hedgewars/uFloat.pas
author smxx
Mon, 01 Mar 2010 19:54:33 +0000
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parent 2784 1a2e3c7c6a46
child 2933 02af54eb7e1e
permissions -rw-r--r--
Engine: * Converted all strings without maximum lengths to ansistrings (eliminates 255 char limit) or shortstrings (needs some testing) * Goal/mission display now stays within screen borders even if it's very long * Extended mine game mode display to respect no timer and random timer
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(*
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 * Hedgewars, a free turn based strategy game
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 * Copyright (c) 2007, 2008 Andrey Korotaev <unC0Rr@gmail.com>
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 *
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 * This program is free software; you can redistribute it and/or modify
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 * it under the terms of the GNU General Public License as published by
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 * the Free Software Foundation; version 2 of the License
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 *
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 * This program is distributed in the hope that it will be useful,
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
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 * GNU General Public License for more details.
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 *
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 * You should have received a copy of the GNU General Public License
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 * along with this program; if not, write to the Free Software
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 * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA
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 *)
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{$INCLUDE "options.inc"}
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unit uFloat;
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interface
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{$IFDEF FPC}
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{$IFDEF ENDIAN_LITTLE}
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type hwFloat = record
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               isNegative: boolean;
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               case byte of
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               0: (Frac, Round: Longword);
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               1: (QWordValue : QWord);
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               end;
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{$ELSE}
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type hwFloat = record
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               isNegative: boolean;
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               case byte of
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               0: (Round, Frac: Longword);
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               1: (QWordValue : QWord);
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               end;
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{$ENDIF}
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function int2hwFloat (const i: LongInt) : hwFloat;
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operator + (const z1, z2: hwFloat) z : hwFloat;
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operator - (const z1, z2: hwFloat) z : hwFloat;
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operator - (const z1: hwFloat) z : hwFloat;
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operator * (const z1, z2: hwFloat) z : hwFloat;
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operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;
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operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;
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operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
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operator < (const z1, z2: hwFloat) b : boolean;
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operator > (const z1, z2: hwFloat) b : boolean;
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function cstr(const z: hwFloat): shortstring;
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function hwRound(const t: hwFloat): LongInt;
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function hwAbs(const t: hwFloat): hwFloat;
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function hwSqr(const t: hwFloat): hwFloat;
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function hwSqrt(const t: hwFloat): hwFloat;
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function Distance(const dx, dy: hwFloat): hwFloat;
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function DistanceI(const dx, dy: LongInt): hwFloat;
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function AngleSin(const Angle: Longword): hwFloat;
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function AngleCos(const Angle: Longword): hwFloat;
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function SignAs(const num, signum: hwFloat): hwFloat;
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{$IFDEF FPC}
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{$J-}
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{$ENDIF}
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{$WARNINGS OFF}
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const  _1div1024: hwFloat = (isNegative: false; QWordValue:     4194304);
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      _1div10000: hwFloat = (isNegative: false; QWordValue:      429496);
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      _1div50000: hwFloat = (isNegative: false; QWordValue:       85899);
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     _1div100000: hwFloat = (isNegative: false; QWordValue:       42950);
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          _1div3: hwFloat = (isNegative: false; QWordValue:  1431655766);
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            hwPi: hwFloat = (isNegative: false; QWordValue: 13493037704);
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       _0_000004: hwFloat = (isNegative: false; QWordValue:       17179);
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         _0_0002: hwFloat = (isNegative: false; QWordValue:      858993);
