openieee: add generated files.

1 files changed, 2363 insertions, 0 deletions

diff --git a/libraries/openieee/numeric_bit-body.v93 b/libraries/openieee/numeric_bit-body.v93
new file mode 100644
index 000000000..ae4d453ed
--- /dev/null
+++ b/libraries/openieee/numeric_bit-body.v93
@@ -0,0 +1,2363 @@
+--  This -*- vhdl -*- file was generated from numeric_bit-body.proto
+--  This -*- vhdl -*- file is part of GHDL.
+--  IEEE 1076.3 compliant numeric bit package body.
+--  The implementation is based only on the specifications.
+--  Copyright (C) 2015 Tristan Gingold
+--
+--  GHDL is free software; you can redistribute it and/or modify it under
+--  the terms of the GNU General Public License as published by the Free
+--  Software Foundation; either version 2, or (at your option) any later
+--  version.
+--
+--  GHDL is distributed in the hope that it will be useful, but WITHOUT ANY
+--  WARRANTY; without even the implied warranty of MERCHANTABILITY or
+--  FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
+--  for more details.
+--
+--  You should have received a copy of the GNU General Public License
+--  along with GCC; see the file COPYING2.  If not see
+--  <http://www.gnu.org/licenses/>.
+
+package body NUMERIC_BIT is
+  constant NO_WARNING : Boolean := False;
+
+  constant null_unsigned : unsigned (0 downto 1) := (others => '0');
+  constant null_signed   :   signed (0 downto 1) := (others => '0');
+
+  subtype nat1 is natural range 0 to 1;
+
+  type nat1_to_sl_type is array (nat1) of bit;
+  constant nat1_to_01 : nat1_to_sl_type := (0 => '0', 1 => '1');
+
+  subtype sl_01 is bit;
+
+  type carry_array is array (sl_01, sl_01, sl_01) of sl_01;
+  constant compute_carry : carry_array :=
+    ('0' => ('0' => ('0' => '0', '1' => '0'),
+             '1' => ('0' => '0', '1' => '1')),
+     '1' => ('0' => ('0' => '0', '1' => '1'),
+             '1' => ('0' => '1', '1' => '1')));
+  constant compute_sum : carry_array :=
+    ('0' => ('0' => ('0' => '0', '1' => '1'),
+             '1' => ('0' => '1', '1' => '0')),
+     '1' => ('0' => ('0' => '1', '1' => '0'),
+             '1' => ('0' => '0', '1' => '1')));
+
+  type compare_type is (compare_unknown,
+                        compare_lt,
+                        compare_eq,
+                        compare_gt);
+
+  function MAX (L, R : natural) return natural is
+  begin
+    if L > R then
+      return L;
+    else
+      return R;
+    end if;
+  end MAX;
+
+  function TO_INTEGER (ARG : UNSIGNED) return NATURAL
+  is
+    variable res : natural := 0;
+  begin
+    if arg'length = 0 then
+      assert NO_WARNING
+        report "NUMERIC_BIT.TO_INTEGER: null array detected, returning 0"
+        severity warning;
+      return 0;
+    end if;
+
+    for i in arg'range loop
+      res := res + res;
+      if arg (i) = '1' then
+        res := res + 1;
+      end if;
+    end loop;
+
+    return res;
+  end TO_INTEGER;
+
+  function TO_INTEGER (ARG :   SIGNED) return INTEGER
+  is
+    alias argn : SIGNED (ARG'Length -1 downto 0) is arg;
+    variable res : integer := 0;
+    variable b : bit;
+  begin
+    if argn'length = 0 then
+      assert NO_WARNING
+        report "NUMERIC_BIT.TO_INTEGER: null array detected, returning 0"
+        severity warning;
+      return 0;
+    end if;
+    if argn (argn'left) = '1' then
+      --  Negative value
+      b := '0';
+    else
+      b := '1';
+    end if;
+
+    for i in argn'range loop
+      res := res + res;
+      if argn (i) = b then
+        res := res + 1;
+      end if;
+    end loop;
+
+    if b = '0' then
+      --  Avoid overflow.
