Struct Sum 

pub struct Sum;

sum as a Reduction.

Trait Implementations

impl Clone for Sum

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for Sum

impl Debug for Sum

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F: Native> Inverse<Complex<F>> for Sum

fn inverse(acc: Complex<F>, x: Complex<F>) -> (Complex<F>, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: Complex<F>, b: Complex<F>) -> (Complex<F>, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[Complex<F>]) -> (Complex<F>, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl<F: Native> Inverse<F> for Sum

fn inverse(acc: F, x: F) -> (F, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: F, b: F) -> (F, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[F]) -> (F, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl Inverse<i16> for Sum

fn inverse(acc: i64, x: i16) -> (i64, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: i64, b: i64) -> (i64, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[i16]) -> (i64, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl Inverse<i32> for Sum

fn inverse(acc: i64, x: i32) -> (i64, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: i64, b: i64) -> (i64, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[i32]) -> (i64, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl Inverse<i64> for Sum

fn inverse(acc: i64, x: i64) -> (i64, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: i64, b: i64) -> (i64, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[i64]) -> (i64, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl Inverse<u8> for Sum

fn inverse(acc: i64, x: u8) -> (i64, bool)

acc with the item x taken away, and whether it fits.

fn undo(a: i64, b: i64) -> (i64, bool)

The fold a with the fold b of the next run taken away, and whether it fits.

fn alternating(x: &[u8]) -> (i64, bool)

The right fold of the slice x by the inverse, and whether it fits: for sums through a sum at each parity (alternated), and for products through the pairs’ quotients (pairwise).

fn fits(_: Self::Total) -> bool

Whether a running total fits, as every one does apart from a float quotient outside the normal range.

impl<F: Native> Reduction<Complex<F>> for Sum

Each sum of complex numbers adds their real parts and their imaginary parts, in any order.

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = Complex<F>

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> Complex<F>

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: Complex<F>, x: Complex<F>) -> Complex<F>

acc combined with one more item.

fn merge(a: Complex<F>, b: Complex<F>) -> (Complex<F>, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn identity() -> Complex<F>

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn slice(x: &[Complex<F>]) -> (Complex<F>, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan( x: &[Complex<F>], start: Option<Complex<F>>, out: &mut Vec<Complex<F>>, ) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn checked(acc: Self::Total, x: T) -> (Self::Total, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

impl<F: Native> Reduction<F> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

const SPLIT: usize = 64

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

type Total = F

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> F

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(a: F, b: F) -> F

acc combined with one more item.

fn merge(a: F, b: F) -> (F, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn identity() -> F

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn rows(data: &[F], columns: usize, out: &mut [F]) -> bool

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn slice(x: &[F]) -> (F, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[F], start: Option<F>, out: &mut Vec<F>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn checked(acc: Self::Total, x: T) -> (Self::Total, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

impl Reduction<f16> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = f32

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> f32

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: f32, x: f16) -> f32

acc combined with one more item.

fn merge(a: f32, b: f32) -> (f32, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn identity() -> f32

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn slice(x: &[f16]) -> (f32, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[f16], start: Option<f32>, out: &mut Vec<f32>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn checked(acc: Self::Total, x: T) -> (Self::Total, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

impl Reduction<i16> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = i64

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> i64

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: i64, x: i16) -> i64

acc combined with one more item.

fn checked(acc: i64, x: i16) -> (i64, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn merge(a: i64, b: i64) -> (i64, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn slice(x: &[i16]) -> (i64, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[i16], start: Option<i64>, out: &mut Vec<i64>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn identity() -> Self::Total

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

impl Reduction<i32> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = i64

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> i64

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: i64, x: i32) -> i64

acc combined with one more item.

fn checked(acc: i64, x: i32) -> (i64, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn merge(a: i64, b: i64) -> (i64, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn slice(x: &[i32]) -> (i64, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[i32], start: Option<i64>, out: &mut Vec<i64>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn identity() -> Self::Total

