org.bouncycastle.pqc.crypto.falcon.FPREngine Maven / Gradle / Ivy
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The Bouncy Castle Crypto package is a Java implementation of cryptographic algorithms. This jar contains JCE provider and lightweight API for the Bouncy Castle Cryptography APIs for JDK 1.5 to JDK 1.8.
package org.bouncycastle.pqc.crypto.falcon;
class FPREngine
{
private static final FalconFPR[] inv_sigma;
private static final FalconFPR[] sigma_min;
private static final FalconFPR[] gm_tab;
private static final FalconFPR[] p2_tab;
static
{
inv_sigma = new FalconFPR[]{
new FalconFPR(0.0), /* unused */
new FalconFPR(0.0069054793295940891952143765991630516),
new FalconFPR(0.0068102267767177975961393730687908629),
new FalconFPR(0.0067188101910722710707826117910434131),
new FalconFPR(0.0065883354370073665545865037227681924),
new FalconFPR(0.0064651781207602900738053897763485516),
new FalconFPR(0.0063486788828078995327741182928037856),
new FalconFPR(0.0062382586529084374473367528433697537),
new FalconFPR(0.0061334065020930261548984001431770281),
new FalconFPR(0.0060336696681577241031668062510953022),
new FalconFPR(0.0059386453095331159950250124336477482)
};
sigma_min = new FalconFPR[]{
new FalconFPR(0.0), /* unused */
new FalconFPR(1.1165085072329102588881898380334015),
new FalconFPR(1.1321247692325272405718031785357108),
new FalconFPR(1.1475285353733668684571123112513188),
new FalconFPR(1.1702540788534828939713084716509250),
new FalconFPR(1.1925466358390344011122170489094133),
new FalconFPR(1.2144300507766139921088487776957699),
new FalconFPR(1.2359260567719808790104525941706723),
new FalconFPR(1.2570545284063214162779743112075080),
new FalconFPR(1.2778336969128335860256340575729042),
new FalconFPR(1.2982803343442918539708792538826807)
};
gm_tab = new FalconFPR[]{
new FalconFPR(0), new FalconFPR(0), /* unused */
new FalconFPR(-0.000000000000000000000000000), new FalconFPR(1.000000000000000000000000000),
new FalconFPR(0.707106781186547524400844362), new FalconFPR(0.707106781186547524400844362),
new FalconFPR(-0.707106781186547524400844362), new FalconFPR(0.707106781186547524400844362),
new FalconFPR(0.923879532511286756128183189), new FalconFPR(0.382683432365089771728459984),
new FalconFPR(-0.382683432365089771728459984), new FalconFPR(0.923879532511286756128183189),
new FalconFPR(0.382683432365089771728459984), new FalconFPR(0.923879532511286756128183189),
new FalconFPR(-0.923879532511286756128183189), new FalconFPR(0.382683432365089771728459984),
new FalconFPR(0.980785280403230449126182236), new FalconFPR(0.195090322016128267848284868),
new FalconFPR(-0.195090322016128267848284868), new FalconFPR(0.980785280403230449126182236),
new FalconFPR(0.555570233019602224742830814), new FalconFPR(0.831469612302545237078788378),
new FalconFPR(-0.831469612302545237078788378), new FalconFPR(0.555570233019602224742830814),
new FalconFPR(0.831469612302545237078788378), new FalconFPR(0.555570233019602224742830814),
new FalconFPR(-0.555570233019602224742830814), new FalconFPR(0.831469612302545237078788378),
new FalconFPR(0.195090322016128267848284868), new FalconFPR(0.980785280403230449126182236),
new FalconFPR(-0.980785280403230449126182236), new FalconFPR(0.195090322016128267848284868),
new FalconFPR(0.995184726672196886244836953), new FalconFPR(0.098017140329560601994195564),
new FalconFPR(-0.098017140329560601994195564), new FalconFPR(0.995184726672196886244836953),
new FalconFPR(0.634393284163645498215171613), new FalconFPR(0.773010453362736960810906610),
new FalconFPR(-0.773010453362736960810906610), new FalconFPR(0.634393284163645498215171613),
new FalconFPR(0.881921264348355029712756864), new FalconFPR(0.471396736825997648556387626),
new FalconFPR(-0.471396736825997648556387626), new FalconFPR(0.881921264348355029712756864),
