Struct Standard 

pub struct Standard<T>(/* private fields */);

Typed standard arithmetic algebra (add = +, mul = *).

The type parameter T carries the scalar type, making the algebra Alg::Scalar-centric. This is the canonical core model — HasAlgebra provides UX sugar for automatic inference (e.g., f64 → Standard<f64>).

This is the default algebra for built-in numeric types (f32, f64, Complex32, Complex64).

Examples

use tenferro_algebra::{HasAlgebra, Standard};

// f64 maps to Standard<f64> algebra automatically
fn check_algebra<T: HasAlgebra<Algebra = Standard<T>>>() {}
check_algebra::<f64>();
check_algebra::<f32>();

Trait Implementations

impl<T> Algebra for Standard<T>

where T: Scalar,

type Scalar = T

The scalar element type for tensors under this algebra.

impl<T> Semiring for Standard<T>

where T: Scalar + Zero + One,

Standard arithmetic implements Semiring with + and *.

Examples

use tenferro_algebra::{Semiring, Standard};

let z = <Standard<f64> as Semiring>::zero();
let o = <Standard<f64> as Semiring>::one();
assert_eq!(z, 0.0);
assert_eq!(o, 1.0);

fn zero() -> T

Additive identity element.

fn one() -> T

Multiplicative identity element.

fn add(a: T, b: T) -> T

Semiring addition.

fn mul(a: T, b: T) -> T

Semiring multiplication.

impl<S> TensorAnalyticPrims<Standard<S>> for CpuBackend

where S: Scalar + 'static,

type Plan = CpuAnalyticPlan

type Context = CpuContext

fn plan( _ctx: &mut <CpuBackend as TensorAnalyticPrims<Standard<S>>>::Context, desc: &AnalyticPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorAnalyticPrims<Standard<S>>>::Plan, Error>

Plan an analytic-family operation for the given input/output shapes.

fn execute( _ctx: &mut <CpuBackend as TensorAnalyticPrims<Standard<S>>>::Context, plan: &<CpuBackend as TensorAnalyticPrims<Standard<S>>>::Plan, alpha: S, inputs: &[&Tensor<S>], beta: S, output: &mut Tensor<S>, ) -> Result<(), Error>

Execute a previously planned analytic-family operation.

fn has_analytic_support(desc: AnalyticPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.

impl<S> TensorIndexingPrims<Standard<S>> for CpuBackend

where S: Scalar + 'static,

type Plan = CpuIndexingPlan

Backend-specific execution plan.

type Context = CpuContext

Backend execution context.

fn plan( _ctx: &mut <CpuBackend as TensorIndexingPrims<Standard<S>>>::Context, desc: &IndexingPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorIndexingPrims<Standard<S>>>::Plan, Error>

Plan an indexing operation for the given input/index/output shapes.

fn execute( _ctx: &mut <CpuBackend as TensorIndexingPrims<Standard<S>>>::Context, plan: &<CpuBackend as TensorIndexingPrims<Standard<S>>>::Plan, inputs: &[&Tensor<S>], indices: &Tensor<i64>, output: &mut Tensor<S>, ) -> Result<(), Error>

Execute a previously planned indexing operation.

fn has_indexing_support(_desc: IndexingPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.

impl TensorRngPrims<Standard<f64>> for CpuBackend

type Plan = (RngPrimsDescriptor, Vec<usize>)

Backend-specific execution plan.

type Context = CpuContext

Backend execution context.

fn plan( _ctx: &mut <CpuBackend as TensorRngPrims<Standard<f64>>>::Context, desc: &RngPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorRngPrims<Standard<f64>>>::Plan, Error>

Plan a tensor RNG operation for the given output shape.

fn execute( _ctx: &mut <CpuBackend as TensorRngPrims<Standard<f64>>>::Context, plan: &<CpuBackend as TensorRngPrims<Standard<f64>>>::Plan, generator: &mut Generator, output: &mut Tensor<f64>, ) -> Result<(), Error>

Execute a previously planned RNG operation.

fn has_rng_support(desc: RngPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.

