Struct snarkvm_wasm::FqParameters

pub struct FqParameters;

Trait Implementations

impl FftParameters for FqParameters

type BigInteger = BigInteger384

const POWERS_OF_ROOTS_OF_UNITY: &'static [BigInteger384] = &[BigInteger([2022196864061697551, 17419102863309525423, 8564289679875062096, 17152078065055548215, 17966377291017729567, 68610905582439508]), BigInteger([1097558877362951325, 10990216524069526157, 1703764964909126124, 5337477398168494451, 8388789446441546832, 83780176967333390]), BigInteger([6021325183928272861, 3071743451473281050, 17793609045682579055, 4499483110946763311, 3694917660005904773, 35840689841924604]), BigInteger([4148421423508782473, 16486417951907259381, 13681320370461884655, 9543156358084556689, 15654115908807492478, 85178773442619605]), BigInteger([4440291260215189129, 8134083368238958870, 5850770822935137603, 18388642548453398432, 4033689956485938698, 96943229116346922]), BigInteger([13321959743753581084, 13957307756377123667, 8022065601003020126, 15105587473044942004, 3436102915385715417, 16497947308509307]), BigInteger([12740765449271843915, 13529810863058982449, 15988003695485397690, 5204094055301492127, 12204797504641322421, 54884696873855227]), BigInteger([7200341240129221640, 128866105844736666, 1972097482351781478, 7508123272393265315, 18134316519918384483, 90386983337599854]), BigInteger([11182828541229423812, 3352059565776569042, 745605881396983371, 10544136951768851167, 13944324842745283530, 76153606183323606]), BigInteger([5451839093323299025, 11344095019039321738, 3696612540108785619, 849808749100130193, 7737394061630388518, 41447732009599376]), BigInteger([4914435911578270728, 11442571726223078752, 200783168592117624, 5223206539372270413, 12471543125846282538, 14780043884677376]), BigInteger([6835942096487989968, 9916740166863458597, 15149601694743014865, 3251390487756549529, 16202626875757167903, 78637381314787701]), BigInteger([10024136201786834022, 2737410832464918544, 11569195233337582907, 6882399291950297037, 17956512286065493665, 87559046345038795]), BigInteger([7787906257689135971, 4007925209220880779, 5799259275421890332, 5651393587803319504, 5361114559272044762, 78591763064139593]), BigInteger([8749978828541193864, 7615081815133949072, 13070992874042179472, 1364907361524039183, 10109099343823847681, 104282651814875028]), BigInteger([16730838284865363583, 15400461195736119534, 4032519462999757033, 15551203984340620330, 382650037072032689, 76641657953301822]), BigInteger([8166159088317375095, 1704530912566839702, 13372111531284600631, 9715437978473519961, 4887487291063440487, 6286512958015546]), BigInteger([1768534497835661159, 1244838626041538416, 9153540930636989172, 12437852256056737422, 2519703766117714353, 37580752840997918]), BigInteger([13468864600499712370, 15009260878077565, 14291559461807896332, 9284492953958434183, 18315507429112290509, 41332741727179643]), BigInteger([8269976866043356680, 16766307433795223092, 339184897717558508, 9029309210784216270, 16947438621423748249, 1154969810162894]), BigInteger([10598383875620927263, 1261087173785984910, 11498737931675819777, 8568819297979713299, 1166319621891739467, 53485818962535716]), BigInteger([1592802484188722575, 16097103819145948294, 7922347041881118053, 14182139815326903761, 1080552542780789890, 84770178757176689]), BigInteger([17305426336106269005, 8862145762498523999, 13494918675279718853, 3717788643186382361, 10515687947609219968, 112422016356963276]), BigInteger([10874618176231306138, 13631539808973743734, 11959456582258358795, 13957665559292951976, 7355794120017380469, 51180796759257049]), BigInteger([9944918783779352295, 11674736477566853654, 4430181012666063989, 5365556697595744810, 13024803618277831802, 80199608722292197]), BigInteger([11841292144630778493, 3327346977638983511, 9717945600717261357, 17521983842610332579, 17551948704477232338, 38629783630845674]), BigInteger([13053061452543995362, 1573516732916099269, 7734072523617387500, 15879247754331170173, 4985704564687245967, 50017930811101333]), BigInteger([5968032006797444201, 4356970211500493920, 14567417169078198555, 5589343791883175912, 13942140483976875481, 77532733089031308]), BigInteger([1520419837524800053, 4505352024184739223, 11163238693972155221, 14849828818714008227, 2337273235727598583, 119043856166660542]), BigInteger([17856003618470058414, 17971666744702441889, 17477339519519243281, 1190648955970084811, 8535065801186549950, 88202116378298476]), BigInteger([3613548573764529932, 17312871435250531950, 14583594317345501622, 15714261421593485983, 3619881023171270578, 102701416776282826]), BigInteger([2906047431783924967, 3246340428391821303, 9728912894597247012, 14160632400906136931, 17644388830484393402, 38484906188769515]), BigInteger([17914929175761583691, 10159064175292721773, 17508169904588375801, 231704298035432102, 16645242204034044467, 72146101474673684]), BigInteger([3958533722314001392, 10367882774307637822, 12047882728743649441, 405962725023303708, 2571821397758431564, 49080211914402704]), BigInteger([590761718662001177, 7169147383307934023, 3111750625130109315, 3509576743298836380, 9392819985844593396, 2903460257980110]), BigInteger([10894310132299876932, 7222012151301227611, 7759303741675735532, 18168258420254565546, 1036933145679827201, 84980589105836606]), BigInteger([6223094491993811174, 10029382893184057307, 1782107595179881914, 4749850940526401858, 17559628252757726982, 20954496417456641]), BigInteger([9716738584996322209, 2920283958606294680, 5037648889630024082, 10095866865449441757, 15798169953625136889, 75996191339425194]), BigInteger([4358863173918119755, 15055260416528219604, 14884179962427098601, 16487815824678336974, 9163017981789726811, 95112432538757947]), BigInteger([2011658397676046806, 15717875473168825780, 280862458342309401, 2045794038349364078, 15857429573515749114, 147064043817050]), BigInteger([16760038912651623103, 790302385909476981, 6794528760947774914, 1897898981979607280, 9930859122245863541, 62625600058823796]), BigInteger([6859520296144159969, 909173910965215762, 15967585281779797458, 10442593522875662584, 7918433044340205291, 104628130661177253]), BigInteger([7212508657599325242, 1584945223518302852, 9963925208591887870, 11598974258151462965, 3264112703271587886, 20341848365764212]), BigInteger([2142683228075401710, 5947621269725846341, 5696548463751032717, 13780290877820379740, 10702692037250602632, 33891554982109078]), BigInteger([10965161018967488287, 18251363109856037426, 7036083669251591763, 16109345360066746489, 4679973768683352764, 96952949334633821])]

