/*
MIT License

Copyright (c) 2021 Philipp Schuster

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of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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*/
//! A simple and fast `no_std` library to get the frequency spectrum of a digital signal
//! (e.g. audio) using FFT. It follows the KISS principle and consists of simple building
//! blocks/optional features.
//!
//! In short, this is a convenient wrapper around an FFT implementation. You choose the
//! implementation at compile time via Cargo features. As of version 0.4.0 this uses
//! "microfft"-crate.

#![no_std]

// use alloc crate, because this is no_std
#[cfg_attr(test, macro_use)]
extern crate alloc;

use alloc::vec::Vec;

use crate::fft::{Complex32, Fft, FftImpl};
pub use crate::frequency::{Frequency, FrequencyValue};
pub use crate::limit::FrequencyLimit;
pub use crate::spectrum::{ComplexSpectrumScalingFunction, FrequencySpectrum};
use core::convert::identity;

mod fft;
mod frequency;
mod limit;
pub mod scaling;
mod spectrum;
#[cfg(test)]
mod tests;
pub mod windows;

/// Definition of a simple function that gets applied on each frequency magnitude
/// in the spectrum. This is easier to write, especially for Rust beginners.
/// Everything that can be achieved with this, can also be achieved with parameter
/// `total_scaling_fn`.
///
/// The scaling only affects the value/amplitude of the frequency
/// but not the frequency itself.
pub type SimpleSpectrumScalingFunction<'a> = &'a dyn Fn(f32) -> f32;

/// Takes an array of samples (length must be a power of 2),
/// e.g. 2048, applies an FFT (using the specified FFT implementation) on it
/// and returns all frequencies with their volume/magnitude.
///
/// By default, no normalization/scaling is done at all and the results,
/// i.e. the frequency magnitudes/amplitudes/values are the raw result from
/// the FFT algorithm, except that complex numbers are transformed
/// to their magnitude.
///
/// * `samples` raw audio, e.g. 16bit audio data but as f32.
///             You should apply an window function (like Hann) on the data first.
///             The final frequency resolution is `sample_rate / (N / 2)`
///             e.g. `44100/(16384/2) == 5.383Hz`, i.e. more samples =>
///             better accuracy/frequency resolution.
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
/// * `frequency_limit` Frequency limit. See [`FrequencyLimit´]
/// * `per_element_scaling_fn` See [`crate::SimpleSpectrumScalingFunction`] for details.
///                            This is easier to write, especially for Rust beginners. Everything
///                            that can be achieved with this, can also be achieved with
///                            parameter `total_scaling_fn`.
///                            See [`crate::scaling`] for example implementations.
/// * `total_scaling_fn` See [`crate::spectrum::SpectrumTotalScaleFunctionFactory`] for details.
///                      See [`crate::scaling`] for example implementations.
///
/// ## Returns value
/// New object of type [`FrequencySpectrum`].
///
/// ## Panics
/// * When `samples` contains NaN or infinite values (regarding f32/float).
/// * When `samples.len()` isn't a power of two and `samples.len() > 4096`
///   (restriction by `microfft`-crate)
pub fn samples_fft_to_spectrum(
    samples: &[f32],
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    per_element_scaling_fn: Option<SimpleSpectrumScalingFunction>,
    total_scaling_fn: Option<ComplexSpectrumScalingFunction>,
) -> FrequencySpectrum {
    // check input value doesn't contain any NaN
    assert!(
        !samples.iter().any(|x| x.is_nan()),
        "NaN values in samples not supported!"
    );
    assert!(
        !samples.iter().any(|x| x.is_infinite()),
        "Infinity values in samples not supported!"
    );

    // With FFT we transform an array of time-domain waveform samples
    // into an array of frequency-domain spectrum samples
    // https://www.youtube.com/watch?v=z7X6jgFnB6Y

    // FFT result has same length as input
    // (but when we interpret the result, we don't need all indices)

