Struct concrete_core::math::fft::Fft

pub struct Fft { /* fields omitted */ }

A fast fourier transformer.

This transformer type allows to send polynomials of a fixed size, back and forth in the fourier domain.

Implementations

impl Fft

pub fn new(size: PolynomialSize) -> Fft

Generates a new transformer for polynomials a given size.

Example

use concrete_core::math::fft::Fft;
use concrete_core::math::polynomial::PolynomialSize;
let fft = Fft::new(PolynomialSize(256));
assert_eq!(fft.polynomial_size(), PolynomialSize(256));

pub fn polynomial_size(&self) -> PolynomialSize

Returns the polynomial size accepted by this transformer.

Example

use concrete_core::math::fft::Fft;
use concrete_core::math::polynomial::PolynomialSize;
let fft = Fft::new(PolynomialSize(256));
assert_eq!(fft.polynomial_size(), PolynomialSize(256));

pub fn forward_as_torus<OutCont, InCont, Coef>(
    &mut self,
    fourier_poly: &mut FourierPolynomial<OutCont>,
    poly: &Polynomial<InCont>
) where
    FourierPolynomial<OutCont>: AsMutTensor<Element = Complex64>,
    Polynomial<InCont>: AsRefTensor<Element = Coef>,
    Coef: UnsignedTorus, 

Performs the forward fourier transform of the poly polynomial, viewed as a polynomial of torus coefficients, and stores the result in fourier_poly.

Note

It should be noted that this method is subotpimal, as it only uses half of the computational power of the transformer. For a faster approach, you should consider processing the polynomials two by two with the Fft::forward_two_as_torus method.

Example

use concrete_core::math::fft::{Fft, FourierPolynomial, Complex64};
use concrete_core::math::polynomial::{Polynomial, PolynomialSize};
use concrete_core::math::random::{fill_with_random_uniform};
use concrete_core::math::tensor::AsRefTensor;
use concrete_core::crypto::UnsignedTorus;
let mut fft = Fft::new(PolynomialSize(256));
let mut fourier_poly = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut poly = Polynomial::allocate(0u32, PolynomialSize(256));
fill_with_random_uniform(&mut poly);
fft.forward_as_torus(&mut fourier_poly, &poly);
let mut out = Polynomial::allocate(0u32, PolynomialSize(256));
fft.add_backward_as_torus(&mut out, &mut fourier_poly);
out.as_tensor()
   .iter()
   .zip(poly.as_tensor().iter())
   .for_each(|(output, expected)| assert_eq!(*output, *expected));

pub fn forward_two_as_torus<InCont1, InCont2, OutCont1, OutCont2, Coef>(
    &mut self,
    fourier_poly_1: &mut FourierPolynomial<OutCont1>,
    fourier_poly_2: &mut FourierPolynomial<OutCont2>,
    poly_1: &Polynomial<InCont1>,
    poly_2: &Polynomial<InCont2>
) where
    Polynomial<InCont1>: AsRefTensor<Element = Coef>,
    Polynomial<InCont2>: AsRefTensor<Element = Coef>,
    FourierPolynomial<OutCont1>: AsMutTensor<Element = Complex64>,
    FourierPolynomial<OutCont2>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedTorus, 

Performs the forward fourier transform of the poly_1 and poly_2 polynomials, viewed as polynomials of torus coefficients, and stores the result in fourier_poly_1 and fourier_poly_2.

