
112 Z. Drmag
Let t be the computed value of the tangent and let ~ = fl(t/(1 + t2)). Then the first triad
in (10) can in the floating point computation be represented by 2
a~ := (r + Z)(a~- ta~), IIEIl~ < r
The next one reads
aq := (I + F)(aq + a(I + Z)(ap - taq))
= (x + F)(~ + ,,(~ - ta~))+ ~(I + F)E(~ - t~), IIFII~ <
~,
and we easily see the forward manifestation of the wrong choice. 3 In the case of grading (
[lapl]2 > I]aqll2 ) the first triad in (11)is replaced by the modified transformation, and the
next one is skipped.
2.3 OVERALL ERROR BOUND. RELIABILITY ...