-----------------------------------------------------------------------
-- package pc_2_coeff_22, coefficients for a Predictor-Corrector integrator
-- Copyright (C) 2008-2009 Jonathan S. Parker.
--
-- This program is free software: you can redistribute it and/or modify
-- it under the terms of the GNU General Public License as published by
-- the Free Software Foundation, either version 3 of the License, or
-- (at your option) any later version.
--
-- This program is distributed in the hope that it will be useful,
-- but WITHOUT ANY WARRANTY; without even the implied warranty of
-- MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-- GNU General Public License for more details.
-- You should have received a copy of the GNU General Public License
-- along with this program.  If not, see  http://www.gnu.org/licenses/
--
-- As a special exception, if other files instantiate generics from
-- this unit, or you link this unit with other files to produce an
-- executable, this  unit  does not  by itself cause  the resulting
-- executable to be covered by the GNU General Public License. This
-- exception does not however invalidate any other reasons why the
-- executable file  might be covered by the  GNU Public License.
-----------------------------------------------------------------------
-- package pc_2_coeff_22

generic

   type Real is digits <>;

package pc_2_coeff_22 is

   subtype PC_Rule_Range  is Integer range 0..31;
   type Integration_Rule  is array(PC_Rule_Range) of Real;

   Starting_Id_of_First_Deriv_of_Y : constant PC_Rule_Range := 15;
   -- Center_Integration Rule, applied to (d/dt)**2 Y, takes a dY/dt here, and
   -- Integrates it one indice forward.

   Extrap_Factor: constant Real := 1.0 / 24.0; -- val unknown

   Corrector_33_22 : constant Integration_Rule :=
   (
   -8.02130559997354078604776522542254439E-4,
    1.24416532870088974691741276214884268E-2,
   -8.64795984660665687642672166948211787E-2,
    3.50230302101274679029708692614152597E-1,
   -8.91121460953578667337715179019697046E-1,
    1.39383153917014648240732079853746142E+0,
   -1.07121283818712541646971756034689810E+0,
   -2.97295767060760759428837790575625762E-1,
    1.28052482910646884772471445763110385E+0,
   -3.48796383077358912539756432632846449E-1,
   -1.18323146225282708847281583111056865E+0,
    6.13830360683718379636023405051540400E-1,
    1.15669753037498753526808006354467904E+0,
   -6.94338273293159923319315200784758205E-1,
   -1.25077139904584256785139807653322816E+0,
    7.20794822429374825729635224538098316E-1,
    1.77492750390194010614093059728166958E+0,
    3.48406301508706280013183366668745917E-1,
   -3.24702653757985544407247498269540941E-1,
    1.55113657266486316345543277158075854E+0,
    2.51118592351726418774359026068146849E+0,
    3.82957536377735794971423254482703827E-1,
   -6.54923221588828602513601179436160298E-1,
    1.98098310154670126300578248795171698E+0,
    2.62677613787930934327036702584321002E+0,
   -8.86789566789142290186373972323935862E-1,
    2.85598769943888482178532669984860663E-1,
    4.02778278621156389145728011748586155E+0,
   -2.15859907174040020406160913348832844E+0,
    2.94403131132369272781778743704178050E+0,
    2.00939488060088412087622634816136813E-1,
    1.13310419806709432866152258587289993E+0
   );

   Final_Step_Corrector_33_22 : constant Real
            :=  5.28831586172462713631478685086144395E-2;

   Predictor_31_22 : constant Integration_Rule :=
   (
    0.0,
    3.82206142445544963446204148715951607E-2,
   -6.33908224331091016776700383111987143E-1,
    4.77108082172046540302262546600367877E+0,
   -2.13112230306056104385071748550271682E+1,
    6.16394218004587635365556288368891905E+1,
   -1.16455265845403402132194278236324202E+2,
    1.31160078589256480618203936959714671E+2,
   -4.73620760128097778046470502754138483E+1,
   -8.61155833650963992491864075194045219E+1,
    1.09596202456069853887869187577271935E+2,
    2.70006891539818698623550090779730573E+1,
   -1.23689026778934313461788121734000576E+2,
    1.26308792943455875969362146348904466E+1,
    1.25351440983592524456909109664479950E+2,
   -3.90915067214200967699893349056174838E+1,
   -1.25005696132419709068005825586513917E+2,
    6.31400058836348955981727456733231437E+1,
    1.25202212204700030730203205988430657E+2,
   -9.01202664128768808476121572162738365E+1,
   -1.13346070602251991153852098206722707E+2,
    1.35832428576795315596340908178178692E+2,
    7.65648954748416679820099605596069319E+1,
   -1.90778807698391251633999872762198544E+2,
    4.29249448929317005301844046601429694E+1,
    1.90302308174625292773031958813598645E+2,
   -2.76219723414219806259983408912758259E+2,
    2.10878867270091505775711508404456506E+2,
   -1.02199587368891636464946651890028622E+2,
    3.55597890257171711903655577067406769E+1,
   -6.79799476949725817083394168801447862E+0,
    2.03327116014154443810644155483740520E+0
    );