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

impl Reduction<i64> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = i64

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> i64

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: i64, x: i64) -> i64

acc combined with one more item.

fn checked(acc: i64, x: i64) -> (i64, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn merge(a: i64, b: i64) -> (i64, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn slice(x: &[i64]) -> (i64, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[i64], start: Option<i64>, out: &mut Vec<i64>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn identity() -> Self::Total

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.

impl Reduction<u8> for Sum

const COMMUTATIVE: bool = true

Whether disjoint subsequences may be merged in any order.

type Total = i64

The type of a fold: the item type, i64 for a sum or product of integers narrower than 64 bits, f32 for a sum or product of f16s, i16 for an XNOR of bytes, the C of SumAs, f64 for Squares, a Scaled product for ScaledProduct, or a total with the parity of its count for Alternated.

fn unit() -> i64

The fold of no items: 0, 1, -∞ or ∞, the integer type’s least or greatest value, all ones, or false or true.

fn step(acc: i64, x: u8) -> i64

acc combined with one more item.

fn checked(acc: i64, x: u8) -> (i64, bool)

step, and whether its result fits. An integer sum or product wraps where it doesn’t.

fn merge(a: i64, b: i64) -> (i64, bool)

The folds of two neighbouring runs of items combined into the fold of both, and whether it fits.

fn slice(x: &[u8]) -> (i64, bool)

The fold of x, which is unit() where x is empty, and whether it fits. The default takes each item in turn by checked.

fn scan(x: &[u8], start: Option<i64>, out: &mut Vec<i64>) -> bool

Appends the running folds of x to out, the first combining start where it is given, and gives whether every one fits. The default takes each item in turn by checked (checked_steps).

fn identity() -> Self::Total

The exact identity of step, which leaves every total unchanged. For float sums it’s -0.0, because adding unit(), 0.0, turns a total of -0.0 into 0.0. For every other reduction it’s unit().

fn one(x: T) -> (Self::Total, bool)

The fold of the one item x, checked(identity(), x), and whether it fits.

fn chain(a: Self::Total, b: Self::Total) -> (Self::Total, bool)

merge, for a chain of folds whose every step waits for the one before, as van Herk-Gil-Werman’s suffixes and prefixes do. As in merge, a folds the earlier items. Float maximums and minimums override it with Folds::step_max and step_min, which use AArch64’s one-instruction fmaxnm and fminnm. LLVM can’t vectorize those, so they stay out of merge.

fn rows(data: &[T], columns: usize, out: &mut [Self::Total]) -> bool

where Self: Sized, T: Copy,

Folds each row of data, a matrix with columns items in each row, into the matching item of out, and gives whether every fold fits. The default is fold_rows, which folds each row of 16 items or more by slice. Float sums and products, integer maximums and minimums, and bitwise folds fold rows of 16 to 63 items by checked instead, eight rows side by side (rows_side_by_side). Each of their steps is one instruction, so keeping several rows’ steps in flight costs less than a call of slice for each row. Other reductions keep fold_rows, where slice vectorizes within the row: an integer sum’s step checks for overflow, and a float maximum’s or minimum’s slice runs Folds’ vector kernels. Nobody has timed float maximums side by side since their step became one select on x86.

fn short_lanes( _data: &[T], _len: usize, _start: Option<Self::Total>, _out: &mut Vec<Self::Total>, ) -> Option<bool>

where Self: Sized,

Appends the running folds of data’s lanes of len consecutive items to out, each lane from start, through a route that runs many short lanes at once, and gives whether every fold fits. A reduction without such a route gives None and appends nothing, as the default does. scan_along then runs the lanes itself. The Boolean reductions run lanes of 1 to 64 items through Logical, 64 items to a word.

const SPLIT: usize = 8

The most classes for which crate::search::ClassNumbers folds each class into four totals by position. Each step of a class’s total waits on the last through memory, so a reduction whose step takes longer gains from the split over more classes.