Transcendental math library (Sqrt/Sin/Cos/Ln/Exp/ArcTan/Power/Pi/Abs)

• Type: feature
• Status: done
• Owner: —
• Opened: 2026-06-18 (companion to feature-float-str-val, #5 of the language arc)
• Resolved: 2026-06-18 (commit 5e8436e) — added to lib/rtl/math.pas, byte-identical to FPC at 8 decimals, cross-bootstrap clean.

Scope

Pure-Pascal floating-point transcendentals in lib/rtl/math.pas (no libm — keeps the no-libc design): Pi, Abs(Double), Sqrt (Newton), Exp/Ln (range reduction + Taylor/atanh series), Sin/Cos (mod-2π reduction + Taylor), ArcTan (half-angle reduction + Taylor), Power(Double,Double) (= exp(e·ln b)). The existing integer Min/Max/Power/Gcd/Lcm are unchanged; float Power is an overload, float Abs is new.

Bugs found + handled along the way

• Long float literals (>~16 significant digits) mis-parsed — coeff saturated at 18 digits but kept counting dropped fractional digits, scaling the value off by powers of ten (3.14159…846 → 0.0314). Fixed in StrToDoubleBits (lexer.inc): only count absorbed fractional digits; dropped integer-part digits bump the exponent. Cross-bootstrap byte-identical.
• Result (float) read-modified in a loop → 0 — pre-existing codegen bug, filed as feature-result-in-loop. Worked around: accumulate in a local, assign Result once.
• int→float assignment missing conversion (feature-int-to-float-assign) — the whole lib uses float literals (2.0, not 2) to avoid it.

Acceptance

test/test_math.pas exercises all functions; output byte-identical to FPC (uses math) at 8 decimals incl. the identity sin²+cos²=1. make test green.

Log

• 2026-06-18 — implemented; resolved.