CORDIC-PM-UT1

CORDIC IP Core User’s Guide August 2012 IPUG81_01.3 Table of Contents Chapter 1. Introduction .......................................................................................................................... 4 Quick Facts ........................................................................................................................................................... 4 Features ................................................................................................................................................................ 7 Chapter 2. Functional Description ........................................................................................................ 9 General Description of the CORDIC Algorithm ..................................................................................................... 9 Block Diagram..................................................................................................................................................... 11 Data Path ................................................................................................................................................... 11 CORDIC Functions .................................................................................................................................... 12 Interface Diagram................................................................................................................................................ 14 Configuring the CORDIC IP Core ....................................................................................................................... 15 Basic Options ............................................................................................................................................. 15 Advanced Options...................................................................................................................................... 16 Timing Specifications .......................................................................................................................................... 18 Chapter 3. Parameter Settings ............................................................................................................ 20 Basic Options Tab............................................................................................................................................... 20 Mode .......................................................................................................................................................... 21 Architecture ................................................................................................................................................ 21 Iterations .................................................................................................................................................... 21 Compensation ............................................................................................................................................ 21 Pre-Rotation ............................................................................................................................................... 21 Advanced Options Tab........................................................................................................................................ 21 Data Width ................................................................................................................................................. 21 Rounding.................................................................................................................................................... 21 Optional Ports ............................................................................................................................................ 21 Synthesis Options ...................................................................................................................................... 22 Chapter 4. IP Core Generation............................................................................................................. 23 Licensing the IP Core.......................................................................................................................................... 23 Getting Started .................................................................................................................................................... 23 IPexpress-Created Files and Top Level Directory Structure............................................................................... 25 Instantiating the Core ......................................................................................................................................... 27 Running Functional Simulation .......................................................................................................................... 27 Synthesizing and Implementing the Core in a Top-Level Design ...................................................................... 27 Hardware Evaluation........................................................................................................................................... 28 Enabling Hardware Evaluation in Diamond................................................................................................ 28 Enabling Hardware Evaluation in ispLEVER.............................................................................................. 28 Updating/Regenerating the IP Core .................................................................................................................... 28 Regenerating an IP Core in Diamond ........................................................................................................ 29 Regenerating an IP Core in ispLEVER ...................................................................................................... 29 Chapter 5. Core Verification ................................................................................................................ 31 Chapter 6. Support Resources ............................................................................................................ 32 Lattice Technical Support.................................................................................................................................... 32 Online Forums............................................................................................................................................ 32 Telephone Support Hotline ........................................................................................................................ 32 E-mail Support ........................................................................................................................................... 32 Local Support ............................................................................................................................................. 32 Internet ....................................................................................................................................................... 32 References.......................................................................................................................................................... 32 LatticeEC/ECP ........................................................................................................................................... 32 LatticeECP2M ............................................................................................................................................ 