If we limit ourselves to Math::BigFloat, I just don't see any easy way of escaping the fact that, in i2dd(), Math::BigFloat->new( sprintf "%.17f", $hi ) is simply not a good enough base 10 approximation of $hi.

For the given example, you're subtracting 3.1415926535897931000000000000000 from 3.1415926535897932384626433832795 in order to get the least significant double.
But you need to be subtracting 3.1415926535897931159979634685442 which is a far more accurate base 10 approximation of 0x1.921fb54442d18p+1. That results in a value of 0.0000000000000001224646799147353, which has a hex representation of 0x1.1a62633145c06p-53. Correctly it would be 0x1.1a62633145c07p-53 - the discrepancy being due to the rounding done in converting to base 10 values for the calculations.

In any case, the problem is that I can't see any simple way of coercing Math::BigFloat into arriving at more accurate values - as it apparently can't convert hex floats to Math::BigFloat values.

All of which brings me back to using something like mpfr.
AFAIK, my Math::MPFR ppm packages will work fine with your MSVC-built perls, but it has probably been a while since this has been properly tested.
The ppd file specifies a couple of prerequisites to install, one of which (Math::Float128) may not work correctly for you. The other is Math::Decimal64.
If you want to avoid installing those pre-requisite modules, just save a copy of my scratchpad in the cwd as Math-MPFR.ppd and run:
ppm install Math-MPFR.ppd --force
Otherwise you can run:
ppm install http://www.sisyphusion.tk/ppm/Math-Decimal64.ppd --force
ppm install http://www.sisyphusion.tk/ppm/Math-Float128.ppd --force
ppm install http://www.sisyphusion.tk/ppm/Math-MPFR.ppd --force
The prerequisites are needed only if you want to call a function that takes/returns a Math::Float128 or Math::Decimal64 object. (I don't foresee that you have any need to be calling those functions.)

I fully understand and really don't mind at all if you don't want to go down that path - and I'm sure that other alternatives exist.
But I'm pretty much out of ideas (and energy) if Math::MPFR is to be excluded. (Without it, there's just too many hoops for me).
With Math::MPFR installed, sub i2dd becomes (eg): 
sub i2dd {
  use Math::MPFR qw(:mpfr);
  my $prec = Rmpfr_get_default_prec();
  Rmpfr_set_default_prec(2098);
  my $val = Math::MPFR->new($_[0]);
  my $hi = Rmpfr_get_d($val, MPFR_RNDN);
  $val -= $hi;
  my $lo = Rmpfr_get_d($val, MPFR_RNDN);

  # Revert to original precision:
  Rmpfr_set_default_prec($prec);

  return($hi, $lo);
}

[download]
(Of course, the sub can be set up to operate more efficiently than as presented - I just wanted it to cover all angles.)

Cheers,
Rob

In reply to Re^12: Math::BigFloat to native double? by syphilis
in thread Math::BigFloat to native double? by BrowserUk

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