Development of a practical tracing system for significant digits of variables in numerical calculations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25330070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Computer system
• Research Institution: Hiroshima City University
• Principal Investigator: Kitamura Toshiaki 広島市立大学, 情報科学研究科, 教授 (10324683)
• Research Collaborator: ANIYA Souseki 広島市立大学, 大学院情報科学研究科, 博士後期課程学生
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 計算機アーキテクチャ / 演算精度低下検出 / 長精度計算 / 桁落ち

Outline of Final Research Achievements

There is a risk which trusts a wrong result of numerical calculations due to a precision decline at a floating-point operation. In this research, to improve the reliability of numerical calculations, we plan to trace the significant digits by detecting cancellation of significant digits of variables at each operation, and to give the significant digits of final results. Unfortunately, a strict algorithm to find the significant digits of the result of operation from those of input operands, which is same as a forward error analysis, is too pessimistic. So, we propose more realistic algorithm to find a significant digits of result; (1) neglect the rounding error; (2) introduce “the occurrence rate of cancellation of significant digits”, and if the input operand’s significant digits are already small and that rate is high, we decrease the influence of cancelation to the result. We verified the validity of this algorithm, and also we studied feasibility of practical system development.

Free Research Field

総合領域：情報学、計算機システム・ネットワーク