workbench/classes/gadgets/colorwheel/fixmathtrans.c

   1 /*
   2     Copyright © 1995-2001, The AROS Development Team. All rights reserved.
   3     $Id$
   4 */
   5
   6 #include "colorwheel_intern.h"
   7 #include "fixmath.h"
   8
   9 #define MAX_TRIG        1024
  10
  11 #if FIXED_MATH
  12
  13 /****************************************************************************/
  14
  15 Fixed32 SinCosTab[MAX_TRIG] = {
  16         0,402,804,1206,1608,2010,2412,2814,3216,3617,4019,4420,
  17         4821,5222,5623,6023,6424,6824,7224,7623,8022,8421,8820,9218,
  18         9616,10014,10411,10808,11204,11600,11996,12391,12785,13180,13573,13966,
  19         14359,14751,15143,15534,15924,16314,16703,17091,17479,17867,18253,18639,
  20         19024,19409,19792,20175,20557,20939,21320,21699,22078,22457,22834,23210,
  21         23586,23961,24335,24708,25080,25451,25821,26190,26558,26925,27291,27656,
  22         28020,28383,28745,29106,29466,29824,30182,30538,30893,31247,31600,31952,
  23         32303,32652,33000,33347,33692,34036,34379,34721,35062,35401,35738,36075,
  24         36410,36744,37076,37407,37736,38064,38391,38716,39040,39362,39683,40002,
  25         40320,40636,40951,41264,41576,41886,42194,42501,42806,43110,43412,43713,
  26         44011,44308,44604,44898,45190,45480,45769,46056,46341,46624,46906,47186,
  27         47464,47741,48015,48288,48559,48828,49095,49361,49624,49886,50146,50404,
  28         50660,50914,51166,51417,51665,51912,52156,52399,52639,52878,53114,53349,
  29         53581,53812,54040,54267,54491,54714,54934,55152,55368,55582,55794,56004,
  30         56212,56418,56621,56823,57022,57219,57414,57607,57798,57986,58172,58356,
  31         58538,58718,58896,59071,59244,59415,59583,59750,59914,60076,60235,60392,
  32         60547,60700,60851,60999,61145,61288,61429,61568,61705,61839,61971,62101,
  33         62228,62353,62476,62596,62714,62830,62943,63054,63162,63268,63372,63473,
  34         63572,63669,63763,63854,63944,64031,64115,64197,64277,64354,64429,64501,
  35         64571,64639,64704,64766,64827,64884,64940,64993,65043,65091,65137,65180,
  36         65220,65259,65294,65328,65358,65387,65413,65436,65457,65476,65492,65505,
  37         65516,65525,65531,65535,
  38 // Cosine starts here and ends above :)
  39         65536,65535,65531,65525,65516,65505,65492,65476,65457,65436,65413,65387,
  40         65358,65328,65294,65259,65220,65180,65137,65091,65043,64993,64940,64884,
  41         64827,64766,64704,64639,64571,64501,64429,64354,64277,64197,64115,64031,
  42         63944,63854,63763,63669,63572,63473,63372,63268,63162,63054,62943,62830,
  43         62714,62596,62476,62353,62228,62101,61971,61839,61705,61568,61429,61288,
  44         61145,60999,60851,60700,60547,60392,60235,60076,59914,59750,59583,59415,
  45         59244,59071,58896,58718,58538,58356,58172,57986,57798,57607,57414,57219,
  46         57022,56823,56621,56418,56212,56004,55794,55582,55368,55152,54934,54714,
  47         54491,54267,54040,53812,53581,53349,53114,52878,52639,52399,52156,51912,
  48         51665,51417,51166,50914,50660,50404,50146,49886,49624,49361,49095,48828,
  49         48559,48288,48015,47741,47464,47186,46906,46624,46341,46056,45769,45480,
  50         45190,44898,44604,44308,44011,43713,43412,43110,42806,42501,42194,41886,
  51         41576,41264,40951,40636,40320,40002,39683,39362,39040,38716,38391,38064,
  52         37736,37407,37076,36744,36410,36075,35738,35401,35062,34721,34379,34036,
