(*

 * Hedgewars, a free turn based strategy game

 * Copyright (c) 2004-2011 Andrey Korotaev <unC0Rr@gmail.com>

 *

 * 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; version 2 of the License

 *

 * 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, write to the Free Software

 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA

 *)

{$INCLUDE "options.inc"}

unit uFloat;

(*

 * This unit provides a custom data type, hwFloat.

 *

 * hwFloat represents a floating point number - the value and operations

 * of this numbers are independent from the hardware architecture

 * the game runs on.

 *

 * This is important for calculations that affect the course of the game

 * and would lead to different results if based on a hardware dependent

 * data type.

 *

 * Note: Not all comparisons are implemented.

 *

 * Note: Below you'll find a list of hwFloat constants:

 *       E.g. _1 is an hwFloat with value 1.0, and -_0_9 is -0.9

 *       Use and extend the list if needed, rather than using int2hwFloat()

 *       with integer constants.

 *)

interface

{$IFDEF FPC}

{$IFDEF ENDIAN_LITTLE}

type hwFloat = record

               isNegative: boolean;

               case byte of

               0: (Frac, Round: Longword);

               1: (QWordValue : QWord);

               end;

{$ELSE}

type hwFloat = record

               isNegative: boolean;

               case byte of

               0: (Round, Frac: Longword);

               1: (QWordValue : QWord);

               end;

{$ENDIF}

// Returns an hwFloat that represents the value of integer parameter i

function int2hwFloat (const i: LongInt) : hwFloat; inline;

function hwFloat2Float (const i: hwFloat) : extended; inline;

// The implemented operators

operator + (const z1, z2: hwFloat) z : hwFloat; inline;

operator - (const z1, z2: hwFloat) z : hwFloat; inline;

operator - (const z1: hwFloat) z : hwFloat; inline;

operator * (const z1, z2: hwFloat) z : hwFloat; inline;

operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat; inline;

operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat; inline;

operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat; inline;

operator < (const z1, z2: hwFloat) b : boolean; inline;

operator > (const z1, z2: hwFloat) b : boolean; inline;

// Various functions for hwFloat (some are inlined in the resulting code for better performance)

function cstr(const z: hwFloat): shortstring; // Returns a shortstring representations of the hwFloat.

function hwRound(const t: hwFloat): LongInt; inline; // Does NOT really round but returns the integer representation of the hwFloat without fractional digits. (-_0_9 -> -0, _1_5 -> _1)

function hwAbs(const t: hwFloat): hwFloat; inline; // Returns the value of t with positive sign.

function hwSqr(const t: hwFloat): hwFloat; inline; // Returns the square value of parameter t.

function hwSqrt(const t: hwFloat): hwFloat; inline; // Returns the the positive square root of parameter t.

function Distance(const dx, dy: hwFloat): hwFloat; // Returns the distance between two points in 2-dimensional space, of which the parameters are the horizontal and vertical distance.

function DistanceI(const dx, dy: LongInt): hwFloat; // Same as above for integer parameters.

function AngleSin(const Angle: Longword): hwFloat;

function AngleCos(const Angle: Longword): hwFloat;

function SignAs(const num, signum: hwFloat): hwFloat; inline; // Returns an hwFloat with the value of parameter num and the sign of signum.

function hwSign(r: hwFloat): LongInt; inline; // Returns an integer with value 1 and sign of parameter r.

{$IFDEF FPC}

{$J-}

{$ENDIF}

{$WARNINGS OFF}

// some hwFloat constants

const  _1div1024: hwFloat = (isNegative: false; QWordValue:     4194304);

      _1div10000: hwFloat = (isNegative: false; QWordValue:      429496);

      _1div50000: hwFloat = (isNegative: false; QWordValue:       85899);

     _1div100000: hwFloat = (isNegative: false; QWordValue:       42950);

          _1div3: hwFloat = (isNegative: false; QWordValue:  1431655766);

            hwPi: hwFloat = (isNegative: false; QWordValue: 13493037704);

