Use f32 instead of f64 in modular synth chain

[Woyten]

It is not guaranteed that this will actually improve the performance.

[Woyten]

Benchmark results

Parameters

• Commit: f3a8747
• CPU: Intel Core i7-6700HQ CPU @ 2.60GHz
• OS: Ubuntu 20.04.1 LTS
• Metric: Max. number of concurrent waveforms without audio buffer underrun (--out-buf 2048)

Organ 1

• f64: 200 (= 800 Sin stages)
• f32: 300 (= 1200 Sin stages)

Plucked String

• f64: 510
• f32: 480

Fat Sawtooth 1

• f64: 800 (= 1600 Sawtooth stages)
• f32: 790 (= 1580 Sawtooth stagess)

Triangle Harp

• f64: 900
• f32: 880

Conclusion

• When using regular arithmetic on a 64-bit CPU f64 offers a slightly better performance than f32. This result is not completely unexpected since 64-bit CPUs are designed to consume f64s in a single instruction. The fact that an f64 consumes twice as much memory as an f32 does not seem to play a significant role.
• However, for more complex arithmetic involving convergence like {float}::sin, f32 clearly is faster than f64. The obvious explanation is that since f64 has a higher precision than f32 more iteration steps are required until a value is fully converged.

Follow-Up

• For the sake of consistency and since a numeric precision loss is undesired, use f64 everywhere.
• The cost for transforming an f64 buffer from and to an f32 audio buffer is expected to be negligible.
• Check if there are other ways of improving f64::sin without sacrificing numeric precision.

[Woyten]

Consistent usage of f64 implemented in 206b416209647e52c6ff402d63a12656024bd88f

New benchmark results:

• Organ 1: 200
• Plucked String: 680
• Fat Sawtooth 1: 810
• Triangle Harp: 860