IEEE-754 binary floating-point arithmetic implemented from first principles.
- Use clause
-
library IEEE;
use IEEE.FLOAT_GENERIC_PKG.all; - Source
-
ieee/float_generic_pkg-body.vhdlin the IEEE 1076 OSR, tag1076-2019
Apache License 2.0, © 2019 IEEE P1076 WG Authors - Length
- 5712 lines
- Declaration
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Overview
This is the reference implementation of FLOAT_GENERIC_PKG,
published with IEEE Std 1076-2019. The body represents the formal
semantics of the package per §16.11: implementers may compile it
as-is or substitute a more efficient implementation, but the resulting
behaviour shall not differ from the semantics defined here. The interface
lives on the declaration page.
The body implements IEEE-754 binary arithmetic from first principles - sign-magnitude separation, exponent alignment, normalisation, rounding, and explicit handling of denormals, zeros, infinities, and NaNs. Use your browser’s find (Ctrl/Cmd+F) to locate a specific function within this listing.
VHDL source listing
Package preamble
-- -----------------------------------------------------------------
--
-- Copyright 2019 IEEE P1076 WG Authors
--
-- See the LICENSE file distributed with this work for copyright and
-- licensing information and the AUTHORS file.
--
-- This file to you under the Apache License, Version 2.0 (the "License").
-- You may obtain a copy of the License at
--
-- http://www.apache.org/licenses/LICENSE-2.0
--
-- Unless required by applicable law or agreed to in writing, software
-- distributed under the License is distributed on an "AS IS" BASIS,
-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
-- implied. See the License for the specific language governing
-- permissions and limitations under the License.
--
-- 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 and local constants
boundary_typefphdlsynth_or_real NAFP NSLV
boundary_typefphdlsynth_or_real NAFP NSLV -----------------------------------------------------------------------------
-- 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');
Local helper functions
mine gen_expon_base log2 check_round smallfracttest_boundary fp_round break_number float_to_unsigned
mine gen_expon_base log2 check_round smallfracttest_boundary fp_round break_number float_to_unsigned -- 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;
Vector representation conversion functions
to_sulv to_slv
to_sulv to_slv ---------------------------------------------------------------------------
-- 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 intermediate_result : UNRESOLVED_float(arg'length-1 downto 0);
begin -- function to_std_ulogic_vector
if arg'length < 1 then
return NSLV;
end if;
intermediate_result := arg;
return STD_ULOGIC_VECTOR (intermediate_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;
Normalization, classification, and vendor utility functions
normalize Classfpbreak_number
normalize Classfpbreak_number -- 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
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 operators and functions
"abs" "-" add subtract multiply short_divide reciprocal divide dividebyp2 mac remainder modulo sqrt Is_Negative
"abs" "-" add subtract multiply short_divide reciprocal divide dividebyp2 mac remainder modulo sqrt Is_Negative -- 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 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;
Comparison, matching, and min/max functions
eq lt gt ne le ge "?=" "?/=" "?>" "?>=" "?<" "?<=" std_match find_rightmost find_leftmost "=" "/=" ">=" "<=" ">" "<" maximum minimum
eq lt gt ne le ge "?=" "?/=" "?>" "?>=" "?<" "?<=" std_match find_rightmost find_leftmost "=" "/=" ">=" "<=" ">" "<" maximum minimum -- 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;
Resize and conversion functions
resize to_float32 to_float64 to_float128 to_float to_integer to_unsigned to_signed to_ufixed to_sfixed to_real realtobits bitstoreal to_01 Is_X to_X01 to_X01Z to_UX01
resize to_float32 to_float64 to_float128 to_float to_integer to_unsigned to_signed to_ufixed to_sfixed to_real realtobits bitstoreal to_01 Is_X to_X01 to_X01Z to_UX01Resize and floating-point format conversion
resize to_float32 to_float64 to_float128
resize to_float32 to_float64 to_float128 -----------------------------------------------------------------------------
-- 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 expon_out : SIGNED (exponent_width-1 downto 0); -- output fract
variable fract_out : UNSIGNED (fraction_width downto 0); -- output fract
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;
Conversions to floating-point
to_float
to_float -- 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 : UNRESOLVED_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 : UNRESOLVED_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 : UNRESOLVED_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 : UNRESOLVED_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
downto 0); -- unsigned version of argument
variable argx : SIGNED (integer_width - in_fraction_width downto 0);