+      res := -res - 1;
+    end if;
+
+    return res;
+  end TO_INTEGER;
+
+  function TO_UNSIGNED (ARG, SIZE : NATURAL) return UNSIGNED
+  is
+    variable res : UNSIGNED (SIZE - 1 downto 0);
+    variable a : natural := arg;
+    variable d : nat1;
+  begin
+    if size = 0 then
+      return null_unsigned;
+    end if;
+    for i in res'reverse_range loop
+      d := a rem 2;
+      res (i) := nat1_to_01 (d);
+      a := a / 2;
+    end loop;
+    if a /= 0 then
+      assert NO_WARNING
+        report "NUMERIC_BIT.TO_UNSIGNED: vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end TO_UNSIGNED;
+
+  function TO_SIGNED (ARG : INTEGER; SIZE : NATURAL) return SIGNED
+  is
+    variable res : SIGNED (SIZE - 1 downto 0);
+    variable v : integer := arg;
+    variable b0, b1 : bit;
+    variable d : nat1;
+  begin
+    if size = 0 then
+      return null_signed;
+    end if;
+    if arg < 0 then
+      --  Use one complement to avoid overflow:
+      --   -v = (not v) + 1
+      --   not v = -v - 1
+      --   not v = -(v + 1)
+      v := -(arg + 1);
+      b0 := '1';
+      b1 := '0';
+    else
+      v := arg;
+      b0 := '0';
+      b1 := '1';
+    end if;
+
+    for i in res'reverse_range loop
+      d := v rem 2;
+      v := v / 2;
+      if d = 0 then
+        res (i) := b0;
+      else
+        res (i) := b1;
+      end if;
+    end loop;
+    if v /= 0 or res (res'left) /= b0 then
+      assert NO_WARNING
+        report "NUMERIC_BIT.TO_SIGNED: vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end TO_SIGNED;
+
+
+  function "+" (l : UNSIGNED; r : UNSIGNED) return UNSIGNED
+  is
+    constant lft : integer := MAX (l'length, r'length) - 1;
+    subtype res_type is UNSIGNED (lft downto 0);
+    alias la : UNSIGNED (l'length - 1 downto 0) is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if la'left < 0 or ra'left < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '0';
+    for i in 0 to lft loop
+       if i > la'left then
+          lb := '0';
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := '0';
+       else
+          rb := ra (i);
+       end if;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    return res;
+  end "+";
+
+  function "+" (l : SIGNED; r : SIGNED) return SIGNED
+  is
+    constant lft : integer := MAX (l'length, r'length) - 1;
+    subtype res_type is SIGNED (lft downto 0);
+    alias la : SIGNED (l'length - 1 downto 0) is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if la'left < 0 or ra'left < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '0';
+    for i in 0 to lft loop
+       if i > la'left then
+          lb := l (l'left);
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := r (r'left);
+       else
+          rb := ra (i);
+       end if;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    return res;
+  end "+";
+
+  function "+" (l : UNSIGNED; r : NATURAL) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '0';
+    r1 := r;
+    for i in res'reverse_range loop
+       lb := la (i);
+
+       r2 := r1 / 2;
+       rd := r1 - 2 * r2;
+       r1 := r2;
+       rb := nat1_to_01 (rd);
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if r1 /= 0 then
+      assert NO_WARNING
+        report "NUMERIC_STD.""+"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "+";
+
+  function "+" (l : NATURAL; r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (r'length - 1 downto 0);
+    alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '0';
+    l1 := l;
+    for i in res'reverse_range loop
+       rb := ra (i);
+
+       l2 := l1 / 2;
+       ld := l1 - 2 * l2;
+       l1 := l2;
+       lb := nat1_to_01 (ld);
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if l1 /= 0 then
+      assert NO_WARNING
+        report "NUMERIC_STD.""+"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "+";
+
+  function "+" (l : SIGNED; r : INTEGER) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '0';
+    r1 := r;
+    for i in res'reverse_range loop
+       lb := la (i);
+
+       r2 := r1 / 2;
+       if r1 < 0 then
+          rd := 2 * r2 - r1;
+          r1 := r2 - rd;
+        else
+          rd := r1 - 2 * r2;
+          r1 := r2;
+        end if;
+       rb := nat1_to_01 (rd);
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if r1 /= -rmsb then
+      assert NO_WARNING
+        report "NUMERIC_STD.""+"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "+";
+
+  function "+" (l : INTEGER; r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (r'length - 1 downto 0);
+    alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '0';
+    l1 := l;
+    for i in res'reverse_range loop
+       rb := ra (i);
+
+       l2 := l1 / 2;
+       if l1 < 0 then
+          ld := 2 * l2 - l1;
+          l1 := l2 - ld;
+        else
+          ld := l1 - 2 * l2;
+          l1 := l2;
+        end if;
+       lb := nat1_to_01 (ld);
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if l1 /= -lmsb then
+      assert NO_WARNING
+        report "NUMERIC_STD.""+"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "+";
+
+  function "-" (l : UNSIGNED; r : UNSIGNED) return UNSIGNED
+  is
+    constant lft : integer := MAX (l'length, r'length) - 1;
+    subtype res_type is UNSIGNED (lft downto 0);
+    alias la : UNSIGNED (l'length - 1 downto 0) is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if la'left < 0 or ra'left < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '1';
+    for i in 0 to lft loop
+       if i > la'left then
+          lb := '0';
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := '0';
+       else
+          rb := ra (i);
+       end if;
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    return res;
+  end "-";
+
+  function "-" (l : SIGNED; r : SIGNED) return SIGNED
+  is
+    constant lft : integer := MAX (l'length, r'length) - 1;
+    subtype res_type is SIGNED (lft downto 0);
+    alias la : SIGNED (l'length - 1 downto 0) is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if la'left < 0 or ra'left < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '1';
+    for i in 0 to lft loop
+       if i > la'left then
+          lb := l (l'left);
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := r (r'left);
+       else
+          rb := ra (i);
+       end if;
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    return res;
+  end "-";
+
+  function "-" (l : UNSIGNED; r : NATURAL) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '1';
+    r1 := r;