new FalconFPR(0.290284677254462367636192376), new FalconFPR(0.956940335732208864935797887),
new FalconFPR(-0.956940335732208864935797887), new FalconFPR(0.290284677254462367636192376),
new FalconFPR(0.956940335732208864935797887), new FalconFPR(0.290284677254462367636192376),
new FalconFPR(-0.290284677254462367636192376), new FalconFPR(0.956940335732208864935797887),
new FalconFPR(0.471396736825997648556387626), new FalconFPR(0.881921264348355029712756864),
new FalconFPR(-0.881921264348355029712756864), new FalconFPR(0.471396736825997648556387626),
new FalconFPR(0.773010453362736960810906610), new FalconFPR(0.634393284163645498215171613),
new FalconFPR(-0.634393284163645498215171613), new FalconFPR(0.773010453362736960810906610),
new FalconFPR(0.098017140329560601994195564), new FalconFPR(0.995184726672196886244836953),
new FalconFPR(-0.995184726672196886244836953), new FalconFPR(0.098017140329560601994195564),
new FalconFPR(0.998795456205172392714771605), new FalconFPR(0.049067674327418014254954977),
new FalconFPR(-0.049067674327418014254954977), new FalconFPR(0.998795456205172392714771605),
new FalconFPR(0.671558954847018400625376850), new FalconFPR(0.740951125354959091175616897),
new FalconFPR(-0.740951125354959091175616897), new FalconFPR(0.671558954847018400625376850),
new FalconFPR(0.903989293123443331586200297), new FalconFPR(0.427555093430282094320966857),
new FalconFPR(-0.427555093430282094320966857), new FalconFPR(0.903989293123443331586200297),
new FalconFPR(0.336889853392220050689253213), new FalconFPR(0.941544065183020778412509403),
new FalconFPR(-0.941544065183020778412509403), new FalconFPR(0.336889853392220050689253213),
new FalconFPR(0.970031253194543992603984207), new FalconFPR(0.242980179903263889948274162),
new FalconFPR(-0.242980179903263889948274162), new FalconFPR(0.970031253194543992603984207),
new FalconFPR(0.514102744193221726593693839), new FalconFPR(0.857728610000272069902269984),
new FalconFPR(-0.857728610000272069902269984), new FalconFPR(0.514102744193221726593693839),
new FalconFPR(0.803207531480644909806676513), new FalconFPR(0.595699304492433343467036529),
new FalconFPR(-0.595699304492433343467036529), new FalconFPR(0.803207531480644909806676513),
new FalconFPR(0.146730474455361751658850130), new FalconFPR(0.989176509964780973451673738),
new FalconFPR(-0.989176509964780973451673738), new FalconFPR(0.146730474455361751658850130),
new FalconFPR(0.989176509964780973451673738), new FalconFPR(0.146730474455361751658850130),
new FalconFPR(-0.146730474455361751658850130), new FalconFPR(0.989176509964780973451673738),
new FalconFPR(0.595699304492433343467036529), new FalconFPR(0.803207531480644909806676513),
new FalconFPR(-0.803207531480644909806676513), new FalconFPR(0.595699304492433343467036529),
new FalconFPR(0.857728610000272069902269984), new FalconFPR(0.514102744193221726593693839),
new FalconFPR(-0.514102744193221726593693839), new FalconFPR(0.857728610000272069902269984),
new FalconFPR(0.242980179903263889948274162), new FalconFPR(0.970031253194543992603984207),
new FalconFPR(-0.970031253194543992603984207), new FalconFPR(0.242980179903263889948274162),
new FalconFPR(0.941544065183020778412509403), new FalconFPR(0.336889853392220050689253213),
new FalconFPR(-0.336889853392220050689253213), new FalconFPR(0.941544065183020778412509403),
new FalconFPR(0.427555093430282094320966857), new FalconFPR(0.903989293123443331586200297),
new FalconFPR(-0.903989293123443331586200297), new FalconFPR(0.427555093430282094320966857),
new FalconFPR(0.740951125354959091175616897), new FalconFPR(0.671558954847018400625376850),
new FalconFPR(-0.671558954847018400625376850), new FalconFPR(0.740951125354959091175616897),
new FalconFPR(0.049067674327418014254954977), new FalconFPR(0.998795456205172392714771605),
