speedups for Legendre/Meissel/Lehmer/LMOS old prime count 
      adds  47c1106   Add tests for kronecker
      adds  1392ff5   restore Win32 support
      adds  f8e4968   Merge pull request #4 from bulk88/master
      adds  d0f54d5   Merge branch 'master' of
      adds  2696cc6   Add moebius/exp_mangoldt to util.c
      adds  0d7529a   Shuffle functions between XS/Util/PP; significant XS 
      adds  f3a9765   Cleanup compiler warnings
      adds  bcff6a3   Change back to dTHX for now
      adds  8c60054   Hacky workaround to for MPU:GMP not understanding leading 
      adds  d7eee04   Remove redundancy in inner loop of 
      adds  913840e   remove dTHX usage
      adds  e1e4923   don't set global SP to itself after vcallsubn
      adds  361219e   Merge pull request #5 from bulk88/master
      adds  053dfe0   Move divisor_sum to XS; more XS interface cleanup
      adds  4518c36   Wrap large constants in UVCONST for 64-bit Perl on 32-bit 
      adds  517233e   More XS changes, plus small optimizations from bulk88
      adds  91f7c61   Workaround for 5.6.2 PP
      adds  4e0e6ab   various XSUB optimizations
      adds  9ed115d   more XS tweaks
      adds  25e1031   Merge XS changes from bulk88
      adds  9d022c9   Simplify my_svuv/my_sviv
      adds  150fa33   non-XSUB tweaks
      adds  51548ea   Merge branch 'master' of into bulk88-pr6
      adds  2fe6d93   Modifications to previous merge
      adds  df94359   Stop checking return of New/Renew and its propagations
      adds  9d3bad1   Don't compile Legendre/Meissel/Lehmer/LMOS prime counts 
by default
      adds  4a10314   Move factor_exp and divisors to XS->Perl, merge with 
      adds  c1aa052   fix declaration after code and redefinition warning for 
      adds  bf712bd   Merge pull request #7 from bulk88/master
      adds  3cc157e   Merge euler_phi and moebius XS
      adds  0885daa   More updates from bulk88 suggestions
      adds  4f56222   Next set of XS changes
      adds  0e33406   Input validation
      adds  50b9d5c   XS tweaks from bulk88
      adds  3b96223   Fixes for 5.6.2
      adds  2d8120a   Use constant
      adds  2f048d2   Input validation and better 5.6.2 support
      adds  7d90dd0   Fix threading argument
      adds  1de1b84   Work around RT 49569 (Math::BigInt::FastCalc)
      adds  f4899e1   Add Kronecker tests
      adds  5efbc2e   Add bigint tests for new functions
      adds  ae9cc5e   Add tests for legendre_phi
      adds  4edb0a1   PP legendre phi wasn't making enough primes via public API
      adds  8a8f04f   nth_prime for legendre phi, not next_prime
      adds  114a02a   Add test for t/81-bignum.t no-clobber
      adds  a33b4a9   Update version number and date
      adds  0846451   Move prime_count, nth_prime to XS
      adds  e12aceb   More XS->Perl changes.  Add constant SV* returns for 
      adds  3645d32   Modify const SV for threads
      adds  068ad54   Another case of RT71548
      adds  c0b5a3b   Change sieve macro advance to not read ahead (valgrind)
      adds  128e95f   Change comment to match current number of array items
      adds  d3f0a05   Add gcd function.  Fix forcomposites.  Fix test for GMP 
function definition.
      adds  7fd13a8   Refactor forprimes
      adds  af8d7a0   Use memcpy doubling -- fewer calls needed
      adds  59238c0   Go back to 200M threshold vs. 2M for looking in cache
      adds  6b69260   use constant with hash.  Saves a tiny bit of startup time
      adds  5be2033   Removed old SQUFOF code.  Faster is_perfect_square.  
Streamline trial division pre-factoring.
      adds  06eadfb   Tweaks to SQUFOF, pbrent, and strategy
      adds  f60d046   Speedup for palindromic primes
      adds  4f9aa60   Make is_bpsw_prime a first class function (though 
currently not exported)
      adds  1692d44   is_perfect_square doesn't use isqrt
      adds  ffd4fd9   mapes -> tablephi.  Caching legendre phi
      adds  0c0f9d4   Speed up some testing.  Move znorder to
      adds  94c37ca   Add lcm.  Better PP legendre_phi.  Prune PP documentation.
      adds  6b634d0   Try to use Pari in benchmark, but silently remove if not 
      adds  2fea141   Performance tweaks (small) for bigints
      adds  dbf2bd3   Performance updates for no-GMP, focusing on making test 
suite run faster.
      adds  443caad   Right number of extra tests, remove references to old 
      adds  9c98f1b   First cut znlog
      adds  0f0531c   XS tweaks
      adds  52d9da9   Merge pull request #8 from bulk88/master
      adds  ad2592f   Remove flags on get_cv
      adds  68a3c9d   Make sure we can use  as an int
      adds  c0c2eb9   Adjust use of constant to allow backward compatibility
      adds  2ac307a   Back off internal PP prime count in test, to help out 
very slow machines
      adds  06d2159   Double speed of AKS for small numbers on slow-modulo 
machines.  poly_mod_mul checks for overflow in all terms are summed
      adds  b2e7644   Merge branch 'master' of
      adds  2b100bd   Small aks speedup
      adds  2cc07a3   Move PP AKS to only run with EXTENDED_TESTING.  It's 
horribly slow, a function nobody should practically use for anything, and they 
would run the C or GMP version anyway.
