[kahrendt]

Summary

Within one segment of an anchor, offset_us() and time_position() multiplied a sample count by 10^6 and a microsecond count by the rate in int64. Both overflowed (undefined behavior) once one segment had run about 278 days at 384 kHz, or about 6 years at 48 kHz, so a long-running live input would map positions and cells to wrong times.

Change

• scaled_floor(), scaled_ceil() and scaled_round() in sched/timeline.h, next to floor_div(): n * mul / div with n split at a multiple of div, so only the remainder's product (below div * mul) is formed. Same results as before wherever the old products fit.
• offset_us() and time_position() use them. This adds one 64-bit divide per call, per cell or frame, never per sample.
• Folded in: two products of the same kind in GroupAudio, a resampled instance's start position ((first - origin) * in.rate, undefined after about 4 years at 192 kHz in, 384 kHz out) and finish_drain()'s output count (span * 2 * out_rate, which wrapped in uint64 at the same point). Both run once per instance start or drain.
• segment_output_index() is unchanged: its picosecond term never exceeds a second, so splitting it would add a divide for nothing.

Tests

• SchedTimeline.TimeAndPositionYearsIntoOneSegment: one segment of 300 days at 384 kHz and 7 years at 48 and 44.1 kHz maps positions, times and cells as the Control rows at a second (and before p0) do. The 300-day row trips UBSan without the change.
• SchedTimeline.ScaledDivisionRounding: floor, ceil and half-up rounding of the helpers, negative inputs, and rows whose unsplit product passes 2^63.
• Gap: the GroupAudio call sites' overflow region is covered only through the helper table, since the pipeline harness cannot reach a segment years long; their wiring is pinned by the existing GroupAudio tests at ordinary durations.

Closes #94

[Copilot]

🟡 Changes recommended

The new helpers still have intermediate overflows for valid boundary inputs whose results fit int64.

1 open finding

• Prevent intermediate overflow in scaled division helpers · New

What changed in this PR

Addresses #94 by reducing intermediate overflow in timeline and resampling calculations for long-running audio streams.

Changes:

• Adds scaled floor, ceiling, and rounding helpers.
• Applies them to timeline mappings and resampling start/drain calculations.
• Adds rounding and months-to-years regression cases.

File	Description
tests/​test_sched_timeline.cpp	Adds scaled-arithmetic and long-duration mapping tests.
src/​sched/​timeline.h	Defines the scaled division helpers.
src/​sched/​timeline.cpp	Uses helpers for position/time conversions.
src/​group_audio.cpp	Uses helpers for resampling start and drain counts.

🧠 Review effort: Balanced

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