Struct NewtonInversion 

pub struct NewtonInversion {
    pub iterations: u64,
    pub denominator_cap_2k: u64,
}

A structure that defines the custom operation NewtonInversion that computes an inversion of a number via the Newton-Raphson method.

In particular, this operation computes an approximation of 2^{denominator_cap_2k} / input.

Input must be of the scalar type UINT64 or INT64 and be in (0, 2^{denominator_cap_2k - 1}) range. The input is also assumed to be small enough (less than 2³²), otherwise integer overflows are possible, yielding incorrect results.

Optionally, an initial approximation for the Newton-Raphson method can be provided. In this case, the operation might be faster and of lower depth, however, it must be guaranteed that 2^{denominator_cap_2k - 1} <= input * initial_approximation < 2^{denominator_cap_2k + 1}.

Custom operation arguments

• Node containing an unsigned or signed 64-bit array or scalar to invert
• Negative values are currently unsupported as sign extraction is quite expensive
• (optional) Node containing an array or scalar that serves as an initial approximation of the Newton-Raphson method

Custom operation returns

New NewtonInversion node

Example

let c = create_context().unwrap();
let g = c.create_graph().unwrap();
let t = array_type(vec![2, 3], UINT64);
let n1 = g.input(t.clone()).unwrap();
let guess_n = g.input(t.clone()).unwrap();
let n2 = g.custom_op(CustomOperation::new(NewtonInversion {iterations: 10, denominator_cap_2k: 4}), vec![n1, guess_n]).unwrap();

Fields

iterations: u64

Number of iterations of the Newton-Raphson method; rule of thumb is to set it to 1 + log(denominator_cap_2k)

denominator_cap_2k: u64

Number of output bits that are approximated

Trait Implementations

impl CustomOperationBody for NewtonInversion

fn instantiate( &self, context: Context, arguments_types: Vec<Type>, ) -> Result<Graph>

Defines the logic of a custom operation.

fn get_name(&self) -> String

Specifies and returns the name of this custom operation.

impl Debug for NewtonInversion

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

Formats the value using the given formatter.

impl<'de> Deserialize<'de> for NewtonInversion

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Hash for NewtonInversion

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for NewtonInversion

fn eq(&self, other: &NewtonInversion) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Serialize for NewtonInversion

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl Eq for NewtonInversion

impl StructuralPartialEq for NewtonInversion