-- +---------------------------+
-- | Copyright 1996 DOULOS |
-- | Generic Library |
-- | opened: 25 Nov 1995 |
-- +---------------------------+
-- Synthesis script: read -f vhdl ops_2sC.bdy
library ieee;
library vfp;
package body twos_complement_operators is
use ieee.std_logic_1164.all;
use vfp.twos_complement_types.all;
use vfp.generic_functions.all;
use vfp.generic_conversions.all;
use vfp.std_operators.all;
function "not" ( -- 25.11.95
a: twos_complement
) return twos_complement is
variable yi: twos_complement(a'length-1 downto 0);
begin
for i in 0 to a'length-1 loop
yi(i) := not (a(i));
end loop;
return yi;
end "not";
function "and" ( -- 24.11.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
if (a'length /= b'length) then
assert false
report "Error 0000." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = and." &
"The wordlength of a and b MUST be the same."
severity error;
else
for i in 0 to a'length-1 loop
y(i) := a(i) and b(i);
end loop;
end if;
return y;
end "and";
function "or" ( -- 25.11.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
if (a'length /= b'length) then
assert false
report "Error 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = or." &
"The wordlength of a and b MUST be the same."
severity error;
else
for i in 0 to a'length-1 loop
y(i) := a(i) or b(i);
end loop;
end if;
return y;
end "or";
function "xor" ( -- 25.11.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
if (a'length /= b'length) then
assert false
report "Error 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = xor." &
"The wordlength of a and b MUST be the same."
severity error;
else
for i in 0 to a'length-1 loop
y(i) := a(i) xor b(i);
end loop;
end if;
return y;
end "xor";
function "nand" ( -- 25.11.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
if (a'length /= b'length) then
assert false
report "Error 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = nand." &
"The wordlength of a and b MUST be the same."
severity error;
else
for i in 0 to a'length-1 loop
y(i) := a(i) nand b(i);
end loop;
end if;
return y;
end "nand";
function "nor" ( -- 25.11.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
if (a'length /= b'length) then
assert false
report "Error 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = nor." &
"The wordlength of a and b MUST be the same."
severity error;
else
for i in 0 to a'length-1 loop
y(i) := a(i) nor b(i);
end loop;
end if;
return y;
end "nor";
-- function "xnor" ( -- 25.11.95
-- a, b: twos_complement
-- ) return twos_complement is
-- variable y: twos_complement(a'length-1 downto 0);
-- begin
-- if (a'length /= b'length) then
-- assert false
-- report "Error 0001." &
-- "Library = vfp." &
-- "Package Body = twos_complement_operators." &
-- "Function = xnor." &
-- "The wordlength of a and b MUST be the same."
-- severity error;
-- else
-- for i in 0 to a'length-1 loop
-- y(i) := a(i) xnor b(i);
-- end loop;
-- end if;
-- return y;
-- end "xnor";
function "+" ( -- 25.11.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := longest (a, b);
variable a_sign_extended, b_sign_extended: twos_complement(y_length-1 downto 0);
variable y: twos_complement(y_length-1 downto 0);
variable carry: std_ulogic;
begin
carry := '0';
if (a'length < b'length) then
for i in b'length-1 downto a'length loop
a_sign_extended(i) := a(a'length-1);
end loop;
a_sign_extended(a'length-1 downto 0) := a;
for i in 0 to b'length-1 loop
y(i) := a_sign_extended(i) xor b(i) xor carry;
carry := (a_sign_extended(i) and b(i)) or
(a_sign_extended(i) and carry) or
(b(i) and carry);
end loop;
elsif (a'length > b'length) then
for i in a'length-1 downto b'length loop
b_sign_extended(i) := b(b'length-1);
end loop;
b_sign_extended(b'length-1 downto 0) := b;
for i in 0 to a'length-1 loop
y(i) := a(i) xor b_sign_extended(i) xor carry;
carry := (a(i) and b_sign_extended(i)) or
(a(i) and carry) or
(b_sign_extended(i) and carry);
end loop;
else -- i.e., (a'length = b'length)
for i in 0 to a'length-1 loop
y(i) := a(i) xor b(i) xor carry;
carry := (a(i) and b(i)) or
(a(i) and carry) or
(b(i) and carry);
end loop;
end if;
return y;
end "+";