new FalconFPR(-0.998795456205172392714771605), new FalconFPR(0.049067674327418014254954977),
new FalconFPR(0.999698818696204220115765650), new FalconFPR(0.024541228522912288031734529),
new FalconFPR(-0.024541228522912288031734529), new FalconFPR(0.999698818696204220115765650),
new FalconFPR(0.689540544737066924616730630), new FalconFPR(0.724247082951466920941069243),
new FalconFPR(-0.724247082951466920941069243), new FalconFPR(0.689540544737066924616730630),
new FalconFPR(0.914209755703530654635014829), new FalconFPR(0.405241314004989870908481306),
new FalconFPR(-0.405241314004989870908481306), new FalconFPR(0.914209755703530654635014829),
new FalconFPR(0.359895036534988148775104572), new FalconFPR(0.932992798834738887711660256),
new FalconFPR(-0.932992798834738887711660256), new FalconFPR(0.359895036534988148775104572),
new FalconFPR(0.975702130038528544460395766), new FalconFPR(0.219101240156869797227737547),
new FalconFPR(-0.219101240156869797227737547), new FalconFPR(0.975702130038528544460395766),
new FalconFPR(0.534997619887097210663076905), new FalconFPR(0.844853565249707073259571205),
new FalconFPR(-0.844853565249707073259571205), new FalconFPR(0.534997619887097210663076905),
new FalconFPR(0.817584813151583696504920884), new FalconFPR(0.575808191417845300745972454),
new FalconFPR(-0.575808191417845300745972454), new FalconFPR(0.817584813151583696504920884),
new FalconFPR(0.170961888760301226363642357), new FalconFPR(0.985277642388941244774018433),
new FalconFPR(-0.985277642388941244774018433), new FalconFPR(0.170961888760301226363642357),
new FalconFPR(0.992479534598709998156767252), new FalconFPR(0.122410675199216198498704474),
new FalconFPR(-0.122410675199216198498704474), new FalconFPR(0.992479534598709998156767252),
new FalconFPR(0.615231590580626845484913563), new FalconFPR(0.788346427626606262009164705),
new FalconFPR(-0.788346427626606262009164705), new FalconFPR(0.615231590580626845484913563),
new FalconFPR(0.870086991108711418652292404), new FalconFPR(0.492898192229784036873026689),
new FalconFPR(-0.492898192229784036873026689), new FalconFPR(0.870086991108711418652292404),
new FalconFPR(0.266712757474898386325286515), new FalconFPR(0.963776065795439866686464356),
new FalconFPR(-0.963776065795439866686464356), new FalconFPR(0.266712757474898386325286515),
new FalconFPR(0.949528180593036667195936074), new FalconFPR(0.313681740398891476656478846),
new FalconFPR(-0.313681740398891476656478846), new FalconFPR(0.949528180593036667195936074),
new FalconFPR(0.449611329654606600046294579), new FalconFPR(0.893224301195515320342416447),
new FalconFPR(-0.893224301195515320342416447), new FalconFPR(0.449611329654606600046294579),
new FalconFPR(0.757208846506484547575464054), new FalconFPR(0.653172842953776764084203014),
new FalconFPR(-0.653172842953776764084203014), new FalconFPR(0.757208846506484547575464054),
new FalconFPR(0.073564563599667423529465622), new FalconFPR(0.997290456678690216135597140),
new FalconFPR(-0.997290456678690216135597140), new FalconFPR(0.073564563599667423529465622),
new FalconFPR(0.997290456678690216135597140), new FalconFPR(0.073564563599667423529465622),
new FalconFPR(-0.073564563599667423529465622), new FalconFPR(0.997290456678690216135597140),
new FalconFPR(0.653172842953776764084203014), new FalconFPR(0.757208846506484547575464054),
new FalconFPR(-0.757208846506484547575464054), new FalconFPR(0.653172842953776764084203014),
new FalconFPR(0.893224301195515320342416447), new FalconFPR(0.449611329654606600046294579),
new FalconFPR(-0.449611329654606600046294579), new FalconFPR(0.893224301195515320342416447),
new FalconFPR(0.313681740398891476656478846), new FalconFPR(0.949528180593036667195936074),
new FalconFPR(-0.949528180593036667195936074), new FalconFPR(0.313681740398891476656478846),
new FalconFPR(0.963776065795439866686464356), new FalconFPR(0.266712757474898386325286515),
