Struct Slope 

pub struct Slope<K, const SIDE: usize = 0>(pub K);

K’s partial derivative in its argument SIDE, as a function object at f32 and f64: of K’s argument and result where K takes one argument, and of its two arguments and its result where it takes two. Each item runs K’s recipe on floats ([Floats]), which see no constant. A slope that is NaN where no argument is, such as Pow’s in y at an infinite x and a negative y, is its value, as Subtract gives NaN for ∞ - ∞. A slope in an argument that has none, such as Polygamma’s in its order, is NaN.

Tuple Fields

0: K

Trait Implementations

impl<K: Clone, const SIDE: usize> Clone for Slope<K, SIDE>

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<K: Copy, const SIDE: usize> Copy for Slope<K, SIDE>

impl<K: Debug, const SIDE: usize> Debug for Slope<K, SIDE>

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

Formats the value using the given formatter.

impl<K: Formula<1>> Formula<2> for Slope<K>

const MAP_ONLY: bool = true

Whether kernels of this formula only map. Modified writes, folds, scans and walks of adjacent items build no code for it: each refuses it at compile time, as it refuses a formula of another arity. A derivative’s slope (derivative::Slope) only maps.

fn supports(&self, dtype: DType) -> bool

fn emit<F: Float, O: Ops<F> + ?Sized>( &self, o: &O, [x, r]: [O::V; 2], ) -> Option<O::V>

const BOOLEAN: bool = false

const FAILS_NAN: bool = false

Whether a NaN result from arguments that aren’t NaN is a Domain error, which the default emit_valid checks (nan_valid). A constant, so a checked loop over items reads it at compile time and never calls a method for it.

const HAS_EXACT: bool = false

Whether exact computes this formula on rationals.

const INTEGER_FORMULA: bool = false

Whether integer runs this formula’s emit on integers, so that range arithmetic over emit_valid bounds an integer kernel’s failures (may_raise). A row with a native_integer body supports integers and leaves this false.

fn result_dtype(&self, input: DType) -> DType

fn computing_dtype(&self, input: DType) -> Option<DType>

fn character_rule(&self) -> Option<Rule>

fn ordered_kinds(&self, [x, y]: [i32; 2]) -> Option<i32>

fn character_policy(&self, types: [DType; 2]) -> Result<Option<Policy>, Error>

fn exact(&self, _args: [&BigRational; N]) -> Result<Option<BigRational>, Error>

fn range(&self, _args: [Range; N]) -> Range

fn domain(&self, _dtype: DType, _args: [Range; N]) -> Option<[Range; N]>

A box at the computing dtype containing args on which graph-numeric results do not raise a data error.

fn identity(&self) -> [Option<f64>; N]

fn fold(&self) -> Option<Reduce>

fn inverse_fold(&self) -> Option<Reduce>

fn truth_table(&self) -> Option<u8>

The function’s results on Booleans, as bits: bit 2x+y for two arguments, bit x for one. A Boolean kernel computes by it (operation::map_truth).

fn truth(&self) -> Option<Reduce>

fn same(&self, _arg: Range) -> Option<Range>

Refines the real result interval when both operands denote the same value.

fn reads(&self) -> Reads

fn emit_test<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], ) -> Option<O::B>

fn emit_against<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _c: F, _v: O::V, _left: bool, ) -> Option<O::B>

This comparison of v with the one number c through o, where that has a cheaper recipe than comparing item by item, as a held constant has. left says whether v is the left argument. None for other formulas.

fn bands(&self) -> Option<(Tolerance, Band, Band)>

This comparison’s tolerance, and the bands that an item on the left and on the right of one number must lie in (tolerant::Banding), through which it compares many items with one number (tolerant::against). None for other formulas.

fn emit_repair<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], ) -> Option<O::B>

fn repair_routine(&self) -> Option<Repair>

fn emit_valid<F: Float, O: Ops<F> + ?Sized>( &self, _variant: Variant, o: &O, x: [O::V; N], result: O::V, ) -> Option<(Kind, O::B)>

fn real<F: Native>( &self, ops: &NativeOps<{ crate::FUSED }>, x: [F; N], ) -> Option<F>

fn integer<I: Overflowing>(&self, _ops: &IntegerOps<I>, _x: [I; N]) -> Option<I>

fn complex<F: Native>( &self, _ops: &NativeOps<{ crate::FUSED }>, _x: [Complex<F>; N], ) -> Option<Complex<F>>

const REAL_COMPLEX: bool = false

Whether real_complex gives this formula’s complex results from real arguments.

