Expand description
Autogenerated: ‘src/ExtractionOCaml/word_by_word_montgomery’ –lang Rust –inline 25519_scalar 64 ‘2^252 + 27742317777372353535851937790883648493’ mul square add sub opp from_montgomery to_montgomery nonzero selectznz to_bytes from_bytes one msat divstep divstep_precomp curve description: 25519_scalar machine_wordsize = 64 (from “64”) requested operations: mul, square, add, sub, opp, from_montgomery, to_montgomery, nonzero, selectznz, to_bytes, from_bytes, one, msat, divstep, divstep_precomp m = 0x1000000000000000000000000000000014def9dea2f79cd65812631a5cf5d3ed (from “2^252 + 27742317777372353535851937790883648493”)
NOTE: In addition to the bounds specified above each function, all functions synthesized for this Montgomery arithmetic require the input to be strictly less than the prime modulus (m), and also require the input to be in the unique saturated representation. All functions also ensure that these two properties are true of return values.
Computed values: eval z = z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) bytes_eval z = z[0] + (z[1] << 8) + (z[2] << 16) + (z[3] << 24) + (z[4] << 32) + (z[5] << 40) + (z[6] << 48) + (z[7] << 56) + (z[8] << 64) + (z[9] << 72) + (z[10] << 80) + (z[11] << 88) + (z[12] << 96) + (z[13] << 104) + (z[14] << 112) + (z[15] << 120) + (z[16] << 128) + (z[17] << 136) + (z[18] << 144) + (z[19] << 152) + (z[20] << 160) + (z[21] << 168) + (z[22] << 176) + (z[23] << 184) + (z[24] << 192) + (z[25] << 200) + (z[26] << 208) + (z[27] << 216) + (z[28] << 224) + (z[29] << 232) + (z[30] << 240) + (z[31] << 248) twos_complement_eval z = let x1 := z[0] + (z[1] << 64) + (z[2] << 128) + (z[3] << 192) in if x1 & (2^256-1) < 2^255 then x1 & (2^256-1) else (x1 & (2^256-1)) - 2^256
Structs§
- fiat_
25519_ scalar_ montgomery_ domain_ field_ element - The type fiat_25519_scalar_montgomery_domain_field_element is a field element in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
- fiat_
25519_ scalar_ non_ montgomery_ domain_ field_ element - The type fiat_25519_scalar_non_montgomery_domain_field_element is a field element NOT in the Montgomery domain. Bounds: [[0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff], [0x0 ~> 0xffffffffffffffff]]
Functions§
- fiat_
25519_ scalar_ add - The function fiat_25519_scalar_add adds two field elements in the Montgomery domain.
- fiat_
25519_ scalar_ addcarryx_ u64 - The function fiat_25519_scalar_addcarryx_u64 is an addition with carry.
- fiat_
25519_ scalar_ cmovznz_ u64 - The function fiat_25519_scalar_cmovznz_u64 is a single-word conditional move.
- fiat_
25519_ scalar_ divstep - The function fiat_25519_scalar_divstep computes a divstep.
- fiat_
25519_ scalar_ divstep_ precomp - The function fiat_25519_scalar_divstep_precomp returns the precomputed value for Bernstein-Yang-inversion (in montgomery form).
- fiat_
25519_ scalar_ from_ bytes - The function fiat_25519_scalar_from_bytes deserializes a field element NOT in the Montgomery domain from bytes in little-endian order.
- fiat_
25519_ scalar_ from_ montgomery - The function fiat_25519_scalar_from_montgomery translates a field element out of the Montgomery domain.
- fiat_
25519_ scalar_ msat - The function fiat_25519_scalar_msat returns the saturated representation of the prime modulus.
- fiat_
25519_ scalar_ mul - The function fiat_25519_scalar_mul multiplies two field elements in the Montgomery domain.
- fiat_
25519_ scalar_ mulx_ u64 - The function fiat_25519_scalar_mulx_u64 is a multiplication, returning the full double-width result.
- fiat_
25519_ scalar_ nonzero - The function fiat_25519_scalar_nonzero outputs a single non-zero word if the input is non-zero and zero otherwise.
- fiat_
25519_ scalar_ opp - The function fiat_25519_scalar_opp negates a field element in the Montgomery domain.
- fiat_
25519_ scalar_ selectznz - The function fiat_25519_scalar_selectznz is a multi-limb conditional select.
- fiat_
25519_ scalar_ set_ one - The function fiat_25519_scalar_set_one returns the field element one in the Montgomery domain.
- fiat_
25519_ scalar_ square - The function fiat_25519_scalar_square squares a field element in the Montgomery domain.
- fiat_
25519_ scalar_ sub - The function fiat_25519_scalar_sub subtracts two field elements in the Montgomery domain.
- fiat_
25519_ scalar_ subborrowx_ u64 - The function fiat_25519_scalar_subborrowx_u64 is a subtraction with borrow.
- fiat_
25519_ scalar_ to_ bytes - The function fiat_25519_scalar_to_bytes serializes a field element NOT in the Montgomery domain to bytes in little-endian order.
- fiat_
25519_ scalar_ to_ montgomery - The function fiat_25519_scalar_to_montgomery translates a field element into the Montgomery domain.
Type Aliases§
- fiat_
25519_ scalar_ i1 - fiat_25519_scalar_i1 represents values of 1 bits, stored in one byte.
- fiat_
25519_ scalar_ i2 - fiat_25519_scalar_i2 represents values of 2 bits, stored in one byte.
- fiat_
25519_ scalar_ u1 - fiat_25519_scalar_u1 represents values of 1 bits, stored in one byte.
- fiat_
25519_ scalar_ u2 - fiat_25519_scalar_u2 represents values of 2 bits, stored in one byte.