@skenvy/collatz
Version:
Functions related to the Collatz/Syracuse/3N+1 problem, implemented in JavaScript.
55 lines (54 loc) • 2.9 kB
JavaScript
/** The four known cycles (besides 0 cycling to itself), for the default parameterisation. */
export const KNOWN_CYCLES = [[1n, 4n, 2n], [-1n, -2n], [-5n, -14n, -7n, -20n, -10n],
[-17n, -50n, -25n, -74n, -37n, -110n, -55n, -164n, -82n, -41n, -122n, -61n, -182n, -91n, -272n, -136n, -68n, -34n]];
/** The current value up to which has been proven numerically, for the default parameterisation. */
export const VERIFIED_MAXIMUM = 295147905179352825856n;
/** The current value down to which has been proven numerically, for the default parameterisation. */
export const VERIFIED_MINIMUM = -272n; // TODO: Check the actual lowest bound.
/**
* SequenceState for Cycle Control
* @remarks
* Descriptive flags to indicate when some event occurs in the hailstone sequences
* or tree graph reversal, when set to verbose, or stopping time check.
*/
export var SequenceState;
(function (SequenceState) {
/** A Hailstone sequence state that indicates the stopping
* time, a value less than the initial, has been reached. */
SequenceState["STOPPING_TIME"] = "STOPPING_TIME";
/** A Hailstone sequence state that indicates the total
* stopping time, a value of 1, has been reached. */
SequenceState["TOTAL_STOPPING_TIME"] = "TOTAL_STOPPING_TIME";
/** A Hailstone and TreeGraph sequence state that indicates the
* first occurence of a value that subsequently forms a cycle. */
SequenceState["CYCLE_INIT"] = "CYCLE_INIT";
/** A Hailstone and TreeGraph sequence state that indicates the
* last occurence of a value that has already formed a cycle. */
SequenceState["CYCLE_LENGTH"] = "CYCLE_LENGTH";
/** A Hailstone and TreeGraph sequence state that indicates the sequence
* or traversal has executed some imposed 'maximum' amount of times. */
SequenceState["MAX_STOP_OUT_OF_BOUNDS"] = "MAX_STOP_OUT_OF_BOUNDS";
/** A Hailstone sequence state that indicates the sequence terminated
* by reaching "0", a special type of "stopping time". */
SequenceState["ZERO_STOP"] = "ZERO_STOP";
})(SequenceState || (SequenceState = {}));
/**
* Provides the appropriate lambda to use to check if iterations on an initial
* value have reached either the stopping time, or total stopping time.
* @param n - The initial value to confirm against a stopping time check.
* @param totalStop - If false, the lambda will confirm that iterations of n
* have reached the oriented stopping time to reach a value closer to 0.
* If true, the lambda will simply check equality to 1.
* @returns the lambda (arrow function expression) to check for the stopping time.
*/
export function stoppingTimeTerminus(n, totalStop) {
if (totalStop) {
return (x) => { return x === 1n; };
}
else if (n >= 0n) {
return (x) => { return x < n && x > 0; };
}
else {
return (x) => { return x > n && x < 0; };
}
}