[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85138-en":3,"doc-seo-85138-105":28,"detail-sidebar-cat-0-en-105":90},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},85138,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","WINT: A Novel Weighted Integer Representation with Improved Error Characteristics","Weighted Integer (WINT) introduces a configurable mantissa–exponent number format designed for computing tasks that need large dynamic range while keeping low error under strict memory constraints. WINT lets users choose mantissa (m) and exponent (e) bit allocations to tailor precision–range tradeoffs during design time. An analytical framework derives Mean Relative Error (MRE), with O(1) harmonic and Taylor approximations replacing exponentially growing exact computations. Experiments across 8–32-bit configurations show exponent-bit choices that reduce MRE and increase range versus integer baselines, with harmonic/Taylor accuracy within 0.2%.","WINT: A Novel Weighted Integer Representation with Improved Error Characteristics  \nCheng-Yen Lee, Zach Assad, Gautham Nemani, Sunil P. Khatri  \nDepartment of Electrical and Computer Engineering, Texas A&M University, College Station, TX, USA {cylee, xachariah, gnemani, [sunilkhatri](sunilkhatri}@tamu.edu)[}](sunilkhatri}@tamu.edu)[@tamu.edu](sunilkhatri}@tamu.edu)  \narXiv :2607 .09775v 1 [ cs .AR] 7 Jul 2026  \nAbstract—In computing, there is a need for number representation schemes that provide large dynamic range with low error. Many applications, including embedded systems and edge machine learning, have stringent memory constraints yet require large dynamic range for data representation. We present Weighted Integer (WINT), a simple and configurable mantissaexponent number format with user-selectable mantissa (m) and exponent (e) bit allocations (also referred to as configurations) that enables application-specific precision versus range tradeoffsat design time. We develop a complete analytical framework for computing Mean Relative Error (MRE), the primary metric for characterizing WINT’s error. Since exact MRE calculations grow exponentially with mantissa size, we introduce harmonic and Taylor series approximation methods that achieve O(1) time complexity regardless of configuration. The Taylor series and harmonic approximations demonstrate significant speedups over the exact method while maintaining accuracy within 0.2% for the configurations presented. Our experiments across 8 to 32-bit configurations show that allocating 2 exponent bits consistently yields both lower MRE by 12–33% and 2 × greater range than the integer baseline for bit widths of 12 and above. Allocating 3 exponent bits extends range by 16 × while reducing MRE by 15–50% for bit widths of 16 and above.  \nIndex Terms—weighted integer representation, configurable number format, mean relative error, harmonic number, precisionrange tradeoff  \nI. INTRODUCTION  \nNumber representation is fundamental to digital computing. The choice of representation determines what values can be stored, how much memory is required, and what errors may be incurred. These factors directly affect both the correctness and efficiency of computation, with implications that vary widely across application domains. A format well-suited for scientific simulation may be unnecessarily complex for an embedded controller, while a format optimized for neural network inference may lack the precision required for financial calculations. No single format is optimal for all applications; rather, users must select representations that best match their specific requirements for range, precision, and implementation complexity, often under tight memory and power constraints. Two dominant representations are integer and floating-point, each with distinct trade-offs.  \nStandard unsigned integers represent whole numbers from 0 to 2K −1, where K is the total bit width. Integer representation is simple, widely supported, and requires no decoding beyond reading the binary value directly. However, the range is limited by the bit width—a 16-bit integer cannot represent values larger than 65,535 . Furthermore, when quantizing real non-integer values to integers, rounding to the nearest whole number incurs representation error.  \nFloating-point formats, such as IEEE 754 [1], overcome the range and precision limitations of integers by partitioning the total K bits into three fields: a 1-bit sign value S, an m-bit mantissa M , and an e-bit exponent E , such that K = 1+m+e. The value is computed as (−1)S × (1 .M) × 2 (E−Bias), where the implicit leading 1 and exponent “Bias” are defined by the standard. However, this expanded range and precision comes at the cost of complexity: decoding requires bias subtraction, handling of an implicit leading bit, and management of special encodings for NaN and infinity. The bit allocations are also fixed by the standard—FP32, for example, mandates 8 exponent bits and 23 mantiss","cbCaiavqXvaIelaq","https://ap.wps.com/l/cbCaiavqXvaIelaq","pdf",329283,1,"English","en",105,"# Introduction\n## Background: Integer vs Floating-Point Trade-offs\n## Motivation: Memory-Constrained Dynamic Range Requirements\n## Proposed Method: Weighted Integer (WINT)\n## Error Metric and Analytical Framework (MRE)","[{\"question\":\"What problem does WINT target in number representation for computing?\",\"answer\":\"WINT targets the need for large dynamic range with low error in memory-constrained applications such as embedded systems and edge machine learning.\"},{\"question\":\"How is WINT configured and what trade-off does it enable?\",\"answer\":\"WINT is configured by choosing mantissa bits (m) and exponent bits (e), enabling application-specific precision versus range trade-offs at design time.\"},{\"question\":\"How is Mean Relative Error (MRE) computed for WINT, and why are approximations used?\",\"answer\":\"MRE is the primary metric comparing actual values to their nearest representable WINT values. Exact MRE calculations grow exponentially with mantissa size, so harmonic and Taylor series approximations provide O(1) time complexity with small accuracy loss (within 0.2% for the presented configurations).\"}]",1784201332,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":85,"head_meta":87,"extra_data":89,"updated_unix":26},"wint-a-novel-weighted-integer-representation-with-improved-error-characteristics","",{"@graph":34,"@context":84},[35,52,67],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/wint-a-novel-weighted-integer-representation-with-improved-error-characteristics/85138/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":61,"encodingFormat":59,"isAccessibleForFree":62,"interactionStatistic":63},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":64,"interactionType":65,"userInteractionCount":20},"InteractionCounter",{"@type":66},"ViewAction",{"@type":68,"mainEntity":69},"FAQPage",[70,76,80],{"name":71,"@type":72,"acceptedAnswer":73},"What problem does WINT target in number representation for computing?","Question",{"text":74,"@type":75},"WINT targets the need for large dynamic range with low error in memory-constrained applications such as embedded systems and edge machine learning.","Answer",{"name":77,"@type":72,"acceptedAnswer":78},"How is WINT configured and what trade-off does it enable?",{"text":79,"@type":75},"WINT is configured by choosing mantissa bits (m) and exponent bits (e), enabling application-specific precision versus range trade-offs at design time.",{"name":81,"@type":72,"acceptedAnswer":82},"How is Mean Relative Error (MRE) computed for WINT, and why are approximations used?",{"text":83,"@type":75},"MRE is the primary metric comparing actual values to their nearest representable WINT values. Exact MRE calculations grow exponentially with mantissa size, so harmonic and Taylor series approximations provide O(1) time complexity with small accuracy loss (within 0.2% for the presented configurations).","https://schema.org",{"og:url":50,"og:type":86,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":88,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":91},[92,96,100,104,109,114,119,122,126,129,133],{"id":20,"doc_module":4,"doc_module_name":44,"category_name":93,"show_sort_weight":94,"slug":95},"Story & Novel",90,"story-novel",{"id":45,"doc_module":4,"doc_module_name":44,"category_name":97,"show_sort_weight":98,"slug":99},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":44,"category_name":101,"show_sort_weight":102,"slug":103},"Exam",70,"exam",{"id":105,"doc_module":4,"doc_module_name":44,"category_name":106,"show_sort_weight":107,"slug":108},5,"Comic",60,"comic",{"id":110,"doc_module":4,"doc_module_name":44,"category_name":111,"show_sort_weight":112,"slug":113},6,"Technology",50,"technology",{"id":115,"doc_module":4,"doc_module_name":44,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":44,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":44,"category_name":124,"show_sort_weight":27,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":27,"doc_module":4,"doc_module_name":44,"category_name":127,"show_sort_weight":27,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":44,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":44,"category_name":135,"show_sort_weight":105,"slug":136},19,"General","general"]