+    for i in res'reverse_range loop
+       lb := la (i);
+
+       r2 := r1 / 2;
+       rd := r1 - 2 * r2;
+       r1 := r2;
+       rb := nat1_to_01 (rd);
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if r1 /= 0 then
+      assert NO_WARNING
+        report "NUMERIC_STD.""-"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "-";
+
+  function "-" (l : NATURAL; r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (r'length - 1 downto 0);
+    alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_UNSIGNED;
+    end if;
+    carry := '1';
+    l1 := l;
+    for i in res'reverse_range loop
+       rb := ra (i);
+
+       l2 := l1 / 2;
+       ld := l1 - 2 * l2;
+       l1 := l2;
+       lb := nat1_to_01 (ld);
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if l1 /= 0 then
+      assert NO_WARNING
+        report "NUMERIC_STD.""-"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "-";
+
+  function "-" (l : SIGNED; r : INTEGER) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '1';
+    r1 := r;
+    for i in res'reverse_range loop
+       lb := la (i);
+
+       r2 := r1 / 2;
+       if r1 < 0 then
+          rd := 2 * r2 - r1;
+          r1 := r2 - rd;
+        else
+          rd := r1 - 2 * r2;
+          r1 := r2;
+        end if;
+       rb := nat1_to_01 (rd);
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if r1 /= -rmsb then
+      assert NO_WARNING
+        report "NUMERIC_STD.""-"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "-";
+
+  function "-" (l : INTEGER; r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (r'length - 1 downto 0);
+    alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+    variable res : res_type;
+    variable lb, rb, carry : bit;
+  begin
+    if res'length < 0 then
+       return null_SIGNED;
+    end if;
+    carry := '1';
+    l1 := l;
+    for i in res'reverse_range loop
+       rb := ra (i);
+
+       l2 := l1 / 2;
+       if l1 < 0 then
+          ld := 2 * l2 - l1;
+          l1 := l2 - ld;
+        else
+          ld := l1 - 2 * l2;
+          l1 := l2;
+        end if;
+       lb := nat1_to_01 (ld);
+      rb := not rb;
+      res (i) := compute_sum (carry, rb, lb);
+      carry := compute_carry (carry, rb, lb);
+    end loop;
+    if l1 /= -lmsb then
+      assert NO_WARNING
+        report "NUMERIC_STD.""-"": vector is truncated"
+        severity warning;
+    end if;
+    return res;
+  end "-";
+
+  function "*" (L : UNSIGNED; R : UNSIGNED) return UNSIGNED
+  is
+     alias la : UNSIGNED (L'Length - 1 downto 0) is l;
+     alias ra : UNSIGNED (R'Length - 1 downto 0) is r;
+     variable res : UNSIGNED (L'length + R'Length -1 downto 0) := (others => '0');
+     variable rb, lb, vb, carry : bit;
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_UNSIGNED;
+     end if;
+     --  Shift and add L.
+     for i in natural range 0 to ra'left loop
+       rb := ra (i);
+       if rb = '1' then
+          --  Compute res := res + shift_left (l, i).
+          carry := '0';
+          for j in la'reverse_range loop
+            lb := la (j);
+            vb := res (i + j);
+            res (i + j) := compute_sum (carry, vb, lb);
+            carry := compute_carry (carry, vb, lb);
+          end loop;
+          --  Propagate carry.
+          for j in i + la'length to res'left loop
+             exit when carry = '0';
+             vb := res (j);
+             res (j) := carry xor vb;
+             carry := carry and vb;
+          end loop;
+       end if;
+     end loop;
+     return res;
+  end "*";
+
+  function "*" (L : SIGNED; R : SIGNED) return SIGNED
+  is
+     alias la : SIGNED (L'Length - 1 downto 0) is l;
+     alias ra : SIGNED (R'Length - 1 downto 0) is r;
+     variable res : SIGNED (L'length + R'Length -1 downto 0) := (others => '0');
+     variable rb, lb, vb, carry : bit;
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_SIGNED;
+     end if;
+     --  Shift and add L.
+     for i in natural range 0 to ra'left - 1 loop
+       rb := ra (i);
+       if rb = '1' then
+          --  Compute res := res + shift_left (l, i).
+          carry := '0';
+          for j in la'reverse_range loop
+            lb := la (j);
+            vb := res (i + j);
+            res (i + j) := compute_sum (carry, vb, lb);
+            carry := compute_carry (carry, vb, lb);
+          end loop;
+          --  Sign extend and propagate carry.
+          lb := la (la'left);
+          for j in i + l'length to res'left loop
+             vb := res (j);
+             res (j) := compute_sum (carry, vb, lb);
+             carry := compute_carry (carry, vb, lb);
+          end loop;
+       end if;
+     end loop;
+     if ra (ra'left) = '1' then
+        --  R is a negative number.  It is considered as:
+        --   -2**n + (Rn-1 Rn-2 ... R0).
+        --  Compute res := res - 2**n * l.
+        carry := '1';
+        for i in la'reverse_range loop
+          vb := res (ra'length - 1 + i);
+          lb := not la (i);
+          res (ra'length - 1+ i) := compute_sum (carry, vb, lb);
+          carry := compute_carry (carry, vb, lb);
+        end loop;
+        vb := res (res'left);
+        lb := not la (la'left);
+        res (res'left) := compute_sum (carry, vb, lb);
+     end if;
+     return res;
+  end "*";
+
+  function "*" (L : UNSIGNED; R : NATURAL) return UNSIGNED
+  is
+     constant size : natural := l'length;
+  begin
+     if size = 0 then
+        return null_UNSIGNED;
+     end if;
+     return l * to_UNSIGNED (r, size);
+  end "*";
+
+  function "*" (L : SIGNED; R : INTEGER) return SIGNED
+  is
+     constant size : natural := l'length;
+  begin
+     if size = 0 then
+        return null_SIGNED;
+     end if;
+     return l * to_SIGNED (r, size);
+  end "*";
+
+  function "*" (L : NATURAL; R : UNSIGNED) return UNSIGNED
+  is
+     constant size : natural := r'length;
+  begin
+     if size = 0 then
+        return null_UNSIGNED;
+     end if;
+     return r * to_UNSIGNED (l, size);
+  end "*";
+
+  function "*" (L : INTEGER; R : SIGNED) return SIGNED
+  is
+     constant size : natural := r'length;
+  begin
+     if size = 0 then
+        return null_SIGNED;
+     end if;
+     return r * to_SIGNED (l, size);
+  end "*";
+
+  function has_0x (a : UNSIGNED) return bit
+  is
+     variable res : bit := '0';
+  begin
+     for i in a'range loop
+      res := res or a (i);
+    end loop;
+    return res;
+  end has_0x;
+
+    --  All index range are normalized (N downto 0).
