perf: optimize log in datafusion-functions

[andygrove]

This PR was created by an LLM as a draft PR. I will mark it as ready for review after human review.

Which issue does this PR close?

N/A — autonomous exploratory PR.

Rationale for this change

Hoist the scalar base's natural logarithm out of the per-row loop in log(base, x), since f64::log(base) is ln(x)/ln(base) and recomputed ln(base) on every row, halving the transcendental calls with bit-identical results.

What changes are included in this PR?

Hoist the scalar base's natural logarithm out of the per-row loop in log(base, x), since f64::log(base) is ln(x)/ln(base) and recomputed ln(base) on every row, halving the transcendental calls with bit-identical results.

Are these changes tested?

Correctness: unit tests + seeded differential fuzz (bit-identical Arrow output vs main).

Benchmark (criterion):

• log_f64_array_base: 3.204% faster (base 37537ns -> cand 36335ns)
• log_f32_scalar_base: -0.358% faster (base 13815ns -> cand 13865ns)
• log_f64_default_base: 6.02% faster (base 18314ns -> cand 17211ns)
• log_f32_array_base: -0.329% faster (base 24782ns -> cand 24863ns)
• log_f64_scalar_base: 6.153% faster (base 18284ns -> cand 17159ns)

Full criterion output:

log_f64_default_base    time:   [17.193 µs 17.203 µs 17.220 µs]
                        change: [−6.1581% −6.0197% −5.9020%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 4 outliers among 100 measurements (4.00%)
  2 (2.00%) high mild
  2 (2.00%) high severe

log_f64_scalar_base     time:   [17.140 µs 17.146 µs 17.152 µs]
                        change: [−6.2343% −6.1533% −6.0954%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 1 outliers among 100 measurements (1.00%)
  1 (1.00%) high severe

log_f32_scalar_base     time:   [13.859 µs 13.867 µs 13.877 µs]
                        change: [+0.2720% +0.3581% +0.4457%] (p = 0.00 < 0.05)
                        Change within noise threshold.
Found 8 outliers among 100 measurements (8.00%)
  1 (1.00%) low mild
  3 (3.00%) high mild
  4 (4.00%) high severe

log_f64_array_base      time:   [36.240 µs 36.363 µs 36.489 µs]
                        change: [−3.3640% −3.2036% −3.0253%] (p = 0.00 < 0.05)
                        Performance has improved.
Found 10 outliers among 100 measurements (10.00%)
  10 (10.00%) high mild

log_f32_array_base      time:   [24.855 µs 24.868 µs 24.892 µs]
                        change: [+0.2349% +0.3285% +0.4056%] (p = 0.00 < 0.05)
                        Change within noise threshold.
Found 9 outliers among 100 measurements (9.00%)
  2 (2.00%) low mild
  3 (3.00%) high mild
  4 (4.00%) high severe

Are there any user-facing changes?