  53         33692,33347,33000,32652,32303,31952,31600,31247,30893,30538,30182,29824,
  54         29466,29106,28745,28383,28020,27656,27291,26925,26558,26190,25821,25451,
  55         25080,24708,24335,23961,23586,23210,22834,22457,22078,21699,21320,20939,
  56         20557,20175,19792,19409,19024,18639,18253,17867,17479,17091,16703,16314,
  57         15924,15534,15143,14751,14359,13966,13573,13180,12785,12391,11996,11600,
  58         11204,10808,10411,10014,9616,9218,8820,8421,8022,7623,7224,6824,
  59         6424,6023,5623,5222,4821,4420,4019,3617,3216,2814,2412,2010,
  60         1608,1206,804,402,
  61         0,-402,-804,-1206,-1608,-2010,-2412,-2814,-3216,-3617,-4019,-4420,
  62         -4821,-5222,-5623,-6023,-6424,-6824,-7224,-7623,-8022,-8421,-8820,-9218,
  63         -9616,-10014,-10411,-10808,-11204,-11600,-11996,-12391,-12785,-13180,-13573,-13966,
  64         -14359,-14751,-15143,-15534,-15924,-16314,-16703,-17091,-17479,-17867,-18253,-18639,
  65         -19024,-19409,-19792,-20175,-20557,-20939,-21320,-21699,-22078,-22457,-22834,-23210,
  66         -23586,-23961,-24335,-24708,-25080,-25451,-25821,-26190,-26558,-26925,-27291,-27656,
  67         -28020,-28383,-28745,-29106,-29466,-29824,-30182,-30538,-30893,-31247,-31600,-31952,
  68         -32303,-32652,-33000,-33347,-33692,-34036,-34379,-34721,-35062,-35401,-35738,-36075,
  69         -36410,-36744,-37076,-37407,-37736,-38064,-38391,-38716,-39040,-39362,-39683,-40002,
  70         -40320,-40636,-40951,-41264,-41576,-41886,-42194,-42501,-42806,-43110,-43412,-43713,
  71         -44011,-44308,-44604,-44898,-45190,-45480,-45769,-46056,-46341,-46624,-46906,-47186,
  72         -47464,-47741,-48015,-48288,-48559,-48828,-49095,-49361,-49624,-49886,-50146,-50404,
  73         -50660,-50914,-51166,-51417,-51665,-51912,-52156,-52399,-52639,-52878,-53114,-53349,
  74         -53581,-53812,-54040,-54267,-54491,-54714,-54934,-55152,-55368,-55582,-55794,-56004,
  75         -56212,-56418,-56621,-56823,-57022,-57219,-57414,-57607,-57798,-57986,-58172,-58356,
  76         -58538,-58718,-58896,-59071,-59244,-59415,-59583,-59750,-59914,-60076,-60235,-60392,
  77         -60547,-60700,-60851,-60999,-61145,-61288,-61429,-61568,-61705,-61839,-61971,-62101,
  78         -62228,-62353,-62476,-62596,-62714,-62830,-62943,-63054,-63162,-63268,-63372,-63473,
  79         -63572,-63669,-63763,-63854,-63944,-64031,-64115,-64197,-64277,-64354,-64429,-64501,
  80         -64571,-64639,-64704,-64766,-64827,-64884,-64940,-64993,-65043,-65091,-65137,-65180,
  81         -65220,-65259,-65294,-65328,-65358,-65387,-65413,-65436,-65457,-65476,-65492,-65505,
  82         -65516,-65525,-65531,-65535,
  83         -65536,-65535,-65531,-65525,-65516,-65505,-65492,-65476,-65457,-65436,-65413,-65387,
  84         -65358,-65328,-65294,-65259,-65220,-65180,-65137,-65091,-65043,-64993,-64940,-64884,
  85         -64827,-64766,-64704,-64639,-64571,-64501,-64429,-64354,-64277,-64197,-64115,-64031,
  86         -63944,-63854,-63763,-63669,-63572,-63473,-63372,-63268,-63162,-63054,-62943,-62830,
  87         -62714,-62596,-62476,-62353,-62228,-62101,-61971,-61839,-61705,-61568,-61429,-61288,
  88         -61145,-60999,-60851,-60700,-60547,-60392,-60235,-60076,-59914,-59750,-59583,-59415,
  89         -59244,-59071,-58896,-58718,-58538,-58356,-58172,-57986,-57798,-57607,-57414,-57219,
  90         -57022,-56823,-56621,-56418,-56212,-56004,-55794,-55582,-55368,-55152,-54934,-54714,
  91         -54491,-54267,-54040,-53812,-53581,-53349,-53114,-52878,-52639,-52399,-52156,-51912,