+    --  NUM and QUOT have the same range.
+    --  DEM and REMAIN have the same range.
+    --  No 'X'.
+    procedure divmod (num, dem : UNSIGNED; quot, remain : out UNSIGNED)
+    is
+       variable reg : unsigned (dem'left + 1 downto 0) := (others => '0');
+       variable sub : unsigned (dem'range) := (others => '0');
+       variable carry, d : bit;
+    begin
+       for i in num'range loop
+          --  Shift
+          reg (reg'left downto 1) := reg (reg'left - 1 downto 0);
+          reg (0) := num (i);
+          --  Substract
+          carry := '1';
+          for j in dem'reverse_range loop
+             d := not dem (j);
+             sub (j) := compute_sum (carry, reg (j), d);
+             carry := compute_carry (carry, reg (j), d);
+          end loop;
+          carry := compute_carry (carry, reg (reg'left), '1');
+          --  Test
+          if carry = '0' then
+             --  Greater than
+             quot (i) := '0';
+          else
+             quot (i) := '1';
+             reg (reg'left) := '0';
+             reg (sub'range) := sub;
+          end if;
+        end loop;
+        remain := reg (dem'range);
+    end divmod;
+    
+  function size_unsigned (n : natural) return natural
+  is
+     --  At least one bit (even for 0).
+     variable res : natural := 1;
+     variable n1 : natural := n;
+  begin
+     while n1 > 1 loop
+        res := res + 1;
+        n1 := n1 / 2;
+     end loop;
+     return res;
+  end size_unsigned;
+
+  function size_signed (n : integer) return natural
+  is
+     variable res : natural := 1;
+     variable n1 : natural;
+  begin
+     if n >= 0 then
+        n1 := n;
+     else
+        -- Use /N = -X -1 = -(X + 1)  (No overflow).
+        n1 := -(n + 1);
+     end if;
+     while n1 /= 0 loop
+        res := res + 1;
+        n1 := n1 / 2;
+     end loop;
+     return res;
+  end size_signed;
+
+  function "/" (L : UNSIGNED; R : UNSIGNED) return UNSIGNED
+  is
+     subtype l_type is UNSIGNED (L'length - 1 downto 0);
+     subtype r_type is UNSIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     variable quot : l_type;
+     variable rema : r_type;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_unsigned;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""/"": division by 0"
+        severity error;
+     divmod (la, ra, quot, rema);
+     return quot;
+  end "/";
+
+  function "/" (L : UNSIGNED; R : NATURAL) return UNSIGNED
+  is
+     constant r_size : natural := size_unsigned (r);
+  begin
+     if l'length = 0 then
+        return null_unsigned;
+     end if;
+     return l / to_unsigned (r, r_size);
+  end "/";
+
+  function "/" (L : NATURAL; R : UNSIGNED) return UNSIGNED
+  is
+     constant l_size : natural := size_unsigned (l);
+  begin
+     if r'length = 0 then
+        return null_unsigned;
+     end if;
+     return resize (to_unsigned (l, l_size) / r, r'length);
+  end "/";
+
+  function "rem" (L : UNSIGNED; R : UNSIGNED) return UNSIGNED
+  is
+     subtype l_type is UNSIGNED (L'length - 1 downto 0);
+     subtype r_type is UNSIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     variable quot : l_type;
+     variable rema : r_type;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_unsigned;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""rem"": division by 0"
+        severity error;
+     divmod (la, ra, quot, rema);
+     return rema;
+  end "rem";
+
+  function "rem" (L : UNSIGNED; R : NATURAL) return UNSIGNED
+  is
+     constant r_size : natural := size_unsigned (r);
+  begin
+     if l'length = 0 then
+        return null_unsigned;
+     end if;
+     return resize (l rem to_unsigned (r, r_size), l'length);
+  end "rem";
+
+  function "rem" (L : NATURAL; R : UNSIGNED) return UNSIGNED
+  is
+     constant l_size : natural := size_unsigned (l);
+  begin
+     if r'length = 0 then
+        return null_unsigned;
+     end if;
+     return to_unsigned (l, l_size) rem r;
+  end "rem";
+
+  function "mod" (L : UNSIGNED; R : UNSIGNED) return UNSIGNED
+  is
+     subtype l_type is UNSIGNED (L'length - 1 downto 0);
+     subtype r_type is UNSIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     variable quot : l_type;
+     variable rema : r_type;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_unsigned;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""mod"": division by 0"
+        severity error;
+     divmod (la, ra, quot, rema);
+     return rema;
+  end "mod";
+
+  function "mod" (L : UNSIGNED; R : NATURAL) return UNSIGNED
+  is
+     constant r_size : natural := size_unsigned (r);
+  begin
+     if l'length = 0 then
+        return null_unsigned;
+     end if;
+     return resize (l mod to_unsigned (r, r_size), l'length);
+  end "mod";
+
+  function "mod" (L : NATURAL; R : UNSIGNED) return UNSIGNED
+  is
+     constant l_size : natural := size_unsigned (l);
+  begin
+     if r'length = 0 then
+        return null_unsigned;
+     end if;
+     return to_unsigned (l, l_size) mod r;
+  end "mod";
+
+  function has_0x (a : SIGNED) return bit
+  is
+     variable res : bit := '0';
+  begin
+     for i in a'range loop
+      res := res or a (i);
+    end loop;
+    return res;
