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79623b0765
pqcrypto/crypto_sign/falcon-512/avx2/fpr.c
John M. Schanck 79623b0765 Add AVX2 Falcon
2021-03-24 21:02:49 +00:00

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#include "inner.h"
/*
* Floating-point operations.
*
* This file implements the non-inline functions declared in
* fpr.h, as well as the constants for FFT / iFFT.
*
* ==========================(LICENSE BEGIN)============================
*
* Copyright (c) 2017-2019 Falcon Project
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
* ===========================(LICENSE END)=============================
*
* @author Thomas Pornin <thomas.pornin@nccgroup.com>
*/
const fpr fpr_gm_tab[] = {
{0}, {0}, /* unused */
{-0.000000000000000000000000000}, { 1.000000000000000000000000000},
{ 0.707106781186547524400844362}, { 0.707106781186547524400844362},
{-0.707106781186547524400844362}, { 0.707106781186547524400844362},
{ 0.923879532511286756128183189}, { 0.382683432365089771728459984},
{-0.382683432365089771728459984}, { 0.923879532511286756128183189},
{ 0.382683432365089771728459984}, { 0.923879532511286756128183189},
{-0.923879532511286756128183189}, { 0.382683432365089771728459984},
{ 0.980785280403230449126182236}, { 0.195090322016128267848284868},
{-0.195090322016128267848284868}, { 0.980785280403230449126182236},
{ 0.555570233019602224742830814}, { 0.831469612302545237078788378},
{-0.831469612302545237078788378}, { 0.555570233019602224742830814},
{ 0.831469612302545237078788378}, { 0.555570233019602224742830814},
{-0.555570233019602224742830814}, { 0.831469612302545237078788378},
{ 0.195090322016128267848284868}, { 0.980785280403230449126182236},
{-0.980785280403230449126182236}, { 0.195090322016128267848284868},
{ 0.995184726672196886244836953}, { 0.098017140329560601994195564},
{-0.098017140329560601994195564}, { 0.995184726672196886244836953},
{ 0.634393284163645498215171613}, { 0.773010453362736960810906610},
{-0.773010453362736960810906610}, { 0.634393284163645498215171613},
{ 0.881921264348355029712756864}, { 0.471396736825997648556387626},
{-0.471396736825997648556387626}, { 0.881921264348355029712756864},
{ 0.290284677254462367636192376}, { 0.956940335732208864935797887},
{-0.956940335732208864935797887}, { 0.290284677254462367636192376},
{ 0.956940335732208864935797887}, { 0.290284677254462367636192376},
{-0.290284677254462367636192376}, { 0.956940335732208864935797887},
{ 0.471396736825997648556387626}, { 0.881921264348355029712756864},
{-0.881921264348355029712756864}, { 0.471396736825997648556387626},
{ 0.773010453362736960810906610}, { 0.634393284163645498215171613},
{-0.634393284163645498215171613}, { 0.773010453362736960810906610},
{ 0.098017140329560601994195564}, { 0.995184726672196886244836953},
{-0.995184726672196886244836953}, { 0.098017140329560601994195564},
{ 0.998795456205172392714771605}, { 0.049067674327418014254954977},
{-0.049067674327418014254954977}, { 0.998795456205172392714771605},
{ 0.671558954847018400625376850}, { 0.740951125354959091175616897},
{-0.740951125354959091175616897}, { 0.671558954847018400625376850},
{ 0.903989293123443331586200297}, { 0.427555093430282094320966857},
{-0.427555093430282094320966857}, { 0.903989293123443331586200297},
{ 0.336889853392220050689253213}, { 0.941544065183020778412509403},
{-0.941544065183020778412509403}, { 0.336889853392220050689253213},
{ 0.970031253194543992603984207}, { 0.242980179903263889948274162},
