A Method for the Development of
Combined Floating- and Fixed-Point
SystemC Models
Yves Vanderperren
[email protected]
5. European SystemC Users Group Meeting
All rights reserved
05/03/2002
 2002 - Alcatel Microelectronics
Outline
t
Introduction: Gap between Floating- and Fixed-Point
t
Floating- and Fixed-Point Values
t
Bridging the Gap to Fixed-Point with
t
Conclusions
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
2
Introduction:
Gap between Floating- and
Fixed-Point
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
3
Gap Floating- vs. Fixed-point
?
Floating-Point
“unlimited” range
05/03/2002
Fixed-Point
limited precision
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
4
Gap Floating- vs. Fixed-Point
•
Floating-Point
t
Fixed-Point
Conversion of the SystemC model to fixed-point
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
5
Gap Floating- vs. Fixed-Point
‚
fixed-point
design
...
simulation
Floating-Point
t
t
Fixed-Point design
space exploration
Fixed-Point
Conversion of the SystemC model to fixed-point
Fixed-point design space exploration
l
scale properly
t
t
l
minimize cost & power with precision constraint
t
05/03/2002
avoid overflow
avoid quantization error
use as few bits as possible
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
6
Gap Floating- vs. Fixed-Point
t
Example :
SC_MODULE(accumulator) {
SC_MODULE(accumulator) {
// input ports
// input ports
sc_in<double> In;
sc_in<double> In;
sc_in<bool>
Rst;
sc_in<bool>
Rst;
sc_in_clk
Clk;
sc_in_clk
Clk;
// output ports
// output ports
sc_out<double> Out;
sc_out<double> Out;
...
...
};
};
05/03/2002
SC_MODULE(accumulator)
SC_MODULE(accumulator) {{
//
// input
input ports
ports
sc_in<sc_fixed<8,1>
sc_in<sc_fixed<8,1> >> In;
In;
sc_in<bool>
Rst;
sc_in<bool> Rst;
sc_in_clk
sc_in_clk Clk;
Clk;
floating
point
//
// output
output ports
ports
sc_out<sc_fixed<8,1>
sc_out<sc_fixed<8,1> >> Out;
Out;
fixed
point
...
...
};
};
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
7
Gap Floating- vs. Fixed-Point
fixed-point
design
stsetepp
s
i
ththis
e
r
k
mmaakeeaasiseier
e
simulation
ioionn
s
r
e s
oonnvver
c
id c
aavvooid
Floating-Point
t
t
Fixed-Point design
space exploration
...
Fixed-Point
Conversion of the SystemC model to fixed-point
Fixed-point design space exploration
l
scale properly
t
t
l
minimize cost & power with precision constraint
t
05/03/2002
avoid overflow
avoid quantization error
use as few bits as possible
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
8
Floating- and Fixed-Point Values
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
9
Floating- and Fixed-Point Values
t
Fixed-point representation: binary word
l
l
t
wl: total word length
iwl: integer word length
MSB
biwl-1
LSB
...
b1
b0
...
biwl-wl
binary
point
Link to floating-point: Slope & Bias encoding scheme
n fl ≅ n fx = slope ⋅ nq + bias
if unsigned : nq =
iwl −1
∑
0.11
0.10
bi 2 i
0.01
0.00
i =iwl − wl
if signed : nq = −biwl −1 2
nq
fixed point
value nfx
iwl −1
+
∑
1.10
floating point
value nfl
slope
bias = 0
1.11
iwl − 2
bi 2
i
1.01
i =iwl − wl
1.00
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
10
Floating- and Fixed-Point Values
t
Example :
l
l
l
l
sensor measuring water temperature
range is limited: 0 to 100 ºC
bias is 0
to be mapped onto 8 bits unsigned
6 1 bit ⇔ 1 °C leads to a waste of precision
4 1 bit ⇔ 100/255 °C is better
fixed point value
(bits)
6
4
00000110
00000000
0°C
0°C
00000101
00000001
1°C
0.4°C
00000100
00000010
2°C
0.8°C
100°C
39.2°C
00000011
00000010
slope-1 = 100/255 [°C/bit]
…
01100100
…
11111111
00000001
00000000
imposs.
100°C
fl. point value
(degrees)
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
11
Bridging the Gap
to Fixed-Point with
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
12
Fixed-Point with SystemC
t
SystemC enables fixed-point or floating-point models
6
6specific
specificoperations
operations
DUT
floating
point
double
in
TB
6
6conversion
conversionneeded
needed
out
float
6
6maintenance
maintenance
6
6no
noscale,
scale,no
nolink
link
between
fl.
&
between fl. &fx.
fx.
DUT
fixed
point
sc_fixed<…>
TB
05/03/2002
6
622models
models
out
fixed
6
6fixed-point
fixed-pointdesign
design
space
spaceexploration
exploration
6
6...
...
