This floating point unit is conform to IEEE 754-2008 standards. Supported operations are compare, min-max, conversions, addition, subtruction, multiplication, fused multiply add, square root and division in single and double precisions. Except square root and division all operations are pipelined.
This unit uses canonical nan (not a number) form, if it generates any nan as output. E.g. 0x7FC00000 for single precision and 0x7FF8000000000000 for double precision. Therefore extra conditions are added in order compare outputs with testfloat data correctly by nan generation.
Square root and division calculations are using same subunit but different path (algorithm). This subunit has a generic variable performance. For functional iterations which are fast please use 1 and fixed point iterations which are slow use 0. This unit has also own multiplier.
DESIGN
This floating point unit uses only one path for both single and double precisions by scaling up both of them to the pseudo extended precision. The main benefit of this implementation is that the design needs few resources because we do not implement extension in pipeline to handle subnormal numbers. It means that all floating numbers are normalized thanks to pseudo extended precision. The main disadvantage of this unit is that it is not suitable for single instruction multiple data (simd) architecture.
sign
exponent
mantissa
single
1
8
23
double
1
11
52
pseudo
1
12
52
LATENCY
Single and Double Precision
comp
max
conv
add
sub
mul
fma
1
1
1
3
3
3
3
Single Precision
performance
division
square root
0
29
28
1
14
17
Double Precision
performance
division
square root
0
58
57
1
14
17
SIGNALS
INPUT
fp_unit_i.fp_exe_i.data1 => rs1
fp_unit_i.fp_exe_i.data2 => rs2
fp_unit_i.fp_exe_i.data3 => rs3
fp_unit_i.fp_exe_i.op => operation type
fp_unit_i.fp_exe_i.fmt => precision type
fp_unit_i.fp_exe_i.rm => rounding mode
fp_unit_i.fp_exe_i.enable => activate unit
TYPE
op
type
fmadd
$(rs1×rs2)+rs3$
fmsub
$(rs1×rs2)-rs3$
fnmsub
$-(rs1×rs2)+rs3$
fnmadd
$-(rs1×rs2)-rs3$
fadd
$rs1+rs2$
fsub
$rs1-rs2$
fmul
$rs1*rs2$
fdiv
$rs1/rs2$
fsqrt
$\sqrt{rs1}$
op
rm
type
fsgnj
"000"
J
fsgnj
"001"
JN
fsgnj
"010"
JX
op
rm
type
fcmp
"000"
EQ
fcmp
"001"
LT
fcmp
"010"
LE
op
rm
type
fmax
"000"
MIN
fmax
"001"
MAX
op
op.fcvt_op
fmt
type
fcvt_f2i
"00"
"00"
CONVERSION FROM FLOAT TO INT32
fcvt_f2i
"01"
"00"
CONVERSION FROM FLOAT TO UINT32
fcvt_f2i
"10"
"00"
CONVERSION FROM FLOAT TO INT64
fcvt_f2i
"11"
"00"
CONVERSION FROM FLOAT TO UINT64
fcvt_f2i
"00"
"01"
CONVERSION FROM DOUBLE TO INT32
fcvt_f2i
"01"
"01"
CONVERSION FROM DOUBLE TO UINT32
fcvt_f2i
"10"
"01"
CONVERSION FROM DOUBLE TO INT64
fcvt_f2i
"11"
"01"
CONVERSION FROM DOUBLE TO UINT64
op
op.fcvt_op
fmt
type
fcvt_i2f
"00"
"00"
CONVERSION FROM INT32 TO FLOAT
fcvt_i2f
"01"
"00"
CONVERSION FROM UINT32 TO FLOAT
fcvt_i2f
"10"
"00"
CONVERSION FROM INT64 TO FLOAT
fcvt_i2f
"11"
"00"
CONVERSION FROM UINT64 TO FLOAT
fcvt_i2f
"00"
"01"
CONVERSION FROM INT32 TO DOUBLE
fcvt_i2f
"01"
"01"
CONVERSION FROM UINT32 TO DOUBLE
fcvt_i2f
"10"
"01"
CONVERSION FROM INT64 TO DOUBLE
fcvt_i2f
"11"
"01"
CONVERSION FROM UINT64 TO DOUBLE
op
op.fcvt_op
fmt
type
fcvt_f2f
"01"
"00"
CONVERSION FROM DOUBLE TO FLOAT
fcvt_f2f
"00"
"01"
CONVERSION FROM FLOAT TO DOUBLE
fmt
type
"00"
FLOAT
"01"
DOUBLE
rm
type
"000"
RNE
"001"
RTZ
"010"
RDN
"011"
RUP
"100"
RMM
OUTPUT
fp_unit_o.fp_exe_o.result => calculation result
fp_unit_o.fp_exe_o.flags => exception flags
fp_unit_o.fp_exe_o.ready => ready status
TYPE
flags
type
"00001"
NX
"00010"
UF
"00100"
OF
"01000"
DZ
"10000"
NV
TOOLS
The installation scripts of necessary tools are located in directory tools. These scripts need root permission in order to install packages and tools for simulation and testcase generation. Please run these scripts in directory tools locally.
GENERATE
To generate test cases you could use following command:
make generate
SIMULATION
To simulate the design together with generated test cases you could run following command:
make simulate
This command requires two options for hardware description languages VERILOG and VHDL. The possible settings of these options can be found in the makefile.
Some example executions of this command look like as follows: