In the multiplication by a constant (C.X), it has been proved that the adder-depth (number of cascaded additions/subtractions) determines not only the speed (which is obvious) but also the power consumption (limitation of the glitch propagation). We proved that for an N-bit constant, the upper-bound in cascaded additions/subtractions using the radix-2r arithmetic is equal to log[(N+1)/r]/log(2)+r-2, where r=2.W[((N+1).log(2))^0.5]/log(2) and W is the Lambert function.
Article Radix-2r Arithmetic for Multiplication by a Constant: Furthe...
Article Radix-2r Arithmetic for Multiplication by a Constant
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