author | unc0rr |
Sun, 12 Apr 2009 18:51:35 +0000 | |
changeset 1972 | e7a7c5eb5d86 |
parent 1915 | c357f5b55320 |
child 2300 | d633bc70c893 |
permissions | -rw-r--r-- |
351 | 1 |
(* |
1066 | 2 |
* Hedgewars, a free turn based strategy game |
883 | 3 |
* Copyright (c) 2007, 2008 Andrey Korotaev <unC0Rr@gmail.com> |
351 | 4 |
* |
5 |
* This program is free software; you can redistribute it and/or modify |
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* it under the terms of the GNU General Public License as published by |
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* the Free Software Foundation; version 2 of the License |
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* |
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* This program is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU General Public License for more details. |
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* |
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* You should have received a copy of the GNU General Public License |
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA |
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*) |
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||
19 |
unit uFloat; |
|
20 |
interface |
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21 |
||
1629 | 22 |
{$INCLUDE options.inc} |
23 |
||
351 | 24 |
{$IFDEF FPC} |
25 |
{$ifdef FPC_LITTLE_ENDIAN} |
|
26 |
type hwFloat = record |
|
27 |
isNegative: boolean; |
|
28 |
case byte of |
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29 |
0: (Frac, Round: Longword); |
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30 |
1: (QWordValue : QWord); |
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31 |
end; |
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32 |
{$else FPC_LITTLE_ENDIAN} |
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type hwFloat = record |
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34 |
isNegative: boolean; |
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35 |
case byte of |
|
36 |
0: (Round, Frac: Longword); |
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37 |
1: (QWordValue : QWord); |
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38 |
end; |
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39 |
{$endif FPC_LITTLE_ENDIAN} |
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40 |
||
515 | 41 |
function int2hwFloat (const i: LongInt) : hwFloat; |
351 | 42 |
|
515 | 43 |
operator + (const z1, z2: hwFloat) z : hwFloat; |
44 |
operator - (const z1, z2: hwFloat) z : hwFloat; |
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45 |
operator - (const z1: hwFloat) z : hwFloat; |
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351 | 46 |
|
515 | 47 |
operator * (const z1, z2: hwFloat) z : hwFloat; |
48 |
operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat; |
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49 |
operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat; |
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50 |
operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat; |
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351 | 51 |
|
515 | 52 |
operator < (const z1, z2: hwFloat) b : boolean; |
53 |
operator > (const z1, z2: hwFloat) b : boolean; |
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351 | 54 |
|
515 | 55 |
function cstr(const z: hwFloat): string; |
56 |
function hwRound(const t: hwFloat): LongInt; |
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57 |
function hwAbs(const t: hwFloat): hwFloat; |
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58 |
function hwSqr(const t: hwFloat): hwFloat; |
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59 |
function hwSqrt(const t: hwFloat): hwFloat; |
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function Distance(const dx, dy: hwFloat): hwFloat; |
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61 |
function DistanceI(const dx, dy: LongInt): hwFloat; |