new FalconFPR(-0.266712757474898386325286515), new FalconFPR(0.963776065795439866686464356),
new FalconFPR(0.492898192229784036873026689), new FalconFPR(0.870086991108711418652292404),
new FalconFPR(-0.870086991108711418652292404), new FalconFPR(0.492898192229784036873026689),
new FalconFPR(0.788346427626606262009164705), new FalconFPR(0.615231590580626845484913563),
new FalconFPR(-0.615231590580626845484913563), new FalconFPR(0.788346427626606262009164705),
new FalconFPR(0.122410675199216198498704474), new FalconFPR(0.992479534598709998156767252),
new FalconFPR(-0.992479534598709998156767252), new FalconFPR(0.122410675199216198498704474),
new FalconFPR(0.985277642388941244774018433), new FalconFPR(0.170961888760301226363642357),
new FalconFPR(-0.170961888760301226363642357), new FalconFPR(0.985277642388941244774018433),
new FalconFPR(0.575808191417845300745972454), new FalconFPR(0.817584813151583696504920884),
new FalconFPR(-0.817584813151583696504920884), new FalconFPR(0.575808191417845300745972454),
new FalconFPR(0.844853565249707073259571205), new FalconFPR(0.534997619887097210663076905),
new FalconFPR(-0.534997619887097210663076905), new FalconFPR(0.844853565249707073259571205),
new FalconFPR(0.219101240156869797227737547), new FalconFPR(0.975702130038528544460395766),
new FalconFPR(-0.975702130038528544460395766), new FalconFPR(0.219101240156869797227737547),
new FalconFPR(0.932992798834738887711660256), new FalconFPR(0.359895036534988148775104572),
new FalconFPR(-0.359895036534988148775104572), new FalconFPR(0.932992798834738887711660256),
new FalconFPR(0.405241314004989870908481306), new FalconFPR(0.914209755703530654635014829),
new FalconFPR(-0.914209755703530654635014829), new FalconFPR(0.405241314004989870908481306),
new FalconFPR(0.724247082951466920941069243), new FalconFPR(0.689540544737066924616730630),
new FalconFPR(-0.689540544737066924616730630), new FalconFPR(0.724247082951466920941069243),
new FalconFPR(0.024541228522912288031734529), new FalconFPR(0.999698818696204220115765650),
new FalconFPR(-0.999698818696204220115765650), new FalconFPR(0.024541228522912288031734529),
new FalconFPR(0.999924701839144540921646491), new FalconFPR(0.012271538285719926079408262),
new FalconFPR(-0.012271538285719926079408262), new FalconFPR(0.999924701839144540921646491),
new FalconFPR(0.698376249408972853554813503), new FalconFPR(0.715730825283818654125532623),
new FalconFPR(-0.715730825283818654125532623), new FalconFPR(0.698376249408972853554813503),
new FalconFPR(0.919113851690057743908477789), new FalconFPR(0.393992040061048108596188661),
new FalconFPR(-0.393992040061048108596188661), new FalconFPR(0.919113851690057743908477789),
new FalconFPR(0.371317193951837543411934967), new FalconFPR(0.928506080473215565937167396),
new FalconFPR(-0.928506080473215565937167396), new FalconFPR(0.371317193951837543411934967),
new FalconFPR(0.978317370719627633106240097), new FalconFPR(0.207111376192218549708116020),
new FalconFPR(-0.207111376192218549708116020), new FalconFPR(0.978317370719627633106240097),
new FalconFPR(0.545324988422046422313987347), new FalconFPR(0.838224705554838043186996856),
new FalconFPR(-0.838224705554838043186996856), new FalconFPR(0.545324988422046422313987347),
new FalconFPR(0.824589302785025264474803737), new FalconFPR(0.565731810783613197389765011),
new FalconFPR(-0.565731810783613197389765011), new FalconFPR(0.824589302785025264474803737),
new FalconFPR(0.183039887955140958516532578), new FalconFPR(0.983105487431216327180301155),
new FalconFPR(-0.983105487431216327180301155), new FalconFPR(0.183039887955140958516532578),
new FalconFPR(0.993906970002356041546922813), new FalconFPR(0.110222207293883058807899140),
new FalconFPR(-0.110222207293883058807899140), new FalconFPR(0.993906970002356041546922813),
