Professor Tomás Lang (1938 - 2018) had a distinguished and long record of outstanding research contributions to computer arithmetic and computer architecture fields. His work includes seminal results on digit-recurrence algorithms and implementations for division and square root, fast left-to-right multiplication, various CORDIC computations, implementations for 3D geometric transformations, and low-latency floating-point arithmetic. He has also made contributions to the design of low-power arithmetic, online arithmetic, fast adders, systolic algorithms, and decimal arithmetic. His results have had a strong impact on research in arithmetic and on industrial practice. His contributions to this symposium and the IEEE Transactions on Computers have been extensive.

In the computer architecture field he made notable contributions to research in vector multiprocessors, interconnection networks, scheduling, and memory models. Professor Lang was a great mentor and a colleague: he worked with many of the most active members of the ARITH community and influenced their careers.

He coauthored two textbooks on digital systems - "Systems and Hardware/Firmware Algorithms", Wiley 1985, and "Introduction to Digital Systems", Wiley 1998. In the arithmetic field he coauthored a monograph "Division and Square Root: Digit-Recurrence Algorithms and Implementations", Kluwer 1994, and a textbook "Digital Arithmetic", Morgan-Kaufmann 2004.

Tomás Lang received the BS degree in electrical engineering from the Universidad de Chile in 1965, the MS degree from the University of California, Berkeley in 1966, and the PhD degree from Stanford University in 1974. He was a professor and then professor emeritus in the Department of Electrical Engineering and Computer Science at the University of California, Irvine. Previously, he was a professor in the Department of Computer Architecture at the Polytechnic University of Catalonia, Spain, and a professor in the Department of Computer Science at the University of California, Los Angeles.

Tomas is no longer with us, leaving a big void among his colleagues and students. He was a remarkable researcher with many significant contributions to our field.

He was a great colleague and mentor. We worked together for over 20 years - I introduced him to arithmetic then he showed me how talented he was. It was a pleasure to work with him, from brainstorming, looking at ideas, to finding solutions which made a difference in the field. His egoless and modest personality, an impeccable work dedication, open mind and care for others are not frequently found. In his quiet ways, he did show strong and tactful leadership.

Tomas got me used to espresso many years ago - I even did not drink coffee then - so every time I have it, I always think of Tomas and Kerckhoff caffe at UCLA, where we would get our espressos in small, flimsy plastic cups, sit and drink under sycamore trees, trash the world leaders, and brainstorm about next ideas. Tomas knew well the literature, art, movies, photography, and music, so it was never boring being with him. Indeed, these were very good times.

I will miss him, his company, sharp wits, smile, and exceptional mind.

Milos Ercegovac

I feel deeply sad. Tomas was on my MSc Thesis committee and he paid attention to every detail, giving me hard time as I was just rushing to finish. Mostly, I remember his smile and his humor. His life was a remarkable story, for those who know more about him. He was professor of mine, a mentor, and later a friend.

His contributions to computer arithmetic will continue to live and will be read by generations, but we have lost a great human being. This is irreplaceable.

Vojin Oklobdzija

This is a very bad news for many people. Personally, Tomas was my mentor and my friend. He showed me the way to make good research, being ethical and happy at the same time.

Without him, the Computer Architecture department (that he created here in Barcelona) would not have even exist and by sure, because him, we tried to do the best to make Tomas happy.

Mateo Valero

With a lot of sadness I learned that Tomas passed away.

Very nice and discreet person, a great researcher and a wonderful teacher.

Marco Re, University of Rome "Tor Vergata"

Tomás taught me that something as simple as an addition could hide an unlimited land of creative discoveries. Not to mention when having fantasies about division and square root.

To be an arithmetician you must have some sense of perfection, rigor, perseverance and "savoir-faire". He taught me that it is not enough to show that something works. It should be proved to be correct! Fortunately, when I was taking my first steps in Computer Science, Tomás crossed in my path.

Thanks for giving me the right guidance at the right time. I will never forget your smile.

Jordi Cortadella

Tomas was a mentor to me throughout my graduate studies at UCLA. My love for computer sciences, in particular hardware systems, comes partly from his teachings. His desire to achieve perfection could be frustrating at times but at the end it taught me how to write technical papers in a logical way. Somehow he managed to do all of this while being a genuinely nice person.

We will miss you Tomas,

Marc Tremblay, Ph.D.

I got to know Professor Lang when I entered graduate studies at UCI in 1993. He introduced me to computer arithmetic and to the design of digital systems. One of the first tasks he assigned me was to understand the algorithm for division by reading the detail on the printouts of his book, in press at that time. I got to learn words such as redundancy, signed-digit, carry-save and on-the-fly, but I did not really understood why we needed this weird stuff! Now, every year, when I teach the lecture on division, I always get amazed by the beauty and elegance of this weird stuff when everything fall in the right place!

I still have the folder of printouts in my bookshelf.

Years later, when visiting UCI and referring to him as Professor Lang, he told me: "Call me Tomás, you earned it". I felt very elated.

Alberto Nannarelli

We sadly say goodbye to a remarkable researcher and colleague. I only had the opportunity of meeting him in person once, but I had the pleasure to work remotely with him. Tomas was and will always be one of my references in computer arithmetic.

Javier Hormigo

Thanks, Tomás, for letting me work with you and learn from you.

Javier Bruguera

Thank you Tomas, my Friend and Mentor. You'll live forever in my hearth.

Ciao

Paolo Montuschi

Tomas will always stay in my memory. As my PhD advisor and mentor, he instilled in me profound principles about research, teaching, and pursue of knowledge. Such lessons continued afterwards in our academic collaborations, which albeit limited in time where very fruitful. Even though his demeanor was rather quiet, his prowess was remarkable. He never sought the spotlight, yet to those that knew and work closely with him, he was a luminary radiating light onto others. His legacy will remain with me forever, as well as the memories of our days together, discussing ideas, writing a paper, collaborating on a book, enjoying an evening at the movies or an afternoon in his house with his family.

Jaime Moreno

Tomas Lang led a long distinguished career as an academic, a researcher, and an author. I knew him as my Ph. D. student at Stanford, impressed with him from the beginning of our work together. His thesis was in the area of processor-to-memory interconnections. The paper entitled "Interconnections between processors and memory modules using the shuffle-exchange network," (1976, IEEE Trans. on Computers) which came from that work reported new efficient ways of realizing arbitrary permutations of data in parallel computers. The thesis launched Tomas into a career dedicated to high-speed computation. He continued work in multiprocessor connections and scheduling for about a decade and then shifted gears to computer arithmetic, as he realized that arithmetic operations were becoming crucial for achieving efficient high-speed computation. A landmark paper with Milos Ercegovac in 1985 revealed a way to speed up division by predicting quotient digits. He followed this work with many innovations in the field. His continuing collaboration with Milos resulted in a stunning collection of books on computer arithmetic. It is fair to say that these books shaped the teaching of computer arithmetic for the next generation of students. These books continue to influence researchers two and three decades after they appeared. With sorrow I mark his passing. I join my colleagues in celebrating the life of Tomas Lang for his dedication to research and students, and for the gift of his legacy in computer arithmetic.

Harold Stone, Princeton, NJ, 2018.