+
−(*
+
− * 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.