new FalconFPR(0.624859488142386377084072816), new FalconFPR(0.780737228572094478301588484),
new FalconFPR(-0.780737228572094478301588484), new FalconFPR(0.624859488142386377084072816),
new FalconFPR(0.876070094195406607095844268), new FalconFPR(0.482183772079122748517344481),
new FalconFPR(-0.482183772079122748517344481), new FalconFPR(0.876070094195406607095844268),
new FalconFPR(0.278519689385053105207848526), new FalconFPR(0.960430519415565811199035138),
new FalconFPR(-0.960430519415565811199035138), new FalconFPR(0.278519689385053105207848526),
new FalconFPR(0.953306040354193836916740383), new FalconFPR(0.302005949319228067003463232),
new FalconFPR(-0.302005949319228067003463232), new FalconFPR(0.953306040354193836916740383),
new FalconFPR(0.460538710958240023633181487), new FalconFPR(0.887639620402853947760181617),
new FalconFPR(-0.887639620402853947760181617), new FalconFPR(0.460538710958240023633181487),
new FalconFPR(0.765167265622458925888815999), new FalconFPR(0.643831542889791465068086063),
new FalconFPR(-0.643831542889791465068086063), new FalconFPR(0.765167265622458925888815999),
new FalconFPR(0.085797312344439890461556332), new FalconFPR(0.996312612182778012627226190),
new FalconFPR(-0.996312612182778012627226190), new FalconFPR(0.085797312344439890461556332),
new FalconFPR(0.998118112900149207125155861), new FalconFPR(0.061320736302208577782614593),
new FalconFPR(-0.061320736302208577782614593), new FalconFPR(0.998118112900149207125155861),
new FalconFPR(0.662415777590171761113069817), new FalconFPR(0.749136394523459325469203257),
new FalconFPR(-0.749136394523459325469203257), new FalconFPR(0.662415777590171761113069817),
new FalconFPR(0.898674465693953843041976744), new FalconFPR(0.438616238538527637647025738),
new FalconFPR(-0.438616238538527637647025738), new FalconFPR(0.898674465693953843041976744),
new FalconFPR(0.325310292162262934135954708), new FalconFPR(0.945607325380521325730945387),
new FalconFPR(-0.945607325380521325730945387), new FalconFPR(0.325310292162262934135954708),
new FalconFPR(0.966976471044852109087220226), new FalconFPR(0.254865659604514571553980779),
new FalconFPR(-0.254865659604514571553980779), new FalconFPR(0.966976471044852109087220226),
new FalconFPR(0.503538383725717558691867071), new FalconFPR(0.863972856121586737918147054),
new FalconFPR(-0.863972856121586737918147054), new FalconFPR(0.503538383725717558691867071),
new FalconFPR(0.795836904608883536262791915), new FalconFPR(0.605511041404325513920626941),
new FalconFPR(-0.605511041404325513920626941), new FalconFPR(0.795836904608883536262791915),
new FalconFPR(0.134580708507126186316358409), new FalconFPR(0.990902635427780025108237011),
new FalconFPR(-0.990902635427780025108237011), new FalconFPR(0.134580708507126186316358409),
new FalconFPR(0.987301418157858382399815802), new FalconFPR(0.158858143333861441684385360),
new FalconFPR(-0.158858143333861441684385360), new FalconFPR(0.987301418157858382399815802),
new FalconFPR(0.585797857456438860328080838), new FalconFPR(0.810457198252594791726703434),
new FalconFPR(-0.810457198252594791726703434), new FalconFPR(0.585797857456438860328080838),
new FalconFPR(0.851355193105265142261290312), new FalconFPR(0.524589682678468906215098464),
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new FalconFPR(0.339776884406826857828825803), new FalconFPR(0.940506070593268323787291309),
new FalconFPR(-0.940506070593268323787291309), new FalconFPR(0.339776884406826857828825803),
new FalconFPR(0.970772140728950302138169611), new FalconFPR(0.240003022448741486568922365),
new FalconFPR(-0.240003022448741486568922365), new FalconFPR(0.970772140728950302138169611),
new FalconFPR(0.516731799017649881508753876), new FalconFPR(0.856147328375194481019630732),
new FalconFPR(-0.856147328375194481019630732), new FalconFPR(0.516731799017649881508753876),