{-0.242980179903263889948274162}, { 0.970031253194543992603984207},
{ 0.514102744193221726593693839}, { 0.857728610000272069902269984},
{-0.857728610000272069902269984}, { 0.514102744193221726593693839},
{ 0.803207531480644909806676513}, { 0.595699304492433343467036529},
{-0.595699304492433343467036529}, { 0.803207531480644909806676513},
{ 0.146730474455361751658850130}, { 0.989176509964780973451673738},
{-0.989176509964780973451673738}, { 0.146730474455361751658850130},
{ 0.989176509964780973451673738}, { 0.146730474455361751658850130},
{-0.146730474455361751658850130}, { 0.989176509964780973451673738},
{ 0.595699304492433343467036529}, { 0.803207531480644909806676513},
{-0.803207531480644909806676513}, { 0.595699304492433343467036529},
{ 0.857728610000272069902269984}, { 0.514102744193221726593693839},
{-0.514102744193221726593693839}, { 0.857728610000272069902269984},
{ 0.242980179903263889948274162}, { 0.970031253194543992603984207},
{-0.970031253194543992603984207}, { 0.242980179903263889948274162},
{ 0.941544065183020778412509403}, { 0.336889853392220050689253213},
{-0.336889853392220050689253213}, { 0.941544065183020778412509403},
{ 0.427555093430282094320966857}, { 0.903989293123443331586200297},
{-0.903989293123443331586200297}, { 0.427555093430282094320966857},
{ 0.740951125354959091175616897}, { 0.671558954847018400625376850},
{-0.671558954847018400625376850}, { 0.740951125354959091175616897},
{ 0.049067674327418014254954977}, { 0.998795456205172392714771605},
{-0.998795456205172392714771605}, { 0.049067674327418014254954977},
{ 0.999698818696204220115765650}, { 0.024541228522912288031734529},
{-0.024541228522912288031734529}, { 0.999698818696204220115765650},
{ 0.689540544737066924616730630}, { 0.724247082951466920941069243},
{-0.724247082951466920941069243}, { 0.689540544737066924616730630},
{ 0.914209755703530654635014829}, { 0.405241314004989870908481306},
{-0.405241314004989870908481306}, { 0.914209755703530654635014829},
{ 0.359895036534988148775104572}, { 0.932992798834738887711660256},
{-0.932992798834738887711660256}, { 0.359895036534988148775104572},
{ 0.975702130038528544460395766}, { 0.219101240156869797227737547},
{-0.219101240156869797227737547}, { 0.975702130038528544460395766},
{ 0.534997619887097210663076905}, { 0.844853565249707073259571205},
{-0.844853565249707073259571205}, { 0.534997619887097210663076905},
{ 0.817584813151583696504920884}, { 0.575808191417845300745972454},
{-0.575808191417845300745972454}, { 0.817584813151583696504920884},
{ 0.170961888760301226363642357}, { 0.985277642388941244774018433},
{-0.985277642388941244774018433}, { 0.170961888760301226363642357},
{ 0.992479534598709998156767252}, { 0.122410675199216198498704474},
{-0.122410675199216198498704474}, { 0.992479534598709998156767252},
{ 0.615231590580626845484913563}, { 0.788346427626606262009164705},
{-0.788346427626606262009164705}, { 0.615231590580626845484913563},
{ 0.870086991108711418652292404}, { 0.492898192229784036873026689},
{-0.492898192229784036873026689}, { 0.870086991108711418652292404},
{ 0.266712757474898386325286515}, { 0.963776065795439866686464356},
{-0.963776065795439866686464356}, { 0.266712757474898386325286515},
{ 0.949528180593036667195936074}, { 0.313681740398891476656478846},
{-0.313681740398891476656478846}, { 0.949528180593036667195936074},
{ 0.449611329654606600046294579}, { 0.893224301195515320342416447},
