How does CMTime avoid rounding errors, and how can sloppy conversion make audio and video drift?

Predict first

How far does the rounded sum drift?

import CoreMedia

let frame = CMTime(value: 1001, timescale: 30000)          // one frame at 29.97 fps, exactly
let thirty = CMTimeMultiply(frame, multiplier: 30)
print("30 NTSC frames:", thirty.value, "/", thirty.timescale, "=", thirty.seconds, "s")

let rounded = CMTime(seconds: 1.0 / 29.97, preferredTimescale: 600)
print("one frame stored at timescale 600:", rounded.value, "/", rounded.timescale)
var drifting = CMTime.zero
for _ in 0..<30 { drifting = CMTimeAdd(drifting, rounded) }
print("30 of them added up:", drifting.seconds, "s | equal to the exact 30 frames:", drifting == thirty)
print("drift per 30 frames:", String(format: "%.1f", (thirty.seconds - drifting.seconds) * 1000), "ms")

let oneThird = CMTime(value: 1, timescale: 3)
print("1/3 s as 200/600 compares equal:", CMTimeCompare(oneThird, CMTime(value: 200, timescale: 600)) == 0)
let mixed = CMTimeAdd(CMTime(value: 1, timescale: 44100), CMTime(value: 1, timescale: 48000))
print("1/44100 + 1/48000 uses timescale", mixed.timescale, "(value", mixed.value, ")")

print("CMTime.invalid.isValid:", CMTime.invalid.isValid, "| invalid + 1 s still valid:", CMTimeAdd(.invalid, CMTime(value: 1, timescale: 1)).isValid)
print("CMTime.invalid.seconds is NaN:", CMTime.invalid.seconds.isNaN)

let a = CMTimeRange(start: .zero, duration: CMTime(value: 5, timescale: 1)), b = CMTimeRange(start: CMTime(value: 3, timescale: 1), duration: CMTime(value: 5, timescale: 1))
print("ranges 0..<5 and 3..<8: intersection", a.intersection(b).start.seconds, "+", a.intersection(b).duration.seconds, "| union duration", a.union(b).duration.seconds)

• 30 exact frames 1.001 s, rounded sum 1.0 s (1.0 ms drift), invalid stays invalid
• both sums are exactly 1.001 s
• invalid plus 1 s is valid