Add ieee 2008 packages.

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+-- --------------------------------------------------------------------
+--
+-- Copyright © 2008 by IEEE. All rights reserved.
+--
+-- This source file is an essential part of IEEE Std 1076-2008,
+-- IEEE Standard VHDL Language Reference Manual. This source file may not be
+-- copied, sold, or included with software that is sold without written 
+-- permission from the IEEE Standards Department. This source file may be 
+-- copied for individual use between licensed users. This source file is
+-- provided on an AS IS basis. The IEEE disclaims ANY WARRANTY EXPRESS OR
+-- IMPLIED INCLUDING ANY WARRANTY OF MERCHANTABILITY AND FITNESS FOR USE
+-- FOR A PARTICULAR PURPOSE. The user of the source file shall indemnify
+-- and hold IEEE harmless from any damages or liability arising out of the
+-- use thereof.
+--
+--   Title     :  Floating-point package (Generic package body)
+--             :
+--   Library   :  This package shall be compiled into a library
+--             :  symbolically named IEEE.
+--             :
+--   Developers:  Accellera VHDL-TC and IEEE P1076 Working Group
+--             :
+--   Purpose   :  This packages defines basic binary floating point
+--             :  arithmetic functions
+--             :
+--   Note      :  This package may be modified to include additional data
+--             :  required by tools, but it must in no way change the
+--             :  external interfaces or simulation behavior of the
+--             :  description. It is permissible to add comments and/or
+--             :  attributes to the package declarations, but not to change
+--             :  or delete any original lines of the package declaration.
+--             :  The package body may be changed only in accordance with
+--             :  the terms of Clause 16 of this standard.
+--             :
+-- --------------------------------------------------------------------
+-- $Revision: 1220 $
+-- $Date: 2008-04-10 17:16:09 +0930 (Thu, 10 Apr 2008) $
+-- --------------------------------------------------------------------
+
+package body float_generic_pkg is
+
+  -- Author David Bishop (dbishop@vhdl.org)
+  -----------------------------------------------------------------------------
+  -- type declarations
+  -----------------------------------------------------------------------------
+
+  -- This deferred constant will tell you if the package body is synthesizable
+  -- or implemented as real numbers, set to "true" if synthesizable.
+  constant fphdlsynth_or_real : BOOLEAN := true;  -- deferred constant
+
+  -- types of boundary conditions
+  type boundary_type is (normal, infinity, zero, denormal);
+
+  -- null range array constant
+  constant NAFP : UNRESOLVED_float (0 downto 1)  := (others => '0');
+  constant NSLV : STD_ULOGIC_VECTOR (0 downto 1) := (others => '0');
+
+  -- Special version of "minimum" to do some boundary checking
+  function mine (L, R : INTEGER)
+    return INTEGER is
+  begin  -- function minimum
+    if (L = INTEGER'low or R = INTEGER'low) then
+      report float_generic_pkg'instance_name
+        & " Unbounded number passed, was a literal used?"
+        severity error;
+      return 0;
+    end if;
+    return minimum (L, R);
+  end function mine;
+
+  -- Generates the base number for the exponent normalization offset.
+  function gen_expon_base (
+    constant exponent_width : NATURAL)
+    return SIGNED
+  is
+    variable result : SIGNED (exponent_width-1 downto 0);
+  begin
+    result                    := (others => '1');
+    result (exponent_width-1) := '0';
+    return result;
+  end function gen_expon_base;
+
+  -- Integer version of the "log2" command (contributed by Peter Ashenden)
+  function log2 (A : NATURAL) return NATURAL is
+    variable quotient : NATURAL;
+    variable result   : NATURAL := 0;
+  begin
+    quotient := A / 2;
+    while quotient > 0 loop
+      quotient := quotient / 2;
+      result   := result + 1;
+    end loop;
+    return result;
+  end function log2;
+
+  -- Function similar to the ILOGB function in MATH_REAL
+  function log2 (A : REAL) return INTEGER is
+    variable Y : REAL;
+    variable N : INTEGER := 0;
+  begin
+    if (A = 1.0 or A = 0.0) then
+      return 0;
+    end if;
+    Y := A;
+    if(A > 1.0) then
+      while Y >= 2.0 loop
+        Y := Y / 2.0;
+        N := N + 1;
+      end loop;
+      return N;
+    end if;
+    -- O < Y < 1
+    while Y < 1.0 loop
+      Y := Y * 2.0;
+      N := N - 1;
+    end loop;
+    return N;
+  end function log2;
+
+  -- purpose: Test the boundary conditions of a Real number
+  procedure test_boundary (
+    arg                     : in REAL;     -- Input, converted to real
+    constant fraction_width : in NATURAL;  -- length of FP output fraction
+    constant exponent_width : in NATURAL;  -- length of FP exponent
+    constant denormalize    : in BOOLEAN := true;  -- Use IEEE extended FP
+    variable btype : out boundary_type;
+    variable log2i : out INTEGER
+    ) is
+    constant expon_base : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    constant exp_min : SIGNED (12 downto 0) :=
+      -(resize(expon_base, 13)) + 1;    -- Minimum normal exponent
+    constant exp_ext_min : SIGNED (12 downto 0) :=
+      exp_min - fraction_width;         -- Minimum for denormal exponent
+    variable log2arg : INTEGER;         -- log2 of argument
+  begin  -- function test_boundary
+    -- Check to see if the exponent is big enough
+    -- Note that the argument is always an absolute value at this point.
+    log2arg := log2(arg);
+    if arg = 0.0 then
+      btype := zero;
+    elsif exponent_width > 11 then      -- Exponent for Real is 11 (64 bit)
+      btype := normal;
+    else
+      if log2arg < to_integer(exp_min) then
+        if denormalize then
+          if log2arg < to_integer(exp_ext_min) then
+            btype := zero;
+          else
+            btype := denormal;
+          end if;
+        else
+          if log2arg < to_integer(exp_min)-1 then
+            btype := zero;
+          else
+            btype := normal;              -- Can still represent this number
+          end if;
+        end if;
+      elsif exponent_width < 11 then
+        if log2arg > to_integer(expon_base)+1 then
+          btype := infinity;
+        else
+          btype := normal;
+        end if;
+      else
+        btype := normal;
+      end if;
+    end if;
+    log2i := log2arg;
+  end procedure test_boundary;
+
+  -- purpose: Rounds depending on the state of the "round_style"
+  -- Logic taken from
+  -- "What Every Computer Scientist Should Know About Floating Point Arithmetic"
+  -- by David Goldberg (1991)
+  function check_round (
+    fract_in             : STD_ULOGIC;  -- input fraction
+    sign                 : STD_ULOGIC;  -- sign bit
+    remainder            : UNSIGNED;    -- remainder to round from
+    sticky               : STD_ULOGIC := '0';      -- Sticky bit
+    constant round_style : round_type)  -- rounding type
+    return BOOLEAN
+  is
+    variable result     : BOOLEAN;
+    variable or_reduced : STD_ULOGIC;
+  begin  -- function check_round
+    result := false;
+    if (remainder'length > 0) then      -- if remainder in a null array
+      or_reduced := or (remainder & sticky);
+      rounding_case : case round_style is
+        when round_nearest =>           -- Round Nearest, default mode
+          if remainder(remainder'high) = '1' then  -- round
+            if (remainder'length > 1) then
+              if ((or (remainder(remainder'high-1
+                                 downto remainder'low)) = '1'
+                   or sticky = '1')
+                  or fract_in = '1') then
+                -- Make the bottom bit zero if possible if we are at 1/2
+                result := true;
+              end if;
+            else
+              result := (fract_in = '1' or sticky = '1');
+            end if;
+          end if;
+        when round_inf =>               -- round up if positive, else truncate.
+          if or_reduced = '1' and sign = '0' then
+            result := true;
+          end if;
+        when round_neginf =>        -- round down if negative, else truncate.
+          if or_reduced = '1' and sign = '1' then
+            result := true;
+          end if;
+        when round_zero =>              -- round toward 0   Truncate
+          null;
+      end case rounding_case;
+    end if;
+    return result;
+  end function check_round;
+
+  -- purpose: Rounds depending on the state of the "round_style"
+  -- unsigned version
+  procedure fp_round (
+    fract_in  : in  UNSIGNED;           -- input fraction
+    expon_in  : in  SIGNED;             -- input exponent
+    fract_out : out UNSIGNED;           -- output fraction
+    expon_out : out SIGNED) is          -- output exponent
+  begin  -- procedure fp_round
+    if and (fract_in) = '1' then        -- Fraction is all "1"
+      expon_out := expon_in + 1;
+      fract_out := to_unsigned(0, fract_out'high+1);
+    else
+      expon_out := expon_in;
+      fract_out := fract_in + 1;
+    end if;
+  end procedure fp_round;
+
+  -- This version of break_number doesn't call "classfp"
+  procedure break_number (              -- internal version
+    arg         : in  UNRESOLVED_float;
+    fptyp       : in  valid_fpstate;
+    denormalize : in  BOOLEAN := true;
+    fract       : out UNSIGNED;
+    expon       : out SIGNED) is
+    constant fraction_width : NATURAL := -arg'low;  -- length of FP output fraction
+    constant exponent_width : NATURAL := arg'high;  -- length of FP output exponent
+    constant expon_base     : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable exp : SIGNED (expon'range);
+  begin
+    fract (fraction_width-1 downto 0) :=
+      UNSIGNED (to_slv(arg(-1 downto -fraction_width)));
+    breakcase : case fptyp is
+      when pos_zero | neg_zero =>
+        fract (fraction_width) := '0';
+        exp                    := -expon_base;
+      when pos_denormal | neg_denormal =>
+        if denormalize then
+          exp                    := -expon_base;
+          fract (fraction_width) := '0';
+        else
+          exp                    := -expon_base - 1;
+          fract (fraction_width) := '1';
+        end if;
+      when pos_normal | neg_normal | pos_inf | neg_inf =>
+        fract (fraction_width) := '1';
+        exp                    := SIGNED(arg(exponent_width-1 downto 0));
+        exp (exponent_width-1) := not exp(exponent_width-1);
+      when others =>
+        assert NO_WARNING
+          report FLOAT_GENERIC_PKG'instance_name
+          & "BREAK_NUMBER: " &
+          "Meta state detected in fp_break_number process"
+          severity warning;
+        -- complete the case, if a NAN goes in, a NAN comes out.
+        exp                    := (others => '1');
+        fract (fraction_width) := '1';
+    end case breakcase;
+    expon := exp;
+  end procedure break_number;
+
+  -- purpose: floating point to UNSIGNED
+  -- Used by to_integer, to_unsigned, and to_signed functions
+  procedure float_to_unsigned (
+    arg                  : in  UNRESOLVED_float;    -- floating point input
+    variable sign        : out STD_ULOGIC;          -- sign of output
+    variable frac        : out UNSIGNED;            -- unsigned biased output
+    constant denormalize : in  BOOLEAN;             -- turn on denormalization
+    constant bias        : in  NATURAL;             -- bias for fixed point
+    constant round_style : in  round_type) is       -- rounding method
+    constant fraction_width : INTEGER := -mine(arg'low, arg'low);  -- length of FP output fraction
+    constant exponent_width : INTEGER := arg'high;  -- length of FP output exponent
+    variable fract          : UNSIGNED (frac'range);  -- internal version of frac
+    variable isign          : STD_ULOGIC;           -- internal version of sign
+    variable exp            : INTEGER;  -- Exponent
+    variable expon          : SIGNED (exponent_width-1 downto 0);  -- Vectorized exp
+    -- Base to divide fraction by
+    variable frac_shift     : UNSIGNED (frac'high+3 downto 0);  -- Fraction shifted
+    variable shift          : INTEGER;
+    variable remainder      : UNSIGNED (2 downto 0);
+    variable round          : STD_ULOGIC;           -- round BIT
+  begin
+    isign                   := to_x01(arg(arg'high));
+    -- exponent /= '0', normal floating point
+    expon                   := to_01(SIGNED(arg (exponent_width-1 downto 0)), 'X');
+    expon(exponent_width-1) := not expon(exponent_width-1);
+    exp                     := to_integer (expon);
+    -- Figure out the fraction
+    fract                   := (others => '0');     -- fill with zero
+    fract (fract'high)      := '1';     -- Add the "1.0".
+    shift                   := (fract'high-1) - exp;
+    if fraction_width > fract'high then             -- Can only use size-2 bits
+      fract (fract'high-1 downto 0) := UNSIGNED (to_slv (arg(-1 downto
+                                                             -fract'high)));
+    else                                -- can use all bits
+      fract (fract'high-1 downto fract'high-fraction_width) :=
+        UNSIGNED (to_slv (arg(-1 downto -fraction_width)));
+    end if;
+    frac_shift := fract & "000";
+    if shift < 0 then                   -- Overflow
+      fract := (others => '1');
+    else
+      frac_shift := shift_right (frac_shift, shift);
+      fract      := frac_shift (frac_shift'high downto 3);
+      remainder  := frac_shift (2 downto 0);
+      -- round (round_zero will bypass this and truncate)
+      case round_style is
+        when round_nearest =>
+          round := remainder(2) and
+                   (fract (0) or (or (remainder (1 downto 0))));
+        when round_inf =>
+          round := remainder(2) and not isign;
+        when round_neginf =>
+          round := remainder(2) and isign;
+        when others =>
+          round := '0';
+      end case;
+      if round = '1' then
+        fract := fract + 1;
+      end if;
+    end if;
+    frac := fract;
+    sign := isign;
+  end procedure float_to_unsigned;
+
+  -- purpose: returns a part of a vector, this function is here because
+  -- or (fractr (to_integer(shiftx) downto 0));
+  -- can't be synthesized in some synthesis tools.
+  function smallfract (
+    arg   : UNSIGNED;
+    shift : NATURAL)
+    return STD_ULOGIC
+  is
+    variable orx : STD_ULOGIC;
+  begin
+    orx := arg(shift);
+    for i in arg'range loop
+      if i < shift then
+        orx := arg(i) or orx;
+      end if;
+    end loop;
+    return orx;
+  end function smallfract;
+  ---------------------------------------------------------------------------
+  -- Visible functions
+  ---------------------------------------------------------------------------
+
+  -- purpose: converts the negative index to a positive one
+  -- negative indices are illegal in 1164 and 1076.3
+  function to_sulv (
+    arg : UNRESOLVED_float)             -- fp vector
+    return STD_ULOGIC_VECTOR
+  is
+    variable result : STD_ULOGIC_VECTOR (arg'length-1 downto 0);
+  begin  -- function to_std_ulogic_vector
+    if arg'length < 1 then
+      return NSLV;
+    end if;
+    result := STD_ULOGIC_VECTOR (arg);
+    return result;
+  end function to_sulv;
+
+  -- Converts an fp into an SULV
+  function to_slv (arg : UNRESOLVED_float) return STD_LOGIC_VECTOR is
+  begin
+    return to_sulv (arg);
+  end function to_slv;
+
+  -- purpose: normalizes a floating point number
+  -- This version assumes an "unsigned" input with
+  function normalize (
+    fract                   : UNRESOLVED_UNSIGNED;   -- fraction, unnormalized
+    expon                   : UNRESOLVED_SIGNED;   -- exponent, normalized by -1
+    sign                    : STD_ULOGIC;         -- sign BIT
+    sticky                  : STD_ULOGIC := '0';  -- Sticky bit (rounding)
+    constant exponent_width : NATURAL    := float_exponent_width;  -- size of output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- size of output fraction
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant denormalize    : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant nguard         : NATURAL    := float_guard_bits)  -- guard bits
+    return UNRESOLVED_float
+  is
+    variable sfract     : UNSIGNED (fract'high downto 0);  -- shifted fraction
+    variable rfract     : UNSIGNED (fraction_width-1 downto 0);   -- fraction
+    variable exp        : SIGNED (exponent_width+1 downto 0);  -- exponent
+    variable rexp       : SIGNED (exponent_width+1 downto 0);  -- result exponent
+    variable rexpon     : UNSIGNED (exponent_width-1 downto 0);   -- exponent
+    variable result     : UNRESOLVED_float (exponent_width downto -fraction_width);  -- result
+    variable shiftr     : INTEGER;      -- shift amount
+    variable stickyx    : STD_ULOGIC;   -- version of sticky
+    constant expon_base : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable round, zerores, infres : BOOLEAN;
+  begin  -- function normalize
+    zerores := false;
+    infres  := false;
+    round   := false;
+    shiftr  := find_leftmost (to_01(fract), '1')     -- Find the first "1"
+               - fraction_width - nguard;  -- subtract the length we want
+    exp := resize (expon, exp'length) + shiftr;
+    if (or (fract) = '0') then   -- Zero
+      zerores := true;
+    elsif ((exp <= -resize(expon_base, exp'length)-1) and denormalize)
+      or ((exp < -resize(expon_base, exp'length)-1) and not denormalize) then
+      if (exp >= -resize(expon_base, exp'length)-fraction_width-1)
+        and denormalize then
+        exp    := -resize(expon_base, exp'length)-1;
+        shiftr := -to_integer (expon + expon_base);  -- new shift
+      else                              -- return zero
+        zerores := true;
+      end if;
+    elsif (exp > expon_base-1) then     -- infinity
+      infres := true;
+    end if;
+    if zerores then
+      result := zerofp (fraction_width => fraction_width,
+                        exponent_width => exponent_width);
+    elsif infres then
+      result := pos_inffp (fraction_width => fraction_width,
+                           exponent_width => exponent_width);
+    else
+      sfract := fract srl shiftr;       -- shift
+      if shiftr > 0 then
+--        stickyx := sticky or (or (fract (shiftr-1 downto 0)));
+        stickyx := sticky or smallfract (fract, shiftr-1);
+      else
+        stickyx := sticky;
+      end if;
+      if nguard > 0 then
+        round := check_round (
+          fract_in    => sfract (nguard),
+          sign        => sign,
+          remainder   => sfract(nguard-1 downto 0),
+          sticky      => stickyx,
+          round_style => round_style);
+      end if;
+      if round then
+        fp_round(fract_in  => sfract (fraction_width-1+nguard downto nguard),
+                 expon_in  => exp(rexp'range),
+                 fract_out => rfract,
+                 expon_out => rexp);
+      else
+        rfract := sfract (fraction_width-1+nguard downto nguard);
+        rexp   := exp(rexp'range);
+      end if;
+      -- result
+      rexpon := UNSIGNED (rexp(exponent_width-1 downto 0));
+      rexpon (exponent_width-1)          := not rexpon(exponent_width-1);
+      result (rexpon'range)              := UNRESOLVED_float(rexpon);
+      result (-1 downto -fraction_width) := UNRESOLVED_float(rfract);
+    end if;
+    result (exponent_width) := sign;    -- sign BIT
+    return result;
+  end function normalize;
+
+  -- purpose: normalizes a floating point number
+  -- This version assumes a "ufixed" input
+  function normalize (
+    fract                   : UNRESOLVED_ufixed;  -- unsigned fixed point
+    expon                   : UNRESOLVED_SIGNED;  -- exponent, normalized by -1
+    sign                    : STD_ULOGIC;         -- sign bit
+    sticky                  : STD_ULOGIC := '0';  -- Sticky bit (rounding)
+    constant exponent_width : NATURAL    := float_exponent_width;  -- size of output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- size of output fraction
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant denormalize    : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant nguard         : NATURAL    := float_guard_bits)   -- guard bits
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable arguns : UNSIGNED (fract'high + fraction_width + nguard
+                                downto 0) := (others => '0');
+  begin  -- function normalize
+    arguns (arguns'high downto maximum (arguns'high-fract'length+1, 0)) :=
+      UNSIGNED (to_slv (fract));
+    result := normalize (fract          => arguns,
+                         expon          => expon,
+                         sign           => sign,
+                         sticky         => sticky,
+                         fraction_width => fraction_width,
+                         exponent_width => exponent_width,
+                         round_style    => round_style,
+                         denormalize    => denormalize,
+                         nguard         => nguard);
+    return result;
+  end function normalize;
+
+  -- purpose: normalizes a floating point number
+  -- This version assumes a "ufixed" input with a "size_res" input
+  function normalize (
+    fract                : UNRESOLVED_ufixed;  -- unsigned fixed point
+    expon                : UNRESOLVED_SIGNED;  -- exponent, normalized by -1
+    sign                 : STD_ULOGIC;  -- sign bit
+    sticky               : STD_ULOGIC := '0';  -- Sticky bit (rounding)
+    size_res             : UNRESOLVED_float;   -- used for sizing only
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant denormalize : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant nguard      : NATURAL    := float_guard_bits)   -- guard bits
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL := -size_res'low;
+    constant exponent_width : NATURAL := size_res'high;
+    variable result         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable arguns : UNSIGNED (fract'high + fraction_width + nguard
+                                downto 0) := (others => '0');
+  begin  -- function normalize
+    arguns (arguns'high downto maximum (arguns'high-fract'length+1, 0)) :=
+      UNSIGNED (to_slv (fract));
+    result := normalize (fract          => arguns,
+                         expon          => expon,
+                         sign           => sign,
+                         sticky         => sticky,
+                         fraction_width => fraction_width,
+                         exponent_width => exponent_width,
+                         round_style    => round_style,
+                         denormalize    => denormalize,
+                         nguard         => nguard);
+    return result;
+  end function normalize;
+
+  -- Regular "normalize" function with a "size_res" input.
