libraries/integer.rt (1312198) - rtensor

integer.rt

# functions for integer calculations and number theory
# use this by pasting file contents into the code-area

# factorial of n
fact(n) = if[n == 0, 1, n * fact(n - 1)]

# is n prime?
prime(n) = for[(g = 2), floor(n / g) * g < n, \
    (g = if(<(n - g^2 - 1), n, g + 1)), g] == n

# digits of n in base b (big-endian)
digits(n, b) = digits(floor(n / b), b), (n - b * floor(n / b))
digits(0, b) = zero(0)

# a modulo b
mod(a,b) = a - b * floor(a / b)

# greatest common divisor of m and n
gcd(m, n) = gcd(n, mod(m, n))
gcd(m, 0) = m

# factorial-base digits of n (little-endian)
fd(n, k) = if[n < fact(k - 1), \
    zero(0), \
    (.. mod(n / fact(k - 1), k)) .. fd(n, k + 1)]
fd(n) = fd(n, 1)

# internal helper
except(v, i) = if[all((len(v) == 2, i == 1)), \
    .. v[2], \
    if[len(v) == i, \
        trim(v), \
        (except(trim(v), i), v[len(v)])]]
pad(v, n) = if[len(v) == n, v, pad((v, 0), n)]

# permutation indexed by k, of order n
permi(n, v, u) = (.. u[v[len(v)] + 1]) .. \
    perm(n, trim(v), except(u, v[len(v)] + 1))
permi(n, zero(0), u) = zero(0)
perm(n, k) = permi(n, pad(fd(k), n), 1 .. n)

rtensor

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