hedgewars/uFloat.pas
author nemo
Wed, 14 Mar 2018 11:36:43 -0400
changeset 13201 25502e6b3e08
parent 11046 47a8c19ecb60
child 15649 ea189ee9394f
permissions -rw-r--r--
While the intent was good, saving column width/sort was unfortunately not handling the addition of new columns and old configs were losing columns. If this is restored, it should have some check on column with invalidation of config.

(*
 * 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.