Address opendp-num fuzz findings (DASHU-007/008/015/022/026)

[cmpute]

Reviewed the opendp-num differential/property-fuzz findings against the current source (~/opendp-num/findings). Of the nine dashu findings:

• DASHU-020 / DASHU-021 — already fixed by Round to_f64/to_f32 once, to the subnormal-aware precision #91 (verified: convert_base_odd/significand_bits + the subnormal-halfway and high-precision regression tests are present).
• DASHU-023 / DASHU-024 — deferred (directed rounding at FBig's exponent-range extremes; both masked by the OpenDP adapter). Tracked with TODO comments at the exp_internal overflow branch and Context::powi. Fixing properly needs mode-aware range saturation — out of scope here.
• The five below are fixed.

DASHU-015 (dashu-int) — to_f64 reports inexact as Exact

to_f64_small used a saturating f as DoubleWord round-trip for the exactness test; at DoubleWord::MAX the value rounds up to 2^BITS, the cast clamps back to DoubleWord::MAX, and the comparison reports Equal → wrongly tagged Exact. Detect the saturation case first. Same guard applied to the 16/32-bit RefLarge → f64 path.

DASHU-026 (dashu-float) — round_fract debug assert OOMs

The debug assert built B^precision. For a sparse sticky tail (where precision is the exponent gap — reached via exp_m1 of a large-magnitude input) this allocated gigabytes in debug builds. Replaced with a log2_bounds-based precondition check that allocates nothing and only fires on a proven violation.

DASHU-022 (dashu-float) — exact results panic under unlimited precision

assert_limited_precision ran before the exact zero/one shortcuts, so precision-0 values (FBig::try_from(0.0), FBig::ONE/ZERO) panicked in exp/exp_m1/sqrt/ln/ln_1p despite exact results. Shortcuts hoisted above the assertion.

DASHU-008 (dashu-int) — GCD scratchpad under-allocation

GCD reserved scratch once from the initial operand lengths, but each euclidean step dispatches on the current lengths, so a later lopsided Burnikel-Ziegler step was under-reserved → "internal error: not enough memory allocated" (runtime .expect, so debug and release). Now sized for the loop-wide worst case: mul::memory_requirement_up_to(rhs_len, rhs_len / 2) (independent of lhs_len; returns zero_layout for small operands automatically). Applies to both the gcd and extended-gcd reservations.

DASHU-007 (dashu-float) — add correctly-rounded log2

Previously only the f32-precision log2_bounds estimate existed, so directed log2 was wrong by many ULPs. Added FBig::log2 / Context::log2 / CachedFBig::log2 computed as ln(x)/ln(2) at an elevated working precision. The result magnitude tracks the division's error amplification, so a few guard digits certify the final round across the whole range. log2(2^k) = k; log2(1) = 0 is certified Exact via the shortcut.

Verification

• cargo test --workspace --exclude dashu-python — all pass (incl. new regression tests; 85 float doctests)
• cargo clippy --all-features --all-targets --workspace --exclude dashu-python -- -D warnings — clean
• cargo fmt --all -- --check — clean
• Sharpness: stashing the DASHU-008 fix reproduces the exact memory.rs:150 panic; the DASHU-026 regression (exp_m1(-2^62), which under the old assert would try to allocate ~8×10¹⁷ bits) completes in 0.00 s.
• Changelogs updated (## Unreleased) for dashu-int, dashu-float, dashu-ratio.

🤖 Generated with Claude Code

[Shoeboxam]

Some admittedly robotic feedback that is nonetheless helpful:

log2 finding

The PR computes ln(x) / ln(2) once at a fixed elevated precision and then rounds to the requested precision. That is only near-correct: an intermediate result near a rounding boundary can double-round to the adjacent value. For example, with (B=2), (p=53), and (x=492\cdot2^{-135}), the PR uses 62 working bits and returns a result one ULP too low.

Directed rounding is also not preserved by rounding both operands in the same direction: Up(ln(x)) / Up(ln(2)) is not necessarily an upper bound because enlarging the positive denominator lowers the quotient. The current implementation is at lines 687–693 of the diff. ([GitHub]1)

Suggested implementation

Rebase on the Ziv machinery from PR #92 and use outward interval division, retrying until both interval endpoints round to the same target value. PR #92 already follows this certified-error-interval approach for transcendental functions. ([GitHub]2)

impl<R: ErrorBounds> Context<R> {
    fn log2_internal<const B: Word>(
        &self,
        x: &Repr<B>,
        mut cache: Option<&mut ConstCache>,
    ) -> Rounded<FBig<R, B>> {
        if x.is_one() {
            return Exact(FBig::ZERO);
        }

        self.ziv_interval(self.base_guard_digits::<B>() + 4, |guard| {
            let p = self.precision + guard;
            let work = Context::<mode::HalfEven>::new(p);

            // Each result satisfies true value ∈ [value - error, value + error].
            let (lx, ex) =
                work.ln_compute(x, p, false, reborrow_cache(&mut cache));

            let two = Repr::new(IBig::from(2), 0);
            let (l2, e2) =
                work.ln_compute(&two, p, false, reborrow_cache(&mut cache));

            let nx_lo = &lx.repr - &ex.repr;
            let nx_hi = &lx.repr + &ex.repr;
            let d_lo = &l2.repr - &e2.repr;
            let d_hi = &l2.repr + &e2.repr;

            debug_assert!(d_lo > Repr::zero());

            let down = Context::<mode::Down>::new(p);
            let up = Context::<mode::Up>::new(p);

            // Denominator is positive. Select endpoint pairing according
            // to the numerator sign.
            if nx_lo >= Repr::zero() {
                (
                    down.div(&nx_lo, &d_hi).unwrap().value(),
                    up.div(&nx_hi, &d_lo).unwrap().value(),
                )
            } else if nx_hi <= Repr::zero() {
                (
                    down.div(&nx_lo, &d_lo).unwrap().value(),
                    up.div(&nx_hi, &d_hi).unwrap().value(),
                )
            } else {
                // The ln(x) interval still crosses zero. Returning a broad
                // interval forces ziv_interval to retry at higher precision.
                (
                    down.div(&nx_lo, &d_lo).unwrap().value(),
                    up.div(&nx_hi, &d_lo).unwrap().value(),
                )
            }
        })
    }
}

ziv_interval should round both outward endpoints under R; it accepts only when they produce the same target value, and otherwise increases guard. It should report Exact only when the interval is a singleton; otherwise conservatively report Inexact.

[cmpute]

@Shoeboxam Thanks for your note on the guaranteed rounding. The whole Ziv thing is on another PR (#92), however unfortunately that requires break changes, so I will keep the simple version of log2 here.