hedgewars: comparison hedgewars/uFloat.pas

equal deleted inserted replaced

-:41b0a9955c47
+:ddcdedd3330b
 (*
 * Hedgewars, a free turn based strategy game
-* Copyright (c) 2004-2011 Andrey Korotaev <unC0Rr@gmail.com>
+* 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
 *
 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;
+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;
 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}
 _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_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);
 uses uSinTable;
 {$IFDEF FPC}
-function int2hwFloat (const i: LongInt) : hwFloat;
+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;
+function hwFloat2Float (const i: hwFloat) : extended; inline;
 begin
-hwFloat2Float:= i.QWordValue / $100000000;
+hwFloat2Float:= i.Frac / $100000000 + i.Round;
-if i.isNegative then hwFloat2Float:= -hwFloat2Float;
+if i.isNegative then
-end;
+hwFloat2Float:= -hwFloat2Float;
+end;
-operator = (const z1, z2: hwFloat) z:boolean; inline;
+{$IFNDEF WEB}
+operator = (const z1, z2: hwFloat) z : boolean; inline;
 begin
 z:= (z1.isNegative = z2.isNegative) and (z1.QWordValue = z2.QWordValue);
 end;
+{$IFDEF PAS2C}
-operator + (const z1, z2: hwFloat) z : hwFloat;
+operator <> (const z1, z2: hwFloat) z : boolean; inline;
+begin
+z:= (z1.isNegative <> z2.isNegative) or (z1.QWordValue <> z2.QWordValue);
+end;
+{$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
+end
-begin
+else
-z.isNegative:= z2.isNegative;
+begin
-z.QWordValue:= z2.QWordValue - z1.QWordValue
+z.isNegative:= z2.isNegative;
-end
+z.QWordValue:= z2.QWordValue - z1.QWordValue
-end;
+end
+end;
-operator - (const z1, z2: hwFloat) z : hwFloat;
+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
+end
-begin
+else
-z.isNegative:= not z2.isNegative;
+begin
-z.QWordValue:= z2.QWordValue - z1.QWordValue
+z.isNegative:= not z2.isNegative;
-end
+z.QWordValue:= z2.QWordValue - z1.QWordValue
-else begin
+end
-z.isNegative:= z1.isNegative;
+else
-z.QWordValue:= z1.QWordValue + z2.QWordValue
+begin
-end
+z.isNegative:= z1.isNegative;
-end;
+z.QWordValue:= z1.QWordValue + z2.QWordValue
+end
-operator - (const z1: hwFloat) z : hwFloat;
+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;
+operator * (const z1, z2: hwFloat) z : hwFloat; inline;
 begin
 z.isNegative:= z1.isNegative xor z2.isNegative;
-z.QWordValue:= QWord(z1.Round) * z2.Frac +
+z.QWordValue:= QWord(z1.Round) * z2.Frac + QWord(z1.Frac) * z2.Round + ((QWord(z1.Frac) * z2.Frac) shr 32);
-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;
+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;
+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
+while ((t.QWordValue and $8000000000000000) = 0) and ((z2.QWordValue and $8000000000000000) = 0) do
-((z2.QWordValue and $8000000000000000) = 0) do
+begin
-begin
+t.QWordValue:= t.QWordValue shl 1;
-t.QWordValue:= t.QWordValue shl 1;
+z2.QWordValue:= z2.QWordValue shl 1
-z2.QWordValue:= z2.QWordValue shl 1
+end;
-end;
+if z2.Round > 0 then
-if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round)
+z.Frac:= (t.QWordValue) div (z2.Round)
-else z.Frac:= 0
+else
-end
+z.Frac:= 0
-end;
+end
+end;
-operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
+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;
-operator < (const z1, z2: hwFloat) b : boolean;
-begin
-if z1.isNegative xor z2.isNegative then
-b:= z1.isNegative
-else
-if z1.QWordValue = z2.QWordValue then
-b:= false
-else
-b:= (z1.QWordValue < z2.QWordValue) xor z1.isNegative
-end;