      adds  209e008   Reduce some variable scoping
      adds  6a81827   Trim PP testing
      adds  641c247   Use long double interface for the other three FP functions
      adds  5370db0   decl after code fix
      adds  91a51f7   When doing XS bigint downgrade on old Perl, set the string
      adds  9512fca   Perl 5.6.2 workarounds for bigint downgrade
      adds  7406eed   Performance for PP, and a few pre-5.8 64-bit workarounds
      adds  4670b90   More tests run on 5.6.2 64-bit now
      adds  a0d9c79   Trim some tests, convert some proofs to new cert format, 
more tests work with pre-5.8 64-bit
      adds  83600eb   Turn off default irand in tests that don't care
      adds  c62ac0d   znlog tests and PP placeholder
      adds  209e98f   Switch more funcs to long double, and return results as NV
      adds  f5cc219   Add clz and ctz
      adds  c54a128   More clz,ctz,log2floor changes
      adds  c6a03f4   Use new clz/ctz/log2floor
      adds  2d499fa   Fix arguments for non-public *_factor functions
      adds  b3075fa   Add ppport.h finally
      adds  73f085a   Merge bulk88 XS changes.  Add ppport.h use.
      adds  5167498   spacing
      adds  49d0199   small performance increase for next_prime
      adds  4d3882c   Add simple (and likely buggy) Pollard Rho DLP
      adds  e86068b   Call Math::BigInt importer only if it hasn't been loaded 
      adds  e0d50c8   Changes for Math::BigInt::Pari (it doesn't play well with 
      adds  94aeed2   Remove the old -nobigint flag.  Better random ndigit for 
some old examples.
      adds  3f1b612   Honor rounds in Fermat
      adds  d0fee2d   Fix stupid cpp typo
      adds  7e26ad4   Push some constants into a shared header file
      adds  c4ee137   Use constants.h.  Simplify prev/next prime.  Simplify 
chebyshev functions.  Results in smaller object files.
      adds  99ae304   ranged totient faster and uses less memory
      adds  5aaf977   Adjust PP testing to reflect some functions now being in 
      adds  821b7b6   Rearrange factor main loop
      adds  64fe821   remove _is_prime7, remove _XS_ header from a couple C 
      adds  a1bd930   Minor changes to examples
      adds  441bbd9   Fix MSC support for ctz/clz, hopefully
      adds  19fb51c   Simple Pari comparator (random values for functions in 
Pari and MPU)
      adds  67f971f   Pari's nth prime doesn't want 0
      adds  b57e190   Move jordan_totient to XS->PP from Util
      adds  5b7938a   znorder and znlog adjustments for edge cases
      adds  3e72965   Updated Pari compare test
      adds  dff2ed6   LogarithmicIntegral using bignum and no-MPFR returns (1) 
better results, (2) rounded to a sane number of digits
      adds  0447ce3   signed/unsigned warning
      adds  d08d2fa   Pari compare test done
      adds  4733aa9   Adjust comments
      adds  d75a685   Adjust MANIFEST
      adds  ed35421   Simplify next_prime / prev_prime
      adds  3054619   BigInt was upgrading to float in some cases
      adds  569d1f8   Documentation updates
      adds  a13a939   Make sure logl(constants) are only done once
      adds  4bc4849   Merge branch 'master' of
      adds  a17fe6b   Adjust factor recipe, 3-5% faster for large inputs.
      adds  9e49408   Adjust primes sub to reflect new segment sieve behavior
      adds  14e86ff   Simplify primes()
      adds  9728b39   Fix 32-bit unsigned long issues
      adds  a17cb94   Load PP and Math::BigInt only when used.  More work needed
      adds  987e1d8   No validation means we weren't stripping weirdness from 
input bit counts. Use int("bits") to normalize.
      adds  f2d43c3   Move some functions from to util.c.  Faster, and 
reduces startup bloat.
      adds  0297d2a   Start work on separate PP front end
      adds  c3fa258   Put back some PP validation, as it does bigint magic
      adds  8a947e3   Bump version number
      adds  b16de00   More movement to PP front end
      adds  0dbc616   More startup measurements
      adds  f3e7800   More moving functions out of Util
      adds  60d376c   Clean up some random / proven primes
      adds  b61f82e   Add some more terms to integer zeta table.  Speeds up 
prime_count_approx by 1.5x
      adds  4df059c   Small RiemannR speedup
      adds  72fe357   Some TODO items are done
      adds  71a3bd1   znlog update
      adds  bdbbdcf   Remove the empty function call entirely for non-threads
      adds  1f31843   Update some examples
      adds  9a3fc47   Update examples and examples/README
      adds  71acd7e   Add 1 to skipped 5.6.2 tests
      adds  45cade1   Move benchmarks to separate bench directory
      adds  9055b54   Adjust yafu tests
      adds  c47d1ee   Move last tests out of examples, into bench and xt
      adds  575a4ce   Add Porter sequence example
      adds  e29ece1   Update Changes
      adds  c6adc48   Remove unused popcnt on 32-bit
      adds  344cff1   Minor documentation update
      adds  381a71f   Add some Project Euler examples
      adds  11fe74b   Merge branch 'master' of
      adds  e63256b   First round: add is_perfect_power, is_perfect_square, 
      adds  a011aa1   Add todo about perfect power.  Going to change name.
