intel ALTERA_CORDIC IP Core User Guide
- June 9, 2024
- Intel
Table of Contents
intel ALTERA_CORDIC IP Core
ALTERA_CORDIC IP Core User Guide
- Use the ALTERA_CORDIC IP core to implement a set of fixed-point functions with the CORDIC algorithm.
- ALTERA_CORDIC IP Core Features on page 3
- DSP IP Core Device Family Support on page 3
- ALTERA_CORDIC IP Core Functional Description on page 4
- ALTERA_CORDIC IP Core Parameters on page 7
- ALTERA_CORDIC IP Core Signals on page 9
ALTERA_CORDIC IP Core Features
- Supports fixed-point implementations.
- Supports both latency and frequency driven IP cores.
- Supports both VHDL and Verilog HDL code generation.
- Produces fully unrolled implementations.
- Produces faithfully rounded results to either of the two closest representable numbers in the output.
DSP IP Core Device Family Support
Intel offers the following device support levels for Intel FPGA IP cores:
- Advance support—the IP core is available for simulation and compilation for this device family. FPGA programming file (.pof) support is not available for Quartus Prime Pro Stratix 10 Edition Beta software and as such IP timing closure cannot be guaranteed. Timing models include initial engineering estimates of delays based on early post-layout information. The timing models are subject to change as silicon testing improves the correlation between the actual silicon and the timing models. You can use this IP core for system architecture and resource utilization studies, simulation, pinout, system latency assessments, basic timing assessments (pipeline budgeting), and I/O transfer strategy (data-path width, burst depth, I/O standards tradeoffs).
- Preliminary support—Intel verifies the IP core with preliminary timing models for this device family. The IP core meets all functional requirements, but might still be undergoing timing analysis for the device family. You can use it in production designs with caution.
- Final support—Intelverifies the IP core with final timing models for this device family. The IP core meets all functional and timing requirements for the device family. You can use it in production designs.
Intel Corporation. All rights reserved. Intel, the Intel logo, and other Intel marks are trademarks of Intel Corporation or its subsidiaries. Intel warrants performance of its FPGA and semiconductor products to current specifications in accordance with Intel’s standard warranty, but reserves the right to make changes to any products and services at any time without notice. Intel assumes no responsibility or liability arising out of the application or use of any information, product, or service described herein except as expressly agreed to in writing by Intel. Intel customers are advised to obtain the latest version of device specifications before relying on any published information and before placing orders for products or services. *Other names and brands may be claimed as the property of others.
DSP IP Core Device Family Support
| Device Family | Support |
|---|---|
| Arria® II GX | Final |
| Arria II GZ | Final |
| Arria V | Final |
| Intel® Arria 10 | Final |
| Cyclone® IV | Final |
| Cyclone V | Final |
| Intel MAX® 10 FPGA | Final |
| Stratix® IV GT | Final |
| Stratix IV GX/E | Final |
| Stratix V | Final |
| Intel Stratix 10 | Advance |
| Other device families | No support |
ALTERA_CORDIC IP Core Functional Description
- SinCos Function on page 4
- Atan2 Function on page 5
- Vector Translate Function on page 5
- Vector Rotate Function on page 6
SinCos Function
Computes the sine and cosine of angle a.
SinCos Function
ALTERA_CORDIC IP Core User Guide 683808 | 2017.05.08
The function supports two configurations, depending on the sign attribute
of a:
- If a is signed, the allowed input range is [-π,+π] and the output range for the sine and cosine is ∈[−1,1].
- If a is unsigned, the IP core restricts the input to [0,+π/2] and restricts the output range to [0,1].
Atan2 Function
Computes the function atan2(y, x) from inputs y and x.
Atan2 Function
- If x and y are signed, the IP core determines the input range from the fixed-point formats.
- The output range is [-π,+π].
Vector Translate Function
The vector translate function is an extension of the atan2 function. It
outputs the magnitude of the input vector and the angle a=atan2(y,x).
Vector Translate Function
The function takes inputs x and y and outputs a=atan2(y, x) and M = K( x2+y2)0.5. M is the magnitude of the input vector v=(x,y)T, scaled by a CORDIC specific constant that converges to 1.646760258121, which is transcendental, hence has no fixed value. The functions supports two configurations, depending on the sign attribute of x and y:
- If the inputs are signed, the formats give the allowed input range. In this configuration the output range for a is∈[−π,+π]. The output range for M depends on the input range of x and y, according with the magnitude formula.
- If the inputs are unsigned, the IP core restricts the output value for a [0,+π/2]. The magnitude value still depends on the formula.
