Crate kahan_pairs 

Generate pairs of integers.

This crate implements an algorithm described by Prof. W. Kahan to enumerate pairs of positive integers.

Correctness

The results returned by this crate are correct for all values of n up to 2^52. Results for values of n greater than that may be incorrect, due to floating point imprecision.

no-std support

This crate has two features: std and libm. These features are mutually exclusive, and will cause a compile error if both are enabled simultaneously, or if neither are enabled.

The std feature is enabled by default, and allows the crate to use the f64 sqrt and trunc intrinsics, which are necessary for certain steps of the algorithm. If running in a no-std environment is desired, the std feature can be disabled, and the libm feature enabled, which will replace the use of the aforementioned intrinsics with the equivalent functions from libm.

Usage

use kahan_pairs::pairs;

let mut pairs = pairs();

assert_eq!(pairs.next(), Some((1, 1)));
assert_eq!(pairs.next(), Some((1, 2)));
assert_eq!(pairs.next(), Some((2, 1)));
assert_eq!(pairs.next(), Some((1, 3)));
assert_eq!(pairs.next(), Some((2, 2)));

Starting from 0 instead of 1:

use kahan_pairs::pairs_0;

let mut pairs = pairs_0();

assert_eq!(pairs.next(), Some((0, 0)));
assert_eq!(pairs.next(), Some((0, 1)));
assert_eq!(pairs.next(), Some((1, 0)));
assert_eq!(pairs.next(), Some((0, 2)));
assert_eq!(pairs.next(), Some((1, 1)));

Calculate for any n:

use kahan_pairs::nth_pair;

assert_eq!(nth_pair(100), (9, 6));
assert_eq!(nth_pair(99_999), (318, 130));

use kahan_pairs::nth_pair_0;

assert_eq!(nth_pair_0(105), (13, 0));
assert_eq!(nth_pair_0(99_999), (317, 129));

Structs

Pairs

An iterator over every unique pair of positive integers, excluding 0

Pairs0

An iterator over every unique pair of positive integers, including 0

Functions

get_nth_pair

Infallibly return the nth pair of positive integers, according to the crate’s namesake algorithm

get_nth_pair_0

Infallibly return the nth pair of positive integers, according to a version of the crate’s namesake algorithm that includes 0 in the output

nth_pair

Return the nth pair of positive integers, according to the crate’s namesake algorithm

nth_pair_0

Return the nth pair of positive integers, according to a version of the crate’s namesake algorithm that includes 0 in the output

pairs

Return an iterator that enumerates every unique pair of positive integers, excluding 0

pairs_0

Return an iterator that enumerates every unique pair of positive integers, including 0

try_nth_pair

Return the nth pair of positive integers, according to the crate’s namesake algorithm, or None if n == 0

try_nth_pair_0

Return the nth pair of positive integers, according to a version of the crate’s namesake algorithm that includes 0 in the output, or None if n == 0