fix: handle boundary cases for divide and log functions

[orelbn]

Description

• Resolves issue: Failed Special Boundary Tests with math.log() #1277
• Root cause is scalar division edge behavior, surfaced via log(x, base) (log(x) / log(base)).
• Normalizes divide-by-zero boundaries to complex-infinity semantics (Complex(Infinity, NaN)) for:
  • Complex/Complex with zero denominator
  • number/number when numerator is ±Infinity and denominator is 0
• This aligns with issue discussion, pointing out -Infinity/0 and complex divide-by-zero inconsistencies and proposing complex infinity style handling:
  • Failed Special Boundary Tests with math.log() #1277 (comment)
  • Failed Special Boundary Tests with math.log() #1277 (comment)
• Related design discussion on complex infinity consistency in PR thread:
  • bugfix/804: Added handling of complex numbers negative bases and positive infinity exponent #2097

Tests

• Updated boundary expectations in:
  • test/unit-tests/function/arithmetic/divide.test.js
  • test/unit-tests/function/arithmetic/log.test.js
• Added/covered key regressions:
  • log(0, 1)
  • log(-1, 1)
  • log(-1, -1)
  • log(0, 0)
  • Complex divide-by-zero paths like i/0, (1+i)/0, (1-i)/(0+0i).
• Verified locally:
  • npx mocha test/unit-tests/function/arithmetic/log.test.js test/unit-tests/function/arithmetic/divide.test.js

Breaking Changes

• No API signature changes.
• Behavioral change in edge cases:
  • Some operations that previously returned directional infinities like Infinity + Infinity i now return Complex(Infinity, NaN).
  • Scalar ±Infinity / 0 now returns Complex(Infinity, NaN) instead of numeric ±Infinity.
• Consumers asserting exact real/imag infinity signs in these boundary cases may need test updates.
• Consumers expecting numeric return type for ±Infinity / 0 must adapt to Complex output in that boundary case.

Impact on Codebase

• Positive consistency impact

  • Edge handling is centralized in src/function/arithmetic/divideScalar.js, reducing duplicated special-case logic in higher-level functions.
  • src/function/arithmetic/log.js remains generic (divideScalar(self(x), self(base))), improving maintainability.

• Cross-function behavioral impact

  • Function paths using scalar Complex/Complex and number/number (±Infinity / 0) division now inherit normalized complex-infinity behavior.
  • This improves mathematical coherence for complex limits but can alter legacy outputs in rare edge cases.

• Testing impact

  • Existing tests that encoded directional infinity for divide-by-zero were updated to undetermined-phase semantics.
  • Added regression coverage reduces risk of reintroducing inconsistent infinity behavior through future refactors.

• Risk profile

  • Low-to-moderate runtime risk: scope is small and localized to scalar division branches.
  • Main risk is downstream expectation drift (user code/tests depending on old directional outputs or numeric type for ±Infinity / 0), not broad numerical regressions in finite-domain operations.

Note I reviewed the code and made sure to understand the issue to the best of my ability, but I mainly used agentic coding to try and solve the issue. If there is any fundamental misunderstanding or issue arising from this approach, please let me know.

[gwhitney]

@orelbn thank you so much for your interest and taking the time to generate a PR in an effort to address the long-standing issue #1277. However, the core of your PR consists of a "patch" to the behavior of Complex.js and we're not going to go down that path in math.js. If there is non-ideal behavior in Complex.js that is leading to this issue in mathjs, please file a report with Complex.js, and once the behavior is fixed there, we will update to the new release of Complex.js. Thanks! (and so closing this PR)

[orelbn]

No problem, thanks for the feedback!