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
13
Fixed-Point with SystemC
t
Gap bridged by introducing a new data type
l
l
carrying BOTH floating- and fixed-point values,
and the associated slope
conditions evaluated using the floating- or the fixed-point value,
depending on a precision mode flag
DUT
fl. point
DUT
fl. & fx.
point
TB
DUT
fx. point
in
TB
out
fl&fx
TB
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
14
Fixed-Point with SystemC
t
Definition of the new
data type
fx_double
floating point value
scale
fixed point value
fixed point parameters
precision mode
t
double
double
bits
word length, quantization mode, overflow mode
flag: floating- or fixed-point mode
Example of arithmetic operation
25.36
[°C]
100/255 [°C/bit]
b#01000000 {⇔ 25.1 [°C]}
(8,8,SC_TRN,SC_WRAP)
Floating-point mode
+
note:
05/03/2002
45
[°C]
100/255 [°C/bit]
b#01110010 {⇔ 44.7 [°C]}
(8,8,SC_TRN,SC_WRAP)
Floating-point mode
=
70.36
[°C]
100/255 [°C/bit]
b#10110010 {⇔ 69.8 [°C]}
(8,8,SC_TRN,SC_WRAP)
Floating-point mode
70.36 [°C] / (100/255 [°C/bit] ) = b#10110011
propagation
of rounding
errors
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
15
Fixed-Point with SystemC
t
Example of relational operation
25.36
[°C]
100/255 [°C/bit]
b#01000000 {⇔ 25.1 [°C]}
(8,8,SC_TRN,SC_WRAP)
Floating-point mode
25.36
[°C]
100/255 [°C/bit]
b#01000000 {⇔ 25.1 [°C]}
(8,8,SC_TRN,SC_WRAP)
Fixed-point mode
05/03/2002
>
25.2
[°C]
100/255 [°C/bit]
b#01000000 {⇔ 25.1 [°C]}
(8,8,SC_TRN,SC_WRAP)
Floating-point mode
>
25.2
[°C]
100/255 [°C/bit]
b#01000000 {⇔ 25.1 [°C]}
(8,8,SC_TRN,SC_WRAP)
Fixed-point mode
Yes
No
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
16
Gap Floating- vs. Fixed-Point
t
Example :
combined
SC_MODULE(accumulator)
SC_MODULE(accumulator) {{
//
// input
input ports
ports
sc_in<double>
sc_in<double> In;
In;
sc_in<bool>
Rst;
sc_in<bool>
Rst;
sc_in_clk
Clk;
sc_in_clk
Clk;
//
// output
output ports
ports
sc_out<double>
sc_out<double> Out;
Out;
...
...
};
};
SC_MODULE(accumulator)
SC_MODULE(accumulator) {{
//
// input
input ports
ports
sc_in<sc_fixed<8,1>
sc_in<sc_fixed<8,1> >> In;
In;
sc_in<bool>
sc_in<bool> Rst;
Rst;
sc_in_clk
sc_in_clk Clk;
Clk;
SC_MODULE(accumulator) {
SC_MODULE(accumulator) {
// input ports
// input ports
sc_in<fx_double>
sc_in<fx_double> In;
In;
sc_in<bool> Rst;
sc_in<bool> Rst;
sc_in_clk
Clk;
sc_in_clk
Clk;
//
// output
output ports
ports
sc_out<fx_double> Out;
sc_out<fx_double> Out;
...
...
};
};
//
// output
output ports
ports
sc_out<sc_fixed<8,1>
sc_out<sc_fixed<8,1> >> Out;
Out;
...
...
};
};
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
17
Fixed-Point with SystemC
t
Experimental results
ρ xx (n) =
L −1
∑ x(n − L − k ) ⋅ x* (n − k )
k =0
fx
config
DUT
fl. & fx.
point
in
05/03/2002
TB
out
fl&fx
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
18
Fixed-Point with SystemC
t
Experimental results (
normalized
speed
Floating-point
Fixed-point
Fixed-point+
Floating-point
v2.0)
…
…but
butreduced
reduceddesign
designtime
time! !
fx_double
fx_double
(with type verif.)
20
18
16
14
12
10
8
6
4
2
0
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
19
Conclusions
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
20
Conclusions
t
Pros & Cons
4
4no
noconversion
conversion
6
6simulation
simulationspeed
speed
4
4common
commonoperations
operations
6
6good
goodstyle
stylerequired
required
4
4common
commoninterfaces,
interfaces,
enhanced
enhancedreuse
reuse
4
411model
model
4
4maintenance
maintenance
4
4scale
scalepropagation
propagation
4
4dynamic
dynamicscale
scale
4
4fixed-point
fixed-pointdesign
design
space
exploration
space exploration
Questions?
4
4strong
strongtype-checking
type-checking
05/03/2002
A Method for the Development of Combined Floating- and Fixed-Point SystemC Models,  2002 - Alcatel Microelectronics
21