Vector Rotate Function
The vector rotate function takes a vector v= (x,y)T given by the two
coordinates x and y and an angle a. The function produces a similarity
rotation of vector v by the angle a to produce the vector v0=(x0,y0)T.
Vector Rotate Function
The rotation is a similarity rotation because the magnitude of the produced
vector v0 is scaled up by the CORDIC specific constant K(˜1.646760258121). The
equations of the coordinates for vector v0 are:
- x0 = K(xcos(a)−ysin(a))
- y0 = K(xsin(a)+ ycos(a))
If you set the sign attribute to true for the x,y inputs for the function, the IP core restricts their range to [−1,1]. You provide the number of fractional bits. The input angle a is allowed in the range [−π,+π], and has the same number of fractional bits as the other inputs. You provide the output fractional bits and the total width of the output is w=wF+3, signed. For unsigned inputs x,y, the IP core restricts the range to [0,1], the angle a to [0,π].
ALTERA_CORDIC IP Core Parameters
SinCos Parameters
| Parameter | Values | Description |
|---|
Input data widths
Fraction F| 1 to 64| Number of fraction bits.
Width w| Derived| Width of fixed-point data.
Sign| signed or unsigned| The sign of the fixed-point data.
Output data widths
Fraction| 1 to 64, where
F OUT ≤ F IN
| Number of fraction bits.
Width| Derived| Width of fixed-point data.
Sign| Derived| The sign of the fixed-point data.
Generate enable port| On or off| Turn on for enable signal.
Atan2 Parameters
| Parameter | Values | Description |
|---|
Input data widths
Fraction| 1 to 64| Number of fraction bits.
Width| 3 to 64| Width of fixed-point data.
Sign| signed or unsigned| The sign of the fixed-point data.
Output data widths
Fraction| | Number of fraction bits.
Width| Derived| Width of fixed-point data.
Sign| Derived| The sign of the fixed-point data.
Generate enable port| On or off| Turn on for enable signal.
LUT Size Optimization| | Turn on to move some of the typical CORDIC
operations into look up tables to reduce implementation cost.
Manually Specify LUT Size| | Turn on to input the LUT size. Larger values
(9-11) enable mapping some computations to memory blocks Only when LUT Size
Optimization is on..
Vector Translate Parameters
| Parameter | Values | Description |
|---|
Input data widths
Fraction| 1 to 64| Number of fraction bits.
Width| Signed: 4 to
64; unsigned: F
to 65
| Width of fixed-point data.
continued…
Parameter| Values| Description
---|---|---
Sign| signed or unsigned| The sign of the fixed-point data
Output data widths
Fraction| 1 to 64| Number of fraction bits.
Width| Derived| Width of fixed-point data.
Sgn| Derived| The sign of the fixed-point data
Generate enable port| On or off| Turn on for enable signal.
Scale factor compensation| On or off| For vector translate, a CORDIC specific
constant that converges to 1.6467602… scales the magnitude of the vector
(x2+y2)0.5 so that the value for the magnitude, M , is M = K(x2+y2)0.5.
The format of the output depends on the input format. The largest output value occurs when both the inputs are equal to the maximum representable input value, j.
In this context:
M = K ( j 2+ j 2)0.5
= K (2 j 2)0.5
= K 20.5( j 2)0.5
= K 20.5 j ~2.32 j
Therefore, two extra bits left of the MSB of j are required to ensure M is representable. If scale factor compensation is selected, M becomes: M = j0.5 ~ 1.41 j
One extra bit is sufficient for representing the range of M. Scale factor compensation affects the total width of the output.
Vector Rotate Parameters
| Parameter | Values | Description |
|---|
Input data widths
X,Y inputs
Fraction| 1 to 64| Number of fraction bits.
Width| Derived| Width of fixed-point data.
Sign| signed or unsigned| The sign of the fixed-point data.
Angle input
Fraction| Derived| –
Width| Derived| –
Sign| Derived| –
Output data widths
Fraction| 1 to 64| Number of fraction bits.
Width| Derived| Width of fixed-point data.
Sign| Derived| The sign of the fixed-point data
Generate enable port| On or off| Turn on for enable signal.