+  function normalize (
+    fract                : UNRESOLVED_UNSIGNED;              -- unsigned
+    expon                : UNRESOLVED_SIGNED;  -- exponent - 1, normalized
+    sign                 : STD_ULOGIC;  -- sign bit
+    sticky               : STD_ULOGIC := '0';  -- Sticky bit (rounding)
+    size_res             : UNRESOLVED_float;   -- used for sizing only
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant denormalize : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant nguard      : NATURAL    := float_guard_bits)   -- guard bits
+    return UNRESOLVED_float is
+  begin
+    return normalize (fract          => fract,
+                      expon          => expon,
+                      sign           => sign,
+                      sticky         => sticky,
+                      fraction_width => -size_res'low,
+                      exponent_width => size_res'high,
+                      round_style    => round_style,
+                      denormalize    => denormalize,
+                      nguard         => nguard);
+  end function normalize;
+
+  -- Returns the class which X falls into
+  function Classfp (
+    x           : UNRESOLVED_float;     -- floating point input
+    check_error : BOOLEAN := float_check_error)   -- check for errors
+    return valid_fpstate
+  is
+    constant fraction_width : INTEGER := -mine(x'low, x'low);  -- length of FP output fraction
+    constant exponent_width : INTEGER := x'high;  -- length of FP output exponent
+    variable arg            : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- classfp
+    if (arg'length < 1 or fraction_width < 3 or exponent_width < 3
+        or x'left < x'right) then
+      report FLOAT_GENERIC_PKG'instance_name
+        & "CLASSFP: " &
+        "Floating point number detected with a bad range"
+        severity error;
+      return isx;
+    end if;
+    -- Check for "X".
+    arg := to_01 (x, 'X');
+    if (arg(0) = 'X') then
+      return isx;                       -- If there is an X in the number
+      -- Special cases, check for illegal number
+    elsif check_error and
+      (and (STD_ULOGIC_VECTOR (arg (exponent_width-1 downto 0)))
+       = '1') then                      -- Exponent is all "1".
+      if or (to_slv (arg (-1 downto -fraction_width)))
+        /= '0' then  -- Fraction must be all "0" or this is not a number.
+        if (arg(-1) = '1') then         -- From "W. Khan - IEEE standard
+          return nan;            -- 754 binary FP Signaling nan (Not a number)
+        else
+          return quiet_nan;
+        end if;
+        -- Check for infinity
+      elsif arg(exponent_width) = '0' then
+        return pos_inf;                 -- Positive infinity
+      else
+        return neg_inf;                 -- Negative infinity
+      end if;
+      -- check for "0"
+    elsif or (STD_LOGIC_VECTOR (arg (exponent_width-1 downto 0)))
+      = '0' then                        -- Exponent is all "0"
+      if or (to_slv (arg (-1 downto -fraction_width)))
+        = '0' then                      -- Fraction is all "0"
+        if arg(exponent_width) = '0' then
+          return pos_zero;              -- Zero
+        else
+          return neg_zero;
+        end if;
+      else
+        if arg(exponent_width) = '0' then
+          return pos_denormal;          -- Denormal number (ieee extended fp)
+        else
+          return neg_denormal;
+        end if;
+      end if;
+    else
+      if arg(exponent_width) = '0' then
+        return pos_normal;              -- Normal FP number
+      else
+        return neg_normal;
+      end if;
+    end if;
+  end function Classfp;
+
+  procedure break_number (
+    arg         : in  UNRESOLVED_float;
+    denormalize : in  BOOLEAN := float_denormalize;
+    check_error : in  BOOLEAN := float_check_error;
+    fract       : out UNRESOLVED_UNSIGNED;
+    expon       : out UNRESOLVED_SIGNED;
+    sign        : out STD_ULOGIC) is
+    constant fraction_width : NATURAL := -mine(arg'low, arg'low);  -- length of FP output fraction
+    variable fptyp          : valid_fpstate;
+  begin
+    fptyp := Classfp (arg, check_error);
+    sign  := to_x01(arg(arg'high));
+    break_number (
+      arg         => arg,
+      fptyp       => fptyp,
+      denormalize => denormalize,
+      fract       => fract,
+      expon       => expon);
+  end procedure break_number;
+  
+  procedure break_number (
+    arg         : in  UNRESOLVED_float;
+    denormalize : in  BOOLEAN := float_denormalize;
+    check_error : in  BOOLEAN := float_check_error;
+    fract       : out UNRESOLVED_ufixed;  -- 1 downto -fraction_width
+    expon       : out UNRESOLVED_SIGNED;  -- exponent_width-1 downto 0
+    sign        : out STD_ULOGIC) is
+    constant fraction_width : NATURAL := -mine(arg'low, arg'low);  -- length of FP output fraction
+    variable fptyp          : valid_fpstate;
+    variable ufract         : UNSIGNED (fraction_width downto 0);  -- unsigned fraction
+  begin
+    fptyp := Classfp (arg, check_error);
+    sign  := to_x01(arg(arg'high));
+    break_number (
+      arg         => arg,
+      fptyp       => fptyp,
+      denormalize => denormalize,
+      fract       => ufract,
+      expon       => expon);
+    fract (0 downto -fraction_width) := ufixed (ufract);
+  end procedure break_number;
+
+  -- Arithmetic functions
+  function "abs" (
+    arg : UNRESOLVED_float)             -- floating point input
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (arg'range);  -- result
+  begin
+    if (arg'length > 0) then
+      result            := to_01 (arg, 'X');
+      result (arg'high) := '0';         -- set the sign bit to positive     
+      return result;
+    else
+      return NAFP;
+    end if;
+  end function "abs";
+
+  -- IEEE 754 "negative" function
+  function "-" (
+    arg : UNRESOLVED_float)                          -- floating point input
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (arg'range);  -- result
+  begin
+    if (arg'length > 0) then
+      result            := to_01 (arg, 'X');
+      result (arg'high) := not result (arg'high);    -- invert sign bit
+      return result;
+    else
+      return NAFP;
+    end if;
+  end function "-";
+
+  -- Addition, adds two floating point numbers
+  function add (
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    constant addguard         : NATURAL := guard;         -- add one guard bit
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable fractl, fractr   : UNSIGNED (fraction_width+1+addguard downto 0);  -- fractions
+    variable fractc, fracts   : UNSIGNED (fractl'range);  -- constant and shifted variables
+    variable urfract, ulfract : UNSIGNED (fraction_width downto 0);
+    variable ufract           : UNSIGNED (fraction_width+1+addguard downto 0);
+    variable exponl, exponr   : SIGNED (exponent_width-1 downto 0);  -- exponents
+    variable rexpon           : SIGNED (exponent_width downto 0);  -- result exponent
+    variable shiftx           : SIGNED (exponent_width downto 0);  -- shift fractions
+    variable sign             : STD_ULOGIC;   -- sign of the output
+    variable leftright        : BOOLEAN;      -- left or right used
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable sticky           : STD_ULOGIC;   -- Holds precision for rounding
+  begin  -- addition
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    if (lfptype = isx or rfptype = isx) then
+      fpresult := (others => 'X');
+    elsif (lfptype = nan or lfptype = quiet_nan or
+           rfptype = nan or rfptype = quiet_nan)
+      -- Return quiet NAN, IEEE754-1985-7.1,1
+      or (lfptype = pos_inf and rfptype = neg_inf)
+      or (lfptype = neg_inf and rfptype = pos_inf) then
+      -- Return quiet NAN, IEEE754-1985-7.1,2
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (lfptype = pos_inf or rfptype = pos_inf) then   -- x + inf = inf
+      fpresult := pos_inffp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+    elsif (lfptype = neg_inf or rfptype = neg_inf) then   -- x - inf = -inf
+      fpresult := neg_inffp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+    elsif (lfptype = neg_zero and rfptype = neg_zero) then   -- -0 + -0 = -0
+      fpresult := neg_zerofp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+    else
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      lfptype := classfp (lresize, false);    -- errors already checked
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rfptype := classfp (rresize, false);    -- errors already checked
+      break_number (
+        arg         => lresize,
+        fptyp       => lfptype,
+        denormalize => denormalize,
+        fract       => ulfract,
+        expon       => exponl);
+      fractl                                           := (others => '0');
+      fractl (fraction_width+addguard downto addguard) := ulfract;
+      break_number (
+        arg         => rresize,
+        fptyp       => rfptype,
+        denormalize => denormalize,
+        fract       => urfract,
+        expon       => exponr);
+      fractr                                           := (others => '0');
+      fractr (fraction_width+addguard downto addguard) := urfract;
+      shiftx := (exponl(exponent_width-1) & exponl) - exponr;
+      if shiftx < -fractl'high then
+        rexpon    := exponr(exponent_width-1) & exponr;
+        fractc    := fractr;
+        fracts    := (others => '0');   -- add zero
+        leftright := false;
+        sticky    := or (fractl);
+      elsif shiftx < 0 then
+        shiftx    := - shiftx;
+        fracts    := shift_right (fractl, to_integer(shiftx));
+        fractc    := fractr;
+        rexpon    := exponr(exponent_width-1) & exponr;
+        leftright := false;
+--        sticky    := or (fractl (to_integer(shiftx) downto 0));
+        sticky    := smallfract (fractl, to_integer(shiftx));
+      elsif shiftx = 0 then
+        rexpon := exponl(exponent_width-1) & exponl;
+        sticky := '0';
+        if fractr > fractl then
+          fractc    := fractr;
+          fracts    := fractl;
+          leftright := false;
+        else
+          fractc    := fractl;
+          fracts    := fractr;
+          leftright := true;
+        end if;
+      elsif shiftx > fractr'high then
+        rexpon    := exponl(exponent_width-1) & exponl;
+        fracts    := (others => '0');   -- add zero
+        fractc    := fractl;
+        leftright := true;
+        sticky    := or (fractr);
+      elsif shiftx > 0 then
+        fracts    := shift_right (fractr, to_integer(shiftx));
+        fractc    := fractl;
+        rexpon    := exponl(exponent_width-1) & exponl;
+        leftright := true;
+--        sticky    := or (fractr (to_integer(shiftx) downto 0));
+        sticky    := smallfract (fractr, to_integer(shiftx));
+      end if;
+      -- add
+      fracts (0) := fracts (0) or sticky;     -- Or the sticky bit into the LSB
+      if l(l'high) = r(r'high) then
+        ufract := fractc + fracts;
+        sign   := l(l'high);
+      else                              -- signs are different
+        ufract := fractc - fracts;      -- always positive result
+        if leftright then               -- Figure out which sign to use
+          sign := l(l'high);
+        else
+          sign := r(r'high);
+        end if;
+      end if;
+      if or (ufract) = '0' then
+        sign := '0';                    -- IEEE 854, 6.3, paragraph 2.
+      end if;
+      -- normalize
+      fpresult := normalize (fract          => ufract,
+                             expon          => rexpon,
+                             sign           => sign,
+                             sticky         => sticky,
+                             fraction_width => fraction_width,
+                             exponent_width => exponent_width,
+                             round_style    => round_style,
+                             denormalize    => denormalize,
+                             nguard         => addguard);
+    end if;
+    return fpresult;
+  end function add;
+
+  -- Subtraction, Calls "add".
+  function subtract (
+    l, r                 : UNRESOLVED_float;     -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    variable negr : UNRESOLVED_float (r'range);  -- negative version of r
+  begin
+    negr := -r;                         -- r := -r
+    return add (l           => l,
+                r           => negr,
+                round_style => round_style,
+                guard       => guard,
+                check_error => check_error,
+                denormalize => denormalize);
+  end function subtract;
+
+  -- Floating point multiply
+  function multiply (
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    constant multguard        : NATURAL := guard;           -- guard bits
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable fractl, fractr   : UNSIGNED (fraction_width downto 0);  -- fractions
+    variable rfract           : UNSIGNED ((2*(fraction_width))+1 downto 0);  -- result fraction
+    variable sfract           : UNSIGNED (fraction_width+1+multguard downto 0);  -- result fraction
+    variable shifty           : INTEGER;      -- denormal shift
+    variable exponl, exponr   : SIGNED (exponent_width-1 downto 0);  -- exponents
+    variable rexpon           : SIGNED (exponent_width+1 downto 0);  -- result exponent
+    variable fp_sign          : STD_ULOGIC;   -- sign of result
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable sticky           : STD_ULOGIC;   -- Holds precision for rounding
+  begin  -- multiply
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    if (lfptype = isx or rfptype = isx) then
+      fpresult := (others => 'X');
+    elsif ((lfptype = nan or lfptype = quiet_nan or
+            rfptype = nan or rfptype = quiet_nan)) then
+      -- Return quiet NAN, IEEE754-1985-7.1,1
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (((lfptype = pos_inf or lfptype = neg_inf) and
+            (rfptype = pos_zero or rfptype = neg_zero)) or
+           ((rfptype = pos_inf or rfptype = neg_inf) and
+            (lfptype = pos_zero or lfptype = neg_zero))) then    -- 0 * inf
+      -- Return quiet NAN, IEEE754-1985-7.1,3
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (lfptype = pos_inf or rfptype = pos_inf
+           or lfptype = neg_inf or rfptype = neg_inf) then  -- x * inf = inf
+      fpresult := pos_inffp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+      -- figure out the sign
+      fp_sign := l(l'high) xor r(r'high);     -- figure out the sign
+      fpresult (exponent_width) := fp_sign;
+    else
+      fp_sign := l(l'high) xor r(r'high);     -- figure out the sign
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      lfptype := classfp (lresize, false);    -- errors already checked
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rfptype := classfp (rresize, false);    -- errors already checked
+      break_number (
+        arg         => lresize,
+        fptyp       => lfptype,
+        denormalize => denormalize,
+        fract       => fractl,
+        expon       => exponl);
+      break_number (
+        arg         => rresize,
+        fptyp       => rfptype,
+        denormalize => denormalize,
+        fract       => fractr,
+        expon       => exponr);
+      if (rfptype = pos_denormal or rfptype = neg_denormal) then
+        shifty := fraction_width - find_leftmost(fractr, '1');
+        fractr := shift_left (fractr, shifty);
+      elsif (lfptype = pos_denormal or lfptype = neg_denormal) then
+        shifty := fraction_width - find_leftmost(fractl, '1');
+        fractl := shift_left (fractl, shifty);
+      else
+        shifty := 0;
+        -- Note that a denormal number * a denormal number is always zero.
+      end if;
+      -- multiply
+      -- add the exponents
+      rexpon := resize (exponl, rexpon'length) + exponr - shifty + 1;
+      rfract := fractl * fractr;        -- Multiply the fraction
+      sfract := rfract (rfract'high downto
+                        rfract'high - (fraction_width+1+multguard));
+      sticky := or (rfract (rfract'high-(fraction_width+1+multguard)
+                                   downto 0));
+      -- normalize
+      fpresult := normalize (fract          => sfract,
+                             expon          => rexpon,
+                             sign           => fp_sign,
+                             sticky         => sticky,
+                             fraction_width => fraction_width,
+                             exponent_width => exponent_width,
+                             round_style    => round_style,
+                             denormalize    => denormalize,
+                             nguard         => multguard);
+    end if;
+    return fpresult;
+  end function multiply;
+
+  function short_divide (
+    lx, rx : UNSIGNED)
+    return UNSIGNED
+  is
+    -- This is a special divider for the floating point routines.
+    -- For a true unsigned divider, "stages" needs to = lx'high
+    constant stages       : INTEGER := lx'high - rx'high;  -- number of stages
+    variable partial      : UNSIGNED (lx'range);
+    variable q            : UNSIGNED (stages downto 0);
+    variable partial_argl : SIGNED (rx'high + 2 downto 0);
+    variable partial_arg  : SIGNED (rx'high + 2 downto 0);
+  begin
+    partial := lx;
+    for i in stages downto 0 loop
+      partial_argl := resize ("0" & SIGNED (partial(lx'high downto i)),
+                              partial_argl'length);
+      partial_arg := partial_argl - SIGNED ("0" & rx);
+      if (partial_arg (partial_arg'high) = '1') then       -- negative
+        q(i) := '0';
+      else
+        q(i) := '1';
+        partial (lx'high+i-stages downto lx'high+i-stages-rx'high) :=
+          UNSIGNED (partial_arg(rx'range));
+      end if;
+    end loop;
+    -- to make the output look like that of the unsigned IEEE divide.
+    return resize (q, lx'length);
+  end function short_divide;
+
+  -- 1/X function.  Needed for algorithm development.
+  function reciprocal (
+    arg                  : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL := -mine(arg'low, arg'low);  -- length of FP output fraction
+    constant exponent_width : NATURAL := arg'high;  -- length of FP output exponent
+    constant divguard       : NATURAL := guard;     -- guard bits
+    function onedivy (
+      arg : UNSIGNED)
+      return UNSIGNED
+    is
+      variable q   : UNSIGNED((2*arg'high)+1 downto 0);
+      variable one : UNSIGNED (q'range);
+    begin
+      one           := (others => '0');
+      one(one'high) := '1';
+      q := short_divide (one, arg);     -- Unsigned divide
+      return resize (q, arg'length+1);
+    end function onedivy;
+    variable fptype        : valid_fpstate;
+    variable expon         : SIGNED (exponent_width-1 downto 0);   -- exponents
+    variable denorm_offset : NATURAL range 0 to 2;
+    variable fract         : UNSIGNED (fraction_width downto 0);
+    variable fractg        : UNSIGNED (fraction_width+divguard downto 0);
+    variable sfract        : UNSIGNED (fraction_width+1+divguard downto 0);  -- result fraction
+    variable fpresult      : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- reciprocal
+    fptype := classfp(arg, check_error);
+    classcase : case fptype is
+      when isx =>
+        fpresult := (others => 'X');
+      when nan | quiet_nan =>
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        fpresult := qnanfp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+      when pos_inf | neg_inf =>         -- 1/inf, return 0
+        fpresult := zerofp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+      when neg_zero | pos_zero =>       -- 1/0
+        report FLOAT_GENERIC_PKG'instance_name
+          & "RECIPROCAL: Floating Point divide by zero"
+          severity error;
+        fpresult := pos_inffp (fraction_width => fraction_width,
+                               exponent_width => exponent_width);
+      when others =>
+        if (fptype = pos_denormal or fptype = neg_denormal)
+          and ((arg (-1) or arg(-2)) /= '1') then
+          -- 1/denormal = infinity, with the exception of 2**-expon_base
+          fpresult := pos_inffp (fraction_width => fraction_width,
+                                 exponent_width => exponent_width);
+          fpresult (exponent_width) := to_x01 (arg (exponent_width));
+        else
+          break_number (
+            arg         => arg,
+            fptyp       => fptype,
+            denormalize => denormalize,
+            fract       => fract,
+            expon       => expon);
+          fractg := (others => '0');
+          if (fptype = pos_denormal or fptype = neg_denormal) then
+            -- The reciprocal of a denormal number is typically zero,
+            -- except for two special cases which are trapped here.
+            if (to_x01(arg (-1)) = '1') then
+              fractg (fractg'high downto divguard+1) :=
+                fract (fract'high-1 downto 0);      -- Shift to not denormal
+              denorm_offset := 1;       -- add 1 to exponent compensate
+            else                        -- arg(-2) = '1'
+              fractg (fractg'high downto divguard+2) :=
+                fract (fract'high-2 downto 0);      -- Shift to not denormal
+              denorm_offset := 2;       -- add 2 to exponent compensate
+            end if;
+          else
+            fractg (fractg'high downto divguard) := fract;
+            denorm_offset                        := 0;
+          end if;
+          expon  := - expon - 3 + denorm_offset;
+          sfract := onedivy (fractg);
+          -- normalize
+          fpresult := normalize (fract          => sfract,
+                                 expon          => expon,
+                                 sign           => arg(exponent_width),
+                                 sticky         => '1',
+                                 fraction_width => fraction_width,
+                                 exponent_width => exponent_width,
+                                 round_style    => round_style,
+                                 denormalize    => denormalize,
+                                 nguard         => divguard);
+        end if;
+    end case classcase;
+    return fpresult;
+  end function reciprocal;
+
+  -- floating point division
+  function divide (
+    l, r                 : UNRESOLVED_float;       -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    constant divguard         : NATURAL := guard;  -- division guard bits
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable ulfract, urfract : UNSIGNED (fraction_width downto 0);
+    variable fractl           : UNSIGNED ((2*(fraction_width+divguard)+1) downto 0);  -- left
+    variable fractr           : UNSIGNED (fraction_width+divguard downto 0);  -- right
+    variable rfract           : UNSIGNED (fractl'range);    -- result fraction
+    variable sfract           : UNSIGNED (fraction_width+1+divguard downto 0);  -- result fraction
+    variable exponl, exponr   : SIGNED (exponent_width-1 downto 0);  -- exponents
+    variable rexpon           : SIGNED (exponent_width+1 downto 0);  -- result exponent
+    variable fp_sign, sticky  : STD_ULOGIC;        -- sign of result
+    variable shifty, shiftx   : INTEGER;           -- denormal number shift
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- divide
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    classcase : case rfptype is
+      when isx =>
+        fpresult := (others => 'X');
+      when nan | quiet_nan =>
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        fpresult := qnanfp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+      when pos_inf | neg_inf =>
+        if lfptype = pos_inf or lfptype = neg_inf  -- inf / inf
+          or lfptype = quiet_nan or lfptype = nan then
+          -- Return quiet NAN, IEEE754-1985-7.1,4
+          fpresult := qnanfp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+        else                            -- x / inf = 0
+          fpresult := zerofp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+          fp_sign := l(l'high) xor r(r'high);        -- sign
+          fpresult (fpresult'high) := fp_sign;  -- sign
+        end if;
+      when pos_zero | neg_zero =>
+        if lfptype = pos_zero or lfptype = neg_zero         -- 0 / 0
+          or lfptype = quiet_nan or lfptype = nan then
+          -- Return quiet NAN, IEEE754-1985-7.1,4
+          fpresult := qnanfp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+        else
+          report float_generic_pkg'instance_name
+            & "DIVIDE: Floating Point divide by zero"
+            severity error;
+          -- Infinity, define in 754-1985-7.2
+          fpresult := pos_inffp (fraction_width => fraction_width,
+                                 exponent_width => exponent_width);
+          fp_sign := l(l'high) xor r(r'high);        -- sign
+          fpresult (fpresult'high) := fp_sign;  -- sign
+        end if;
+      when others =>
+        classcase2 : case lfptype is
+          when isx =>
+            fpresult := (others => 'X');
+          when nan | quiet_nan =>
+            -- Return quiet NAN, IEEE754-1985-7.1,1
+            fpresult := qnanfp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+          when pos_inf | neg_inf =>     -- inf / x = inf
+            fpresult := pos_inffp (fraction_width => fraction_width,
+                                   exponent_width => exponent_width);
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            fpresult(exponent_width) := fp_sign;
+          when pos_zero | neg_zero =>   -- 0 / X = 0
+            fpresult := zerofp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            fpresult(exponent_width) := fp_sign;
+          when others =>
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            lresize := resize (arg            => to_x01(l),
+                               exponent_width => exponent_width,
+                               fraction_width => fraction_width,
+                               denormalize_in => denormalize,
+                               denormalize    => denormalize);
+            lfptype := classfp (lresize, false);   -- errors already checked
+            rresize := resize (arg            => to_x01(r),
+                               exponent_width => exponent_width,
+                               fraction_width => fraction_width,
+                               denormalize_in => denormalize,
+                               denormalize    => denormalize);
+            rfptype := classfp (rresize, false);   -- errors already checked
+            break_number (
+              arg         => lresize,
+              fptyp       => lfptype,
+              denormalize => denormalize,
+              fract       => ulfract,
+              expon       => exponl);
+            -- right side
+            break_number (
+              arg         => rresize,
+              fptyp       => rfptype,
+              denormalize => denormalize,
+              fract       => urfract,
+              expon       => exponr);
+            -- Compute the exponent
+            rexpon := resize (exponl, rexpon'length) - exponr - 2;
+            if (rfptype = pos_denormal or rfptype = neg_denormal) then
+              -- Do the shifting here not after.  That way we have a smaller
+              -- shifter, and need a smaller divider, because the top
+              -- bit in the divisor will always be a "1".