33 © 2012 Lattice Semiconductor Corp. All Lattice trademarks, registered trademarks, patents, and disclaimers are as listed at www.latticesemi.com/legal. All other brand or product names are trademarks or registered trademarks of their respective holders. The specifications and information herein are subject to change without notice. IPUG81_1.3, August 2012 2 CORDIC IP Core User’s Guide Table of Contents LatticeECP3 ............................................................................................................................................... 33 LatticeSCM................................................................................................................................................. 33 LatticeXP.................................................................................................................................................... 33 LatticeXP2.................................................................................................................................................. 33 Revision History .................................................................................................................................................. 33 ............................................................................................................................................................................ 33 Appendix A. Resource Utilization ....................................................................................................... 34 LatticeEC Devices............................................................................................................................................... 34 Ordering Part Number................................................................................................................................ 34 LatticeECP Devices ............................................................................................................................................ 35 Ordering Part Number................................................................................................................................ 35 LatticeECP2 Devices .......................................................................................................................................... 35 Ordering Part Number................................................................................................................................ 35 LatticeECP2M Devices ....................................................................................................................................... 35 Ordering Part Number................................................................................................................................ 35 LatticeECP3 Devices .......................................................................................................................................... 36 Ordering Part Number................................................................................................................................ 36 LatticeSC and LatticeSCM Devices .................................................................................................................... 36 Ordering Part Number................................................................................................................................ 36 LatticeXP Devices ............................................................................................................................................... 36 Ordering Part Number................................................................................................................................ 36 LatticeXP2 Devices ............................................................................................................................................. 37 Ordering Part Number................................................................................................................................ 37 IPUG81_1.3, August 2012 3 CORDIC IP Core User’s Guide Chapter 1: Introduction This user’s guide provides a description of Lattice’s Coordinate Rotation Digital Computer (CORDIC) IP core. The CORDIC IP core is configurable and supports several functions, including rotation, translation, sin and cos, and arctan. Two architecture configurations are supported for the arithmetic unit: parallel, in which the output data is calculated in a single clock cycle, and word-serial, in which the output data is calculated over multiple clock cycles. The input and output data widths and computation iterative numbers are configurable over a wide range of values. The IP core uses full precision arithmetic internally while supporting variable output precision and several choices of rounding algorithms. Quick Facts Table 1-1 through Table 1-7 give quick facts about the CORDIC IP core for LatticeECP™, LattceECP2™, LatticeECP2M™, LatticeECP3™, LatticeSC/M™, LatticeXP™, and LatticeXP2™ devices, respectively. Table 1-1. CORDIC IP Core for LatticeECP Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements Resource Utilization FPGA Families Supported Rotate Serial Translate Serial LatticeECP Minimal Device Needed LFECP6E3T114 LFECP6E3T114 LFECP6E3T114 LFECP6E3T114 Targeted Device LFECP20E5F484C LFECP20E5F484C LFECP20E5F484C LFECP20E5F484C Data Path Width 16 16 16 16 1300 1200 600 700 LUTs sysMEM EBRs Registers Lattice Implementation Design Tool Support Translate Parallel Synthesis 0 0 0 0 1300 1200 300 400 Lattice Diamond™ 1.0 or ispLEVER® 8.1 Synopsys® Synplify™ Pro for Lattice D-2009.12L-1 Aldec® Active-HDL™ 8.2 Lattice Edition Simulation IPUG81_1.3, August 2012 Mentor Graphics® ModelSim™ SE 6.3F 4 CORDIC IP Core User’s Guide Introduction Table 1-2. CORDIC IP Core for LatticeECP2 Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements Resource Utilization Translate Parallel FPGA Families Supported Translate Serial LatticeECP2 Minimal Device Needed LFE2-6E5T144C LFE2-6E5T144C LFE2-6E5T144C LFE2-6E5T144C Targeted Device LFE2-20E7F484C LFE2-20E7F484C LFE2-20E7F484C LFE2-20E7F484C Data Path Width 16 16 16 16 1300 1300 600 600 0 0 0 0 1200 1200 300 400 LUTs sysMEM EBRs Registers Lattice Implementation Design Tool Support Rotate Serial Lattice Diamond 1.0 or ispLEVER 8.1 Synthesis Synopsys Synplify Pro for Lattice D-2009.12L-1 Aldec Active-HDL 8.2 Lattice Edition Simulation Mentor Graphics ModelSim SE 6.3F Table 1-3. CORDIC IP Core for LatticeECP2M Devices Quick Facts CORDIC IP Configuration Core Requirements Resource Utilization Rotate Parallel Translate Parallel Minimal Device Needed LFE2M20E5F256C LFE2M20E5F256C LFE2M20E5F256C LFE2M20E5F256C Targeted Device LFE2M20E7F484C LFE2M20E7F484C LFE2M20E7F484C LFE2M20E7F484C Data Path Width 16 16 16 16 1300 1300 600 600 0 0 0 0 1200 1200 300 400 FPGA Families Supported LUTs sysMEM EBRs Registers Synthesis Lattice Diamond 1.0 or ispLEVER 8.1 Synopsys Synplify Pro for Lattice D-2009.12L-1 Aldec Active-HDL 8.2 Lattice Edition Simulation IPUG81_1.3, August 2012 Translate Serial LatticeECP2M Lattice Implementation Design Tool Support Rotate Serial Mentor Graphics ModelSim SE 6.3F 5 CORDIC IP Core User’s Guide Introduction Table 1-4. CORDIC IP Core for LatticeECP3 Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements Resource Utilization Translate Parallel FPGA Families Supported Translate Serial LatticeECP3 LFE3-17EA6FTN256CES LFE3-17EA6FTN256CES LFE3-17EA6FTN256CES LFE3-17EA6FTN256CES Targeted Device LFE3-70E8FN484CES LFE3-70E8FN484CES LFE3-70E8FN484CES LFE3-70E8FN484CES Data Path Width 16 16 16 16 1300 1300 600 700 Minimal Device Needed LUTs sysMEM EBRs Registers 0 0 0 0 1300 1200 300 400 Lattice