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std.range.Sequence/sequence - multiple declarations

Function 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.

auto auto sequence(alias fun, State...) (
  State args
);

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

Example

Odd numbers, using function in string form: 

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

Example

Triangular numbers, using function in lambda form: 

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

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

Example

Fibonacci numbers, using function in explicit form: 

import std.math : pow, round, sqrt;
static ulong computeFib(S)(S state, size_t n)
{
    // Binet's formula
    return cast(ulong)(round((pow(state[0], n+1) - pow(state[1], n+1)) /
                             state[2]));
}
auto fib = sequence!computeFib(
    (1.0 + sqrt(5.0)) / 2.0,    // Golden Ratio
    (1.0 - sqrt(5.0)) / 2.0,    // Conjugate of Golden Ratio
    sqrt(5.0));

// Note random access with [] operator
writeln(fib[1]); // 1
writeln(fib[4]); // 5
writeln(fib[3]); // 3
writeln(fib[2]); // 2
writeln(fib[9]); // 55

Struct 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.

struct Sequence(alias fun, State) ;

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

Example

Odd numbers, using function in string form: 

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

Example

Triangular numbers, using function in lambda form: 

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

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

Example

Fibonacci numbers, using function in explicit form: 

import std.math : pow, round, sqrt;
static ulong computeFib(S)(S state, size_t n)
{
    // Binet's formula
    return cast(ulong)(round((pow(state[0], n+1) - pow(state[1], n+1)) /
                             state[2]));
}
auto fib = sequence!computeFib(
    (1.0 + sqrt(5.0)) / 2.0,    // Golden Ratio
    (1.0 - sqrt(5.0)) / 2.0,    // Conjugate of Golden Ratio
    sqrt(5.0));

// Note random access with [] operator
writeln(fib[1]); // 1
writeln(fib[4]); // 5
writeln(fib[3]); // 3
writeln(fib[2]); // 2
writeln(fib[9]); // 55

Authors

Andrei Alexandrescu, David Simcha, Jonathan M Davis, and Jack Stouffer. Credit for some of the ideas in building this module goes to Leonardo Maffi.

License

Boost License 1.0.