Unified Digit Selection for Radix-4 Recurrence Division and Square Root

David Harris; James Stine; Milos Ercegovac; Alberto Nannarelli; Katherine Parry; Cedar Turek

doi:10.1109/TC.2023.3305760

Unified Digit Selection for Radix-4 Recurrence Division and Square Root

David Harris, James Stine, Milos Ercegovac, Alberto Nannarelli, Katherine Parry, Cedar Turek

Research output: Contribution to journal › Journal article › Research › peer-review

169 Downloads (Pure)

Abstract

Division and square root are fundamental operations required by most computer systems. They are commonly implemented in hardware using radix-4 recurrence, which produces a 2-bit result digit on each step. Unified digit selection logic chooses the next quotient or square root digit based on a residual and divisor or square root approximation. This paper presents the first derivation of digit selection constants for unified radix-4 recurrence division and square root.

Original language	English
Article number	10224657
Journal	IEEE Transactions on Computers
Volume	73
Issue number	1
Pages (from-to)	292 - 300
ISSN	2326-3814
DOIs	https://doi.org/10.1109/TC.2023.3305760
Publication status	Published - 2023

Keywords

Hardware
Optical wavelength conversion
Approximation algorithms
Adders
Upper bound
Three-dimensional displays
Thermometers

Access to Document

10.1109/TC.2023.3305760

FulltextAccepted author manuscript, 904 KB

OpenUrl availability

Full text

Cite this

@article{d78b49be511a4de280ee1a353bd65e8e,

title = "Unified Digit Selection for Radix-4 Recurrence Division and Square Root",

abstract = "Division and square root are fundamental operations required by most computer systems. They are commonly implemented in hardware using radix-4 recurrence, which produces a 2-bit result digit on each step. Unified digit selection logic chooses the next quotient or square root digit based on a residual and divisor or square root approximation. This paper presents the first derivation of digit selection constants for unified radix-4 recurrence division and square root.",

keywords = "Hardware, Optical wavelength conversion, Approximation algorithms, Adders, Upper bound, Three-dimensional displays, Thermometers",

author = "David Harris and James Stine and Milos Ercegovac and Alberto Nannarelli and Katherine Parry and Cedar Turek",

year = "2023",

doi = "10.1109/TC.2023.3305760",

language = "English",

volume = "73",

pages = "292 -- 300",

journal = "IEEE Transactions on Computers",

issn = "2326-3814",

publisher = "IEEE Globecom",

number = "1",

}

TY - JOUR

T1 - Unified Digit Selection for Radix-4 Recurrence Division and Square Root

AU - Harris, David

AU - Stine, James

AU - Ercegovac, Milos

AU - Nannarelli, Alberto

AU - Parry, Katherine

AU - Turek, Cedar

PY - 2023

Y1 - 2023

N2 - Division and square root are fundamental operations required by most computer systems. They are commonly implemented in hardware using radix-4 recurrence, which produces a 2-bit result digit on each step. Unified digit selection logic chooses the next quotient or square root digit based on a residual and divisor or square root approximation. This paper presents the first derivation of digit selection constants for unified radix-4 recurrence division and square root.

AB - Division and square root are fundamental operations required by most computer systems. They are commonly implemented in hardware using radix-4 recurrence, which produces a 2-bit result digit on each step. Unified digit selection logic chooses the next quotient or square root digit based on a residual and divisor or square root approximation. This paper presents the first derivation of digit selection constants for unified radix-4 recurrence division and square root.

KW - Hardware

KW - Optical wavelength conversion

KW - Approximation algorithms

KW - Adders

KW - Upper bound

KW - Three-dimensional displays

KW - Thermometers

U2 - 10.1109/TC.2023.3305760

DO - 10.1109/TC.2023.3305760

M3 - Journal article

SN - 2326-3814

VL - 73

SP - 292

EP - 300

JO - IEEE Transactions on Computers

JF - IEEE Transactions on Computers

IS - 1

M1 - 10224657

ER -

Unified Digit Selection for Radix-4 Recurrence Division and Square Root

Abstract

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this