(gmp.info.gz) Lucas Numbers Algorithm
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(gmp.info.gz) Fibonacci Numbers Algorithm
(gmp.info.gz) Other Algorithms
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Lucas Numbers
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`mpz_lucnum2_ui' derives a pair of Lucas numbers from a pair of
Fibonacci numbers with the following simple formulas.
L[k] = F[k] + 2*F[k-1]
L[k-1] = 2*F[k] - F[k-1]
`mpz_lucnum_ui' is only interested in L[n], and some work can be
saved. Trailing zero bits on n can be handled with a single square
each.
L[2k] = L[k]^2 - 2*(-1)^k
And the lowest 1 bit can be handled with one multiply of a pair of
Fibonacci numbers, similar to what `mpz_fib_ui' does.
L[2k+1] = 5*F[k-1]*(2*F[k]+F[k-1]) - 4*(-1)^k
Info Catalog
(gmp.info.gz) Fibonacci Numbers Algorithm
(gmp.info.gz) Other Algorithms
(gmp.info.gz) Random Number Algorithms
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