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

const TWO_ADICITY: u32 = 46u32

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 TWO_ADIC_ROOT_OF_UNITY: BigInteger384 = BigInteger([2022196864061697551u64, 17419102863309525423u64, 8564289679875062096u64, 17152078065055548215u64, 17966377291017729567u64, 68610905582439508u64])

2^s root of unity, defined as GENERATOR^t.

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 FqParameters

const GENERATOR: BigInteger384 = BigInteger([18161750659790013178, 10940260503947051403, 2338003791965605956, 14680817040264804354, 841925479686732267, 43193913801202386])

GENERATOR = -5

const MODULUS: BigInteger384 = BigInteger([9586122913090633729, 1660523435060625408, 2230234197602682880, 1883307231910630287, 14284016967150029115, 121098312706494698])

MODULUS = 258664426012969094010652733694893533536393512754914660539884262666720468348340822774968888139573360124440321458177

const T: BigInteger384 = BigInteger([8435453208297608227, 9853568280881552429, 7479357291536088013, 1657802422768920715, 16796279350917535980, 1720])

T = (MODULUS - 1) // 2^S = 3675842578061421676390135839012792950148785745837396071634149488243117337281387659330802195819009059

const T_MINUS_ONE_DIV_TWO: BigInteger384 = BigInteger([13441098641003579921, 14150156177295552022, 12963050682622819814, 828901211384460357, 8398139675458767990, 860])

(T - 1) // 2 = 1837921289030710838195067919506396475074392872918698035817074744121558668640693829665401097909504529

const CAPACITY: u32 = 376u32

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

const INV: u64 = 9_586_122_913_090_633_727u64

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

const MODULUS_BITS: u32 = 377u32

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

const MODULUS_MINUS_ONE_DIV_TWO: BigInteger384 = BigInteger([4793061456545316864, 830261717530312704, 10338489135656117248, 10165025652810090951, 7142008483575014557, 60549156353247349])

(Self::MODULUS - 1) / 2

const R: BigInteger384 = BigInteger([202099033278250856u64, 5854854902718660529u64, 11492539364873682930u64, 8885205928937022213u64, 5545221690922665192u64, 39800542322357402u64])

R = 2^256 % Self::MODULUS

const R2: BigInteger384 = BigInteger([13224372171368877346, 227991066186625457, 2496666625421784173, 13825906835078366124, 9475172226622360569, 30958721782860680])

R2 = R^2 % Self::MODULUS

const REPR_SHAVE_BITS: u32 = 7u32

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

impl PoseidonDefaultParameters for FqParameters

const PARAMS_OPT_FOR_CONSTRAINTS: [PoseidonDefaultParametersEntry; 7] = [PoseidonDefaultParametersEntry::new(2, 17, 8, 31, 0), PoseidonDefaultParametersEntry::new(3, 5, 8, 56, 0), PoseidonDefaultParametersEntry::new(4, 5, 8, 56, 0), PoseidonDefaultParametersEntry::new(5, 5, 8, 57, 0), PoseidonDefaultParametersEntry::new(6, 5, 8, 57, 0), PoseidonDefaultParametersEntry::new(7, 5, 8, 57, 0), PoseidonDefaultParametersEntry::new(8, 5, 8, 57, 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 Fp384Parameters for FqParameters