  92         -51665,-51417,-51166,-50914,-50660,-50404,-50146,-49886,-49624,-49361,-49095,-48828,
  93         -48559,-48288,-48015,-47741,-47464,-47186,-46906,-46624,-46341,-46056,-45769,-45480,
  94         -45190,-44898,-44604,-44308,-44011,-43713,-43412,-43110,-42806,-42501,-42194,-41886,
  95         -41576,-41264,-40951,-40636,-40320,-40002,-39683,-39362,-39040,-38716,-38391,-38064,
  96         -37736,-37407,-37076,-36744,-36410,-36075,-35738,-35401,-35062,-34721,-34379,-34036,
  97         -33692,-33347,-33000,-32652,-32303,-31952,-31600,-31247,-30893,-30538,-30182,-29824,
  98         -29466,-29106,-28745,-28383,-28020,-27656,-27291,-26925,-26558,-26190,-25821,-25451,
  99         -25080,-24708,-24335,-23961,-23586,-23210,-22834,-22457,-22078,-21699,-21320,-20939,
 100         -20557,-20175,-19792,-19409,-19024,-18639,-18253,-17867,-17479,-17091,-16703,-16314,
 101         -15924,-15534,-15143,-14751,-14359,-13966,-13573,-13180,-12785,-12391,-11996,-11600,
 102         -11204,-10808,-10411,-10014,-9616,-9218,-8820,-8421,-8022,-7623,-7224,-6824,
 103         -6424,-6023,-5623,-5222,-4821,-4420,-4019,-3617,-3216,-2814,-2412,-2010,
 104         -1608,-1206,-804,-402
 105 };
 106
 107 /****************************************************************************/
 108
 109 /* Fixed32 */
 110 unsigned short TanTab[MAX_TRIG+1] = {
 111         0,63,127,191,255,319,383,447,511,575,639,
 112         703,767,831,895,959,1023,1087,1151,1215,1279,
 113         1343,1407,1471,1535,1599,1663,1727,1791,1855,1919,
 114         1983,2047,2111,2175,2239,2303,2366,2430,2494,2558,
 115         2622,2686,2750,2814,2878,2942,3005,3069,3133,3197,
 116         3261,3325,3388,3452,3516,3580,3644,3708,3771,3835,
 117         3899,3963,4026,4090,4154,4218,4281,4345,4409,4473,
 118         4536,4600,4664,4727,4791,4855,4918,4982,5046,5109,
 119         5173,5236,5300,5363,5427,5491,5554,5618,5681,5745,
 120         5808,5872,5935,5999,6062,6126,6189,6252,6316,6379,
 121         6443,6506,6569,6633,6696,6759,6823,6886,6949,7013,
 122         7076,7139,7202,7266,7329,7392,7455,7518,7581,7645,
 123         7708,7771,7834,7897,7960,8023,8086,8149,8212,8275,
 124         8338,8401,8464,8527,8590,8653,8716,8779,8841,8904,
 125         8967,9030,9093,9155,9218,9281,9344,9406,9469,9532,
 126         9594,9657,9720,9782,9845,9907,9970,10032,10095,10157,
 127         10220,10282,10345,10407,10470,10532,10594,10657,10719,10781,
 128         10843,10906,10968,11030,11092,11155,11217,11279,11341,11403,
 129         11465,11527,11589,11651,11713,11775,11837,11899,11961,12023,
 130         12085,12146,12208,12270,12332,12394,12455,12517,12579,12640,
 131         12702,12764,12825,12887,12948,13010,13071,13133,13194,13256,
 132         13317,13378,13440,13501,13562,13624,13685,13746,13807,13869,
 133         13930,13991,14052,14113,14174,14235,14296,14357,14418,14479,
 134         14540,14601,14662,14723,14784,14844,14905,14966,15026,15087,
 135         15148,15208,15269,15330,15390,15451,15511,15572,15632,15693,
 136         15753,15813,15874,15934,15994,16054,16115,16175,16235,16295,
 137         16355,16415,16475,16535,16595,16655,16715,16775,16835,16895,
 138         16955,17015,17074,17134,17194,17253,17313,17373,17432,17492,
 139         17551,17611,17670,17730,17789,17849,17908,17967,18027,18086,
 140         18145,18204,18264,18323,18382,18441,18500,18559,18618,18677,
 141         18736,18795,18854,18912,18971,19030,19089,19147,19206,19265,
 142         19323,19382,19440,19499,19557,19616,19674,19733,19791,19849,