    // applies the f32 samples onto the FFT algorithm implementation
    // chosen at compile time (via Cargo feature).
    // If a complex FFT implementation was chosen, this will internally
    // transform all data to Complex numbers.
    let buffer = FftImpl::fft_apply(samples);

    // This function:
    // 1) calculates the corresponding frequency of each index in the FFT result
    // 2) filters out unwanted frequencies
    // 3) calculates the magnitude (absolute value) at each frequency index for each complex value
    // 4) optionally scales the magnitudes
    // 5) collects everything into the struct "FrequencySpectrum"
    fft_result_to_spectrum(
        samples.len(),
        &buffer,
        sampling_rate,
        frequency_limit,
        per_element_scaling_fn,
        total_scaling_fn,
    )
}

/// Transforms the FFT result into the spectrum by calculating the corresponding frequency of each
/// FFT result index and optionally calculating the magnitudes of the complex numbers if a complex
/// FFT implementation is chosen.
///
/// ## Parameters
/// * `samples_len` Length of samples. This is a dedicated field because it can't always be
///                 derived from `fft_result.len()`. There are for example differences for
///                  `fft_result.len()` in real and complex FFT.
/// * `fft_result` Result buffer from FFT. Has the same length as the samples array.
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
/// * `frequency_limit` Frequency limit. See [`FrequencyLimit´]
/// * `per_element_scaling_fn` Optional per element scaling function, e.g. `20 * log(x)`.
///                            To see where this equation comes from, check out
///                            this paper:
///                            https://www.sjsu.edu/people/burford.furman/docs/me120/FFT_tutorial_NI.pdf
/// * `total_scaling_fn` See [`crate::spectrum::SpectrumTotalScaleFunctionFactory`].
///
/// ## Return value
/// New object of type [`FrequencySpectrum`].
#[inline(always)]
fn fft_result_to_spectrum(
    samples_len: usize,
    fft_result: &[Complex32],
    sampling_rate: u32,
    frequency_limit: FrequencyLimit,
    per_element_scaling_fn: Option<&dyn Fn(f32) -> f32>,
    total_scaling_fn: Option<ComplexSpectrumScalingFunction>,
) -> FrequencySpectrum {
    let maybe_min = frequency_limit.maybe_min();
    let maybe_max = frequency_limit.maybe_max();

    let frequency_resolution = fft_calc_frequency_resolution(sampling_rate, samples_len as u32);

