+
−(*
+
− * Hedgewars, a free turn based strategy game
+
− * Copyright (c) 2007, 2008 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
+
− *)
+
−
+
−{$INCLUDE "options.inc"}
+
−
+
−unit uFloat;
+
−interface
+
−
+
−{$IFDEF FPC}
+
−{$IFDEF ENDIAN_LITTLE}
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−type hwFloat = record
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−               isNegative: boolean;
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−               case byte of
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−               0: (Frac, Round: Longword);
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−               1: (QWordValue : QWord);
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−               end;
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−{$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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−
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−operator * (const z1, z2: hwFloat) z : hwFloat;
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−operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;
+
−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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−
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−function cstr(const z: hwFloat): string;
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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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−
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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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−
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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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−{$ENDIF}
+
−
+
−implementation
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−uses uConsts, uMisc;
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−
+
−{$IFDEF FPC}
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−
+
−function int2hwFloat (const i: LongInt) : hwFloat;
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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
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−end;
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−
+
−operator + (const z1, z2: hwFloat) z : hwFloat;
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−begin
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−if z1.isNegative = z2.isNegative 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
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−else
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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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−      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;
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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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−      z.isNegative:= not z2.isNegative;
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−      z.QWordValue:= z2.QWordValue - z1.QWordValue
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−      end
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−else 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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−end;
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−
+
−operator - (const z1: hwFloat) z : hwFloat;
+
−begin
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−z:= z1;
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−z.isNegative:= not z.isNegative
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−end;
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−
+
−
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−operator * (const z1, z2: hwFloat) z : hwFloat;
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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;
+
−end;
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−
+
−operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;
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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)
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−end;
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−
+
−operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;
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−var t: hwFloat;
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−begin
+
−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;
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−if t.QWordValue = 0 then
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−   z.Frac:= 0
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−else
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−   begin
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−   while ((t.QWordValue and $8000000000000000) = 0) and
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−         ((z2.QWordValue and $8000000000000000) = 0) do
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−         begin
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−         t.QWordValue:= t.QWordValue shl 1;
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−         z2.QWordValue:= z2.QWordValue shl 1
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−         end;
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−   if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round)
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−                   else z.Frac:= 0
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−   end
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−end;
+
−
+
−operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
+
−begin
+
−z.isNegative:= z1.isNegative xor (z2 < 0);
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−z.QWordValue:= z1.QWordValue div abs(z2)
+
−end;
+
−
+
−operator < (const z1, z2: hwFloat) b : boolean;
+
−begin
+
−if z1.isNegative xor z2.isNegative then
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−   b:= z1.isNegative
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−else
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−   if z1.QWordValue = z2.QWordValue then
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−      b:= false
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−   else
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−      b:= (z1.QWordValue < z2.QWordValue) xor z1.isNegative
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−end;
+
−
+
−operator > (const z1, z2: hwFloat) b : boolean;
+
−begin
+
−if z1.isNegative xor z2.isNegative then
+
−   b:= z2.isNegative
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−else
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−   if z1.QWordValue = z2.QWordValue then
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−      b:= false
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−   else
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−      b:= (z1.QWordValue > z2.QWordValue) xor z2.isNegative
+
−end;
+
−
+
−function cstr(const z: hwFloat): string;
+
−var tmpstr: string;
+
−begin
+
−str(z.Round, cstr);
+
−if z.Frac <> 0 then
+
−   begin
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−   str(z.Frac / $100000000:1:15, tmpstr);
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−   delete(tmpstr, 1, 2);
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−   cstr:= cstr + '.' + tmpstr
+
−   end;
+
−if z.isNegative then cstr:= '-' + cstr
+
−end;
+
−
+
−function hwRound(const t: hwFloat): LongInt;
+
−begin
+
−if t.isNegative then hwRound:= -(t.Round and $7FFFFFFF)
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−                else hwRound:= t.Round and $7FFFFFFF
+
−end;
+
−
+
−function hwAbs(const t: hwFloat): hwFloat;
+
−begin
+
−hwAbs:= t;
+
−hwAbs.isNegative:= false
+
−end;
+
−
+
−function hwSqr(const t: hwFloat): hwFloat;
+
−begin
+
−hwSqr.isNegative:= false;
+
−hwSqr.QWordValue:=
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−	  ((QWord(t.Round) * t.Round) shl 32)
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−	+ QWord(t.Round) * t.Frac * 2
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−	+ ((QWord(t.Frac) * t.Frac) shr 32);
+
−end;
+
−
+
−function hwSqrt(const t: hwFloat): hwFloat;
+
−var l, r: QWord;
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−    c: hwFloat;
+
−begin
+
−hwSqrt.isNegative:= false;
+
−
+
−if t.Round = 0 then
+
−   begin
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−   l:= t.QWordValue;
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−   r:= $100000000
+
−   end else
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−   begin
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−   l:= $100000000;
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−   r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5
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−   if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF
+
−   end;
+
−
+
−repeat
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−  c.QWordValue:= (l + r) div 2;
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−  if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue
+
−until r - l <= 1;
+
−
+
−hwSqrt.QWordValue:= l
+
−end;
+
−
+
−function Distance(const dx, dy: hwFloat): hwFloat;
+
−begin
+
−Distance:= hwSqrt(hwSqr(dx) + hwSqr(dy))
+
−end;
+
−
+
−function DistanceI(const dx, dy: LongInt): hwFloat;
+
−begin
+
−DistanceI:= hwSqrt(int2hwFloat(sqr(dx) + sqr(dy)))
+
−end;
+
−
+
−function SignAs(const num, signum: hwFloat): hwFloat;
+
−begin
+
−SignAs.QWordValue:= num.QWordValue;
+
−SignAs.isNegative:= signum.isNegative
+
−end;
+
−
+
−{$INCLUDE "SinTable.inc"}
+
−
+
−function AngleSin(const Angle: Longword): hwFloat;
+
−begin
+
−{$IFDEF DEBUGFILE}
+
−TryDo((Angle >= 0) and (Angle <= 2048), 'Sin param exceeds limits', true);
+
−{$ENDIF}
+
−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
+
−{$IFDEF DEBUGFILE}
+
−TryDo((Angle >= 0) and (Angle <= 2048), 'Cos param exceeds limits', true);
+
−{$ENDIF}
+
−AngleCos.isNegative:= Angle > 1024;
+
−if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle]
+
−                else AngleCos.QWordValue:= SinTable[Angle - 1024]
+
−end;
+
−
+
−{$ENDIF}
+
−
+
−end.