function "-" ( -- 29.11.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := longest (a, b);
variable a_sign_extended, b_sign_extended: twos_complement(y_length-1 downto 0);
variable y: twos_complement(y_length-1 downto 0);
variable carry: std_ulogic;
begin
carry := '1';
if (a'length < b'length) then
for i in b'length-1 downto a'length loop
a_sign_extended(i) := a(a'length-1);
end loop;
a_sign_extended(a'length-1 downto 0) := a;
for i in 0 to b'length-1 loop
y(i) := a_sign_extended(i) xor (not b(i)) xor carry;
carry := (a_sign_extended(i) and (not b(i))) or
(a_sign_extended(i) and carry) or
(not (b(i)) and carry);
end loop;
elsif (a'length > b'length) then
for i in a'length-1 downto b'length loop
b_sign_extended(i) := b(b'length-1);
end loop;
b_sign_extended(b'length-1 downto 0) := b;
for i in 0 to a'length-1 loop
y(i) := a(i) xor (not b_sign_extended(i)) xor carry;
carry := (a(i) and (not b_sign_extended(i))) or
(a(i) and carry) or
((not b_sign_extended(i)) and carry);
end loop;
else -- i.e., (a'length = b'length)
for i in 0 to a'length-1 loop
y(i) := a(i) xor (not b(i)) xor carry;
carry := (a(i) and (not b(i))) or
(a(i) and carry) or
((not b(i)) and carry);
end loop;
end if;
return y;
end "-";
function "*" ( -- 30.11.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := a'length + b'length;
variable y_sign: std_ulogic;
-- variable a_1sC, multiplicand: twos_complement(a'length-1 downto 0);
-- variable b_1sC, multiplier: twos_complement(b'length-1 downto 0);
variable a_1sC, multiplicand: std_ulogic_vector(a'length-1 downto 0);
variable b_1sC, multiplier: std_ulogic_vector(b'length-1 downto 0);
variable carry: std_ulogic;
-- variable partial_product: twos_complement(a'length-1 downto 0);
variable partial_product: std_ulogic_vector(a'length-1 downto 0);
variable product_lsb: twos_complement(b'length-1 downto 0);
variable product: twos_complement(y_length-1 downto 0);
variable y_1sC: twos_complement(y_length-1 downto 0);
variable y: twos_complement(y_length-1 downto 0);
begin
-- firstly, the sign of the result is extracted -- BB x 02
y_sign := a(a'length-1) xor b(b'length-1); -- 1
-- second, the operands are converted to absolute values --
if (a(a'length-1) = '1') then --
a_1sC := to_std_ulogic_vector (not a); -- 44
carry := '1'; --
for i in 0 to a'length-1 loop -- 0 1 2 3 4 5 6 7
multiplicand(i) := a_1sC(i) xor carry; -- 1 0 1 0 0 0 1 0
carry := a_1sC(i) and carry; -- 0 0 0 0 0 0 0 0
end loop; -- 45
else --
multiplicand := to_std_ulogic_vector (a); --
end if; --
if (b(b'length-1) = '1') then --
b_1sC := to_std_ulogic_vector (not b); --
carry := '1'; --
for i in 0 to b'length-1 loop --
multiplier(i) := b_1sC(i) xor carry; --
carry := b_1sC(i) and carry; --
end loop; --
else --
multiplier := to_std_ulogic_vector (b); -- 02
end if; --
-- thirdly, the multiplication of the absolute values takes place
for i in 0 to (multiplicand'length - 1) loop --
partial_product(i) := '0'; -- 00
end loop; --
for i in 0 to multiplier'length-1 loop -- 0 1 2 3 4 5 6 7
if (multiplier(i) = '1') then --
-- partial_product := partial_product(a'length-1 downto 1) + multiplicand; --
partial_product := partial_product + multiplicand; --
product_lsb(i) := partial_product(0); --
partial_product := '0' & partial_product(a'length-1 downto 1); --
else --
product_lsb(i) := partial_product(0); -- 0
partial_product := '0' & partial_product(a'length-1 downto 1); -- 0
end if; -- pp = 00
end loop; -- lsb = 8A
-- now the result's absolute value is converted to it's 2's complement value
product := to_twos_complement (partial_product) & product_lsb; --
if (y_sign = '1') then --
y_1sC := not product; -- FF75
carry := '1'; --
for i in 0 to y_1sC'length-1 loop --
y(i) := y_1sC(i) xor carry; --
carry := y_1sC(i) and carry; --
end loop; -- FF76
else --
y := product; --
end if; --
return y; --
end "*";
function "/" ( -- 29.11.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := a'length + b'length;
constant a_extended_length: integer := b'length-1;
variable y_sign: std_ulogic;
variable a_1sC, a_abs: twos_complement(a'length-1 downto 0);
variable b_1sC, b_abs: twos_complement(b'length-1 downto 0);
variable carry: std_ulogic;