      adds  6be7d4a   Merge branch 'master' of
      adds  f174dde   Change to is_power, still needs work
      adds  25dc64a   is_power updates
      adds  c02ce28   PP is_power with negative arguments
      adds  777992a   Update some PE examples
      adds  31c2079   Trimming suggested by bulk88 (croak after New, move 
memset to just the needed branch)
      adds  9d134eb   Wrap dlp_prho debugging vomit inside #ifdef DEBUG, as 
nobody else wants to see that detail
      adds  6600baf   Code movement
      adds  cc4ccdf   Update PE 357 example
      adds  dd68fe4   Add inverse totient example
      adds  35f3847   PP is_power(n,a) has to deal with 0 return unlike the 
split XS code
      adds  d29c977   Better is_power
      adds  ee46293   Fix 5.6.2 issue with is_power
      adds  382d4e2   euler_phi(0,n) had wrong [1] when n >= 100
      adds  fee1203   Merge with master
      adds  5c2ca94   Typo in bigint section
      adds  e7fcbc3   More or less initial pbrent based on mulmod speed
      adds  6841339   Add two more PE examples
      adds  fa0226e   Add perfect power test in factoring
      adds  6661699   Small speedup for is_power(x,2)
      adds  b38f21d   Add a PE example
      adds  26aaca2   Only test for squares and cubes in factor.  Lowers cost.
      adds  759e933   Add xt ispower test and some more PE examples
      adds  4133fac   Slight speedup
      adds  141a8de   Small totient speedup
      adds  301c9a0   Revised example of Math::Factor::XS::matches
      adds  c8486c2   Add PE example
      adds  8a200c7   Remove unused line
      adds  bc9f900   Remove old test and print comment
      adds  66ebfeb   Spelling error: Dedekind
      adds  b7c29e9   Small change to PP znprimroot
      adds  96ca911   Doc updates
      adds  6b52eda   Update version number
      adds  a3f4d07   Updates for AKS
      adds  a330409   Small AKS update
      adds  d7f425d   Try harder to use lgamma
      adds  db88ec8   Add some threshold returns to protect vs. messed up 
rounding modes
      adds  3783549   Custom lgamma so improved AKS works on all platforms
      adds  ce4360f   ActiveState's gcc can't find builtins.  Pre-2005 compiler?
      adds  b779d4a   Allow threading failures with diagnostics
      adds  c575796   No MS intrinsics with MSC clang
      adds  8333e29   ispower test and 5.6.2 borkness
      adds  966eb2c   Change NaN generation method
      adds  06930b0   Speedup for znprimroot
      adds  481ac3b   Don't use Win32 intrins on WinCE
      adds  d1b89ec   fix sign warning in new znprimroot code
      adds  ba4ac8a   32-bit with Math::BigInt::GMP causes havoc because of its 
      adds  21fc61f   Allow some author tests to run better on 32-bit Perl
      adds  9230a69   Partitions uses Math::BigInt only when needed
      adds  b098e7d   logl -> log
      adds  0306484   Bump version
      adds  ab1d4d1   Don't use Math::BigInt::Pari for threading tests.  
Math::Pari + threads = bad juju
      adds  edf7c2b   PP jordan totient, be more aggressive about BigInt args.  
ActiveState weirdness?
      adds  c379974   Add float.h to includes
      adds  1b2723a   Bump version number
      adds  cf53b7d   Update PP F-U primality test
      adds  3ac854a   Don't die in t/04 if platform doesn't have NaN (some 
      adds  9dbf097   Speedup for exp_mangoldt
      adds  f74438f   Documentation updates
      adds  dd6d999   Speedup exp_mangoldt for large numbers -- primality + 
power detection instead of factoring
      adds  4eb186d   Shawe-Taylor random provable primes.  No documentation.
      adds  67508d1   Shawe-Taylor random proven primes from FIPS 186-4
      adds  2f3f0f8   Don't let ST random prime give up so easily
      adds  d57550a   random ST primes streamline the 32-bit case, allow 2-bit 
to return 2
      adds  714c336   Update benchmark time
      adds  db84c0c   Add coverage areas
      adds  f12cbbb   Add twin_prime_count
      adds  edc0a9e   Add twin_prime_count_approx
      adds  3b566e5   give twin_prime_count a much denser table (92 vs. 5)
      adds  8bdf350   Expand twin prime table
      adds  9e1d2af   Add nth_twin_prime
      adds  b0ed22a   Merge branch 'master' of
      adds  16bebc8   Add PP nth_twin_prime
      adds  c81f075   AKS comments
      adds  2caa6e5   Small nth_twin_prime speedup.  xt test for 
      adds  7cf90ba   Add xt nth_twin_prime test
      adds  ce3f38a   Documentation tweaks
      adds  649d33e   Add new functions to tests
      adds  61eb52f   Add PP twin_prime_count_approx
      adds  2b7dae3   Concerns about each
      adds  175ee9b   Move a big hash to closure instead of sub local
      adds  3b6009c   Improve test coverage
      adds  1107ef2   Trim some PP tests for performance
      adds  51eb534   Inverse Riemann R for nth_prime_approx
      adds  b7b1849   Add nth_twin_prime_approx, tighten twin_prime_count_approx
      adds  d307891   Finish nth_twin_prime_approx
      adds  6b0ad3d   Make sure nth_twin_prime goes to PP when the argument 
will overflow the C code
      adds  d35d25c   Tighten nth_prime_{upper,lower}
      adds  242de60   Edge case for legendre_phi
      adds  9cfeab9   speedups for legendre_phi with very large a
      adds  6be3cee   Add one more big-a optimization to legendre_phi
      adds  6e9b8a2   Add slightly faster ranged totient for start = 0
      adds  f7325af   Fix an old random_prime() bigint case.  No effect on 
proven, ndigit, or nbit random primes.
