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//! A library implementing a spaced repetition algorithm.
#![warn(missing_docs)]
use chrono::{DateTime, Duration, TimeZone, Utc};
use serde::{Deserialize, Serialize};
use std::cmp::Ordering;
#[cfg(test)]
mod tests;
/// The repetition state of a learnable item.
#[derive(Clone, Debug, Serialize, Deserialize)]
pub enum RepetitionState {
/// The item has made it through the initial learning phase and will now be repeated at larger intervals.
Reviewing {
/// The ease factor of the word.
/// It influences how fast the intervals between repetitions get larger.
ease_factor: f64,
/// The time of the last repetition.
last_repetition: DateTime<Utc>,
/// The time of the next repetition.
next_repetition: DateTime<Utc>,
},
/// The item is in the initial learning phase where it is repeated in shorter intervals.
Learning {
/// The count of easy repetition results.
/// [RepetitionResult::Easy] increments this by one, and [RepetitionResult::Hard] and [RepetitionResult::Again] decrement this by one.
easy_count: i16,
/// The current stage of the item within the learning phase.
stage: u16,
/// The time of the next repetition.
next_repetition: DateTime<Utc>,
},
}
impl RepetitionState {
/// Construct a new repetition state in learning stage 0, with its first repetition being at the given `datetime`.
pub fn new<TZ: TimeZone>(datetime: DateTime<TZ>) -> Self {
Self::Learning {
easy_count: 0,
stage: 0,
next_repetition: datetime.with_timezone(&Utc),
}
}
/// Update the repetition state after an item was repeated by the user.
/// The time of the repetition was `datetime`, and the result of the repetition was `result`.
/// The configuration of the algorithm is given as `configuration`.
pub fn update<TZ: TimeZone>(
self,
datetime: DateTime<TZ>,
result: RepetitionResult,
configuration: &Configuration,
) -> Result<Self, Error> {
let datetime = datetime.with_timezone(&Utc);
match self {
RepetitionState::Reviewing {
ease_factor,
last_repetition,
next_repetition,
} => {
let ease_factor = match result {
RepetitionResult::Again => {
ease_factor * configuration.reviewing_phase_ease_factor_again_update
}
RepetitionResult::Hard => {
ease_factor * configuration.reviewing_phase_ease_factor_hard_update
}
RepetitionResult::Normal => ease_factor,
RepetitionResult::Easy => {
ease_factor * configuration.reviewing_phase_ease_factor_easy_update
}
}
.min(configuration.reviewing_phase_max_ease_factor)
.max(configuration.reviewing_phase_min_ease_factor);
let next_repetition = next_repetition.max(datetime);
let last_interval = next_repetition - last_repetition;
let last_interval_seconds = last_interval.num_seconds() as f64;
let next_interval_seconds = match result {
RepetitionResult::Again => {
configuration.reviewing_phase_initial_delay_seconds as f64 * ease_factor
/ configuration.reviewing_phase_initial_ease_factor
}
RepetitionResult::Hard => {
if let Some(fixed_factor) =
configuration.reviewing_phase_hard_fixed_interval_factor
{
last_interval_seconds * fixed_factor
} else {
last_interval_seconds * ease_factor
}
}
RepetitionResult::Normal => last_interval_seconds * ease_factor,
RepetitionResult::Easy => {
last_interval_seconds
* ease_factor
* configuration.reviewing_phase_easy_one_time_interval_bonus
}
};
// Add one percent because I am not totally sure how accurately i64 -> f64 conversion works.
if next_interval_seconds * 1.01 >= i64::MAX as f64 {
return Err(Error::Overflow);
}
let next_interval = Duration::seconds(next_interval_seconds as i64);
Ok(Self::Reviewing {
ease_factor,
last_repetition: datetime,
next_repetition: datetime + next_interval,
})
}
RepetitionState::Learning {
easy_count, stage, ..
} => {
match result {
// If the user chooses again during learning, the word starts from the beginning.
RepetitionResult::Again => {
if let Some(delay_seconds) = configuration
.learning_phase_stage_delay_seconds
.first()
.cloned()
{
Ok(Self::Learning {
stage: 0,
easy_count: easy_count.checked_sub(1).ok_or(Error::Overflow)?,
next_repetition: datetime + Duration::seconds(delay_seconds.into()),
})
} else {
Err(Error::ConfigurationMissesLearningStage)
}
}
RepetitionResult::Hard => {
if let Some(delay_seconds) = configuration
.learning_phase_stage_delay_seconds
.get(usize::from(stage.max(1) - 1)) // Cannot overflow because it is at least one.
