Fix cube roots: real odd roots of negative bases

[aantthony]

Summary

Closes #15.

(-8)^(1/3) (and any negative base with a fractional exponent) previously evaluated to NaN everywhere — both in the CPU evaluator (Math.pow(-8, 1/3) is NaN in JS) and in the rendered curve (GLSL's pow() is undefined for negative bases). The only existing special case was for exponents that are (numerically) exact integers.

This matches how graphing calculators like Desmos handle it: for a negative base a and exponent b, find b's rational form p/q in lowest terms via a tolerance search over small denominators. If q is odd, the root is real: sign * |a|^b, where sign is negative iff the reduced numerator p is odd. If q is even (an even root, e.g. (-4)^(1/2)), or no small-denominator match is found (an irrational-looking exponent), the result stays NaN, same as before.

Changes

• lib/expr.ts: added realPow(a, b), used by evaluate()'s ^ case instead of a bare Math.pow. Handles the CPU-side path (hover values, root-finding, etc).
• lib/glsl.ts: rewrote the eq_pow() GLSL helper with the same rational-exponent algorithm (GLSL has no big-int/rational type, so it's implemented with a fixed denominator search q = 1..12 and the existing eq_gcd helper instead of a real gcd loop). Used for rendering curves/surfaces.
• lib/expr.test.ts: added a describe('negative base with fractional exponent (real odd roots)') block covering cube roots, p/q with even numerator, negative exponents, even roots staying undefined, and that a typed decimal like 0.33333 is not snapped to 1/3.

Both implementations use the same tolerance (1e-6) and max denominator (12), and are commented as needing to stay in sync since GLSL source text and TS can't share code directly.

Examples verified

Input	Result
8^(1/3)	2 (unaffected, positive base)
(-8)^(1/3)	-2
(-8)^(2/3)	4
(-1)^(1/3)	-1
(-8)^(-1/3)	-0.5
(-4)^(1/2)	NaN (even root, correctly undefined)
(-8)^(1/4)	NaN (q=4 even)
(-8)^(0.33333)	NaN (deliberately not snapped — see tolerance note below)
(-2)^3, (-2)^2	-8, 4 (existing integer-exponent behavior unchanged)

On the tolerance choice: 1e-6 is tight enough that an exponent entered as an actual fraction (1/3 parses to 0.3333333333333333, ~1e-16 from the true rational) always snaps, while a typed decimal approximation like 0.33333 (~3.3e-6 away from 1/3) is left undefined rather than silently guessed at. This is documented in a comment on realPow().

Test plan

• npx vitest run — all 495 tests pass (including the new cases)
• npx tsc --noEmit and npx tsc -p web --noEmit — clean
• npx tsc -p worker --noEmit has pre-existing errors in this sandbox unrelated to this change (missing wrangler types-generated ambient globals — confirmed identical errors on a clean checkout with wrangler unavailable in this environment)

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[Copilot]

Pull request overview

Adds real odd-root support for negative bases in CPU and GLSL evaluation.

Changes:

• Introduces realPow() with rational-exponent detection.
• Updates GLSL power handling.
• Adds evaluator tests for odd and even roots.

Reviewed changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 1 comment.

File	Description
lib/expr.ts	Adds CPU-side real-power evaluation.
lib/glsl.ts	Adds equivalent shader-side handling.
lib/expr.test.ts	Tests negative-base fractional powers.

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