Exact real arithmetic - Keith Briggs
Exact real arithmetic - Keith Briggs
Exact real arithmetic - Keith Briggs
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IEEE floating point<br />
☞ finite set of rationals and approximate operations:<br />
F = { m 2 e : |m| < 2 53 , |e| < 1024, NaN, Inf }<br />
O = { +, −, ∗, / }, round to even or nearest<br />
☞ problems!<br />
x 0 = F(0.9)<br />
x k+1 = F(3.999)∗x k ∗(1−x k ) k = 0, 1, 2, . . .<br />
☞ in F, x 53 > 0.5, but the exact result is<br />
x 53 = 0.130235874811773733039643730080570 . . .<br />
<strong>Keith</strong> <strong>Briggs</strong> <strong>Exact</strong> <strong>real</strong> <strong>arithmetic</strong> 5 of 32
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