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         _0_0005: hwFloat = (isNegative: false; QWordValue:     2147484);
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          _0_001: hwFloat = (isNegative: false; QWordValue:     4294967);
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          _0_003: hwFloat = (isNegative: false; QWordValue:    12884902);
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          _0_004: hwFloat = (isNegative: false; QWordValue:    17179869);
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          _0_005: hwFloat = (isNegative: false; QWordValue:    21474836);
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           _0_01: hwFloat = (isNegative: false; QWordValue:    42949673);
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           _0_02: hwFloat = (isNegative: false; QWordValue:    85899345);
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           _0_03: hwFloat = (isNegative: false; QWordValue:   128849018);
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           _0_08: hwFloat = (isNegative: false; QWordValue:   343597383);
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            _0_1: hwFloat = (isNegative: false; QWordValue:   429496730);
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           _0_15: hwFloat = (isNegative: false; QWordValue:   644245094);
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            _0_2: hwFloat = (isNegative: false; QWordValue:   858993459);
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           _0_25: hwFloat = (isNegative: false; QWordValue:  1073741824);
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            _0_3: hwFloat = (isNegative: false; QWordValue:  1288490189);
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           _0_35: hwFloat = (isNegative: false; QWordValue:  1503238553);
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          _0_375: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3 div 8);
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           _0_39: hwFloat = (isNegative: false; QWordValue:  1675037245);
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            _0_4: hwFloat = (isNegative: false; QWordValue:  1717986918);
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           _0_45: hwFloat = (isNegative: false; QWordValue:  1932735283);
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            _0_5: hwFloat = (isNegative: false; QWordValue:  2147483648);
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           _0_55: hwFloat = (isNegative: false; QWordValue:  2362232012);
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            _0_6: hwFloat = (isNegative: false; QWordValue:  2576980377);
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            _0_7: hwFloat = (isNegative: false; QWordValue:  3006477107);
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            _0_8: hwFloat = (isNegative: false; QWordValue:  3435973837);
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           _0_84: hwFloat = (isNegative: false; QWordValue:  3607772528);
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           _0_87: hwFloat = (isNegative: false; QWordValue:  3736621547);
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            _0_9: hwFloat = (isNegative: false; QWordValue:  3865470566);
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           _0_93: hwFloat = (isNegative: false; QWordValue:  3994319585);
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           _0_96: hwFloat = (isNegative: false; QWordValue:  4123168604);
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          _0_995: hwFloat = (isNegative: false; QWordValue:  4273492459);
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          _0_998: hwFloat = (isNegative: false; QWordValue:  4294967296);
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          _0_999: hwFloat = (isNegative: false; QWordValue:  4290672328);
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            _1_9: hwFloat = (isNegative: false; QWordValue:  8160437862);
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              _0: hwFloat = (isNegative: false; QWordValue:           0);
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              _1: hwFloat = (isNegative: false; QWordValue:  4294967296);
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            _1_5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3 div 2);
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              _2: hwFloat = (isNegative: false; QWordValue:  4294967296 * 2);
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              _3: hwFloat = (isNegative: false; QWordValue:  4294967296 * 3);
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              _4: hwFloat = (isNegative: false; QWordValue:  4294967296 * 4);
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              _5: hwFloat = (isNegative: false; QWordValue:  4294967296 * 5);
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              _6: hwFloat = (isNegative: false; QWordValue:  4294967296 * 6);
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             _10: hwFloat = (isNegative: false; QWordValue:  4294967296 * 10);
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             _16: hwFloat = (isNegative: false; QWordValue:  4294967296 * 16);
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             _19: hwFloat = (isNegative: false; QWordValue:  4294967296 * 19);
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             _20: hwFloat = (isNegative: false; QWordValue:  4294967296 * 20);
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         _0_3x70: hwFloat = (isNegative: false; QWordValue:  1288490189 * 70);
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             _25: hwFloat = (isNegative: false; QWordValue:  4294967296 * 25);
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             _30: hwFloat = (isNegative: false; QWordValue:  4294967296 * 30);
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            _128: hwFloat = (isNegative: false; QWordValue:  4294967296 * 128);
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            _256: hwFloat = (isNegative: false; QWordValue:  4294967296 * 256);
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            _300: hwFloat = (isNegative: false; QWordValue:  4294967296 * 300);
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            _450: hwFloat = (isNegative: false; QWordValue:  4294967296 * 450);
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           _1024: hwFloat = (isNegative: false; QWordValue:  4294967296 * 1024);