+  end has_0x;
+
+  function "-" (ARG : SIGNED) return SIGNED
+  is
+     subtype arg_type is SIGNED (ARG'length - 1 downto 0);
+     alias arga : arg_type is arg;
+     variable res : arg_type;
+     variable carry, a : bit;
+  begin
+     if arga'length = 0 then
+        return null_signed;
+     end if;
+     carry := '1';
+     for i in arga'reverse_range loop
+       a := not arga (i);
+       res (i) := carry xor a;
+       carry := carry and a;
+     end loop;
+     return res;
+  end "-";
+
+  function "abs" (ARG : SIGNED) return SIGNED
+  is
+     subtype arg_type is SIGNED (ARG'length - 1 downto 0);
+     alias arga : arg_type is arg;
+     variable res : arg_type;
+     variable carry, a : bit;
+  begin
+     if arga'length = 0 then
+        return null_signed;
+     end if;
+     if arga (arga'left) = '0' then
+        return arga;
+     end if;
+     carry := '1';
+     for i in arga'reverse_range loop
+       a := not arga (i);
+       res (i) := carry xor a;
+       carry := carry and a;
+     end loop;
+     return res;
+  end "abs";
+
+  function "/" (L : SIGNED; R : SIGNED) return SIGNED
+  is
+     subtype l_type is SIGNED (L'length - 1 downto 0);
+     subtype r_type is SIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     subtype l_utype is UNSIGNED (l_type'range);
+     subtype r_utype is UNSIGNED (r_type'range);
+     variable lu : l_utype;
+     variable ru : r_utype;
+     variable quot : l_utype;
+     variable rema : r_utype;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_signed;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""/"": division by 0"
+        severity error;
+     if la (la'left) = '1' then
+        lu := unsigned (-la);
+     else
+        lu := unsigned (la);
+     end if;
+     if ra (ra'left) = '1' then
+        ru := unsigned (-ra);
+     else
+        ru := unsigned (ra);
+     end if;
+     divmod (lu, ru, quot, rema);
+     if (ra (ra'left) xor la (la'left)) = '1' then
+       return -signed (quot);
+     else
+       return signed (quot);
+     end if;
+  end "/";
+
+  function "/" (L : SIGNED; R : INTEGER) return SIGNED
+  is
+     constant r_size : natural := size_signed (r);
+  begin
+     if l'length = 0 then
+        return null_signed;
+     end if;
+     return l / to_signed (r, r_size);
+  end "/";
+
+  function "/" (L : INTEGER; R : SIGNED) return SIGNED
+  is
+     constant l_size : natural := size_signed (l);
+  begin
+     if r'length = 0 then
+        return null_signed;
+     end if;
+     return resize (to_signed (l, max (l_size, r'length)) / r, r'length);
+  end "/";
+
+  function "rem" (L : SIGNED; R : SIGNED) return SIGNED
+  is
+     subtype l_type is SIGNED (L'length - 1 downto 0);
+     subtype r_type is SIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     subtype l_utype is UNSIGNED (l_type'range);
+     subtype r_utype is UNSIGNED (r_type'range);
+     variable lu : l_utype;
+     variable ru : r_utype;
+     variable quot : l_utype;
+     variable rema : r_utype;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_signed;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""rem"": division by 0"
+        severity error;
+     if la (la'left) = '1' then
+        lu := unsigned (-la);
+     else
+        lu := unsigned (la);
+     end if;
+     if ra (ra'left) = '1' then
+        ru := unsigned (-ra);
+     else
+        ru := unsigned (ra);
+     end if;
+     divmod (lu, ru, quot, rema);
+     --  Result of rem has the sign of the dividend.
+     if la (la'left) = '1' then
+       return -signed (rema);
+     else
+       return signed (rema);
+     end if;
+  end "rem";
+
+  function "rem" (L : SIGNED; R : INTEGER) return SIGNED
+  is
+     constant r_size : natural := size_signed (r);
+  begin
+     if l'length = 0 then
+        return null_signed;
+     end if;
+     return resize (l rem to_signed (r, r_size), l'length);
+  end "rem";
+
+  function "rem" (L : INTEGER; R : SIGNED) return SIGNED
+  is
+     constant l_size : natural := size_signed (l);
+  begin
+     if r'length = 0 then
+        return null_signed;
+     end if;
+     return to_signed (l, l_size) rem r;
+  end "rem";
+
+  function "mod" (L : SIGNED; R : SIGNED) return SIGNED
+  is
+     subtype l_type is SIGNED (L'length - 1 downto 0);
+     subtype r_type is SIGNED (R'length - 1 downto 0);
+     alias la : l_type is l;
+     alias ra : r_type is r;
+     subtype l_utype is UNSIGNED (l_type'range);
+     subtype r_utype is UNSIGNED (r_type'range);
+     variable lu : l_utype;
+     variable ru : r_utype;
+     variable quot : l_utype;
+     variable rema : r_utype;
+     variable r0 : bit := has_0x (r);
+  begin
+     if la'length = 0 or ra'length = 0 then
+        return null_signed;
+     end if;
+     assert r0 /= '0'
+        report "NUMERIC_STD.""mod"": division by 0"
+        severity error;
+     if la (la'left) = '1' then
+        lu := unsigned (-la);
+     else
+        lu := unsigned (la);
+     end if;
+     if ra (ra'left) = '1' then
+        ru := unsigned (-ra);
+     else
+        ru := unsigned (ra);
+     end if;
+     divmod (lu, ru, quot, rema);
+     --  Result of mod has the sign of the divisor.