.cloned()
{
Ok(Self::Learning {
stage,
easy_count: easy_count.checked_sub(1).ok_or(Error::Overflow)?,
next_repetition: datetime
.checked_add_signed(Duration::seconds(delay_seconds.into()))
.ok_or(Error::Overflow)?,
})
} else {
Err(Error::ConfigurationMissesLearningStage)
}
}
RepetitionResult::Normal => {
if let Some(delay_seconds) = configuration
.learning_phase_stage_delay_seconds
.get(usize::from(stage))
.cloned()
{
Ok(Self::Learning {
stage: stage.checked_add(1).ok_or(Error::Overflow)?,
easy_count,
next_repetition: datetime
.checked_add_signed(Duration::seconds(delay_seconds.into()))
.ok_or(Error::Overflow)?,
})
} else {
let (delay_seconds, ease_factor) = configuration
.compute_reviewing_phase_initial_delay_seconds_and_ease_factor(
easy_count,
)?;
Ok(Self::Reviewing {
ease_factor,
last_repetition: datetime,
next_repetition: datetime
.checked_add_signed(Duration::seconds(delay_seconds.into()))
.ok_or(Error::Overflow)?,
})
}
}
RepetitionResult::Easy => {
if usize::from(stage)
>= configuration.learning_phase_stage_delay_seconds.len()
|| (configuration.learning_phase_easy_may_skip_last_stage
&& usize::from(
stage
.checked_add(configuration.learning_phase_easy_skip_stages)
.ok_or(Error::Overflow)?,
) >= configuration.learning_phase_stage_delay_seconds.len())
{
let (delay_seconds, ease_factor) = configuration
.compute_reviewing_phase_initial_delay_seconds_and_ease_factor(
easy_count,
)?;
Ok(Self::Reviewing {
ease_factor,
last_repetition: datetime,
next_repetition: datetime
.checked_add_signed(Duration::seconds(delay_seconds.into()))
.ok_or(Error::Overflow)?,
})
} else {
let stage = (stage + configuration.learning_phase_easy_skip_stages)
.min(
u16::try_from(
configuration.learning_phase_stage_delay_seconds.len(),
)
.map_err(|_| Error::Overflow)?
.checked_sub(1)
.ok_or(Error::ConfigurationMissesLearningStage)?,
);
let delay_seconds = configuration
.learning_phase_stage_delay_seconds
.get(usize::from(stage))
.cloned()
.unwrap();
Ok(Self::Learning {
stage: stage.checked_add(1).ok_or(Error::Overflow)?,
easy_count: easy_count.checked_add(1).ok_or(Error::Overflow)?,
next_repetition: datetime
.checked_add_signed(Duration::seconds(delay_seconds.into()))
.ok_or(Error::Overflow)?,
})
}
}
}
}
}
}
}
/// The configuration of the algorithm.
#[derive(Clone, Debug, Serialize, Deserialize)]
pub struct Configuration {
/// The delays between repetitions in the initial learning phase.
/// These are given as seconds.
///
/// **Warning:** This vector must contain at least one value.
///
/// **Example:**
/// Setting learning_stages to `[10, 60]` causes the item to be repeated 10 seconds after the initial repetition, and another 60 seconds after that.
pub learning_phase_stage_delay_seconds: Vec<u16>,
/// The amount of stages skipped if the user chooses easy in the learning phase.
/// A value of zero resembles the behaviour of a normal result.
pub learning_phase_easy_skip_stages: u16,
/// If true, if the user chooses easy in the learning phase and this would skip past the last stage, the item directly enters the reviewing phase.
/// If false, then the item will always enter the last stage, and only after successfully repeating again the item may enter the reviewing phase.
pub learning_phase_easy_may_skip_last_stage: bool,
/// The initial delay in the reviewing phase in seconds.
pub reviewing_phase_initial_delay_seconds: u32,
/// The initial ease factor used in the reviewing phase.
pub reviewing_phase_initial_ease_factor: f64,
/// The minimum ease factor used in the reviewing phase.
pub reviewing_phase_min_ease_factor: f64,
/// The maximum ease factor used in the reviewing phase.
pub reviewing_phase_max_ease_factor: f64,
/// The maximum number of easy results from the learning phase to be applied to the initial ease factor when entering the reviewing phase.
pub reviewing_phase_initial_ease_max_easy_count: u16,
/// The maximum number of hard results from the learning phase to be applied to the initial ease factor when entering the reviewing phase.
pub reviewing_phase_initial_ease_max_hard_count: u16,
/// The factor applied to the ease factor on an easy result.
pub reviewing_phase_ease_factor_easy_update: f64,
/// The factor applied to the ease factor on a hard result.
pub reviewing_phase_ease_factor_hard_update: f64,
/// The factor applied to the ease factor on an again result.
pub reviewing_phase_ease_factor_again_update: f64,
/// A factor applied to the length of the learning interval on an easy answer, additionally to the ease factor.
