author | Wuzzy <Wuzzy2@mail.ru> |
Fri, 03 Nov 2017 05:03:47 +0100 | |
changeset 12826 | f3e07e53460d |
parent 11046 | 47a8c19ecb60 |
permissions | -rw-r--r-- |
(* * 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.