math.integer-sqrt

pub fn integer_sqrt(n: i64) -> i64

fune!(math.integer-sqrt@^1);  // then call integer_sqrt(…)

use super::funejson::Value;  ← the fune runtime: the JSON value the test vectors use; fune build keeps it only where a signature takes one

const MAX_SAFE: i64 = (1i64 << 53) - 1;

/// The largest whole number whose square does not exceed `n`.
///
/// The floating-point square root is only a first guess: it is corrected with
/// exact `i128` arithmetic, so a number just below a perfect square never
/// rounds up to its root.
///
/// # Panics
/// Panics if `n` is negative or above 2^53 - 1.
pub fn integer_sqrt(n: i64) -> i64 {
    if !(0..=MAX_SAFE).contains(&n) {
        panic!("n must be a whole number from 0 to 2^53 - 1, received {}", n);
    }
    let target = n as i128;
    let mut r = (n as f64).sqrt().floor() as i128;
    while r * r > target {
        r -= 1;
    }
    while (r + 1) * (r + 1) <= target {
        r += 1;
    }
    r as i64
}

pub fn fune_vector(args: &[Value]) -> Value {
    if let Value::Float(f) = &args[0] {
        panic!("n must be a whole number from 0 to 2^53 - 1, received {}", f);
    }
    Value::Int(integer_sqrt(args[0].as_i64()))
}

Install

fune build

With that line in your source, in a Rust project (language rust in fune.project), fune build resolves it and nothing else, pins them in fune.lock, downloads only the Rust package of each, and builds the code above into your project’s .fune/build, one readable file per capability with a header linking back here. A crate’s build.rs runs it before every compile. Or pin a range in fune.project and build in one step:

fune add math.integer-sqrt

The manifest, vectors and README with only the Rust implementation. Install it without the registry with fune add ./math.integer-sqrt-1.0.0-rust.fune, or fetch it from a terminal with fune pull math.integer-sqrt@1.0.0:rust.

The whole function, every language, is one file too: math.integer-sqrt-1.0.0.fune, 5,586 bytes, sha256 7dc41dbf6a7e06cbd778a22b43f531a03b95d9e48c91f9ab7de1cbf549641f8c. It installs into a project of any language.

// fune: before math.integer-sqrt

// fune: after math.integer-sqrt

// fune: step math.integer-sqrt after <n|label>

More from the author

Inputs are limited to 0 .. 2^53 - 1, the range where a JavaScript number is still an exact integer, so the three languages agree on every answer. A negative or fractional input, or one beyond that range, is an error.

To round a square root of a fraction `p / q` rather than truncate it, note that `floor(sqrt(p / q)) = integerSqrt(floor(p / q))`: the floor of a square root only changes at whole numbers. `inventory.eoq` uses this.

Files