+              shifty := fraction_width - find_leftmost(urfract, '1');
+              urfract := shift_left (urfract, shifty);
+              rexpon := rexpon + shifty;
+            end if;
+            fractr := (others => '0');
+            fractr (fraction_width+divguard downto divguard) := urfract;
+            if (lfptype = pos_denormal or lfptype = neg_denormal) then
+              shiftx := fraction_width - find_leftmost(ulfract, '1');
+              ulfract := shift_left (ulfract, shiftx);
+              rexpon := rexpon - shiftx;
+            end if;
+            fractl  := (others => '0');
+            fractl (fractl'high downto fractl'high-fraction_width) := ulfract;
+            -- divide
+            rfract := short_divide (fractl, fractr);        -- unsigned divide
+            sfract := rfract (sfract'range);       -- lower bits
+            sticky := '1';
+            -- normalize
+            fpresult := normalize (fract          => sfract,
+                                   expon          => rexpon,
+                                   sign           => fp_sign,
+                                   sticky         => sticky,
+                                   fraction_width => fraction_width,
+                                   exponent_width => exponent_width,
+                                   round_style    => round_style,
+                                   denormalize    => denormalize,
+                                   nguard         => divguard);
+        end case classcase2;
+    end case classcase;
+    return fpresult;
+  end function divide;
+
+  -- division by a power of 2
+  function dividebyp2 (
+    l, r                 : UNRESOLVED_float;      -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable ulfract, urfract : UNSIGNED (fraction_width downto 0);
+    variable exponl, exponr   : SIGNED(exponent_width-1 downto 0);  -- exponents
+    variable rexpon           : SIGNED(exponent_width downto 0);  -- result exponent
+    variable fp_sign          : STD_ULOGIC;       -- sign of result
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- divisionbyp2
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    classcase : case rfptype is
+      when isx =>
+        fpresult := (others => 'X');
+      when nan | quiet_nan =>
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        fpresult := qnanfp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+      when pos_inf | neg_inf =>
+        if lfptype = pos_inf or lfptype = neg_inf then      -- inf / inf
+          -- Return quiet NAN, IEEE754-1985-7.1,4
+          fpresult := qnanfp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+        else                            -- x / inf = 0
+          fpresult := zerofp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+          fp_sign := l(l'high) xor r(r'high);        -- sign
+          fpresult (fpresult'high) := fp_sign;  -- sign
+        end if;
+      when pos_zero | neg_zero =>
+        if lfptype = pos_zero or lfptype = neg_zero then    -- 0 / 0
+          -- Return quiet NAN, IEEE754-1985-7.1,4
+          fpresult := qnanfp (fraction_width => fraction_width,
+                              exponent_width => exponent_width);
+        else
+          report FLOAT_GENERIC_PKG'instance_name
+            & "DIVIDEBYP2: Floating Point divide by zero"
+            severity error;
+          -- Infinity, define in 754-1985-7.2
+          fpresult := pos_inffp (fraction_width => fraction_width,
+                                 exponent_width => exponent_width);
+          fp_sign := l(l'high) xor r(r'high);        -- sign
+          fpresult (fpresult'high) := fp_sign;  -- sign
+        end if;
+      when others =>
+        classcase2 : case lfptype is
+          when isx =>
+            fpresult := (others => 'X');
+          when nan | quiet_nan =>
+            -- Return quiet NAN, IEEE754-1985-7.1,1
+            fpresult := qnanfp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+          when pos_inf | neg_inf =>     -- inf / x = inf
+            fpresult := pos_inffp (fraction_width => fraction_width,
+                                   exponent_width => exponent_width);
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            fpresult (exponent_width) := fp_sign;  -- sign
+          when pos_zero | neg_zero =>   -- 0 / X = 0
+            fpresult := zerofp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            fpresult (exponent_width) := fp_sign;  -- sign
+          when others =>
+            fp_sign := l(l'high) xor r(r'high);        -- sign
+            lresize := resize (arg            => to_x01(l),
+                               exponent_width => exponent_width,
+                               fraction_width => fraction_width,
+                               denormalize_in => denormalize,
+                               denormalize    => denormalize);
+            lfptype := classfp (lresize, false);  -- errors already checked
+            rresize := resize (arg            => to_x01(r),
+                               exponent_width => exponent_width,
+                               fraction_width => fraction_width,
+                               denormalize_in => denormalize,
+                               denormalize    => denormalize);
+            rfptype := classfp (rresize, false);  -- errors already checked
+            break_number (
+              arg         => lresize,
+              fptyp       => lfptype,
+              denormalize => denormalize,
+              fract       => ulfract,
+              expon       => exponl);
+            -- right side
+            break_number (
+              arg         => rresize,
+              fptyp       => rfptype,
+              denormalize => denormalize,
+              fract       => urfract,
+              expon       => exponr);
+            assert (or (urfract (fraction_width-1 downto 0)) = '0')
+              report FLOAT_GENERIC_PKG'instance_name
+              & "DIVIDEBYP2: "
+              & "Dividebyp2 called with a non power of two divisor"
+              severity error;
+            rexpon := (exponl(exponl'high)&exponl)
+                      - (exponr(exponr'high)&exponr) - 1;
+            -- normalize
+            fpresult := normalize (fract          => ulfract,
+                                   expon          => rexpon,
+                                   sign           => fp_sign,
+                                   sticky         => '1',
+                                   fraction_width => fraction_width,
+                                   exponent_width => exponent_width,
+                                   round_style    => round_style,
+                                   denormalize    => denormalize,
+                                   nguard         => 0);
+        end case classcase2;
+    end case classcase;
+    return fpresult;
+  end function dividebyp2;
+
+  -- Multiply accumulate  result = l*r + c
+  function mac (
+    l, r, c              : UNRESOLVED_float;      -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL :=
+      -mine (mine(l'low, r'low), c'low);   -- length of FP output fraction
+    constant exponent_width : NATURAL :=
+      maximum (maximum(l'high, r'high), c'high);  -- length of FP output exponent
+    variable lfptype, rfptype, cfptype : valid_fpstate;
+    variable fpresult                  : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable fractl, fractr            : UNSIGNED (fraction_width downto 0);  -- fractions
+    variable fractx                    : UNSIGNED (fraction_width+guard downto 0);
+    variable fractc, fracts            : UNSIGNED (fraction_width+1+guard downto 0);
+    variable rfract                    : UNSIGNED ((2*(fraction_width))+1 downto 0);  -- result fraction
+    variable sfract, ufract            : UNSIGNED (fraction_width+1+guard downto 0);  -- result fraction
+    variable exponl, exponr, exponc    : SIGNED (exponent_width-1 downto 0);  -- exponents
+    variable rexpon, rexpon2           : SIGNED (exponent_width+1 downto 0);  -- result exponent
+    variable shifty                    : INTEGER;      -- denormal shift
+    variable shiftx                    : SIGNED (rexpon'range);  -- shift fractions
+    variable fp_sign                   : STD_ULOGIC;  -- sign of result
+    variable lresize, rresize          : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable cresize                   : UNRESOLVED_float (exponent_width downto -fraction_width - guard);
+    variable leftright                 : BOOLEAN;     -- left or right used
+    variable sticky                    : STD_ULOGIC;  -- Holds precision for rounding
+  begin  -- multiply
+    if (fraction_width = 0 or l'length < 7 or r'length < 7 or c'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+      cfptype := classfp (c, check_error);
+    end if;
+    if (lfptype = isx or rfptype = isx or cfptype = isx) then
+      fpresult := (others => 'X');
+    elsif (lfptype = nan or lfptype = quiet_nan or
+           rfptype = nan or rfptype = quiet_nan or
+           cfptype = nan or cfptype = quiet_nan) then
+      -- Return quiet NAN, IEEE754-1985-7.1,1
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (((lfptype = pos_inf or lfptype = neg_inf) and
+            (rfptype = pos_zero or rfptype = neg_zero)) or
+           ((rfptype = pos_inf or rfptype = neg_inf) and
+            (lfptype = pos_zero or lfptype = neg_zero))) then  -- 0 * inf
+      -- Return quiet NAN, IEEE754-1985-7.1,3
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (lfptype = pos_inf or rfptype = pos_inf
+           or lfptype = neg_inf or rfptype = neg_inf  -- x * inf = inf
+           or cfptype = neg_inf or cfptype = pos_inf) then  -- x + inf = inf
+      fpresult := pos_inffp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+      -- figure out the sign
+      fpresult (exponent_width) := l(l'high) xor r(r'high);
+    else
+      fp_sign := l(l'high) xor r(r'high);  -- figure out the sign
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      lfptype := classfp (lresize, false);        -- errors already checked
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rfptype := classfp (rresize, false);        -- errors already checked
+      cresize := resize (arg            => to_x01(c),
+                         exponent_width => exponent_width,
+                         fraction_width => -cresize'low,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      cfptype := classfp (cresize, false);        -- errors already checked
+      break_number (
+        arg         => lresize,
+        fptyp       => lfptype,
+        denormalize => denormalize,
+        fract       => fractl,
+        expon       => exponl);
+      break_number (
+        arg         => rresize,
+        fptyp       => rfptype,
+        denormalize => denormalize,
+        fract       => fractr,
+        expon       => exponr);
+      break_number (
+        arg         => cresize,
+        fptyp       => cfptype,
+        denormalize => denormalize,
+        fract       => fractx,
+        expon       => exponc);
+      if (rfptype = pos_denormal or rfptype = neg_denormal) then
+        shifty := fraction_width - find_leftmost(fractr, '1');
+        fractr := shift_left (fractr, shifty);
+      elsif (lfptype = pos_denormal or lfptype = neg_denormal) then
+        shifty := fraction_width - find_leftmost(fractl, '1');
+        fractl := shift_left (fractl, shifty);
+      else
+        shifty := 0;
+        -- Note that a denormal number * a denormal number is always zero.
+      end if;
+      -- multiply
+      rfract := fractl * fractr;        -- Multiply the fraction
+      -- add the exponents
+      rexpon := resize (exponl, rexpon'length) + exponr - shifty + 1;
+      shiftx := rexpon - exponc;
+      if shiftx < -fractl'high then
+        rexpon2 := resize (exponc, rexpon2'length);
+        fractc  := "0" & fractx;
+        fracts  := (others => '0');
+        sticky  := or (rfract);
+      elsif shiftx < 0 then
+        shiftx := - shiftx;
+        fracts := shift_right (rfract (rfract'high downto rfract'high
+                                       - fracts'length+1),
+                               to_integer(shiftx));
+        fractc    := "0" & fractx;
+        rexpon2   := resize (exponc, rexpon2'length);
+        leftright := false;
+        sticky := or (rfract (to_integer(shiftx)+rfract'high
+                                     - fracts'length downto 0));
+      elsif shiftx = 0 then
+        rexpon2 := resize (exponc, rexpon2'length);
+        sticky  := or (rfract (rfract'high - fractc'length downto 0));
+        if rfract (rfract'high downto rfract'high - fractc'length+1) > fractx
+        then
+          fractc := "0" & fractx;
+          fracts := rfract (rfract'high downto rfract'high
+                            - fracts'length+1);
+          leftright := false;
+        else
+          fractc := rfract (rfract'high downto rfract'high
+                            - fractc'length+1);
+          fracts    := "0" & fractx;
+          leftright := true;
+        end if;
+      elsif shiftx > fractx'high then
+        rexpon2   := rexpon;
+        fracts    := (others => '0');
+        fractc    := rfract (rfract'high downto rfract'high - fractc'length+1);
+        leftright := true;
+        sticky := or (fractx & rfract (rfract'high - fractc'length
+                                              downto 0));
+      else                              -- fractx'high > shiftx > 0
+        rexpon2   := rexpon;
+        fracts    := "0" & shift_right (fractx, to_integer (shiftx));
+        fractc    := rfract (rfract'high downto rfract'high - fractc'length+1);
+        leftright := true;
+        sticky := or (fractx (to_integer (shiftx) downto 0)
+                             & rfract (rfract'high - fractc'length downto 0));
+      end if;
+      fracts (0) := fracts (0) or sticky;  -- Or the sticky bit into the LSB
+      if fp_sign = to_X01(c(c'high)) then
+        ufract  := fractc + fracts;
+        fp_sign := fp_sign;
+      else                              -- signs are different
+        ufract := fractc - fracts;      -- always positive result
+        if leftright then               -- Figure out which sign to use
+          fp_sign := fp_sign;
+        else
+          fp_sign := c(c'high);
+        end if;
+      end if;
+      -- normalize
+      fpresult := normalize (fract          => ufract,
+                             expon          => rexpon2,
+                             sign           => fp_sign,
+                             sticky         => sticky,
+                             fraction_width => fraction_width,
+                             exponent_width => exponent_width,
+                             round_style    => round_style,
+                             denormalize    => denormalize,
+                             nguard         => guard);
+    end if;
+    return fpresult;
+  end function mac;
+
+  -- "rem" function
+  function remainder (
+    l, r                 : UNRESOLVED_float;       -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    constant divguard         : NATURAL := guard;  -- division guard bits
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable ulfract, urfract : UNSIGNED (fraction_width downto 0);
+    variable fractr, fractl   : UNSIGNED (fraction_width+divguard downto 0);  -- right
+    variable rfract           : UNSIGNED (fractr'range);    -- result fraction
+    variable sfract           : UNSIGNED (fraction_width+divguard downto 0);  -- result fraction
+    variable exponl, exponr   : SIGNED (exponent_width-1 downto 0);  -- exponents
+    variable rexpon           : SIGNED (exponent_width downto 0);  -- result exponent
+    variable fp_sign          : STD_ULOGIC;        -- sign of result
+    variable shifty           : INTEGER;           -- denormal number shift
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- remainder
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    if (lfptype = isx or rfptype = isx) then
+      fpresult := (others => 'X');
+    elsif (lfptype = nan or lfptype = quiet_nan)
+      or (rfptype = nan or rfptype = quiet_nan)
+      -- Return quiet NAN, IEEE754-1985-7.1,1
+      or (lfptype = pos_inf or lfptype = neg_inf)  -- inf rem x
+      -- Return quiet NAN, IEEE754-1985-7.1,5
+      or (rfptype = pos_zero or rfptype = neg_zero) then    -- x rem 0
+      -- Return quiet NAN, IEEE754-1985-7.1,5
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (rfptype = pos_inf or rfptype = neg_inf) then     -- x rem inf = 0
+      fpresult := zerofp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (abs(l) < abs(r)) then
+      fpresult := l;
+    else
+      fp_sign := to_X01(l(l'high));     -- sign
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      lfptype := classfp (lresize, false);         -- errors already checked
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rfptype := classfp (rresize, false);         -- errors already checked
+      fractl  := (others => '0');
+      break_number (
+        arg         => lresize,
+        fptyp       => lfptype,
+        denormalize => denormalize,
+        fract       => ulfract,
+        expon       => exponl);
+      fractl (fraction_width+divguard downto divguard) := ulfract;
+      -- right side
+      fractr                                           := (others => '0');
+      break_number (
+        arg         => rresize,
+        fptyp       => rfptype,
+        denormalize => denormalize,
+        fract       => urfract,
+        expon       => exponr);
+      fractr (fraction_width+divguard downto divguard) := urfract;
+      rexpon                                           := (exponr(exponr'high)&exponr);
+      shifty                                           := to_integer(exponl - rexpon);
+      if (shifty > 0) then
+        fractr := shift_right (fractr, shifty);
+        rexpon := rexpon + shifty;
+      end if;
+      if (fractr /= 0) then
+        -- rem
+        rfract := fractl rem fractr;    -- unsigned rem
+        sfract := rfract (sfract'range);           -- lower bits
+        -- normalize
+        fpresult := normalize (fract          => sfract,
+                               expon          => rexpon,
+                               sign           => fp_sign,
+                               fraction_width => fraction_width,
+                               exponent_width => exponent_width,
+                               round_style    => round_style,
+                               denormalize    => denormalize,
+                               nguard         => divguard);
+      else
+        -- If we shift "fractr" so far that it becomes zero, return zero.
+        fpresult := zerofp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+      end if;
+    end if;
+    return fpresult;
+  end function remainder;
+
+  -- "mod" function
+  function modulo (
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant guard       : NATURAL    := float_guard_bits;  -- number of guard bits
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := - mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype : valid_fpstate;
+    variable fpresult         : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable remres           : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- remainder
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      lfptype := isx;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    if (lfptype = isx or rfptype = isx) then
+      fpresult := (others => 'X');
+    elsif (lfptype = nan or lfptype = quiet_nan)
+      or (rfptype = nan or rfptype = quiet_nan)
+      -- Return quiet NAN, IEEE754-1985-7.1,1
+      or (lfptype = pos_inf or lfptype = neg_inf)           -- inf rem x
+      -- Return quiet NAN, IEEE754-1985-7.1,5
+      or (rfptype = pos_zero or rfptype = neg_zero) then    -- x rem 0
+      -- Return quiet NAN, IEEE754-1985-7.1,5
+      fpresult := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    elsif (rfptype = pos_inf or rfptype = neg_inf) then     -- x rem inf = 0
+      fpresult := zerofp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+    else
+      remres := remainder (l           => abs(l),
+                           r           => abs(r),
+                           round_style => round_style,
+                           guard       => guard,
+                           check_error => false,
+                           denormalize => denormalize);
+      -- MOD is the same as REM, but you do something different with
+      -- negative values
+      if (is_negative (l)) then
+        remres := - remres;
+      end if;
+      if (is_negative (l) = is_negative (r) or remres = 0) then
+        fpresult := remres;
+      else
+        fpresult := add (l           => remres,
+                         r           => r,
+                         round_style => round_style,
+                         guard       => guard,
+                         check_error => false,
+                         denormalize => denormalize);        
+      end if;
+    end if;
+    return fpresult;
+  end function modulo;
+
+  -- Square root of a floating point number.  Done using Newton's Iteration.
+  function sqrt (
+    arg                  : UNRESOLVED_float;        -- floating point input
+    constant round_style : round_type := float_round_style;
+    constant guard       : NATURAL    := float_guard_bits;
+    constant check_error : BOOLEAN    := float_check_error;
+    constant denormalize : BOOLEAN    := float_denormalize)
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL := guard-arg'low;  -- length of FP output fraction
+    constant exponent_width : NATURAL := arg'high;  -- length of FP output exponent
+    variable sign           : STD_ULOGIC;
+    variable fpresult       : float (arg'range);
+    variable fptype         : valid_fpstate;
+    variable iexpon         : SIGNED(exponent_width-1 downto 0);  -- exponents
+    variable expon          : SIGNED(exponent_width downto 0);    -- exponents
+    variable ufact          : ufixed (0 downto arg'low);
+    variable fact           : ufixed (2 downto -fraction_width);  -- fraction
+    variable resb           : ufixed (fact'high+1 downto fact'low);
+  begin  -- square root
+    fptype := Classfp (arg, check_error);
+    classcase : case fptype is
+      when isx =>
+        fpresult := (others => 'X');
+      when nan | quiet_nan |
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        neg_normal | neg_denormal | neg_inf =>      -- sqrt (neg)
+        -- Return quiet NAN, IEEE754-1985-7.1.6
+        fpresult := qnanfp (fraction_width => fraction_width-guard,
+                            exponent_width => exponent_width);
+      when pos_inf =>                   -- Sqrt (inf), return infinity
+        fpresult := pos_inffp (fraction_width => fraction_width-guard,
+                               exponent_width => exponent_width);
+      when pos_zero =>                  -- return 0
+        fpresult := zerofp (fraction_width => fraction_width-guard,
+                            exponent_width => exponent_width);
+      when neg_zero =>                  -- IEEE754-1985-6.3 return -0
+        fpresult := neg_zerofp (fraction_width => fraction_width-guard,
+                                exponent_width => exponent_width);
+      when others =>
+        break_number (arg         => arg,
+                      denormalize => denormalize,
+                      check_error => false,
+                      fract       => ufact,
+                      expon       => iexpon,
+                      sign        => sign);
+        expon := resize (iexpon+1, expon'length);   -- get exponent
+        fact  := resize (ufact, fact'high, fact'low);
+        if (expon(0) = '1') then
+          fact := fact sla 1;           -- * 2.0
+        end if;
+        expon := shift_right (expon, 1);            -- exponent/2
+        -- Newton's iteration - root := (1 + arg) / 2
+        resb  := (fact + 1) sra 1;
+        for j in 0 to fraction_width/4 loop
+          --   root := (root + (arg/root))/2
+          resb := resize (arg            => (resb + (fact/resb)) sra 1,
+                          left_index     => resb'high,
+                          right_index    => resb'low,
+                          round_style    => fixed_truncate,
+                          overflow_style => fixed_wrap);
+        end loop;
+        fpresult := normalize (fract          => resb,
+                               expon          => expon-1,
+                               sign           => '0',
+                               exponent_width => arg'high,
+                               fraction_width => -arg'low,
+                               round_style    => round_style,
+                               denormalize    => denormalize,
+                               nguard         => guard);
+    end case classcase;
+    return fpresult;
+  end function sqrt;
+
+  function Is_Negative (arg : UNRESOLVED_float) return BOOLEAN is
+    -- Technically -0 should return "false", but I'm leaving that case out.