-operator > (const z1, z2: hwFloat) b : boolean;
-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) xor z2.isNegative
-end;
 function cstr(const z: hwFloat): shortstring;
 var tmpstr: shortstring;
 begin
 str(z.Round, cstr);
 if z.Frac <> 0 then
 begin
-str(z.Frac / $100000000:1:10, tmpstr);
+str(z.Frac / $100000000, tmpstr);
 delete(tmpstr, 1, 2);
-cstr:= cstr + '.' + tmpstr
+cstr:= cstr + '.' + copy(tmpstr, 1, 10)
 end;
-if z.isNegative then cstr:= '-' + cstr
+if z.isNegative then
+cstr:= '-' + cstr
 end;
 function hwRound(const t: hwFloat): LongInt;
 begin
-if t.isNegative then hwRound:= -(t.Round and $7FFFFFFF)
+if t.isNegative then
-else hwRound:= t.Round and $7FFFFFFF
+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;
+function hwSqr(const t: hwFloat): hwFloat; inline;
 begin
 hwSqr.isNegative:= false;
-hwSqr.QWordValue:=
+hwSqr.QWordValue:= ((QWord(t.Round) * t.Round) shl 32) + QWord(t.Round) * t.Frac * 2 + ((QWord(t.Frac) * t.Frac) shr 32);
-((QWord(t.Round) * t.Round) shl 32)
+end;
-+ QWord(t.Round) * t.Frac * 2
-+ ((QWord(t.Frac) * t.Frac) shr 32);
+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
+end
-begin
+else
-l:= $100000000;
+begin
-r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5
+if t.QWordValue > $FFFFFFFFFFFF then // t.Round > 65535.9999
-if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF
+begin
-end;
+l:= $10000000000; // 256
+r:= $FFFFFFFFFFFF; // 65535.9999
+end else
+if t.QWordValue >= rThreshold then
+begin
+l:= lThreshold;
+r:= $10000000000; // 256
+end else
+begin
+l:= $100000000;
+r:= lThreshold;
+end;
+end;
 repeat
-c.QWordValue:= (l + r) div 2;
+c.QWordValue:= (l + r) shr 1;
-if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue
+if hwSqr(c).QWordValue > t.QWordValue then
+r:= c.QWordValue
+else
+l:= c.QWordValue
 until r - l <= 1;
 hwSqrt.QWordValue:= l
 end;
 end;
 function hwSign(r: hwFloat): LongInt;
 begin
 // yes, we have negative zero for a reason
-if r.isNegative then hwSign:= -1 else hwSign:= 1
+if r.isNegative then
+hwSign:= -1
+else
+hwSign:= 1
+end;
+function hwSignf(r: real): LongInt;
+begin
+if r < 0 then
+hwSignf:= -1
+else
+hwSignf:= 1
 end;
 function AngleSin(const Angle: Longword): hwFloat;
 begin
 //TryDo((Angle >= 0) and (Angle <= 2048), 'Sin param exceeds limits', true);
 AngleSin.isNegative:= false;
-if Angle < 1024 then AngleSin.QWordValue:= SinTable[Angle]
+if Angle < 1024 then
-else AngleSin.QWordValue:= SinTable[2048 - Angle]
+AngleSin.QWordValue:= SinTable[Angle]
+else
+AngleSin.QWordValue:= SinTable[2048 - Angle]
 end;
 function AngleCos(const Angle: Longword): hwFloat;
 begin
 //TryDo((Angle >= 0) and (Angle <= 2048), 'Cos param exceeds limits', true);
 AngleCos.isNegative:= Angle > 1024;
-if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle]
+if Angle < 1024 then
-else AngleCos.QWordValue:= SinTable[Angle - 1024]
+AngleCos.QWordValue:= SinTable[1024 - Angle]
-end;
+else
+AngleCos.QWordValue:= SinTable[Angle - 1024]
-function isZero(const z: hwFloat): boolean; inline;
+end;
-begin
-isZero := z.QWordValue = 0;
+function vector2Angle(const x, y: hwFloat): LongInt;
-end;
+var d, nf: hwFloat;
+l, r, c, oc: Longword;
+n: QWord;
+begin
+d:= _1 / Distance(x, y);
+nf:= y * d;
+n:= nf.QWordValue;
+l:= 0;
+r:= 1024;
+c:= 0;
+repeat
+oc:= c;
+c:= (l + r) shr 1;
+if n >= SinTable[c] then
+l:= c
+else
+r:= c;
+until (oc = c);
+if x.isNegative then c:= 2048 - c;
+if y.isNegative then c:= - c;
+vector2Angle:= c
+end;
 {$ENDIF}
 end.

branch	hedgeroid
changeset 7855	ddcdedd3330b
parent 7715	8b653edac2a2
child 8026	4a4f21070479
child 8838	aa2ffd427f6a