Diamond 1.0 or ispLEVER 8.1 Lattice Implementation Design Tool Support Rotate Serial Synthesis Synopsys Synplify Pro for Lattice D-2009.12L-1 Aldec Active-HDL 8.2 Lattice Edition Simulation Mentor Graphics ModelSim SE 6.3F Table 1-5. CORDIC IP Core for LatticeSC/M Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements Resource Utilization Translate Parallel FPGA Families Supported Translate Serial LatticeSC/M Minimal Device Needed LFSC3GA15 E-5F256C LFSC3GA15 E-5F256C LFSC3GA15 E-5F256C LFSC3GA15 E-5F256C Targeted Device LFSC3GA25 E-7F900C LFSC3GA25 E-7F900C LFSC3GA25 E-7F900C LFSC3GA25 E-7F900C Data Path Width LUTs sysMEM EBRs Registers 16 16 16 16 1700 1700 900 1000 0 0 0 0 1300 1300 400 400 Lattice Implementation Design Tool Support Rotate Serial Synthesis Lattice Diamond 1.0 or ispLEVER 8.1 Synopsys Synplify Pro for Lattice D-2009.12L-1 Aldec Active-HDL 8.2 Lattice Edition Simulation IPUG81_1.3, August 2012 Mentor Graphics ModelSim SE 6.3F 6 CORDIC IP Core User’s Guide Introduction Table 1-6. CORDIC IP Core for LatticeXP Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements Resource Utilization FPGA Families Supported Rotate Serial Translate Serial LatticeXP Minimal Device Needed LFXP3C3Q208C LFXP3C3Q208C LFXP3C3Q208C LFXP3C3Q208C Targeted Device LFXP20E5F484C LFXP20E5F484C LFXP20E5F484C LFXP20E5F484C Data Path Width 16 16 16 16 1300 1200 600 700 LUTs sysMEM EBRs Registers 0 0 0 0 1300 1200 300 400 Lattice Implementation Design Tool Support Translate Parallel Lattice Diamond 1.0 or ispLEVER 8.1 Synopsys Synplify Pro for Lattice D-2009.12L-1 Synthesis Aldec Active-HDL 8.2 Lattice Edition Simulation Mentor Graphics ModelSim SE 6.3F . Table 1-7. CORDIC IP Core for LatticeXP2 Devices Quick Facts CORDIC IP Configuration Rotate Parallel Core Requirements FPGA Families Supported Targeted Device LFXP2-30E-7F484C LUTs Registers 16 16 16 16 1300 1300 600 600 0 0 0 0 1200 1200 300 400 Lattice Implementation Synthesis Translate Serial LatticeXP2 LFXP2-5E-5M132C sysMEM EBRs Design Tool Support Rotate Serial Minimal Device Needed Data Path Width Resource Utilization Translate Parallel Lattice Diamond 1.0 or ispLEVER 8.1 Synopsys Synplify Pro for Lattice D-2009.12L-1 Aldec Active-HDL 8.2 Lattice Edition Simulation Mentor Graphics ModelSim SE 6.3F Features • Functions supported: – Vector rotation (polar to rectangular) – Vector translation (rectangular to polar) – Sin and cos – Arctan • Input data widths from 8 to 32 bits • Configurable number of iterations used to derive output from 4 to 32 IPUG81_1.3, August 2012 7 CORDIC IP Core User’s Guide Introduction • Optional pre-rotation module • Optional amplitude compensation scaling module to compensate for the CORDIC algorithm’s output amplitude scale factor • Selectable rounding algorithm: truncation, rounding up, rounding away from zero, convergent rounding • Selectable parallel architectural configuration for throughput optimization • Selectable word-serial architectural configuration for area optimization • Signed 2’s complement data • Optional clock enable (ce) and synchronous reset (sr) control signals • Full precision internal arithmetic IPUG81_1.3, August 2012 8 CORDIC IP Core User’s Guide Chapter 2: Functional Description This chapter provides a functional description of the CORDIC IP core. General Description of the CORDIC Algorithm The CORDIC algorithm is an iterative method that uses simple arithmetic operations such as addition, subtraction, bit shift and table look up to perform hyperbolic and trigonometric functions.The CORDIC algorithm was initially designed to perform a vector rotation, where the vector  x y  is rotated through the angle  yielding a new vector  x y  . Using a matrix form, a planar rotation for a vector of  x y  is defined as: x = x cos  – y sin  (1) y = y cos  + x sin  Note that  is the angle that is to be traversed. With the CORDIC algorithm, the traversal is accomplished in iterative steps in which each step completes a small part of the rotation. A single step is defined by the following equation: x i + 1 = cos  i  x i – y i tan  i  (2) y i + 1 = cos  i  y i + x i tan  i  The number of multipliers required is reduced by selecting the angle steps such that the tangent of a step is a power of 2. The angle for each step is given by: i  i = arctan  1  2  (3) Multiplying or dividing by a power of 2 can be implemented using a simple shift operation. All iteration-angles summed must equal the rotation angle .   di i =  where d i =  -1;+1  (4) i=0 This results in the following equation for tan  i : tan  i = d i 2 –i (5) Combining equations 2 and 5 results in: –i x i + 1 = cos  i  x i – y i  d i  2  (6) –i y i + 1 = cos  i  y i + x i  d i  2  The iterative rotation can now be expressed as: –i xi + 1 = Ki  xi – yi  di  2  (7) –i yi + 1 = Ki  yi + xi  di  2  where: –1 –i K i = cos  tan 2  = 1   1 + 2 IPUG81_1.3, August 2012 9 – 2i  CORDIC IP Core User’s Guide Functional Description di =  1 The CORDIC rotator is normally operated in one of two modes. The first, called rotation, rotates the input vector by a specified angle. The second mode, called vectoring, rotates the input vector to the x-axis while recording the angle required to make that rotation. For rotation mode, the CORDIC equations are: xi + 1 = xi – yi  di  2 –i yi + 1 = yi + xi  di  2 –i –1 (8) –i z i + 1 = z i – d i  tan  2  where d i = – 1 if z i  0 , +1 otherwise. Here z i is the residual angle in the angle accumulator with the initial value z 0 as the angle to be rotated. In vectoring mode, the CORDIC vectoring function works by seeking to minimize the y component of the residual vector at each rotation. The sign of the residual y component is used to determine which direction to rotate next. If the angle accumulator is initialized with zero, it will contain the traversed angle at the end of the iterations. For vectoring mode, the CORDIC equations are: –i (9) xi + 1 = xi – yi  di  2 yi + 1 = yi + xi  di  2 z i + 1 = z i – d i  tan –1 –i –i  2  where d i = -1 if y i  0 +1 otherwise In sin/cos mode, the unit vector is rotated by the input phase angle  generating the output vector  cos(  sin     . The rotation mode CORDIC operation can simultaneously compute the sine and cosine of the input angle . Setting the x component to 1 and y component to zero reduces the rotation mode. This results the equations 11 from equations 1: (10) x' = cos  y' = sin  In arctangent mode,  = arctan  y 0  x 0  is directly computed using the vectoring mode if the angle accumulator is initialized with zero. z n = z 0 + arctan  y 0  x 0  IPUG81_1.3, August 2012 10 (11) CORDIC IP Core User’s Guide Functional Description Block Diagram Figure 2-1 shows a block diagram of the CORDIC IP Core. Figure 2-1. CORDIC IP Core Block Diagram Parameter Arctangent ROM x y z In Registers Preprocessor CORDIC Arithmetic Unit Controller Postprocessor Round Mode x y z rfi Data Path Pre-processor The CORDIC rotation and vectoring algorithms are limited to rotation angles between -/2 and /2 This limitation is due to the use of 2° for the tangent in the first iteration. For composite rotation angles larger than /2, an additional rotation is required. CORDIC Arithmetic Unit The CORDIC arithmetic unit performs the actual CORDIC algorithm. Two architecture configurations are available for the arithmetic unit: parallel (with single-cycle data throughput) and word-serial (with multiple-cycle throughput). The parallel configuration has a pipeline-structured core and can perform a CORDIC transformation each clock cycle, producing a new output every cycle. In contrast with the parallel structure, word-serial architecture produces a new output every N cycles. Here N is the user input in the