      adds  7f6602e   More optimizations for euler_phi(0,n)
      adds  ae3923b   Version comparison, make no warnings with test versions
      adds  047642b   Don't do test for ST random prime without new Digest::SHA
      adds  b604e2c   Fix typos
      adds  2e07559   Jordan totient even number shortcut
      adds  3f94d58   Update precalc and timings
      adds  19ce027   improve twin prime approximations
      adds  8107ad6   Add PP requirement for benchmark
      adds  0286fdb   Better AKS testing, change to znorder from naive order
      adds  9099e0e   Add numseqs example file, first version
      adds  c6dd262   Add last sequences to numseqs examples
      adds  7996de2   Add PythagoreanHypots to numseqs example
      adds  508de1a   add valuation function
      adds  f0ac1b2   croak with sane message when lucas_sequence given n < 2
      adds  3e76756   Add lucas_sequence tests
      adds  59d0b4f   New monty modinverse, nice primality speedup
      adds  413ed83   Update benchmark
      adds  9733e53   Improved code for mont_prod64
      adds  63471f6   Use 64-bit Montgomery math in primality tests even for 
32-bit inputs
      adds  d605825   Full trial divide of small factor inputs
      adds  94f1901   Another couple percent speedup for very small factor 
      adds  c973a39   Fix forcomposite with endpoint past max prime
      adds  cd7a0ea   forcomposites, edge cases and performance
      adds  d51a718   Speedup for znprimroot
      adds  1dc5d3c   Replace complicated invmod with simpler version that 
works properly for all n
      adds  ebf3ea9   Bump version number
      adds  25db44d   Add invmod
      adds  e9c4273   znorder arguments in PP code
      adds  174b334   invmod edge cases, add tests
      adds  5f3c9e7   is_pseudoprime / is_strong_pseudoprime
      adds  54052c0   Compiler warnings
      adds  7c3aca2   Simple forpart
      adds  c0821f9   Update to forpart
      adds  7c2fb0a   forpart now does restricted partitions
      adds  7ac02a4   forpart better interface, add docs, PP, tests
      adds  e1d98f3   vecsum()
      adds  631e5b1   Some forpart restriction speedups
      adds  d25bd70   Validate input in PPFE for gcd, lcm, vecsum
      adds  935293c   Add binomial(n,k)
      adds  cc14faa   More aggressive binomial reduction
      adds  87e369e   forpart edge cases
      adds  45cf33b   Make MPFR free cache after eint
      adds  2034ccd   init entire array to ensure good behavior in n=0 case
      adds  8f60e41   Extend binomial to negative arguments
      adds  84b1ee9   Full Kronenburg extension for binomial
      adds  30fe98f   Work around old Math::BigInt bug
      adds  d761934   Add Catalan sequence using binomial
      adds  da99011   Move some examples to vecsum from List::Util::sum
      adds  8141459   Allow GMP binomial
      adds  a6fd1c9   Fix for old Math::BigInt and negative args
      adds  d4e2847   binomial documentation update
      adds  49bf429   Add MephistoWaltz, PisanoPeriod, ProthNumbers
      adds  00289a6   Add native integer code to PP binomial
      adds  5a2daa4   whitespace and timings
      adds  a728180   BM and BBS examples
      adds  6c54973   Allow better optimization for invmod and large modulus
      adds  af182d1   Add binomial, valuation, and invmod
      adds  15cfa24   Updates for release
      adds  355312a   PP next_prime much faster to return first bigint prime.  
Huge speedup for xt/
      adds  b0a007a   vecsum edge case: fix and add test
      adds  7fb739c   Improve DLP (gcd before invmod)
      adds  7d39f7a   Further DLP rho improvements (speed up znlog)
      adds  ad24ac1   Add BSGS for znlog
      adds  11230eb   Add PP BSGS
      adds  7833a27   Use naive slot allocator in XS BSGS for nice speedup
      adds  7e468a2   Push DLP Rho ahead of BSGS 16M
      adds  d78d419   Fix PP 0-return cases (e.g. a=1)
      adds  8816d88   More znlog speedups
      adds  03d9e48   8-bit at a time inverse replacing 2-bit.
