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The following list is not up to date:

See also various .pm files.

General:
 * Copy on write (helps for $x = -$x; cases etc) (seems to make it slower :/
 * run config() and die_on_nan() tests under Subclass.pm

Math::BigFloat:
 * finish upgrading and downgrading
 * ! bround()/bfround(): some bugs may lurk in there
 * accuracy() & precision() maybe not finished (bnorm() in every op, testcases)
 * do not reduce numbers in new(), rather do it in anything that outputs it
   like bsstr(), bstr(), mantissa(), exponent() and parts(). Reducing the
   number after each op is slow with a binary core math lib like BitVect.
 * add bfract() that returns just the fractional part?
 * tests for frsft() and flsft() with $n != 2
 * blog() is still quite slow for non-integer results. See if we can reuse the
   integer calculation somehow
 * finish broot() by using different algorithm

Math::BigInt:
 * Finite non-integers should be handled consistently. The may appear as input
   and as a result of a computation. Alternatives are: round, truncate, die,
   and return NaN.
 * finish 'upgrade'
 * remove rounding overhead when no rounding is done, e.g. no $object has A nor
   P and neither of bround(), bround(), accuracy() or precision() was called
 * bround() is only used by MBF for -$scale = -$len, anyway. POD is wrong for
   this, too
 * overload of cos()/sin()/exp()/atan2() is too DWIM (should return BigInt or
   BigFloat, not scalar) - also document it
 * +5 % 0 or -5 % 0 == NaN (should it be something else?)
 * certain shortcuts returning bzero(), bone() etc may not set the requested
   rounding parameters, so that $x->foo($y,$a,$p,$r) may return $x without a
   set $a or $p, thus failing later on:

        use Test;
        BEGIN { plan tests => 1; }
        use Math::BigInt;
        $x = Math::BigInt->bone();
        $x->bsqrt(3,0,'odd');           # $x = 0, but _a is not 3!
        ok ($x + '12345','12300');      # fails (12346 instead of 12300)

   The shortcuts in code that return $x->bzero() or similar things need to
   do $x->bzero($a,$p); and this needs tests.
   Update: Should now work for most things. Check for completeness.

Given the fact that we are be able to plug-in a much faster core-lib, the
following are pretty much ultra-low-priority:

Math::BigInt::Calc:
 * look at div() for more speed (I have the hunch that the general _div()
   routine does way too much work for normal div (e.g. when we don't need
   the reminder). A simplified version could take care of this.
 * alternative mul() method using shifts
 * implement in Calc (and GMP etc) to calculate band(), bior(), bxor() for
   negative inputs (_signed_or() etc)
 * _root() doesn't scale too well

Please send me test-reports, your experiences with this and your ideas - I love
to hear about my work!