Floating-point division and square root implementation using a Taylor-series expansion algorithm

Abstract

Abstract-Hardware support for floating-point (FP) arithmetic is an essential feature of modern microprocessor design. Although division and square root are relatively infrequent operations in traditional general-purpose applications, they are indispensable and becoming increasingly important in many modern applications. In this paper, a fused floating-point multiply/divide/square root unit based on Taylor-series expansion algorithm is presented. The implementation results of the proposed fused unit based on standard cell methodology in IBM 90nm technology exhibits that the incorporation of square root function to an existing multiply/divide unit requires only a modest 23% area increase and the same low latency for divide and square root operation can be achieved (12 cycles). The proposed arithmetic unit also exhibits a reasonably good area-performance balance.

On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods

“…Square rooting technology is ubiquitously implemented in IEEE, science, and mathematics platforms such as in computing for root mean square, solving linear equations, in vision apparatus and computer graphics. Square rooting algorithms are also used in engineering platforms like field programmable gates arrays and spectrum analysers [1,2,3,4,5,6,7,8,9,10] The Babylonians were able to formulate a remarkable iterative loop [11,12], for computation of positive square roots in circa 1500 BC this primitive mathematical program emanating from the ancient Babylonian epoch is still implemented today in many computing models. Kosheleva [13], explains how the Babylonian method emerges naturally from somehow loose and archaic methods, he shows that by just taking the first term of the binomial series and making a slight mathematical tweak will generate a method that links well to the primitive Babylonian algorithm.…”

An Architecture for Improving Variable Radix Real and Complex Division Using Recurrence Division

“…This fixes one of the primary issues for high radix division, but the hardware requirements of SRT division, and algorithms like it, are prohibitively large. Faster algorithms and architectures exist, such as those based on Newton-Raphson iterations or series expansions [9], [10], but since these designs use large multipliers, power consumption and area can easily become unmanageable for real-world constraints. Some of these drawbacks can be mitigated either directly with expanded look-up tables, prescaling tables and postscaling that can be used for higher radix architectures [11].…”

Fast calculation of inverse square root with the use of magic constant – analytical approach

“…Many algorithms can be used to approximate inverse square root functions [12,13,14,15,16]. All of these algorithms require initial seed to approximate function.…”