IronKernel.Math

IronKernel.Math

Statistics, combinatorics, and number theory for IronKernel. The runtime's numeric tower is already strong — integers promote to big integers, division of exacts gives exact ratios in least terms — so this package adds what the tower does not: the procedures that combine numbers, exact wherever the mathematics allows.

(mean (list 1 2))          ; => 3/2, exactly
(isqrt (expt 10 100))      ; => 10^50, exactly — sqrt would round
(binomial 52 5)            ; => 2598960
(prime-factors 360)        ; => (2 2 2 3 3 5)

Only stdev is inherently inexact — it takes a square root — and says so by returning one.

Use

ik add IronKernel.Math 0.1.0

Or, from a checkout of this repository:

cd lib/IronKernel.Test && ik pack        # seed the local feed
cd ../IronKernel.Collections && ik pack
cd ../IronKernel.Math
ik test
ik pack

API

Constants

pi, tau, euler, golden-ratio — each the double nearest the mathematical value.

Basics

Form	Meaning
(sign x)	−1, 0, or 1, always exact, for any real.
(clamp x lo hi)	Signals if lo > hi.
(lerp a b t)	a at t=0, b at t=1; exact on exact inputs.
(isqrt n)	Largest integer whose square does not exceed n. Newton's method on exact integers — correct at sizes where sqrt's double rounds.

Statistics

All take a non-empty list of reals and preserve exactness.

Form	Meaning
(sum xs) / (product xs)	0 and 1 on the empty list.
(mean xs)	An exact ratio on exact inputs.
(median xs)	Sorts internally; even count gives the mean of the two middles.
(variance xs)	Population variance, exact.
(sample-variance xs)	Bessel's n−1 correction; wants at least two elements.
(stdev xs) / (sample-stdev xs)	Inexact, by nature.

Combinatorics

Form	Meaning
(factorial n)	Exact at any size.
(binomial n k)	n choose k by the rising product — k steps, never a full factorial. Out-of-range k gives 0.
(permutations n k)	Ordered selections: the falling factorial.

Number theory

Form	Meaning
(prime? n)	Trial division stepping 6k±1 — exact at any size, suited to 64-bit-scale numbers, not cryptographic ones.
(next-prime n)	Smallest prime strictly greater than n.
(primes-upto n)	Sieve of Eratosthenes, bound included.
(prime-factors n)	With multiplicity, ascending; (prime-factors 1) is ().
(divisors n)	Every positive divisor, ascending, in O(√n).
(totient n)	Euler's φ, from the distinct prime factors, exactly.
(coprime? a b)	gcd is 1.

Notes

• Pure Kernel: no CLR interop, no host I/O. List work (folds, sort, distinct) comes from IronKernel.Collections, a runtime dependency.
• Domain errors signal rather than answer: (isqrt -1), (factorial -1), (prime? 7.0), (sample-variance (list 1)) are all errors.