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           _2048: hwFloat = (isNegative: false; QWordValue:  4294967296 * 2048);
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           _4096: hwFloat = (isNegative: false; QWordValue:  4294967296 * 4096);
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          _10000: hwFloat = (isNegative: false; QWordValue:  4294967296 * 10000);
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         cLittle: hwFloat = (isNegative: false; QWordValue:           1);
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         cHHKick: hwFloat = (isNegative: false; QWordValue:    42949673);  // _0_01
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{$WARNINGS ON}
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{$ENDIF}
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{$IFNDEF FPC}
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type hwFloat = Extended;
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{$ENDIF}
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implementation
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uses uConsts, uMisc;
351
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{$IFDEF FPC}
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function int2hwFloat (const i: LongInt) : hwFloat;
351
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begin
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int2hwFloat.isNegative:= i < 0;
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int2hwFloat.Round:= abs(i);
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int2hwFloat.Frac:= 0
351
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end;
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operator + (const z1, z2: hwFloat) z : hwFloat;
351
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begin
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if z1.isNegative = z2.isNegative then
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   159
   begin
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   z.isNegative:= z1.isNegative;
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   z.QWordValue:= z1.QWordValue + z2.QWordValue
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   end
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else
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   if z1.QWordValue > z2.QWordValue then
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   165
      begin
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      z.isNegative:= z1.isNegative;
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      z.QWordValue:= z1.QWordValue - z2.QWordValue
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      end else
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      begin
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      z.isNegative:= z2.isNegative;
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      z.QWordValue:= z2.QWordValue - z1.QWordValue
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      end
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end;
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operator - (const z1, z2: hwFloat) z : hwFloat;
351
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begin
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if z1.isNegative = z2.isNegative then
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   if z1.QWordValue > z2.QWordValue then
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      begin
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      z.isNegative:= z1.isNegative;
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      z.QWordValue:= z1.QWordValue - z2.QWordValue
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      end else
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      begin
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   184
      z.isNegative:= not z2.isNegative;
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   185
      z.QWordValue:= z2.QWordValue - z1.QWordValue
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   186
      end
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   187
else begin
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     z.isNegative:= z1.isNegative;
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   189
     z.QWordValue:= z1.QWordValue + z2.QWordValue
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   190
     end
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   191
end;
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operator - (const z1: hwFloat) z : hwFloat;
351
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begin
29bc9c36ad5f Fixed-point arithmetics in engine.
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z:= z1;
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z.isNegative:= not z.isNegative
29bc9c36ad5f Fixed-point arithmetics in engine.
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   197
end;
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operator * (const z1, z2: hwFloat) z : hwFloat;
351
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begin
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z.isNegative:= z1.isNegative xor z2.isNegative;
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z.QWordValue:= QWord(z1.Round) * z2.Frac +
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               QWord(z1.Frac) * z2.Round +
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               ((QWord(z1.Frac) * z2.Frac) shr 32);
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z.Round:= z.Round + QWord(z1.Round) * z2.Round;
29bc9c36ad5f Fixed-point arithmetics in engine.
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   207
end;
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operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;
351
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begin
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z.isNegative:= z1.isNegative xor (z2 < 0);
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z.QWordValue:= z1.QWordValue * abs(z2)
351
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   213
end;
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operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;
351
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var t: hwFloat;
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begin
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z.isNegative:= z1.isNegative xor z2.isNegative;
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z.Round:= z1.QWordValue div z2.QWordValue;
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t:= z1 - z2 * z.Round;
29bc9c36ad5f Fixed-point arithmetics in engine.
