//! `FloatSum`: ADR 009 clause 8's sign of a zero total, against IEEE addition.
//! Evidence: `context/test-evidence/numtower.md`.

use numtower::FloatSum;
use proptest::prelude::*;

/// Both zeros and small integers: totals that cancel, and every sum below 2^53 is exact.
fn addend() -> impl Strategy<Value = f64> {
    prop_oneof![
        Just(0.0),
        Just(-0.0),
        (-3i32..=3).prop_map(f64::from),
        prop::sample::select(vec![0.5, -0.5]),
    ]
}

fn sum_of(values: &[f64]) -> FloatSum {
    let mut sum = FloatSum::new();
    for v in values {
        sum.add(*v, 1);
    }
    sum
}

/// What adding the same addends in `f64` gives, starting from `-0.0` as `Sum for f64` does.
fn ieee(values: &[f64]) -> f64 {
    values.iter().sum()
}

fn same_bits(a: f64, b: f64) -> bool {
    a.to_bits() == b.to_bits()
}

#[test]
fn the_sign_of_a_zero_total_follows_ieee_for_the_cases_that_decide_it() {
    assert!(same_bits(sum_of(&[-0.0, -0.0]).value(), -0.0));
    assert!(same_bits(sum_of(&[-0.0, 0.0]).value(), 0.0));
    assert!(same_bits(sum_of(&[0.0, 0.0]).value(), 0.0));
    assert!(same_bits(sum_of(&[1.0, -1.0]).value(), 0.0));
    assert!(same_bits(sum_of(&[-0.0, 1.0, -1.0]).value(), 0.0));
    assert!(same_bits(sum_of(&[]).value(), -0.0), "as Sum for f64 is");
}

proptest! {
    #[test]
    fn a_sum_has_the_bits_ieee_gives_the_same_addends(
        values in prop::collection::vec(addend(), 0..12),
    ) {
        let (got, want) = (sum_of(&values).value(), ieee(&values));
        prop_assert!(same_bits(got, want), "{got:?} for {want:?} over {values:?}");
    }

    #[test]
    fn retracting_addends_leaves_the_sum_of_the_rest(
        values in prop::collection::vec(addend(), 1..12),
        keep in 0usize..12,
    ) {
        let keep = keep.min(values.len());
        let mut sum = sum_of(&values);
        for v in &values[keep..] {
            sum.add(*v, -1);
        }
        let (got, want) = (sum.value(), ieee(&values[..keep]));
        prop_assert!(same_bits(got, want), "{got:?} for {want:?} over {values:?} keeping {keep}");
    }

    #[test]
    fn absorbing_two_sums_is_adding_all_the_addends(
        values in prop::collection::vec(addend(), 0..12),
        cut in 0usize..12,
    ) {
        let cut = cut.min(values.len());
        let mut left = sum_of(&values[..cut]);
        left.absorb(&sum_of(&values[cut..]));
        let (got, want) = (left.value(), sum_of(&values).value());
        prop_assert!(same_bits(got, want), "{got:?} for {want:?} over {values:?} cut at {cut}");
    }
}