Example

use concrete_core::math::fft::{Fft, FourierPolynomial, Complex64};
use concrete_core::math::polynomial::{Polynomial, PolynomialSize};
use concrete_core::math::random::{fill_with_random_uniform};
use concrete_core::math::tensor::AsRefTensor;
use concrete_core::crypto::UnsignedTorus;
use concrete_core::numeric::UnsignedInteger;
let mut fft = Fft::new(PolynomialSize(256));
let mut fourier_poly_1 = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut fourier_poly_2 = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut poly_1 = Polynomial::allocate(0u32, PolynomialSize(256));
let mut poly_2 = Polynomial::allocate(0u32, PolynomialSize(256));
fill_with_random_uniform(&mut poly_1);
fill_with_random_uniform(&mut poly_2);
fft.forward_two_as_torus(&mut fourier_poly_1, &mut fourier_poly_2, &poly_1, &poly_2);
let mut out_1 = Polynomial::allocate(0u32, PolynomialSize(256));
let mut out_2 = Polynomial::allocate(0u32, PolynomialSize(256));
fft.add_backward_two_as_torus(
    &mut out_1,
    &mut out_2,
    &mut fourier_poly_1,
    &mut fourier_poly_2
);
out_1.as_tensor()
   .iter()
   .zip(poly_1.as_tensor().iter())
   .for_each(|(out, exp)| assert_eq!(out, exp));
out_2.as_tensor()
   .iter()
   .zip(poly_2.as_tensor().iter())
   .for_each(|(out, exp)| assert_eq!(out, exp));

pub fn forward_as_integer<OutCont, InCont, Coef>(
    &mut self,
    fourier_poly: &mut FourierPolynomial<OutCont>,
    poly: &Polynomial<InCont>
) where
    FourierPolynomial<OutCont>: AsMutTensor<Element = Complex64>,
    Polynomial<InCont>: AsRefTensor<Element = Coef>,
    Coef: UnsignedInteger, 

Performs the forward fourier transform of the poly polynomial, viewed as a polynomial of integer coefficients, and stores the result in fourier_poly.

Note

It should be noted that this method is subotpimal, as it only uses half of the computational power of the transformer. For a faster approach, you should consider processing the polynomials two by two with the Fft::forward_two_as_integer method.

Example

use concrete_core::math::fft::{Fft, FourierPolynomial, Complex64};
use concrete_core::math::polynomial::{Polynomial, PolynomialSize};
use concrete_core::math::random::{fill_with_random_uniform};
use concrete_core::math::tensor::AsRefTensor;
use concrete_core::numeric::UnsignedInteger;
let mut fft = Fft::new(PolynomialSize(256));
let mut fourier_poly = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut poly = Polynomial::allocate(0u32, PolynomialSize(256));
fill_with_random_uniform(&mut poly);
fft.forward_as_integer(&mut fourier_poly, &poly);
let mut out = Polynomial::allocate(0u32, PolynomialSize(256));
fft.add_backward_as_integer(&mut out, &mut fourier_poly);
out.as_tensor()
   .iter()
   .zip(poly.as_tensor().iter())
   .for_each(|(out, exp)| assert_eq!(*out, *exp));

pub fn forward_two_as_integer<InCont1, InCont2, OutCont1, OutCont2, Coef>(
    &mut self,
    fourier_poly_1: &mut FourierPolynomial<OutCont1>,
    fourier_poly_2: &mut FourierPolynomial<OutCont2>,
    poly_1: &Polynomial<InCont1>,
    poly_2: &Polynomial<InCont2>
) where
    Polynomial<InCont1>: AsRefTensor<Element = Coef>,
    Polynomial<InCont2>: AsRefTensor<Element = Coef>,
    FourierPolynomial<OutCont1>: AsMutTensor<Element = Complex64>,
    FourierPolynomial<OutCont2>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedInteger, 

Performs the forward fourier transform of the poly_1 and poly_2 polynomials, viewed as polynomials of integer coefficients, and stores the result in fourier_poly_1 and fourier_poly_2.

Example

use concrete_core::math::fft::{Fft, FourierPolynomial, Complex64};
use concrete_core::math::polynomial::{Polynomial, PolynomialSize};
use concrete_core::math::random::{fill_with_random_uniform};
use concrete_core::math::tensor::AsRefTensor;
use concrete_core::numeric::UnsignedInteger;
let mut fft = Fft::new(PolynomialSize(256));
let mut fourier_poly_1 = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut fourier_poly_2 = FourierPolynomial::allocate(
    Complex64::new(0.,0.),
    PolynomialSize(256)
);
let mut poly_1 = Polynomial::allocate(0u32, PolynomialSize(256));
let mut poly_2 = Polynomial::allocate(0u32, PolynomialSize(256));
fill_with_random_uniform(&mut poly_1);
fill_with_random_uniform(&mut poly_2);
fft.forward_two_as_integer(&mut fourier_poly_1, &mut fourier_poly_2, &poly_1, &poly_2);
let mut out_1 = Polynomial::allocate(0u32, PolynomialSize(256));
let mut out_2 = Polynomial::allocate(0u32, PolynomialSize(256));
fft.add_backward_two_as_integer(
    &mut out_1,
    &mut out_2,
    &mut fourier_poly_1,
    &mut fourier_poly_2
);
out_1.as_tensor()
   .iter()
   .zip(poly_1.as_tensor().iter())
   .for_each(|(out, exp)| assert_eq!(out, exp));
out_2.as_tensor()
   .iter()
   .zip(poly_2.as_tensor().iter())
   .for_each(|(out, exp)| assert_eq!(out, exp));

