Struct snarkvm_wasm::FrParameters

pub struct FrParameters;

Trait Implementations

impl FftParameters for FrParameters

const TWO_ADIC_ROOT_OF_UNITY: BigInteger256 = BigInteger([12646347781564978760u64, 6783048705277173164u64, 268534165941069093u64, 1121515446318641358u64])

TWO_ADIC_ROOT_OF_UNITY = 8065159656716812877374967518403273466521432693661810619979959746626482506078 Encoded in Montgomery form, the value is (8065159656716812877374967518403273466521432693661810619979959746626482506078 * R % q) = 7039866554349711480672062101017509031917008525101396696252683426045173093960

type BigInteger = BigInteger256

const POWERS_OF_ROOTS_OF_UNITY: &'static [BigInteger256] = &[BigInteger([12646347781564978760, 6783048705277173164, 268534165941069093, 1121515446318641358]), BigInteger([9908812190343590727, 989981212292874635, 13217848517394370016, 313220887743686251]), BigInteger([4570942453055933478, 14327950181157151272, 8177734713484223276, 732395113570565582]), BigInteger([7547026561639937065, 11733968610145256351, 8343216976141027051, 576989125389526455]), BigInteger([15503117548499178639, 2308620569553928151, 16285062430639685160, 103769458534362861]), BigInteger([8608407781632583430, 6271302370352858992, 1070338101025660973, 538942973387907962]), BigInteger([6401736382236295208, 1153288719752352283, 14823640363840104239, 499246014633910619]), BigInteger([17833850933386010261, 6090852137313170745, 12528041030915574153, 857737301371729770]), BigInteger([1982048757083514280, 12158391317477180280, 13684570609270614441, 840786117129730731]), BigInteger([18189047035874409266, 10063848728508956944, 18125989563719264563, 109154778261203350]), BigInteger([4145860318443588715, 480045415555849201, 15185689511254420012, 997424544238423752]), BigInteger([12380934610292147810, 14921791250714101079, 7953234348116523713, 740566716969780590]), BigInteger([17523206016699816339, 8210268852326501515, 12102826939441359278, 69320453637394156]), BigInteger([13184634841845083965, 5035641472528052881, 10848835132746879957, 1093292728521196096]), BigInteger([3644591431389930536, 17535182174514028817, 2333780137994975086, 1211430046545197955]), BigInteger([15764618857955124109, 17001304349044012093, 11249158843350648159, 1304234597518548509]), BigInteger([17023740166556598291, 17327346947230052231, 15227607426000437488, 524356170404741496]), BigInteger([15508095723619167236, 8916154698977858924, 4872918458681303657, 507246242966933127]), BigInteger([13933261170268378635, 6975150440507062408, 285981162592700355, 909990229706841196]), BigInteger([1796369225555089555, 18439169056424861976, 8554690303853538396, 739593369575156928]), BigInteger([8849035624997270559, 11082174508102696985, 5797273297011026936, 458094565250654809]), BigInteger([5944936778479914843, 369725202543584470, 22913969483319861, 1123237285519395196]), BigInteger([8228193452833987056, 3247446711273005067, 7285244012699814841, 165660218100066147]), BigInteger([16110965290454180518, 5418683100417587062, 11303731202360030209, 290121373407754357]), BigInteger([10742665076645341070, 7056370150642984550, 12615465793934837989, 548498362185685512]), BigInteger([8097456064175987351, 10585807130451162109, 5877015307964227995, 477368390704686837]), BigInteger([15676770081073062471, 12262153699415403306, 7528677848461606057, 649917933945894399]), BigInteger([18271947154240526633, 11103933895114620578, 16558660923152452318, 925331653431062360]), BigInteger([3907589926240897769, 11045697709584246531, 90835143142482923, 870886311473863909]), BigInteger([3528144693560331180, 11121597045360901952, 11405196888439666838, 670327805282996966]), BigInteger([13456528212939925364, 9040660049171970165, 4374817133042500768, 422841521572866881]), BigInteger([17220360707710309003, 7704697058569325505, 14703012148831508770, 113932329837224644]), BigInteger([15456395681208503803, 6416534260312397167, 4409371950760456950, 855302230113322418]), BigInteger([14648805411005782346, 659899539555743592, 13712138229698623536, 688628542983365223]), BigInteger([17553691999655354057, 12414962864428128502, 12778610342023380950, 309906985245362430]), BigInteger([13671771363231792901, 13550649581906397391, 14960300922341772840, 197239424530289859]), BigInteger([14840183457516239942, 7651729362259515675, 11442121706837547178, 409184120412760908]), BigInteger([5849560869621087513, 6649867980513935874, 16080766030443795594, 905356649678185654]), BigInteger([13302147401216114106, 3611900969696901525, 3470557722594359823, 950175460673052306]), BigInteger([16339580035428004219, 4845663562592066382, 6914211203719332907, 510216861370749871]), BigInteger([2145222547635311650, 10230679325758658394, 7207487648880633871, 209805430256584658]), BigInteger([9208812316068886018, 11169310505015993932, 8317257015293247865, 1090372203370214591]), BigInteger([18408280738886485821, 14547869021980959191, 6047025381655759581, 725535874718029226]), BigInteger([1670730338129557402, 7866724895305809984, 10026936948289003902, 781269171506367679]), BigInteger([4882877962169421051, 8060560647985508350, 4729166814476724001, 1147730753089737444]), BigInteger([5461406015399410446, 5014654494648953692, 8156709087178280082, 1299557346046566890])]

