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UID:pretalx-juliacon-2026-SRHZCN@pretalx.com
DTSTART;TZID=CET:20260813T100000
DTEND;TZID=CET:20260813T103000
DESCRIPTION:Basic computer arithmetic operations\, such as +\, ×\, or ÷ a
 re correctly rounded\, whilst mathematical functions such as ex\, ln(x)\, 
 or sin(x) in general are not\, meaning that separate implementations may p
 rovide different results when presented with an exact same input\, and tha
 t their accuracy may differ. We present a methodology and a software tool 
 that is suited for exhaustive and non-exhaustive testing of mathematical f
 unctions of Julia in various floating-point formats. The software tool is 
 useful to the users of Julia\, to quantise the level of accuracy of the ma
 thematical functions and interpret possible effects of errors on their sci
 entific computation codes that depend on these functions. It is also usefu
 l to the developers and maintainers of the functions in Julia Base\, to te
 st the modifications to existing functions and to test the accuracy of new
  functions. The software (a test bench) is designed to be easy to set up f
 or running the accuracy tests in automatic regression testing. Our focus i
 s to provide software that is user friendly and allows to avoid the need f
 or specialised knowledge of floating-point arithmetic or the workings of m
 athematical functions\; users only need to supply a list of formats\, choo
 se the rounding modes\, and specify the input space search strategies base
 d on how long they can afford the testing to run. We have utilized the tes
 t bench to determine the errors of a subset of mathematical functions in t
 he latest version of Julia\, for binary16\, binary32\, and binary64 IEEE 7
 54 floating-point formats\, and found 0.49 to 0.51ULPs in binary16\, and 0
 .5 to 2.4ULPs of error in binary32 and binary64. The functions that may be
  correctly rounded (error of 0.5ULP) in all the three formats are sqrt and
  cbrt. The following functions may be correctly rounded only for binary16:
  sinh\, asin\, cospi\, sinpi\, atanh\, log2\, tanh.
DTSTAMP:20260502T093454Z
LOCATION:Room 6
SUMMARY:Accuracy of Mathematical Functions in Julia - Mantas Mikaitis
URL:https://pretalx.com/juliacon-2026/talk/SRHZCN/
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