/// This factor is applied only one an easy answer, and does not affect the update of the ease factor.
pub reviewing_phase_easy_one_time_interval_bonus: f64,
/// If set, the learning interval is updated by this exact factor on an hard answer, without accounting for the ease factor.
/// The ease factor is still updated in the background.
pub reviewing_phase_hard_fixed_interval_factor: Option<f64>,
}
impl Configuration {
fn compute_reviewing_phase_initial_ease_factor(&self, easy_count: i16) -> Result<f64, Error> {
if self.reviewing_phase_initial_ease_factor < 1.0 {
return Err(Error::ReviewingPhaseInitialEaseFactorLowerThanOne);
}
match easy_count.cmp(&0) {
Ordering::Equal => Ok(self.reviewing_phase_initial_ease_factor),
Ordering::Greater => {
let easy_count = easy_count.min(
self.reviewing_phase_initial_ease_max_easy_count
.try_into()
.map_err(|_| Error::Overflow)?,
);
if self.reviewing_phase_ease_factor_easy_update < 1.0 {
return Err(Error::ReviewingPhaseEaseFactorEasyUpdateLowerThanOne);
}
Ok((self.reviewing_phase_initial_ease_factor
* self
.reviewing_phase_ease_factor_easy_update
.powi(easy_count.into()))
.min(self.reviewing_phase_max_ease_factor))
}
Ordering::Less => {
let hard_count = easy_count.checked_mul(-1).ok_or(Error::Overflow)?.min(
self.reviewing_phase_initial_ease_max_hard_count
.try_into()
.map_err(|_| Error::Overflow)?,
);
if self.reviewing_phase_ease_factor_hard_update > 1.0 {
return Err(Error::ReviewingPhaseEaseFactorHardUpdateGreaterThanOne);
}
Ok((self.reviewing_phase_initial_ease_factor
* self
.reviewing_phase_ease_factor_hard_update
.powi(hard_count.into()))
.max(self.reviewing_phase_min_ease_factor))
}
}
}
fn compute_reviewing_phase_initial_delay_seconds_and_ease_factor(
&self,
easy_count: i16,
) -> Result<(u32, f64), Error> {
let initial_ease_factor = self.compute_reviewing_phase_initial_ease_factor(easy_count)?;
let ease_ratio = initial_ease_factor / self.reviewing_phase_initial_ease_factor;
let initial_delay_seconds =
(f64::from(self.reviewing_phase_initial_delay_seconds) * ease_ratio).round();
// Subtract one because I am not totally sure how accurately u32 -> f64 conversion works.
if initial_delay_seconds >= (u32::MAX - 1) as f64 {
Err(Error::Overflow)
} else {
Ok((initial_delay_seconds as u32, initial_ease_factor))
}
}
}
/// The result of a repetition as specified by the user.
#[derive(Clone, Copy, Debug, Serialize, Deserialize, Eq, PartialEq)]
pub enum RepetitionResult {
/// The user was not able to repeat the item.
Again,
/// The user was able to repeat the item, but found it especially hard.
Hard,
/// The user was able to repeat the item, with average difficulty.
Normal,
/// The user was able to repeat the item, and found it especially easy.
Easy,
}
/// The error type used by this crate.
#[derive(Debug, Clone, Eq, PartialEq)]
pub enum Error {
/// The configuration has no or not enough stages in the learning phase.
/// The stages in the learning phase are defined by [Configuration::learning_phase_stage_delay_seconds].
ConfigurationMissesLearningStage,
/// The value of [Configuration::reviewing_phase_ease_factor_easy_update] is lower than one.
ReviewingPhaseEaseFactorEasyUpdateLowerThanOne,
/// The value of [Configuration::reviewing_phase_ease_factor_hard_update] is greater than one.
ReviewingPhaseEaseFactorHardUpdateGreaterThanOne,
/// The value of [Configuration::reviewing_phase_initial_ease_factor] is lower than one.
ReviewingPhaseInitialEaseFactorLowerThanOne,
/// An overflow occurred.
Overflow,
}