?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Rigorous+Roundoff+Error+Analysis+of+Probabilistic+Floating-Point+Computations&rft.creator=Constantinides%2C+G&rft.creator=Dahlqvist%2C+F&rft.creator=Rakamaric%2C+Z&rft.creator=Salvia%2C+R&rft.description=We+present+a+detailed+study+of+roundoff+errors+in+probabilistic+floating-point+computations.+We+derive+closed-form+expressions+for+the+distribution+of+roundoff+errors+associated+with+a+random+variable%2C+and+we+prove+that+roundoff+errors+are+generally+close+to+being+uncorrelated+with+their+generating+distribution.+Based+on+these+theoretical+advances%2C+we+propose+a+model+of+IEEE+floating-point+arithmetic+for+numerical+expressions+with+probabilistic+inputs+and+an+algorithm+for+evaluating+this+model.+Our+algorithm+provides+rigorous+bounds+to+the+output+and+error+distributions+of+arithmetic+expressions+over+random+variables%2C+evaluated+in+the+presence+of+roundoff+errors.+It+keeps+track+of+complex+dependencies+between+random+variables+using+an+SMT+solver%2C+and+is+capable+of+providing+sound+but+tight+probabilistic+bounds+to+roundoff+errors+using+symbolic+affine+arithmetic.+We+implemented+the+algorithm+in+the+PAF+tool%2C+and+evaluated+it+on+FPBench%2C+a+standard+benchmark+suite+for+the+analysis+of+roundoff+errors.+Our+evaluation+shows+that+PAF+computes+tighter+bounds+than+current+state-of-the-art+on+almost+all+benchmarks.&rft.subject=Science+%26+Technology%2C+Technology%2C+Computer+Science%2C+Hardware+%26+Architecture%2C+Computer+Science%2C+Software+Engineering%2C+Computer+Science%2C+Theory+%26+Methods%2C+Computer+Science&rft.publisher=Springer&rft.contributor=Silva%2C+A&rft.contributor=Leino%2C+KRM&rft.date=2021-07-15&rft.type=Proceedings+paper&rft.publisher=33rd+International+Conference+on+Computer-Aided+Verification+(CAV)&rft.language=eng&rft.source=+++++In%3A+Silva%2C+A+and+Leino%2C+KRM%2C+(eds.)++(Proceedings)+33rd+International+Conference+on+Computer-Aided+Verification+(CAV).+(pp.+pp.+626-650).++Springer+(2021)+++++&rft.format=text&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10135337%2F1%2FConstantinides2021_Chapter_RigorousRoundoffErrorAnalysisO.pdf&rft.identifier=https%3A%2F%2Fdiscovery.ucl.ac.uk%2Fid%2Feprint%2F10135337%2F&rft.rights=open