+  begin
+    return (to_x01(arg(arg'high)) = '1');
+  end function Is_Negative;
+
+  -- compare functions
+  -- =, /=, >=, <=, <, >
+
+  function eq (                         -- equal =
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    variable lfptype, rfptype       : valid_fpstate;
+    variable is_equal, is_unordered : BOOLEAN;
+    constant fraction_width         : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width         : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lresize, rresize       : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- equal
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return false;
+    else
+      lfptype := classfp (l, check_error);
+      rfptype := classfp (r, check_error);
+    end if;
+    if (lfptype = neg_zero or lfptype = pos_zero) and
+      (rfptype = neg_zero or rfptype = pos_zero) then
+      is_equal := true;
+    else
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      is_equal := (to_slv(lresize) = to_slv(rresize));
+    end if;
+    if (check_error) then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return is_equal and not is_unordered;
+  end function eq;
+
+  function lt (                         -- less than <
+    l, r                 : UNRESOLVED_float;         -- floating point input
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    constant fraction_width             : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width             : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype           : valid_fpstate;
+    variable expl, expr                 : UNSIGNED (exponent_width-1 downto 0);
+    variable fractl, fractr             : UNSIGNED (fraction_width-1 downto 0);
+    variable is_less_than, is_unordered : BOOLEAN;
+    variable lresize, rresize           : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      is_less_than := false;
+    else
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      if to_x01(l(l'high)) = to_x01(r(r'high)) then  -- sign bits
+        expl := UNSIGNED(lresize(exponent_width-1 downto 0));
+        expr := UNSIGNED(rresize(exponent_width-1 downto 0));
+        if expl = expr then
+          fractl := UNSIGNED (to_slv(lresize(-1 downto -fraction_width)));
+          fractr := UNSIGNED (to_slv(rresize(-1 downto -fraction_width)));
+          if to_x01(l(l'high)) = '0' then            -- positive number
+            is_less_than := (fractl < fractr);
+          else
+            is_less_than := (fractl > fractr);       -- negative
+          end if;
+        else
+          if to_x01(l(l'high)) = '0' then            -- positive number
+            is_less_than := (expl < expr);
+          else
+            is_less_than := (expl > expr);           -- negative
+          end if;
+        end if;
+      else
+        lfptype := classfp (l, check_error);
+        rfptype := classfp (r, check_error);
+        if (lfptype = neg_zero and rfptype = pos_zero) then
+          is_less_than := false;        -- -0 < 0 returns false.
+        else
+          is_less_than := (to_x01(l(l'high)) > to_x01(r(r'high)));
+        end if;
+      end if;
+    end if;
+    if check_error then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return is_less_than and not is_unordered;
+  end function lt;
+
+  function gt (                         -- greater than >
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype : valid_fpstate;
+    variable expl, expr       : UNSIGNED (exponent_width-1 downto 0);
+    variable fractl, fractr   : UNSIGNED (fraction_width-1 downto 0);
+    variable is_greater_than  : BOOLEAN;
+    variable is_unordered     : BOOLEAN;
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- greater_than
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      is_greater_than := false;
+    else
+      lresize := resize (arg            => to_x01(l),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      rresize := resize (arg            => to_x01(r),
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => denormalize,
+                         denormalize    => denormalize);
+      if to_x01(l(l'high)) = to_x01(r(r'high)) then              -- sign bits
+        expl := UNSIGNED(lresize(exponent_width-1 downto 0));
+        expr := UNSIGNED(rresize(exponent_width-1 downto 0));
+        if expl = expr then
+          fractl := UNSIGNED (to_slv(lresize(-1 downto -fraction_width)));
+          fractr := UNSIGNED (to_slv(rresize(-1 downto -fraction_width)));
+          if to_x01(l(l'high)) = '0' then     -- positive number
+            is_greater_than := fractl > fractr;
+          else
+            is_greater_than := fractl < fractr;                  -- negative
+          end if;
+        else
+          if to_x01(l(l'high)) = '0' then     -- positive number
+            is_greater_than := expl > expr;
+          else
+            is_greater_than := expl < expr;   -- negative
+          end if;
+        end if;
+      else
+        lfptype := classfp (l, check_error);
+        rfptype := classfp (r, check_error);
+        if (lfptype = pos_zero and rfptype = neg_zero) then
+          is_greater_than := false;     -- 0 > -0 returns false.
+        else
+          is_greater_than := to_x01(l(l'high)) < to_x01(r(r'high));
+        end if;
+      end if;
+    end if;
+    if check_error then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return is_greater_than and not is_unordered;
+  end function gt;
+
+  -- purpose: /= function
+  function ne (                         -- not equal /=
+    l, r                 : UNRESOLVED_float;
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    variable is_equal, is_unordered : BOOLEAN;
+  begin
+    is_equal := eq (l           => l,
+                    r           => r,
+                    check_error => false,
+                    denormalize => denormalize);
+    if check_error then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return not (is_equal and not is_unordered);
+  end function ne;
+
+  function le (                               -- less than or equal to <=
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    variable is_greater_than, is_unordered : BOOLEAN;
+  begin
+    is_greater_than := gt (l           => l,
+                           r           => r,
+                           check_error => false,
+                           denormalize => denormalize);
+    if check_error then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return not is_greater_than and not is_unordered;
+  end function le;
+
+  function ge (                               -- greater than or equal to >=
+    l, r                 : UNRESOLVED_float;  -- floating point input
+    constant check_error : BOOLEAN := float_check_error;
+    constant denormalize : BOOLEAN := float_denormalize)
+    return BOOLEAN
+  is
+    variable is_less_than, is_unordered : BOOLEAN;
+  begin
+    is_less_than := lt (l           => l,
+                        r           => r,
+                        check_error => false,
+                        denormalize => denormalize);
+    if check_error then
+      is_unordered := Unordered (x => l,
+                                 y => r);
+    else
+      is_unordered := false;
+    end if;
+    return not is_less_than and not is_unordered;
+  end function ge;
+
+  function "?=" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width         : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width         : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype       : valid_fpstate;
+    variable is_equal, is_unordered : STD_ULOGIC;
+    variable lresize, rresize       : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- ?=
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      lfptype := classfp (l, float_check_error);
+      rfptype := classfp (r, float_check_error);
+    end if;
+    if (lfptype = neg_zero or lfptype = pos_zero) and
+      (rfptype = neg_zero or rfptype = pos_zero) then
+      is_equal := '1';
+    else
+      lresize := resize (arg            => l,
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => float_denormalize,
+                         denormalize    => float_denormalize);
+      rresize := resize (arg            => r,
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => float_denormalize,
+                         denormalize    => float_denormalize);
+      is_equal := to_sulv(lresize) ?= to_sulv(rresize);
+    end if;
+    if (float_check_error) then
+      if (lfptype = nan or lfptype = quiet_nan or
+          rfptype = nan or rfptype = quiet_nan) then
+        is_unordered := '1';
+      else
+        is_unordered := '0';
+      end if;
+    else
+      is_unordered := '0';
+    end if;
+    return is_equal and not is_unordered;
+  end function "?=";
+
+  function "?/=" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width         : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width         : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lfptype, rfptype       : valid_fpstate;
+    variable is_equal, is_unordered : STD_ULOGIC;
+    variable lresize, rresize       : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- ?/=
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      lfptype := classfp (l, float_check_error);
+      rfptype := classfp (r, float_check_error);
+    end if;
+    if (lfptype = neg_zero or lfptype = pos_zero) and
+      (rfptype = neg_zero or rfptype = pos_zero) then
+      is_equal := '1';
+    else
+      lresize := resize (arg            => l,
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => float_denormalize,
+                         denormalize    => float_denormalize);
+      rresize := resize (arg            => r,
+                         exponent_width => exponent_width,
+                         fraction_width => fraction_width,
+                         denormalize_in => float_denormalize,
+                         denormalize    => float_denormalize);
+      is_equal := to_sulv(lresize) ?= to_sulv(rresize);
+    end if;
+    if (float_check_error) then
+      if (lfptype = nan or lfptype = quiet_nan or
+          rfptype = nan or rfptype = quiet_nan) then
+        is_unordered := '1';
+      else
+        is_unordered := '0';
+      end if;
+    else
+      is_unordered := '0';
+    end if;
+    return not (is_equal and not is_unordered);
+  end function "?/=";
+
+  function "?>" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width : NATURAL := -mine(l'low, r'low);
+    variable founddash      : BOOLEAN := false;
+  begin
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      for i in L'range loop
+        if L(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      for i in R'range loop
+        if R(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      if founddash then
+        report float_generic_pkg'instance_name
+          & " ""?>"": '-' found in compare string"
+          severity error;
+        return 'X';
+      elsif is_x(l) or is_x(r) then
+        return 'X';
+      elsif l > r then
+        return '1';
+      else
+        return '0';
+      end if;
+    end if;
+  end function "?>";
+
+  function "?>=" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width : NATURAL := -mine(l'low, r'low);
+    variable founddash      : BOOLEAN := false;
+  begin
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      for i in L'range loop
+        if L(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      for i in R'range loop
+        if R(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      if founddash then
+        report float_generic_pkg'instance_name
+          & " ""?>="": '-' found in compare string"
+          severity error;
+        return 'X';
+      elsif is_x(l) or is_x(r) then
+        return 'X';
+      elsif l >= r then
+        return '1';
+      else
+        return '0';
+      end if;
+    end if;
+  end function "?>=";
+
+  function "?<" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width : NATURAL := -mine(l'low, r'low);
+    variable founddash      : BOOLEAN := false;
+  begin
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      for i in L'range loop
+        if L(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      for i in R'range loop
+        if R(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      if founddash then
+        report float_generic_pkg'instance_name
+          & " ""?<"": '-' found in compare string"
+          severity error;
+        return 'X';
+      elsif is_x(l) or is_x(r) then
+        return 'X';
+      elsif l < r then
+        return '1';
+      else
+        return '0';
+      end if;
+    end if;
+  end function "?<";
+
+  function "?<=" (L, R : UNRESOLVED_float) return STD_ULOGIC is
+    constant fraction_width : NATURAL := -mine(l'low, r'low);
+    variable founddash      : BOOLEAN := false;
+  begin
+    if (fraction_width = 0 or l'length < 7 or r'length < 7) then
+      return 'X';
+    else
+      for i in L'range loop
+        if L(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      for i in R'range loop
+        if R(i) = '-' then
+          founddash := true;
+        end if;
+      end loop;
+      if founddash then
+        report float_generic_pkg'instance_name
+          & " ""?<="": '-' found in compare string"
+          severity error;
+        return 'X';
+      elsif is_x(l) or is_x(r) then
+        return 'X';
+      elsif l <= r then
+        return '1';
+      else
+        return '0';
+      end if;
+    end if;
+  end function "?<=";
+
+  function std_match (L, R : UNRESOLVED_float) return BOOLEAN is
+  begin
+    if (L'high = R'high and L'low = R'low) then
+      return std_match(to_sulv(L), to_sulv(R));
+    else
+      report float_generic_pkg'instance_name
+        & "STD_MATCH: L'RANGE /= R'RANGE, returning FALSE"
+        severity warning;
+      return false;
+    end if;
+  end function std_match;
+
+  function find_rightmost (arg : UNRESOLVED_float; y : STD_ULOGIC) return INTEGER is
+  begin
+    for_loop : for i in arg'reverse_range loop
+      if arg(i) ?= y then
+        return i;
+      end if;
+    end loop;
+    return arg'high+1;                  -- return out of bounds 'high
+  end function find_rightmost;
+
+  function find_leftmost (arg : UNRESOLVED_float; y : STD_ULOGIC) return INTEGER is
+  begin
+    for_loop : for i in arg'range loop
+      if arg(i) ?= y then
+        return i;
+      end if;
+    end loop;
+    return arg'low-1;                   -- return out of bounds 'low
+  end function find_leftmost;
+
+  -- These override the defaults for the compare operators.
+  function "=" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return eq(l, r);
+  end function "=";
+
+  function "/=" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return ne(l, r);
+  end function "/=";
+
+  function ">=" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return ge(l, r);
+  end function ">=";
+
+  function "<=" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return le(l, r);
+  end function "<=";
+
+  function ">" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return gt(l, r);
+  end function ">";
+
+  function "<" (l, r : UNRESOLVED_float) return BOOLEAN is
+  begin
+    return lt(l, r);
+  end function "<";
+
+  -- purpose: maximum of two numbers (overrides default)
+  function maximum (
+    L, R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin
+    if ((L'length < 1) or (R'length < 1)) then return NAFP;
+    end if;
+    lresize := resize (l, exponent_width, fraction_width);
+    rresize := resize (r, exponent_width, fraction_width);
+    if lresize > rresize then return lresize;
+    else return rresize;
+    end if;
+  end function maximum;
+
+  function minimum (
+    L, R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    constant fraction_width   : NATURAL := -mine(l'low, r'low);  -- length of FP output fraction
+    constant exponent_width   : NATURAL := maximum(l'high, r'high);  -- length of FP output exponent
+    variable lresize, rresize : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin
+    if ((L'length < 1) or (R'length < 1)) then return NAFP;
+    end if;
+    lresize := resize (l, exponent_width, fraction_width);
+    rresize := resize (r, exponent_width, fraction_width);
+    if lresize > rresize then return rresize;
+    else return lresize;
+    end if;
+  end function minimum;
+
+  -----------------------------------------------------------------------------
+  -- conversion functions
+  -----------------------------------------------------------------------------
+
+  -- Converts a floating point number of one format into another format
+  function resize (
+    arg                     : UNRESOLVED_float;        -- Floating point input
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant check_error    : BOOLEAN    := float_check_error;
+    constant denormalize_in : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant in_fraction_width : NATURAL := -arg'low;  -- length of FP output fraction
+    constant in_exponent_width : NATURAL := arg'high;  -- length of FP output exponent
+    variable result            : UNRESOLVED_float (exponent_width downto -fraction_width);
+                                        -- result value
+    variable fptype            : valid_fpstate;
+    variable expon_in          : SIGNED (in_exponent_width-1 downto 0);
+    variable fract_in          : UNSIGNED (in_fraction_width downto 0);
+    variable round             : BOOLEAN;
+    variable expon_out         : SIGNED (exponent_width-1 downto 0);  -- output fract
+    variable fract_out         : UNSIGNED (fraction_width downto 0);  -- output fract
+    variable passguard         : NATURAL;
+  begin
+    fptype := classfp(arg, check_error);
+    if ((fptype = pos_denormal or fptype = neg_denormal) and denormalize_in
+        and (in_exponent_width < exponent_width
+             or in_fraction_width < fraction_width))
+      or in_exponent_width > exponent_width
+      or in_fraction_width > fraction_width then
+      -- size reduction
+      classcase : case fptype is
+        when isx =>
+          result := (others => 'X');
+        when nan | quiet_nan =>
+          result := qnanfp (fraction_width => fraction_width,
+                            exponent_width => exponent_width);
+        when pos_inf =>
+          result := pos_inffp (fraction_width => fraction_width,
+                               exponent_width => exponent_width);
+        when neg_inf =>
+          result := neg_inffp (fraction_width => fraction_width,
+                               exponent_width => exponent_width);
+        when pos_zero | neg_zero =>
+          result := zerofp (fraction_width => fraction_width,   -- hate -0
+                            exponent_width => exponent_width);
+        when others =>
+          break_number (
+            arg         => arg,
+            fptyp       => fptype,
+            denormalize => denormalize_in,
+            fract       => fract_in,
+            expon       => expon_in);
+          if fraction_width > in_fraction_width and denormalize_in then
+            -- You only get here if you have a denormal input
+            fract_out := (others => '0');              -- pad with zeros
+            fract_out (fraction_width downto
+                       fraction_width - in_fraction_width) := fract_in;
+            result := normalize (
+              fract          => fract_out,
+              expon          => expon_in,
+              sign           => arg(arg'high),
+              fraction_width => fraction_width,
+              exponent_width => exponent_width,
+              round_style    => round_style,
+              denormalize    => denormalize,
+              nguard         => 0);
+          else
+            result := normalize (
+              fract          => fract_in,
+              expon          => expon_in,
+              sign           => arg(arg'high),
+              fraction_width => fraction_width,
+              exponent_width => exponent_width,
+              round_style    => round_style,
+              denormalize    => denormalize,
+              nguard         => in_fraction_width - fraction_width);
+          end if;
+      end case classcase;
+    else                                -- size increase or the same size
+      if exponent_width > in_exponent_width then
+        expon_in := SIGNED(arg (in_exponent_width-1 downto 0));
+        if fptype = pos_zero or fptype = neg_zero then
+          result (exponent_width-1 downto 0) := (others => '0');
+        elsif expon_in = -1 then        -- inf or nan (shorts out check_error)
+          result (exponent_width-1 downto 0) := (others => '1');
+        else
+          -- invert top BIT
+          expon_in(expon_in'high)   := not expon_in(expon_in'high);
+          expon_out := resize (expon_in, expon_out'length);  -- signed expand
+          -- Flip it back.
+          expon_out(expon_out'high) := not expon_out(expon_out'high);
+          result (exponent_width-1 downto 0) := UNRESOLVED_float(expon_out);
+        end if;
+        result (exponent_width) := arg (in_exponent_width);     -- sign
+      else                              -- exponent_width = in_exponent_width
+        result (exponent_width downto 0) := arg (in_exponent_width downto 0);
+      end if;
+      if fraction_width > in_fraction_width then
+        result (-1 downto -fraction_width) := (others => '0');  -- zeros
+        result (-1 downto -in_fraction_width) :=
+          arg (-1 downto -in_fraction_width);
+      else                              -- fraction_width = in_fraciton_width
+        result (-1 downto -fraction_width) :=
+          arg (-1 downto -in_fraction_width);
+      end if;
+    end if;
+    return result;
+  end function resize;
+
+  function resize (
+    arg                     : UNRESOLVED_float;  -- floating point input
+    size_res                : UNRESOLVED_float;
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant check_error    : BOOLEAN    := float_check_error;
+    constant denormalize_in : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := resize (arg            => arg,
+                        exponent_width => size_res'high,
+                        fraction_width => -size_res'low,
+                        round_style    => round_style,
+                        check_error    => check_error,
+                        denormalize_in => denormalize_in,
+                        denormalize    => denormalize);
+      return result;
+    end if;
+  end function resize;
+
+  function to_float32 (
+    arg                     : UNRESOLVED_float;
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant check_error    : BOOLEAN    := float_check_error;
+    constant denormalize_in : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float32 is
+  begin
+    return resize (arg            => arg,
+                   exponent_width => float32'high,
+                   fraction_width => -float32'low,
+                   round_style    => round_style,
+                   check_error    => check_error,
+                   denormalize_in => denormalize_in,
+                   denormalize    => denormalize);
+  end function to_float32;
+
+  function to_float64 (
+    arg                     : UNRESOLVED_float;
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant check_error    : BOOLEAN    := float_check_error;
+    constant denormalize_in : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float64 is
+  begin
+    return resize (arg            => arg,
+                   exponent_width => float64'high,
+                   fraction_width => -float64'low,
+                   round_style    => round_style,
+                   check_error    => check_error,
+                   denormalize_in => denormalize_in,
+                   denormalize    => denormalize);
+  end function to_float64;
+
+  function to_float128 (
+    arg                     : UNRESOLVED_float;
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant check_error    : BOOLEAN    := float_check_error;
+    constant denormalize_in : BOOLEAN    := float_denormalize;  -- Use IEEE extended FP
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float128 is
+  begin
+    return resize (arg            => arg,
+                   exponent_width => float128'high,
+                   fraction_width => -float128'low,
+                   round_style    => round_style,
+                   check_error    => check_error,
+                   denormalize_in => denormalize_in,
+                   denormalize    => denormalize);
+  end function to_float128;
+
+  -- to_float (Real)
+  -- typically not Synthesizable unless the input is a constant.
+  function to_float (
+    arg                     : REAL;
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style;  -- rounding option
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    variable result     : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable arg_real   : REAL;         -- Real version of argument
+    variable validfp    : boundary_type;      -- Check for valid results
+    variable exp        : INTEGER;      -- Integer version of exponent
+    variable expon      : UNSIGNED (exponent_width - 1 downto 0);
+                                        -- Unsigned version of exp.
+    constant expon_base : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable fract     : UNSIGNED (fraction_width-1 downto 0);
+    variable frac      : REAL;          -- Real version of fraction
+    constant roundfrac : REAL := 2.0 ** (-2 - fract'high);  -- used for rounding
+    variable round     : BOOLEAN;       -- to round or not to round
+  begin
+    result   := (others => '0');
+    arg_real := arg;
+    if arg_real < 0.0 then
+      result (exponent_width) := '1';
+      arg_real                := - arg_real;  -- Make it positive.
+    else
+      result (exponent_width) := '0';
+    end if;
+    test_boundary (arg            => arg_real,
+                   fraction_width => fraction_width,
+                   exponent_width => exponent_width,
+                   denormalize    => denormalize,
+                   btype          => validfp,
+                   log2i          => exp);
+    if validfp = zero then
+      return result;                    -- Result initialized to "0".