IPexpress™ GUI for the “Iteration Number” parameter. Arctan ROM –1 –i The arc tangent ROM stores the tan  2  values. Its data width is variable, address width is log2(number of iterations-1), address depth is 2 ^ log2(number of iterations-1). Controller The controller module control generates all signals necessary for carrying out the iterations, including ROM addressing, ready for input (rfi) and output valid (outvalid). I/O port definition details are explained in Table 2-5. Post-processor The CORDIC algorithm introduces a scale factor that causes a magnitude gain that must be compensated for at the end (see Equation 8). The post-processor module contains logic to correct the scale factor. In addition, it corrects the phase rotation introduced by the pre-processor module (if present). Rounding The rounding module provides four types of rounding, depending on the ROUNDING parameter: • None (truncation) – Discards all bits to the right of the output least significant bit and leaves the output uncorrected. • Rounding up – Rounds up if the fractional part is exactly one-half. • Rounding away from zero – Rounds away from zero if the fractional part is exactly one-half. IPUG81_1.3, August 2012 11 CORDIC IP Core User’s Guide Functional Description • Convergent rounding – Rounds to the nearest even value if the fractional part is exactly one-half. CORDIC Functions Vector Rotation Polar to Rectangular Translation: In vector rotation mode, the input vector  x y  is rotated by a specified angle, , giving the a new output vector,  x y  . Because of the CORDIC algorithm scale factor, a magnitude gain will be introduced as shown in Figure 2-2. This magnitude gain is compensated for by the CORDIC IP post-processor module. Figure 2-2. Vector Rotation The inputs, xin, yin and phasein, are limited to the ranges given in Table 2-1. Inputs outside the ranges will produce unpredictable results. Table 2-1. Vector Rotation Input/Output Signal Description xin Input X Coordinate Range: -1  xin  1 yin Input Y Coordinate Range: -1  yin  1 phasein Input Rotation Angle Range: -  Phasein   xout Output X Coordinate Range: - 2  xout  2 yout Output Y Coordinate Range: - 2  yout  2 Vector Translation Rectangular to Polar Translation: In vector translation mode, the input vector  x y  is rotated through whatever angle is necessary to align the result vector with the x-axis, as shown in Figure 2-3. Output is the angle rotated and the magnitude on the x-axis after rotation. IPUG81_1.3, August 2012 12 CORDIC IP Core User’s Guide Functional Description Figure 2-3. Vector Translation The inputs, xin and yin, are limited to the ranges given in Table 2-2. Inputs outside the ranges will produce unpredictable results. Table 2-2. Vector Translation Input/Output Signal Description xin Input X Coordinate Range: -1  xin  1 yin Input Y Coordinate Range: -1  yin  1 xout Output Magnitude Range: - 2  xout  phaseout Output Phase Range: -  Phaseout  2 Sin and Cos In sin/cos mode, the unit vector is rotated by the input phase angle  providing the output vector  cos(  sin     . The input angle, phasein, is limited to the range given in Table 2-3. Inputs outside this range will produce unpredictable results. Table 2-3. Sin and Cos Input/Output Signal Description phasein Input Phase Range: -  Phasein  xout Output cos() Range: -1  xout  1 yout Output sin() Range: -1  yout  1 Arctan In arctan mode, the input vector,  x y  is rotated until the y component is zero, yielding the output angle, arctan  y  x  . The inputs xin and yin are limited to the ranges given in Table 2-4. Inputs outside the ranges will produce unpredictable results. IPUG81_1.3, August 2012 13 CORDIC IP Core User’s Guide Functional Description Table 2-4. Arctan Input/Output Signal Description xin Input X Coordinate Range: -1  xin  1 yin Input Y Coordinate Range: -1  yin  1 phaseout Output Phase Range: -  Phaseout  Interface Diagram The top-level interface diagram for the CORDIC IP core is shown in Figure 2-4. The description of the Input/Output (I/O) ports for the CORDIC IP core is provided in Table 2-5. Figure 2-4. Top-Level Interface for CORDIC IP Core clk rstn sr ce rfi CORDIC xin yin phasein inpvalid xout yout phaseout outvalid Table 2-5. Top-Level Port Definitions Port Bits I/O Description General I/Os clk 1 I System clock for data and control inputs and outputs. rstn 1 I System-wide asynchronous active-low reset signal. xin DINWIDTH I X component of input sample yin DINWIDTH I Y component of input sample phasein DINWIDTH I Phase component of input sample inpvalid 1 I Input valid signal. The input data is read in only when inpvalid is high. xout DOUTWIDTH O X component of output sample yout DOUTWIDTH O Y component of output sample phaseout DOUTWIDTH O Y component of output sample outvalid 1 O Output data qualifier. Output data is valid only when this signal is high. 1 O Ready for input. This output, when high, indicates that the IP core is ready to receive the next input data. A valid data may be applied at xin, yin and phasein only if rfi was high during the previous clock cycle. ce 1 I Clock Enable. Independent. sr 1 I Synchronous Reset. Independent. rfi Optional I/Os IPUG81_1.3, August 2012 14 CORDIC IP Core User’s Guide Functional Description Configuring the CORDIC IP Core Basic Options The options for mode, architecture, number of iterations and compensation are independent and specified in the “Basic Options” tab of the GUI. Refer to “Basic Options Tab” on page 20. Architecture Specification The CORDIC IP core provides two architecture configurations for the arithmetic unit: parallel (with single cycle data throughput) and word-serial (with multiple-cycle throughput). Because of the pipelined structure, the core can perform a CORDIC transformation each clock cycle, thus producing a new output every cycle. In contrast with parallel structures, word-serial architecture produces a new output every N cycles. Figure 2-5 shows a basic CORDIC arithmetic unit. Figure 2-5. Basic CORDIC Arithmetic Unit x_in y_in z_in sign bit x_out >>i >>i ± ± const ± x_out x_out Iterations Specification Parameter iteration specifies the number of internal add-sub iterations performed by the CORDIC processor in deriving the result. It determines the accuracy of the output: if the number is larger, the accuracy of the output is higher. Pre-rotation Specification When the pre-rotation module is selected, the CORDIC operational range extends to the full circle; otherwise the operational range is limited between -/2 and /2. Angle ranges outside the ranges will produce an unpredictable result if the pre-rotation module is not selected. The following describes an initial pre-rotation ±/2: x' = – d  y (12) y' = d  x z' = z + d    2 Compensation Specification In the CORDIC algorithm, the magnitude outputs, xout and yout, are generated with a magnitude gain. The compensation module provides three configurations to compensate for the CORDIC magnitude scale factor. • None – The outputs xout and yout will not be compensated. It is the user’s obligation to compensate and scale for the magnitude outputs gain introduced by the CORDIC algorithm. Refer to page 9 of this document for details, especially the ‘K’ factor in equation 7. • LUT-based – The outputs xout and yout are compensated using a LUT-based multiplier. • DSP-based – The outputs xout and yout are compensated using a DSP-based multiplier. IPUG81_1.3, August 2012 15 CORDIC IP Core User’s Guide Functional Description Advanced Options The controls in this tab are used to define the various data widths and rounding methods used in the data path. The widths of the input data and output data can be defined independently. Round Method