impl TensorRngPrims<Standard<i32>> for CpuBackend

type Plan = (RngPrimsDescriptor, Vec<usize>)

Backend-specific execution plan.

type Context = CpuContext

Backend execution context.

fn plan( _ctx: &mut <CpuBackend as TensorRngPrims<Standard<i32>>>::Context, desc: &RngPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorRngPrims<Standard<i32>>>::Plan, Error>

Plan a tensor RNG operation for the given output shape.

fn execute( _ctx: &mut <CpuBackend as TensorRngPrims<Standard<i32>>>::Context, plan: &<CpuBackend as TensorRngPrims<Standard<i32>>>::Plan, generator: &mut Generator, output: &mut Tensor<i32>, ) -> Result<(), Error>

Execute a previously planned RNG operation.

fn has_rng_support(desc: RngPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.

impl<S> TensorScalarPrims<Standard<S>> for CpuBackend

where S: Scalar + 'static,

type Plan = CpuScalarPlan

type Context = CpuContext

fn plan( _ctx: &mut <CpuBackend as TensorScalarPrims<Standard<S>>>::Context, desc: &ScalarPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorScalarPrims<Standard<S>>>::Plan, Error>

Plan a scalar-family operation for the given input/output shapes.

fn execute( _ctx: &mut <CpuBackend as TensorScalarPrims<Standard<S>>>::Context, plan: &<CpuBackend as TensorScalarPrims<Standard<S>>>::Plan, alpha: S, inputs: &[&Tensor<S>], beta: S, output: &mut Tensor<S>, ) -> Result<(), Error>

Execute a previously planned scalar-family operation.

fn has_scalar_support(desc: ScalarPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.

impl<S> TensorSemiringCore<Standard<S>> for CpuBackend

where S: Scalar,

type Plan = CpuPlan<S>

Backend-specific plan type.

type Context = CpuContext

Backend-specific execution context.

fn plan( ctx: &mut CpuContext, desc: &SemiringCoreDescriptor, shapes: &[&[usize]], ) -> Result<CpuPlan<S>, Error>

Plan a semiring-core operation.

fn execute( ctx: &mut CpuContext, plan: &CpuPlan<S>, alpha: S, inputs: &[&Tensor<S>], beta: S, output: &mut Tensor<S>, ) -> Result<(), Error>

Execute a semiring-core operation.

impl<S> TensorSemiringFastPath<Standard<S>> for CpuBackend

where S: Scalar,

type Plan = CpuPlan<S>

Backend-specific plan type.

type Context = CpuContext

Backend-specific execution context.

fn plan( ctx: &mut CpuContext, desc: &SemiringFastPathDescriptor, shapes: &[&[usize]], ) -> Result<CpuPlan<S>, Error>

Plan an optional semiring fast path.

fn execute( ctx: &mut CpuContext, plan: &CpuPlan<S>, alpha: S, inputs: &[&Tensor<S>], beta: S, output: &mut Tensor<S>, ) -> Result<(), Error>

Execute an optional semiring fast path.

fn has_fast_path(desc: SemiringFastPathDescriptor) -> bool

Query whether the optional path is available.

impl<S> TensorSortPrims<Standard<S>> for CpuBackend

where S: Scalar + PartialOrd + 'static,

type Plan = CpuSortPlan

Backend-specific execution plan.

type Context = CpuContext

Backend execution context.

fn plan( _ctx: &mut <CpuBackend as TensorSortPrims<Standard<S>>>::Context, desc: &SortPrimsDescriptor, shapes: &[&[usize]], ) -> Result<<CpuBackend as TensorSortPrims<Standard<S>>>::Plan, Error>

Plan a sort operation for the given input shape.

fn execute( _ctx: &mut <CpuBackend as TensorSortPrims<Standard<S>>>::Context, plan: &<CpuBackend as TensorSortPrims<Standard<S>>>::Plan, input: &Tensor<S>, values_out: &mut Tensor<S>, indices_out: &mut Tensor<i64>, ) -> Result<(), Error>

Execute a previously planned sort operation.

fn has_sort_support(_desc: &SortPrimsDescriptor) -> bool

Report whether the backend advertises support for the given descriptor.