Source code in the langur programming language

val .farey = f(.n) {
    var .a, .b, .c, .d = 0, 1, 1, .n
    while[=[[0, 1]]] .c <= .n {
        val .k = (.n + .b) // .d
        .a, .b, .c, .d = .c, .d, .k x .c - .a, .k x .d - .b
        _while ~= [[.a, .b]]
    }
}

val .testFarey = f() {
    writeln "Farey sequence for orders 1 through 11"
    for .i of 11 {
        writeln $"\.i:2;: ", join " ", map(f $"\.f[1];/\.f[2];", .farey(.i))
    }
}

.testFarey()

writeln()
writeln "count of Farey sequence fractions for 100 to 1000 by hundreds"
for .i = 100; .i <= 1000; .i += 100 {
    writeln $"\.i:4;: ", len(.farey(.i))
}