{-0.893224301195515320342416447}, { 0.449611329654606600046294579},
{ 0.757208846506484547575464054}, { 0.653172842953776764084203014},
{-0.653172842953776764084203014}, { 0.757208846506484547575464054},
{ 0.073564563599667423529465622}, { 0.997290456678690216135597140},
{-0.997290456678690216135597140}, { 0.073564563599667423529465622},
{ 0.997290456678690216135597140}, { 0.073564563599667423529465622},
{-0.073564563599667423529465622}, { 0.997290456678690216135597140},
{ 0.653172842953776764084203014}, { 0.757208846506484547575464054},
{-0.757208846506484547575464054}, { 0.653172842953776764084203014},
{ 0.893224301195515320342416447}, { 0.449611329654606600046294579},
{-0.449611329654606600046294579}, { 0.893224301195515320342416447},
{ 0.313681740398891476656478846}, { 0.949528180593036667195936074},
{-0.949528180593036667195936074}, { 0.313681740398891476656478846},
{ 0.963776065795439866686464356}, { 0.266712757474898386325286515},
{-0.266712757474898386325286515}, { 0.963776065795439866686464356},
{ 0.492898192229784036873026689}, { 0.870086991108711418652292404},
{-0.870086991108711418652292404}, { 0.492898192229784036873026689},
{ 0.788346427626606262009164705}, { 0.615231590580626845484913563},
{-0.615231590580626845484913563}, { 0.788346427626606262009164705},
{ 0.122410675199216198498704474}, { 0.992479534598709998156767252},
{-0.992479534598709998156767252}, { 0.122410675199216198498704474},
{ 0.985277642388941244774018433}, { 0.170961888760301226363642357},
{-0.170961888760301226363642357}, { 0.985277642388941244774018433},
{ 0.575808191417845300745972454}, { 0.817584813151583696504920884},
{-0.817584813151583696504920884}, { 0.575808191417845300745972454},
{ 0.844853565249707073259571205}, { 0.534997619887097210663076905},
{-0.534997619887097210663076905}, { 0.844853565249707073259571205},
{ 0.219101240156869797227737547}, { 0.975702130038528544460395766},
{-0.975702130038528544460395766}, { 0.219101240156869797227737547},
{ 0.932992798834738887711660256}, { 0.359895036534988148775104572},
{-0.359895036534988148775104572}, { 0.932992798834738887711660256},
{ 0.405241314004989870908481306}, { 0.914209755703530654635014829},
{-0.914209755703530654635014829}, { 0.405241314004989870908481306},
{ 0.724247082951466920941069243}, { 0.689540544737066924616730630},
{-0.689540544737066924616730630}, { 0.724247082951466920941069243},
{ 0.024541228522912288031734529}, { 0.999698818696204220115765650},
{-0.999698818696204220115765650}, { 0.024541228522912288031734529},
{ 0.999924701839144540921646491}, { 0.012271538285719926079408262},
{-0.012271538285719926079408262}, { 0.999924701839144540921646491},
{ 0.698376249408972853554813503}, { 0.715730825283818654125532623},
{-0.715730825283818654125532623}, { 0.698376249408972853554813503},
{ 0.919113851690057743908477789}, { 0.393992040061048108596188661},
{-0.393992040061048108596188661}, { 0.919113851690057743908477789},
{ 0.371317193951837543411934967}, { 0.928506080473215565937167396},
{-0.928506080473215565937167396}, { 0.371317193951837543411934967},
{ 0.978317370719627633106240097}, { 0.207111376192218549708116020},
{-0.207111376192218549708116020}, { 0.978317370719627633106240097},
{ 0.545324988422046422313987347}, { 0.838224705554838043186996856},
{-0.838224705554838043186996856}, { 0.545324988422046422313987347},
{ 0.824589302785025264474803737}, { 0.565731810783613197389765011},
{-0.565731810783613197389765011}, { 0.824589302785025264474803737},