new FalconFPR(0.805031331142963597922659282), new FalconFPR(0.593232295039799808047809426),
new FalconFPR(-0.593232295039799808047809426), new FalconFPR(0.805031331142963597922659282),
new FalconFPR(0.149764534677321517229695737), new FalconFPR(0.988721691960323767604516485),
new FalconFPR(-0.988721691960323767604516485), new FalconFPR(0.149764534677321517229695737),
new FalconFPR(0.989622017463200834623694454), new FalconFPR(0.143695033150294454819773349),
new FalconFPR(-0.143695033150294454819773349), new FalconFPR(0.989622017463200834623694454),
new FalconFPR(0.598160706996342311724958652), new FalconFPR(0.801376171723140219430247777),
new FalconFPR(-0.801376171723140219430247777), new FalconFPR(0.598160706996342311724958652),
new FalconFPR(0.859301818357008404783582139), new FalconFPR(0.511468850437970399504391001),
new FalconFPR(-0.511468850437970399504391001), new FalconFPR(0.859301818357008404783582139),
new FalconFPR(0.245955050335794611599924709), new FalconFPR(0.969281235356548486048290738),
new FalconFPR(-0.969281235356548486048290738), new FalconFPR(0.245955050335794611599924709),
new FalconFPR(0.942573197601446879280758735), new FalconFPR(0.333999651442009404650865481),
new FalconFPR(-0.333999651442009404650865481), new FalconFPR(0.942573197601446879280758735),
new FalconFPR(0.430326481340082633908199031), new FalconFPR(0.902673318237258806751502391),
new FalconFPR(-0.902673318237258806751502391), new FalconFPR(0.430326481340082633908199031),
new FalconFPR(0.743007952135121693517362293), new FalconFPR(0.669282588346636065720696366),
new FalconFPR(-0.669282588346636065720696366), new FalconFPR(0.743007952135121693517362293),
new FalconFPR(0.052131704680283321236358216), new FalconFPR(0.998640218180265222418199049),
new FalconFPR(-0.998640218180265222418199049), new FalconFPR(0.052131704680283321236358216),
new FalconFPR(0.995480755491926941769171600), new FalconFPR(0.094963495329638998938034312),
new FalconFPR(-0.094963495329638998938034312), new FalconFPR(0.995480755491926941769171600),
new FalconFPR(0.636761861236284230413943435), new FalconFPR(0.771060524261813773200605759),
new FalconFPR(-0.771060524261813773200605759), new FalconFPR(0.636761861236284230413943435),
new FalconFPR(0.883363338665731594736308015), new FalconFPR(0.468688822035827933697617870),
new FalconFPR(-0.468688822035827933697617870), new FalconFPR(0.883363338665731594736308015),
new FalconFPR(0.293219162694258650606608599), new FalconFPR(0.956045251349996443270479823),
new FalconFPR(-0.956045251349996443270479823), new FalconFPR(0.293219162694258650606608599),
new FalconFPR(0.957826413027532890321037029), new FalconFPR(0.287347459544729526477331841),
new FalconFPR(-0.287347459544729526477331841), new FalconFPR(0.957826413027532890321037029),
new FalconFPR(0.474100214650550014398580015), new FalconFPR(0.880470889052160770806542929),
new FalconFPR(-0.880470889052160770806542929), new FalconFPR(0.474100214650550014398580015),
new FalconFPR(0.774953106594873878359129282), new FalconFPR(0.632018735939809021909403706),
new FalconFPR(-0.632018735939809021909403706), new FalconFPR(0.774953106594873878359129282),
new FalconFPR(0.101069862754827824987887585), new FalconFPR(0.994879330794805620591166107),
new FalconFPR(-0.994879330794805620591166107), new FalconFPR(0.101069862754827824987887585),
new FalconFPR(0.981379193313754574318224190), new FalconFPR(0.192080397049892441679288205),
new FalconFPR(-0.192080397049892441679288205), new FalconFPR(0.981379193313754574318224190),
new FalconFPR(0.558118531220556115693702964), new FalconFPR(0.829761233794523042469023765),
new FalconFPR(-0.829761233794523042469023765), new FalconFPR(0.558118531220556115693702964),
new FalconFPR(0.833170164701913186439915922), new FalconFPR(0.553016705580027531764226988),
