Real Reciprocal HDL Optimized
Libraries:
Fixed-Point Designer HDL Support /
Math Operations
Description
The Real Reciprocal HDL Optimized block computes 1/u, where u is a real scalar.
Examples
Implement Hardware-Efficient Real Divide HDL Optimized
How to use the Real Divide HDL Optimized block.
Customize Output Value of Real Divide HDL Optimized Block When Denominator Is Zero
Use the divideByZero port to customize the value of the block output when division by zero occurs.
Limitations
Data type override is not supported for the Real Reciprocal HDL Optimized block.
Ports
Input
u — Value to take reciprocal of
scalar | vector | matrix
Value to take the reciprocal of, specified as a real-valued scalar, vector, or matrix.
Slope-bias representation is not supported for fixed-point data types.
Data Types: single
| double
| fixed point
validIn — Whether input is valid
Boolean
scalar
Whether input is valid, specified as a Boolean scalar. This control signal
indicates when the data from the u input
port is valid. When this value is 1
(true
), the
block captures the value at the u input port. When this value is
0
(false
), the block ignores the input
samples.
Data Types: Boolean
Output
y — Reciprocal
real scalar
Reciprocal, returned as a real scalar with the data type specified by the Output datatype parameter.
Data Types: single
| double
| fixed point
divideByZero — Whether the value at output is the result of division by zero
Boolean
scalar
Since R2024b
Whether the value at the y output
port is the result of a division by zero operation, returned as a Boolean scalar. When
the value of this signal is 1
(true
), the
corresponding output value at the y port is the result of division by
zero. When the value of this signal is 0
(false
), the corresponding output value at the y port
is the result of division by a nonzero value.
See Division by Zero Behavior for a description of the default divide by zero behavior.
Dependencies
To enable this port, select the Show divide by zero port parameter.
Data Types: Boolean
validOut — Whether output data is valid
Boolean
scalar
Whether output data is valid, returned as a Boolean scalar. When the value of this
control signal is 1
(true
), the block has
successfully computed the output at port y. When
this value is 0
(false
), the output data is not
valid.
Data Types: Boolean
Parameters
Output datatype — Data type of output
fixdt(1,18,10)
(default) | single
| double
| fixdt(1,16,0)
| <data type expression>
Data type of output y,
specified as fixdt(1,18,10)
, single
,
double
, fixdt(1,16,0)
, or as a user-specified
data type expression. The type can be specified directly or expressed as a data type
object, such as Simulink.NumericType
.
In R2024b: Unsigned data types are supported for this parameter.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | OutputType |
Values: | fixdt(1,18,10) (default) | single | double | fixdt(1,16,0) | <data type expression> |
Data Types: | char | string |
Example: set_param(gcb,"OutputType","fixdt(1,16,0)")
Show divide by zero port — Whether to show the divideByZero
port
off
(default) | on
Since R2024b
Select this parameter to show the divideByZero port.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | dbzPort |
Values: | 0 (false) (default) | 1 (true) |
Data Types: | logical |
Example: set_param(gcb,"dbzPort",1)
Automatically select CORDIC maximum shift value based on input word length — Automatically select CORDIC maximum shift value based on input word length
on
(default) | off
Since R2024b
Automatically select the CORDIC maximum shift value based on input word length. When
this parameter is selected, the default CORDIC maximumShiftValue
is
equal to wl - 1
, where wl = u.WordLength +
~issigned(u)
.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | autoMaximumShiftVal |
Values: | on (default) | off |
Data Types: | char | string |
Example: set_param(gcb,"autoMaximumShiftVal","off")
CORDIC maximum shift value — Maximum shift value of hyperbolic vectoring CORDIC
wl - 1
(default) | 10
| positive integer-valued scalar
Since R2024b
Maximum shift value of hyperbolic vectoring CORDIC, specified as a positive
integer-valued scalar. The default value for this parameter is wl -
1
, where wl = u.WordLength + ~issigned(u)
.
