(*
* 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
*)
unit uFloat;
interface
{$IFDEF FPC}
{$ifdef FPC_LITTLE_ENDIAN}
type hwFloat = record
isNegative: boolean;
case byte of
0: (Frac, Round: Longword);
1: (QWordValue : QWord);
end;
{$else FPC_LITTLE_ENDIAN}
type hwFloat = record
isNegative: boolean;
case byte of
0: (Round, Frac: Longword);
1: (QWordValue : QWord);
end;
{$endif FPC_LITTLE_ENDIAN}
function int2hwFloat (const i: LongInt) : hwFloat;
operator + (const z1, z2: hwFloat) z : hwFloat;
operator - (const z1, z2: hwFloat) z : hwFloat;
operator - (const z1: hwFloat) z : hwFloat;
operator * (const z1, z2: hwFloat) z : hwFloat;
operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat;
operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;
operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
operator < (const z1, z2: hwFloat) b : boolean;
operator > (const z1, z2: hwFloat) b : boolean;
function cstr(const z: hwFloat): string;
function hwRound(const t: hwFloat): LongInt;
function hwAbs(const t: hwFloat): hwFloat;
function hwSqr(const t: hwFloat): hwFloat;
function hwSqrt(const t: hwFloat): hwFloat;
function Distance(const dx, dy: hwFloat): hwFloat;
function DistanceI(const dx, dy: LongInt): hwFloat;
function AngleSin(const Angle: Longword): hwFloat;
function AngleCos(const Angle: Longword): hwFloat;
function SignAs(const num, signum: hwFloat): hwFloat;
{$J-}
{$WARNINGS OFF}
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_0002: hwFloat = (isNegative: false; QWordValue: 858993);
_0_001: hwFloat = (isNegative: false; QWordValue: 4294967);
_0_003: hwFloat = (isNegative: false; QWordValue: 12884902);
_0_004: hwFloat = (isNegative: false; QWordValue: 17179869);
_0_005: hwFloat = (isNegative: false; QWordValue: 21474836);
_0_01: hwFloat = (isNegative: false; QWordValue: 42949673);
_0_02: hwFloat = (isNegative: false; QWordValue: 85899345);
_0_03: hwFloat = (isNegative: false; QWordValue: 128849018);
_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_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_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);
_1_9: hwFloat = (isNegative: false; QWordValue: 8160437862);
_0: hwFloat = (isNegative: false; QWordValue: 0);
_1: hwFloat = (isNegative: false; QWordValue: 4294967296);
_1_5: hwFloat = (isNegative: false; QWordValue: 4294967296 * 3 div 2);
_2: hwFloat = (isNegative: false; QWordValue: 4294967296 * 2);
_3: hwFloat = (isNegative: false; QWordValue: 4294967296 * 3);
_4: hwFloat = (isNegative: false; QWordValue: 4294967296 * 4);
_5: hwFloat = (isNegative: false; QWordValue: 4294967296 * 5);
_6: hwFloat = (isNegative: false; QWordValue: 4294967296 * 6);
_10: hwFloat = (isNegative: false; QWordValue: 4294967296 * 10);
_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);
_128: hwFloat = (isNegative: false; QWordValue: 4294967296 * 128);
_300: hwFloat = (isNegative: false; QWordValue: 4294967296 * 300);
_450: hwFloat = (isNegative: false; QWordValue: 4294967296 * 450);
_1024: hwFloat = (isNegative: false; QWordValue: 4294967296 * 1024);
_2048: hwFloat = (isNegative: false; QWordValue: 4294967296 * 2048);
_10000: hwFloat = (isNegative: false; QWordValue: 4294967296 * 10000);
cLittle: hwFloat = (isNegative: false; QWordValue: 1);
cHHKick: hwFloat = (isNegative: false; QWordValue: 42949673); // _0_01
{$WARNINGS ON}
{$ENDIF}
{$IFNDEF FPC}
type hwFloat = Extended;
{$ENDIF}
implementation
uses uConsts, uMisc;
{$IFDEF FPC}
function int2hwFloat (const i: LongInt) : hwFloat;
begin
int2hwFloat.isNegative:= i < 0;
int2hwFloat.Round:= abs(i);
int2hwFloat.Frac:= 0
end;
operator + (const z1, z2: hwFloat) z : hwFloat;
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;
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;
operator - (const z1: hwFloat) z : hwFloat;
begin
z:= z1;
z.isNegative:= not z.isNegative
end;
operator * (const z1, z2: hwFloat) z : hwFloat;
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;
begin
z.isNegative:= z1.isNegative xor (z2 < 0);
z.QWordValue:= z1.QWordValue * abs(z2)
end;
operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat;
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
((z2.QWordValue and $8000000000000000) = 0) do
begin
t.QWordValue:= t.QWordValue shl 1;
z2.QWordValue:= z2.QWordValue shl 1
end;
if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round)
else z.Frac:= 0
end
end;
operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat;
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): string;
var tmpstr: string;
begin
str(z.Round, cstr);
if z.Frac <> 0 then
begin
str(z.Frac / $100000000:1:15, tmpstr);
delete(tmpstr, 1, 2);
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
else hwRound:= t.Round
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:= QWord(t.Round) * t.Frac * 2 + ((QWord(t.Frac) * t.Frac) shr 32);
hwSqr.Round:= hwSqr.Round + t.Round * t.Round
end;
function hwSqrt(const t: hwFloat): hwFloat;
var l, r: QWord;
c: hwFloat;
begin
hwSqrt.isNegative:= false;
if t.Round = 0 then
begin
l:= t.QWordValue;
r:= $100000000
end else
begin
l:= $100000000;
r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5
if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF
end;
repeat
c.QWordValue:= (l + r) div 2;
if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue
until r - l <= 1;
hwSqrt.QWordValue:= l
end;
function Distance(const dx, dy: hwFloat): hwFloat;
begin
Distance:= hwSqrt(hwSqr(dx) + hwSqr(dy))
end;
function DistanceI(const dx, dy: LongInt): hwFloat;
begin
DistanceI:= hwSqrt(int2hwFloat(sqr(dx) + sqr(dy)))
end;
function SignAs(const num, signum: hwFloat): hwFloat;
begin
SignAs.QWordValue:= num.QWordValue;
SignAs.isNegative:= signum.isNegative
end;
{$INCLUDE SinTable.inc}
function AngleSin(const Angle: Longword): hwFloat;
begin
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
AngleCos.isNegative:= Angle > 1024;
if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle]
else AngleCos.QWordValue:= SinTable[Angle - 1024]
end;
{$ENDIF}
end.