hedgewars/uFloat.pas
author unc0rr
Sun, 02 Dec 2012 01:25:11 +0400
changeset 8178 8bd087478b48
parent 7715 8b653edac2a2
child 8026 4a4f21070479
child 8838 aa2ffd427f6a
permissions -rw-r--r--
Fix QSettings problems: - Reopen file in ReadOnly mode if it was open in ReadWrite mode and is being read. This is needed for stupid QSettings which opens file in ReadWrite mode just to call readAll() on it. - Implement setSize(0)

(*
 * Hedgewars, a free turn based strategy game
 * Copyright (c) 2004-2012 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 : 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 hwPow(const t: hwFloat; p: LongWord): hwFloat; inline; // Returns the power of the value
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 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;
{$IFDEF FPC}
{$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_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:  1288490189*4);
            _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:  3435973837*4);
             _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:  3435973837 * 8);
              _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
{$WARNINGS ON}
{$ENDIF}

{$IFNDEF FPC}
type hwFloat = Extended;
{$ENDIF}

implementation
uses uSinTable;


{$IFDEF FPC}

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;

{$IFNDEF WEB}
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:= not((z1.QWordValue = z2.QWordValue) or ((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;
{$ENDIF}
{$IFDEF WEB}
(*
    Mostly to be kind to JS as of 2012-08-27 where there is no int64/uint64.  This may change though.
*)
operator = (const z1, z2: hwFloat) z : boolean; inline;
begin
    z:= (z1.isNegative = z2.isNegative) and (z1.Frac = z2.Frac) and (z1.Round = z2.Round);
end;

operator <> (const z1, z2: hwFloat) z : boolean; inline;
begin
    z:= (z1.isNegative <> z2.isNegative) or (z1.Frac <> z2.Frac) or (z1.Round <> z2.Round);
end;

operator + (const z1, z2: hwFloat) z : hwFloat; inline;
begin
if z1.isNegative = z2.isNegative then
    begin
    z:= z1;
    z.Frac:= z.Frac + z2.Frac;
    z.Round:= z.Round + z2.Round;
    if z.Frac<z1.Frac then inc(z.Round)
    end
else
    if (z1.Round > z2.Round) or ((z1.Round = z2.Round) and (z1.Frac > z2.Frac)) then
        begin
        z.isNegative:= z1.isNegative;
        z.Round:= z1.Round - z2.Round;
        z.Frac:= z1.Frac - z2.Frac;
        if z2.Frac > z1.Frac then dec(z.Round)
        end
    else
        begin
        z.isNegative:= z2.isNegative;
        z.Round:= z2.Round - z1.Round;
        z.Frac:= z2.Frac-z1.Frac;
        if z2.Frac < z1.Frac then dec(z.Round)
        end
end;

operator - (const z1, z2: hwFloat) z : hwFloat; inline;
begin
if z1.isNegative = z2.isNegative then
    if (z1.Round > z2.Round) or ((z1.Round = z2.Round) and (z1.Frac > z2.Frac)) then
        begin
        z.isNegative:= z1.isNegative;
        z.Round:= z1.Round - z2.Round;
        z.Frac:= z1.Frac-z2.Frac;
        if z2.Frac > z1.Frac then dec(z.Round)
        end
    else
        begin
        z.isNegative:= not z2.isNegative;
        z.Round:= z2.Round - z1.Round;
        z.Frac:= z2.Frac-z1.Frac;
        if z2.Frac < z1.Frac then dec(z.Round)
        end
else
    begin
    z:= z1;
    z.Frac:= z.Frac + z2.Frac;
    z.Round:= z.Round + z2.Round;
    if z.Frac<z1.Frac then inc(z.Round)
    end
end;

operator < (const z1, z2: hwFloat) b : boolean; inline;
begin
if z1.isNegative xor z2.isNegative then
    b:= z1.isNegative
else
(*  Not so sure this specialcase is a win w/ Round/Frac. have to do more tests anyway.
    if (z1.Round = z2.Round and (z1.Frac = z2.Frac)) then
        b:= false
    else *)
        b:= ((z1.Round < z2.Round) or ((z1.Round = z2.Round) and (z1.Frac < z2.Frac))) <> 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.Round > z2.Round) or ((z1.Round = z2.Round) and (z1.Frac > z2.Frac))) <> z1.isNegative
end;

function isZero(const z: hwFloat): boolean; inline; 
begin
isZero := (z.Round = 0) and (z.Frac = 0);
end;
{$ENDIF}

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: 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; 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 hwPow(const t: hwFloat;p: LongWord): hwFloat;
begin
hwPow:= t;
if p mod 2 = 0 then hwPow.isNegative:= false;

while p > 0 do
    begin
    hwPow.QWordValue:= QWord(hwPow.Round) * t.Frac + QWord(hwPow.Frac) * t.Round + ((QWord(hwPow.Frac) * t.Frac) shr 32);
    dec(p)
    end
end;

function hwSqrt(const t: hwFloat): hwFloat;
const pwr = 8; // even value, feel free to adjust
      rThreshold = 1 shl (pwr + 32);
      lThreshold = 1 shl (pwr div 2 + 32);
var l, r: QWord;
    c: hwFloat;
begin
hwSqrt.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;

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 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;

{$ENDIF}

end.