| /trunk/doc/private/sincostan.c |
|---|
| 0,0 → 1,115 |
| #include <stdlib.h> |
| #include <stdio.h> |
| const int FACTORY_COS_LOOKUP[1024] = { |
| 16384, 16383, 16382, 16381, 16379, 16376, 16372, 16368, 16364, 16359, 16353, 16346, 16339, 16331, 16323, |
| 16314, 16305, 16294, 16284, 16272, 16260, 16248, 16234, 16221, 16206, 16191, 16175, 16159, 16142, 16125, |
| 16107, 16088, 16069, 16049, 16028, 16007, 15985, 15963, 15940, 15917, 15893, 15868, 15842, 15817, 15790, |
| 15763, 15735, 15707, 15678, 15649, 15618, 15588, 15557, 15525, 15492, 15459, 15426, 15392, 15357, 15322, |
| 15286, 15249, 15212, 15175, 15136, 15098, 15058, 15018, 14978, 14937, 14895, 14853, 14811, 14767, 14723, |
| 14679, 14634, 14589, 14543, 14496, 14449, 14401, 14353, 14304, 14255, 14205, 14155, 14104, 14053, 14001, |
| 13948, 13895, 13842, 13788, 13733, 13678, 13622, 13566, 13510, 13452, 13395, 13337, 13278, 13219, 13159, |
| 13099, 13039, 12977, 12916, 12854, 12791, 12728, 12665, 12601, 12536, 12471, 12406, 12340, 12273, 12207, |
| 12139, 12072, 12003, 11935, 11866, 11796, 11726, 11656, 11585, 11513, 11442, 11370, 11297, 11224, 11151, |
| 11077, 11003, 10928, 10853, 10777, 10701, 10625, 10548, 10471, 10394, 10316, 10237, 10159, 10080, 10000, |
| 9920, 9840, 9760, 9679, 9597, 9516, 9434, 9351, 9269, 9186, 9102, 9018, 8934, 8850, 8765, 8680, 8595, |
| 8509, 8423, 8336, 8250, 8163, 8075, 7988, 7900, 7812, 7723, 7634, 7545, 7456, 7366, 7276, 7186, 7096, |
| 7005, 6914, 6822, 6731, 6639, 6547, 6455, 6362, 6270, 6176, 6083, 5990, 5896, 5802, 5708, 5614, 5519, |
| 5424, 5329, 5234, 5139, 5043, 4948, 4852, 4756, 4659, 4563, 4466, 4369, 4273, 4175, 4078, 3981, 3883, |
| 3785, 3687, 3589, 3491, 3393, 3295, 3196, 3097, 2998, 2900, 2801, 2702, 2602, 2503, 2404, 2304, 2205, |
| 2105, 2005, 1905, 1806, 1706, 1606, 1505, 1405, 1305, 1205, 1105, 1004, 904, 804, 703, 603, 502, 402, |
| 301, 201, 100, -100, -201, -301, -402, -502, -603, -703, -804, -904, -1004, -1105, -1205, -1305, -1405, |
| -1505, -1606, -1706, -1806, -1905, -2005, -2105, -2205, -2304, -2404, -2503, -2602, -2702, -2801, -2900, |
| -2998, -3097, -3196, -3295, -3393, -3491, -3589, -3687, -3785, -3883, -3981, -4078, -4175, -4273, -4369, |
| -4466, -4563, -4659, -4756, -4852, -4948, -5043, -5139, -5234, -5329, -5424, -5519, -5614, -5708, -5802, |
| -5896, -5990, -6083, -6176, -6270, -6362, -6455, -6547, -6639, -6731, -6822, -6914, -7005, -7096, -7186, |
| -7276, -7366, -7456, -7545, -7634, -7723, -7812, -7900, -7988, -8075, -8163, -8250, -8336, -8423, -8509, |
| -8595, -8680, -8765, -8850, -8934, -9018, -9102, -9186, -9269, -9351, -9434, -9516, -9597, -9679, -9760, |
| -9840, -9920, -10000, -10080, -10159, -10237, -10316, -10394, -10471, -10548, -10625, -10701, -10777, |
| -10853, -10928, -11003, -11077, -11151, -11224, -11297, -11370, -11442, -11513, -11585, -11656, -11726, |
| -11796, -11866, -11935, -12003, -12072, -12139, -12207, -12273, -12340, -12406, -12471, -12536, -12601, |
| -12665, -12728, -12791, -12854, -12916, -12977, -13039, -13099, -13159, -13219, -13278, -13337, -13395, |
| -13452, -13510, -13566, -13622, -13678, -13733, -13788, -13842, -13895, -13948, -14001, -14053, -14104, |
| -14155, -14205, -14255, -14304, -14353, -14401, -14449, -14496, -14543, -14589, -14634, -14679, -14723, |