Dependencies
To enable this parameter, clear the Automatically select CORDIC maximum shift value based on input word length parameter.
Tips
See Customizable Pipelining for more information.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | maximumShiftValue |
Values: | 10 (default) | positive integer-valued scalar |
Data Types: | char | string |
Example: set_param(gcb,"maximumShiftValue","10")
Number of iterations per pipeline register — Number of CORDIC iterations to perform per pipeline stage
1
(default) | positive integer-valued scalar
Since R2024b
Number of CORDIC iterations to perform per pipeline stage, specified as a positive integer-valued scalar.
See Customizable Pipelining for more information. See How to Interface with the Real Reciprocal HDL Optimized Block and Hardware Resource Utilization for more information and examples showing how this parameter impacts latency and hardware resource utilization.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | nIterPerReg |
Values: | 1 (default) | positive integer-valued scalar |
Data Types: | char | string |
Example: set_param(gcb,"nIterPerReg","2")
More About
Algorithms
CORDIC
CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see More About). The CORDIC algorithm eliminates the need for explicit multipliers.
Division by Zero Behavior
When the input u
is zero and has a fixed-point data type, then the
output y
is equal to upperbound(
.Output
datatype
)
For floating-point inputs, the Real Divide HDL Optimized block follows IEEE® Standard 754.
How to Interface with the Real Reciprocal HDL Optimized Block
Because of its fully pipelined nature, the Real Reciprocal HDL Optimized
block is able to accept input data on any cycle, including consecutive clock cycles. To send
input data to the block, the validIn
signal must be true. When the block
has finished the computation and is ready to send the output, it will change
validOut
to true for one clock cycle. For inputs set of consecutive
cycles, validOut
will also be set to true on consecutive cycles.
The latency is defined from the input to the corresponding output. For example in the
figure below, from In1
to Out1
, In2
to Out2
, In3
to Out3
.
The latency depends on the input data type, as summarized in the table.
Input Type | Latency |
---|---|
Fixed point or scaled double |
where
and |
Floating point | 0 |
Customizable Pipelining
The Real Reciprocal HDL Optimized block uses fully pipelined architecture
that implements iterative normalization and a CORDIC-based division algorithm. If the input
u is a
fixed-point or scaled double data type, the block uses multiple pipeline stages for
computation. If the input is a signed data type, the normalization requires
nextpow2(u.WordLength)
iterations. The number of CORDIC iterations
depends on the value of the CORDIC maximum shift
value parameter. A larger word length can provide higher resolution, but
requires more iterations to process. The Real Reciprocal HDL Optimized block
can perform multiple iterations per pipeline stage, which results in lower latency at the
cost of a longer critical path in the generated HDL code.
For example, if the word length of the input u is
18
, then normalization requires 5
iterations. If the
Automatically select
CORDIC maximum shift value based on input word length parameter is selected,
the CORDIC maximum shift value is 18 - 1 = 17
and requires
17
iterations. The total number of iterations is 5 + 17 =
22
and the latency of the block is ceil((total number of
iterations)/nIterPerReg) + 1
. If the number of iterations per pipeline register
is set to 1
, then the block latency is 23
; if the
number of iterations per pipeline register is set to 2
, then the block
latency is 12
. If the number of iterations per pipeline register is
greater than the total number of required iterations, the block performs all iterations in
one pipeline stage and the total latency is minimized to 2
.
Hardware Resource Utilization
This block supports HDL code generation using the Simulink® HDL Workflow Advisor. For an example, see HDL Code Generation and FPGA Synthesis from Simulink Model (HDL Coder) and Implement Digital Downconverter for FPGA (DSP HDL Toolbox).
This example data was generated by synthesizing the block on a Xilinx® Zynq®-7000 xc7z045 SoC. The synthesis tool was Vivado® v2023.1.2.
