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lib/Math/BigFloat.pm  view on Meta::CPAN

        $pi = bless {
                     sign => '+',
                     _m   => $LIB -> _new($digits),
                     _es  => CORE::length($digits) > 1 ? '-' : '+',
                     _e   => $LIB -> _new($n - 1),
                    }, $class;

    } else {

        # For large accuracy, the arctan formulas become very inefficient with
        # Math::BigFloat, so use Brent-Salamin (aka AGM or Gauss-Legendre).

        # Use a few more digits in the intermediate computations.
        $n += 8;

        $HALF = $class -> new($HALF) unless ref($HALF);
        my ($an, $bn, $tn, $pn)
          = ($class -> bone, $HALF -> copy() -> bsqrt($n),
             $HALF -> copy() -> bmul($HALF), $class -> bone);
        while ($pn < $n) {

lib/Math/BigFloat.pm  view on Meta::CPAN

    # We set Y here to multiples of 10 so that $x becomes below 1 - the smaller
    # $x is the faster it gets. Since 2*$x takes about 10 times as long, we
    # make it faster by about a factor of 100 by dividing $x by 10.

    # The same observation is valid for numbers smaller than 0.1, e.g.
    # computing log(1) is fastest, and the further away we get from 1, the
    # longer it takes. So we also 'break' this down by multiplying $x with 10
    # and subtract the log(10) afterwards to get the correct result.

    # To get $x even closer to 1, we also divide by 2 and then use log(2) to
    # correct for this. For instance if $x is 2.4, we use the formula:
    #  blog(2.4 * 2) == blog(1.2) + blog(2)
    # and thus calculate only blog(1.2) and blog(2), which is faster in total
    # than calculating blog(2.4).

    # In addition, the values for blog(2) and blog(10) are cached.

    # Calculate the number of digits before the dot, i.e., 1 + floor(log10(x)):
    #   x = 123      => dbd =  3
    #   x = 1.23     => dbd =  1
    #   x = 0.0123   => dbd = -1