+     if rema = r_utype'(others => '0') then
+        --  If the remainder is 0, then the modulus is 0.
+        return signed (rema);
+     else
+        if ra (ra'left) = '1' then
+           if la (la'left) = '1' then
+              return -signed (rema);
+           else
+              return ra + signed (rema);
+           end if;
+        else
+           if la (la'left) = '1' then
+              return ra - signed (rema);
+           else
+              return signed (rema);
+           end if;
+        end if;
+     end if;
+  end "mod";
+
+  function "mod" (L : SIGNED; R : INTEGER) return SIGNED
+  is
+     constant r_size : natural := size_signed (r);
+  begin
+     if l'length = 0 then
+        return null_signed;
+     end if;
+     return resize (l mod to_signed (r, r_size), l'length);
+  end "mod";
+
+  function "mod" (L : INTEGER; R : SIGNED) return SIGNED
+  is
+     constant l_size : natural := size_signed (l);
+  begin
+     if r'length = 0 then
+        return null_signed;
+     end if;
+     return to_signed (l, l_size) mod r;
+  end "mod";
+
+
+  function resize (ARG : UNSIGNED; NEW_SIZE: natural) return UNSIGNED
+  is
+     alias arg1 : UNSIGNED (ARG'length - 1 downto 0) is arg;
+     variable res : UNSIGNED (new_size - 1 downto 0) := (others => '0');
+  begin
+     if new_size = 0 then
+        return null_UNSIGNED;
+     end if;
+     if arg1'length = 0 then
+        return res;
+     end if;
+     if arg1'length > new_size then
+        --  Reduction.
+        res := arg1 (res'range);
+     else
+        --  Expansion
+        res (arg1'range) := arg1;
+    end if;
+    return res;
+  end resize;
+
+  function resize (ARG : SIGNED; NEW_SIZE: natural) return SIGNED
+  is
+     alias arg1 : SIGNED (ARG'length - 1 downto 0) is arg;
+     variable res : SIGNED (new_size - 1 downto 0) := (others => '0');
+  begin
+     if new_size = 0 then
+        return null_SIGNED;
+     end if;
+     if arg1'length = 0 then
+        return res;
+     end if;
+     if arg1'length > new_size then
+        --  Reduction.
+        res (res'left) := arg1 (arg1'left);
+        res (res'left - 1 downto 0) := arg1 (res'left - 1 downto 0);
+     else
+        --  Expansion
+        res (arg1'range) := arg1;
+        res (res'left downto arg1'length) := (others => arg1 (arg1'left));
+    end if;
+    return res;
+  end resize;
+
+  function "not" (l : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    variable res : res_type;
+  begin
+    for I in res_type'range loop
+      res (I) := not la (I);
+    end loop;
+    return res;
+  end "not";
+
+  function "not" (l : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    variable res : res_type;
+  begin
+    for I in res_type'range loop
+      res (I) := not la (I);
+    end loop;
+    return res;
+  end "not";
+
+  function "and" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""and"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) and ra (I);
+      end loop;
+    end if;
+    return res;
+  end "and";
+
+  function "and" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""and"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) and ra (I);
+      end loop;
+    end if;
+    return res;
+  end "and";
+
+  function "nand" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""nand"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) nand ra (I);
+      end loop;
+    end if;
+    return res;
+  end "nand";
+
+  function "nand" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""nand"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) nand ra (I);
+      end loop;
+    end if;
+    return res;
+  end "nand";
+
+  function "or" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""or"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) or ra (I);
+      end loop;
+    end if;
+    return res;
+  end "or";
+
+  function "or" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""or"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) or ra (I);
+      end loop;
+    end if;
+    return res;
+  end "or";
+
+  function "nor" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""nor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) nor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "nor";
+
+  function "nor" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""nor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) nor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "nor";
+
+  function "xor" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""xor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) xor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "xor";
+
+  function "xor" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""xor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) xor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "xor";
+
+  function "xnor" (l, r : UNSIGNED) return UNSIGNED
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""xnor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) xnor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "xnor";
+
+  function "xnor" (l, r : SIGNED) return SIGNED
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+    alias ra : SIGNED (r'length - 1 downto 0) is r;
+    variable res : res_type;
+  begin
+    if la'left /= ra'left then
+      assert false
+        report "NUMERIC_STD.""xnor"": arguments are not of the same length"
+        severity failure;
+      res := (others => '0');
+    else
+      for I in res_type'range loop
+        res (I) := la (I) xnor ra (I);
+      end loop;
+    end if;
+    return res;
+  end "xnor";
+
+  function ucompare (l : UNSIGNED; r : UNSIGNED) return compare_type
+  is
+     constant sz : integer := MAX (l'length, r'length) - 1;
+     alias la : UNSIGNED (l'length - 1 downto 0) is l;
+     alias ra : UNSIGNED (r'length - 1 downto 0) is r;
+     variable lb, rb : bit;
+     variable res : compare_type;
+  begin
+     res := compare_eq;
+    for i in 0 to sz loop
+       if i > la'left then
+          lb := '0';
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := '0';
+       else
+          rb := ra (i);
+       end if;
+       if lb = '1' and rb = '0' then
+         res := compare_gt;
+       elsif lb = '0' and rb = '1' then
+         res := compare_lt;
+       end if;
+     end loop;
+
+     return res;
+  end ucompare;
+
+  function scompare (l : SIGNED; r : SIGNED) return compare_type
+  is
+     constant sz : integer := MAX (l'length, r'length) - 1;
+     alias la : SIGNED (l'length - 1 downto 0) is l;
+     alias ra : SIGNED (r'length - 1 downto 0) is r;
+     variable lb, rb : bit;
+     variable res : compare_type;
+  begin
+     --  Consider sign bit as S * -(2**N).