 143         19908,19966,20024,20082,20140,20199,20257,20315,20373,20431,
 144         20489,20547,20605,20662,20720,20778,20836,20894,20951,21009,
 145         21067,21124,21182,21239,21297,21354,21412,21469,21526,21584,
 146         21641,21698,21755,21813,21870,21927,21984,22041,22098,22155,
 147         22212,22269,22326,22383,22439,22496,22553,22610,22666,22723,
 148         22779,22836,22893,22949,23005,23062,23118,23175,23231,23287,
 149         23343,23400,23456,23512,23568,23624,23680,23736,23792,23848,
 150         23904,23960,24015,24071,24127,24183,24238,24294,24349,24405,
 151         24461,24516,24571,24627,24682,24738,24793,24848,24903,24958,
 152         25014,25069,25124,25179,25234,25289,25344,25398,25453,25508,
 153         25563,25618,25672,25727,25782,25836,25891,25945,26000,26054,
 154         26108,26163,26217,26271,26326,26380,26434,26488,26542,26596,
 155         26650,26704,26758,26812,26866,26920,26973,27027,27081,27135,
 156         27188,27242,27295,27349,27402,27456,27509,27562,27616,27669,
 157         27722,27775,27829,27882,27935,27988,28041,28094,28147,28200,
 158         28252,28305,28358,28411,28463,28516,28569,28621,28674,28726,
 159         28779,28831,28884,28936,28988,29040,29093,29145,29197,29249,
 160         29301,29353,29405,29457,29509,29561,29613,29664,29716,29768,
 161         29819,29871,29923,29974,30026,30077,30129,30180,30231,30283,
 162         30334,30385,30436,30487,30539,30590,30641,30692,30743,30793,
 163         30844,30895,30946,30997,31047,31098,31149,31199,31250,31300,
 164         31351,31401,31451,31502,31552,31602,31653,31703,31753,31803,
 165         31853,31903,31953,32003,32053,32103,32153,32202,32252,32302,
 166         32351,32401,32451,32500,32550,32599,32648,32698,32747,32796,
 167         32846,32895,32944,32993,33042,33091,33140,33189,33238,33287,
 168         33336,33385,33433,33482,33531,33579,33628,33677,33725,33774,
 169         33822,33870,33919,33967,34015,34064,34112,34160,34208,34256,
 170         34304,34352,34400,34448,34496,34544,34591,34639,34687,34735,
 171         34782,34830,34877,34925,34972,35020,35067,35114,35162,35209,
 172         35256,35303,35351,35398,35445,35492,35539,35586,35632,35679,
 173         35726,35773,35820,35866,35913,35960,36006,36053,36099,36146,
 174         36192,36238,36285,36331,36377,36423,36470,36516,36562,36608,
 175         36654,36700,36746,36792,36837,36883,36929,36975,37020,37066,
 176         37112,37157,37203,37248,37294,37339,37384,37430,37475,37520,
 177         37565,37611,37656,37701,37746,37791,37836,37881,37926,37970,
 178         38015,38060,38105,38149,38194,38239,38283,38328,38372,38417,
 179         38461,38505,38550,38594,38638,38682,38726,38771,38815,38859,
 180         38903,38947,38991,39034,39078,39122,39166,39210,39253,39297,
 181         39340,39384,39428,39471,39514,39558,39601,39645,39688,39731,
 182         39774,39817,39861,39904,39947,39990,40033,40076,40118,40161,
 183         40204,40247,40290,40332,40375,40418,40460,40503,40545,40588,
 184         40630,40672,40715,40757,40799,40841,40884,40926,40968,41010,
 185         41052,41094,41136,41178,41220,41262,41303,41345,41387,41428,
 186         41470,41512,41553,41595,41636,41678,41719,41760,41802,41843,
 187         41884,41926,41967,42008,42049,42090,42131,42172,42213,42254,
 188         42295,42336,42376,42417,42458,42498,42539,42580,42620,42661,
 189         42701,42742,42782,42822,42863,42903,42943,42984,43024,43064,