| -14767, -14811, -14853, -14895, -14937, -14978, -15018, -15058, -15098, -15136, -15175, -15212, -15249, |
| -15286, -15322, -15357, -15392, -15426, -15459, -15492, -15525, -15557, -15588, -15618, -15649, -15678, |
| -15707, -15735, -15763, -15790, -15817, -15842, -15868, -15893, -15917, -15940, -15963, -15985, -16007, |
| -16028, -16049, -16069, -16088, -16107, -16125, -16142, -16159, -16175, -16191, -16206, -16221, -16234, |
| -16248, -16260, -16272, -16284, -16294, -16305, -16314, -16323, -16331, -16339, -16346, -16353, -16359, |
| -16364, -16368, -16372, -16376, -16379, -16381, -16382, -16383, -16384, -16384, -16383, -16382, -16381, |
| -16379, -16376, -16372, -16368, -16364, -16359, -16353, -16346, -16339, -16331, -16323, -16314, -16305, |
| -16294, -16284, -16272, -16260, -16248, -16234, -16221, -16206, -16191, -16175, -16159, -16142, -16125, |
| -16107, -16088, -16069, -16049, -16028, -16007, -15985, -15963, -15940, -15917, -15893, -15868, -15842, |
| -15817, -15790, -15763, -15735, -15707, -15678, -15649, -15618, -15588, -15557, -15525, -15492, -15459, |
| -15426, -15392, -15357, -15322, -15286, -15249, -15212, -15175, -15136, -15098, -15058, -15018, -14978, |
| -14937, -14895, -14853, -14811, -14767, -14723, -14679, -14634, -14589, -14543, -14496, -14449, -14401, |
| -14353, -14304, -14255, -14205, -14155, -14104, -14053, -14001, -13948, -13895, -13842, -13788, -13733, |
| -13678, -13622, -13566, -13510, -13452, -13395, -13337, -13278, -13219, -13159, -13099, -13039, -12977, |
| -12916, -12854, -12791, -12728, -12665, -12601, -12536, -12471, -12406, -12340, -12273, -12207, -12139, |
| -12072, -12003, -11935, -11866, -11796, -11726, -11656, -11585, -11513, -11442, -11370, -11297, -11224, |
| -11151, -11077, -11003, -10928, -10853, -10777, -10701, -10625, -10548, -10471, -10394, -10316, -10237, |
| -10159, -10080, -10000, -9920, -9840, -9760, -9679, -9597, -9516, -9434, -9351, -9269, -9186, -9102, |
| -9018, -8934, -8850, -8765, -8680, -8595, -8509, -8423, -8336, -8250, -8163, -8075, -7988, -7900, -7812, |
| -7723, -7634, -7545, -7456, -7366, -7276, -7186, -7096, -7005, -6914, -6822, -6731, -6639, -6547, -6455, |
| -6362, -6270, -6176, -6083, -5990, -5896, -5802, -5708, -5614, -5519, -5424, -5329, -5234, -5139, -5043, |
| -4948, -4852, -4756, -4659, -4563, -4466, -4369, -4273, -4175, -4078, -3981, -3883, -3785, -3687, -3589, |
| -3491, -3393, -3295, -3196, -3097, -2998, -2900, -2801, -2702, -2602, -2503, -2404, -2304, -2205, -2105, |
| -2005, -1905, -1806, -1706, -1606, -1505, -1405, -1305, -1205, -1105, -1004, -904, -804, -703, -603, -502, |
| -402, -301, -201, -100, 100, 201, 301, 402, 502, 603, 703, 804, 904, 1004, 1105, 1205, 1305, 1405, 1505, |
| 1606, 1706, 1806, 1905, 2005, 2105, 2205, 2304, 2404, 2503, 2602, 2702, 2801, 2900, 2998, 3097, 3196, |
| 3295, 3393, 3491, 3589, 3687, 3785, 3883, 3981, 4078, 4175, 4273, 4369, 4466, 4563, 4659, 4756, 4852, |
| 4948, 5043, 5139, 5234, 5329, 5424, 5519, 5614, 5708, 5802, 5896, 5990, 6083, 6176, 6270, 6362, 6455, |
| 6547, 6639, 6731, 6822, 6914, 7005, 7096, 7186, 7276, 7366, 7456, 7545, 7634, 7723, 7812, 7900, 7988, |
| 8075, 8163, 8250, 8336, 8423, 8509, 8595, 8680, 8765, 8850, 8934, 9018, 9102, 9186, 9269, 9351, 9434, |