      adds  7dfd642   Switch to unrolled montgomery inverse
      adds  147577b   Alternate RiemannR calculation
      adds  158919d   Alternate RiemannR, fix bignum Li
      adds  06c4aa3   BSGS no longer requires g to be invertible
      adds  3c14c5e   Add CRT to util, add Pohlig-Hellman, use PH in znlog
      adds  fc5d25b   Remove unused variables
      adds  61f043c   Add some tests from Pari bug trackers; fix PP znlog with 
      adds  745d8c9   RiemannZeta and RiemannR updates
      adds  30860c6   Add gcdext and chinese, neither are finished yet
      adds  061ba9e   Finish up gcdext
      adds  6e31b9e   Finish chinese
      adds  c0bff5b   Streamline UV setting in forprimes hot loop
      adds  0d54aee   Load Math::BigFloat when required in lehmer
      adds  7f182b2   Merge branch 'master' of
      adds  dc04966   Fiddle with sieve/partial-sieve crossover
      adds  72bb578   Bump segment sizes up.  Will want dynamic adjustment
      adds  037a65b   Dynamic segment sieve sizes; remove partial sieve
      adds  d80b05b   Update csrand example
      adds  2216a97   Latest Montgomery product change from W. Izykowski
      adds  c80e837   Update performance numbers
      adds  8538e9c   Fix type change in forprimes
      adds  7ec8608   Update primality times; document weird closure-in-block 
      adds  9f30282   Updates to PP 
      adds  0583e2b   Add release tests for documentation examples
      adds  3453d8d   Revise PP sieve parsing, uses less memory
      adds  4b1aaa9   Small changes for compilation
      adds  b0e1167   PrimeArray examples added to t/33-examples.t
      adds  fb42fc5   work around bug in 5.20.0
      adds  832143e   Partial sieve + test for small windows
      adds  2e04de1   Skip znlog bigint test if not using GMP backend or 
      adds  fe6f54f   Speed PP pbrent and znlog
      adds  e590acc   znorder edge case; work around the usual 
Math::BigInt::GMP bug
      adds  91e1419   range and bigint edge cases
      adds  3c0cd5f   Make sure examples test works with 32-bit
      adds  db78b26   Spelling
      adds  e16a1b0   Add one more digit to Zeta with MPFR
      adds  97753ea   More workarounds for borked 64-bit Perl
      adds  8434612   nth_twin_prime_approx upper limit
      adds  dce8c79   PP factor methods should skip basic factor when possible
      adds  1a0fe56   reftyped needs to handle negative numbers
      adds  6f427e0   Back off random strong prime from 190 to 140 bits
      adds  3651a89   Use GMP gcdext and vecsum if available
      adds  c4f4d39   RiemannR with huge input should return inf
      adds  9922404   weirdness with vecsum and the GMP hash
      adds  63048ef   PP chinese: push lcm*s into bigint loop.
      adds  fd70dc3   Bump strong prime back to 180 bits in test, for 5.6
      adds  9b75478   Add xt/chinese test, fix 64-bit chinese, PP addmod
      adds  f73d047   Speed up nth_twin_prime
      adds  e2e9159   Update release version and date
      adds  20c0a59   Update upper bound in comment
      adds  c283ee2   Add MCE and serial versions of fibprime
      adds  199a5c7   SternDiatomic added
      adds  56a1e07   Add tests for chinese with large inputs
      adds  d0d48a9   PP ranged moebius fencepost fix
      adds  d23ca81   Moebius should try calling GMP directly
      adds  13eb112   Add GMP (via PP) processing options for euler_phi and 
      adds  87e35d1   znorder via PP; sort divisors with qsort
      adds  9ce942f   Fixup some synopsis examples
      adds  ec06b8f   csrand must have bits > 64
      adds  65bff7d   Add Micali-Schnorr CSPRNG to examples/csrand
      adds  952bc43   reftyped should accept undef
      adds  d382958   Merge branch 'master' of
      adds  b1e65c5   Add Math::GMP version of CSPRNG example script
      adds  cb1168e   Many synopsis test pass.
      adds  aef209e   Make sure BBS uses at least 3500 bits
      adds  ba485c7   Add foroddcomposites
      adds  41eb565   Remove deprecated: miller_rabin and all_factors
      adds  9681b4e   Comment note that all the commented out tests have passed 
      adds  779359c   Merge branch 'master' of
      adds  36ef9fd   Very slight speedup for carmichael_lambda
      adds  4d762ba   small factor and carmichael_lambda speedup
      adds  792f765   TODO alternate prefix sums for LMO
      adds  d6ba961   Add twin_primes()
      adds  39d5fe3   Simplify PP twin_primes() and make more efficient
      adds  5a4f313   Tests for twin primes
      adds  819699b   Fix forpart with amax=>0
      adds  3a942b6   Add test for forpart with amax 0
      adds  5ee7e61   Small speedup for twin prime counting
      adds  695dab1   Update description
      adds  fd762a8   Update comment
      adds  9fe683c   Speed up for Emirps
      adds  ea27913   Add use_primeinc config option for random primes
      adds  dcb3689   Use faster ranged totient when input is < 100 instead of 
= 0
      adds  7d0a85a   is_perfect_square uses isqrt
      adds  6312f27   Merge the 3 extra-strong-Lucas param selections into one 
static function
      adds  b055d4c   Update version number
      adds  f28af92   Hacks to PP chinese for 5.6.2
      adds  9952004   PP optimize for primes with small arguments
      adds  1294e45   Merge branch 'master' of
      adds  66cedd7   HOLF premult; 10% speedup for 49 to 64 bit factoring
      adds  1b2ae75   Merge branch 'master' of