fn real_complex<F: Native>( &self, _ops: &NativeOps<{ crate::FUSED }>, _x: [F; N], ) -> Option<Complex<F>>

The complex result from real arguments, where that costs less than from the arguments as complex numbers. None sends the item to complex.

fn native_slices(&self) -> Option<NativeSlices<Self, N>>

fn emit_partials<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], _result: O::V, _needed: [bool; N], ) -> [Option<O::V>; N]

impl<K: Formula<2>, const SIDE: usize> Formula<3> for Slope<K, SIDE>

const MAP_ONLY: bool = true

Whether kernels of this formula only map. Modified writes, folds, scans and walks of adjacent items build no code for it: each refuses it at compile time, as it refuses a formula of another arity. A derivative’s slope (derivative::Slope) only maps.

fn supports(&self, dtype: DType) -> bool

fn emit<F: Float, O: Ops<F> + ?Sized>( &self, o: &O, [x, y, r]: [O::V; 3], ) -> Option<O::V>

const BOOLEAN: bool = false

const FAILS_NAN: bool = false

Whether a NaN result from arguments that aren’t NaN is a Domain error, which the default emit_valid checks (nan_valid). A constant, so a checked loop over items reads it at compile time and never calls a method for it.

const HAS_EXACT: bool = false

Whether exact computes this formula on rationals.

const INTEGER_FORMULA: bool = false

Whether integer runs this formula’s emit on integers, so that range arithmetic over emit_valid bounds an integer kernel’s failures (may_raise). A row with a native_integer body supports integers and leaves this false.

fn result_dtype(&self, input: DType) -> DType

fn computing_dtype(&self, input: DType) -> Option<DType>

fn character_rule(&self) -> Option<Rule>

fn ordered_kinds(&self, [x, y]: [i32; 2]) -> Option<i32>

fn character_policy(&self, types: [DType; 2]) -> Result<Option<Policy>, Error>

fn exact(&self, _args: [&BigRational; N]) -> Result<Option<BigRational>, Error>

fn range(&self, _args: [Range; N]) -> Range

fn domain(&self, _dtype: DType, _args: [Range; N]) -> Option<[Range; N]>

A box at the computing dtype containing args on which graph-numeric results do not raise a data error.

fn identity(&self) -> [Option<f64>; N]

fn fold(&self) -> Option<Reduce>

fn inverse_fold(&self) -> Option<Reduce>

fn truth_table(&self) -> Option<u8>

The function’s results on Booleans, as bits: bit 2x+y for two arguments, bit x for one. A Boolean kernel computes by it (operation::map_truth).

fn truth(&self) -> Option<Reduce>

fn same(&self, _arg: Range) -> Option<Range>

Refines the real result interval when both operands denote the same value.

fn reads(&self) -> Reads

fn emit_test<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], ) -> Option<O::B>

fn emit_against<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _c: F, _v: O::V, _left: bool, ) -> Option<O::B>

This comparison of v with the one number c through o, where that has a cheaper recipe than comparing item by item, as a held constant has. left says whether v is the left argument. None for other formulas.

fn bands(&self) -> Option<(Tolerance, Band, Band)>

This comparison’s tolerance, and the bands that an item on the left and on the right of one number must lie in (tolerant::Banding), through which it compares many items with one number (tolerant::against). None for other formulas.

fn emit_repair<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], ) -> Option<O::B>

fn repair_routine(&self) -> Option<Repair>

fn emit_valid<F: Float, O: Ops<F> + ?Sized>( &self, _variant: Variant, o: &O, x: [O::V; N], result: O::V, ) -> Option<(Kind, O::B)>

fn real<F: Native>( &self, ops: &NativeOps<{ crate::FUSED }>, x: [F; N], ) -> Option<F>

fn integer<I: Overflowing>(&self, _ops: &IntegerOps<I>, _x: [I; N]) -> Option<I>

fn complex<F: Native>( &self, _ops: &NativeOps<{ crate::FUSED }>, _x: [Complex<F>; N], ) -> Option<Complex<F>>

const REAL_COMPLEX: bool = false

Whether real_complex gives this formula’s complex results from real arguments.

fn real_complex<F: Native>( &self, _ops: &NativeOps<{ crate::FUSED }>, _x: [F; N], ) -> Option<Complex<F>>

The complex result from real arguments, where that costs less than from the arguments as complex numbers. None sends the item to complex.

fn native_slices(&self) -> Option<NativeSlices<Self, N>>

fn emit_partials<F: Float, O: Ops<F> + ?Sized>( &self, _o: &O, _x: [O::V; N], _result: O::V, _needed: [bool; N], ) -> [Option<O::V>; N]