{ 0.183039887955140958516532578}, { 0.983105487431216327180301155},
{-0.983105487431216327180301155}, { 0.183039887955140958516532578},
{ 0.993906970002356041546922813}, { 0.110222207293883058807899140},
{-0.110222207293883058807899140}, { 0.993906970002356041546922813},
{ 0.624859488142386377084072816}, { 0.780737228572094478301588484},
{-0.780737228572094478301588484}, { 0.624859488142386377084072816},
{ 0.876070094195406607095844268}, { 0.482183772079122748517344481},
{-0.482183772079122748517344481}, { 0.876070094195406607095844268},
{ 0.278519689385053105207848526}, { 0.960430519415565811199035138},
{-0.960430519415565811199035138}, { 0.278519689385053105207848526},
{ 0.953306040354193836916740383}, { 0.302005949319228067003463232},
{-0.302005949319228067003463232}, { 0.953306040354193836916740383},
{ 0.460538710958240023633181487}, { 0.887639620402853947760181617},
{-0.887639620402853947760181617}, { 0.460538710958240023633181487},
{ 0.765167265622458925888815999}, { 0.643831542889791465068086063},
{-0.643831542889791465068086063}, { 0.765167265622458925888815999},
{ 0.085797312344439890461556332}, { 0.996312612182778012627226190},
{-0.996312612182778012627226190}, { 0.085797312344439890461556332},
{ 0.998118112900149207125155861}, { 0.061320736302208577782614593},
{-0.061320736302208577782614593}, { 0.998118112900149207125155861},
{ 0.662415777590171761113069817}, { 0.749136394523459325469203257},
{-0.749136394523459325469203257}, { 0.662415777590171761113069817},
{ 0.898674465693953843041976744}, { 0.438616238538527637647025738},
{-0.438616238538527637647025738}, { 0.898674465693953843041976744},
{ 0.325310292162262934135954708}, { 0.945607325380521325730945387},
{-0.945607325380521325730945387}, { 0.325310292162262934135954708},
{ 0.966976471044852109087220226}, { 0.254865659604514571553980779},
{-0.254865659604514571553980779}, { 0.966976471044852109087220226},
{ 0.503538383725717558691867071}, { 0.863972856121586737918147054},
{-0.863972856121586737918147054}, { 0.503538383725717558691867071},
{ 0.795836904608883536262791915}, { 0.605511041404325513920626941},
{-0.605511041404325513920626941}, { 0.795836904608883536262791915},
{ 0.134580708507126186316358409}, { 0.990902635427780025108237011},
{-0.990902635427780025108237011}, { 0.134580708507126186316358409},
{ 0.987301418157858382399815802}, { 0.158858143333861441684385360},
{-0.158858143333861441684385360}, { 0.987301418157858382399815802},
{ 0.585797857456438860328080838}, { 0.810457198252594791726703434},
{-0.810457198252594791726703434}, { 0.585797857456438860328080838},
{ 0.851355193105265142261290312}, { 0.524589682678468906215098464},
{-0.524589682678468906215098464}, { 0.851355193105265142261290312},
{ 0.231058108280671119643236018}, { 0.972939952205560145467720114},
{-0.972939952205560145467720114}, { 0.231058108280671119643236018},
{ 0.937339011912574923201899593}, { 0.348418680249434568419308588},
{-0.348418680249434568419308588}, { 0.937339011912574923201899593},
{ 0.416429560097637182562598911}, { 0.909167983090522376563884788},
{-0.909167983090522376563884788}, { 0.416429560097637182562598911},
{ 0.732654271672412834615546649}, { 0.680600997795453050594430464},
{-0.680600997795453050594430464}, { 0.732654271672412834615546649},
{ 0.036807222941358832324332691}, { 0.999322384588349500896221011},
{-0.999322384588349500896221011}, { 0.036807222941358832324332691},
{ 0.999322384588349500896221011}, { 0.036807222941358832324332691},
