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modify factor impl to eliminate overflow issue

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This change does the following:

1. Updates the arithmetic functions in `src/factor/numeric.rs` to
   correctly handle all cases up to 2^64. When numbers are larger
   than 2^63, we fall back to slightly slower routines that check
   for and handle overflow.

2. Since the arithmetic functions will now not overflow, we no longer
   need the safety net trial division implementation. We now always
   use Pollard's rho after eliminating small (<=13 bit) primes.

3. Slight tweak in `src/factor/gen_table.rs` to generate the first
   1027 primes, which means we test every prime of 13 or fewer bits
   before going into Pollard's rho. Includes corresponding update in
   `src/factor/prime_table.rs` and the Makefile to reflect this.

4. Add a new test that generates random numbers with exclusively
   large (14 to 50 bit) prime factors. This exercises the possible
   overflow paths.

5. Add another new test that checks the `is_prime()` function against
   a few dozen 64-bit primes. Again this is to exercise possible
   overflow paths.
This commit is contained in:
kwantam 2015-05-08 00:06:17 -04:00
parent 7565c27c00
commit ff24d48e73
6 changed files with 550 additions and 55 deletions
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2
Makefile
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@ -307,7 +307,7 @@ $(SRCDIR)/cksum/crc_table.rs: $(SRCDIR)/cksum/gen_table.rs
cd $(SRCDIR)/cksum && $(RUSTC) $(RUSTCBINFLAGS) gen_table.rs && ./gen_table && $(RM) gen_table
$(SRCDIR)/factor/prime_table.rs: $(SRCDIR)/factor/gen_table.rs
cd $(SRCDIR)/factor && $(RUSTC) $(RUSTCBINFLAGS) gen_table.rs && ./gen_table 1000 > $@ && $(RM) gen_table
cd $(SRCDIR)/factor && $(RUSTC) $(RUSTCBINFLAGS) gen_table.rs && ./gen_table > $@ && $(RM) gen_table
crates:
echo $(EXES)