fix(numtower): a nonzero ExactSum is never negative zero (improvise-z2vr)

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01VdfEGXA7aJ6ftMsCc9PJze

context/test-evidence/numtower.md

@@ -485,3 +485,11 @@ and both properties, since one `+0.0` or one cancelling pair must make the zero
 
 Adds `keep` and `gone`, then retracts `gone`; the read and the sum itself must equal a fresh sum
 of `keep`. It is why both counters are net weights and why `PartialEq` compares the sign.
+
+### a_sum_that_is_not_zero_never_reads_as_negative_zero
+
+The first version of the sign rule returned `-0.0` whenever the `-0.0` count was positive and the
+other count was nil, without checking that the finite total was zero. The weights here (+5.0 and -7.0
+net to one "other" addend, and the `-0.0` is held) make the counts say "negative zero" over a total of
+-2. Found by the existing `the_accumulator_reads_the_exact_sum_or_its_stated_roundings`, which read
+`#i-0.0` for a nonzero sum; the rival is that version.

crates/numtower/src/sum.rs

@@ -40,9 +40,7 @@ impl PartialEq for ExactSum {
         propagate(&mut mine);
         propagate(&mut theirs);
         let counts = |s: &ExactSum| (s.nan, s.pos_inf, s.neg_inf);
-        mine == theirs
-            && counts(self) == counts(o)
-            && self.negative_zero() == o.negative_zero()
+        mine == theirs && counts(self) == counts(o) && self.negative_zero() == o.negative_zero()
     }
 }
 
@@ -148,9 +146,9 @@ impl ExactSum {
             (true, _, _) | (false, true, true) => f64::NAN,
             (false, true, false) => f64::INFINITY,
             (false, false, true) => f64::NEG_INFINITY,
-            (false, false, false) => match self.negative_zero() {
-                true => -0.0,
-                false => ratio_to_f64(&self.total(), &(BigInt::one() << 1074)),
+            (false, false, false) => match (self.negative_zero(), self.total()) {
+                (true, total) if total.is_zero() => -0.0,
+                (_, total) => ratio_to_f64(&total, &(BigInt::one() << 1074)),
             },
         }
     }

crates/numtower/tests/zero_sign.rs

@@ -78,3 +78,12 @@ proptest! {
         prop_assert_eq!(sum, fresh);
     }
 }
+
+#[test]
+fn a_sum_that_is_not_zero_never_reads_as_negative_zero() {
+    let mut sum = ExactSum::new();
+    sum.add(-0.0, 1);
+    sum.add(5.0, 1);
+    sum.add(7.0, -1);
+    assert_eq!(sum.value(), -2.0);
+}