{-0.036807222941358832324332691}, { 0.999322384588349500896221011},
{ 0.680600997795453050594430464}, { 0.732654271672412834615546649},
{-0.732654271672412834615546649}, { 0.680600997795453050594430464},
{ 0.909167983090522376563884788}, { 0.416429560097637182562598911},
{-0.416429560097637182562598911}, { 0.909167983090522376563884788},
{ 0.348418680249434568419308588}, { 0.937339011912574923201899593},
{-0.937339011912574923201899593}, { 0.348418680249434568419308588},
{ 0.972939952205560145467720114}, { 0.231058108280671119643236018},
{-0.231058108280671119643236018}, { 0.972939952205560145467720114},
{ 0.524589682678468906215098464}, { 0.851355193105265142261290312},
{-0.851355193105265142261290312}, { 0.524589682678468906215098464},
{ 0.810457198252594791726703434}, { 0.585797857456438860328080838},
{-0.585797857456438860328080838}, { 0.810457198252594791726703434},
{ 0.158858143333861441684385360}, { 0.987301418157858382399815802},
{-0.987301418157858382399815802}, { 0.158858143333861441684385360},
{ 0.990902635427780025108237011}, { 0.134580708507126186316358409},
{-0.134580708507126186316358409}, { 0.990902635427780025108237011},
{ 0.605511041404325513920626941}, { 0.795836904608883536262791915},
{-0.795836904608883536262791915}, { 0.605511041404325513920626941},
{ 0.863972856121586737918147054}, { 0.503538383725717558691867071},
{-0.503538383725717558691867071}, { 0.863972856121586737918147054},
{ 0.254865659604514571553980779}, { 0.966976471044852109087220226},
{-0.966976471044852109087220226}, { 0.254865659604514571553980779},
{ 0.945607325380521325730945387}, { 0.325310292162262934135954708},
{-0.325310292162262934135954708}, { 0.945607325380521325730945387},
{ 0.438616238538527637647025738}, { 0.898674465693953843041976744},
{-0.898674465693953843041976744}, { 0.438616238538527637647025738},
{ 0.749136394523459325469203257}, { 0.662415777590171761113069817},
{-0.662415777590171761113069817}, { 0.749136394523459325469203257},
{ 0.061320736302208577782614593}, { 0.998118112900149207125155861},
{-0.998118112900149207125155861}, { 0.061320736302208577782614593},
{ 0.996312612182778012627226190}, { 0.085797312344439890461556332},
{-0.085797312344439890461556332}, { 0.996312612182778012627226190},
{ 0.643831542889791465068086063}, { 0.765167265622458925888815999},
{-0.765167265622458925888815999}, { 0.643831542889791465068086063},
{ 0.887639620402853947760181617}, { 0.460538710958240023633181487},
{-0.460538710958240023633181487}, { 0.887639620402853947760181617},
{ 0.302005949319228067003463232}, { 0.953306040354193836916740383},
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{ 0.339776884406826857828825803}, { 0.940506070593268323787291309},
{-0.940506070593268323787291309}, { 0.339776884406826857828825803},
{ 0.970772140728950302138169611}, { 0.240003022448741486568922365},
{-0.240003022448741486568922365}, { 0.970772140728950302138169611},
{ 0.516731799017649881508753876}, { 0.856147328375194481019630732},
{-0.856147328375194481019630732}, { 0.516731799017649881508753876},
{ 0.805031331142963597922659282}, { 0.593232295039799808047809426},
{-0.593232295039799808047809426}, { 0.805031331142963597922659282},
{ 0.149764534677321517229695737}, { 0.988721691960323767604516485},
{-0.988721691960323767604516485}, { 0.149764534677321517229695737},
{ 0.989622017463200834623694454}, { 0.143695033150294454819773349},
{-0.143695033150294454819773349}, { 0.989622017463200834623694454},