Specification The CORDIC IP core provides four rounding modes. Examples of round method are given in Table 2-6. • Truncation – The outputs, xout, yout and phaseout, are truncated. The LSBs are removed to match the specified output width. • Rounding up – The outputs, xout, yout and phaseout, are rounded up (0.5 rounded up). • Rounding away from zero – The outputs, xout, yout and phaseout, are rounded (0.5 rounded up, -0.5 rounded down). • Convergent rounding – The outputs, xout, yout and phaseout, are rounded towards the nearest even number. Table 2-6. Round Method Truncation Rounding Up Rounding Away from Zero Convergent Rounding 1.50 1 2 2 2 -1.50 -2 -1 -2 -2 0.50 0 1 1 0 -0.50 -1 0 -1 0 0.25 0 0 0 0 -0.25 -1 0 0 0 0.65 0 1 1 0 Input/Output Width Specification The input/output data widths can be configured in the range 8 to 32 bits. Data Format Specification The data signals are: xin, yin, xout and yout. The input data signals, xin and yin, must be in the range [-1,1]. Input data outside the range will produce unpredictable results. • Input Data Signals  Input data signals are represented in decimal format using bus format (as little endian). For N-bit input data signal, the (N-2) LSB represent the fractional component to the left of the decimal place and the MSB represents the sign bit. For example, when the DINWIDTH is 8, +1 and –1 are represented as: “01000000” => 01.000000 => +1.0 “11000000” => 11.000000 => -1.0 When the DINWIDTH is 12, +1 and –1 are represented as: “010000000000” => 01.0000000000 => +1.0 “110000000000” => 11.0000000000 => -1.0 • Output Data Signals  If compensation is LUT- based or DSP-based, the output data signal format is the same as the input data signal format. The range of the output data signal is  – 2 2  . For N-bit output data signal, the (N-2) LSB represent the fractional component to the left of the decimal place and the MSB represents the sign bit. IPUG81_1.3, August 2012 16 CORDIC IP Core User’s Guide Functional Description For example, when the DOUTWIDTH is 8, in the data format, +1 and –1 are represented: “01000000” => 01.000000 => +1.0 “11000000” => 11.000000 => -1.0 When the DOUTWIDTH is 12, in the data format, +1 and –1 are represented: “010000000000” => 01.0000000000 => +1.0 “110000000000” => 11.0000000000 => -1.0 If compensation is None, the output data signals format is different from the input data signals. Due to the magnitude gain introduced by the CORDIC algorithm, without the compensation, the range of the output data signal can be larger than 2 or less than -2, so it will need 2 bits to represent the decimal number. For the N-bit output data signal, the (N-3) LSB represent the fractional component to the left of the decimal place and the MSB represents the sign bit. For example, when the DOUTWIDTH is 8, in the data format, +1 and –1 are represented: “00100000” => 001.00000 => +1.0 “11000000” => 111.00000 => -1.0 When the DOUTWIDTH is 12, in the data format, +2 and –2 are represented: “010000000000” => 010.000000000 => +2.0 “110000000000” => 110.000000000 => -2.0 +2.25 and –2.25 are represented: “010010000000” => 010.010000000 => +2.25 “101110000000” => 101.110000000 => -2.25 Phase Format Specification • Phase Signals The phase signals are phasein and phaseout. The input phase signal, phasein, must be in the range [- ¼, ¼]. Input phase outside this range will produce unpredictable results. The phase signals, phasein and phaseout, are always the same representation. For N-bit phase signal, the (N-3) LSB represents the fractional component to the left of the decimal place and the MSB represents the sign bit. For example, when the DINWIDTH is 10, in the data format, +¼ and -¼ are represented: “0110010010” => 011.0010010 => + “1001101110” => 100.1101110 => - When the DINWIDTH is 13, in the data format, +¼ and -¼ are represented: “0110010010001” => 011.0010010001 => + “1001101101111” => 100.1101101111 => - Synthesis Options Specification There are two synthesis options for controlling IP generation flow, the “Frequency constraint” and “Pipelining and retiming”. The “Pipelining and retiming” option is used to move existing registers in order to balance the delays between registers. Users can adjust these two options to optimize for timing and area. IPUG81_1.3, August 2012 17 CORDIC IP Core User’s Guide Functional Description Timing Specifications Timing diagrams for the CORDIC IP core are given in the Figure 2-6, Figure 2-7, and Figure 2-8. Figure 2-6. Timing Diagram for Parallel CORDIC (Rotation Mode) with Continuous Input Figure 2-7. Timing Diagram for Parallel CORDIC (Sin/Cos Mode) with Gapped Inputs IPUG81_1.3, August 2012 18 CORDIC IP Core User’s Guide Functional Description Figure 2-8. Timing Diagram for Serial CORDIC (Translation Mode) IPUG81_1.3, August 2012 19 CORDIC IP Core User’s Guide Chapter 3: Parameter Settings The IPexpress tool is used to create IP and architectural modules in the Diamond and ispLEVER software. Refer to “IP Core Generation” on page 23 for a description on how to generate the IP. Table 3-1 provides the list of user configurable parameters for the CORDIC IP core. The parameter settings are specified using the CORDICI IP core Configuration GUI in IPexpress. Table 3-1. Parameter Specifications for the CORDIC IP Core Parameter Range/Options Default CORDIC Specifications Mode Architecture Iterations Compensation Prerotation Rotate, Translate, Sin/Cos, Arctan Rotate Word-Serial, Parallel Parallel 4 - 32 16 None, LUT based, DSP based None Disable, Enable Enable I/O Specifications Input data width 8 - 32 16 Output data width 8 - 32 16 Truncation, Rounding up, Round away from zero, Convergent rounding Truncation Synchronous Reset Disable, Enable Disable Clock Enable Disable, Enable Disable 1- 400 250 Disable, Enable Disable Precision Control Roundmethod Optional Ports Synthesis Options Frequency constraint Pipelining and retiming Basic Options Tab Figure 3-1 shows the CORDIC Basic Options tab in the IPexpress tool. Figure 3-1. CORDIC Basic Options Tab IPUG81_1.3, August 2012 20 CORDIC IP Core User’s Guide Parameter Settings Mode Specifies the CORDIC function to be performed. Architecture Specifies the architecture configuration for the CORDIC core: parallel (with single-cycle data throughput) or wordserial (with multiple-cycle throughput). Iterations Specifies the number of internal add-sub iterations to perform. Compensation Specifies CORDIC magnitude scaling compensation. The outputs are compensated using a LUT-based multiplier or the block multiplier. Pre-Rotation Specifies whether the pre-rotation module is instantiated. Advanced Options Tab Figure 3-2 shows the CORDIC Advanced Options tab in the IPexpress tool. Figure 3-2. CORDIC Advanced Options Tab Data Width Consists of two dropdown menus: Input Data Width and Output Data Width. Rounding Identifies the rounding method to be used when it is necessary to drop one or more LSBs from the true output. Optional Ports Synchronous Reset Specifies whether a synchronous reset port is needed. A synchronous reset signal resets all the registers in the IP core. IPUG81_1.3, August 2012 21 CORDIC IP Core User’s Guide Parameter Settings Clock Enable Specifies whether a clock enable port is needed in the IP. Clock enable control can be used for power saving when the core is not used. Use of clock enable port increases the resource utilization and may affect performance due to increased routing congestion. Synthesis Options Frequency Constraint (MHz) Specifies frequency constraint for synthesis and PAR. The value specified here will be included in the .lpf file with an additional 50MHz overconstraining adjustment factor (overconstraining typically provides improved