variable a_extended: twos_complement(a_extended_length-1 downto 0);
variable dividend_match: twos_complement(b'length-1 downto 0);
variable quotient: twos_complement(a'length-1 downto 0);
variable remainder: twos_complement(b'length-1 downto 0);
variable quotient_abs, quotient_1sC: twos_complement(a'length-1 downto 0);
variable remainder_abs, remainder_1sC: twos_complement(b'length-1 downto 0);
variable y: twos_complement(y_length-1 downto 0);
begin
-- firstly, the sign of the result is extracted
y_sign := a(a'length-1) xor b(b'length-1);
-- second, the operands are converted to absolute values
if (a(a'length-1) = '1') then
a_1sC := not a;
carry := '1';
for i in 0 to a'length-1 loop
a_abs(i) := a_1sC(i) xor carry;
carry := a_1sC(i) and carry;
end loop;
else
a_abs := a;
end if;
if (b(b'length-1) = '1') then
b_1sC := not b;
carry := '1';
for i in 0 to b'length-1 loop
b_abs(i) := b_1sC(i) xor carry;
carry := b_1sC(i) and carry;
end loop;
else
b_abs := b;
end if;
-- thirdly, the division of the absolute values takes place
for i in a_extended_length-1 downto 0 loop
a_extended(i) := '0';
end loop;
dividend_match(b_abs'length-1 downto 1) := a_extended;
for i in a_abs'length-1 downto 0 loop
dividend_match := dividend_match(b_abs'length-1 downto 1) & a_abs(i);
if (b_abs <= dividend_match) then
dividend_match := dividend_match - b_abs;
quotient_abs(i) := '1';
else
quotient_abs(i) := '0';
end if;
end loop;
remainder_abs := dividend_match;
-- now the result's absolute value is converted to it's 2's complement value
-- note that the sign of the remainder follows the sign of the dividend
if (y_sign = '1') then
quotient_1sC := not quotient_abs;
carry := '1';
for i in 0 to quotient_1sC'length-1 loop
quotient(i) := quotient_1sC(i) xor carry;
carry := quotient_1sC(i) and carry;
end loop;
else
quotient := quotient_abs;
end if;
if (a(a'length-1) = '1') then
remainder_1sC := not remainder_abs;
carry := '1';
for i in 0 to remainder_1sC'length-1 loop
remainder(i) := remainder_1sC(i) xor carry;
carry := remainder_1sC(i) and carry;
end loop;
else
remainder := remainder_abs;
end if;
y := quotient & remainder;
return y;
end "/";
function "mod" ( -- 2.12.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := a'length + b'length;
constant a_extended_length: integer := b'length-1;
variable a_1sC, a_abs: twos_complement(a'length-1 downto 0);
variable b_1sC, b_abs: twos_complement(b'length-1 downto 0);
variable carry: std_ulogic;
variable a_extended: twos_complement(a_extended_length-1 downto 0);
variable dividend_match: twos_complement(b'length-1 downto 0);
variable remainder: twos_complement(b'length-1 downto 0);
variable remainder_abs, remainder_1sC: twos_complement(b'length-1 downto 0);
variable y: twos_complement(b'length-1 downto 0);
begin
-- firstly, the operands are converted to absolute values
if (a(a'length-1) = '1') then
a_1sC := not a;
carry := '1';
for i in 0 to a'length-1 loop
a_abs(i) := a_1sC(i) xor carry;
carry := a_1sC(i) and carry;
end loop;
else
a_abs := a;
end if;
if (b(b'length-1) = '1') then
b_1sC := not b;
carry := '1';
for i in 0 to b'length-1 loop
b_abs(i) := b_1sC(i) xor carry;
carry := b_1sC(i) and carry;
end loop;
else
b_abs := b;
end if;
-- secondly, the division of the absolute values takes place
for i in a_extended_length-1 downto 0 loop
a_extended(i) := '0';
end loop;
dividend_match(b_abs'length-1 downto 1) := a_extended;
for i in a_abs'length-1 downto 0 loop
dividend_match := dividend_match(b_abs'length-1 downto 1) & a_abs(i);
if (b_abs <= dividend_match) then
dividend_match := dividend_match - b_abs;
end if;
end loop;
remainder_abs := dividend_match;
-- now the result's absolute value is converted to it's 2's complement value
-- note that the sign of the remainder follows the sign of the dividend
if (a(a'length-1) = '1') then
remainder_1sC := not remainder_abs;
carry := '1';
for i in 0 to remainder_1sC'length-1 loop
remainder(i) := remainder_1sC(i) xor carry;
carry := remainder_1sC(i) and carry;
end loop;
else
remainder := remainder_abs;
end if;
y := remainder;
return y;
end "mod";
function "rem" ( -- 2.12.95
a, b: twos_complement
) return twos_complement is
constant y_length: integer := a'length + b'length;
