surge-tables

SurgeTables: Waveshaping and Envelope Utilities for the Surge Synthesizer System

SurgeTables is a Rust crate that provides a variety of waveshaping, envelope, and sinc tables for the Surge Synthesizer System. It includes utilities for generating and accessing tables, as well as mathematical functions to support synthesis operations.

SurgeTables

SurgeTables is a collection of tables and utilities used in the Surge Synthesizer System, supporting various waveshaping, envelope, and sinc operations. The crate is divided into several subcomponents, each focusing on a specific aspect of sound synthesis.

SineTables

SineTables contains precomputed sine wave values for efficient lookup during synthesis. These sine wave values are stored in different formats, such as f32, f64, and i16.

WaveshapeTables

WaveshapeTables provides tables and utilities for waveshaping synthesis. Waveshaping is a nonlinear distortion technique used to modify the harmonic content of a signal. It supports functions such as lookup_waveshape and lookup_waveshape_warp for accessing these tables and applying the desired transformations.

GainTables

GainTables provides utilities for converting between decibel (dB) and linear scales, as well as functions for applying clipping and scaling to audio signals. The db_to_linear function, for example, converts a decibel value to its corresponding linear gain value:

linear_gain = 10^(dB/20)

EnvelopeTables

EnvelopeTables provides tables and functions for handling the linear and low-pass filtered (LPF) envelope rates in the synthesizer. The envelope_rate_linear and envelope_rate_lpf functions provide utilities for controlling these rates.

SincTables

SincTables contains tables and utilities for windowed sinc functions, which are used for resampling and other signal processing tasks. The windowed_sinc function generates a sinc function windowed by a specified window function:

windowed_sinc(x) = sinc(x) * window_function(x)

where sinc(x) = sin(πx) / (πx) for x ≠ 0 and sinc(0) = 1.

MaybeOwningTablesHandle and TablesHandle

These types provide a convenient way to handle and manage the lifetime of the tables created by the various subcomponents in the crate.

With SurgeTables, users can efficiently access and manipulate a variety of tables and mathematical functions to support the waveshaping, envelope, and sinc operations in the Surge Synthesizer System.

2> /file surge-rs/surge-tables/src/envelope.rs

EnvelopeTables

1. What is this table used for?

   The EnvelopeTables struct contains two tables: table_envrate_lpf and table_envrate_linear. These tables are used for efficient lookup of envelope rates in the Surge Synthesizer System. The envelope rates determine how quickly an envelope progresses through its stages (attack, decay, sustain, release) and are crucial for shaping the amplitude and timbre of a synthesized sound.

2. Which calculations are involved in the precomputation?

   The precomputation involves the calculation of two tables:

   • table_envrate_lpf: This table contains values related to the low-pass filtered (LPF) envelope rates. The precomputation involves an exponential decay calculation with a time constant based on the sample rate and a power-of-two mapping.

   • table_envrate_linear: This table contains values related to the linear envelope rates. The precomputation involves a simple division by the time constant based on the sample rate and a power-of-two mapping.

3. How much performance are we saving?

   By precomputing these envelope rate values and storing them in tables, we save performance by avoiding the need to recalculate these values in real-time during the synthesis process. This can lead to significant performance improvements, especially when dealing with complex synthesizer patches and polyphony.

4. How can we improve this table?

   Some possible improvements to the EnvelopeTables include:

   • Interpolation: The current implementation uses linear interpolation to access the table values. Other interpolation methods, such as cubic or spline interpolation, could provide more accurate results at the cost of additional complexity.

   • Adaptive table size: The current implementation uses a fixed table size of 512. Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.

   • Alternative precomputation methods: Exploring different methods for generating the envelope rate values in the precomputation step could lead to more accurate or faster results. This may involve using different mathematical approximations or algorithms for the exponential decay and linear rate calculations.

3> /file surge-rs/surge-tables/src/gain.rs

GainTables

1. What is this table used for?

   The GainTables struct contains a table called table_db, which is used for efficient conversion between decibel (dB) and linear scales. This is useful for operations involving gain, attenuation, or other processes where logarithmic scales are involved. The table also provides a clipscale function to calculate the scaling factor depending on the filter subtype (Rough or Smooth).

2. Which calculations are involved in the precomputation?

   The precomputation involves the calculation of a single table:

   • table_db: This table contains values for converting decibel values to linear gain values. The precomputation involves calculating the linear gain for a given dB value using the formula: linear_gain = 10^(0.05 * (dB - 384)).

3. How much performance are we saving?

   By precomputing these decibel-to-linear gain values and storing them in a table, we save performance by avoiding the need to recalculate these values in real-time during the synthesis process. This can lead to noticeable performance improvements, especially when processing audio signals that require frequent conversions between decibel and linear scales.

4. How can we improve this table?

   Some possible improvements to the GainTables include:

   • Interpolation: The current implementation uses linear interpolation to access the table values. Other interpolation methods, such as cubic or spline interpolation, could provide more accurate results at the cost of additional complexity.

   • Adaptive table size: The current implementation uses a fixed table size of 512. Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.

   • Additional gain-related functions: Expanding the GainTables struct to include other gain-related functions, such as linear-to-decibel conversions or different types of gain scaling, could make the table more versatile and useful for a wider range of audio processing tasks.