      adds  996d289   Comment about older perl 5.8s
      adds  ee825f2   Add link to TODO
      adds  5faff5e   Comment for vecsum
      adds  1d2bce8   Merge branch 'master' of
      adds  15221cf   Change znorder from Das to Cohen
      adds  8976d4b   Tweak factoring parameters
      adds  7a3d863   Fix AIX XLC long double issues
      adds  b44d081   Speed up isprime for small inputs on no-montgomery-math 
      adds  d0fd27c   Tested List::Gen
      adds  9742cf7   Add forcomb
      adds  60e0b62   Add ntheory module alias
      adds  7c384a4   Add forperm
      adds  e602614   Add Algorithm::Combinatorics to see-also section
      adds  5780e19   Change from Heap's permutation to lexicographical
      adds  9a18e69   PP versions of forcomb and forperm
      adds  2a0319f   Add factorial; add tests for forcomb, forperm, factorial
      adds  a9cd1d6   Add ecm_factor as option, finish adding is_bpsw_prime
      adds  ab10a11   Update version number
      adds  ecffc10   Test ecm in simple factoring test
      adds  48c1d58   Version to 0.44_001
      adds  96dc42b   Fixes for Win32 and older MPUGMP
      adds  754ec1f   Redo PP forcomb loop, PP code returns one empty array for 
      adds  9a012a2   Unused additional Li implementaiton, may be useful for 
the PP code later
      adds  b468103   forperm 0 and forcomb n.0 return an one empty list
      adds  e69a289   Fix spelling error in references
      adds  0b8c804   Add Fibonacci pseudoprime test to lucas sequences test
      adds  e3fcf1f   Only a few Fibonacci pseudoprimes if PP without GMP
      adds  bf0bd8a   Update TODO
      adds  6e0992c   Add basic Frobenius primality test
      adds  57d47c4   Fix XS call-through for Frobenius
      adds  fc25ad5   Add Perrin pseudoprime, Frobenius has arguments
      adds  c09c452   crude PP lambertw function
      adds  70007bc   Documentation for Perrin and Frobenius
      adds  0d5eb0b   Speedup for divisor_sum(n,k) with large k
      adds  080ccd8   Add lambertw
      adds  3e37882   Cleanup for release tests
      adds  e0bd1ab   Add PP Perrin and Frobenius primality tests
      adds  fa92bbd   Tests for more pseudoprimes and lambertw
      adds  1c0ea5b   grammar fix in docs
      adds  2c1c6fb   documentation for ntheory; provide modules
      adds  b42219d   Update docs
      adds  82e151d   Upper/lower bounds were having problems with bignums -- 
      adds  4505505   Last change ignored non-Math::BigFloats
      adds  def779d   Add vecmin and vecmax functions
      adds  a5b1ff3   Internal start on bernfrac
      adds  8186009   Add bernfrac and bernreal
      adds  bbb498d   Tests for bernfrac and bernreal
      adds  26e40b3   Add caching of small values (under 100) to bernfrac
      adds  4422ffc   Add Pi; look for better factorials in backend; add 
bernreal precision
      adds  d9d373b   Update for Pi
      adds  f66f9bd   Update Pi
      adds  d14d8bc   Add Pi test
      adds  22934e2   Compiler warnings
      adds  e025489   Tests for Pi
      adds  2d9a2b5   Release tests
      adds  5c4ae12   Add simple tests for ntheory alias
      adds  4ccb0d4   Add Pi to reference card
      adds  efd2e39   Add vecprod
      adds  12ef2de   Small changes for release
      adds  6ec4589   Update version number
      adds  cdd6722   Long double changes
      adds  6c38725   Update version number
      adds  9282eac   Fix forcomb with k=0, reading out of array bounds
      adds  8041c2f   More fiddling with NaN, guessing at ActiveState
      adds  cc23688   Update version number
      adds  10c7fd5   Add MPUGMP to dep list automatically
      adds  9eec921   Fix memory leak in segment primes
      adds  18c5d66   Redo bernfrac to make sure we load bigint before bigfloat
      adds  d0dcfef   simple PP stirling numbers
      adds  3a32b02   Add Stirling numbers
      adds  4122428   Workaround broken Math::BigInt::GMP, call GMP stirling
      adds  4fff136   Tests and docs for stirling
      adds  01da8e0   Add PPFE front end for stirling
      adds  ad96e3f   Add simple product tree
      adds  975f558   Edge cases for new PP vecprod
      adds  602e1ef   Update version number
      adds  69dc807   Update Change date
      adds  682c93f   Another nan/infinity change
      adds  df5ebcf   Put Carp use in correct package
      adds  6635faa   Changes to ZetaBigFloat
      adds  24acd4d   Add Pi*B_n variant of zeta calculation
      adds  1df97ab   Speedup forpart with large nmin
      adds  efbab8b   Documentation fixes
      adds  06aa680   Add prime gap verifier
      adds  2645632   For non-objects that overflow UV, do string vecmin/vecmax
      adds  6ad0deb   Speedup for PP divisors
      adds  f19688e   Changes for 5.6.2
      adds  16d70e2   Trim some time consuming tests
      adds  814744f   Rewrite PP FU test, work around 5.6.2 segfault
      adds  f68d5b5   Small PP speedup
      adds  4d7172d   Revert prime count approx test change
      adds  ab85454   Simplify a bit of zeta bigfloat
      adds  b873994   Speedup for PP factoring: revised trial factor, small 
input Rho, more initial trial factoring
      adds  541fc50   Simplify divisors from factors
      adds  3471ec0   Doc change to verify-primegaps example
      adds  07e89db   Improve test coverage
      adds  028a7a6   PP: new trial factor, new primorial, update pbrent, 
update factor
      adds  e4559e2   Update factor recipe to match ::PP