    // collect frequency => frequency value in Vector of Pairs/Tuples
    let frequency_vec = fft_result
        .into_iter()
        // See https://stackoverflow.com/a/4371627/2891595 for more information as well as
        // https://www.gaussianwaves.com/2015/11/interpreting-fft-results-complex-dft-frequency-bins-and-fftshift/
        //
        // The indices 0 to N/2 (inclusive) are usually the most relevant. Although, index
        // N/2-1 is declared as the last useful one on stackoverflow (because in typical applications
        // Nyquist-frequency + above are filtered out), we include everything here.
        // with 0..=(samples_len / 2) (inclusive) we get all frequencies from 0 to Nyquist theorem.
        //
        // Indices (samples_len / 2)..len() are mirrored/negative. You can also see this here:
        // https://www.gaussianwaves.com/gaussianwaves/wp-content/uploads/2015/11/realDFT_complexDFT.png
        .take(FftImpl::fft_relevant_res_samples_count(samples_len))
        // to (index, fft-result)-pairs
        .enumerate()
        // calc index => corresponding frequency
        .map(|(fft_index, fft_result)| {
            (
                // Calculate corresponding frequency of each index of FFT result.
                //
                // Explanation for the algorithm:
                // https://stackoverflow.com/questions/4364823/
                //
                // N complex samples          : [0], [1], [2], [3], ... , ..., [2047] => 2048 samples for example
                //   (Or N real samples packed
                //   into N/2 complex samples
                //   (real FFT algorithm))
                // Complex FFT Result         : [0], [1], [2], [3], ... , ..., [2047]
                // Relevant part of FFT Result: [0], [1], [2], [3], ... , [1024]      => indices 0 to N/2 (inclusive) are important
                //                               ^                         ^
                // Frequency                  : 0Hz, .................... Sampling Rate/2 => "Nyquist frequency"
                //                              0Hz is also called        (e.g. 22050Hz for 44100Hz sampling rate)
                //                              "DC Component"
                //
                // frequency step/resolution is for example: 1/2048 * 44100 = 21.53 Hz
                //                                             2048 samples, 44100 sample rate
                //
                // equal to: 1.0 / samples_len as f32 * sampling_rate as f32
                fft_index as f32 * frequency_resolution,
                // in this .map() step we do nothing with this yet
                fft_result,
            )
        })
        // #######################
        // ### BEGIN filtering: results in lower calculation and memory overhead!
        // check lower bound frequency (inclusive)
        .filter(|(fr, _fft_result)| {
            if let Some(min_fr) = maybe_min {
                // inclusive!
                *fr >= min_fr
            } else {
                true
            }
        })
        // check upper bound frequency (inclusive)
        .filter(|(fr, _fft_result)| {
            if let Some(max_fr) = maybe_max {
                // inclusive!
                *fr <= max_fr
            } else {
                true
            }
        })
        // ### END filtering
        // #######################
        // FFT result is always complex: calc magnitude
        //   sqrt(re*re + im*im) (re: real part, im: imaginary part)
        .map(|(fr, complex_res)| (fr, complex_to_magnitude(&complex_res)))
        // apply optionally scale function
        .map(|(fr, val)| (fr, per_element_scaling_fn.unwrap_or(&identity)(val)))
        // transform to my thin convenient orderable f32 wrappers
        .map(|(fr, val)| (Frequency::from(fr), FrequencyValue::from(val)))
        // collect all into an sorted vector (from lowest frequency to highest)
        .collect::<Vec<(Frequency, FrequencyValue)>>();

    // create spectrum object
    let spectrum = FrequencySpectrum::new(frequency_vec, frequency_resolution);

    // optionally scale
    if let Some(total_scaling_fn) = total_scaling_fn {
        spectrum.apply_complex_scaling_fn(total_scaling_fn)
    }

    spectrum
}

/// Calculate the frequency resolution of the FFT. It is determined by the sampling rate
/// in Hertz and N, the number of samples given into the FFT. With the frequency resolution,
/// we can determine the corresponding frequency of each index in the FFT result buffer.
///
/// For "real FFT" implementations
///
/// ## Parameters
/// * `samples_len` Number of samples put into the FFT
/// * `sampling_rate` sampling_rate, e.g. `44100 [Hz]`
///
/// ## Return value
/// Frequency resolution in Hertz.
///
/// ## More info
/// * https://www.researchgate.net/post/How-can-I-define-the-frequency-resolution-in-FFT-And-what-is-the-difference-on-interpreting-the-results-between-high-and-low-frequency-resolution
/// * https://stackoverflow.com/questions/4364823/
#[inline(always)]
fn fft_calc_frequency_resolution(sampling_rate: u32, samples_len: u32) -> f32 {
    sampling_rate as f32 / samples_len as f32
}

/// Maps a [`Complex32`] to it's magnitude as `f32`. This is done
/// by calculating `sqrt(re*re + im*im)`. This is required to convert
/// the complex FFT result back to real values.
///
/// ## Parameters
/// * `val` A single value from the FFT output buffer of type [`Complex32`].
fn complex_to_magnitude(val: &Complex32) -> f32 {
    // calculates sqrt(re*re + im*im), i.e. magnitude of complex number
    let sum = val.re * val.re + val.im * val.im;
    let sqrt = libm::sqrtf(sum);
    debug_assert!(sqrt != f32::NAN, "sqrt is NaN!");
    sqrt
}