4> /file surge-rs/surge-tables/src/sinc.rs

SincTables

1. What is this table used for?

   The SincTables struct contains three tables: table, table_1x, and table_i16. These tables store precomputed windowed sinc function values, which are commonly used in digital signal processing, particularly in interpolation and resampling tasks. By precomputing these values, the SincTables can be used to perform efficient interpolation in real-time audio processing.

2. Which calculations are involved in the precomputation?

   The precomputation involves the calculation of three tables:

   • table: This table stores windowed sinc function values for a specific cutoff frequency cutoff.

   • table_1x: This table stores windowed sinc function values for a different cutoff frequency cutoff1x.

   • table_i16: This table stores windowed sinc function values for another cutoff frequency cutoff_i16, but in 16-bit integer format.

   The precomputation calculates the windowed sinc function values using the following steps:

   1. Calculate the time t for each table entry using the get_table_t function.

   2. Calculate the windowed sinc function value using the windowed_sinc function, which involves the product of a symmetric Blackman window and the sinc function with the given cutoff frequency.

   3. Store the calculated values in the respective tables.

3. How much performance are we saving?

   By precomputing the windowed sinc function values and storing them in tables, the performance of real-time audio processing tasks, such as interpolation and resampling, can be significantly improved. This is because the computationally expensive sinc and Blackman window calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.

4. How can we improve this table?

   Some possible improvements to the SincTables include:

   • Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.

   • Additional interpolation methods: Expanding the SincTables struct to include other interpolation methods could make the table more versatile and useful for a wider range of audio processing tasks.

   • Optimizing sinc and window functions: The current implementation calculates the windowed sinc values using standard Blackman window and sinc functions. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.

5> /file surge-rs/surge-tables/src/sine.rs

SineTables

1. What is this table used for?

   The SineTables struct contains two tables: table_sin and table_sin_offset. These tables store precomputed sine function values and their corresponding offsets. By precomputing these values, the SineTables can be used to perform efficient trigonometric calculations, such as oscillations and frequency modulation, in real-time audio processing.

2. Which calculations are involved in the precomputation?

   The precomputation involves the calculation of two tables:

   • table_sin: This table stores sine function values for angles between 0 and 2π, uniformly spaced with a step size of 2π / SIN_TABLE_SIZE_D.

   • table_sin_offset: This table stores the difference between consecutive sine function values in table_sin.

   The precomputation calculates the sine function values and their offsets using the following steps:

   1. Calculate the angle t for each table entry as 2π * (i / SIN_TABLE_SIZE_D), where i is the index of the entry.

   2. Calculate the sine function value sin(t) and store it in table_sin.

   3. Calculate the sine function value `sin(t

      • 2π / SIN_TABLE_SIZE_D)and store the difference between this value andsin(t)intable_sin_offset`.

3. How much performance are we saving?

   By precomputing the sine function values and their offsets and storing them in tables, the performance of real-time audio processing tasks that involve trigonometric calculations can be significantly improved. This is because the computationally expensive sine calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.

4. How can we improve this table?

   Some possible improvements to the SineTables include:

   • Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.

   • Additional trigonometric functions: Expanding the SineTables struct to include other trigonometric functions, such as cosine or tangent, could make the table more versatile and useful for a wider range of audio processing tasks.

   • Optimizing sine function calculations: The current implementation calculates the sine values using the standard sine function. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.

6> /file surge-rs/surge-tables/src/waveshape.rs

WaveshapeTables

1. What is this table used for?

   The WaveshapeTables struct contains a table of precomputed waveshaping function values that can be used to quickly modify the shape of audio waveforms in real-time audio processing. By using these precomputed values, the performance of audio processing tasks involving waveshaping can be significantly improved.

2. Which waveshaping functions are included?

   The WaveshapeTables struct includes precomputed values for five different waveshaping functions:

   1. wst_tanh: Hyperbolic tangent function.

   2. wst_hard: A hard clipping function, based on the fifth power of the absolute value of x, followed by a hyperbolic tangent and a power of 0.2.

   3. wst_asym: An asymmetric waveshaping function using the "shafted_tanh" function, which is shifted by 0.5.

   4. wst_sine: Sine function.

   5. wst_digi: A digital-style waveshaping function using the hyperbolic tangent function with a different scaling factor.

3. How much performance are we saving?

   By precomputing the waveshaping function values and storing them in tables, the performance of real-time audio processing tasks involving waveshaping can be significantly improved. This is because the computationally expensive waveshaping function calculations are avoided during real-time processing, and the precomputed values can be quickly accessed from the tables.

4. How can we improve this table?

   Some possible improvements to the WaveshapeTables include:

   • Adaptive table sizes: Allowing for user-defined table sizes could enable users to balance memory usage and lookup accuracy based on their specific needs.

   • Additional waveshaping functions: Expanding the WaveshapeTables struct to include more waveshaping functions could make the table more versatile and useful for a wider range of audio processing tasks.

   • Optimizing waveshaping function calculations: The current implementation calculates the waveshaping function values using standard functions. Optimized versions of these functions, such as those found in specialized libraries, could potentially improve the accuracy or performance of the tables.

   • Interpolation: Implementing interpolation between table entries could improve the accuracy of the waveshaping functions when using the lookup methods.