       _0_000004: hwFloat = (isNegative: false; QWordValue:       17179);

       _0_000064: hwFloat = (isNegative: false; QWordValue:      274878);

         _0_0002: hwFloat = (isNegative: false; QWordValue:      858993);

         _0_0005: hwFloat = (isNegative: false; QWordValue:     2147484);

          _0_001: hwFloat = (isNegative: false; QWordValue:     4294967);

          _0_003: hwFloat = (isNegative: false; QWordValue:    12884902);

          _0_004: hwFloat = (isNegative: false; QWordValue:    17179869);

          _0_005: hwFloat = (isNegative: false; QWordValue:    21474836);

          _0_008: hwFloat = (isNegative: false; QWordValue:    34359738);

           _0_01: hwFloat = (isNegative: false; QWordValue:    42949673);

           _0_02: hwFloat = (isNegative: false; QWordValue:    85899345);

           _0_03: hwFloat = (isNegative: false; QWordValue:   128849018);

           _0_08: hwFloat = (isNegative: false; QWordValue:   343597383);

            _0_1: hwFloat = (isNegative: false; QWordValue:   429496730);

           _0_15: hwFloat = (isNegative: false; QWordValue:   644245094);

            _0_2: hwFloat = (isNegative: false; QWordValue:   858993459);

           _0_25: hwFloat = (isNegative: false; QWordValue:  1073741824);

            _0_3: hwFloat = (isNegative: false; QWordValue:  1288490189);

           _0_35: hwFloat = (isNegative: false; QWordValue:  1503238553);

          _0_375: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3 div 8);

           _0_39: hwFloat = (isNegative: false; QWordValue:  1675037245);

            _0_4: hwFloat = (isNegative: false; QWordValue:  1717986918);

           _0_45: hwFloat = (isNegative: false; QWordValue:  1932735283);

            _0_5: hwFloat = (isNegative: false; QWordValue:  2147483648);

           _0_55: hwFloat = (isNegative: false; QWordValue:  2362232012);

            _0_6: hwFloat = (isNegative: false; QWordValue:  2576980377);

           _0_64: hwFloat = (isNegative: false; QWordValue:  2748779064);

            _0_7: hwFloat = (isNegative: false; QWordValue:  3006477107);

            _0_8: hwFloat = (isNegative: false; QWordValue:  3435973837);

           _0_84: hwFloat = (isNegative: false; QWordValue:  3607772528);

           _0_87: hwFloat = (isNegative: false; QWordValue:  3736621547);

            _0_9: hwFloat = (isNegative: false; QWordValue:  3865470566);

           _0_93: hwFloat = (isNegative: false; QWordValue:  3994319585);

           _0_96: hwFloat = (isNegative: false; QWordValue:  4123168604);

          _0_995: hwFloat = (isNegative: false; QWordValue:  4273492459);

          _0_999: hwFloat = (isNegative: false; QWordValue:  4290672328);

              _0: hwFloat = (isNegative: false; QWordValue:           0);

              _1: hwFloat = (isNegative: false; QWordValue:  4294967296);

            _1_5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3 div 2);

            _1_9: hwFloat = (isNegative: false; QWordValue:  8160437862);

              _2: hwFloat = (isNegative: false; QWordValue:  4294967296 * 2);

              _3: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3);

              _4: hwFloat = (isNegative: false; QWordValue:  4294967296 * 4);

              _5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 5);

              _6: hwFloat = (isNegative: false; QWordValue:  4294967296 * 6);

             _10: hwFloat = (isNegative: false; QWordValue:  4294967296 * 10);

             _12: hwFloat = (isNegative: false; QWordValue:  4294967296 * 12);

             _16: hwFloat = (isNegative: false; QWordValue:  4294967296 * 16);

             _19: hwFloat = (isNegative: false; QWordValue:  4294967296 * 19);

             _20: hwFloat = (isNegative: false; QWordValue:  4294967296 * 20);

             _25: hwFloat = (isNegative: false; QWordValue:  4294967296 * 25);

             _30: hwFloat = (isNegative: false; QWordValue:  4294967296 * 30);