variable exp, exptmp : SIGNED (exponent_width + 1 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
arg_int := UNSIGNED(to_x01(not STD_LOGIC_VECTOR (argx))) + 1; -- Make it positive with two's complement
else
result (exponent_width) := '0';
arg_int := UNSIGNED(to_x01(STD_LOGIC_VECTOR (argx))); -- new line: direct conversion to unsigned
end if;
-- 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;
Conversions from floating-point to integer, vector, and fixed-point
to_integer to_unsigned to_signed to_ufixed to_sfixed
to_integer to_unsigned to_signed to_ufixed to_sfixed -- 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 conversion functions
to_unsigned to_signed to_ufixed to_sfixed
to_unsigned to_signed to_ufixed 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;
Conversion to REAL, Verilog compatibility, and metavalue conversion
to_real realtobits bitstoreal to_01 Is_X to_X01 to_X01Z to_UX01
to_real realtobits bitstoreal to_01 Is_X to_X01 to_X01Z to_UX01 -- 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;
Default floating-point arithmetic overloads
"+" "-" "*" "/" "rem" "mod"
"+" "-" "*" "/" "rem" "mod" -- 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";
Overloads with REAL and INTEGER arguments
"+" "-" "*" "/" "rem" "mod" "=" "/=" ">=" "<=" ">" "<" "?=" "?/=" "?>" "?>=" "?<" "?<=" minimum maximum
"+" "-" "*" "/" "rem" "mod" "=" "/=" ">=" "<=" ">" "<" "?=" "?/=" "?>" "?>=" "?<" "?<=" minimum maximumArithmetic overloads
"+" "-" "*" "/" "rem" "mod"
"+" "-" "*" "/" "rem" "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";
Comparison overloads
"=" "/=" ">=" "<=" ">" "<"
"=" "/=" ">=" "<=" ">" "<" 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 "<";
Matching relational overloads
"?=" "?/=" "?>" "?>=" "?<" "?<="
"?=" "?/=" "?>" "?>=" "?<" "?<=" -- ?= 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
minimum maximum
minimum maximum -- 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 operators and functions
"not" "and" "or" "nand" "nor" "xor" "xnor"
"not" "and" "or" "nand" "nor" "xor" "xnor"Vector logical operators
"not" "and" "or" "nand" "nor" "xor" "xnor"
"not" "and" "or" "nand" "nor" "xor" "xnor" ----------------------------------------------------------------------------
-- 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";
Scalar-vector mixed logical operators
"and" "or" "nand" "nor" "xor" "xnor"
"and" "or" "nand" "nor" "xor" "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 logical operators
"and" "nand" "or" "nor" "xor" "xnor"
"and" "nand" "or" "nor" "xor" "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
Copysign Scalb Logb Nextafter Unordered Finite Isnan to zerofp nanfp qnanfp pos_inffp neg_inffp neg_zerofp
Copysign Scalb Logb Nextafter Unordered Finite Isnan to zerofp nanfp qnanfp pos_inffp neg_inffp neg_zerofp -----------------------------------------------------------------------------
-- 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);
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;
String conversion and text I/O functions
MVL9plus char_indexed_by_MVL9 MVL9_indexed_by_char MVL9plus_indexed_by_charNBSP MVL9_to_char char_to_MVL9 char_to_MVL9plusto_string to_hstring to_ostring from_string from_ostring from_hstringskip_whitespace check_punctuation fix_colon WRITE READ OWRITE OREAD HWRITE HREAD
MVL9plus char_indexed_by_MVL9 MVL9_indexed_by_char MVL9plus_indexed_by_charNBSP MVL9_to_char char_to_MVL9 char_to_MVL9plusto_string to_hstring to_ostring from_string from_ostring from_hstringskip_whitespace check_punctuation fix_colon WRITE READ OWRITE OREAD HWRITE HREADHelper types and parsing utilities
MVL9plus char_indexed_by_MVL9 MVL9_indexed_by_char MVL9plus_indexed_by_charNBSP MVL9_to_char char_to_MVL9 char_to_MVL9plusskip_whitespace check_punctuation fix_colon
MVL9plus char_indexed_by_MVL9 MVL9_indexed_by_char MVL9plus_indexed_by_charNBSP MVL9_to_char char_to_MVL9 char_to_MVL9plusskip_whitespace check_punctuation fix_colon -- 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 c : CHARACTER;
variable left : positive;
begin
while L /= null and L.all'length /= 0 loop
left := L.all'left;
c := L.all(left);
if (c = ' ' or c = NBSP or c = HT) then
read (L, c);
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;
Binary text I/O procedures
WRITE READ
WRITE READ 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;
Octal text I/O procedures
OWRITE OREAD
OWRITE OREAD 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;
Hexadecimal text I/O procedures
HWRITE HREAD
HWRITE HREAD 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;
Conversion to string functions
to_string to_hstring to_ostring
to_string to_hstring to_ostring 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;
Conversion from string with explicit widths
from_string from_ostring from_hstring
from_string from_ostring from_hstring 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;
Conversion from string using result size
from_string from_ostring from_hstring
from_string from_ostring 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;
