Restore integer truncation semantics from BPSER and BUP in the beta_inc translation

[andreasnoack]

While looking into JuliaStats/StatsFuns.jl#228 (Student-t CDF/quantile performance), I audited the beta_inc translation against the original NSWC Fortran source (https://github.com/jacobwilliams/nswc, BRATIO and its subroutines). The Fortran routines rely on implicit typing — variables starting with I–N are INTEGER unless declared REAL, and assigning a real expression to them truncates. The translation handles this correctly in several places (BRATIO's N = B0, BRCOMP's N = B0 - 1.0, BUP's K = R), but two spots were missed:

1. BPSER (beta_inc_power_series): M = B0 - 1.0 truncates (BPSER declares only N as REAL), and DO 41 I = 1,M is an integer loop. The translation kept m as a Float64 and iterated for i = 1:m over a Float64 range, which constructs a TwicePrecision-backed StepRangeLen on every call — for a loop that typically runs a handful of times. The iteration count happens to coincide with the truncated Fortran semantics, so this is a pure performance fix: ~40 ns flat per call on the min(a,b) < 1 < max(a,b) < 8 branch (the cost is the range construction, not the iterations).

2. BUP (beta_inc_diff): MU = ABS(EXPARG(1)) and K = EXPARG(0) truncate (BUP declares only L as REAL), so the scaling exponent is a whole number. This one has no measurable performance impact and produced bit-identical results in all tests; it is included for fidelity to the original.

Benchmarks (Apple Silicon, @belapsed, this branch vs current master; values bit-identical):

case	master	this PR
beta_inc(0.5, 2.5, 0.3103)	217 ns	179 ns (−17%)
StatsFuns.tdistcdf(5, 1.5)	223 ns	182 ns (−19%)
StatsFuns.tdistinvcdf(5, 0.95)	1004 ns	849 ns (−15%)
StatsFuns.tdistinvcdf(5, 1e-8)	1642 ns	1354 ns (−18%)

The quantile improves because beta_inc_inv evaluates beta_inc on every Newton iteration.

All beta_inc/betanc tests pass with results unchanged.

Disclosure: this PR was prepared by Claude Code at my direction; I have reviewed the changes and the benchmark methodology.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.49%. Comparing base (adbeb4b) to head (e7193aa).

Additional details and impacted files

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  Coverage   94.49%   94.49%           
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  Files          14       14           
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[devmotion]

LGTM. I checked the Fortran source and indeed this PR seems to fix inconsistencies with it.