new FalconFPR(-0.553016705580027531764226988), new FalconFPR(0.833170164701913186439915922),
new FalconFPR(0.198098410717953586179324918), new FalconFPR(0.980182135968117392690210009),
new FalconFPR(-0.980182135968117392690210009), new FalconFPR(0.198098410717953586179324918),
new FalconFPR(0.925049240782677590302371869), new FalconFPR(0.379847208924051170576281147),
new FalconFPR(-0.379847208924051170576281147), new FalconFPR(0.925049240782677590302371869),
new FalconFPR(0.385516053843918864075607949), new FalconFPR(0.922701128333878570437264227),
new FalconFPR(-0.922701128333878570437264227), new FalconFPR(0.385516053843918864075607949),
new FalconFPR(0.709272826438865651316533772), new FalconFPR(0.704934080375904908852523758),
new FalconFPR(-0.704934080375904908852523758), new FalconFPR(0.709272826438865651316533772),
new FalconFPR(0.003067956762965976270145365), new FalconFPR(0.999995293809576171511580126),
new FalconFPR(-0.999995293809576171511580126), new FalconFPR(0.003067956762965976270145365)
};
p2_tab = new FalconFPR[]{
new FalconFPR(2.00000000000),
new FalconFPR(1.00000000000),
new FalconFPR(0.50000000000),
new FalconFPR(0.25000000000),
new FalconFPR(0.12500000000),
new FalconFPR(0.06250000000),
new FalconFPR(0.03125000000),
new FalconFPR(0.01562500000),
new FalconFPR(0.00781250000),
new FalconFPR(0.00390625000),
new FalconFPR(0.00195312500)
};
}
FPREngine()
{
this.fpr_q = new FalconFPR(12289.0);
this.fpr_inverse_of_q = new FalconFPR(1.0 / 12289.0);
this.fpr_inv_2sqrsigma0 = new FalconFPR(0.150865048875372721532312163019);
this.fpr_inv_sigma = inv_sigma;
this.fpr_sigma_min = sigma_min;
this.fpr_log2 = new FalconFPR(0.69314718055994530941723212146);
this.fpr_inv_log2 = new FalconFPR(1.4426950408889634073599246810);
this.fpr_bnorm_max = new FalconFPR(16822.4121);
this.fpr_zero = new FalconFPR(0.0);
this.fpr_one = new FalconFPR(1.0);
this.fpr_two = new FalconFPR(2.0);
this.fpr_onehalf = new FalconFPR(0.5);
this.fpr_invsqrt2 = new FalconFPR(0.707106781186547524400844362105);
this.fpr_invsqrt8 = new FalconFPR(0.353553390593273762200422181052);
this.fpr_ptwo31 = new FalconFPR(2147483648.0);
this.fpr_ptwo31m1 = new FalconFPR(2147483647.0);
this.fpr_mtwo31m1 = new FalconFPR(-2147483647.0);
this.fpr_ptwo63m1 = new FalconFPR(9223372036854775807.0);
this.fpr_mtwo63m1 = new FalconFPR(-9223372036854775807.0);
this.fpr_ptwo63 = new FalconFPR(9223372036854775808.0);
this.fpr_gm_tab = gm_tab;
this.fpr_p2_tab = p2_tab;
}
FalconFPR FPR(double v)
{
FalconFPR x = new FalconFPR(v);
return x;
}
FalconFPR fpr_of(long i)
{
return FPR((double)i);
}
final FalconFPR fpr_q;
final FalconFPR fpr_inverse_of_q;
final FalconFPR fpr_inv_2sqrsigma0;
final FalconFPR[] fpr_inv_sigma;
final FalconFPR[] fpr_sigma_min;
final FalconFPR fpr_log2;
final FalconFPR fpr_inv_log2;
final FalconFPR fpr_bnorm_max;
final FalconFPR fpr_zero;
final FalconFPR fpr_one;
final FalconFPR fpr_two;
final FalconFPR fpr_onehalf;
final FalconFPR fpr_invsqrt2;
final FalconFPR fpr_invsqrt8;
final FalconFPR fpr_ptwo31;
final FalconFPR fpr_ptwo31m1;
final FalconFPR fpr_mtwo31m1;
final FalconFPR fpr_ptwo63m1;
final FalconFPR fpr_mtwo63m1;
final FalconFPR fpr_ptwo63;
final FalconFPR[] fpr_gm_tab;
final FalconFPR[] fpr_p2_tab;
long
fpr_rint(FalconFPR x)
{
/*
* We do not want to use llrint() since it might be not
* constant-time.
*
* Suppose that x >= 0. If x >= 2^52, then it is already an
* integer. Otherwise, if x < 2^52, then computing x+2^52 will
* yield a value that will be rounded to the nearest integer
* with exactly the right rules (round-to-nearest-even).
*
* In order to have constant-time processing, we must do the
* computation for both x >= 0 and x < 0 cases, and use a
* cast to an integer to access the sign and select the proper
* value. Such casts also allow us to find out if |x| < 2^52.