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62 |
function AngleSin(const Angle: Longword): hwFloat; |
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63 |
function AngleCos(const Angle: Longword): hwFloat; |
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64 |
function SignAs(const num, signum: hwFloat): hwFloat; |
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351 | 65 |
|
538 | 66 |
{$J-} |
611 | 67 |
{$WARNINGS OFF} |
351 | 68 |
const _1div1024: hwFloat = (isNegative: false; QWordValue: 4194304); |
69 |
_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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1586 | 76 |
_0_0005: hwFloat = (isNegative: false; QWordValue: 2147484); |
351 | 77 |
_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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365 | 85 |
_0_1: hwFloat = (isNegative: false; QWordValue: 429496730); |
351 | 86 |
_0_15: hwFloat = (isNegative: false; QWordValue: 644245094); |
87 |
_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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91 |
_0_39: hwFloat = (isNegative: false; QWordValue: 1675037245); |
351 | 92 |
_0_4: hwFloat = (isNegative: false; QWordValue: 1717986918); |
93 |
_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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358 | 97 |
_0_7: hwFloat = (isNegative: false; QWordValue: 3006477107); |
351 | 98 |
_0_8: hwFloat = (isNegative: false; QWordValue: 3435973837); |
99 |
_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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1433 | 105 |
_0_998: hwFloat = (isNegative: false; QWordValue: 4294967296); |
351 | 106 |
_0_999: hwFloat = (isNegative: false; QWordValue: 4290672328); |
107 |
_1_9: hwFloat = (isNegative: false; QWordValue: 8160437862); |
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498 | 108 |
_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); |
498 | 111 |
_2: hwFloat = (isNegative: false; QWordValue: 4294967296 * 2); |
112 |
_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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1652 | 120 |
_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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1915 | 124 |
_256: hwFloat = (isNegative: false; QWordValue: 4294967296 * 256); |
1124 | 125 |
_300: hwFloat = (isNegative: false; QWordValue: 4294967296 * 300); |
498 | 126 |
_450: hwFloat = (isNegative: false; QWordValue: 4294967296 * 450); |
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_1024: hwFloat = (isNegative: false; QWordValue: 4294967296 * 1024); |
128 |
_2048: hwFloat = (isNegative: false; QWordValue: 4294967296 * 2048); |
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_4096: hwFloat = (isNegative: false; QWordValue: 4294967296 * 4096); |
498 | 130 |
_10000: hwFloat = (isNegative: false; QWordValue: 4294967296 * 10000); |
351 | 131 |
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cLittle: hwFloat = (isNegative: false; QWordValue: 1); |
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967 | 133 |
cHHKick: hwFloat = (isNegative: false; QWordValue: 42949673); // _0_01 |
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{$WARNINGS ON} |
351 | 135 |
{$ENDIF} |
136 |
||
137 |
{$IFNDEF FPC} |
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type hwFloat = Extended; |
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{$ENDIF} |
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140 |
||
141 |
implementation |
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744 | 142 |
uses uConsts, uMisc; |
351 | 143 |
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{$IFDEF FPC} |
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145 |
||
515 | 146 |
function int2hwFloat (const i: LongInt) : hwFloat; |
351 | 147 |
begin |
498 | 148 |
int2hwFloat.isNegative:= i < 0; |
149 |
int2hwFloat.Round:= abs(i); |
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int2hwFloat.Frac:= 0 |
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351 | 151 |