The following synthesis results show the effect of the Number of iterations per pipeline register parameter on the latency and hardware resource utilization.
nIterPerReg = 1
These parameters were used for synthesis:
Input data type:
sfix18_en10
Output data type:
sfix18_en10
Input dimension: scalar
Automatically select CORDIC maximum shift value based on input word length:
on
Number of iterations per pipeline register:
1
Target frequency: 500 MHz
Latency for this configuration: 23
Resource | Usage | Available | Utilization (%) |
---|---|---|---|
Slice LUTs | 815 | 218600 | 0.37 |
Slice Registers | 703 | 437200 | 0.16 |
DSPs | 0 | 900 | 0.00 |
Block RAM Tile | 0 | 545 | 0.00 |
URAM | 0 | 0 |
Value | |
---|---|
Requirement | 2 ns (500 MHz) |
Data Path Delay | 1.74 ns |
Slack | 0.176 ns |
Clock Frequency | 548.25 MHz |
nIterPerReg = 2
These parameters were used for synthesis:
Input data type:
sfix18_en10
Output data type:
sfix18_en10
Input dimension: scalar
Automatically select CORDIC maximum shift value based on input word length:
on
Number of iterations per pipeline register:
2
Target frequency: 300 MHz
Latency for this configuration: 12
Resource | Usage | Available | Utilization (%) |
---|---|---|---|
Slice LUTs | 705 | 218600 | 0.32 |
Slice Registers | 374 | 437200 | 0.09 |
DSPs | 0 | 900 | 0.00 |
Block RAM Tile | 0 | 545 | 0.00 |
URAM | 0 | 0 |
Value | |
---|---|
Requirement | 3.3333 ns (300 MHz) |
Data Path Delay | 2.65 ns |
Slack | 0.676 ns |
Clock Frequency | 376.32 MHz |
nIterPerReg = 3
These parameters were used for synthesis:
Input data type:
sfix18_en10
Output data type:
sfix18_en10
Input dimension: scalar
Automatically select CORDIC maximum shift value based on input word length:
on
Number of iterations per pipeline register:
3
Target frequency: 200 MHz
Latency for this configuration: 9
Resource | Usage | Available | Utilization (%) |
---|---|---|---|
Slice LUTs | 680 | 218600 | 0.31 |
Slice Registers | 281 | 437200 | 0.06 |
DSPs | 0 | 900 | 0.00 |
Block RAM Tile | 0 | 545 | 0.00 |
URAM | 0 | 0 |
Value | |
---|---|
Requirement | 5 ns (200 MHz) |
Data Path Delay | 3.889 ns |
Slack | 1.125 ns |
Clock Frequency | 258.06 MHz |
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Slope-bias representation is not supported for fixed-point data types.
HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has one default HDL architecture.
General | |
---|---|
ConstrainedOutputPipeline | Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is
|
In R2024b: FlattenHierarchy | Remove PWM Reference Generator block hierarchy from
generated HDL code. The default is |
InputPipeline | Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is
|
OutputPipeline | Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is
|
Supports fixed-point data types only.
Version History
Introduced in R2021aR2024b: Custom pipelining, improved latency and resource utilization, optional divide by zero port
Several improvements have been made to the Real Reciprocal HDL Optimized block:
Custom pipelining is supported via the new CORDIC maximum shift value and Number of iterations per pipeline register parameters.
The latency of this block has been reduced. Latency depends on the specified data type and pipeline configuration. See How to Interface with the Real Reciprocal HDL Optimized Block for more information.
HDL resource utilization has been further optimized to require fewer hardware resources. See Hardware Resource Utilization for example synthesis results.
An optional divideByZero port has been added to output a flag when the corresponding output is a result of division by zero.
R2024b: Support for unsigned output
The Real Reciprocal HDL Optimized block now supports unsigned data types for the Output datatype parameter.
See Also
Blocks
Functions
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