{ 0.598160706996342311724958652}, { 0.801376171723140219430247777},
{-0.801376171723140219430247777}, { 0.598160706996342311724958652},
{ 0.859301818357008404783582139}, { 0.511468850437970399504391001},
{-0.511468850437970399504391001}, { 0.859301818357008404783582139},
{ 0.245955050335794611599924709}, { 0.969281235356548486048290738},
{-0.969281235356548486048290738}, { 0.245955050335794611599924709},
{ 0.942573197601446879280758735}, { 0.333999651442009404650865481},
{-0.333999651442009404650865481}, { 0.942573197601446879280758735},
{ 0.430326481340082633908199031}, { 0.902673318237258806751502391},
{-0.902673318237258806751502391}, { 0.430326481340082633908199031},
{ 0.743007952135121693517362293}, { 0.669282588346636065720696366},
{-0.669282588346636065720696366}, { 0.743007952135121693517362293},
{ 0.052131704680283321236358216}, { 0.998640218180265222418199049},
{-0.998640218180265222418199049}, { 0.052131704680283321236358216},
{ 0.995480755491926941769171600}, { 0.094963495329638998938034312},
{-0.094963495329638998938034312}, { 0.995480755491926941769171600},
{ 0.636761861236284230413943435}, { 0.771060524261813773200605759},
{-0.771060524261813773200605759}, { 0.636761861236284230413943435},
{ 0.883363338665731594736308015}, { 0.468688822035827933697617870},
{-0.468688822035827933697617870}, { 0.883363338665731594736308015},
{ 0.293219162694258650606608599}, { 0.956045251349996443270479823},
{-0.956045251349996443270479823}, { 0.293219162694258650606608599},
{ 0.957826413027532890321037029}, { 0.287347459544729526477331841},
{-0.287347459544729526477331841}, { 0.957826413027532890321037029},
{ 0.474100214650550014398580015}, { 0.880470889052160770806542929},
{-0.880470889052160770806542929}, { 0.474100214650550014398580015},
{ 0.774953106594873878359129282}, { 0.632018735939809021909403706},
{-0.632018735939809021909403706}, { 0.774953106594873878359129282},
{ 0.101069862754827824987887585}, { 0.994879330794805620591166107},
{-0.994879330794805620591166107}, { 0.101069862754827824987887585},
{ 0.981379193313754574318224190}, { 0.192080397049892441679288205},
{-0.192080397049892441679288205}, { 0.981379193313754574318224190},
{ 0.558118531220556115693702964}, { 0.829761233794523042469023765},
{-0.829761233794523042469023765}, { 0.558118531220556115693702964},
{ 0.833170164701913186439915922}, { 0.553016705580027531764226988},
{-0.553016705580027531764226988}, { 0.833170164701913186439915922},
{ 0.198098410717953586179324918}, { 0.980182135968117392690210009},
{-0.980182135968117392690210009}, { 0.198098410717953586179324918},
{ 0.925049240782677590302371869}, { 0.379847208924051170576281147},
{-0.379847208924051170576281147}, { 0.925049240782677590302371869},
{ 0.385516053843918864075607949}, { 0.922701128333878570437264227},
{-0.922701128333878570437264227}, { 0.385516053843918864075607949},
{ 0.709272826438865651316533772}, { 0.704934080375904908852523758},
{-0.704934080375904908852523758}, { 0.709272826438865651316533772},
{ 0.003067956762965976270145365}, { 0.999995293809576171511580126},
{-0.999995293809576171511580126}, { 0.003067956762965976270145365}
};
const fpr fpr_p2_tab[] = {
{ 2.00000000000 },
{ 1.00000000000 },
{ 0.50000000000 },
{ 0.25000000000 },
{ 0.12500000000 },
{ 0.06250000000 },
{ 0.03125000000 },
{ 0.01562500000 },
{ 0.00781250000 },
{ 0.00390625000 },
{ 0.00195312500 }
};
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