end; |
152 |
||
515 | 153 |
operator + (const z1, z2: hwFloat) z : hwFloat; |
351 | 154 |
begin |
155 |
if z1.isNegative = z2.isNegative then |
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begin |
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157 |
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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170 |
end; |
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171 |
||
515 | 172 |
operator - (const z1, z2: hwFloat) z : hwFloat; |
351 | 173 |
begin |
174 |
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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177 |
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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184 |
else begin |
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185 |
z.isNegative:= z1.isNegative; |
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z.QWordValue:= z1.QWordValue + z2.QWordValue |
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187 |
end |
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188 |
end; |
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189 |
||
515 | 190 |
operator - (const z1: hwFloat) z : hwFloat; |
351 | 191 |
begin |
192 |
z:= z1; |
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z.isNegative:= not z.isNegative |
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194 |
end; |
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195 |
||
196 |
||
515 | 197 |
operator * (const z1, z2: hwFloat) z : hwFloat; |
351 | 198 |
begin |
199 |
z.isNegative:= z1.isNegative xor z2.isNegative; |
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200 |
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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203 |
z.Round:= z.Round + QWord(z1.Round) * z2.Round; |
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204 |
end; |
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205 |
||
515 | 206 |
operator * (const z1: hwFloat; const z2: LongInt) z : hwFloat; |
351 | 207 |
begin |
208 |
z.isNegative:= z1.isNegative xor (z2 < 0); |
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515 | 209 |
z.QWordValue:= z1.QWordValue * abs(z2) |
351 | 210 |
end; |
211 |
||
515 | 212 |
operator / (const z1: hwFloat; z2: hwFloat) z : hwFloat; |
351 | 213 |
var t: hwFloat; |
214 |
begin |
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215 |
z.isNegative:= z1.isNegative xor z2.isNegative; |
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216 |
z.Round:= z1.QWordValue div z2.QWordValue; |
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217 |
t:= z1 - z2 * z.Round; |
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218 |
if t.QWordValue = 0 then |
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219 |
z.Frac:= 0 |
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220 |
else |
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221 |
begin |
|
222 |
while ((t.QWordValue and $8000000000000000) = 0) and |
|
223 |
((z2.QWordValue and $8000000000000000) = 0) do |
|
224 |
begin |
|
225 |
t.QWordValue:= t.QWordValue shl 1; |
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226 |
z2.QWordValue:= z2.QWordValue shl 1 |
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227 |
end; |
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228 |
if z2.Round > 0 then z.Frac:= (t.QWordValue) div (z2.Round) |
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229 |
else z.Frac:= 0 |
351 | 230 |
end |
231 |
end; |
|
232 |
||
515 | 233 |
operator / (const z1: hwFloat; const z2: LongInt) z : hwFloat; |
498 | 234 |
begin |
235 |
z.isNegative:= z1.isNegative xor (z2 < 0); |
|
515 | 236 |
z.QWordValue:= z1.QWordValue div abs(z2) |
498 | 237 |
end; |
238 |
||
515 | 239 |
operator < (const z1, z2: hwFloat) b : boolean; |
351 | 240 |
begin |
916 | 241 |
if z1.isNegative xor z2.isNegative then |
351 | 242 |
b:= z1.isNegative |
243 |
else |
|
244 |
if z1.QWordValue = z2.QWordValue then |
|
245 |
b:= false |
|
246 |
else |
|