performance). For example, if this value is 250, the frequency constraint in the .lpf file will be “250MHz PAR_ADJ 50”. Pipelining and Retiming Specifies pipelining and retiming synthesis options for Synplify Pro. This option is not recommended to be selected. IPUG81_1.3, August 2012 22 CORDIC IP Core User’s Guide Chapter 4: IP Core Generation This chapter provides information on how to generate the CORDIC IP core using the Diamond or ispLEVER software IPexpress tool, and how to include the core in a top-level design. Licensing the IP Core An IP core- and device-specific license is required to enable full, unrestricted use of the CORDIC IP core in a complete, top-level design. Instructions on how to obtain licenses for Lattice IP cores are given at: http://www.latticesemi.com/products/intellectualproperty/aboutip/isplevercoreonlinepurchas.cfm Users may download and generate the CORDIC IP core and fully evaluate the core through functional simulation and implementation (synthesis, map, place and route) without an IP license. The CORDIC IP core also supports Lattice’s IP hardware evaluation capability, which makes it possible to create versions of the IP core that operate in hardware for a limited time (approximately four hours) without requiring an IP license. See “Hardware Evaluation” on page 28 for further details. However, a license is required to enable timing simulation, to open the design in the Diamond or ispLEVER EPIC tool, and to generate bitstreams that do not include the hardware evaluation timeout limitation. Getting Started The CORDIC IP core is available for download from the Lattice IP Server using the IPexpress tool. The IP files are automatically installed using ispUPDATE technology in any customer-specified directory. After the IP core has been installed, the IP core will be available in the IPexpress GUI dialog box shown in Figure 4-1. The IPexpress tool GUI dialog box for the CORDIC IP core is shown in Figure 4-1. To generate a specific IP core configuration the user specifies: • Project Path – Path to the directory where the generated IP files will be located. • File Name – “username” designation given to the generated IP core and corresponding folders and files. • (Diamond) Module Output – Verilog or VHDL. • (ispLEVER) Design Entry Type – Verilog HDL or VHDL. • Device Family – Device family to which IP is to be targeted (e.g. LatticeSCM, Lattice ECP2M, LatticeECP3, etc.). Only families that support the particular IP core are listed. • Part Name – Specific targeted part within the selected device family. IPUG81_1.3, August 2012 23 CORDIC IP Core User’s Guide IP Core Generation Figure 4-1. Pexpress Dialog Box (Diamond Version) Note that if the IPexpress tool is called from within an existing project, Project Path, Module Output (Design Entry in ispLEVER), Device Family and Part Name default to the specified project parameters. Refer to the IPexpress tool online help for further information. To create a custom configuration, the user clicks the Customize button in the IPexpress tool dialog box to display the CORDIC IP core Configuration GUI, as shown in Figure 4-2. From this dialog box, the user can select the IP parameter options specific to their application. Refer to “Parameter Settings” on page 20 for more information on the CORDIC IP core parameter settings. IPUG81_1.3, August 2012 24 CORDIC IP Core User’s Guide IP Core Generation Figure 4-2. Configuration GUI (Diamond Version) IPexpress-Created Files and Top Level Directory Structure When the user clicks the Generate button in the IP Configuration dialog box, the IP core and supporting files are generated in the specified “Project Path” directory. The directory structure of the generated files is shown in Figure 4-3. IPUG81_1.3, August 2012 25 CORDIC IP Core User’s Guide IP Core Generation Figure 4-3. LatticeECP2M CORDIC IP Core Directory Structure Table 4-1 provides a list of key files and directories created by the IPexpress tool and how they are used. The IPexpress tool creates several files that are used throughout the design cycle. The names of most of the created files are customized to the user’s module name specified in the IPexpress tool. Table 4-1. File List File Description _inst.v This file provides an instance template for the IP. .v This file provides the CORDIC core for simulation. _beh.v This file provides a behavioral simulation model for the CORDIC core. cordic_params.v This file provides parameters necessary for the simulation. _bb.v This file provides the synthesis black box for the user’s synthesis. .ngo This file provides the synthesized IP core. .lpc This file contains the IPexpress tool options used to recreate or modify the core in the IPexpress tool. .ipx The IPX file holds references to all of the elements of an IP or Module after it is generated from the IPexpress tool (Diamond version only). The file is used to bring in the appropriate files during the design implementation and analysis. It is also used to re-load parameter settings into the IP/Module generation GUI when an IP/Module is being re-generated. _top.[v,vhd] This file provides a module which instantiates the CORDIC core. This file can be easily modified for the user's instance of the CORDIC core. This file is located in the _eval/_/src/rtl/top/ directory. These are all of the files necessary to implement and verify the CORDIC IP core in your own top-level design. The following additional files providing IP core generation status information are also generated in the “Project Path” directory: IPUG81_1.3, August 2012 26 CORDIC IP Core User’s Guide IP Core Generation • _generate.log – Synthesis and map log file. • _gen.log – IPexpress IP generation log file. The \ and subtending directories provide files supporting the CORDIC IP core evaluation. The \ directory contains files/folders with content that is constant for all configurations of the CORDIC IP core. The \ subfolder contains files/folders with content specific to the username configuration. The \cordic_eval directory is created by IPexpress the first time the core is generated and updated each time the core is regenerated. A \ directory is created by IPexpress each time the core is generated and regenerated each time the core with the same file name is regenerated. A separate \ directory is generated for cores with different names, e.g. \, \, etc. Instantiating the Core The generated CORDIC IP core package includes black-box (_bb.v) and instance (_inst.v) templates that can be used to instantiate the core in a top-level design. An example RTL top-level reference source file that can be used as an instantiation template for the IP core is provided in \\cordic_eval\\src\rtl\top. Users may also use this top-level reference as the starting template for the top-level for their complete design. Running Functional Simulation Simulation support for the CORDIC IP core is provided for Aldec Active-HDL (Verilog and VHDL) simulator, Mentor Graphics ModelSim simulator. The functional simulation includes a configuration-specific behavioral model of the CORDIC IP core. The test bench sources stimulus to the core, and monitors output from the core. The generated IP core package includes the configuration-specific behavior model (_beh.v) for functional simulation in the “Project Path” root directory. The simulation scripts supporting ModelSim evaluation simulation is provided in \\cordic_eval\\sim\modelsim\scripts. The simulation script supporting Aldec evaluation simulation is provided in \\cordic_eval\\sim\aldec\scripts. Both Modelsim and Aldec simulation is supported via test bench files provided in \\cordic_eval\testbench. Models required for simulation are provided in the corresponding \models folder. Users may run the Aldec evaluation simulation by doing the following: 1. Open Active-HDL. 2. Under the Tools tab, select Execute Macro. 