+    elsif validfp = infinity then
+      result (exponent_width - 1 downto 0) := (others => '1');  -- Exponent all "1"
+                                        -- return infinity.
+      return result;
+    else
+      if validfp = denormal then        -- Exponent will default to "0".
+        expon := (others => '0');
+        frac  := arg_real * (2.0 ** (to_integer(expon_base)-1));
+      else                              -- Number less than 1. "normal" number
+        expon    := UNSIGNED (to_signed (exp-1, exponent_width));
+        expon(exponent_width-1) := not expon(exponent_width-1);
+        frac     := (arg_real / 2.0 ** exp) - 1.0;  -- Number less than 1.
+      end if;
+      for i in 0 to fract'high loop
+        if frac >= 2.0 ** (-1 - i) then
+          fract (fract'high - i) := '1';
+          frac                   := frac - 2.0 ** (-1 - i);
+        else
+          fract (fract'high - i) := '0';
+        end if;
+      end loop;
+      round := false;
+      case round_style is
+        when round_nearest =>
+          if frac > roundfrac or ((frac = roundfrac) and fract(0) = '1') then
+            round := true;
+          end if;
+        when round_inf =>
+          if frac /= 0.0 and result(exponent_width) = '0' then
+            round := true;
+          end if;
+        when round_neginf =>
+          if frac /= 0.0 and result(exponent_width) = '1' then
+            round := true;
+          end if;
+        when others =>
+          null;                         -- don't round
+      end case;
+      if (round) then
+        if and(fract) = '1' then        -- fraction is all "1"
+          expon := expon + 1;
+          fract := (others => '0');
+        else
+          fract := fract + 1;
+        end if;
+      end if;
+      result (exponent_width-1 downto 0) := UNRESOLVED_float(expon);
+      result (-1 downto -fraction_width) := UNRESOLVED_float(fract);
+      return result;
+    end if;
+  end function to_float;
+
+  -- to_float (Integer)
+  function to_float (
+    arg                     : INTEGER;
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result     : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable arg_int    : NATURAL;      -- Natural version of argument
+    variable expon      : SIGNED (exponent_width-1 downto 0);
+    variable exptmp     : SIGNED (exponent_width-1 downto 0);
+    -- Unsigned version of exp.
+    constant expon_base : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable fract     : UNSIGNED (fraction_width-1 downto 0) := (others => '0');
+    variable fracttmp  : UNSIGNED (fraction_width-1 downto 0);
+    variable round     : BOOLEAN;
+    variable shift     : NATURAL;
+    variable shiftr    : NATURAL;
+    variable roundfrac : NATURAL;       -- used in rounding
+  begin
+    if arg < 0 then
+      result (exponent_width) := '1';
+      arg_int                 := -arg;  -- Make it positive.
+    else
+      result (exponent_width) := '0';
+      arg_int                 := arg;
+    end if;
+    if arg_int = 0 then
+      result := zerofp (fraction_width => fraction_width,
+                        exponent_width => exponent_width);
+    else
+      -- If the number is larger than we can represent in this number system
+      -- we need to return infinity.
+      shift := log2(arg_int);
+      if shift > to_integer(expon_base) then
+        -- worry about infinity
+        if result (exponent_width) = '0' then
+          result := pos_inffp (fraction_width => fraction_width,
+                               exponent_width => exponent_width);
+        else
+          -- return negative infinity.
+          result := neg_inffp (fraction_width => fraction_width,
+                               exponent_width => exponent_width);
+        end if;
+      else                              -- Normal number (can't be denormal)
+        -- Compute Exponent
+        expon   := to_signed (shift-1, expon'length);  -- positive fraction.
+        -- Compute Fraction
+        arg_int := arg_int - 2**shift;  -- Subtract off the 1.0
+        shiftr  := shift;
+        for I in fract'high downto maximum (fract'high - shift + 1, 0) loop
+          shiftr := shiftr - 1;
+          if (arg_int >= 2**shiftr) then
+            arg_int  := arg_int - 2**shiftr;
+            fract(I) := '1';
+          else
+            fract(I) := '0';
+          end if;
+        end loop;
+        -- Rounding routine
+        round := false;
+        if arg_int > 0 then
+          roundfrac := 2**(shiftr-1);
+          case round_style is
+            when round_nearest =>
+              if arg_int > roundfrac or
+                ((arg_int = roundfrac) and fract(0) = '1') then
+                round := true;
+              end if;
+            when round_inf =>
+              if arg_int /= 0 and result (exponent_width) = '0' then
+                round := true;
+              end if;
+            when round_neginf =>
+              if arg_int /= 0 and result (exponent_width) = '1' then
+                round := true;
+              end if;
+            when others =>
+              null;
+          end case;
+        end if;
+        if round then
+          fp_round(fract_in  => fract,
+                   expon_in  => expon,
+                   fract_out => fracttmp,
+                   expon_out => exptmp);
+          fract := fracttmp;
+          expon := exptmp;
+        end if;
+        -- Put the number together and return
+        expon(exponent_width-1)            := not expon(exponent_width-1);
+        result (exponent_width-1 downto 0) := UNRESOLVED_float(expon);
+        result (-1 downto -fraction_width) := UNRESOLVED_float(fract);
+      end if;
+    end if;
+    return result;
+  end function to_float;
+
+  -- to_float (unsigned)
+  function to_float (
+    arg                     : UNSIGNED;
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result   : UNRESOLVED_float (exponent_width downto -fraction_width);
+    constant ARG_LEFT : INTEGER := ARG'length-1;
+    alias XARG        : UNSIGNED(ARG_LEFT downto 0) is ARG;
+    variable sarg     : SIGNED (ARG_LEFT+1 downto 0);  -- signed version of arg
+  begin
+    if arg'length < 1 then
+      return NAFP;
+    end if;
+    sarg (XARG'range) := SIGNED (XARG);
+    sarg (sarg'high)  := '0';
+    result := to_float (arg            => sarg,
+                        exponent_width => exponent_width,
+                        fraction_width => fraction_width,
+                        round_style    => round_style);
+    return result;
+  end function to_float;
+
+  -- to_float (signed)
+  function to_float (
+    arg                     : SIGNED;
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result     : UNRESOLVED_float (exponent_width downto -fraction_width);
+    constant ARG_LEFT   : INTEGER := ARG'length-1;
+    alias XARG          : SIGNED(ARG_LEFT downto 0) is ARG;
+    variable arg_int    : UNSIGNED(xarg'range);  -- Real version of argument
+    variable argb2      : UNSIGNED(xarg'high/2 downto 0);  -- log2 of input
+    variable rexp       : SIGNED (exponent_width - 1 downto 0);
+    variable exp        : SIGNED (exponent_width - 1 downto 0);
+    -- signed version of exp.
+    variable expon      : UNSIGNED (exponent_width - 1 downto 0);
+    -- Unsigned version of exp.
+    constant expon_base : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable round  : BOOLEAN;
+    variable fract  : UNSIGNED (fraction_width-1 downto 0);
+    variable rfract : UNSIGNED (fraction_width-1 downto 0);
+    variable sign   : STD_ULOGIC;         -- sign bit
+  begin
+    if arg'length < 1 then
+      return NAFP;
+    end if;
+    if Is_X (xarg) then
+      result := (others => 'X');
+    elsif (xarg = 0) then
+      result := zerofp (fraction_width => fraction_width,
+                        exponent_width => exponent_width);
+    else                                -- Normal number (can't be denormal)
+      sign := to_X01(xarg (xarg'high));
+      arg_int := UNSIGNED(abs (to_01(xarg)));
+      -- Compute Exponent
+      argb2 := to_unsigned(find_leftmost(arg_int, '1'), argb2'length);  -- Log2
+      if argb2 > UNSIGNED(expon_base) then
+        result := pos_inffp (fraction_width => fraction_width,
+                             exponent_width => exponent_width);
+        result (exponent_width) := sign;
+      else
+        exp     := SIGNED(resize(argb2, exp'length));
+        arg_int := shift_left (arg_int, arg_int'high-to_integer(exp));
+        if (arg_int'high > fraction_width) then
+          fract := arg_int (arg_int'high-1 downto (arg_int'high-fraction_width));
+          round := check_round (
+            fract_in    => fract (0),
+            sign        => sign,
+            remainder   => arg_int((arg_int'high-fraction_width-1)
+                                   downto 0),
+            round_style => round_style);
+          if round then
+            fp_round(fract_in  => fract,
+                     expon_in  => exp,
+                     fract_out => rfract,
+                     expon_out => rexp);
+          else
+            rfract := fract;
+            rexp   := exp;
+          end if;
+        else
+          rexp   := exp;
+          rfract := (others => '0');
+          rfract (fraction_width-1 downto fraction_width-1-(arg_int'high-1)) :=
+            arg_int (arg_int'high-1 downto 0);
+        end if;
+        result (exponent_width) := sign;
+        expon := UNSIGNED (rexp-1);
+        expon(exponent_width-1)            := not expon(exponent_width-1);
+        result (exponent_width-1 downto 0) := UNRESOLVED_float(expon);
+        result (-1 downto -fraction_width) := UNRESOLVED_float(rfract);
+      end if;
+    end if;
+    return result;
+  end function to_float;
+
+  -- std_logic_vector to float
+  function to_float (
+    arg                     : STD_ULOGIC_VECTOR;
+    constant exponent_width : NATURAL := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- length of FP output fraction
+    return UNRESOLVED_float
+  is
+    variable fpvar : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin
+    if arg'length < 1 then
+      return NAFP;
+    end if;
+    fpvar := UNRESOLVED_float(arg);
+    return fpvar;
+  end function to_float;
+
+  -- purpose: converts a ufixed to a floating point
+  function to_float (
+    arg                     : UNRESOLVED_ufixed;  -- unsigned fixed point input
+    constant exponent_width : NATURAL    := float_exponent_width;  -- width of exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- width of fraction
+    constant round_style    : round_type := float_round_style;  -- rounding
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- use ieee extensions
+    return UNRESOLVED_float
+  is
+    variable sarg   : sfixed (arg'high+1 downto arg'low);  -- Signed version of arg
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width);
+  begin  -- function to_float
+    if (arg'length < 1) then
+      return NAFP;
+    end if;
+    sarg (arg'range) := sfixed (arg);
+    sarg (sarg'high) := '0';
+    result := to_float (arg            => sarg,
+                        exponent_width => exponent_width,
+                        fraction_width => fraction_width,
+                        round_style    => round_style,
+                        denormalize    => denormalize);
+    return result;
+  end function to_float;
+
+  function to_float (
+    arg                     : UNRESOLVED_sfixed;    -- signed fixed point
+    constant exponent_width : NATURAL    := float_exponent_width;  -- length of FP output exponent
+    constant fraction_width : NATURAL    := float_fraction_width;  -- length of FP output fraction
+    constant round_style    : round_type := float_round_style;  -- rounding
+    constant denormalize    : BOOLEAN    := float_denormalize)  -- rounding option
+    return UNRESOLVED_float
+  is
+    constant integer_width     : INTEGER := arg'high;
+    constant in_fraction_width : INTEGER := arg'low;
+    variable xresult     : sfixed (integer_width downto in_fraction_width);
+    variable result      : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable arg_int     : UNSIGNED(integer_width - in_fraction_width - 1
+                                    downto 0);  -- signed version of argument
+    variable argx        : SIGNED (integer_width - in_fraction_width downto 0);
+    variable exp, exptmp : SIGNED (exponent_width downto 0);
+    variable expon       : UNSIGNED (exponent_width - 1 downto 0);
+    -- Unsigned version of exp.
+    constant expon_base  : SIGNED (exponent_width-1 downto 0) :=
+      gen_expon_base(exponent_width);   -- exponent offset
+    variable fract, fracttmp : UNSIGNED (fraction_width-1 downto 0) :=
+      (others => '0');
+    variable round : BOOLEAN := false;
+  begin
+    if (arg'length < 1) then
+      return NAFP;
+    end if;
+    xresult := to_01(arg, 'X');
+    argx    := SIGNED(to_slv(xresult));
+    if (Is_X (arg)) then
+      result := (others => 'X');
+    elsif (argx = 0) then
+      result := (others => '0');
+    else
+      result := (others => '0');        -- zero out the result
+      if argx(argx'left) = '1' then     -- toss the sign bit
+        result (exponent_width) := '1';     -- Negative number
+        argx                    := -argx;   -- Make it positive.
+      else
+        result (exponent_width) := '0';
+      end if;
+      arg_int := UNSIGNED(to_x01(STD_LOGIC_VECTOR (argx(arg_int'range))));
+      -- Compute Exponent
+      exp     := to_signed(find_leftmost(arg_int, '1'), exp'length);  -- Log2
+      if exp + in_fraction_width > expon_base then  -- return infinity
+        result (-1 downto -fraction_width)  := (others => '0');
+        result (exponent_width -1 downto 0) := (others => '1');
+        return result;
+      elsif (denormalize and
+             (exp + in_fraction_width <= -resize(expon_base, exp'length))) then
+        exp := -resize(expon_base, exp'length);
+        -- shift by a constant
+        arg_int := shift_left (arg_int,
+                               (arg_int'high + to_integer(expon_base)
+                                + in_fraction_width - 1));
+        if (arg_int'high > fraction_width) then
+          fract := arg_int (arg_int'high-1 downto (arg_int'high-fraction_width));
+          round := check_round (
+            fract_in    => arg_int(arg_int'high-fraction_width),
+            sign        => result(result'high),
+            remainder   => arg_int((arg_int'high-fraction_width-1)
+                                   downto 0),
+            round_style => round_style);
+          if (round) then
+            fp_round (fract_in => arg_int (arg_int'high-1 downto
+                                           (arg_int'high-fraction_width)),
+                      expon_in  => exp,
+                      fract_out => fract,
+                      expon_out => exptmp);
+            exp := exptmp;
+          end if;
+        else
+          fract (fraction_width-1 downto fraction_width-1-(arg_int'high-1)) :=
+            arg_int (arg_int'high-1 downto 0);
+        end if;
+      else
+        arg_int := shift_left (arg_int, arg_int'high-to_integer(exp));
+        exp     := exp + in_fraction_width;
+        if (arg_int'high > fraction_width) then
+          fract := arg_int (arg_int'high-1 downto (arg_int'high-fraction_width));
+          round := check_round (
+            fract_in    => fract(0),
+            sign        => result(result'high),
+            remainder   => arg_int((arg_int'high-fraction_width-1)
+                                   downto 0),
+            round_style => round_style);
+          if (round) then
+            fp_round (fract_in  => fract,
+                      expon_in  => exp,
+                      fract_out => fracttmp,
+                      expon_out => exptmp);
+            fract := fracttmp;
+            exp   := exptmp;
+          end if;
+        else
+          fract (fraction_width-1 downto fraction_width-1-(arg_int'high-1)) :=
+            arg_int (arg_int'high-1 downto 0);
+        end if;
+      end if;
+      expon := UNSIGNED (resize(exp-1, exponent_width));
+      expon(exponent_width-1)            := not expon(exponent_width-1);
+      result (exponent_width-1 downto 0) := UNRESOLVED_float(expon);
+      result (-1 downto -fraction_width) := UNRESOLVED_float(fract);
+    end if;
+    return result;
+  end function to_float;
+
+  -- size_res functions
+  -- Integer to float
+  function to_float (
+    arg                  : INTEGER;
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style);
+      return result;
+    end if;
+  end function to_float;
+
+  -- real to float
+  function to_float (
+    arg                  : REAL;
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style,
+                          denormalize    => denormalize);
+      return result;
+    end if;
+  end function to_float;
+
+  -- unsigned to float
+  function to_float (
+    arg                  : UNRESOLVED_UNSIGNED;
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style);
+      return result;
+    end if;
+  end function to_float;
+
+  -- signed to float
+  function to_float (
+    arg                  : UNRESOLVED_SIGNED;
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style)  -- rounding
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style);
+      return result;
+    end if;
+  end function to_float;
+
+  -- std_ulogic_vector to float
+  function to_float (
+    arg      : STD_ULOGIC_VECTOR;
+    size_res : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low);
+      return result;
+    end if;
+  end function to_float;
+
+  -- unsigned fixed point to float
+  function to_float (
+    arg                  : UNRESOLVED_ufixed;  -- unsigned fixed point input
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style;  -- rounding
+    constant denormalize : BOOLEAN    := float_denormalize)  -- use ieee extensions
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style,
+                          denormalize    => denormalize);
+      return result;
+    end if;
+  end function to_float;
+
+  -- signed fixed point to float
+  function to_float (
+    arg                  : UNRESOLVED_sfixed;
+    size_res             : UNRESOLVED_float;
+    constant round_style : round_type := float_round_style;  -- rounding
+    constant denormalize : BOOLEAN    := float_denormalize)  -- rounding option
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_float (arg            => arg,
+                          exponent_width => size_res'high,
+                          fraction_width => -size_res'low,
+                          round_style    => round_style,
+                          denormalize    => denormalize);
+      return result;
+    end if;
+  end function to_float;
+
+  -- to_integer (float)
+  function to_integer (
+    arg                  : UNRESOLVED_float;   -- floating point input
+     constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error)  -- check for errors
+    return INTEGER
+  is
+    variable validfp : valid_fpstate;   -- Valid FP state
+    variable frac    : UNSIGNED (-arg'low downto 0);         -- Fraction
+    variable fract   : UNSIGNED (1-arg'low downto 0);        -- Fraction
+    variable expon   : SIGNED (arg'high-1 downto 0);
+    variable isign   : STD_ULOGIC;      -- internal version of sign
+    variable round   : STD_ULOGIC;      -- is rounding needed?
+    variable result  : INTEGER;
+    variable base    : INTEGER;         -- Integer exponent
+  begin
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | nan | quiet_nan | pos_zero | neg_zero | pos_denormal | neg_denormal =>
+        result := 0;                    -- return 0
+      when pos_inf =>
+        result := INTEGER'high;
+      when neg_inf =>
+        result := INTEGER'low;
+      when others =>
+        break_number (
+          arg         => arg,
+          fptyp       => validfp,
+          denormalize => false,
+          fract       => frac,
+          expon       => expon);
+        fract (fract'high)            := '0';  -- Add extra bit for 0.6 case
+        fract (fract'high-1 downto 0) := frac;
+        isign                         := to_x01 (arg (arg'high));
+        base                          := to_integer (expon) + 1;
+        if base < -1 then
+          result := 0;
+        elsif base >= frac'high then
+          result := to_integer (fract) * 2**(base - frac'high);
+        else                            -- We need to round
+          if base = -1 then             -- trap for 0.6 case.
+            result := 0;
+          else
+            result := to_integer (fract (frac'high downto frac'high-base));
+          end if;
+          -- rounding routine
+          case round_style is
+            when round_nearest =>
+              if frac'high - base > 1 then
+                round := fract (frac'high - base - 1) and
+                         (fract (frac'high - base)
+                          or (or (fract (frac'high - base - 2 downto 0))));
+              else
+                round := fract (frac'high - base - 1) and
+                         fract (frac'high - base);
+              end if;
+            when round_inf =>
+              round := fract(frac'high - base - 1) and not isign;
+            when round_neginf =>
+              round := fract(frac'high - base - 1) and isign;
+            when others =>
+              round := '0';
+          end case;
+          if round = '1' then
+            result := result + 1;
+          end if;
+        end if;
+        if isign = '1' then
+          result := - result;
+        end if;
+    end case classcase;
+    return result;
+  end function to_integer;
+
+  -- to_unsigned (float)
+  function to_unsigned (
+    arg                  : UNRESOLVED_float;  -- floating point input
+    constant size        : NATURAL;     -- length of output
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error)  -- check for errors
+    return UNRESOLVED_UNSIGNED
+  is
+    variable validfp : valid_fpstate;   -- Valid FP state
+    variable frac    : UNRESOLVED_UNSIGNED (size-1 downto 0);  -- Fraction
+    variable sign    : STD_ULOGIC;      -- not used
+  begin
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | nan | quiet_nan =>
+        frac := (others => 'X');
+      when pos_zero | neg_inf | neg_zero | neg_normal | pos_denormal | neg_denormal =>
+        frac := (others => '0');        -- return 0
+      when pos_inf =>
+        frac := (others => '1');
+      when others =>
+        float_to_unsigned (
+          arg         => arg,
+          frac        => frac,
+          sign        => sign,
+          denormalize => false,
+          bias        => 0,
+          round_style => round_style);
+    end case classcase;
+    return (frac);
+  end function to_unsigned;
+
+  -- to_signed (float)
+  function to_signed (
+    arg                  : UNRESOLVED_float;  -- floating point input
+    constant size        : NATURAL;     -- length of output
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error)  -- check for errors
+    return UNRESOLVED_SIGNED
+  is
+    variable sign    : STD_ULOGIC;      -- true if negative
+    variable validfp : valid_fpstate;   -- Valid FP state
+    variable frac    : UNRESOLVED_UNSIGNED (size-1 downto 0);  -- Fraction
+    variable result  : UNRESOLVED_SIGNED (size-1 downto 0);
+  begin
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | nan | quiet_nan =>
+        result := (others => 'X');
+      when pos_zero | neg_zero | pos_denormal | neg_denormal =>
+        result := (others => '0');      -- return 0
+      when pos_inf =>
+        result               := (others => '1');
+        result (result'high) := '0';
+      when neg_inf =>
+        result               := (others => '0');
+        result (result'high) := '1';
+      when others =>
+        float_to_unsigned (
+          arg         => arg,
+          sign        => sign,
+          frac        => frac,
+          denormalize => false,
+          bias        => 0,
+          round_style => round_style);
+        result (size-1)          := '0';
+        result (size-2 downto 0) := UNRESOLVED_SIGNED(frac (size-2 downto 0));
+        if sign = '1' then
+          -- Because the most negative signed number is 1 less than the most
+          -- positive signed number, we need this code.
