Computer Arithmetic and Algorithms
Computer arithmetic forms the computational heart of digital systems, providing the hardware implementations that enable processors to perform mathematical operations efficiently. From simple addition to complex transcendental function evaluation, the algorithms and architectures used for computer arithmetic directly impact system performance, power consumption, and silicon area utilization.
This category explores the fundamental algorithms and hardware structures that implement arithmetic operations in digital systems. Understanding these concepts is essential for computer architects, digital designers, and anyone developing systems where computational performance is critical. The topics range from basic integer operations through advanced floating-point implementations and specialized units for scientific computing and cryptographic applications.
Articles
Integer Arithmetic Algorithms
Implement efficient mathematical operations. Topics include addition algorithms (carry-skip, carry-select, prefix), multiplication algorithms (Booth, modified Booth, Baugh-Wooley), division algorithms (restoring, non-restoring, SRT), square root algorithms, modular arithmetic, Montgomery multiplication, residue number systems, and redundant number systems.
Floating-Point Arithmetic
Handle real numbers in hardware. Coverage encompasses IEEE 754 standard implementation, rounding modes, denormalized numbers, exception handling, fused multiply-add, floating-point unit design, precision and range trade-offs, and decimal floating-point.
Elementary Functions
Compute transcendental functions. This section addresses CORDIC algorithms, polynomial approximations, table-based methods, range reduction, argument reduction, convergence division, reciprocal approximation, and special function units.
Arithmetic for Cryptography
Support security operations. Topics include modular exponentiation, elliptic curve arithmetic, Galois field arithmetic, prime number generation, random number generation, hash function implementation, and side-channel resistant arithmetic.
About This Category
Computer Arithmetic and Algorithms bridges the gap between mathematical theory and practical hardware implementation. The algorithms presented here have evolved over decades of research and engineering, representing carefully optimized solutions to the challenges of implementing arithmetic in finite precision with limited resources. Whether designing a high-performance processor, an energy-efficient embedded system, or a specialized accelerator, mastery of these concepts enables engineers to make informed decisions about trade-offs between speed, area, power, and accuracy.