   Center_Integration_32_22 : constant Integration_Rule :=
   (
   -5.48186298516234652810704051430422655E-6,
    9.83867415088779031208187158666710319E-5,
   -8.07566491514156651234056438130100106E-4,
    3.97340757417976466081704231342063697E-3,
   -1.28356892096129410337836800376618841E-2,
    2.76864991077874453604989378001785406E-2,
   -3.73245825355348862199480292460505598E-2,
    2.12653218023217359291463822190892211E-2,
    2.13745306335366393296921989209611924E-2,
   -4.56656788294881115637614729100805322E-2,
    3.89437307673685355200946981995831816E-3,
    6.22684247056539251232690828593738376E-2,
   -3.61385003611128933128201417801336908E-2,
   -9.55657510587708441101932722470146491E-2,
    1.33596784912141525960540060966517392E-1,
    4.54185521795152227419174766084219910E-1,
    4.54185521795152227419174766084219910E-1,
    1.33596784912141525960540060966517392E-1,
   -9.55657510587708441101932722470146491E-2,
   -3.61385003611128933128201417801336908E-2,
    6.22684247056539251232690828593738376E-2,
    3.89437307673685355200946981995831816E-3,
   -4.56656788294881115637614729100805322E-2,
    2.13745306335366393296921989209611924E-2,
    2.12653218023217359291463822190892211E-2,
   -3.73245825355348862199480292460505598E-2,
    2.76864991077874453604989378001785406E-2,
   -1.28356892096129410337836800376618841E-2,
    3.97340757417976466081704231342063697E-3,
   -8.07566491514156651234056438130100106E-4,
    9.83867415088779031208187158666710319E-5,
   -5.48186298516234652810704051430422655E-6
   );

   Center_to_End_Integration_32_22 : constant Integration_Rule :=
   (
   -2.46055400745919258120729405349163691E-3,
    3.94937734266237896046990985820173913E-2,
   -2.85924604814419907317339235057302237E-1,
    1.21775236041835015679281022068507655E+0,
   -3.31119345468907190517628700742888269E+0,
    5.72250882622795112186390828443613906E+0,
   -5.45219585821552065525673442095904352E+0,
    4.67487319274695445937703915277492695E-1,
    5.04181007527642399830645261263436520E+0,
   -3.55919391785093453217583112024140353E+0,
   -3.53127580678341307884535450947182606E+0,
    4.78039107137706694005293349536141932E+0,
    2.58127452529930794024644881912956886E+0,
   -5.38383054354341648182107088309022155E+0,
   -2.14665605885624873975943985055075865E+0,
    6.20637871667093544879506276387734096E+0,
    3.05624946842682355808916099018747109E+0,
   -5.09128384721184624337245342432563704E+0,
   -9.81525574395439526528573186007045599E-1,
    7.83552753870215262539576158282298399E+0,
    2.35174419853373730752706320570413064E+0,
   -6.89285619244306859389417799474804191E+0,
    1.68408438510945988767883644031839272E+0,
    9.80602637995232916495184306214695197E+0,
   -4.76910099297560210294927249411766282E+0,
   -5.10257080894008187297314868283199883E+0,
    1.47380098655089154766482408672545751E+1,
   -1.15093206885050787659302691253911179E+1,
    8.20228332093864178792515819652974703E+0,
   -1.94051634824961325307374327575866262E+0,
    1.97652535686240736364681749381366289E+0,
    2.52358069475392838192001455271761107E-1
   );

   Center_to_End_Integration
                        : Integration_Rule renames Center_to_End_Integration_32_22;

   Predictor_Rule       : Integration_Rule renames Predictor_31_22;

   Corrector_Rule       : Integration_Rule renames Corrector_33_22;

   Center_Integration   : Integration_Rule renames Center_Integration_32_22;

   Final_Step_Corrector : Real renames Final_Step_Corrector_33_22;

end pc_2_coeff_22;