## Changes for version 0.36

- API Changes
- factor behavior for 0 and 1 more consistent. The results for factor, factor_exp, divisors, and divisor_sum now match Pari, and the omega(1)/Omega(1) exception is removed.
- Thanks to Hugo van der Sanden for bringing this up.

- all_factors changed to divisors. The old name still remains aliased.

- factor behavior for 0 and 1 more consistent. The results for factor, factor_exp, divisors, and divisor_sum now match Pari, and the omega(1)/Omega(1) exception is removed.
- ADDED
- forcomposites like forprimes, but on composites. See Pari 2.6.x.
- fordivisors calls a block for each divisor
- kronecker Kronecker symbol (extension of Jacobi symbol)
- znprimroot Primitive root modulo n
- gcd Greatest common divisor
- lcm Least common multiple
- legendre_phi Legendre's sum

- FUNCTIONALITY AND PERFORMANCE
- Win32 fixes from bulk88 / bulkdd. Thanks!
- XS redundancy removal and fixes from bulk88 and leont. Smaller DLL. This almost includes not compiling a number of prime count methods (Legendre, Meissel, Lehmer, and LMOS) that are not used. Using "-DLEHMER" in the Makefile will compile them, but there should not be any reason to do so.
- Big XS interface reorg. Most functions now go straight to XS, which reduces their overhead. Input number validation is much faster for the general case. Those two combined meant the '-nobigint' import no longer serves any good purpose.
- More functions will go from XS directly to the GMP module, bypassing the Perl layer entirely. The upside is less overhead, both for the case of having GMP, and without. In the contrived case of having XS turned off but the GMP module enabled, things will run slower since they no longer go to GMP.
- Test suite should run faster. Combination of small speedups to hot spots as well as pushing a few slow tasks to EXTENDED_TESTING (these are generally things never used, like pure Perl AKS).
- Some 5.6.2-is-broken workarounds.
- Some LMO edge cases: small numbers that only show up if a #define is changed, and counts > 18440000000000000000. Tested through 2^64-1 now.
- LMO much faster if -march=native is used for gcc on a platform with asm popcnt (e.g. Nahalem+, Barcelona+, ARM Neon, SPARC, Power7, etc.).
- divisors (all_factors) faster for native size numbers with many factors.
- Switch from mapes to a cached primorial/totient small phi method in lehmer.c. Significant for LMOS and Legendre (no longer used or compiled, see earlier. Thanks to Kim Walisch for questioning my earlier decision.
- Rewrite sieve composite map. Segment sieving is faster. It's a little faster than primegen for me, but still slower than primesieve and yafu.
- znorder uses Carmichael Lambda instead of Euler Phi. Faster.
- While Math::BigInt has the bgcd and blcm functions, they are slow for native numbers, even with the Pari or GMP back ends. The gcd/lcm here are 20-100x faster. LCM also returns results consistent with Pari.
- Removed the old SQUFOF code, so the racing version is the only one. It was already the only one being used.

## Modules

- Math::Prime::Util - Utilities related to prime numbers, including fast sieves and factoring
- Math::Prime::Util::ECAffinePoint - Elliptic curve operations for affine points
- Math::Prime::Util::ECProjectivePoint - Elliptic curve operations for projective points
- Math::Prime::Util::MemFree - An auto-free object for Math::Prime::Util
- Math::Prime::Util::PP - Pure Perl version of Math::Prime::Util
- Math::Prime::Util::PrimalityProving - Primality proofs and certificates
- Math::Prime::Util::PrimeArray - A tied array for primes
- Math::Prime::Util::PrimeIterator - An object iterator for primes
- Math::Prime::Util::ZetaBigFloat - Perl Big Float versions of Riemann Zeta and R functions

## Examples

- examples/abundant.pl
- examples/bench-factor-extra.pl
- examples/bench-factor-semiprime.pl
- examples/bench-factor.pl
- examples/bench-is-prime.pl
- examples/bench-isprime-bpsw.pl
- examples/bench-miller-rabin.pl
- examples/bench-mp-nextprime.pl
- examples/bench-mp-prime_count.pl
- examples/bench-mp-psrp.pl
- examples/bench-nthprime.pl
- examples/bench-pcapprox.pl
- examples/bench-pp-count.pl
- examples/bench-pp-isprime.pl
- examples/bench-pp-sieve.pl
- examples/bench-primearray.pl
- examples/bench-primecount.pl
- examples/bench-random-prime-bigint.pl
- examples/bench-random-prime.pl
- examples/find_mr_bases.pl
- examples/parallel_fibprime.pl
- examples/README
- examples/sophie_germain.pl
- examples/test-factor-gnufactor.pl
- examples/test-factor-yafu.pl
- examples/test-nextprime-yafu.pl
- examples/test-primes-yafu.pl
- examples/twin_primes.pl
- examples/verify-cert.pl
- examples/verify-gmp-ecpp-cert.pl
- examples/verify-sage-ecpp-cert.pl