Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and...

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Hybrid CORDIC 3. ROMless 20180303 Copyright (c) 2015 - 2017 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation License".

Transcript of Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and...

Page 1: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Hybrid CORDIC3. ROMless

20180303

Copyright (c) 2015 - 2017 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of theGNU Free Documentation License, Version 1.2 or any later version published by the Free SoftwareFoundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy ofthe license is included in the section entitled "GNU Free Documentation License".

Page 2: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

50 years of CORDIC

Page 3: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

50 years of CORDIC

Page 4: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Timmermann, Low Latency time CORDIC algorithm, 1992

50 years of CORDIC

Page 5: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 6: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 7: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 8: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 9: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

0.785398163

0.707106781

Page 10: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 11: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 12: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 13: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 14: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Chen, w/o ROM Lookup

Page 15: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 16: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 17: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 18: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Chen, w/o ROM Lookup

Page 19: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 20: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 21: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 22: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

sum(y1-y2)ans = 0.042112

41 k= 1:10 42 y1 = 2.^(-k); 43 y1 44 y2 = atan(y1) 45 y3 = y2 - y1 46 k 47 plot(k, y1) 48 plot(k, y3) 49 y3 = y1 - y2 50 plot(k, y3) 51 plot(k, y3, 'o-') 52 grid on 53 axis([0, 10, 0, 0.005]) 54 axis([0, 10, 0, 0.0005]) 55 axis([0, 10, 0, 0.00005]) 56 axis([0, 10, 0, 0.000005]) 57 axis([0, 10, 0, 0.0000005]) 58 axis([0, 10, 0, 0.00000005])

Page 23: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 24: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 25: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 26: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 27: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 28: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 29: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 30: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 31: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 32: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 33: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Chen, w/o ROM Lookup

Page 34: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 35: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 36: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Chen, w/o ROM Lookup

Page 37: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 38: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 39: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 40: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 41: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 42: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

Chen, w/o ROM Lookup

Page 43: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 44: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 45: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.
Page 46: Hybrid CORDIC 3. ROMless 20180303 - · PDF file3/3/2018 · [23] M. Kuhlmann and K. K. Parhi, "P-CORDIC: A precomputation based rotation CORDIC algorithm," EURASIP J. Appl.

CORDIC Based DFT on FPGA for DSP Applications · digital computer (CORDIC) algorithm for the implementation of DFT/FFT. Hence, the CORDIC technique is applied for calculating a vector

CORDIC Based DFT on FPGA for DSP Applications · digital computer (CORDIC) algorithm for the implementation of DFT/FFT. Hence, the CORDIC technique is applied for calculating a vector

LogiCORE IP CORDIC v5 - china. · PDF fileLogiCORE IP CORDIC v5.0 General Description The CORDIC core implements a generalized coordinate ... The CORDIC algorithm introduces a scale

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ST10R272L - 16-BIT LOW VOLTAGE ROMLESS MCU WITH … Sheets/ST Microelectronics PDFS... · ST10R272L 16-BIT LOW VOLTAGE ROMLESS MCU WITH MAC DATASHEET 1 ... (PEC) 16-priority-level

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Implementation of Reconfigurable CORDIC · R.Bharat Kumar and Emandi Jagadeeswararao : Implementation of Reconfigurable CORDIC CORDIC have been suggested for high-throughput computation.

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Area and Energy efficient CORDIC Accelerator for … papers/MIDEM_46(2016)4p197.pdf · Area and Energy efficient CORDIC Accelerator for Embedded Processor Datapaths ... CORDIC architectures

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1 CORDIC ALGORITHM AND IMPLEMENTATIONS CORDIC …web.cs.ucla.edu/digital_arithmetic/files/ch11.pdf · cordic algorithm and implementations 1 cordic method rotation and vectoring mode

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FPGA based implementation of CORDIC using different …akademikpersonel.kocaeli.edu.tr/suhapsahin/bildiri/suhapsahin07.10... · FPGA based implementation of CORDIC using different

CORDIC-like method for solving Kepler’s equation · 3.2. CORDIC-like Newton method The convergenceof the CORDIC-like algorithms in Sect. 2 and 3.1 is linear, while Newton’s method

CORDIC-like method for solving Kepler’s equation · 3.2. CORDIC-like Newton method The convergenceof the CORDIC-like algorithms in Sect. 2 and 3.1 is linear, while Newton’s method

Design of a pipelined radix 4 CORDIC · PDF fileDesign of a pipelined CORDIC processor radix 4 ... In this work we develop a generalization of the CORDIC algorithm for any radix in

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