Scale factor compensation| | Turn on to compensate the CORDIC-specific
constant on the magnitude output. For both signed and unsigned inputs, turning
on decreases by 1 the weight of the magnitude for x0 and y0. The outputs
belong to the interval [-20.5, +20.5]K. Under default settings, the output
interval will therefore be [-20.5K , +20.5K] (with
continued…
Parameter| Values| Description
---|---|---
| | K~1.6467602…), or ~[-2.32, +2.32]. Representing the values in this
interval requires 3 bits left of the binary point, one of which is for the
sign. When you turn on Scale factor compensation , the output interval
becomes [-20.5, +20.5] or ~[-1.41, 1.41], which requires two bits left of the
binary point, one of which is for the sign.
Scale factor compensation affects the total width of the output.
ALTERA_CORDIC IP Core Signals
Common Signals
| Name | Type | Description |
|---|---|---|
| clk | Input | Clock. |
| en | Input | Enable. Only available when you turn on **Generate an enable |
port**.
areset| Input| Reset.
Sin Cos Function Signals
| Name | Type | Configurati on | Range | Description |
|---|---|---|---|---|
| a | Input | Signed input | [ −π, + π ] | Specifies the number of fractional |
bits ( F IN). The total width of this input is F IN+3.Two extra bits are
for the range (representing π ) and one bit for the sign. Provide the input
in two’s complement form.
Unsigned input| [0 , + π/ 2]| Specifies the number of fractional bits (
F IN). The total width of this input is w IN= F IN+1. The one extra bit
accounts for the range (required to represent π/2).
s, c| Output| Signed input| [ − 1 , 1]| Computes sin(a) and cos(a) on a
user-specified output fraction width( F ). The output has width w OUT= F
OUT+2 and is signed.
Unsigned input| [0 , 1]| Computes sin(a) and cos(a) on a user-specified
output fraction width( F OUT). The output has the width w OUT= F OUT+1
and is unsigned.
Atan2 Function Signals
| Name | Type | Configurati on | Range | Details |
|---|---|---|---|---|
| x, y | Input | Signed input | Given by |
w , F
| Specifies the total width ( w ) and number fractional bits ( F ) of the
input. Provide the inputs in two’s complement form.
Unsigned input| Specifies the total width ( w ) and number fractional bits (
F ) of the input.
a| Ouput| Signed input| [ −π, + π ]| Computes atan2(y,x) on a user-
specified output fraction width ( F ). The output has the width w OUT= F
OUT+2 and is signed.
Unsigned input| [0 , + π/ 2]| Computes atan2(y,x) on output fraction width
( F OUT). The output format has the width w OUT = F OUT+2 and is signed.
However, the output value is unsigned.
Name| Direction| Configurati on| Range| Details
---|---|---|---|---
x, y| Input| Signed input| Given by
w , F
| Specifies the total width ( w ) and number fractional bits ( F ) of the
input. Provide the inputs in two’s complement form.
q| Output| | [ −π, + π ]| Computes atan2(y,x) on a user-specified output
fraction width F q. The output has the width w q= F q+3 and is signed.
r| | | Given by
w , F
| Computes K (x2+y2)0.5.
The total width of the output is w r= F q+3, or w r= F q+2 with scale factor compensation.
| | | | The number of meaningful bits depends on the number of iterations
which depends on F q. The format of the output depends on the input format.
| | | | MSB(MOUT)=MSBIN+2, or MSB(MOUT)=MSBIN+1 with scale factor
compensation
x, y| Input| Unsigned input| Given by
w , F
| Specifies the total width ( w ) and number fractional bits ( F ) of the
input.
q| Output| | [0 , + π/ 2]| Computes atan2(y,x) on an output fraction
width F q. The output has the width w q= F q+2 and is signed.
r| | | Given by
w , F
| Computes K( x2+y2)0.5.
The total width of the output is w r= F q+3, or w r= F q+2 with scale factor compensation.
| | | | MSB(MOUT)=MSBIN+2, or MSB(MOUT)=MSBIN+1 with scale factor
compensation.
Name| Direction| Configurati on| Range| Details
---|---|---|---|---
x, y| Input| Signed input| [ − 1 , 1]| Specifies the fraction width ( F
), total number of bits is w = F +2. Provide the inputs in two’s
complement form.
Unsigned input| [0 , 1]| Specifies the fraction width ( F ), total number
of bits is w = F +1.
a| Input| Signed input| [ −π, + π ]| Number of fractional bits is F
(provided previously for x and y), total width is w a = F +3.
Unsigned input| [0 , + π ]| Number of fractional bits is F (provided
previously for x and y), total width is w a = F +2.
x0, y0| Output| Signed input| [ − 20.5 , +20.
5] K
| Number of fractional bits F OUT, where w OUT = F OUT+3 or w OUT =
F OUT+2 with scale factor reduction.
Unsigned input
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