Interpolation Search in C#

using System;
// Interpolation Search in C#
//
// PURPOSE
// Interpolation search estimates the target position from endpoint values, which can help on
// roughly uniform numeric data.
//
// METHOD
// Estimate a position proportional to the target value between endpoint values. Compare
// there and discard the impossible side. Handle equal endpoints separately.
//
// COMPLEXITY
// Expected O(log log n) comparisons for suitable uniform distributions; O(n) worst case,
// O(1) space.
//
// CONTRACT
// Ascending nonnegative integers <= 10000; n <= 10000 so the interpolation product fits
// signed 32-bit. Returns any matching index or -1.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 2.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int interpolation_search(ReadOnlySpan<int> a, int target) {
        checked {
            int n = a.Length;
            alg_require(((n >= 0) && (n <= 1000000)));
            alg_require((a.Length == n));
            alg_require((n <= 10000));
            for (int alg_i = 0; alg_i < a.Length; alg_i++) {
                int alg_value = a[alg_i];
                alg_require(((alg_value >= 0) && (alg_value <= 10000)));
            }
            int low = 0;
            int high = (n - 1);
            int pos = 0;
            while (((low <= high) && (target >= a[low]) && (target <= a[high]))) {
                if ((a[low] == a[high])) {
                    return low;
                }
                pos = (low + (((target - a[low]) * (high - low)) / (a[high] - a[low])));
                if ((a[pos] == target)) {
                    return pos;
                }
                if ((a[pos] < target)) {
                    low = (pos + 1);
                } else {
                    high = (pos - 1);
                }
            }
            return (-1);
        }
    }

    static void Main() {
        int[] a = new int[] {0, 10, 20, 30};
        int target = 20;
        int result = interpolation_search(a, target);
        Console.WriteLine(result);
    }
}