FAUST_FSM_TAPE - Jiles-Atherton Magnetic Hysteresis

FAUST implementation of the Jiles-Atherton (JA) model of ferromagnetic hysteresis — a physically-based mathematical description relating magnetization (M) to applied field (H). Combined with a phase-locked bias oscillator for analog tape emulation.

Author: Thomas Mandolini / OmegaDSP Contact: thomas.mand0369@gmail.com

Project Status: See docs/CURRENT_STATUS.md for current state, open problems, and research directions.

ba.tabulateNd Breakthrough (2025-12-25)

The ultimate optimization: 3D LUT via FAUST's built-in ba.tabulateNd with runtime bias interpolation.

Metric	Value
CPU	~0.2% (M4 Max)
Grid	33×65×9 (M, H, Bias)
Substeps	4×K90 = 360 total
Interpolation	Tricubic
Sound	Better than full physics

# Build the recommended version
cd faust/dev/lib_latest_proto && ./ja_tabulateNd.sh

Key features:

• Runtime bias: Continuous 0.1-0.9 (not discrete presets)
• Lambda tilt: Spectral shaping for tape character
• Compile-time physics: Full JA computed during FAUST compilation
• Runtime = interpolation: Just 64-point tricubic lookup at audio rate

What We're Looking For (GRAME)

1. Variable-count iteration pattern - The C++ reference uses fractional substep accumulation (step count varies 35-37 per sample for better phase continuity). FAUST's fixed unrolled chains (exactly 36/54/66) cause subtle frequency response differences. Is there an idiomatic FAUST pattern for variable iteration counts based on runtime accumulator state?

   Possible workaround: Unroll to max count and gate each stage with ba.if(step_index < steps_this_sample, newState, prevState) to skip inactive steps. CPU stays fixed but physics only advances for active steps. Is there a cleaner pattern?

2. Potential ja.lib library - Reusable Jiles-Atherton hysteresis module with configurable physics parameters

The Algorithm

Jiles-Atherton Model

Core equation for magnetization change:

dM/dH = (c * dMan/dH + (Man - M) / pin) / (1 - c * α * dMan/dH)

Physics parameters:

• Ms (320): Saturation magnetization
• a (720): Anhysteretic curve shape
• k (280): Coercivity (loop width)
• c (0.18): Reversibility ratio
• α (0.015): Mean field coupling

Phase-Locked Bias Oscillator

Fixed bias cycles per audio sample (sample-rate invariant).

Note: Integer cycles required to avoid 12kHz bias leakage (half-integer cycles tested, caused audible tone from residual phase accumulation).

Mode	Cycles/Sample	Substeps	Character
K28	1	28	Maximum grit
K63	3	63	Classic tape
K121	5	121	Standard
K253	11	253	Detailed

Each substep uses midpoint sampling: sin(phi + 0.5 * dphi)

Building

Prerequisites

git clone --depth 1 https://github.com/juce-framework/JUCE.git

FAUST Plugin

cd faust
./rebuild_faust.sh

First build creates the project with faust2juce. Subsequent builds preserve plugin IDs.

Flags: -double (64-bit precision)

C++ Plugin

Open juce_plugin/JA_Hysteresis_CPP.jucer in Projucer, save, build from Xcode.

Or CMake:

cd juce_plugin
cmake -S . -B build -G Xcode && cmake --build build --config Release

A/B Comparison

Both plugins use identical physics, DC blocker (SVF TPT 10 Hz), and parameter ranges.

CPU load (M4 Max, Reaper, AU/VST3):

Implementation	CPU
ba.tabulateNd 3D LUT (4×K90)	~0.2%
FAUST full-physics K180 (4×K45, cascaded)	3.4%
FAUST full-physics K92 (4×K23, cascaded)	1.9%
FAUST full-physics K44 (4×K11, cascaded)	1.0%
C++ scheduler	~2%
FAUST + 2D LUT optimization	<1%

Key finding: 4× cascaded architecture (M course-correction 4 times per sample) dramatically improves harmonic response. K180 matches tabulateNd quality.

Note: The LUT optimization trades some flexibility (fixed bias parameters) for massive CPU reduction. Hybrid 50/50 (48 real + 48 LUT) was tested but NOT recommended — Catmull-Rom interpolation overhead makes it only 0.3-0.5% faster than full physics. See docs/CURRENT_STATUS.md for details.

Recommended: ba.tabulateNd 3D LUT

Location: faust/dev/lib_latest_proto/ja_tabulateNd.dsp

• 3D LUT (M × H × Bias) with 4×K90 cascaded lookups (360 substeps)
• Runtime bias 0.1-0.9 with tricubic interpolation
• ~0.2% CPU — sounds better than full physics
• Build: cd faust/dev/lib_latest_proto && ./ja_tabulateNd.sh

Full-Physics Alternatives

Multi-mode with ondemand (4× cascaded): faust/dev/lib_latest_proto/jahysteresislib_proto_OD_3_modes.dsp

Mode	Cascades	Substeps	CPU	Character
K180 HQ	4×K45	180	3.4%	Sounds like analog hardware
K92 Standard	4×K23	92	1.9%	Great quality, default
K44 Eco	4×K11	44	1.0%	Efficient, still excellent

• Only active mode computes (via ondemand primitive)
• 4× Cascaded Architecture: M course-corrected 4× per sample for improved harmonic response
• Build: cd faust/dev/lib_latest_proto && ./build_OD_3_modes.sh

Single mode: faust/dev/lib_latest_proto/jahysteresislib_proto.dsp

• K96 (96 substeps, 4 cycles × 24) — ~2% CPU

Common features:

• Bias Asymmetry: adds 2nd harmonic for warmth (sin(phase) + asym * sin(2*phase))
• Wavelength Saturation (λ Tilt): frequency-dependent pre-saturation via fi.spectral_tilt(3, 200, 15000, alpha). Simulates shorter wavelengths (higher frequencies) hitting tape harder — instant retro vibes. Range: -0.1 to +0.1, step 0.001.
• Stabilization: diff_scale soft clamp, sigma=1e-3
• Gain compensation: +15.6 dB makeup + piecewise bias compensation
• DC blocker: 7 Hz, Q=0.7071 (Butterworth)
• UI: Grouped controls (Quality, Gain, Bias, Tape [λ Tilt], Physics)

Lite Version (3×K29 Cascaded LUT)

Ultra-low CPU version with discrete bias presets.

Location: faust/test/test_fixed_bias_cascaded_LUT/

• Architecture: 3 sequential K29 LUT lookups (87 total substeps, 3 course-corrections/sample)
• 9 bias presets: 0.1 to 0.9 with measured gain compensation
• CPU: <1%

Build (requires extended timeout):

/opt/homebrew/bin/faust -t 600 -a /opt/homebrew/share/faust/juce/juce-plugin.cpp \
  -scn base_dsp -uim -i jahysteresis_lite_3xK29_9bias.dsp \
  -o jahysteresis_lite_3xK29_9bias/FaustPluginProcessor.cpp

Important: Default faust timeout is 120s. Use -t 600 for complex DSP.

Critical: LUTs must use H range [-40, 40] (not [-1, 1]) to cover full +29dB drive range.

Production Libraries

Located in faust/dev/lib_final/:

Library	Description	CPU
jahysteresis.lib	Full-physics K72, runtime params	~2%
jahysteresis_lite.lib	LUT-optimized, 10 modes (K28-K2101)	<1%

License

Shared for collaboration with GRAME. Contact author for commercial licensing.