             _40: hwFloat = (isNegative: false; QWordValue:  4294967296 * 40);

             _50: hwFloat = (isNegative: false; QWordValue:  4294967296 * 50);

             _70: hwFloat = (isNegative: false; QWordValue:  4294967296 * 70);

            _128: hwFloat = (isNegative: false; QWordValue:  4294967296 * 128);

            _256: hwFloat = (isNegative: false; QWordValue:  4294967296 * 256);

            _300: hwFloat = (isNegative: false; QWordValue:  4294967296 * 300);

            _450: hwFloat = (isNegative: false; QWordValue:  4294967296 * 450);

           _1024: hwFloat = (isNegative: false; QWordValue:  4294967296 * 1024);

           _2048: hwFloat = (isNegative: false; QWordValue:  4294967296 * 2048);

           _4096: hwFloat = (isNegative: false; QWordValue:  4294967296 * 4096);

          _10000: hwFloat = (isNegative: false; QWordValue:  4294967296 * 10000);

         cLittle: hwFloat = (isNegative: false; QWordValue:           1);

         cHHKick: hwFloat = (isNegative: false; QWordValue:    42949673);  // _0_01

{$WARNINGS ON}

{$ENDIF}

{$IFNDEF FPC}

type hwFloat = Extended;

{$ENDIF}

implementation

uses uSinTable;

{$IFDEF FPC}

function int2hwFloat (const i: LongInt) : hwFloat;

begin

int2hwFloat.isNegative:= i < 0;

int2hwFloat.Round:= abs(i);

int2hwFloat.Frac:= 0

end;

function hwFloat2Float (const i: hwFloat) : extended;

begin

hwFloat2Float:= i.QWordValue / $100000000;

if i.isNegative then hwFloat2Float:= -hwFloat2Float;

end;

operator + (const z1, z2: hwFloat) z : hwFloat;

begin

if z1.isNegative = z2.isNegative then

   begin

   z.isNegative:= z1.isNegative;

   z.QWordValue:= z1.QWordValue + z2.QWordValue

   end

else

   if z1.QWordValue > z2.QWordValue then

      begin

      z.isNegative:= z1.isNegative;

      z.QWordValue:= z1.QWordValue - z2.QWordValue

      end else

      begin

      z.isNegative:= z2.isNegative;

      z.QWordValue:= z2.QWordValue - z1.QWordValue

      end

end;

operator - (const z1, z2: hwFloat) z : hwFloat;

begin

if z1.isNegative = z2.isNegative then

   if z1.QWordValue > z2.QWordValue then

      begin

      z.isNegative:= z1.isNegative;

      z.QWordValue:= z1.QWordValue - z2.QWordValue

      end else

      begin

      z.isNegative:= not z2.isNegative;

      z.QWordValue:= z2.QWordValue - z1.QWordValue

      end

else begin

     z.isNegative:= z1.isNegative;

     z.QWordValue:= z1.QWordValue + z2.QWordValue

     end

end;

operator - (const z1: hwFloat) z : hwFloat;

begin

z:= z1;

z.isNegative:= not z.isNegative

end;

operator * (const z1, z2: hwFloat) z : hwFloat;

begin

z.isNegative:= z1.isNegative xor z2.isNegative;

z.QWordValue:= QWord(z1.Round) * z2.Frac +

               QWord(z1.Frac) * z2.Round +

               ((QWord(z1.Frac) * z2.Frac) shr 32);

z.Round:= z.Round + QWord(z1.Round) * z2.Round;

end;

operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;

begin

z.isNegative:= z1.isNegative xor (z2 < 0);

z.QWordValue:= z1.QWordValue * abs(z2)

end;

operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;

var t: hwFloat;

begin

z.isNegative:= z1.isNegative xor z2.isNegative;

z.Round:= z1.QWordValue div z2.QWordValue;

t:= z1 - z2 * z.Round;

