Fixed point type not multiplying correctly

Fixed point type not multiplying correctly

I'm new to Ada, and have been trying out the fixed-point "delta" types. Specifically, I've created a 32-bit delta type range 0.0 .. 1.0. However, when I try to square certain values, I get a CONSTRAINT_ERROR. As far as I know, that should't happen with my specified range. The threshold for this error appears to be sqrt(1/2). I'm using GNAT from MinGW-w64 version 4.8.0.
Test code (all of it compiles in the form of gnatmake <file> with no warnings/errors):
types.ads:
pragma Ada_2012;

with Ada.Unchecked_Conversion;
with Ada.Text_IO;

package Types is
    type Fixed_Type is delta 1.0 / 2**32 range 0.0 .. 1.0
        with Size => 32;
    type Modular_Type is mod 2**32
        with Size => 32;
    function Fixed_To_Mod is new Ada.Unchecked_Conversion(Fixed_Type, Modular_Type);
    package MIO is new Ada.Text_IO.Modular_IO(Modular_Type);
    package FIO is new Ada.Text_IO.Fixed_IO(Fixed_Type);
end Types;
specifics.adb:
pragma Ada_2012;

with Ada.Text_IO;

with Types; use Types;

procedure Specifics is
    package TIO renames Ada.Text_IO;

    procedure TestValue(val: in Fixed_Type) is
        square : Fixed_Type;
    begin
        square := val * val;
        TIO.Put_Line("Value " & Fixed_Type'Image(val) & " squares properly.");
        TIO.Put_Line("Square: " & Fixed_Type'Image(square));
        TIO.New_Line;
    exception
        when Constraint_Error =>
            TIO.Put_Line("Value " & Fixed_Type'Image(val) & " does not square properly.");
            TIO.Put_Line("Square: " & Fixed_Type'Image(val * val));
            TIO.Put_Line("Not sure how that worked.");
            TIO.New_Line;
    end TestValue;

    function ParseFixed(s: in String; last: in Natural; val: out Fixed_Type) return Boolean is
        l : Natural;
    begin
        FIO.Get(s(s'First..last), val, l);
        return TRUE;
    exception
        when others =>
            TIO.Put_Line("Parsing failed.");
            return FALSE;
    end ParseFixed;

    buffer : String(1..20);
    last : Natural;
    f : Fixed_Type;
begin
    loop
        TIO.Put(">>> ");
        TIO.Get_Line(buffer, last);
        exit when buffer(1..last) = "quit";
        if ParseFixed(buffer, last, f) then
            TestValue(f);
        end if;
    end loop;
end Specifics;
Output of specifics.adb:
>>> 0.1
Value  0.1000000001 squares properly.
Square:  0.0100000000

>>> 0.2
Value  0.2000000000 squares properly.
Square:  0.0399999998

>>> 0.4
Value  0.3999999999 squares properly.
Square:  0.1599999999

>>> 0.6
Value  0.6000000001 squares properly.
Square:  0.3600000001

>>> 0.7
Value  0.7000000000 squares properly.
Square:  0.4899999998

>>> 0.75
Value  0.7500000000 does not square properly.
Square: -0.4375000000
Not sure how that worked.

>>> quit
Somehow, multiplying val by itself yielded a negative number, which explains the CONSTRAINT_ERROR... but never mind that, why am I getting a negative number in the first place?
I then decided to test for the point at which squaring the numbers started failing, so I wrote the following snippet:
fixedpointtest.adb:
pragma Ada_2012;

with Ada.Text_IO;

with Types; use Types;

procedure FixedPointTest is
    package TIO renames Ada.Text_IO;