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parents:
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   221
if t.QWordValue = 0 then
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   222
   z.Frac:= 0
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   223
else
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   224
   begin
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   225
   while ((t.QWordValue and $8000000000000000) = 0) and
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unc0rr
parents:
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   226
         ((z2.QWordValue and $8000000000000000) = 0) do
29bc9c36ad5f Fixed-point arithmetics in engine.
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   227
         begin
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   228
         t.QWordValue:= t.QWordValue shl 1;
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   229
         z2.QWordValue:= z2.QWordValue shl 1
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   230
         end;
543
465e2ec8f05f - Better randomness of placing hedgehogs on the land
unc0rr
parents: 538
diff changeset
   231
   if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round)
465e2ec8f05f - Better randomness of placing hedgehogs on the land
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diff changeset
   232
                   else z.Frac:= 0
351
29bc9c36ad5f Fixed-point arithmetics in engine.
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   233
   end
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   234
end;
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operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
498
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   237
begin
9c8b385dc9a1 - Get rid of operator := to have GPC support
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   238
z.isNegative:= z1.isNegative xor (z2 < 0);
515
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unc0rr
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   239
z.QWordValue:= z1.QWordValue div abs(z2)
498
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diff changeset
   240
end;
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   241
515
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operator < (const z1, z2: hwFloat) b : boolean;
351
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unc0rr
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   243
begin
916
1d0022336fbb - Small optimization in hwFloat
unc0rr
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diff changeset
   244
if z1.isNegative xor z2.isNegative then
351
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unc0rr
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   245
   b:= z1.isNegative
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   246
else
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   247
   if z1.QWordValue = z2.QWordValue then
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   248
      b:= false
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   249
   else
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   250
      b:= (z1.QWordValue < z2.QWordValue) xor z1.isNegative
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   251
end;
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   252
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   253
operator > (const z1, z2: hwFloat) b : boolean;
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   254
begin
916
1d0022336fbb - Small optimization in hwFloat
unc0rr
parents: 883
diff changeset
   255
if z1.isNegative xor z2.isNegative then
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   256
   b:= z2.isNegative
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   257
else
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   258
   if z1.QWordValue = z2.QWordValue then
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   259
      b:= false
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   260
   else
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   261
      b:= (z1.QWordValue > z2.QWordValue) xor z2.isNegative
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   262
end;
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   263
2905
f3c79f7193a9 Engine:
smxx
parents: 2784
diff changeset
   264
function cstr(const z: hwFloat): shortstring;
f3c79f7193a9 Engine:
smxx
parents: 2784
diff changeset
   265
var tmpstr: shortstring;
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   266
begin
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   267
str(z.Round, cstr);
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   268
if z.Frac <> 0 then
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   269
   begin
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   270
   str(z.Frac / $100000000:1:15, tmpstr);
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   271
   delete(tmpstr, 1, 2);
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   272
   cstr:= cstr + '.' + tmpstr
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   273
   end;
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   274
if z.isNegative then cstr:= '-' + cstr
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   275
end;
29bc9c36ad5f Fixed-point arithmetics in engine.
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parents:
diff changeset
   276
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   277
function hwRound(const t: hwFloat): LongInt;
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   278
begin
2300
d633bc70c893 prevent overflow
nemo
parents: 1915
diff changeset
   279
if t.isNegative then hwRound:= -(t.Round and $7FFFFFFF)
d633bc70c893 prevent overflow
nemo
parents: 1915
diff changeset
   280
                else hwRound:= t.Round and $7FFFFFFF
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
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   281
end;
29bc9c36ad5f Fixed-point arithmetics in engine.
