Sequence

Sequence is similar to Recurrence except that iteration is presented in the so-called closed form. This means that the nth element in the series is computable directly from the initial values and n itself. This implies that the interface offered by Sequence is a random-access range, as opposed to the regular Recurrence, which only offers forward iteration.

The state of the sequence is stored as a Tuple so it can be heterogeneous.

struct Sequence(alias fun, State)
struct Sequence (
alias fun
State
) {
enum opDollar;
enum bool empty;
}
auto sequence(State args)

Examples

Odd numbers, using function in string form:

auto odds = sequence!("a[0] + n * a[1]")(1, 2);
assert(odds.front == 1);
odds.popFront();
assert(odds.front == 3);
odds.popFront();
assert(odds.front == 5);

Triangular numbers, using function in lambda form:

auto tri = sequence!((a,n) => n*(n+1)/2)();

// Note random access
assert(tri[0] == 0);
assert(tri[3] == 6);
assert(tri[1] == 1);
assert(tri[4] == 10);
assert(tri[2] == 3);

Fibonacci numbers, using function in explicit form:

1 import std.math : pow, round, sqrt;
2 static ulong computeFib(S)(S state, size_t n)
3 {
4     // Binet's formula
5     return cast(ulong)(round((pow(state[0], n+1) - pow(state[1], n+1)) /
6                              state[2]));
7 }
8 auto fib = sequence!computeFib(
9     (1.0 + sqrt(5.0)) / 2.0,    // Golden Ratio
10     (1.0 - sqrt(5.0)) / 2.0,    // Conjugate of Golden Ratio
11     sqrt(5.0));
12 
13 // Note random access with [] operator
14 assert(fib[1] == 1);
15 assert(fib[4] == 5);
16 assert(fib[3] == 3);
17 assert(fib[2] == 2);
18 assert(fib[9] == 55);

Sequence

Examples

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