(*
 * Hedgewars, a free turn based strategy game
 * Copyright (c) 2004-2015 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., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  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

{$IFDEF ENDIAN_LITTLE}
type hwFloat = record
    isNegative: boolean;
    case byte of
        0: (Frac, Round: Longword);
        1: (QWordValue : QWord);
        end;
{$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 : boolean; inline;
{$IFDEF PAS2C}
operator <> (const z1, z2: hwFloat) z : boolean; inline;
{$ENDIF}
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 hwSqrt1(const t: hwFloat): hwFloat; inline; // Returns the the positive square root of parameter t.
function hwSqrt(const x: 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 vector2Angle(const x, y: hwFloat): LongInt;
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.
function hwSignf(r: real): LongInt; inline; // Returns an integer with value 1 and sign of parameter r.
function isZero(const z: hwFloat): boolean; inline;

{$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_0032: hwFloat = (isNegative: false; QWordValue:    13743895);
          _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_0128: hwFloat = (isNegative: false; QWordValue:    54975581);
           _0_02: hwFloat = (isNegative: false; QWordValue:    85899345);
           _0_03: hwFloat = (isNegative: false; QWordValue:   128849018);
           _0_07: hwFloat = (isNegative: false; QWordValue:   300647710);
           _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_2: hwFloat = (isNegative: false; QWordValue:  4294967296 * 6 div 5 + 1);
            _1_5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3 div 2);
            _1_6: hwFloat = (isNegative: false; QWordValue:  4294967296 * 8 div 5);
            _1_9: hwFloat = (isNegative: false; QWordValue:  8160437862);
              _2: hwFloat = (isNegative: false; QWordValue:  4294967296 * 2);
            _2_4: hwFloat = (isNegative: false; QWordValue:  4294967296 * 12 div 5);
              _3: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3);
            _3_2: hwFloat = (isNegative: false; QWordValue:  4294967296 * 16 div 5);
             _PI: hwFloat = (isNegative: false; QWordValue: 13493037704);
              _4: hwFloat = (isNegative: false; QWordValue:  4294967296 * 4);
            _4_5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 9 div 2);
              _5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 5);
              _6: hwFloat = (isNegative: false; QWordValue:  4294967296 * 6);
            _6_4: hwFloat = (isNegative: false; QWordValue:  4294967296 * 32 div 5);
              _7: hwFloat = (isNegative: false; QWordValue:  4294967296 * 7);
             _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);
             _41: hwFloat = (isNegative: false; QWordValue:  4294967296 * 41);
             _49: hwFloat = (isNegative: false; QWordValue:  4294967296 * 49);
             _50: hwFloat = (isNegative: false; QWordValue:  4294967296 * 50);
             _70: hwFloat = (isNegative: false; QWordValue:  4294967296 * 70);
             _90: hwFloat = (isNegative: false; QWordValue:  4294967296 * 90);
            _128: hwFloat = (isNegative: false; QWordValue:  4294967296 * 128);
            _180: hwFloat = (isNegative: false; QWordValue:  4294967296 * 180);
            _250: hwFloat = (isNegative: false; QWordValue:  4294967296 * 250);
            _256: hwFloat = (isNegative: false; QWordValue:  4294967296 * 256);
            _300: hwFloat = (isNegative: false; QWordValue:  4294967296 * 300);
            _360: hwFloat = (isNegative: false; QWordValue:  4294967296 * 360);
            _450: hwFloat = (isNegative: false; QWordValue:  4294967296 * 450);
           _1000: hwFloat = (isNegative: false; QWordValue:  4294967296 * 1000);
           _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}

implementation
uses uSinTable;


function int2hwFloat (const i: LongInt) : hwFloat; inline;
begin
int2hwFloat.isNegative:= i < 0;
int2hwFloat.Round:= abs(i);
int2hwFloat.Frac:= 0
end;

function hwFloat2Float (const i: hwFloat) : extended; inline;
begin
hwFloat2Float:= i.Frac / $100000000 + i.Round;
if i.isNegative then
    hwFloat2Float:= -hwFloat2Float;
end;

operator = (const z1, z2: hwFloat) z : boolean; inline;
begin
    z:= (z1.isNegative = z2.isNegative) and (z1.QWordValue = z2.QWordValue);
end;

{$IFDEF PAS2C}
operator <> (const z1, z2: hwFloat) z : boolean; inline;
begin
    z:= (z1.isNegative <> z2.isNegative) or (z1.QWordValue <> z2.QWordValue);
end;
{$ENDIF}