if t.QWordValue = 0 then

   z.Frac:= 0

else

   begin

   while ((t.QWordValue and $8000000000000000) = 0) and

         ((z2.QWordValue and $8000000000000000) = 0) do

         begin

         t.QWordValue:= t.QWordValue shl 1;

         z2.QWordValue:= z2.QWordValue shl 1

         end;

   if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round)

                   else z.Frac:= 0

   end

end;

operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;

begin

z.isNegative:= z1.isNegative xor (z2 < 0);

z.QWordValue:= z1.QWordValue div abs(z2)

end;

operator < (const z1, z2: hwFloat) b : boolean;

begin

if z1.isNegative xor z2.isNegative then

   b:= z1.isNegative

else

   if z1.QWordValue = z2.QWordValue then

      b:= false

   else

      b:= (z1.QWordValue < z2.QWordValue) xor z1.isNegative

end;

operator > (const z1, z2: hwFloat) b : boolean;

begin

if z1.isNegative xor z2.isNegative then

   b:= z2.isNegative

else

   if z1.QWordValue = z2.QWordValue then

      b:= false

   else

      b:= (z1.QWordValue > z2.QWordValue) xor z2.isNegative

end;

function cstr(const z: hwFloat): shortstring;

var tmpstr: shortstring;

begin

str(z.Round, cstr);

if z.Frac <> 0 then

   begin

   str(z.Frac / $100000000:1:15, tmpstr);

   delete(tmpstr, 1, 2);

   cstr:= cstr + '.' + tmpstr

   end;

if z.isNegative then cstr:= '-' + cstr

end;

function hwRound(const t: hwFloat): LongInt;

begin

if t.isNegative then hwRound:= -(t.Round and $7FFFFFFF)

                else hwRound:= t.Round and $7FFFFFFF

end;

function hwAbs(const t: hwFloat): hwFloat;

begin

hwAbs:= t;

hwAbs.isNegative:= false

end;

function hwSqr(const t: hwFloat): hwFloat;

begin

hwSqr.isNegative:= false;

hwSqr.QWordValue:=

      ((QWord(t.Round) * t.Round) shl 32)

    + QWord(t.Round) * t.Frac * 2

    + ((QWord(t.Frac) * t.Frac) shr 32);

end;

function hwSqrt(const t: hwFloat): hwFloat;

var l, r: QWord;

    c: hwFloat;

begin

hwSqrt.isNegative:= false;

if t.Round = 0 then

   begin

   l:= t.QWordValue;

   r:= $100000000

   end else

   begin

   l:= $100000000;

   r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5

   if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF

   end;

repeat

  c.QWordValue:= (l + r) div 2;

  if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue

until r - l <= 1;

hwSqrt.QWordValue:= l

end;

function Distance(const dx, dy: hwFloat): hwFloat;

begin

Distance:= hwSqrt(hwSqr(dx) + hwSqr(dy))

end;

function DistanceI(const dx, dy: LongInt): hwFloat;

begin

DistanceI:= hwSqrt(int2hwFloat(sqr(dx) + sqr(dy)))

end;

function SignAs(const num, signum: hwFloat): hwFloat;

begin

SignAs.QWordValue:= num.QWordValue;

SignAs.isNegative:= signum.isNegative

end;

function hwSign(r: hwFloat): LongInt;

begin

// yes, we have negative zero for a reason

if r.isNegative then hwSign:= -1 else hwSign:= 1

end;

function AngleSin(const Angle: Longword): hwFloat;

begin

//TryDo((Angle >= 0) and (Angle <= 2048), 'Sin param exceeds limits', true);

AngleSin.isNegative:= false;

if Angle < 1024 then AngleSin.QWordValue:= SinTable[Angle]

                else AngleSin.QWordValue:= SinTable[2048 - Angle]

end;

function AngleCos(const Angle: Longword): hwFloat;

begin

//TryDo((Angle >= 0) and (Angle <= 2048), 'Cos param exceeds limits', true);

AngleCos.isNegative:= Angle > 1024;

if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle]

                else AngleCos.QWordValue:= SinTable[Angle - 1024]

end;

{$ENDIF}

end.