247 |
b:= (z1.QWordValue < z2.QWordValue) xor z1.isNegative |
|
248 |
end; |
|
249 |
||
515 | 250 |
operator > (const z1, z2: hwFloat) b : boolean; |
351 | 251 |
begin |
916 | 252 |
if z1.isNegative xor z2.isNegative then |
351 | 253 |
b:= z2.isNegative |
254 |
else |
|
255 |
if z1.QWordValue = z2.QWordValue then |
|
256 |
b:= false |
|
257 |
else |
|
258 |
b:= (z1.QWordValue > z2.QWordValue) xor z2.isNegative |
|
259 |
end; |
|
260 |
||
515 | 261 |
function cstr(const z: hwFloat): string; |
351 | 262 |
var tmpstr: string; |
263 |
begin |
|
264 |
str(z.Round, cstr); |
|
265 |
if z.Frac <> 0 then |
|
266 |
begin |
|
267 |
str(z.Frac / $100000000:1:15, tmpstr); |
|
268 |
delete(tmpstr, 1, 2); |
|
269 |
cstr:= cstr + '.' + tmpstr |
|
270 |
end; |
|
271 |
if z.isNegative then cstr:= '-' + cstr |
|
272 |
end; |
|
273 |
||
515 | 274 |
function hwRound(const t: hwFloat): LongInt; |
351 | 275 |
begin |
276 |
if t.isNegative then hwRound:= -t.Round |
|
277 |
else hwRound:= t.Round |
|
278 |
end; |
|
279 |
||
515 | 280 |
function hwAbs(const t: hwFloat): hwFloat; |
351 | 281 |
begin |
282 |
hwAbs:= t; |
|
283 |
hwAbs.isNegative:= false |
|
284 |
end; |
|
285 |
||
515 | 286 |
function hwSqr(const t: hwFloat): hwFloat; |
351 | 287 |
begin |
1433 | 288 |
hwSqr.isNegative:= false; |
289 |
hwSqr.QWordValue:= |
|
290 |
((QWord(t.Round) * t.Round) shl 32) |
|
291 |
+ QWord(t.Round) * t.Frac * 2 |
|
292 |
+ ((QWord(t.Frac) * t.Frac) shr 32); |
|
351 | 293 |
end; |
294 |
||
515 | 295 |
function hwSqrt(const t: hwFloat): hwFloat; |
738 | 296 |
var l, r: QWord; |
297 |
c: hwFloat; |
|
357 | 298 |
begin |
299 |
hwSqrt.isNegative:= false; |
|
744 | 300 |
|
301 |
if t.Round = 0 then |
|
302 |
begin |
|
303 |
l:= t.QWordValue; |
|
304 |
r:= $100000000 |
|
305 |
end else |
|
306 |
begin |
|
307 |
l:= $100000000; |
|
953
237fc147950c
Fix bug in hwSqrt when calculating square root of number >= 65536
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|
308 |
r:= t.QWordValue div 2 + $80000000; // r:= t / 2 + 0.5 |
237fc147950c
Fix bug in hwSqrt when calculating square root of number >= 65536
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diff
changeset
|
309 |
if r > $FFFFFFFFFFFF then r:= $FFFFFFFFFFFF |
744 | 310 |
end; |
311 |
||
738 | 312 |
repeat |
313 |
c.QWordValue:= (l + r) div 2; |
|
314 |
if hwSqr(c).QWordValue > t.QWordValue then r:= c.QWordValue else l:= c.QWordValue |
|
315 |
until r - l <= 1; |
|
744 | 316 |
|
738 | 317 |
hwSqrt.QWordValue:= l |
357 | 318 |
end; |
319 |
||
515 | 320 |
function Distance(const dx, dy: hwFloat): hwFloat; |
351 | 321 |
begin |
738 | 322 |
Distance:= hwSqrt(hwSqr(dx) + hwSqr(dy)) |
351 | 323 |
end; |
324 |
||
515 | 325 |
function DistanceI(const dx, dy: LongInt): hwFloat; |
498 | 326 |
begin |
856 | 327 |
DistanceI:= hwSqrt(int2hwFloat(sqr(dx) + sqr(dy))) |
498 | 328 |
end; |
329 |
||
515 | 330 |
function SignAs(const num, signum: hwFloat): hwFloat; |
498 | 331 |
begin |
856 | 332 |
SignAs.QWordValue:= num.QWordValue; |
498 | 333 |
SignAs.isNegative:= signum.isNegative |
334 |
end; |
|
335 |
||
357 | 336 |
{$INCLUDE SinTable.inc} |
337 |
||
515 | 338 |
function AngleSin(const Angle: Longword): hwFloat; |
351 | 339 |
begin |
1629 | 340 |
{$IFDEF DEBUGFILE} |
1640 | 341 |
TryDo((Angle >= 0) and (Angle <= 2048), 'Sin param exceeds limits', true); |
1629 | 342 |
{$ENDIF} |
351 | 343 |
AngleSin.isNegative:= false; |
357 | 344 |
if Angle < 1024 then AngleSin.QWordValue:= SinTable[Angle] |
345 |
else AngleSin.QWordValue:= SinTable[2048 - Angle] |
|
351 | 346 |
end; |
347 |
||
515 | 348 |
function AngleCos(const Angle: Longword): hwFloat; |
351 | 349 |
begin |
1629 | 350 |
{$IFDEF DEBUGFILE} |
1640 | 351 |
TryDo((Angle >= 0) and (Angle <= 2048), 'Cos param exceeds limits', true); |
1629 | 352 |
{$ENDIF} |
357 | 353 |
AngleCos.isNegative:= Angle > 1024; |
354 |
if Angle < 1024 then AngleCos.QWordValue:= SinTable[1024 - Angle] |
|
355 |
else AngleCos.QWordValue:= SinTable[Angle - 1024] |
|
351 | 356 |
end; |
357 |
||
358 |
{$ENDIF} |
|
359 |
||
360 |
end. |