+     lb := la (la'left);
+     rb := ra (ra'left);
+     if lb = '1' and rb = '0' then
+        return compare_lt;
+     elsif lb = '0' and rb = '1' then
+        return compare_gt;
+     else
+        res := compare_eq;
+     end if;
+     for i in 0 to sz - 1 loop
+       if i > la'left then
+          lb := l (l'left);
+       else
+          lb := la (i);
+       end if;
+       if i > ra'left then
+          rb := r (r'left);
+       else
+          rb := ra (i);
+       end if;
+       if lb = '1' and rb = '0' then
+         res := compare_gt;
+       elsif lb = '0' and rb = '1' then
+         res := compare_lt;
+       end if;
+     end loop;
+
+     return res;
+  end scompare;
+
+  function ucompare (l : UNSIGNED; r : NATURAL) return compare_type
+  is
+    subtype res_type is UNSIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+    variable lb, rb : bit;
+    variable res : compare_type;
+  begin
+    res := compare_eq;
+    r1 := r;
+    for i in la'reverse_range loop
+       lb := la (i);
+       r2 := r1 / 2;
+       rd := r1 - 2 * r2;
+       r1 := r2;
+       rb := nat1_to_01 (rd);
+       if lb = '1' and rb = '0' then
+         res := compare_gt;
+       elsif lb = '0' and rb = '1' then
+         res := compare_lt;
+       end if;
+    end loop;
+    if r1 /= 0 then
+       res := compare_lt;
+    end if;
+    return res;
+  end ucompare;
+
+  function scompare (l : SIGNED; r : INTEGER) return compare_type
+  is
+    subtype res_type is SIGNED (l'length - 1 downto 0);
+    alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+    variable lb, rb : bit;
+    variable res : compare_type;
+  begin
+    res := compare_eq;
+    r1 := r;
+    for i in la'reverse_range loop
+       lb := la (i);
+       r2 := r1 / 2;
+       if r1 < 0 then
+          rd := 2 * r2 - r1;
+          r1 := r2 - rd;
+        else
+          rd := r1 - 2 * r2;
+          r1 := r2;
+        end if;
+       rb := nat1_to_01 (rd);
+       if lb = '1' and rb = '0' then
+         res := compare_gt;
+       elsif lb = '0' and rb = '1' then
+         res := compare_lt;
+       end if;
+    end loop;
+    if l (l'left) = '1' then
+      if r >= 0 then
+         res := compare_lt;
+      end if;
+    else
+      if r < 0 then
+         res := compare_gt;
+      end if;
+    end if;
+    return res;
+  end scompare;
+
+  function "=" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res = compare_eq;
+  end "=";
+
+  function "=" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res = compare_eq;
+  end "=";
+
+  function "=" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res = compare_eq;
+  end "=";
+
+  function "=" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq = res;
+  end "=";
+
+  function "=" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res = compare_eq;
+  end "=";
+
+  function "=" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq = res;
+  end "=";
+
+  function "/=" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res /= compare_eq;
+  end "/=";
+
+  function "/=" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res /= compare_eq;
+  end "/=";
+
+  function "/=" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res /= compare_eq;
+  end "/=";
+
+  function "/=" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq /= res;
+  end "/=";
+
+  function "/=" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res /= compare_eq;
+  end "/=";
+
+  function "/=" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""/="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq /= res;
+  end "/=";
+
+  function ">" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res > compare_eq;
+  end ">";
+
+  function ">" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res > compare_eq;
+  end ">";
+
+  function ">" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res > compare_eq;
+  end ">";
+
+  function ">" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq > res;
+  end ">";
+
+  function ">" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res > compare_eq;
+  end ">";
+
+  function ">" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq > res;
+  end ">";
+
+  function ">=" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res >= compare_eq;
+  end ">=";
+
+  function ">=" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res >= compare_eq;
+  end ">=";
+
+  function ">=" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res >= compare_eq;
+  end ">=";
+
+  function ">=" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq >= res;
+  end ">=";
+
+  function ">=" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res >= compare_eq;
+  end ">=";
+
+  function ">=" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD."">="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq >= res;
+  end ">=";
+
+  function "<" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res < compare_eq;
+  end "<";
+
+  function "<" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res < compare_eq;
+  end "<";
+
+  function "<" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res < compare_eq;
+  end "<";
+
+  function "<" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq < res;
+  end "<";
+
+  function "<" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res < compare_eq;
+  end "<";
+
+  function "<" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<"": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq < res;
+  end "<";
+
+  function "<=" (l : UNSIGNED; r : UNSIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res <= compare_eq;
