Research in Computer Arithmetic


Behrooz Parhami: 2007/06/19  ||  E-mail:  ||  Problems:

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On June 19, 2007, Professor Parhami's UCSB ECE website moved to a new location. For an up-to-date version of this page, visit it at the new address:

In the following descriptions, selected items from B. Parhami’s list of publications are provided in brackets. 

Defining the Field

Arithmetic is a branch of mathematics that deals with numbers and numerical computation. Arithmetic operations on pairs of numbers x and y include addition (producing the sum s = x + y), subtraction (yielding the difference d = xy), multiplication (resulting in the product p = x ´ y), and division (generating the quotient q = x / y). Subtraction and division can be viewed as operations that undo the effects of addition and multiplication, respectively. Computer arithmetic is a branch of computer engineering that deals with methods of representing integers (fixed-point numbers) and real values (e.g., floating-point numbers) in digital systems and efficient algorithms for manipulating such numbers by means of hardware circuits or software routines [EncyIS]. On the hardware side, various types of adders, subtractors, multipliers, dividers, square-rooters, and circuit techniques for function evaluation are considered [179]. Both abstract structures and technology-specific designs are dealt with. Software aspects of computer arithmetic include complexity, error characteristics, stability, and certifiability of computational algorithms.

Areas of Work

Performance in many computer applications is critically dependent on the speed of arithmetic operations. The discovery, in the mid 1990s, of design flaws in the arithmetic circuits of Intel’s Pentium processor aptly demonstrated the need for a more systematic approach to the design and verification of arithmetic algorithms and associated hardware designs, especially when they are extensively optimized for speed. Criteria other than speed are also becoming important in the design of algorithms and hardware for computer arithmetic. Examples include accuracy, high throughput, fault tolerance, certifiability, and low power consumption. Dr. Parhami’s research deals with all of the aspects above. Because at very high clock rates, carry propagation (even with the fastest carry networks) becomes a limiting factor for speed, a key area of Professor Parhami’s research deals with redundant number representations and the associated carry-free arithmetic algorithms.

Current Threads

  • Redundant number representations [66], [86], [156], [196], [197], [200], [205], [219]

  • Systolic and on-line arithmetic [89], [187], [188], [189]

  • Configurable arithmetic arrays [140], [187]

  • VLSI-based and ASIC design [130], [136], [168], [194], [205, [206] [219], [jvsp]

  • Theory and limits of computer arithmetic [50], [174], [189], [190], [198], [207]

  • Analysis and optimization of lookup table size [85], [142], [173]

  • Dependable and fault-tolerant arithmetic [201], [204]

  • Residue arithmetic and conversion algorithms [92], [108], [129], [197], [200]


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Dr. Behrooz Parhami, Professor

                     Office phone: +1 805 893 3211
E-mail:                 Messages: +1 805 893 3716
Dept. Electrical & Computer Eng.                  Dept. fax: +1 805 893 3262
Univ. of California, Santa Barbara                Office: Room 5155 Eng. I
Santa Barbara, CA 93106-9560 USA                      Deliveries: Room 4155 Eng. I