3. Browse to folder \\cordic_eval\\sim\aldec\scripts and execute one of the "do" scripts shown. Users may run the ModelSim evaluation simulation by doing the following: 1. Open ModelSim. 2. Under the File tab, select Change Directory and choose the folder \cordic_eval\\sim\modelsim\scripts. 3. Under the Tools tab, select Execute Macro and execute the ModelSim “do” script shown.  Note: When the simulation completes, a pop-up window mayappear asking “Are you sure you want to finish?” Answer No to analyze the results (answering Yes closes ModelSim). Synthesizing and Implementing the Core in a Top-Level Design Synthesis support for the CORDIC IP core is provided for Mentor Graphics Precision or Synopsys Synplify. The CORDIC IP core itself is synthesized and is provided in NGO format when the core is generated in IPexpress. Users may synthesize the core in their own top-level design by instantiating the core in their top-level as described IPUG81_1.3, August 2012 27 CORDIC IP Core User’s Guide IP Core Generation previously and then synthesizing the entire design with either Synplify or Precision RTL Synthesis. The following text describes the evaluation implementation flow for Windows platforms. The flow for Linux and UNIX platforms is described in the Readme file included with the IP core. The top-level files _top.v are provided in \\cordic_eval\\src\rtl\top. Push-button implementation of the reference design is supported via Diamond or ispLEVER project files, .syn for ispLEVER or .ldf for Diamond, locates in the following directory:  \\cordic_eval\\impl\(synplify or precision). To use this project file in Diamond: 1. Choose File > Open > Project. 2. Browse to \\cordic_eval\\impl\synplify (or precision) in the Open Project dialog box. 3. Select and open .ldf. At this point, all of the files needed to support top-level synthesis and implementation will be imported to the project. 4. Select the Process tab in the left-hand GUI window. 5. Implement the complete design via the standard Diamond GUI flow. To use this project file in ispLEVER: 1. Choose File > Open Project. 2. Browse to \\cordic_eval\\impl\synplify (or precision) in the Open Project dialog box. 3. Select and open .syn. At this point, all of the files needed to support top-level synthesis and implementation will be imported to the project. 4. Select the device top-level entry in the left-hand GUI window. 5. Implement the complete design via the standard ispLEVER GUI flow. Hardware Evaluation The CORDIC IP core supports Lattice’s IP hardware evaluation capability, which makes it possible to create versions of the IP core that operate in hardware for a limited period of time (approximately four hours) without requiring the purchase of an IP license. It may also be used to evaluate the core in hardware in user-defined designs. Enabling Hardware Evaluation in Diamond Choose Project > Active Strategy > Translate Design Settings. The hardware evaluation capability may be enabled/disabled in the Strategy dialog box. It is enabled by default. Enabling Hardware Evaluation in ispLEVER In the Processes for Current Source pane, right-click the Build Database process and choose Properties from the dropdown menu. The hardware evaluation capability may be enabled/disabled in the Properties dialog box. It is enabled by default. Updating/Regenerating the IP Core By regenerating an IP core with the IPexpress tool, you can modify any of its settings including device type, design entry method, and any of the options specific to the IP core. Regenerating can be done to modify an existing IP core or to create a new but similar one. IPUG81_1.3, August 2012 28 CORDIC IP Core User’s Guide IP Core Generation Regenerating an IP Core in Diamond To regenerate an IP core in Diamond: 1. In IPexpress, click the Regenerate button. 2. In the Regenerate view of IPexpress, choose the IPX source file of the module or IP you wish to regenerate. 3. IPexpress shows the current settings for the module or IP in the Source box. Make your new settings in the Target box. 4. If you want to generate a new set of files in a new location, set the new location in the IPX Target File box. The base of the file name will be the base of all the new file names. The IPX Target File must end with an .ipx extension. 5. Click Regenerate. The module’s dialog box opens showing the current option settings. 6. In the dialog box, choose the desired options. To get information about the options, click Help. Also, check the About tab in IPexpress for links to technical notes and user guides. IP may come with additional information. As the options change, the schematic diagram of the module changes to show the I/O and the device resources the module will need. 7. To import the module into your project, if it’s not already there, select Import IPX to Diamond Project (not available in stand-alone mode). 8. Click Generate. 9. Check the Generate Log tab to check for warnings and error messages. 10.Click Close. The IPexpress package file (.ipx) supported by Diamond holds references to all of the elements of the generated IP core required to support simulation, synthesis and implementation. The IP core may be included in a user's design by importing the .ipx file to the associated Diamond project. To change the option settings of a module or IP that is already in a design project, double-click the module’s .ipx file in the File List view. This opens IPexpress and the module’s dialog box showing the current option settings. Then go to step 6 above. Regenerating an IP Core in ispLEVER To regenerate an IP core in ispLEVER: 1. In the IPexpress tool, choose Tools > Regenerate IP/Module. 2. In the Select a Parameter File dialog box, choose the Lattice Parameter Configuration (.lpc) file of the IP core you wish to regenerate, and click Open. 3. The Select Target Core Version, Design Entry, and Device dialog box shows the current settings for the IP core in the Source Value box. Make your new settings in the Target Value box. 4. If you want to generate a new set of files in a new location, set the location in the LPC Target File box. The base of the .lpc file name will be the base of all the new file names. The LPC Target File must end with an .lpc extension. 5. Click Next. The IP core’s dialog box opens showing the current option settings. 6. In the dialog box, choose desired options. To get information about the options, click Help. Also, check the About tab in the IPexpress tool for links to technical notes and user guides. The IP core might come with additional information. As the options change, the schematic diagram of the IP core changes to show the I/O and the device resources the IP core will need. IPUG81_1.3, August 2012 29 CORDIC IP Core User’s Guide IP Core Generation 7. Click Generate. 