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   282
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   283
function hwAbs(const t: hwFloat): hwFloat;
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   284
begin
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   285
hwAbs:= t;
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   286
hwAbs.isNegative:= false
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   287
end;
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parents:
diff changeset
   288
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   289
function hwSqr(const t: hwFloat): hwFloat;
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   290
begin
1433
4af291d5d79c Repair flame dependancy on wind
unc0rr
parents: 1124
diff changeset
   291
hwSqr.isNegative:= false;
4af291d5d79c Repair flame dependancy on wind
unc0rr
parents: 1124
diff changeset
   292
hwSqr.QWordValue:=
4af291d5d79c Repair flame dependancy on wind
unc0rr
parents: 1124
diff changeset
   293
	  ((QWord(t.Round) * t.Round) shl 32)
4af291d5d79c Repair flame dependancy on wind
unc0rr
parents: 1124
diff changeset
   294
	+ QWord(t.Round) * t.Frac * 2
4af291d5d79c Repair flame dependancy on wind
unc0rr
parents: 1124
diff changeset
   295
	+ ((QWord(t.Frac) * t.Frac) shr 32);
351
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   296
end;
29bc9c36ad5f Fixed-point arithmetics in engine.
unc0rr
parents:
diff changeset
   297
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parents: 513
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   298
function hwSqrt(const t: hwFloat): hwFloat;
738
d7f640e99b17 Ignore many files, created by build system
unc0rr
parents: 611
diff changeset
   299
var l, r: QWord;
d7f640e99b17 Ignore many files, created by build system
unc0rr
parents: 611
diff changeset
   300
    c: hwFloat;
357
165a040e4cfa - Fix Blow Torch and Air Attack
unc0rr
parents: 355
diff changeset
   301
begin
165a040e4cfa - Fix Blow Torch and Air Attack
unc0rr
parents: 355
diff changeset
   302
hwSqrt.isNegative:= false;
744
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   303
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   304
if t.Round = 0 then
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   305
   begin
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   306
   l:= t.QWordValue;
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   307
   r:= $100000000
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   308
   end else
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   309
   begin
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   310
   l:= $100000000;
953
237fc147950c Fix bug in hwSqrt when calculating square root of number >= 65536
unc0rr
parents: 916
diff changeset
   311
   r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5
237fc147950c Fix bug in hwSqrt when calculating square root of number >= 65536
unc0rr
parents: 916
diff changeset
   312
   if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF
744
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unc0rr
parents: 738
diff changeset
   313
   end;
7a9663194767 - Remove debug
unc0rr
parents: 738
diff changeset
   314
738
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unc0rr
parents: 611
diff changeset
   315
repeat
d7f640e99b17 Ignore many files, created by build system
unc0rr
parents: 611
diff changeset
   316
  c.QWordValue:= (l + r) div 2;
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  if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue
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until r - l <= 1;
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hwSqrt.QWordValue:= l
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end;
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function Distance(const dx, dy: hwFloat): hwFloat;
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begin
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Distance:= hwSqrt(hwSqr(dx) + hwSqr(dy))
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end;
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function DistanceI(const dx, dy: LongInt): hwFloat;
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begin
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DistanceI:= hwSqrt(int2hwFloat(sqr(dx) + sqr(dy)))
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end;
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function SignAs(const num, signum: hwFloat): hwFloat;
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begin
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SignAs.QWordValue:= num.QWordValue;
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SignAs.isNegative:= signum.isNegative
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end;
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{$INCLUDE "SinTable.inc"}
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function AngleSin(const Angle: Longword): hwFloat;
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begin
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{$IFDEF DEBUGFILE}
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TryDo((Angle >= 0) and (Angle <= 2048), 'Sin param exceeds limits', true);
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{$ENDIF}
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AngleSin.isNegative:= false;
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if Angle < 1024 then AngleSin.QWordValue:= SinTable[Angle]
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                else AngleSin.QWordValue:= SinTable[2048 - Angle]
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end;
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function AngleCos(const Angle: Longword): hwFloat;
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begin
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{$IFDEF DEBUGFILE}
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TryDo((Angle >= 0) and (Angle <= 2048), 'Cos param exceeds limits', true);
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{$ENDIF}
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AngleCos.isNegative:= Angle > 1024;
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if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle]
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                else AngleCos.QWordValue:= SinTable[Angle - 1024]
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end;
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{$ENDIF}
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end.