 190         43104,43144,43184,43224,43264,43304,43344,43384,43423,43463,
 191         43503,43543,43582,43622,43661,43701,43740,43780,43819,43859,
 192         43898,43937,43977,44016,44055,44094,44133,44172,44212,44251,
 193         44290,44328,44367,44406,44445,44484,44523,44561,44600,44639,
 194         44677,44716,44754,44793,44831,44870,44908,44946,44985,45023,
 195         45061,45099,45138,45176,45214,45252,45290,45328,45366,45404,
 196         45442,45479,45517,45555,45593,45630,45668,45706,45743,45781,
 197         45818,45856,45893,45931,45968,46005,46043,46080,46117,46154,
 198         46192,46229,46266,46303,46340,46377,46414,46451,46487,46524,
 199         46561,46598,46635,46671,46708,46745,46781,46818,46854,46891,
 200         46927,46963,47000,47036,47072,47109,47145,47181,47217,47253,
 201         47290,47326,47362,47398,47434,47469,47505,47541,47577,47613,
 202         47649,47684,47720,47756,47791,47827,47862,47898,47933,47969,
 203         48004,48039,48075,48110,48145,48181,48216,48251,48286,48321,
 204         48356,48391,48426,48461,48496,48531,48566,48601,48635,48670,
 205         48705,48739,48774,48809,48843,48878,48912,48947,48981,49016,
 206         49050,49084,49119,49153,49187,49222,49256,49290,49324,49358,
 207         49392,49426,49460,49494,49528,49562,49596,49629,49663,49697,
 208         49731,49764,49798,49832,49865,49899,49932,49966,49999,50033,
 209         50066,50099,50133,50166,50199,50233,50266,50299,50332,50365,
 210         50398,50431,50464,50497,50530,50563,50596,50629,50662,50694,
 211         50727,50760,50792,50825,50858,50890,50923,50955,50988,51020,
 212         51053,51085,51117,51150,51182,51214,51247,51279,51311,51343,
 213         51375,51407,51439,51471
 214 };
 215
 216 /****************************************************************************/
 217
 218 Fixed32 FixSqrti(ULONG x) // 16 -> 16.16
 219 {
 220     if( x )
 221     {
 222         register unsigned long int xroot, m2, x2, dx = x;
 223
 224         xroot = 0;
 225         m2 = 1 << 15 * 2;
 226
 227         do
 228         {
 229             x2 = xroot + m2;
 230             xroot >>= 1;
 231
 232             if (x2 <= x)
 233             {
 234                 x -= x2;  xroot += m2;
 235             }
 236         }
 237         while (m2 >>= 2);
 238
 239         dx  = ( (dx) - (xroot*xroot) ) << 16;
 240         dx /= ((long)xroot)<<1;
 241
 242         return (xroot<<16) + dx;
 243     }
 244
 245     return 0;
 246 }
 247
 248 /****************************************************************************/
 249 #if 0
 250 Fixed32 FixSqrt( Fixed32 ecx )
 251 {
 252     LONG eax, ebx, edx;
 253
 254         eax = 0;
 255         ebx = 0x40000000;
 256 #if 1 // low precision 8.8
 257 lp1:
 258         edx = ecx;
 259         edx -= ebx;
 260         if( edx < 0 ) goto lp2;
 261         edx -= eax;
 262         if( edx < 0 ) goto lp2;
 263         ecx = edx;
 264         eax >>= 1;
 265         eax |= ebx;
 266         ebx >>= 2;
 267         if( ebx != 0 ) goto lp1;
 268         eax <<= 8;
 269         return  eax;
 270 lp2:
 271         eax >>= 1;
 272         ebx >>= 2;
 273         if( ebx != 0 ) goto lp1;
 274         eax <<= 8;
 275 #else // high precision 8.16
 276 lp1:
 277         edx = ecx;
 278         edx -= ebx;
 279         if( edx < 0 ) goto lp2;
 280         edx -= eax;
 281         if( edx < 0 ) goto lp2;
 282         ecx = edx;
 283         eax >>= 1;
 284         eax |= ebx;
 285         ebx >>= 2;
 286         if( ebx != 0 ) goto lp1;