+  end "<=";
+
+  function "<=" (l : SIGNED; r : SIGNED) return boolean
+  is
+     variable res : compare_type;
+  begin
+     if l'length = 0 or r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res <= compare_eq;
+  end "<=";
+
+  function "<=" (l : UNSIGNED; r : NATURAL) return boolean
+  is
+     subtype res_type is UNSIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : NATURAL;
+     variable rd : nat1;
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (l, r);
+     return res <= compare_eq;
+  end "<=";
+
+  function "<=" (l : NATURAL; r : UNSIGNED) return boolean
+  is
+     subtype res_type is UNSIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : NATURAL;
+     variable ld : nat1;
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := ucompare (r, l);
+     return compare_eq <= res;
+  end "<=";
+
+  function "<=" (l : SIGNED; r : INTEGER) return boolean
+  is
+     subtype res_type is SIGNED (l'length - 1 downto 0);
+     alias la : res_type is l;
+     variable r1, r2 : INTEGER;
+     variable rd : nat1;
+     constant rmsb : nat1 := boolean'pos(r < 0);
+     variable res : compare_type;
+  begin
+     if l'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (l, r);
+     return res <= compare_eq;
+  end "<=";
+
+  function "<=" (l : INTEGER; r : SIGNED) return boolean
+  is
+     subtype res_type is SIGNED (r'length - 1 downto 0);
+     alias ra : res_type is r;
+     variable l1, l2 : INTEGER;
+     variable ld : nat1;
+     constant lmsb : nat1 := boolean'pos(l < 0);
+     variable res : compare_type;
+  begin
+     if r'length = 0 then
+        assert NO_WARNING
+           report "NUMERIC_STD.""<="": null argument, returning FALSE"
+           severity warning;
+        return false;
+     end if;
+
+     res := scompare (r, l);
+     return compare_eq <= res;
+  end "<=";
+
+  function shift_left (ARG : UNSIGNED; COUNT: NATURAL) return UNSIGNED
+  is
+     subtype res_type is UNSIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+  begin
+     if res'length = 0 then
+        return null_UNSIGNED;
+     end if;
+     if count <= arg1'left then
+       res (res'left downto count) := arg1 (arg1'left - count downto 0);
+     end if;
+     return res;
+  end shift_left;
+
+  function shift_right (ARG : UNSIGNED; COUNT: NATURAL) return UNSIGNED
+  is
+     subtype res_type is UNSIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+  begin
+     if res'length = 0 then
+        return null_UNSIGNED;
+     end if;
+     if count <= arg1'left then
+       res (res'left - count downto 0) := arg1 (arg1'left downto count);
+     end if;
+     return res;
+  end shift_right;
+
+  function rotate_left (ARG : UNSIGNED; COUNT: NATURAL) return UNSIGNED
+  is
+     subtype res_type is UNSIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+     variable cnt : natural;
+  begin
+     if res'length = 0 then
+        return null_UNSIGNED;
+     end if;
+     cnt := count rem res'length;
+     res (res'left downto cnt) := arg1 (res'left - cnt downto 0);
+     res (cnt - 1 downto 0) := arg1 (res'left downto res'left - cnt + 1);
+     return res;
+  end rotate_left;
+
+  function rotate_right (ARG : UNSIGNED; COUNT: NATURAL) return UNSIGNED
+  is
+     subtype res_type is UNSIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+     variable cnt : natural;
+  begin
+     if res'length = 0 then
+        return null_UNSIGNED;
+     end if;
+     cnt := count rem res'length;
+     res (res'left - cnt downto 0) := arg1 (res'left downto cnt);
+     res (res'left downto res'left - cnt + 1) := arg1 (cnt - 1 downto 0);
+     return res;
+  end rotate_right;
+
+  function shift_left (ARG : SIGNED; COUNT: NATURAL) return SIGNED
+  is
+     subtype res_type is SIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+  begin
+     if res'length = 0 then
+        return null_SIGNED;
+     end if;
+     if count <= arg1'left then
+       res (res'left downto count) := arg1 (arg1'left - count downto 0);
+     end if;
+     return res;
+  end shift_left;
+
+  function shift_right (ARG : SIGNED; COUNT: NATURAL) return SIGNED
+  is
+     subtype res_type is SIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => arg1 (arg1'left));
+  begin
+     if res'length = 0 then
+        return null_SIGNED;
+     end if;
+     if count <= arg1'left then
+       res (res'left - count downto 0) := arg1 (arg1'left downto count);
+     end if;
+     return res;
+  end shift_right;
+
+  function rotate_left (ARG : SIGNED; COUNT: NATURAL) return SIGNED
+  is
+     subtype res_type is SIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+     variable cnt : natural;
+  begin
+     if res'length = 0 then
+        return null_SIGNED;
+     end if;
+     cnt := count rem res'length;
+     res (res'left downto cnt) := arg1 (res'left - cnt downto 0);
+     res (cnt - 1 downto 0) := arg1 (res'left downto res'left - cnt + 1);
+     return res;
+  end rotate_left;
+
+  function rotate_right (ARG : SIGNED; COUNT: NATURAL) return SIGNED
+  is
+     subtype res_type is SIGNED (ARG'length - 1 downto 0);
+     alias arg1 : res_type is arg;
+     variable res : res_type := (others => '0');
+     variable cnt : natural;
+  begin
+     if res'length = 0 then
+        return null_SIGNED;
+     end if;
+     cnt := count rem res'length;
+     res (res'left - cnt downto 0) := arg1 (res'left downto cnt);
+     res (res'left downto res'left - cnt + 1) := arg1 (cnt - 1 downto 0);
+     return res;
+  end rotate_right;
+end NUMERIC_BIT;