precision - C: Exponentiation over 256bit integers -


i dealing algorithm operates on unsigned 256-bit integers, , need write function computes value of given formula

uint256 compute(uint16 x) {     return floor(exp2(x / 256)) - 1; }

we can see equation preserves variable bounds (compute(0) == 0, compute(65535) == 1<<255). division should treated division of rational numbers, not integers.

the presented syntax pseudo-c, i'm looking general algorithmic aproach used in other languages.

thank , time.

you can precompute , tabulate 256-bit values of function x in [65280, 65535] (i.e. 255 x 256 + i); lookup table 8 least significant bits of argument. take 8kb of storage.

for lower values of argument, shift tabulated value right 255 - (x >> 8).

if want sheer speed , can afford 64kb of storage, can precompute shifts 0 7, , perform larger shifts copying right byte offset.

alternatively, can consider cordic method exponentials, don't think faster or require less storage.


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