8. Click the Generate Log tab to check for warnings and error messages. IPUG81_1.3, August 2012 30 CORDIC IP Core User’s Guide Chapter 5: Core Verification The functionality of the Lattice CORDIC IP core has been verified via simulation and hardware testing, including a simulation environment verifying proper CORDIC functionality. IPUG81_1.3, August 2012 31 CORDIC IP Core User’s Guide Chapter 6: Support Resources This chapter contains information about Lattice Technical Support, additional references, and document revision history. Lattice Technical Support There are a number of ways to receive technical support. Online Forums The first place to look is Lattice Forums (http://www.latticesemi.com/support/forums.cfm). Lattice Forums contain a wealth of knowledge and are actively monitored by Lattice Applications Engineers. Telephone Support Hotline Receive direct technical support for all Lattice products by calling Lattice Applications from 5:30 a.m. to 6 p.m. Pacific Time. • For USA & Canada: 1-800-LATTICE (528-8423) • For other locations: +1 503 268 8001 In Asia, call Lattice Applications from 8:30 a.m. to 5:30 p.m. Beijing Time (CST), +0800 UTC. Chinese and English language only. • For Asia: +86 21 52989090 E-mail Support • techsupport@latticesemi.com • techsupport-asia@latticesemi.com Local Support Contact your nearest Lattice Sales Office. Internet www.latticesemi.com References • J. E. Volder, “The CORDIC trigonometric computing technique.” IRE Trans. Electron. Comput., vol. EC-8, no. 3, pp. 330-334, Sept. 1959. • Andraka, Ray, “A survey of CORDIC algorithms for FPGA based computers.” Proceedings of the 1998 ACM/SIGDA sixth international symposium on field programmable gate arrays, Feb. 22-24, 1998, Monterrey, CA. pp191-200. • Duprat, J. and Muller, J.M., “ The CORDIC Algorithm: New Results for Fast VLSI Implementation.” IEEE Transactions on Computers, Vol. 42, pp. 168-178, 1993. • Deprettere, E., Dewilde, P., and Udo, R, “Pipelined CORDIC Architecture for Fast VLSI Filtering and Array Processing.” Proc. ICASSP’84, 1984, pp. 41.A.6.1-6.4. LatticeEC/ECP • HB1000, LatticeEC/ECP Family Handbook IPUG81_1.3, August 2012 32 CORDIC IP Core User’s Guide Support Resources LatticeECP2M • HB1003, LatticeECP2M Family Handbook LatticeECP3 • HB1009, LatticeECP3 Family Handbook • TN1196 - LatticeECP3 Marvell 1 GbE (1000BASE-X) Physical/MAC Layer Interoperability • TN1197 - LatticeECP3/Marvell SGMII Physical/MAC Layer Interoperability LatticeSCM • DS1004, LatticeSC/M Family Data Sheet • DS1005, LatticeSC/M Family flexiPCS Data Sheet LatticeXP • HB1001, LatticeXP Family Handbook LatticeXP2 • DS1009, Lattice XP2 Datasheet Revision History Date Document Version IP Core Version May 2009 01.0 1,0 Change Summary Initial release. Divided document into chapters. Added table of contents. June 2010 01.1 1.0 Added Quick Facts tables in Chapter 1, “Introduction.” Added new content in Chapter 4, “IP Core Generation.” Added new content in Chapter 5, “Core Verification.” December 2010 01.2 1.1 Added support for Diamond software throughout. August 2012 01.3 1.1 Configuring the CORDIC IP Core text section, under the Compensation Specification subsection, updated the text associated with the “None” bullet. Updated document with new corporate logo. IPUG81_1.3, August 2012 33 CORDIC IP Core User’s Guide Appendix A: Resource Utilization This appendix gives resource utilization information for Lattice FPGAs using the CORDIC IP core. IPexpress is the Lattice IP configuration utility, and is included as a standard feature of the Diamond and ispLEVER design tools. Details regarding the usage of IPexpress can be found in the IPexpress and Diamond or ispLEVER help system. For more information on the Diamond or ispLEVER design tools, visit the Lattice web site at: www.latticesemi.com/software. Table A-1 lists the parameter settings used in deriving the utilization data shown in Table A-2 through Table A-9. Table A-1. Parameter Settings of the Evaluation Packages Config1 Config2 Config3 Config4 Rotate Rotate Translate Sin and Cos Input Data Width 16 16 16 16 Output Data Width 16 16 16 16 Number of Iteration 16 16 16 16 Parallel Serial Parallel Parallel No No No No Truncation Truncation Truncation Truncation Mode Architecture Compensation Rounding Method Yes Yes Yes Yes User specify User specify User specify User specify Retiming No No No No Synchronous Reset No No No No Pre-rotation fMAX Clock Enable No No No No Enable Hardware Evaluation Yes Yes Yes Yes LatticeEC Devices Table A-2. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM™ EBRs MULT18X18 fMAX (MHz) 1 649 1196 1210 85 0 0 188 2 334 611 271 85 0 0 124 3 640 1179 1178 69 0 0 170 4 611 1146 1105 53 0 0 186 1. Performance and utilization data are generated targeting an LFEC20E-5F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeEC family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeEC devices is CORDIC-E2-U1. IPUG81_1.3, August 2012 34 CORDIC IP Core User’s Guide Resource Utilization LatticeECP Devices Table A-3. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 649 1196 1210 85 0 0 183 2 331 605 278 85 0 0 128 3 642 1181 1181 69 0 0 172 4 612 1146 1105 53 0 0 188 1. Performance and utilization data are generated targeting an LFECP20E-5F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeECP family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeECP devices is CORDIC-E2-U1. LatticeECP2 Devices Table A-4. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 649 1283 1205 85 0 0 278 2 308 602 278 85 0 0 171 3 644 1268 1182 69 0 0 262 4 624 1232 1104 53 0 0 271 1. Performance and utilization data are generated targeting an LFE2-20E-7F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software.  Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeECP2 family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeECP2 devices is CORDIC-P2-U1. LatticeECP2M Devices Table A-5. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 649 1283 1205 85 0 0 279 2 308 602 278 85 0 0 167 3 644 1268 1182 69 0 0 276 4 624 1232 1104 53 0 0 269 1. Performance and utilization data are generated targeting an LFE2M-20E-7F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeECP2M family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeECP2M devices is CORDIC-PM-U1. IPUG81_1.3, August 2012 35 CORDIC IP Core User’s Guide Resource Utilization LatticeECP3 Devices Table A-6. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 647 1280 1207 85 0 0 253 2 318 618 278 85 0 0 176 3 640 1261 1175 69 0 0 320 4 609 1203 1102 53 0 0 298 1. Performance and utilization data are generated targeting an LFE3-70E-8FN484CES device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeECP3 family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeECP3 devices is CORDIC-E3-U1. LatticeSC and LatticeSCM Devices Table A-7. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 833 1631 1224 85 0 0 389 2 402 739 292 85 0 0 235 3 830 1709 1214 69 0 0 332 4 803 1586 1155 53 0 0 390 1. Performance and utilization data are generated targeting an LFSC3GA25E-7F900C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeSC/M family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeSC/M devices is CORDIC-SC-U1. LatticeXP Devices Table A-8. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 649 1196 1210 85 0 0 174 2 334 611 271 85 0 0 114 3 640 1179 1178 69 0 0 156 4 611 1146 1105 53 0 0 176 1. Performance and utilization data are generated targeting an LFXP20E-5F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeXP family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeXP devices is CORDIC-XM-U1. IPUG81_1.3, August 2012 36 CORDIC IP Core User’s Guide Resource Utilization LatticeXP2 Devices Table A-9. Performance and Resource Utilization1 User-Configurable Mode Slices LUTs Registers I/Os sysMEM EBRs MULT18X18 fMAX (MHz) 1 649 1283 1205 85 0 0 275 2 308 602 278 85 0 0 159 3 644 1268 1182 69 0 0 279 4 624 1232 1104 53 0 0 274 1. Performance and utilization data are generated targeting an LFXP2-30E-7F484C device using Lattice Diamond 1.0 and Synplify Pro for Lattice D-2009.12L-1 software. Performance may vary when using a different software version or targeting a different device density or speed grade within the LatticeXP2 family. Ordering Part Number The Ordering Part Number (OPN) for the CORDIC targeting LatticeXP2 devices is CORDIC-X2-U1. IPUG81_1.3, August 2012 37 CORDIC IP Core User’s Guide