CORDIC IMPLEMENTATION OF SINE-COSINE FUNCTIONS: Algorithm and Implementation Floating-Point Format

by Ashutosh Gupta

This work describes the fundamentals of CORDIC (Co- ordinate rotation Digital Computer) algorithm and how CORDIC algorithm can be used to calculate the trigonometric functions (Sine and Cosine) in circular rotation mode. The value of Sine and cosine functions are calculated in IEEE-754-1985 standardized single precision floating point format for better precision, accuracy and portability in the result. A normalization scheme is used which reduces error and requires no extra hardware. The trigonometric function values calculated using CORDIC algorithm are implemented in VHDL (Very High Speed Hardware Description Language), including language and design issues. The algorithm has been implemented in FPGA using VHDL.

72 pages, Paperback

Published September 12, 2010

About the author

I was a pretty shy and reluctant kid, and as far as I remember, I use to feel as if I was trapped within the walls of orthodoxy. I could feel certain rebellious expressions stacking up within me. During my adolescent days, any kind of self-expression never really flourished. There was no exposure to literature or a cinematic brilliance to take me beyond the walls of orthodoxy, and it had to do with my ignorance more than anything else. Being an ‘introvertish rebel’, it didn’t help my cause either. As far as I remember, playing cricket intensively, mimicry, and imitating musical tunes on an old keyboard of mine were my sources to experience an emotional stimulation, and the rest of my time was consumed being a uni-dimensional academic chap.

I believe that college life is a beautiful convergence of eccentric personalities which triggers a drastic change. I wasn’t spared either. I got thoroughly exposed to classic American Cinema, and it was extremely cathartic for me. Movies like Serpico, Taxi Driver, and Schindler’s list vindicated the rebellious streak and compassion that I withheld for a long time. The righteousness portrayed in these movies instilled a belief that my expressions held sanctity and should be channelized, and I delved into the writing business.

Just like any other budding writer or thinker, in its infancy, my writing revolved only around metaphors and being overly creative. I didn’t focus much on the evolution of my thought process and my spectrum was limited, which resulted in shallowness, until I came across the work of Franz Kafka. The beauty he extracted from melancholy opened the floodgates within me, and I embraced my own melancholy. This changed me as a person and as a writer. I realized that writing is not about scribbling just for the sake of it, but there is a whole personality type which one has to live with, having its own merits and demerits.

I believe we all are a work of art and if it is not within our powers to exude this attribute through our actions then we must at least strive to create a work of Art. Writing sustains the hope of universe to realize the magical chemistry of intellect, imagination and emotions, with no favoritism for one in particular. I feel that timeless writing must make way for the sustenance of a gentle arrogance, a bit of it to interrupt the converging lines of established knowledge, and much more of it to give birth to a burning star. As far as I am concerned, both my dynamism and stagnancy rest in writing, and so is the freedom and patience that come respectively with these states.