 287         else goto lp5;
 288 lp2:
 289         eax >>= 1;
 290         ebx >>= 2;
 291         if( ebx != 0L ) goto lp1;
 292 lp5:
 293         ebx = 0x4000;
 294         eax <<= 16;
 295         ecx <<= 16;
 296 lp3:
 297         edx = ecx;
 298         edx -= ebx;
 299         if( edx < 0 ) goto lp4;
 300         edx -= eax;
 301         if( edx < 0 ) goto lp4;
 302         ecx = edx;
 303         eax >>= 1;
 304         eax |= ebx;
 305         ebx >>= 2;
 306         if( ebx != 0 ) goto lp3;
 307         goto lp6;
 308 lp4:
 309         eax >>= 1;
 310         ebx >>= 2;
 311         if( ebx != 0L ) goto lp3;
 312 lp6:
 313 #endif
 314         return eax;
 315 }
 316
 317 /****************************************************************************/
 318
 319 Fixed32 FixSinCos( Fixed32 theta, Fixed32 *sinus )
 320 {
 321     theta = FIXED_TO_INT( FixMul( theta << 9, 20861 ) );
 322     theta &= (MAX_TRIG - 1);
 323
 324     *sinus = SinCosTab[theta];
 325
 326     if( ( theta += 256 ) >= MAX_TRIG )
 327         theta = theta - MAX_TRIG;
 328
 329         return SinCosTab[theta];
 330 }
 331 #endif
 332 /****************************************************************************/
 333
 334 __inline static Fixed32 FixAtan( Fixed32 x )
 335 {
 336     return TanTab[ x >> 6 ]; /*TanTab[ FixDiv( FixMul( x, MAX_TRIG ), 65536 ) ];*/
 337 }
 338
 339 /****************************************************************************/
 340
 341 #undef FixDiv
 342 #define FixDiv( x, y )  (((ULONG)x<<16)/(ULONG)y)
 343
 344 Fixed32 FixAtan2( Fixed32 y, Fixed32 x )
 345 {
 346     if( !x && !y )
 347         return 0;
 348
 349     if (x>= 0)
 350     {
 351         // x >=0
 352         if (y>= 0)
 353         {
 354             // y>= 0
 355             if (x>y)
 356             {
 357                 // octant 0
 358                 return FixAtan( FixDiv(y,x) );
 359             }
 360             else
 361             {
 362                 // octant 1
 363                 return ANG90-1-FixAtan( FixDiv(x,y) );
 364             }
 365         }
 366         else
 367         {
 368             // y<0
 369             y = -y;
 370
 371             if (x>y)
 372             {
 373                 // octant 8
 374                 return -FixAtan(FixDiv(y,x) );
 375             }
 376             else
 377             {
 378                 // octant 7
 379                 return ANG270+FixAtan( FixDiv(x,y) );
 380             }
 381         }
 382     }
 383     else
 384     {
 385         // x<0
 386         x = -x;
 387
 388         if (y>= 0)
 389         {
 390             // y>= 0
 391             if (x>y)
 392             {
 393                 // octant 3
 394                 return ANG180-1-FixAtan( FixDiv(y,x) );
 395             }
 396             else
 397             {
 398                 // octant 2
 399                 return ANG90+ FixAtan( FixDiv(x,y) );
 400             }
 401         }
 402         else
 403         {
 404             // y<0
 405             y = -y;
 406
 407             if (x>y)
 408             {
 409                 // octant 4
 410                 return ANG180+FixAtan( FixDiv(y,x) );
 411             }
 412             else
 413             {
 414                 // octant 5
 415                 return ANG270-1-FixAtan( FixDiv(x,y) );
 416             }
 417         }
 418     }
 419
 420     return 0;
 421 }
 422
 423 /****************************************************************************/
 424
 425 #endif /* FIXED_MATH */