      adds  cd885c8   Bump version number
      adds  492db2a   Allow different accuracy in ZetaBigFloat RiemannR
      adds  064d240   Fix new Zeta accuracy for certain values
      adds  92b70a8   divisor_sum changes
      adds  5381cce   Make is_pseudoprime act like is_strong_pseudoprime
      adds  aeb119c   doc change for ntheory
      adds  0a8f746   vecsum future note and PP shortcut
      adds  b3852b2   Adjust Changes file
      adds  c86d6df   Add hammingweight
      adds  ba6710d   Release testing issues
      adds  20b428e   Add vecreduce function
      adds  2713ecd   popcnt function for 32-bit
      adds  e24b4cd   Update Changes for release
      adds  68be36d   Rename popcount to fix NetBSD misbehavior
      adds  20c0b84   Documentation fixes from Paul Underwood
      adds  cf7beee   is_power takes optional third argument
      adds  3174cca   Update is_power latest change
      adds  a65440f   Speedup for AKS with larger-than-half-word inputs
      adds  afac758   Add AKS change to Changes
      adds  cf2302f   Merge branch 'master' of
      adds  78c33c3   Standalone compilation
      adds  7a26af6   Use bfloor instead of bint.  bint wasn't in pre-2014 
      adds  b0b22e0   Bump version number
      adds  3805ae5   standalone factor accepts multiple numbers per line
      adds  424232d   next_prime / prev_prime do GMP/_to_bigint instead of PP 
      adds  2a8aa19   lucas_sequence via XS
      adds  8561114   Add validation / bigint conversion to PP prev_prime and 
      adds  f964afc   Move unexported ecm_factor out of root PM
      adds  6ccc88a   Move verify_cert old format conversion into
      adds  86c3e01   Make sure bigint next/prev prime returns the input object 
      adds  b8d0653   Test value needs to be 32-bit safe
      adds  bbdbe29   Allow negative n in is_power
      adds  cfb2888   Don't use each on array in test
      adds  c9f0f84 can take oone argument (implied start = 0)
      adds  00fa544   Faster factoring
      adds  8e938ce   Merge branch 'master' of
      adds  df9f7ce   Move uint128_t into ptypes.h
      adds  a617a6d   Faster AKS on some machines
      adds  ed9c724   Add is_mersenne_prime
      adds  5cbb7f7   Use GMP lucas sequence if we are in PP is_mersenne_prime
      adds  3ce17ec   Fixup 5.8.x bugs
      adds  59343b3   Add is_mersenne_prime to ntheory doc
      adds  3e27e1f   Add large Perrin pseudoprime
      adds  f250763   Fix negative is_power for defined a, still need a=0 case
      adds  042a873   Fix ispower with negative input, add some tests
      adds  2f737d2   is_mersenne_prime change to table for known values
      adds  e76ec5c   Remove unused variables
      adds  7651b2e   Skip some expensive tests without GMP
      adds  be92a75   Move is_provable_prime to XS
      adds  e7c9599   Update for release
      adds  be13d74   Initial lucasu and lucasv
      adds  28d5cb1   lucasu and lucasv
      adds  e291557   Merge branch 'master' of
      adds  9ba1155   Add lucasu/lucasv to Changes file
      adds  979e6d3   Revise with some new functions
      adds  1158cce   Obnoxious Q=-1 speedup for lucasu/lucasv, need to find 
better solution
      adds  788826e   Add Axler (2014) prime count bounds
      adds  f22ab15   Comment changes in prime_count_approx comparisons
      adds  1dfa4c0   Fix typo in extended test for mersenne primes
      adds  5833019   Small speedup for p-1 factor
      adds  3694198   Typo in example comment
      adds  c1d955a   Very small pbrent performance improvement
      adds  0dc019d   Typo in example
      adds  4a64764   Merge branch 'master' of
      adds  7743db9   Compiler warnings
      adds  9373fe4   More pbrent for general factor search
      adds  b4b483f   Retweak of recently changed factor parameters
      adds  fc64873   ispower with neg arguments, workaround 
Math::BigInt::Pari/old-perl bug
      adds  1e95dcb   Catch some overflow conditions in lucasu/lucasv
      adds  07799ae   Merge branch 'master' of
      adds  a705270   Update version number
      adds  152828b   Adjust PPFE for negative is_power inputs
      adds  13f335e use lucasu/lucasv instead of hand calc
      adds  06a2acb   Update version number
      adds  7041333   Use Axler (2013) nth_prime bounds
      adds  5f020d1   Add harmreal and harmfrac to PP as dev (needs work)
      adds  983d141   harmfrac and harmreal for Harmonic numbers
      adds  02dd563   Speed up harmreal
      adds  273ebe5   Allow prime count approx to work with string arguments
      adds  134412d   harmreal will use MPFR if possible, and push some of its 
code to PP
      adds  65cefe7   Add Harmonic numbers
      adds  6681a4d   Fix a PP issue with nth_prime
      adds  4294024   Use inverse prime count for nth prime in XS code
      adds  391e85c   Very simple vecextract
      adds  6aaf2aa   nth_prime_lower/upper adjustments
      adds  97b788a   Start add sqrtint
      adds  eee8c1f   Ramanujan primes
      adds  8ed9941   Tests and PP for ramanujan primes
      adds  32a0625   Update for sqrtint
      adds  0972ff3   Adjust documentation
      adds  2deeb2c   New prime count bounds
      adds  28062d8   Add commented out Kulsha li code
      adds  32e90df   Add single base hashed M-R for 2^32 primality
      adds  6607c27   Update last checked Mersenne number
      adds  5732922   znlog updates
