FHElium

fhelium.backend.triton._arithmetic ​

Integer modular arithmetic shared by generated Triton kernels.

montgomery_mul ​

function View source

python
def montgomery_mul(a, b, q, k, radix_bits: tl.constexpr): ...

Return native-compatible REDC: canonical for R32, lazy for R62.

montgomery_reduce ​

function View source

python
def montgomery_reduce(a, q, k, radix_bits: tl.constexpr): ...

add_lazy ​

function View source

python
def add_lazy(a, b, q): ...

subtract_lazy ​

function View source

python
def subtract_lazy(a, b, q): ...

canonicalize ​

function View source

python
def canonicalize(a, q): ...

shoup32_mul ​

function View source

python
def shoup32_mul(value, root, quotient, q): ...

Return value*root modulo q in [0,2q) for value<2q and q<2^30.

quotient carries floor(root*2^32/q) as an unsigned word. The low-word difference equals the nonnegative remainder because its value is below 2q. A standard root preserves the input's Montgomery representation.