Robert Allan James 36389e9d4a starkernel: item 4.3.3a -- Q48.16 trigonometry (Q.SIN/Q.COS) ...

Adds q48_reduce_angle() (range-reduce a signed Q48.16 angle into
[-PI_Q48, PI_Q48] via one integer division plus a bounded fix-up loop) and
q48_sin_approx/q48_cos_approx (Taylor series, terms n=3,5,7,9,11 for sin
and n=2,4,6,8,10 for cos, early exit below 10). Q.SIN/Q.COS registered as
FORTH words in q48_words.c, same pattern as Q.LOG/Q.EXP/Q.SQRT.

Found mid-implementation: this codebase has two independent Q48.16
implementations -- src/word_source/q48_16_words.c (hosted/vendored) and
src/starkernel/math/q48_16.c (kernel-only; the kernel build does not
compile the former at all). The hosted build linked fine after the first
pass; the kernel build failed with undefined references until the same
two functions were added to both .c files and both q48_16.h headers
(include/q48_16.h and include/starkernel/q48_16.h). Not fixed at the root
-- Q.LOG/Q.EXP/Q.SQRT already had this same four-file duplication,
unremarked until now -- just navigated correctly for this item.

Verified live on amd64 via serial injection: sin/cos at 0, +-pi/2, pi, and
3pi (range-reduction across multiple turns) all match expected values
within Taylor-series truncation error (<0.2%).

All three architectures boot clean to ok> with the DoE completing;
dict_hash identical across all three (0x291a660b05fa7b52).

FABRIC.md item 4.3.3a marked done with full acceptance evidence.

2026-08-07 13:39:05 -04:00

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