FPLIB "SINGLE EXTENDED" PRECISION FLOATING POINT FORMAT

Floating point number - (m,e) including mantissa sign
        Decimal value = m * ( 2 ** ( e - ebias ))

        23_____________________0    23_______________________0
        | s .      m           |    |    0            e .    |
        |______________________|    |________________________|

m = 24 bit mantissa (two's complement, normalized fraction)
        23 bit mantissa precision plus 1 bit mantissa sign gives
        precision of approximately 7 decimal digits.  The 24 bit
        mantissa was chosen to maximize precision with efficient
        use of the DSP56300 MPY and MAC instructions.
        A hidden leading 1 is not implemented in this format.

        Binary encoding:  s.xxxxxxx xxxxxxxx xxxxxxxx
        Bit weight:       0  -1                      -23
                        -2  2                       2

        Largest positive mantissa    $7FFFFF = +0.99999988079071044921875
        Smallest positive mantissa   $400000 = +0.5
        Floating point zero mantissa $000000 = 0
        Smallest negative mantissa   $BFFFFF = -0.50000011920928955078125
        Largest negative mantissa    $800000 = -1.0
        Reserved mantissas           $000001 through $3FFFFF
                                     $C00000 through $FFFFFF

        Note that all reserved mantissas are illegal since they
        represent denormalized mantissas.

e = 14 bit exponent (unsigned integer, biased by ebias = +8191)
        Stored as a 24 bit unsigned integer with 10 leading zeros.
        Exponent arithmetic is generally done with 16 bit precision.
        The 14 bit exponent format was chosen to maximize dynamic
        range with efficient detection of exponent overflow and
        exponent underflow.

        Binary encoding:  00000000 00xxxxxx xxxxxxxx.
        Bit weight:                   13            0
                                     2             2

        Largest exponent             $003FFF = 2 ** +8192
        Assumed fixed point exponent $001FFF = 2 ** +0 = +1.0
        Smallest exponent            $000000 = 2 ** -8191
        Reserved exponents           $004000 through $FFFFFF

                        14
        If bit weight  2   is set, exponent overflow has occured.
                        15
        If bit weight  2   is set, exponent underflow has occured.

        Note that no distinct exponents are reserved for plus infinity,
        minus infinity, Not a Number (IEEE NaN), minus zero or
        denormalized numbers.

type
  Float48 = packed record
    exponent: longint;
    mantissa: longint;
  end;

function Float48ToDouble(Value: Float48): double;
var
  i: integer;
  Mask, Shift: longword;
begin
  if (Value.mantissa and $800000)=$800000) then Result:=-1 else Result:=0;
  Mask:=$400000; Shift:=2;
  for i:=1 to 23 do
  begin
    if ((Value.mantissa and Mask)=Mask) then Result:=Result+1/Shift;
    Mask:=Mask shr 1; Shift:=Shift shl 1;
  end;
  Result:=Ldexp(Result, (Value.exponent-8191));
end;