+          if frac(frac'high) = '1' then       -- return most negative number
+            result               := (others => '0');
+            result (result'high) := '1';
+          else
+            result := -result;
+          end if;
+        else
+          if frac(frac'high) = '1' then       -- return most positive number
+            result               := (others => '1');
+            result (result'high) := '0';
+          end if;
+        end if;
+    end case classcase;
+    return result;
+  end function to_signed;
+
+  -- purpose: Converts a float to ufixed
+  function to_ufixed (
+    arg                     : UNRESOLVED_float;            -- fp input
+    constant left_index     : INTEGER;  -- integer part
+    constant right_index    : INTEGER;  -- fraction part
+    constant overflow_style : fixed_overflow_style_type := fixed_overflow_style;  -- saturate
+    constant round_style    : fixed_round_style_type    := fixed_round_style;  -- rounding
+    constant check_error    : BOOLEAN                   := float_check_error;  -- check for errors
+    constant denormalize    : BOOLEAN                   := float_denormalize)
+    return UNRESOLVED_ufixed
+  is
+    constant fraction_width : INTEGER := -mine(arg'low, arg'low);  -- length of FP output fraction
+    constant exponent_width : INTEGER := arg'high;  -- length of FP output exponent
+    constant size           : INTEGER := left_index - right_index + 4;  -- unsigned size
+    variable expon_base     : INTEGER;  -- exponent offset
+    variable validfp        : valid_fpstate;               -- Valid FP state
+    variable exp            : INTEGER;  -- Exponent
+    variable expon          : UNSIGNED (exponent_width-1 downto 0);  -- Vectorized exponent
+    -- Base to divide fraction by
+    variable frac           : UNSIGNED (size-1 downto 0) := (others => '0');  -- Fraction
+    variable frac_shift     : UNSIGNED (size-1 downto 0);  -- Fraction shifted
+    variable shift          : INTEGER;
+    variable result_big     : UNRESOLVED_ufixed (left_index downto right_index-3);
+    variable result         : UNRESOLVED_ufixed (left_index downto right_index);  -- result
+  begin  -- function to_ufixed
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | nan | quiet_nan =>
+        frac := (others => 'X');
+      when pos_zero | neg_inf | neg_zero | neg_normal | neg_denormal =>
+        frac := (others => '0');        -- return 0
+      when pos_inf =>
+        frac := (others => '1');        -- always saturate
+      when others =>
+        expon_base := 2**(exponent_width-1) -1;            -- exponent offset
+        -- Figure out the fraction
+        if (validfp = pos_denormal) and denormalize then
+          exp              := -expon_base +1;
+          frac (frac'high) := '0';      -- Remove the "1.0".
+        else
+          -- exponent /= '0', normal floating point
+          expon                   := UNSIGNED(arg (exponent_width-1 downto 0));
+          expon(exponent_width-1) := not expon(exponent_width-1);
+          exp                     := to_integer (SIGNED(expon)) +1;
+          frac (frac'high)        := '1';   -- Add the "1.0".
+        end if;
+        shift := (frac'high - 3 + right_index) - exp;
+        if fraction_width > frac'high then  -- Can only use size-2 bits
+          frac (frac'high-1 downto 0) := UNSIGNED (to_slv (arg(-1 downto
+                                                               -frac'high)));
+        else                            -- can use all bits
+          frac (frac'high-1 downto frac'high-fraction_width) :=
+            UNSIGNED (to_slv (arg(-1 downto -fraction_width)));
+        end if;
+        frac_shift := frac srl shift;
+        if shift < 0 then               -- Overflow
+          frac := (others => '1');
+        else
+          frac := frac_shift;
+        end if;
+    end case classcase;
+    result_big := to_ufixed (
+      arg         => STD_ULOGIC_VECTOR(frac),
+      left_index  => left_index,
+      right_index => (right_index-3));
+    result := resize (arg            => result_big,
+                      left_index     => left_index,
+                      right_index    => right_index,
+                      round_style    => round_style,
+                      overflow_style => overflow_style);
+    return result;
+  end function to_ufixed;
+
+  -- purpose: Converts a float to sfixed
+  function to_sfixed (
+    arg                     : UNRESOLVED_float;  -- fp input
+    constant left_index     : INTEGER;  -- integer part
+    constant right_index    : INTEGER;  -- fraction part
+    constant overflow_style : fixed_overflow_style_type := fixed_overflow_style;  -- saturate
+    constant round_style    : fixed_round_style_type    := fixed_round_style;  -- rounding
+    constant check_error    : BOOLEAN                   := float_check_error;  -- check for errors
+    constant denormalize    : BOOLEAN                   := float_denormalize)
+    return UNRESOLVED_sfixed
+  is
+    constant fraction_width : INTEGER := -mine(arg'low, arg'low);  -- length of FP output fraction
+    constant exponent_width : INTEGER := arg'high;  -- length of FP output exponent
+    constant size           : INTEGER := left_index - right_index + 4;  -- unsigned size
+    variable expon_base     : INTEGER;  -- exponent offset
+    variable validfp        : valid_fpstate;     -- Valid FP state
+    variable exp            : INTEGER;  -- Exponent
+    variable sign           : BOOLEAN;  -- true if negative
+    variable expon          : UNSIGNED (exponent_width-1 downto 0);  -- Vectorized exponent
+    -- Base to divide fraction by
+    variable frac           : UNSIGNED (size-2 downto 0) := (others => '0');  -- Fraction
+    variable frac_shift     : UNSIGNED (size-2 downto 0);  -- Fraction shifted
+    variable shift          : INTEGER;
+    variable rsigned        : SIGNED (size-1 downto 0);  -- signed version of result
+    variable result_big     : UNRESOLVED_sfixed (left_index downto right_index-3);
+    variable result         : UNRESOLVED_sfixed (left_index downto right_index)
+      := (others => '0');  -- result
+  begin  -- function to_sfixed
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | nan | quiet_nan =>
+        result := (others => 'X');
+      when pos_zero | neg_zero =>
+        result := (others => '0');      -- return 0
+      when neg_inf =>
+        result (left_index) := '1';     -- return smallest negative number
+      when pos_inf =>
+        result              := (others => '1');  -- return largest number
+        result (left_index) := '0';
+      when others =>
+        expon_base := 2**(exponent_width-1) -1;  -- exponent offset
+        if arg(exponent_width) = '0' then
+          sign := false;
+        else
+          sign := true;
+        end if;
+        -- Figure out the fraction
+        if (validfp = pos_denormal or validfp = neg_denormal)
+          and denormalize then
+          exp              := -expon_base +1;
+          frac (frac'high) := '0';      -- Add the "1.0".
+        else
+          -- exponent /= '0', normal floating point
+          expon                   := UNSIGNED(arg (exponent_width-1 downto 0));
+          expon(exponent_width-1) := not expon(exponent_width-1);
+          exp                     := to_integer (SIGNED(expon)) +1;
+          frac (frac'high)        := '1';        -- Add the "1.0".
+        end if;
+        shift := (frac'high - 3 + right_index) - exp;
+        if fraction_width > frac'high then       -- Can only use size-2 bits
+          frac (frac'high-1 downto 0) := UNSIGNED (to_slv (arg(-1 downto
+                                                               -frac'high)));
+        else                            -- can use all bits
+          frac (frac'high-1 downto frac'high-fraction_width) :=
+            UNSIGNED (to_slv (arg(-1 downto -fraction_width)));
+        end if;
+        frac_shift := frac srl shift;
+        if shift < 0 then               -- Overflow
+          frac := (others => '1');
+        else
+          frac := frac_shift;
+        end if;
+        if not sign then
+          rsigned := SIGNED("0" & frac);
+        else
+          rsigned := -(SIGNED("0" & frac));
+        end if;
+        result_big := to_sfixed (
+          arg         => STD_LOGIC_VECTOR(rsigned),
+          left_index  => left_index,
+          right_index => (right_index-3));
+        result := resize (arg            => result_big,
+                          left_index     => left_index,
+                          right_index    => right_index,
+                          round_style    => round_style,
+                          overflow_style => overflow_style);
+    end case classcase;
+    return result;
+  end function to_sfixed;
+
+  -- size_res versions
+  -- float to unsigned
+  function to_unsigned (
+    arg                  : UNRESOLVED_float;  -- floating point input
+    size_res             : UNRESOLVED_UNSIGNED;
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error)  -- check for errors
+    return UNRESOLVED_UNSIGNED
+  is
+    variable result : UNRESOLVED_UNSIGNED (size_res'range);
+  begin
+    if (SIZE_RES'length = 0) then
+      return result;
+    else
+      result := to_unsigned (
+        arg         => arg,
+        size        => size_res'length,
+        round_style => round_style,
+        check_error => check_error);
+      return result;
+    end if;
+  end function to_unsigned;
+
+  -- float to signed
+  function to_signed (
+    arg                  : UNRESOLVED_float;  -- floating point input
+    size_res             : UNRESOLVED_SIGNED;
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error)  -- check for errors
+    return UNRESOLVED_SIGNED
+  is
+    variable result : UNRESOLVED_SIGNED (size_res'range);
+  begin
+    if (SIZE_RES'length = 0) then
+      return result;
+    else
+      result := to_signed (
+        arg         => arg,
+        size        => size_res'length,
+        round_style => round_style,
+        check_error => check_error);
+      return result;
+    end if;
+  end function to_signed;
+
+  -- purpose: Converts a float to unsigned fixed point
+  function to_ufixed (
+    arg                     : UNRESOLVED_float;  -- fp input
+    size_res                : UNRESOLVED_ufixed;
+    constant overflow_style : fixed_overflow_style_type := fixed_overflow_style;  -- saturate
+    constant round_style    : fixed_round_style_type    := fixed_round_style;  -- rounding
+    constant check_error    : BOOLEAN                   := float_check_error;  -- check for errors
+    constant denormalize    : BOOLEAN                   := float_denormalize)
+    return UNRESOLVED_ufixed
+  is
+    variable result : UNRESOLVED_ufixed (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_ufixed (
+        arg            => arg,
+        left_index     => size_res'high,
+        right_index    => size_res'low,
+        overflow_style => overflow_style,
+        round_style    => round_style,
+        check_error    => check_error,
+        denormalize    => denormalize);
+      return result;
+    end if;
+  end function to_ufixed;
+
+  -- float to signed fixed point
+  function to_sfixed (
+    arg                     : UNRESOLVED_float;  -- fp input
+    size_res                : UNRESOLVED_sfixed;
+    constant overflow_style : fixed_overflow_style_type := fixed_overflow_style;  -- saturate
+    constant round_style    : fixed_round_style_type    := fixed_round_style;  -- rounding
+    constant check_error    : BOOLEAN                   := float_check_error;  -- check for errors
+    constant denormalize    : BOOLEAN                   := float_denormalize)
+    return UNRESOLVED_sfixed
+  is
+    variable result : UNRESOLVED_sfixed (size_res'left downto size_res'right);
+  begin
+    if (result'length < 1) then
+      return result;
+    else
+      result := to_sfixed (
+        arg            => arg,
+        left_index     => size_res'high,
+        right_index    => size_res'low,
+        overflow_style => overflow_style,
+        round_style    => round_style,
+        check_error    => check_error,
+        denormalize    => denormalize);
+      return result;
+    end if;
+  end function to_sfixed;
+
+  -- to_real (float)
+  -- typically not Synthesizable unless the input is a constant.
+  function to_real (
+    arg                  : UNRESOLVED_float;        -- floating point input
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return REAL
+  is
+    constant fraction_width : INTEGER := -mine(arg'low, arg'low);  -- length of FP output fraction
+    constant exponent_width : INTEGER := arg'high;  -- length of FP output exponent
+    variable sign           : REAL;     -- Sign, + or - 1
+    variable exp            : INTEGER;  -- Exponent
+    variable expon_base     : INTEGER;  -- exponent offset
+    variable frac           : REAL    := 0.0;       -- Fraction
+    variable validfp        : valid_fpstate;        -- Valid FP state
+    variable expon          : UNSIGNED (exponent_width - 1 downto 0)
+      := (others => '1');               -- Vectorized exponent
+  begin
+    validfp := classfp (arg, check_error);
+    classcase : case validfp is
+      when isx | pos_zero | neg_zero | nan | quiet_nan =>
+        return 0.0;
+      when neg_inf =>
+        return REAL'low;                -- Negative infinity.
+      when pos_inf =>
+        return REAL'high;               -- Positive infinity
+      when others =>
+        expon_base := 2**(exponent_width-1) -1;
+        if to_X01(arg(exponent_width)) = '0' then
+          sign := 1.0;
+        else
+          sign := -1.0;
+        end if;
+        -- Figure out the fraction
+        for i in 0 to fraction_width-1 loop
+          if to_X01(arg (-1 - i)) = '1' then
+            frac := frac + (2.0 **(-1 - i));
+          end if;
+        end loop;  -- i
+        if validfp = pos_normal or validfp = neg_normal or not denormalize then
+          -- exponent /= '0', normal floating point
+          expon                   := UNSIGNED(arg (exponent_width-1 downto 0));
+          expon(exponent_width-1) := not expon(exponent_width-1);
+          exp                     := to_integer (SIGNED(expon)) +1;
+          sign                    := sign * (2.0 ** exp) * (1.0 + frac);
+        else  -- exponent = '0', IEEE extended floating point
+          exp  := 1 - expon_base;
+          sign := sign * (2.0 ** exp) * frac;
+        end if;
+        return sign;
+    end case classcase;
+  end function to_real;
+
+  -- For Verilog compatability
+  function realtobits (arg : REAL) return STD_ULOGIC_VECTOR is
+    variable result : float64;          -- 64 bit floating point
+  begin
+    result := to_float (arg => arg,
+                        exponent_width => float64'high,
+                        fraction_width => -float64'low);
+    return to_sulv (result);
+  end function realtobits;
+
+  function bitstoreal (arg : STD_ULOGIC_VECTOR) return REAL is
+    variable arg64 : float64;           -- arg converted to float
+  begin
+    arg64 := to_float (arg => arg,
+                       exponent_width => float64'high,
+                       fraction_width => -float64'low);
+    return to_real (arg64);
+  end function bitstoreal;
+
+  -- purpose: Removes meta-logical values from FP string
+  function to_01 (
+    arg  : UNRESOLVED_float;            -- floating point input
+    XMAP : STD_LOGIC := '0')
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (arg'range);
+  begin  -- function to_01
+    if (arg'length < 1) then
+      assert NO_WARNING
+        report FLOAT_GENERIC_PKG'instance_name
+        & "TO_01: null detected, returning NULL"
+        severity warning;
+      return NAFP;
+    end if;
+    result := UNRESOLVED_float (STD_LOGIC_VECTOR(to_01(UNSIGNED(to_slv(arg)), XMAP)));
+    return result;
+  end function to_01;
+
+  function Is_X
+    (arg : UNRESOLVED_float)
+    return BOOLEAN is
+  begin
+    return Is_X (to_slv(arg));
+  end function Is_X;
+
+  function to_X01 (arg : UNRESOLVED_float) return UNRESOLVED_float is
+    variable result : UNRESOLVED_float (arg'range);
+  begin
+    if (arg'length < 1) then
+      assert NO_WARNING
+        report FLOAT_GENERIC_PKG'instance_name
+        & "TO_X01: null detected, returning NULL"
+        severity warning;
+      return NAFP;
+    else
+      result := UNRESOLVED_float (to_X01(to_slv(arg)));
+      return result;
+    end if;
+  end function to_X01;
+
+  function to_X01Z (arg : UNRESOLVED_float) return UNRESOLVED_float is
+    variable result : UNRESOLVED_float (arg'range);
+  begin
+    if (arg'length < 1) then
+      assert NO_WARNING
+        report FLOAT_GENERIC_PKG'instance_name
+        & "TO_X01Z: null detected, returning NULL"
+        severity warning;
+      return NAFP;
+    else
+      result := UNRESOLVED_float (to_X01Z(to_slv(arg)));
+      return result;
+    end if;
+  end function to_X01Z;
+
+  function to_UX01 (arg : UNRESOLVED_float) return UNRESOLVED_float is
+    variable result : UNRESOLVED_float (arg'range);
+  begin
+    if (arg'length < 1) then
+      assert NO_WARNING
+        report FLOAT_GENERIC_PKG'instance_name
+        & "TO_UX01: null detected, returning NULL"
+        severity warning;
+      return NAFP;
+    else
+      result := UNRESOLVED_float (to_UX01(to_slv(arg)));
+      return result;
+    end if;
+  end function to_UX01;
+
+  -- These allows the base math functions to use the default values
+  -- of their parameters.  Thus they do full IEEE floating point.
