Add DX7 DAC Quantization to Mark I Engine

[grahamfranz]

Add DX7 DAC Quantization to Mark I Engine

Summary

Implements authentic Yamaha DX7 digital-to-analog converter (DAC) quantization in the Mark I synthesizer engine. The DX7 hardware uses a 12-bit DAC with a 3-bit analog scaler to handle the wide dynamic range of FM synthesis, creating characteristic quantization artifacts that are part of the original synth's sonic character.

Addresses feature request from issue #511 (thanks @dronus). This implementation focuses on the core 12-bit mantissa quantization; additional features like parameterized resistor network error simulation could be explored in future work.

Implementation

The d7DacQuantize() function simulates the hardware behavior:

• 12-bit mantissa quantization: Reduces sample precision to 4095 discrete levels (0xFFF)
• 3-bit adaptive exponent: Automatically selects shift amount (0-4 positions right) based on signal magnitude
• Magnitude-based scaling: Larger input signals use higher exponent values to fit within the 12-bit range

Quantization behavior:

• Input values < 2048: Pass through with no quantization error
• Input values 2048-4095: Quantized to 12-bit precision (Shift = 0)
• Input values 4096-65520: Quantized with right-shift (Shift = 1-4)
• Input values > 65520: Clamped to 12-bit max, output ~65520 at highest shift

Hardware References

• Stack Exchange analysis: https://electronics.stackexchange.com/questions/512992
• DX7 reverse engineering: https://www.righto.com/2022/02/yamaha-dx7-chip-reverse-engineering.html

Testing & Verification

Verified the quantization function correctly:

• ✓ Quantizes large input values aggressively (fitting 12-bit constraint)
• ✓ Preserves small input values with minimal error
• ✓ Maintains symmetric quantization for positive/negative signals
• ✓ Produces characteristic bit-crushing artifacts

Notes

• Applied per-voice before mixing, preserving authentic DX7 signal flow
• Does not reduce overall volume—only adds quantization artifacts
• Effect is subtle but adds authentic hardware character to synthesis