September 2003
Intermediate to advanced
709 pages
26h 51m
English
Content preview from Digital Arithmetic
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Correct Rounding and Monotonicity 551
t0.1
10.2
Argument Range Reduction
Approximation methods can usually be applied only for a limited range of the
argument. Consequently, before applying the approximating algorithm it is nec-
essary to perform a transformation that reduces the range of the argument. More-
over, after obtaining the approximation another transformation produces the final
value. The specific transformations depend on the function and on the approxi-
mating method.
Callingxr the reduced argument, the most-used reduction methods are either
9 additive, in which
Xr = X -- k C .
This type is used, for instance, for
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