TWO_ADIC_ROOT_OF_UNITY^2^i for i := 0..TWO_ADICITY-1

const TWO_ADICITY: u32 = 47u32

Let N be the size of the multiplicative group defined by the field. Then TWO_ADICITY is the two-adicity of N, i.e. the integer s such that N = 2^s * t for some odd integer t. 2^s * t = MODULUS - 1 with t odd. This is the two-adicity of the prime.

const SMALL_SUBGROUP_BASE: Option<u32> = None

An integer b such that there exists a multiplicative subgroup of size b^k for some integer k.

const SMALL_SUBGROUP_BASE_ADICITY: Option<u32> = None

The integer k such that there exists a multiplicative subgroup of size Self::SMALL_SUBGROUP_BASE^k.

const LARGE_SUBGROUP_ROOT_OF_UNITY: Option<Self::BigInteger> = None

GENERATOR^((MODULUS-1) / (2^s * SMALL_SUBGROUP_BASE^SMALL_SUBGROUP_BASE_ADICITY)) Used for mixed-radix FFT.

impl FieldParameters for FrParameters

const GENERATOR: BigInteger256 = BigInteger([2984901390528151251u64, 10561528701063790279u64, 5476750214495080041u64, 898978044469942640u64])

GENERATOR = 22 Encoded in Montgomery form, so the value is (22 * R) % q = 5642976643016801619665363617888466827793962762719196659561577942948671127251

const MODULUS: BigInteger256 = BigInteger([725501752471715841u64, 6461107452199829505u64, 6968279316240510977u64, 1345280370688173398u64])

MODULUS = 8444461749428370424248824938781546531375899335154063827935233455917409239041

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([9586122913090633728, 12453925762954690560, 3484139658120255488, 672640185344086699])

(r - 1)/2 = 4222230874714185212124412469390773265687949667577031913967616727958704619520

const T: BigInteger256 = BigInteger([17149038877957297187, 11113960768935211860, 14608890324369326440, 9558])

t = (r - 1) / 2^s = 60001509534603559531609739528203892656505753216962260608619555

const T_MINUS_ONE_DIV_TWO: BigInteger256 = BigInteger([8574519438978648593, 5556980384467605930, 7304445162184663220, 4779])

(t - 1) / 2 = 30000754767301779765804869764101946328252876608481130304309777

const CAPACITY: u32 = 252u32

The number of bits that can be reliably stored. (Should equal SELF::MODULUS_BITS - 1)

const INV: u64 = 725_501_752_471_715_839u64

INV = -(MODULUS^{-1} mod MODULUS) mod MODULUS

const MODULUS_BITS: u32 = 253u32

The number of bits needed to represent the Self::MODULUS.

const R: BigInteger256 = BigInteger([9015221291577245683u64, 8239323489949974514u64, 1646089257421115374u64, 958099254763297437u64])

R = 2^256 % Self::MODULUS

const R2: BigInteger256 = BigInteger([2726216793283724667u64, 14712177743343147295u64, 12091039717619697043u64, 81024008013859129u64])

R2 = R^2 % Self::MODULUS

const REPR_SHAVE_BITS: u32 = 3u32

The number of bits that must be shaved from the beginning of the representation when randomly sampling.

impl PoseidonDefaultParameters for FrParameters

const PARAMS_OPT_FOR_CONSTRAINTS: [PoseidonDefaultParametersEntry; 7] = [PoseidonDefaultParametersEntry::new(2, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(3, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(4, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(5, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(6, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(7, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(8, 17, 8, 31, 0)]

An array of the parameters optimized for constraints (rate, alpha, full_rounds, partial_rounds, skip_matrices) for rate = 2, 3, 4, 5, 6, 7, 8

impl Fp256Parameters for FrParameters