+  function "+" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return add (l, r);
+  end function "+";
+
+  function "-" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return subtract (l, r);
+  end function "-";
+
+  function "*" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return multiply (l, r);
+  end function "*";
+
+  function "/" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return divide (l, r);
+  end function "/";
+
+  function "rem" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return remainder (l, r);
+  end function "rem";
+
+  function "mod" (l, r : UNRESOLVED_float) return UNRESOLVED_float is
+  begin
+    return modulo (l, r);
+  end function "mod";
+
+  -- overloaded versions
+  function "+" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return add (l, r_float);
+  end function "+";
+
+  function "+" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return add (l_float, r);
+  end function "+";
+
+  function "+" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return add (l, r_float);
+  end function "+";
+
+  function "+" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return add (l_float, r);
+  end function "+";
+
+  function "-" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return subtract (l, r_float);
+  end function "-";
+
+  function "-" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return subtract (l_float, r);
+  end function "-";
+
+  function "-" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return subtract (l, r_float);
+  end function "-";
+
+  function "-" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return subtract (l_float, r);
+  end function "-";
+
+  function "*" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return multiply (l, r_float);
+  end function "*";
+
+  function "*" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return multiply (l_float, r);
+  end function "*";
+
+  function "*" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return multiply (l, r_float);
+  end function "*";
+
+  function "*" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return multiply (l_float, r);
+  end function "*";
+
+  function "/" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return divide (l, r_float);
+  end function "/";
+
+  function "/" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return divide (l_float, r);
+  end function "/";
+
+  function "/" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return divide (l, r_float);
+  end function "/";
+
+  function "/" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return divide (l_float, r);
+  end function "/";
+
+  function "rem" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return remainder (l, r_float);
+  end function "rem";
+
+  function "rem" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return remainder (l_float, r);
+  end function "rem";
+
+  function "rem" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return remainder (l, r_float);
+  end function "rem";
+
+  function "rem" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return remainder (l_float, r);
+  end function "rem";
+
+  function "mod" (l : UNRESOLVED_float; r : REAL) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return modulo (l, r_float);
+  end function "mod";
+
+  function "mod" (l : REAL; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return modulo (l_float, r);
+  end function "mod";
+
+  function "mod" (l : UNRESOLVED_float; r : INTEGER) return UNRESOLVED_float is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return modulo (l, r_float);
+  end function "mod";
+
+  function "mod" (l : INTEGER; r : UNRESOLVED_float) return UNRESOLVED_float is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return modulo (l_float, r);
+  end function "mod";
+
+  function "=" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return eq (l, r_float);
+  end function "=";
+
+  function "/=" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return ne (l, r_float);
+  end function "/=";
+
+  function ">=" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return ge (l, r_float);
+  end function ">=";
+
+  function "<=" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return le (l, r_float);
+  end function "<=";
+
+  function ">" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return gt (l, r_float);
+  end function ">";
+
+  function "<" (l : UNRESOLVED_float; r : REAL) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return lt (l, r_float);
+  end function "<";
+
+  function "=" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return eq (l_float, r);
+  end function "=";
+
+  function "/=" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return ne (l_float, r);
+  end function "/=";
+
+  function ">=" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return ge (l_float, r);
+  end function ">=";
+
+  function "<=" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return le (l_float, r);
+  end function "<=";
+
+  function ">" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return gt (l_float, r);
+  end function ">";
+
+  function "<" (l : REAL; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return lt (l_float, r);
+  end function "<";
+
+  function "=" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return eq (l, r_float);
+  end function "=";
+
+  function "/=" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return ne (l, r_float);
+  end function "/=";
+
+  function ">=" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return ge (l, r_float);
+  end function ">=";
+
+  function "<=" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return le (l, r_float);
+  end function "<=";
+
+  function ">" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return gt (l, r_float);
+  end function ">";
+
+  function "<" (l : UNRESOLVED_float; r : INTEGER) return BOOLEAN is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return lt (l, r_float);
+  end function "<";
+
+  function "=" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return eq (l_float, r);
+  end function "=";
+
+  function "/=" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return ne (l_float, r);
+  end function "/=";
+
+  function ">=" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return ge (l_float, r);
+  end function ">=";
+
+  function "<=" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return le (l_float, r);
+  end function "<=";
+
+  function ">" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return gt (l_float, r);
+  end function ">";
+
+  function "<" (l : INTEGER; r : UNRESOLVED_float) return BOOLEAN is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float(l, r'high, -r'low);
+    return lt (l_float, r);
+  end function "<";
+
+  -- ?= overloads
+  function "?=" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?= r_float;
+  end function "?=";
+
+  function "?/=" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?/= r_float;
+  end function "?/=";
+
+  function "?>" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?> r_float;
+  end function "?>";
+
+  function "?>=" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?>= r_float;
+  end function "?>=";
+
+  function "?<" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?< r_float;
+  end function "?<";
+
+  function "?<=" (l : UNRESOLVED_float; r : REAL) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?<= r_float;
+  end function "?<=";
+
+  -- real and float
+  function "?=" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?= r;
+  end function "?=";
+
+  function "?/=" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?/= r;
+  end function "?/=";
+
+  function "?>" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?> r;
+  end function "?>";
+
+  function "?>=" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?>= r;
+  end function "?>=";
+
+  function "?<" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?< r;
+  end function "?<";
+
+  function "?<=" (l : REAL; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?<= r;
+  end function "?<=";
+
+  -- ?= overloads
+  function "?=" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?= r_float;
+  end function "?=";
+
+  function "?/=" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?/= r_float;
+  end function "?/=";
+
+  function "?>" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?> r_float;
+  end function "?>";
+
+  function "?>=" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?>= r_float;
+  end function "?>=";
+
+  function "?<" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?< r_float;
+  end function "?<";
+
+  function "?<=" (l : UNRESOLVED_float; r : INTEGER) return STD_ULOGIC is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return l ?<= r_float;
+  end function "?<=";
+
+  -- integer and float
+  function "?=" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?= r;
+  end function "?=";
+
+  function "?/=" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?/= r;
+  end function "?/=";
+
+  function "?>" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?> r;
+  end function "?>";
+
+  function "?>=" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?>= r;
+  end function "?>=";
+
+  function "?<" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?< r;
+  end function "?<";
+
+  function "?<=" (l : INTEGER; r : UNRESOLVED_float) return STD_ULOGIC is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return l_float ?<= r;
+  end function "?<=";
+
+  -- minimum and maximum overloads
+  function minimum (l : UNRESOLVED_float; r : REAL)
+    return UNRESOLVED_float
+  is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return minimum (l, r_float);
+  end function minimum;
+
+  function maximum (l : UNRESOLVED_float; r : REAL)
+    return UNRESOLVED_float
+  is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return maximum (l, r_float);
+  end function maximum;
+
+  function minimum (l : REAL; r : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return minimum (l_float, r);
+  end function minimum;
+
+  function maximum (l : REAL; r : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return maximum (l_float, r);
+  end function maximum;
+
+  function minimum (l : UNRESOLVED_float; r : INTEGER)
+    return UNRESOLVED_float
+  is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return minimum (l, r_float);
+  end function minimum;
+
+  function maximum (l : UNRESOLVED_float; r : INTEGER)
+    return UNRESOLVED_float
+  is
+    variable r_float : UNRESOLVED_float (l'range);
+  begin
+    r_float := to_float (r, l'high, -l'low);
+    return maximum (l, r_float);
+  end function maximum;
+
+  function minimum (l : INTEGER; r : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return minimum (l_float, r);
+  end function minimum;
+
+  function maximum (l : INTEGER; r : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable l_float : UNRESOLVED_float (r'range);
+  begin
+    l_float := to_float (l, r'high, -r'low);
+    return maximum (l_float, r);
+  end function maximum;
+
+  ----------------------------------------------------------------------------
+  -- logical functions
+  ----------------------------------------------------------------------------
+  function "not" (L : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+    RESULT := not to_sulv(L);
+    return to_float (RESULT, L'high, -L'low);
+  end function "not";
+
+  function "and" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+   begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) and to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """and"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "and";
+
+  function "or" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) or to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """or"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "or";
+
+  function "nand" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) nand to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """nand"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "nand";
+
+  function "nor" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) nor to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """nor"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "nor";
+
+  function "xor" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) xor to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """xor"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "xor";
+
+  function "xnor" (L, R : UNRESOLVED_float) return UNRESOLVED_float is
+    variable RESULT : STD_ULOGIC_VECTOR(L'length-1 downto 0);  -- force downto
+  begin
+     if (L'high = R'high and L'low = R'low) then
+      RESULT := to_sulv(L) xnor to_sulv(R);
+    else
+      assert NO_WARNING
+        report float_generic_pkg'instance_name
+        & """xnor"": Range error L'RANGE /= R'RANGE"
+        severity warning;
+      RESULT := (others => 'X');
+    end if;
+    return to_float (RESULT, L'high, -L'low);
+  end function "xnor";
+
+  -- Vector and std_ulogic functions, same as functions in numeric_std
+  function "and" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L and to_sulv(R));
+    return result;
+  end function "and";
+
+  function "and" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) and R);
+    return result;
+  end function "and";
+
+  function "or" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L or to_sulv(R));
+    return result;
+  end function "or";
+
+  function "or" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) or R);
+    return result;
+  end function "or";
+
+  function "nand" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L nand to_sulv(R));
+    return result;
+  end function "nand";
+
+  function "nand" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) nand R);
+    return result;
+  end function "nand";
+
+  function "nor" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L nor to_sulv(R));
+    return result;
+  end function "nor";
+
+  function "nor" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) nor R);
+    return result;
+  end function "nor";
+
+  function "xor" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L xor to_sulv(R));
+    return result;
+  end function "xor";
+
+  function "xor" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) xor R);
+    return result;
+  end function "xor";
+
+  function "xnor" (L : STD_ULOGIC; R : UNRESOLVED_float)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (R'range);
+  begin
+    result := UNRESOLVED_float (L xnor to_sulv(R));
+    return result;
+  end function "xnor";
+
+  function "xnor" (L : UNRESOLVED_float; R : STD_ULOGIC)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (L'range);
+  begin
+    result := UNRESOLVED_float (to_sulv(L) xnor R);
+    return result;
+  end function "xnor";
+
+  -- Reduction operators, same as numeric_std functions
+
+  function "and" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return and to_sulv(l);
+  end function "and";
+
+  function "nand" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return nand to_sulv(l);
+  end function "nand";
+
+  function "or" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return or to_sulv(l);
+  end function "or";
+
+  function "nor" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return nor to_sulv(l);
+  end function "nor";
+
+  function "xor" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return xor to_sulv(l);
+  end function "xor";
+
+  function "xnor" (l : UNRESOLVED_float) return STD_ULOGIC is
+  begin
+    return xnor to_sulv(l);
+  end function "xnor";
+
+  -----------------------------------------------------------------------------
+  -- Recommended Functions from the IEEE 754 Appendix
+  -----------------------------------------------------------------------------
+  -- returns x with the sign of y.
+  function Copysign (
+    x, y : UNRESOLVED_float)            -- floating point input
+    return UNRESOLVED_float is
+  begin
+    return y(y'high) & x (x'high-1 downto x'low);
+  end function Copysign;
+
+  -- Returns y * 2**n for integral values of N without computing 2**n
+  function Scalb (
+    y                    : UNRESOLVED_float;      -- floating point input
+    N                    : INTEGER;     -- exponent to add    
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL := -mine(y'low, y'low);  -- length of FP output fraction
+    constant exponent_width : NATURAL := y'high;  -- length of FP output exponent
+    variable arg, result    : UNRESOLVED_float (exponent_width downto -fraction_width);  -- internal argument
+    variable expon          : SIGNED (exponent_width-1 downto 0);  -- Vectorized exp
+    variable exp            : SIGNED (exponent_width downto 0);
+    variable ufract         : UNSIGNED (fraction_width downto 0);
+    constant expon_base     : SIGNED (exponent_width-1 downto 0)
+      := gen_expon_base(exponent_width);          -- exponent offset
+    variable fptype : valid_fpstate;
+  begin
+    -- This can be done by simply adding N to the exponent.
+    arg    := to_01 (y, 'X');
+    fptype := classfp(arg, check_error);
+    classcase : case fptype is
+      when isx =>
+        result := (others => 'X');
+      when nan | quiet_nan =>
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        result := qnanfp (fraction_width => fraction_width,
+                          exponent_width => exponent_width);
+      when others =>
+        break_number (
+          arg         => arg,
+          fptyp       => fptype,
+          denormalize => denormalize,
+          fract       => ufract,
+          expon       => expon);
+        exp := resize (expon, exp'length) + N;
+        result := normalize (
+          fract          => ufract,
+          expon          => exp,
+          sign           => to_x01 (arg (arg'high)),
+          fraction_width => fraction_width,
+          exponent_width => exponent_width,
+          round_style    => round_style,
+          denormalize    => denormalize,
+          nguard         => 0);
+    end case classcase;
+    return result;
+  end function Scalb;
+
+  -- Returns y * 2**n for integral values of N without computing 2**n
+  function Scalb (
+    y                    : UNRESOLVED_float;   -- floating point input
+    N                    : UNRESOLVED_SIGNED;  -- exponent to add    
+    constant round_style : round_type := float_round_style;  -- rounding option
+    constant check_error : BOOLEAN    := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN    := float_denormalize)  -- Use IEEE extended FP
+    return UNRESOLVED_float
+  is
+    variable n_int : INTEGER;
+  begin
+    n_int := to_integer(N);
+    return Scalb (y           => y,
+                  N           => n_int,
+                  round_style => round_style,
+                  check_error => check_error,
+                  denormalize => denormalize);
+  end function Scalb;
+
+  -- returns the unbiased exponent of x
+  function Logb (
+    x : UNRESOLVED_float)               -- floating point input
+    return INTEGER
+  is
+    constant fraction_width : NATURAL := -mine (x'low, x'low);  -- length of FP output fraction
+    constant exponent_width : NATURAL := x'high;  -- length of FP output exponent
+    variable result         : INTEGER;  -- result
+    variable arg            : UNRESOLVED_float (exponent_width downto -fraction_width);  -- internal argument
+    variable expon          : SIGNED (exponent_width - 1 downto 0);
+    variable fract          : UNSIGNED (fraction_width downto 0);
+    constant expon_base     : INTEGER := 2**(exponent_width-1) -1;  -- exponent
+                                        -- offset +1
+    variable fptype         : valid_fpstate;
+  begin
+    -- Just return the exponent.
+    arg    := to_01 (x, 'X');
+    fptype := classfp(arg);
+    classcase : case fptype is
+      when isx | nan | quiet_nan =>
+        -- Return quiet NAN, IEEE754-1985-7.1,1
+        result := 0;
+      when pos_denormal | neg_denormal =>
+        fract (fraction_width) := '0';
+        fract (fraction_width-1 downto 0) :=
+          UNSIGNED (to_slv(arg(-1 downto -fraction_width)));
+        result := find_leftmost (fract, '1')      -- Find the first "1"
+                  - fraction_width;     -- subtract the length we want
+        result := -expon_base + 1 + result;
+      when others =>
+        expon                   := SIGNED(arg (exponent_width - 1 downto 0));
+        expon(exponent_width-1) := not expon(exponent_width-1);
+        expon                   := expon + 1;
+        result                  := to_integer (expon);
+    end case classcase;
+    return result;
+  end function Logb;
+
+  -- returns the unbiased exponent of x
+  function Logb (
+    x : UNRESOLVED_float)               -- floating point input
+    return UNRESOLVED_SIGNED
+  is
+    constant exponent_width : NATURAL := x'high;  -- length of FP output exponent
+    variable result         : SIGNED (exponent_width - 1 downto 0);  -- result
+  begin
+    -- Just return the exponent.
+    result := to_signed (Logb (x), exponent_width);
+    return result;
+  end function Logb;
+
+  -- returns the next representable neighbor of x in the direction toward y
+  function Nextafter (
+    x, y                 : UNRESOLVED_float;      -- floating point input
+    constant check_error : BOOLEAN := float_check_error;  -- check for errors
+    constant denormalize : BOOLEAN := float_denormalize)
+    return UNRESOLVED_float
+  is
+    constant fraction_width : NATURAL := -mine(x'low, x'low);  -- length of FP output fraction
+    constant exponent_width : NATURAL := x'high;  -- length of FP output exponent
+    function "=" (
+      l, r : UNRESOLVED_float)          -- inputs
+      return BOOLEAN is
+    begin  -- function "="
+      return eq (l           => l,
+                 r           => r,
+                 check_error => false);
+    end function "=";
+    function ">" (
+      l, r : UNRESOLVED_float)          -- inputs
+      return BOOLEAN is
+    begin  -- function ">"
+      return gt (l           => l,
+                 r           => r,
+                 check_error => false);
+    end function ">";
+    variable fract              : UNSIGNED (fraction_width-1 downto 0);
+    variable expon              : UNSIGNED (exponent_width-1 downto 0);
+    variable sign               : STD_ULOGIC;
+    variable result             : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable validfpx, validfpy : valid_fpstate;  -- Valid FP state
+  begin  -- fp_Nextafter
+    -- If Y > X, add one to the fraction, otherwise subtract.
+    validfpx := classfp (x, check_error);
+    validfpy := classfp (y, check_error);
+    if validfpx = isx or validfpy = isx then
+      result := (others => 'X');
+      return result;
+    elsif (validfpx = nan or validfpy = nan) then
+      return nanfp (fraction_width => fraction_width,
+                    exponent_width => exponent_width);
+    elsif (validfpx = quiet_nan or validfpy = quiet_nan) then
+      return qnanfp (fraction_width => fraction_width,
+                     exponent_width => exponent_width);
+    elsif x = y then                    -- Return X
+      return x;
+    else
+      fract := UNSIGNED (to_slv (x (-1 downto -fraction_width)));  -- Fraction
+      expon := UNSIGNED (x (exponent_width - 1 downto 0));     -- exponent
+      sign  := x(exponent_width);       -- sign bit
+      if (y > x) then
+        -- Increase the number given
+        if validfpx = neg_inf then
+          -- return most negative number
+          expon     := (others => '1');
+          expon (0) := '0';
+          fract     := (others => '1');
+        elsif validfpx = pos_zero or validfpx = neg_zero then
+          -- return smallest denormal number
+          sign     := '0';
+          expon    := (others => '0');
+          fract    := (others => '0');
+          fract(0) := '1';
+        elsif validfpx = pos_normal then
+          if and (fract) = '1' then     -- fraction is all "1".
+            if and (expon (exponent_width-1 downto 1)) = '1'
+              and expon (0) = '0' then
+                                        -- Exponent is one away from infinity.
+              assert NO_WARNING
+                report FLOAT_GENERIC_PKG'instance_name
+                & "FP_NEXTAFTER: NextAfter overflow"
+                severity warning;
+              return pos_inffp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+            else
+              expon := expon + 1;
+              fract := (others => '0');
+            end if;
+          else
+            fract := fract + 1;
+          end if;
+        elsif validfpx = pos_denormal then
+          if and (fract) = '1' then     -- fraction is all "1".
+            -- return smallest possible normal number
+            expon    := (others => '0');
+            expon(0) := '1';
+            fract    := (others => '0');
+          else
+            fract := fract + 1;
+          end if;
+        elsif validfpx = neg_normal then
+          if or (fract) = '0' then      -- fraction is all "0".
+            if or (expon (exponent_width-1 downto 1)) = '0' and
+              expon (0) = '1' then      -- Smallest exponent
+              -- return the largest negative denormal number
+              expon := (others => '0');
+              fract := (others => '1');
+            else
+              expon := expon - 1;
+              fract := (others => '1');
+            end if;
+          else
+            fract := fract - 1;
+          end if;
+        elsif validfpx = neg_denormal then
+          if or (fract(fract'high downto 1)) = '0'
+            and fract (0) = '1' then    -- Smallest possible fraction
+            return zerofp (fraction_width => fraction_width,
+                           exponent_width => exponent_width);
+          else
+            fract := fract - 1;
+          end if;
+        end if;
+      else
+        -- Decrease the number
+        if validfpx = pos_inf then
+          -- return most positive number
+          expon     := (others => '1');
+          expon (0) := '0';
+          fract     := (others => '1');
+        elsif validfpx = pos_zero
+          or classfp (x) = neg_zero then
+          -- return smallest negative denormal number
+          sign     := '1';
+          expon    := (others => '0');
+          fract    := (others => '0');
+          fract(0) := '1';
+        elsif validfpx = neg_normal then
+          if and (fract) = '1' then     -- fraction is all "1".
+            if and (expon (exponent_width-1 downto 1)) = '1'
+              and expon (0) = '0' then
+                                        -- Exponent is one away from infinity.
+              assert NO_WARNING
+                report FLOAT_GENERIC_PKG'instance_name
+                & "FP_NEXTAFTER: NextAfter overflow"
+                severity warning;
+              return neg_inffp (fraction_width => fraction_width,
+                                exponent_width => exponent_width);
+            else
+              expon := expon + 1;       -- Fraction overflow
+              fract := (others => '0');
+            end if;
+          else
+            fract := fract + 1;
+          end if;
+        elsif validfpx = neg_denormal then
+          if and (fract) = '1' then     -- fraction is all "1".
+            -- return smallest possible normal number
+            expon    := (others => '0');
+            expon(0) := '1';
+            fract    := (others => '0');
+          else
+            fract := fract + 1;
+          end if;
+        elsif validfpx = pos_normal then
+          if or (fract) = '0' then      -- fraction is all "0".
+            if or (expon (exponent_width-1 downto 1)) = '0' and
+              expon (0) = '1' then      -- Smallest exponent
+              -- return the largest positive denormal number
+              expon := (others => '0');
+              fract := (others => '1');
+            else
+              expon := expon - 1;
+              fract := (others => '1');
+            end if;
+          else
+            fract := fract - 1;
+          end if;
+        elsif validfpx = pos_denormal then
+          if or (fract(fract'high downto 1)) = '0'
+            and fract (0) = '1' then    -- Smallest possible fraction
+            return zerofp (fraction_width => fraction_width,
+                           exponent_width => exponent_width);
+          else
+            fract := fract - 1;
+          end if;
+        end if;
+      end if;
+      result (-1 downto -fraction_width)  := UNRESOLVED_float(fract);
+      result (exponent_width -1 downto 0) := UNRESOLVED_float(expon);
+      result (exponent_width)             := sign;
+      return result;
+    end if;
+  end function Nextafter;
+
+  -- Returns True if X is unordered with Y.
+  function Unordered (
+    x, y : UNRESOLVED_float)            -- floating point input
+    return BOOLEAN
+  is
+    variable lfptype, rfptype : valid_fpstate;
+  begin
+    lfptype := classfp (x);
+    rfptype := classfp (y);
+    if (lfptype = nan or lfptype = quiet_nan or
+        rfptype = nan or rfptype = quiet_nan or
+        lfptype = isx or rfptype = isx) then
+      return true;
+    else
+      return false;
+    end if;
+  end function Unordered;
+
+  function Finite (
+    x : UNRESOLVED_float)
+    return BOOLEAN
+  is
+    variable fp_state : valid_fpstate;  -- fp state
+  begin
+    fp_state := Classfp (x);
+    if (fp_state = pos_inf) or (fp_state = neg_inf) then
+      return true;
+    else
+      return false;
+    end if;
+  end function Finite;
+
+  function Isnan (
+    x : UNRESOLVED_float)
+    return BOOLEAN
+  is
+    variable fp_state : valid_fpstate;  -- fp state
+  begin
+    fp_state := Classfp (x);
+    if (fp_state = nan) or (fp_state = quiet_nan) then
+      return true;
+    else
+      return false;
+    end if;
+  end function Isnan;
+
+  -- Function to return constants.
+  function zerofp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    constant result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                                          -- zero
+  begin
+    return result;
+  end function zerofp;
+
+  function nanfp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                  -- zero
+  begin
+    result (exponent_width-1 downto 0) := (others => '1');
+    -- Exponent all "1"
+    result (-1)                        := '1';  -- MSB of Fraction "1"
+    -- Note: From W. Khan "IEEE Standard 754 for Binary Floating Point"
+    -- The difference between a signaling NAN and a quiet NAN is that
+    -- the MSB of the Fraction is a "1" in a Signaling NAN, and is a
+    -- "0" in a quiet NAN.
+    return result;
+  end function nanfp;
+
+  function qnanfp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                  -- zero
+  begin
+    result (exponent_width-1 downto 0) := (others => '1');
+    -- Exponent all "1"
+    result (-fraction_width)           := '1';  -- LSB of Fraction "1"
+    -- (Could have been any bit)
+    return result;
+  end function qnanfp;
+
+  function pos_inffp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                  -- zero
+  begin
+    result (exponent_width-1 downto 0) := (others => '1');  -- Exponent all "1"
+    return result;
+  end function pos_inffp;
+
+  function neg_inffp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                  -- zero
+  begin
+    result (exponent_width downto 0) := (others => '1');  -- top bits all "1"
+    return result;
+  end function neg_inffp;
+
+  function neg_zerofp (
+    constant exponent_width : NATURAL := float_exponent_width;  -- exponent
+    constant fraction_width : NATURAL := float_fraction_width)  -- fraction
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width) :=
+      (others => '0');                                          -- zero
+  begin
+    result (exponent_width) := '1';
+    return result;
+  end function neg_zerofp;
+
+  -- size_res versions
+  function zerofp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return zerofp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function zerofp;
+
+  function nanfp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return nanfp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function nanfp;
+
+  function qnanfp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return qnanfp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function qnanfp;
+
+  function pos_inffp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return pos_inffp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function pos_inffp;
+
+  function neg_inffp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return neg_inffp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function neg_inffp;
+
+  function neg_zerofp (
+    size_res : UNRESOLVED_float)        -- variable is only use for sizing
+    return UNRESOLVED_float is
+  begin
+    return neg_zerofp (
+      exponent_width => size_res'high,
+      fraction_width => -size_res'low);
+  end function neg_zerofp;
+
+  -- Textio functions
+  -- purpose: writes float into a line (NOTE changed basetype)
+  type MVL9plus is ('U', 'X', '0', '1', 'Z', 'W', 'L', 'H', '-', error);
+  type char_indexed_by_MVL9 is array (STD_ULOGIC) of CHARACTER;
+  type MVL9_indexed_by_char is array (CHARACTER) of STD_ULOGIC;
+  type MVL9plus_indexed_by_char is array (CHARACTER) of MVL9plus;
+
+  constant NBSP         : CHARACTER            := CHARACTER'val(160);  -- space character
+  constant MVL9_to_char : char_indexed_by_MVL9 := "UX01ZWLH-";
+  constant char_to_MVL9 : MVL9_indexed_by_char :=
+    ('U' => 'U', 'X' => 'X', '0' => '0', '1' => '1', 'Z' => 'Z',
+     'W' => 'W', 'L' => 'L', 'H' => 'H', '-' => '-', others => 'U');
+  constant char_to_MVL9plus : MVL9plus_indexed_by_char :=
+    ('U' => 'U', 'X' => 'X', '0' => '0', '1' => '1', 'Z' => 'Z',
+     'W' => 'W', 'L' => 'L', 'H' => 'H', '-' => '-', others => error);
+
+  -- purpose: Skips white space
+  procedure skip_whitespace (
+    L : inout LINE) is
+    variable readOk : BOOLEAN;
+    variable c      : CHARACTER;
+  begin
+    while L /= null and L.all'length /= 0 loop
+      if (L.all(1) = ' ' or L.all(1) = NBSP or L.all(1) = HT) then
+        read (l, c, readOk);
+      else
+        exit;
+      end if;
+    end loop;
+  end procedure skip_whitespace;
+
+  -- purpose: Checks the punctuation in a line
+  procedure check_punctuation (
+    arg   : in  STRING;
+    colon : out BOOLEAN;                -- There was a colon in the line
+    dot   : out BOOLEAN;                -- There was a dot in the line
+    good  : out BOOLEAN;                -- True if enough characters found
+    chars : in INTEGER) is
+    -- Examples.  Legal inputs are "0000000", "0000.000", "0:000:000"
+    alias xarg            : STRING (1 to arg'length) is arg;  -- make it downto range
+    variable icolon, idot : BOOLEAN;    -- internal
+    variable j : INTEGER := 0;          -- charters read
+  begin
+    good   := false;
+    icolon := false;
+    idot   := false;
+    for i in 1 to arg'length loop
+      if xarg(i) = ' ' or xarg(i) = NBSP or xarg(i) = HT or j = chars then
+        exit;
+      elsif xarg(i) = ':' then
+        icolon := true;
+      elsif xarg(i) = '.' then
+        idot := true;
+      elsif xarg (i) /= '_' then
+        j := j + 1;
+      end if;
+    end loop;
+    if j = chars then
+      good := true;                     -- There are enough charactes to read
+    end if;
+    colon := icolon;
+    if idot and icolon then
+      dot := false;
+    else
+      dot := idot;
+    end if;
+  end procedure check_punctuation;
+
+  -- purpose: Searches a line for a ":" and replaces it with a ".".
