#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 */ 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}, { 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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 } };