pub fn add_backward_as_torus<OutCont, InCont, Coef>(
    &mut self,
    poly: &mut Polynomial<OutCont>,
    fourier_poly: &mut FourierPolynomial<InCont>
) where
    Polynomial<OutCont>: AsMutTensor<Element = Coef>,
    FourierPolynomial<InCont>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedTorus, 

Performs the backward fourier transform of the fourier_poly polynomial, viewed as a polynomial of torus coefficients, and adds the result to poly.

See Fft::forward_as_torus for an example.

Note

It should be noted that this method is subotpimal, as it only uses half of the computational power of the transformer. For a faster approach, you should consider processing the polynomials two by two with the Fft::add_backward_two_as_torus method.

pub fn add_backward_as_integer<OutCont, InCont, Coef>(
    &mut self,
    poly: &mut Polynomial<OutCont>,
    fourier_poly: &mut FourierPolynomial<InCont>
) where
    Polynomial<OutCont>: AsMutTensor<Element = Coef>,
    FourierPolynomial<InCont>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedInteger, 

Performs the backward fourier transform of the fourier_poly polynomial, viewed as a polynomial of integer coefficients, and adds the result to poly.

See Fft::forward_as_integer for an example.

Note

It should be noted that this method is subotpimal, as it only uses half of the computational power of the transformer. For a faster approach, you should consider processing the polynomials two by two with the Fft::add_backward_two_as_integer method.

pub fn add_backward_two_as_torus<OutCont1, OutCont2, InCont1, InCont2, Coef>(
    &mut self,
    poly_1: &mut Polynomial<OutCont1>,
    poly_2: &mut Polynomial<OutCont2>,
    fourier_poly_1: &mut FourierPolynomial<InCont1>,
    fourier_poly_2: &mut FourierPolynomial<InCont2>
) where
    Polynomial<OutCont1>: AsMutTensor<Element = Coef>,
    Polynomial<OutCont2>: AsMutTensor<Element = Coef>,
    FourierPolynomial<InCont1>: AsMutTensor<Element = Complex64>,
    FourierPolynomial<InCont2>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedTorus, 

Performs the backward fourier transform of the fourier_poly_1 and fourier_poly_2 polynomials, viewed as polynomials of torus elements, and adds the result to the
poly_1 and poly_2 polynomials.

See Fft::forward_two_as_torus for an example.

pub fn add_backward_two_as_integer<OutCont1, OutCont2, InCont1, InCont2, Coef>(
    &mut self,
    poly_1: &mut Polynomial<OutCont1>,
    poly_2: &mut Polynomial<OutCont2>,
    fourier_poly_1: &mut FourierPolynomial<InCont1>,
    fourier_poly_2: &mut FourierPolynomial<InCont2>
) where
    Polynomial<OutCont1>: AsMutTensor<Element = Coef>,
    Polynomial<OutCont2>: AsMutTensor<Element = Coef>,
    FourierPolynomial<InCont1>: AsMutTensor<Element = Complex64>,
    FourierPolynomial<InCont2>: AsMutTensor<Element = Complex64>,
    Coef: UnsignedInteger, 

Performs the backward fourier transform of the fourier_poly_1 and fourier_poly_2 polynomials, viewed as polynomials of integer coefficients, and adds the result to the
poly_1 and poly_2 polynomials.

See Fft::forward_two_as_integer for an example.