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macro_rules! impl_first_diff {
($name:ident, $ty:ty, $zero:expr) => {
/// First difference — `x[n] - x[n-1]`.
///
/// Returns the change between consecutive samples.
/// `None` on the first sample (no previous value to diff against).
///
/// # Use Cases
/// - Computing returns from prices
/// - Velocity from position
/// - Rate of change of any signal
#[derive(Debug, Clone)]
pub struct $name {
prev: $ty,
initialized: bool,
}
impl $name {
/// Creates a new first-difference filter.
#[inline]
#[must_use]
pub const fn new() -> Self {
Self {
prev: $zero,
initialized: false,
}
}
/// Feeds a sample. Returns `Some(x[n] - x[n-1])` or `None` on first sample.
#[inline]
#[must_use]
pub fn update(&mut self, sample: $ty) -> Option<$ty> {
if !self.initialized {
self.prev = sample;
self.initialized = true;
return Option::None;
}
let diff = sample - self.prev;
self.prev = sample;
Option::Some(diff)
}
/// Resets to uninitialized state.
#[inline]
pub fn reset(&mut self) {
self.prev = $zero;
self.initialized = false;
}
}
impl Default for $name {
#[inline]
fn default() -> Self {
Self::new()
}
}
};
}
macro_rules! impl_second_diff {
($name:ident, $ty:ty, $zero:expr) => {
/// Second difference — `x[n] - 2*x[n-1] + x[n-2]`.
///
/// Returns the acceleration (change in change) of a signal.
/// `None` until the third sample.
///
/// # Use Cases
/// - Acceleration from position
/// - Curvature detection
/// - "Is the rate of change itself changing?"
#[derive(Debug, Clone)]
pub struct $name {
prev2: $ty,
prev1: $ty,
count: u64,
}
impl $name {
/// Creates a new second-difference filter.
#[inline]
#[must_use]
pub const fn new() -> Self {
Self {
prev2: $zero,
prev1: $zero,
count: 0,
}
}
/// Feeds a sample. Returns `Some(x[n] - 2*x[n-1] + x[n-2])` or `None`
/// until 3 samples have been fed.
#[inline]
#[must_use]
pub fn update(&mut self, sample: $ty) -> Option<$ty> {
self.count += 1;
if self.count == 1 {
self.prev1 = sample;
return Option::None;
}
if self.count == 2 {
self.prev2 = self.prev1;
self.prev1 = sample;
return Option::None;
}
let two = (2 as $ty);
let diff2 = sample - two * self.prev1 + self.prev2;
self.prev2 = self.prev1;
self.prev1 = sample;
Option::Some(diff2)
}
/// Resets to uninitialized state.
#[inline]
pub fn reset(&mut self) {
self.prev2 = $zero;
self.prev1 = $zero;
self.count = 0;
}
}
impl Default for $name {
#[inline]
fn default() -> Self {
Self::new()
}
}
};
}
impl_first_diff!(FirstDiffF64, f64, 0.0);
impl_first_diff!(FirstDiffF32, f32, 0.0);
impl_first_diff!(FirstDiffI64, i64, 0);
impl_first_diff!(FirstDiffI32, i32, 0);
impl_first_diff!(FirstDiffI128, i128, 0);
impl_second_diff!(SecondDiffF64, f64, 0.0);
impl_second_diff!(SecondDiffF32, f32, 0.0);
impl_second_diff!(SecondDiffI64, i64, 0);
impl_second_diff!(SecondDiffI32, i32, 0);
impl_second_diff!(SecondDiffI128, i128, 0);
#[cfg(test)]
mod tests {
use super::*;
// First diff
#[test]
fn first_diff_none_on_first() {
let mut fd = FirstDiffF64::new();
assert!(fd.update(100.0).is_none());
}
#[test]
#[allow(clippy::float_cmp)]
fn first_diff_computes() {
let mut fd = FirstDiffF64::new();
let _ = fd.update(100.0);
assert_eq!(fd.update(110.0), Some(10.0));
assert_eq!(fd.update(105.0), Some(-5.0));
}
#[test]
fn first_diff_i64() {
let mut fd = FirstDiffI64::new();
let _ = fd.update(100);
assert_eq!(fd.update(130), Some(30));
}
#[test]
fn first_diff_reset() {
let mut fd = FirstDiffF64::new();
let _ = fd.update(100.0);
fd.reset();
assert!(fd.update(50.0).is_none()); // re-initialized
}
// Second diff
#[test]
fn second_diff_none_until_third() {
let mut sd = SecondDiffF64::new();
assert!(sd.update(1.0).is_none());
assert!(sd.update(2.0).is_none());
assert!(sd.update(3.0).is_some());
}
#[test]
#[allow(clippy::float_cmp)]
fn second_diff_linear_is_zero() {
let mut sd = SecondDiffF64::new();
let _ = sd.update(10.0);
let _ = sd.update(20.0);
// Linear: 10, 20, 30 → second diff = 30 - 2*20 + 10 = 0
assert_eq!(sd.update(30.0), Some(0.0));
}
#[test]
#[allow(clippy::float_cmp)]
fn second_diff_quadratic() {
let mut sd = SecondDiffF64::new();
// x^2: 1, 4, 9 → 9 - 2*4 + 1 = 2
let _ = sd.update(1.0);
let _ = sd.update(4.0);
assert_eq!(sd.update(9.0), Some(2.0));
}
#[test]
fn second_diff_i64() {
let mut sd = SecondDiffI64::new();
let _ = sd.update(10);
let _ = sd.update(20);
assert_eq!(sd.update(30), Some(0)); // linear
assert_eq!(sd.update(50), Some(10)); // acceleration
}
#[test]
fn second_diff_reset() {
let mut sd = SecondDiffF64::new();
let _ = sd.update(1.0);
let _ = sd.update(2.0);
sd.reset();
assert!(sd.update(5.0).is_none());
}
#[test]
fn first_diff_i128() {
let mut fd = FirstDiffI128::new();
let _ = fd.update(100);
assert_eq!(fd.update(130), Some(30));
}
#[test]
fn second_diff_i128() {
let mut sd = SecondDiffI128::new();
let _ = sd.update(10);
let _ = sd.update(20);
assert_eq!(sd.update(30), Some(0)); // linear
}
}