Computes the orbit of a number in (0,1] in a base in (1,\infty). Requires GNU awk

wrapper.sh

if [ $# -ne 4 ]; then
    echo "Usage: bash wrapper.sh <precision> <number of iterations> <number to find orbit of> <base>"
    exit 1
fi

gawk -M -v "PREC=$1" -v "ITER=$2" -v "NUM=$3" -v "BASE=$4" \
'BEGIN{
    r = NUM;
    pair[0] = 0.0;
    pair[1] = 0.0;
    printf "0.";
    for (i = 0; i < ITER; i++) {
        betaMap(BASE, r, pair);
        r = pair[1];
        printf "%d", pair[0];
    }
    print;
}

# Computes the quotient and remainder of a and b, storing them in ret[0] and
# ret[1], respectively.
function quotRem(a, b, pair) {
    quot = 0;
    while (a > b) {
        a -= b;
        quot++;
    }

    pair[0] = quot;
    pair[1] = a;
}


# Computes (b * r) mod 1, and stores the result in 
function betaMap(b, r, pair) {
    quotRem((b * r), 1.0, pair);
}'