*/
long sx, tx, rp, rn, m;
int ub;
sx = (long)(x.v - 1.0);
tx = (long)x.v;
rp = (long)(x.v + 4503599627370496.0) - 4503599627370496l;
rn = (long)(x.v - 4503599627370496.0) + 4503599627370496l;
/*
* If tx >= 2^52 or tx < -2^52, then result is tx.
* Otherwise, if sx >= 0, then result is rp.
* Otherwise, result is rn. We use the fact that when x is
* close to 0 (|x| <= 0.25) then both rp and rn are correct;
* and if x is not close to 0, then trunc(x-1.0) yields the
* appropriate sign.
*/
/*
* Clamp rp to zero if tx < 0.
* Clamp rn to zero if tx >= 0.
*/
m = sx >> 63;
rn &= m;
rp &= ~m;
/*
* Get the 12 upper bits of tx; if they are not all zeros or
* all ones, then tx >= 2^52 or tx < -2^52, and we clamp both
* rp and rn to zero. Otherwise, we clamp tx to zero.
*/
ub = (int)(tx >>> 52);
m = -(long)((((ub + 1) & 0xFFF) - 2) >>> 31);
rp &= m;
rn &= m;
tx &= ~m;
/*
* Only one of tx, rn or rp (at most) can be non-zero at this
* point.
*/
return tx | rn | rp;
}
long fpr_floor(FalconFPR x)
{
long r;
/*
* The cast performs a trunc() (rounding toward 0) and thus is
* wrong by 1 for most negative values. The correction below is
* constant-time as long as the compiler turns the
* floating-point conversion result into a 0/1 integer without a
* conditional branch or another non-constant-time construction.
* This should hold on all modern architectures with an FPU (and
* if it is false on a given arch, then chances are that the FPU
* itself is not constant-time, making the point moot).
*/
r = (long)x.v;
return r - (x.v < (double)r ? 1 : 0);
}
long
fpr_trunc(FalconFPR x)
{
return (long)x.v;
}
FalconFPR
fpr_add(FalconFPR x, FalconFPR y)
{
return FPR(x.v + y.v);
}
FalconFPR
fpr_sub(FalconFPR x, FalconFPR y)
{
return FPR(x.v - y.v);
}
FalconFPR
fpr_neg(FalconFPR x)
{
return FPR(-x.v);
}
FalconFPR
fpr_half(FalconFPR x)
{
return FPR(x.v * 0.5);
}
FalconFPR
fpr_double(FalconFPR x)
{
return FPR(x.v + x.v);
}
FalconFPR
fpr_mul(FalconFPR x, FalconFPR y)
{
return FPR(x.v * y.v);
}
FalconFPR
fpr_sqr(FalconFPR x)
{
return FPR(x.v * x.v);
}
FalconFPR
fpr_inv(FalconFPR x)
{
return FPR(1.0 / x.v);
}
FalconFPR
fpr_div(FalconFPR x, FalconFPR y)
{
return FPR(x.v / y.v);
}
FalconFPR
fpr_sqrt(FalconFPR x)
{
return FPR(Math.sqrt(x.v));
}
boolean
fpr_lt(FalconFPR x, FalconFPR y)
{
return x.v < y.v;
}
long
fpr_expm_p63(FalconFPR x, FalconFPR ccs)
{
/*
* Polynomial approximation of exp(-x) is taken from FACCT:
* https://eprint.iacr.org/2018/1234
* Specifically, values are extracted from the implementation
* referenced from the FACCT article, and available at:
* https://github.com/raykzhao/gaussian
* Tests over more than 24 billions of random inputs in the
* 0..log(2) range have never shown a deviation larger than
* 2^(-50) from the true mathematical value.
*/
/*
* Normal implementation uses Horner's method, which minimizes
* the number of operations.
*/
double d, y;
d = x.v;
y = 0.000000002073772366009083061987;
y = 0.000000025299506379442070029551 - y * d;
y = 0.000000275607356160477811864927 - y * d;
y = 0.000002755586350219122514855659 - y * d;
y = 0.000024801566833585381209939524 - y * d;
y = 0.000198412739277311890541063977 - y * d;
y = 0.001388888894063186997887560103 - y * d;
y = 0.008333333327800835146903501993 - y * d;
y = 0.041666666666110491190622155955 - y * d;
y = 0.166666666666984014666397229121 - y * d;
y = 0.500000000000019206858326015208 - y * d;
y = 0.999999999999994892974086724280 - y * d;
y = 1.000000000000000000000000000000 - y * d;
y *= ccs.v;
return (long)(y * fpr_ptwo63.v);
}
}