      adds  cfa314a   znlog use simple trial up to 10k (from 2k)
      adds  c6002a4   detect cycles in dlp_trial, look at order for trial 
      adds  a9469d7   Merge with main
      adds  e59c724   Fix for PP nth_prime on bigints
      adds  ac36bdb   Add documentation and PPFE for vecextract
      adds  4348251   vecextract allow bigint and array ref second argument
      adds  70fc20a   add sqrtl definitions
      adds  9342d94   Add missing threads macro use
      adds  496184b   Add nth_ramanujan_prime
      adds  e4998f4   Add is_ramanujan_prime
      adds  9584cf3   Add new ramanujan functions to change list
      adds  9c48292   vecextract tests
      adds  a5d0ba2   More efficient Ramanujan primes
      adds  34eab45   Speed up is_ramanujan_prime
      adds  f873dae   Remove unused function use
      adds  c142b8b   Update last double-checked Mersenne exponent
      adds  771f834   One more level of ramanujan prime upper
      adds  53281aa   Update for release
      adds  b4c6d6a   Fix for old MPFR; faster PP sieving
      adds  866cf20   Add is_catalan_pseudoprime
      adds  6a2fa62   spelling, doc fixes for is_catalan_pseudoprime
      adds  9708260   add base argument to foreach sieve macro
      adds  fea0809   lucas_seq with even n fixed for XS
      adds  607d96f   Even-n lucas_sequence fix for PP
      adds  6689be5   Use Aebi & Cairns result for semiprime catalan 
      adds  fb6d721   Speedup for is_perrin_pseudoprime
      adds  ca0b3e9   Fix global cleanup assert with MemFree object
      adds  2f44ef3   For memfree, just return if mutexes are not init.
      adds  43295e0   New code for Perrin pseudoprime pretests
      adds  7eeb7a9   Allow squares to be Frobenius pseudoprimes
      adds  9c00322   Initial sum_primes and print_primes
      adds  3b19cda   Fix compilation warnings for recent changes
      adds  62418ce   segments for sum_primes and print_primes
      adds  64c317b   Notice of sum_primes, print_primes functions
      adds  70fbba8   Updates for sum_primes and print_primes including docs
      adds  67da269   Comments about file handles for printing
      adds  e313e28   Update display less often, reduce timing precision 
      adds  04c0121   Add Khashin's Frobenius test
      adds  1236cca   Add some misc xt programs
      adds  57465c7   Fix undefined symbol
      adds  41676ab   Add PP version of Khashin Frobenius test
      adds  728cd58   Add a reset to prho and pbrent so they have better success
      adds  1a1fac4   Small optimization to Khashin code
      adds  40ed29f   Update Mersenne limit with new GIMPS double check limit
      adds  5bb2a2a   Update for release
      adds  0acfc93   Changes date
      adds  73e672a   Imported Upstream version 0.51
       new  2d113a0   Merge tag 'upstream/0.51'
       new  ce41189   Update debian/changelog
       new  be75de9   releasing package libmath-prime-util-perl version 0.51-1

The 3 revisions listed above as "new" are entirely new to this
repository and will be described in separate emails.  The revisions
listed as "adds" were already present in the repository and have only
been added to this reference.

Summary of changes:
 Changes                                  |  29 +++++
 MANIFEST                                 |   4 +
 META.json                                |  14 +--
 META.yml                                 |  14 +--
 Makefile.PL                              |  12 +-
 README                                   |   2 +-
 TODO                                     |  10 ++
 XS.xs                                    |  95 ++++++++-------
 aks.c                                    |   2 +-
 aks.h                                    |   2 +-
 cache.c                                  |   7 +-
 debian/changelog                         |   6 +
 examples/             |  14 +--
 factor.c                                 |  16 +++
 lib/Math/Prime/                   |  72 ++++++++++-
 lib/Math/Prime/Util/     |   4 +-
 lib/Math/Prime/Util/ |   4 +-
 lib/Math/Prime/Util/           |   4 +-
 lib/Math/Prime/Util/                | 157 ++++++++++++++++++++----
 lib/Math/Prime/Util/              |  20 ++++
 lib/Math/Prime/Util/  |   4 +-
 lib/Math/Prime/Util/        |   4 +-
 lib/Math/Prime/Util/     |   4 +-
 lib/Math/Prime/Util/      |   4 +-
 lib/Math/Prime/Util/      |   4 +-
 lib/                           |   8 +-
 primality.c                              | 199 ++++++++++++++++++++++++++++---
 primality.h                              |  13 +-
 sieve.c                                  |   8 +-
 sieve.h                                  |   8 +-
 t/02-can.t                               |  12 +-
 t/11-sumprimes.t                         |  29 +++++
 t/17-pseudoprime.t                       |  35 +++++-
 t/25-lucas_sequences.t                   |   9 +-
 t/92-release-pod-coverage.t              |   6 +-
 util.c                                   | 127 ++++++++++++++++++--
 util.h                                   |   4 +
 xt/                            |  15 +++
 xt/                   |  50 ++++++++
 xt/                      | 119 ++++++++++++++++++
 40 files changed, 987 insertions(+), 163 deletions(-)
 create mode 100644 t/11-sumprimes.t
 create mode 100644 xt/
 create mode 100644 xt/
 create mode 100755 xt/

Alioth's /usr/local/bin/git-commit-notice on 

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