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On the use of integer arithmetic to achieve confirmably correct computation
Author(s) -
Neely Peter M.
Publication year - 1977
Publication title -
software: practice and experience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.437
H-Index - 70
eISSN - 1097-024X
pISSN - 0038-0644
DOI - 10.1002/spe.4380070203
Subject(s) - integer (computer science) , computation , transformation (genetics) , multiple , mathematics , unit (ring theory) , arithmetic , integer programming , argument (complex analysis) , computer science , discrete mathematics , algorithm , biochemistry , chemistry , mathematics education , gene , programming language
An example is provided from biostatistics to show that transformation to a unit normal deviate can be inadvisable. This is used to motivate a definition of commensurable units of measurement. An argument is presented to show that a unit cell size can be determined that is termed the ‘least distinguishable difference’. The recommended commensurable unit is obtained by reseating the least distinguishable difference to unity. Thus, the data are transformed to Integer‐valued variates. Since the transformed data are integer‐valued and optimally ranged for integer accumulation, this is recommended. On most computers integer overflow is detectable, therefore in the absence of overflow one is assured that the intervening computation is correct. A few concluding remarks are appended.