+  procedure fix_colon (
+    arg   : inout STRING;
+    chars : in integer) is
+    alias xarg            : STRING (1 to arg'length) is arg;  -- make it downto range
+    variable j : INTEGER := 0;          -- charters read
+  begin
+    for i in 1 to arg'length loop
+      if xarg(i) = ' ' or xarg(i) = NBSP or xarg(i) = HT or j > chars then
+        exit;
+      elsif xarg(i) = ':' then
+        xarg (i) := '.';
+      elsif xarg (i) /= '_' then
+        j := j + 1;
+      end if;
+    end loop;
+  end procedure fix_colon;
+
+  procedure WRITE (
+    L         : inout LINE;              -- input line
+    VALUE     : in    UNRESOLVED_float;  -- floating point input
+    JUSTIFIED : in    SIDE  := right;
+    FIELD     : in    WIDTH := 0) is
+    variable s     : STRING(1 to value'high - value'low +3);
+    variable sindx : INTEGER;
+  begin  -- function write
+    s(1)  := MVL9_to_char(STD_ULOGIC(VALUE(VALUE'high)));
+    s(2)  := ':';
+    sindx := 3;
+    for i in VALUE'high-1 downto 0 loop
+      s(sindx) := MVL9_to_char(STD_ULOGIC(VALUE(i)));
+      sindx    := sindx + 1;
+    end loop;
+    s(sindx) := ':';
+    sindx    := sindx + 1;
+    for i in -1 downto VALUE'low loop
+      s(sindx) := MVL9_to_char(STD_ULOGIC(VALUE(i)));
+      sindx    := sindx + 1;
+    end loop;
+    WRITE (L, s, JUSTIFIED, FIELD);
+  end procedure WRITE;
+
+  procedure READ (L : inout LINE; VALUE : out UNRESOLVED_float) is
+    -- Possible data:  0:0000:0000000
+    --                 000000000000
+    variable c      : CHARACTER;
+    variable mv     : UNRESOLVED_float (VALUE'range);
+    variable readOk : BOOLEAN;
+    variable lastu  : BOOLEAN := false;         -- last character was an "_"
+    variable i      : INTEGER;          -- index variable
+  begin  -- READ
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    Skip_whitespace (L);
+    READ (l, c, readOk);
+    if VALUE'length > 0 then
+      i := value'high;
+      readloop : loop
+        if readOk = false then          -- Bail out if there was a bad read
+          report float_generic_pkg'instance_name
+            & "READ(float): "
+            & "Error end of file encountered."
+            severity error;
+          return;
+        elsif c = ' ' or c = CR or c = HT then  -- reading done.
+          if (i /= value'low) then
+            report float_generic_pkg'instance_name
+              & "READ(float): "
+              & "Warning: Value truncated."
+              severity warning;
+            return;
+          end if;
+        elsif c = '_' then
+          if i = value'high then        -- Begins with an "_"
+            report float_generic_pkg'instance_name
+              & "READ(float): "
+              & "String begins with an ""_""" severity error;
+            return;
+          elsif lastu then              -- "__" detected
+            report float_generic_pkg'instance_name
+              & "READ(float): "
+              & "Two underscores detected in input string ""__"""
+              severity error;
+            return;
+          else
+            lastu := true;
+          end if;
+        elsif c = ':' or c = '.' then   -- separator, ignore
+          if not (i = -1 or i = value'high-1) then
+            report float_generic_pkg'instance_name
+              & "READ(float):  "
+              & "Warning: Separator point does not match number format: '"
+              & c & "' encountered at location " & INTEGER'image(i) & "."
+              severity warning;
+          end if;
+          lastu := false;
+        elsif (char_to_MVL9plus(c) = error) then
+          report float_generic_pkg'instance_name
+            & "READ(float): "
+            & "Error: Character '" & c & "' read, expected STD_ULOGIC literal."
+            severity error;
+          return;
+        else
+          mv (i) := char_to_MVL9(c);
+          i := i - 1;
+          if i < value'low then
+            VALUE := mv;
+            return;
+          end if;
+          lastu := false;
+        end if;
+        READ (l, c, readOk);
+      end loop readloop;
+    end if;
+  end procedure READ;
+
+  procedure READ (L : inout LINE; VALUE : out UNRESOLVED_float; GOOD : out BOOLEAN) is
+    -- Possible data:  0:0000:0000000
+    --                 000000000000
+    variable c      : CHARACTER;
+    variable mv     : UNRESOLVED_float (VALUE'range);
+    variable lastu  : BOOLEAN := false;         -- last character was an "_"
+    variable i      : INTEGER;          -- index variable
+    variable readOk : BOOLEAN;
+  begin  -- READ
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    Skip_whitespace (L);
+    READ (l, c, readOk);
+    if VALUE'length > 0 then
+      i := value'high;
+      good := false;
+      readloop : loop
+        if readOk = false then          -- Bail out if there was a bad read
+          return;
+        elsif c = ' ' or c = CR or c = HT then  -- reading done
+          return;
+        elsif c = '_' then
+          if i = 0 then                 -- Begins with an "_"
+            return;
+          elsif lastu then              -- "__" detected
+            return;
+          else
+            lastu := true;
+          end if;
+        elsif c = ':' or c = '.' then   -- separator, ignore
+          -- good := (i = -1 or i = value'high-1);
+          lastu := false;
+        elsif (char_to_MVL9plus(c) = error) then
+          return;
+        else
+          mv (i) := char_to_MVL9(c);
+          i := i - 1;
+          if i < value'low then
+            good  := true;
+            VALUE := mv;
+            return;
+          end if;
+          lastu := false;
+        end if;
+        READ (l, c, readOk);
+      end loop readloop;
+    else
+      good := true;                     -- read into a null array
+    end if;
+  end procedure READ;
+
+  procedure OWRITE (
+    L         : inout LINE;              -- access type (pointer)
+    VALUE     : in    UNRESOLVED_float;  -- value to write
+    JUSTIFIED : in    SIDE  := right;    -- which side to justify text
+    FIELD     : in    WIDTH := 0) is     -- width of field
+  begin
+    WRITE (L         => L,
+           VALUE     => to_ostring(VALUE),
+           JUSTIFIED => JUSTIFIED,
+           FIELD     => FIELD);
+  end procedure OWRITE;
+
+  procedure OREAD (L : inout LINE; VALUE : out UNRESOLVED_float) is
+    constant ne         : INTEGER := ((value'length+2)/3) * 3;   -- pad
+    variable slv        : STD_LOGIC_VECTOR (ne-1 downto 0);      -- slv
+    variable slvu       : ufixed (VALUE'range);  -- Unsigned fixed point
+    variable c          : CHARACTER;
+    variable ok         : BOOLEAN;
+    variable nybble     : STD_LOGIC_VECTOR (2 downto 0);         -- 3 bits
+    variable colon, dot : BOOLEAN;
+  begin
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    Skip_whitespace (L);
+    if VALUE'length > 0 then
+      check_punctuation (arg   => L.all,
+                         colon => colon,
+                         dot   => dot,
+                         good  => ok,
+                         chars => ne/3);
+      if not ok then
+        report float_generic_pkg'instance_name & "OREAD: "
+          & "short string encounted: " & L.all
+          & " needs to have " & integer'image (ne/3)
+          & " valid octal characters."
+          severity error;
+        return;
+      elsif dot then
+        OREAD (L, slvu, ok);            -- read it like a UFIXED number
+        if not ok then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "error encounted reading STRING " & L.all
+            severity error;
+          return;
+        else
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      elsif colon then
+        OREAD (L, nybble, ok);          -- read the sign bit
+        if not ok then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "End of string encountered"
+            severity error;
+          return;
+        elsif nybble (2 downto 1) /= "00" then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "Illegal sign bit STRING encounted "
+            severity error;
+          return;
+        end if;
+        read (l, c, ok);                -- read the colon
+        fix_colon (L.all, ne/3);         -- replaces the colon with a ".".
+        OREAD (L, slvu (slvu'high-1 downto slvu'low), ok);  -- read it like a UFIXED number
+        if not ok then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "error encounted reading STRING " & L.all
+            severity error;
+          return;
+        else
+          slvu (slvu'high) := nybble (0);
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      else
+        OREAD (L, slv, ok);
+        if not ok then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "Error encounted during read"
+            severity error;
+          return;
+        end if;
+        if (or (slv(ne-1 downto VALUE'high-VALUE'low+1)) = '1') then
+          report float_generic_pkg'instance_name & "OREAD: "
+            & "Vector truncated."
+            severity error;
+          return;
+        end if;
+        VALUE := to_float (slv(VALUE'high-VALUE'low downto 0),
+                           VALUE'high, -VALUE'low);
+      end if;
+    end if;
+  end procedure OREAD;
+
+  procedure OREAD(L : inout LINE; VALUE : out UNRESOLVED_float; GOOD : out BOOLEAN) is
+    constant ne         : INTEGER := ((value'length+2)/3) * 3;   -- pad
+    variable slv        : STD_LOGIC_VECTOR (ne-1 downto 0);      -- slv
+    variable slvu       : ufixed (VALUE'range);  -- Unsigned fixed point
+    variable c          : CHARACTER;
+    variable ok         : BOOLEAN;
+    variable nybble     : STD_LOGIC_VECTOR (2 downto 0);         -- 3 bits
+    variable colon, dot : BOOLEAN;
+  begin
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    GOOD  := false;
+    Skip_whitespace (L);
+    if VALUE'length > 0 then
+      check_punctuation (arg   => L.all,
+                         colon => colon,
+                         dot   => dot,
+                         good  => ok,
+                         chars => ne/3);
+      if not ok then
+        return;
+      elsif dot then
+        OREAD (L, slvu, ok);            -- read it like a UFIXED number
+        if not ok then
+          return;
+        else
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      elsif colon then
+        OREAD (L, nybble, ok);          -- read the sign bit
+        if not ok then
+          return;
+        elsif nybble (2 downto 1) /= "00" then
+          return;
+        end if;
+        read (l, c, ok);                -- read the colon
+        fix_colon (L.all, ne/3);         -- replaces the colon with a ".".
+        OREAD (L, slvu (slvu'high-1 downto slvu'low), ok);  -- read it like a UFIXED number
+        if not ok then
+          return;
+        else
+          slvu (slvu'high) := nybble (0);
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      else
+        OREAD (L, slv, ok);
+        if not ok then
+          return;
+        end if;
+        if (or (slv(ne-1 downto VALUE'high-VALUE'low+1)) = '1') then
+          return;
+        end if;
+        VALUE := to_float (slv(VALUE'high-VALUE'low downto 0),
+                           VALUE'high, -VALUE'low);
+      end if;
+      GOOD := true;
+    end if;
+  end procedure OREAD;
+
+  procedure HWRITE (
+    L         : inout LINE;              -- access type (pointer)
+    VALUE     : in    UNRESOLVED_float;  -- value to write
+    JUSTIFIED : in    SIDE  := right;    -- which side to justify text
+    FIELD     : in    WIDTH := 0) is     -- width of field
+  begin
+    WRITE (L         => L,
+           VALUE     => to_hstring(VALUE),
+           JUSTIFIED => JUSTIFIED,
+           FIELD     => FIELD);
+  end procedure HWRITE;
+
+  procedure HREAD (L : inout LINE; VALUE : out UNRESOLVED_float) is
+    constant ne         : INTEGER := ((value'length+3)/4) * 4;   -- pad
+    variable slv        : STD_LOGIC_VECTOR (ne-1 downto 0);      -- slv
+    variable slvu       : ufixed (VALUE'range);  -- Unsigned fixed point
+    variable c          : CHARACTER;
+    variable ok         : BOOLEAN;
+    variable nybble     : STD_LOGIC_VECTOR (3 downto 0);         -- 4 bits
+    variable colon, dot : BOOLEAN;
+  begin
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    Skip_whitespace (L);
+    if VALUE'length > 0 then
+      check_punctuation (arg   => L.all,
+                         colon => colon,
+                         dot   => dot,
+                         good  => ok,
+                         chars => ne/4);
+      if not ok then
+        report float_generic_pkg'instance_name & "HREAD: "
+          & "short string encounted: " & L.all
+          & " needs to have " & integer'image (ne/4)
+          & " valid hex characters."
+          severity error;
+        return;
+      elsif dot then
+        HREAD (L, slvu, ok);            -- read it like a UFIXED number
+        if not ok then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "error encounted reading STRING " & L.all
+            severity error;
+          return;
+        else
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      elsif colon then
+        HREAD (L, nybble, ok);          -- read the sign bit
+        if not ok then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "End of string encountered"
+            severity error;
+          return;
+        elsif nybble (3 downto 1) /= "000" then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "Illegal sign bit STRING encounted "
+            severity error;
+          return;
+        end if;
+        read (l, c, ok);                -- read the colon
+        fix_colon (L.all, ne/4);         -- replaces the colon with a ".".
+        HREAD (L, slvu (slvu'high-1 downto slvu'low), ok);  -- read it like a UFIXED number
+        if not ok then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "error encounted reading STRING " & L.all
+            severity error;
+          return;
+        else
+          slvu (slvu'high) := nybble (0);
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      else
+        HREAD (L, slv, ok);
+        if not ok then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "Error encounted during read"
+            severity error;
+          return;
+        end if;
+        if (or (slv(ne-1 downto VALUE'high-VALUE'low+1)) = '1') then
+          report float_generic_pkg'instance_name & "HREAD: "
+            & "Vector truncated."
+            severity error;
+          return;
+        end if;
+        VALUE := to_float (slv(VALUE'high-VALUE'low downto 0),
+                           VALUE'high, -VALUE'low);
+      end if;
+    end if;
+  end procedure HREAD;
+
+  procedure HREAD (L : inout LINE; VALUE : out UNRESOLVED_float; GOOD : out BOOLEAN) is
+    constant ne         : INTEGER := ((value'length+3)/4) * 4;   -- pad
+    variable slv        : STD_LOGIC_VECTOR (ne-1 downto 0);      -- slv
+    variable slvu       : ufixed (VALUE'range);  -- Unsigned fixed point
+    variable c          : CHARACTER;
+    variable ok         : BOOLEAN;
+    variable nybble     : STD_LOGIC_VECTOR (3 downto 0);         -- 4 bits
+    variable colon, dot : BOOLEAN;
+  begin
+    VALUE := (VALUE'range => 'U');      -- initialize to a "U"
+    GOOD  := false;
+    Skip_whitespace (L);
+    if VALUE'length > 0 then
+      check_punctuation (arg   => L.all,
+                         colon => colon,
+                         dot   => dot,
+                         good  => ok,
+                         chars => ne/4);
+      if not ok then
+        return;
+      elsif dot then
+        HREAD (L, slvu, ok);            -- read it like a UFIXED number
+        if not ok then
+          return;
+        else
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      elsif colon then
+        HREAD (L, nybble, ok);          -- read the sign bit
+        if not ok then
+          return;
+        elsif nybble (3 downto 1) /= "000" then
+          return;
+        end if;
+        read (l, c, ok);                -- read the colon
+        fix_colon (L.all, ne/4);         -- replaces the colon with a ".".
+        HREAD (L, slvu (slvu'high-1 downto slvu'low), ok);  -- read it like a UFIXED number
+        if not ok then
+          return;
+        else
+          slvu (slvu'high) := nybble (0);
+          VALUE := UNRESOLVED_float (slvu);
+        end if;
+      else
+        HREAD (L, slv, ok);
+        if not ok then
+          return;
+        end if;
+        if (or (slv(ne-1 downto VALUE'high-VALUE'low+1)) = '1') then
+          return;
+        end if;
+        VALUE := to_float (slv(VALUE'high-VALUE'low downto 0),
+                           VALUE'high, -VALUE'low);
+      end if;
+      GOOD := true;
+    end if;
+  end procedure HREAD;
+
+  function to_string (value : UNRESOLVED_float) return STRING is
+    variable s     : STRING(1 to value'high - value'low +3);
+    variable sindx : INTEGER;
+  begin  -- function write
+    s(1)  := MVL9_to_char(STD_ULOGIC(VALUE(VALUE'high)));
+    s(2)  := ':';
+    sindx := 3;
+    for i in VALUE'high-1 downto 0 loop
+      s(sindx) := MVL9_to_char(STD_ULOGIC(VALUE(i)));
+      sindx    := sindx + 1;
+    end loop;
+    s(sindx) := ':';
+    sindx    := sindx + 1;
+    for i in -1 downto VALUE'low loop
+      s(sindx) := MVL9_to_char(STD_ULOGIC(VALUE(i)));
+      sindx    := sindx + 1;
+    end loop;
+    return s;
+  end function to_string;
+
+  function to_hstring (value : UNRESOLVED_float) return STRING is
+    variable slv : STD_LOGIC_VECTOR (value'length-1 downto 0);
+  begin
+    floop : for i in slv'range loop
+      slv(i) := to_X01Z (value(i + value'low));
+    end loop floop;
+    return to_hstring (slv);
+  end function to_hstring;
+
+  function to_ostring (value : UNRESOLVED_float) return STRING is
+    variable slv : STD_LOGIC_VECTOR (value'length-1 downto 0);
+  begin
+    floop : for i in slv'range loop
+      slv(i) := to_X01Z (value(i + value'low));
+    end loop floop;
+    return to_ostring (slv);
+  end function to_ostring;
+
+  function from_string (
+    bstring                 : STRING;   -- binary string
+    constant exponent_width : NATURAL := float_exponent_width;
+    constant fraction_width : NATURAL := float_fraction_width)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable L      : LINE;
+    variable good   : BOOLEAN;
+  begin
+    L := new STRING'(bstring);
+    READ (L, result, good);
+    deallocate (L);
+    assert (good)
+      report FLOAT_GENERIC_PKG'instance_name
+      & "from_string: Bad string " & bstring
+      severity error;
+    return result;
+  end function from_string;
+
+  function from_ostring (
+    ostring                 : STRING;   -- Octal string
+    constant exponent_width : NATURAL := float_exponent_width;
+    constant fraction_width : NATURAL := float_fraction_width)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable L      : LINE;
+    variable good   : BOOLEAN;
+  begin
+    L := new STRING'(ostring);
+    OREAD (L, result, good);
+    deallocate (L);
+    assert (good)
+      report FLOAT_GENERIC_PKG'instance_name
+      & "from_ostring: Bad string " & ostring
+      severity error;
+    return result;
+  end function from_ostring;
+
+  function from_hstring (
+    hstring                 : STRING;   -- hex string
+    constant exponent_width : NATURAL := float_exponent_width;
+    constant fraction_width : NATURAL := float_fraction_width)
+    return UNRESOLVED_float
+  is
+    variable result : UNRESOLVED_float (exponent_width downto -fraction_width);
+    variable L      : LINE;
+    variable good   : BOOLEAN;
+  begin
+    L := new STRING'(hstring);
+    HREAD (L, result, good);
+    deallocate (L);
+    assert (good)
+      report FLOAT_GENERIC_PKG'instance_name
+      & "from_hstring: Bad string " & hstring
+      severity error;
+    return result;
+  end function from_hstring;
+
+  function from_string (
+    bstring  : STRING;                  -- binary string
+    size_res : UNRESOLVED_float)        -- used for sizing only 
+    return UNRESOLVED_float is
+  begin
+    return from_string (bstring        => bstring,
+                        exponent_width => size_res'high,
+                        fraction_width => -size_res'low);
+  end function from_string;
+
+  function from_ostring (
+    ostring  : STRING;                  -- Octal string
+    size_res : UNRESOLVED_float)        -- used for sizing only 
+    return UNRESOLVED_float is
+  begin
+    return from_ostring (ostring        => ostring,
+                         exponent_width => size_res'high,
+                         fraction_width => -size_res'low);
+  end function from_ostring;
+
+  function from_hstring (
+    hstring  : STRING;                  -- hex string
+    size_res : UNRESOLVED_float)        -- used for sizing only 
+    return UNRESOLVED_float is
+  begin
+    return from_hstring (hstring        => hstring,
+                         exponent_width => size_res'high,
+                         fraction_width => -size_res'low);
+  end function from_hstring;
+
+end package body float_generic_pkg;