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

function isZero(const z: hwFloat): boolean; inline;
begin
isZero := z.QWordValue = 0;
end;

operator < (const z1, z2: hwFloat) b : boolean; inline;
begin
if z1.isNegative xor z2.isNegative then
    b:= z1.isNegative
else
    if z1.QWordValue = z2.QWordValue then
        b:= false
    else
        b:= (z2.QWordValue < z1.QWordValue) = z1.isNegative
end;

operator > (const z1, z2: hwFloat) b : boolean; inline;
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) <> z2.isNegative
end;

operator - (const z1: hwFloat) z : hwFloat; inline;
begin
    z:= z1;
    z.isNegative:= not z.isNegative
end;


operator * (const z1, z2: hwFloat) z : hwFloat; inline;
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; inline;
begin
    z.isNegative:= z1.isNegative xor (z2 < 0);
    z.QWordValue:= z1.QWordValue * abs(z2)
end;

operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat; inline;
var t: QWord;
begin
    z.isNegative:= z1.isNegative xor z2.isNegative;
    z.Round:= z1.QWordValue div z2.QWordValue;
    t:= z1.QWordValue - z2.QWordValue * z.Round;
    z.Frac:= 0;

    if t <> 0 then
        begin
        while ((t and $FF00000000000000) = 0) and ((z2.QWordValue and $FF00000000000000) = 0) do
            begin
            t:= t shl 8;
            z2.QWordValue:= z2.QWordValue shl 8
            end;

        if z2.Round > 0 then
            inc(z.QWordValue, t div z2.Round);
        end
end;

operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat; inline;
begin
    z.isNegative:= z1.isNegative xor (z2 < 0);
    z.QWordValue:= z1.QWordValue div abs(z2)
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, tmpstr);
        delete(tmpstr, 1, 2);
        cstr:= cstr + '.' + copy(tmpstr, 1, 10)
        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; inline;
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 hwSqrt1(const t: hwFloat): hwFloat;
const pwr = 8; // even value, feel free to adjust
      rThreshold: QWord = 1 shl (pwr + 32);
      lThreshold: QWord = 1 shl (pwr div 2 + 32);
var l, r: QWord;
    c: hwFloat;
begin
    hwSqrt1.isNegative:= false;

    if t.Round = 0 then
        begin
        l:= t.QWordValue;
        r:= $100000000
        end
    else
        begin
        if t.QWordValue > $FFFFFFFFFFFF then // t.Round > 65535.9999
            begin
            l:= $10000000000; // 256
            r:= $FFFFFFFFFFFF; // 65535.9999
            end
        else
            if t.QWordValue >= rThreshold then
                begin
                l:= lThreshold;
                r:= $10000000000; // 256
                end
            else
                begin
                l:= $100000000;
                r:= lThreshold;
                end;
    end;

    repeat
        c.QWordValue:= (l + r) shr 1;
        if hwSqr(c).QWordValue > t.QWordValue then
            r:= c.QWordValue
        else
            l:= c.QWordValue
    until r - l <= 1;

    hwSqrt1.QWordValue:= l
end;

function hwSqrt(const x: hwFloat): hwFloat;
var r, t, s, q: QWord;
    i: integer;
begin
    hwSqrt.isNegative:= false;

    t:= $4000000000000000;
    r:= 0;
    q:= x.QWordValue;

    for i:= 0 to 31 do
        begin
        s:= r + t;
        r:= r shr 1;
        if s <= q then
            begin
            dec(q, s);
            inc(r, t);
            end;
        t:= t shr 2;
        end;

    hwSqrt.QWordValue:= r shl 16
end;



function Distance(const dx, dy: hwFloat): hwFloat;
var r: QWord;
begin
    r:= dx.QWordValue or dy.QWordValue;

    if r < $10000 then
        begin
        Distance.QWordValue:= r;
        Distance.isNegative:= false
        end
    else
        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 hwSignf(r: real): LongInt;
begin
if r < 0 then
    hwSignf:= -1
else
    hwSignf:= 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;

function vector2Angle(const x, y: hwFloat): LongInt;
var d, nf: hwFloat;
    l, r, c, oc: Longword;
    n: QWord;
begin
    d:= _1 / Distance(x, y);

    nf:= y * d;
    n:= nf.QWordValue;

    l:= 0;
    r:= 1024;
    c:= 0;

    repeat
        oc:= c;

        c:= (l + r) shr 1;

        if n >= SinTable[c] then
            l:= c
        else
            r:= c;

    until (oc = c);

    if x.isNegative then c:= 2048 - c;
    if y.isNegative then c:= - c;

    vector2Angle:= c
end;

end.