Function montgomery_multiply_inner 

pub const fn montgomery_multiply_inner(
    x: &[Limb],
    y: &[Limb],
    out: &mut [Limb],
    modulus: &[Limb],
    mod_neg_inv: Limb,
) -> Limb

Based on Algorithm 14.36 in Handbook of Applied Cryptography https://cacr.uwaterloo.ca/hac/about/chap14.pdf

Multiply x and y in Montgomery form, producing x•y•R^-1 mod modulus + a•modulus.

This algorithm roughly corresponds to the Finely Integrated Operand Scanning (FIOS) method of “Analyzing and Comparing Montgomery Multiplication Algorithms” by Koc et al https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf but using wide words to track the intermediate products and carry.

The final conditional subtraction of the modulus to produce a result in the range [0, modulus) is not performed here, and must be performed by the caller. In some cases this may be deferred, as demonstrated by the almost_montgomery_mul method.