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std.range.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.

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

Prototype

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

Example

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);

Example

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);

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
assert(fib[1] == 1);
assert(fib[4] == 5);
assert(fib[3] == 3);
assert(fib[2] == 2);
assert(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.

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);
assert(odds.front == 1);
odds.popFront();
assert(odds.front == 3);
odds.popFront();
assert(odds.front == 5);

Example

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);

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
assert(fib[1] == 1);
assert(fib[4] == 5);
assert(fib[3] == 3);
assert(fib[2] == 2);
assert(fib[9] == 55);

Authors

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

License

Boost License 1.0.

Comments