math surface gaps — 16 names missing, all LOUD

Measured against CPython by calling each name; every one below fails to compile with undefined variable (...), so none can produce a wrong answer. That is why this is one low-priority ticket rather than sixteen.

Missing: trunc, e, pow, log(x, base) (the two-argument form — log10/log2 exist), atan2, factorial, isnan, isinf, degrees, radians, inf, nan, tau, copysign, isclose, comb, prod.

Present and correct: pi, sqrt, sin, cos, gcd, fabs, hypot, fmod, floor, ceil, log2, exp (1 ulp — see the log10 ticket).

Notes on a few that are not just aliases:

• isnan / isinf are the ones real code most often needs, because without them a NaN can only be detected by the x != x trick.
• inf / nan as CONSTANTS pair with them; float("inf") already works, so these are spellings of a value that exists.
• trunc differs from floor for negatives (trunc(-2.5) is -2, floor is -3) — a plausible-looking wrong substitution, so implement it rather than aliasing.
• pow(x, y) must be the FLOAT contract (always a float), unlike the ** operator's int-preserving one.
• log(x, base) is the two-argument form; LogN already exists in lib/rtl/math.pas under that name.

Gate

make lib-test + a CPython-diffed test calling each name, including trunc/floor on negatives, isnan/isinf on the three special values, and log(x, base) against log10/log2 for agreement.

Resolution 2026-08-09 (Track B) — 12 in the RTL, 4 escalated

NilPy's import math resolves ordinary names case-insensitively against lib/rtl/math.pas, so fourteen of these are RTL additions and now match CPython exactly, verified by diffing a .npy against python3 until identical:

e, tau, inf, nan, isnan, isinf, atan2, degrees, radians, isclose, factorial, comb — twelve. (prod takes an iterable and is Python-shaped rather than a math gap, so it is not here.)

Three things measurement changed:

inf/nan cannot be built from 1.0/0.0. The obvious form raises ZeroDivisionError the moment a NilPy program says math.inf — the check fires inside the RTL function. They are IEEE bit patterns now (the Sqrt seed's reinterpret trick), which is exact by construction anyway. copysign had the same problem for the opposite reason: the 1.0/y idiom is the only way a COMPARISON can see -0.0, so it reads the sign bit instead.

trunc is deliberately NOT added, and that is the opposite of the ticket's instruction to implement rather than alias. Python's returns an INT; a Double->Double Trunc in the math unit resolves ahead of everything and answers -2.0 where CPython says -2, quietly. That is the same int-contract mismatch that made math.floor/math.ceil frontend intercepts, so it wants a pymath_trunc beside them — an honest undefined variable (trunc) is better than a wrong type in the meantime.

pow, log and copysign could not go in this unit at all, and finding out cost a RED gate on a C test that had nothing to do with the change. pxxcio is auto-pulled into every C program and does uses math, so every name in lib/rtl/math.pas is in scope for C name resolution, case-insensitively — a Pascal Pow made a C program's pow(2,10) answer 1 instead of 1024, and CopySign made copysign(3,-1) answer 0.785398, which is atan2(1,1). Silently. lib/crtl/src/math.c already documents the hazard from the other side (it renamed its own functions __crtl_log2/__crtl_log10 to dodge it); nothing protected this direction. Filed as [[bug-c-pascal-math-names-hijack-libc-through-pxxcio]] with prio: 55, since the trigger is an ordinary Track B edit and the symptom is a silent wrong answer in unrelated code. test/cmath_no_pascal_hijack.c is now a canary for it in lib-test.

log(x, base) had a SECOND reason to stay out. Measured, all three:

CPython does not snap; FPC does; we match FPC. Neither is wrong — each matches its own oracle — so LogN stays FPC-faithful and NilPy needs its own intercept. Note the argument order differs too (log(x, base) vs LogN(base, x)), which is a silent-wrong-answer shape, so both spellings now exist and each is correct under its own name.

All four (pow, log, copysign, trunc) escalated as [[bug-n-math-trunc-and-log-need-frontend-intercepts]] — they want NilPy intercepts, which is also the only route that survives the hijack bug.

One divergence left that is NOT in scope here: math.pow(2.0, 0.5) is 3 ulp off CPython, because Power rides Exp/Ln — [[feature-rtl-ln-exp-are-a-ulp-off-port-the-crtl-dd-core]] is the root cause and already filed.

Regression test: test/lib_math_python_surface.pas, in make lib-test.

Log

• 2026-08-09 — resolved, commit 6fdf3b71f.