constant a_extended_length: integer := b'length-1;
variable a_1sC, a_abs: twos_complement(a'length-1 downto 0);
variable b_1sC, b_abs: twos_complement(b'length-1 downto 0);
variable carry: std_ulogic;
variable a_extended: twos_complement(a_extended_length-1 downto 0);
variable dividend_match: twos_complement(b'length-1 downto 0);
variable remainder: twos_complement(b'length-1 downto 0);
variable remainder_abs, remainder_1sC: twos_complement(b'length-1 downto 0);
variable y: twos_complement(b'length-1 downto 0);
begin
-- firstly, the operands are converted to absolute values
if (a(a'length-1) = '1') then
a_1sC := not a;
carry := '1';
for i in 0 to a'length-1 loop
a_abs(i) := a_1sC(i) xor carry;
carry := a_1sC(i) and carry;
end loop;
else
a_abs := a;
end if;
if (b(b'length-1) = '1') then
b_1sC := not b;
carry := '1';
for i in 0 to b'length-1 loop
b_abs(i) := b_1sC(i) xor carry;
carry := b_1sC(i) and carry;
end loop;
else
b_abs := b;
end if;
-- secondly, the division of the absolute values takes place
for i in a_extended_length-1 downto 0 loop
a_extended(i) := '0';
end loop;
dividend_match(b_abs'length-1 downto 1) := a_extended;
for i in a_abs'length-1 downto 0 loop
dividend_match := dividend_match(b_abs'length-1 downto 1) & a_abs(i);
if (b_abs <= dividend_match) then
dividend_match := dividend_match - b_abs;
end if;
end loop;
remainder_abs := dividend_match;
-- now the result's absolute value is converted to it's 2's complement value
-- note that the sign of the remainder follows the sign of the dividend
if (a(a'length-1) = '1') then
remainder_1sC := not remainder_abs;
carry := '1';
for i in 0 to remainder_1sC'length-1 loop
remainder(i) := remainder_1sC(i) xor carry;
carry := remainder_1sC(i) and carry;
end loop;
else
remainder := remainder_abs;
end if;
y := remainder;
return y;
end "rem";
function "**" ( -- 2.12.95
a, b: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
assert false
report "Error 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = **." &
"The function (twos_complement) ** (twos_complement) is not supported." &
"However, to_twos_complement(to_integer(twos_complementy) ** to_integer(twos_complement)) is supported."
-- See the to_integer and the to_twos_complement conversion functions
severity error;
y := a;
return y;
end "**";
function "abs" ( -- 2.12.95
a: twos_complement
) return twos_complement is
-- the function abs_wordlength returns a'length+1 if a is
-- -2(N-1) otherwise it returns a'length
constant y_length: integer := abs_wordlength(a);
variable a_1sC: twos_complement(a'length-1 downto 0);
variable carry: std_ulogic;
variable y: twos_complement(y_length-1 downto 0);
begin
if (y_length = a'length+1) then
y(a'length) := '1';
end if;
if (a(a'length-1) = '1') then
a_1sC := not a;
carry := '1';
for i in 0 to a'length-1 loop
y(i) := a_1sC(i) xor carry;
carry := a_1sC(i) and carry;
end loop;
else
y := a;
end if;
return y;
end "abs";
function "+" ( -- 2.12.95
a: twos_complement
) return twos_complement is
variable y: twos_complement(a'length-1 downto 0);
begin
assert false
report "Warning 0001." &
"Library = vfp." &
"Package Body = twos_complement_operators." &
"Function = +." &
"The function + (twos_complement) is defined as ... " &
" <return_value> := <actual_parameter> " &
"Thus there is no point in taking the positive value of a twos_complement object."
severity warning;
y := a;
return y;
end "+";
function "-" ( -- 2.12.95
a: twos_complement
) return twos_complement is
-- the function abs_wordlength returns a'length+1 if a is
-- -2(N-1) otherwise it returns a'length
constant y_length: integer := abs_wordlength(a);
variable a_1sC: twos_complement(a'length-1 downto 0);
variable carry: std_ulogic;
variable y: twos_complement(y_length-1 downto 0);
begin
if (y_length = a'length+1) then
y(a'length) := '0';
end if;
a_1sC := not a;
carry := '1';
for i in 0 to a'length-1 loop
y(i) := a_1sC(i) xor carry;
carry := a_1sC(i) and carry;
end loop;
return y;
end "-";
-- an alternative body
-- take the 2s complement vectors & convert them to
-- integers. Then add the integers.
end twos_complement_operators;
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