| 9516, 9597, 9679, 9760, 9840, 9920, 10000, 10080, 10159, 10237, 10316, 10394, 10471, 10548, 10625, 10701, |
| 10777, 10853, 10928, 11003, 11077, 11151, 11224, 11297, 11370, 11442, 11513, 11585, 11656, 11726, 11796, |
| 11866, 11935, 12003, 12072, 12139, 12207, 12273, 12340, 12406, 12471, 12536, 12601, 12665, 12728, 12791, |
| 12854, 12916, 12977, 13039, 13099, 13159, 13219, 13278, 13337, 13395, 13452, 13510, 13566, 13622, 13678, |
| 13733, 13788, 13842, 13895, 13948, 14001, 14053, 14104, 14155, 14205, 14255, 14304, 14353, 14401, 14449, |
| 14496, 14543, 14589, 14634, 14679, 14723, 14767, 14811, 14853, 14895, 14937, 14978, 15018, 15058, 15098, |
| 15136, 15175, 15212, 15249, 15286, 15322, 15357, 15392, 15426, 15459, 15492, 15525, 15557, 15588, 15618, |
| 15649, 15678, 15707, 15735, 15763, 15790, 15817, 15842, 15868, 15893, 15917, 15940, 15963, 15985, 16007, |
| 16028, 16049, 16069, 16088, 16107, 16125, 16142, 16159, 16175, 16191, 16206, 16221, 16234, 16248, 16260, |
| 16272, 16284, 16294, 16305, 16314, 16323, 16331, 16339, 16346, 16353, 16359, 16364, 16368, 16372, 16376, |
| 16379, 16381, 16382, 16383, 16384 }; |
| int factory_cos(int x) { |
| // https://misc.daniel-marschall.de/projects/filter_factory/function_cos.html |
| int res; |
| if (x < 0) x = -x; |
| x &= 0x3ff; // 1023 |
| res = FACTORY_COS_LOOKUP[x]; |
| return res >= 0 ? (res / 32) : res / 32 - 1; |
| } |
| int factory_sin(int x) { |
| // https://misc.daniel-marschall.de/projects/filter_factory/function_sin.html |
| return factory_cos(x - 256); |
| } |
| int factory_tan(int x) { |
| // https://misc.daniel-marschall.de/projects/filter_factory/function_tan.html |
| int v1 = x; |
| int v2 = v1 < 0 ? -v1 : v1; |
| v2 &= 0x3ff; // 1023 |
| v2 = FACTORY_COS_LOOKUP[v2]; |
| v1 -= 256; |
| if (v1 < 0) v1 = -v1; |
| v1 &= 0x3ff; // 1023 |
| v1 = FACTORY_COS_LOOKUP[v1]; |
| if (v2 == 0) return 0; |
| v1 = v1 << 10; // v1 *= 1024; |
| return v1 / v2; |
| } |
| int main() { |
| printf("x;cos;sin;tan\n"); |
| for (int i=-1024*1;i<=1024*1;i++) { |
| int cos = factory_cos(i); |
| int sin = factory_sin(i); |
| int tan = factory_tan(i); |
| printf("%d;%d;%d;%d\n",i,cos,sin,tan); |
| } |
| return 0; |
| } |
| /trunk/doc/private/sincostan.csv |
|---|
| 0,0 → 1,2050 |
| x;cos;sin;tan |
| -1024;512;-4;-6 |
| -1023;512;3;6 |
| -1022;511;6;12 |
| -1021;511;9;18 |
| -1020;511;12;25 |
| -1019;511;15;31 |
| -1018;511;18;37 |
| -1017;511;21;43 |
| -1016;511;25;50 |
| -1015;511;28;56 |
| -1014;511;31;62 |
| -1013;511;34;69 |
| -1012;510;37;75 |
| -1011;510;40;81 |
| -1010;510;43;88 |
| -1009;510;47;94 |
| -1008;509;50;100 |
| -1007;509;53;107 |
| -1006;509;56;113 |
| -1005;508;59;119 |
| -1004;508;62;126 |
| -1003;508;65;132 |
| -1002;507;68;138 |
| -1001;507;72;145 |
| -1000;506;75;151 |
| -999;506;78;158 |
| -998;505;81;164 |
| -997;505;84;171 |
| -996;504;87;177 |
| -995;504;90;183 |
| -994;503;93;190 |
| -993;503;96;196 |
| -992;502;99;203 |
| -991;502;102;209 |
| -990;501;106;216 |
| -989;500;109;223 |
| -988;500;112;229 |
| -987;499;115;236 |
| -986;498;118;242 |
| -985;498;121;249 |
| -984;497;124;256 |
| -983;496;127;262 |
| -982;495;130;269 |
| -981;495;133;276 |
| -980;494;136;282 |
| -979;493;139;289 |
| -978;492;142;296 |
| -977;491;145;303 |
| -976;490;148;310 |
| -975;489;151;316 |
| -974;489;154;323 |
| -973;488;157;330 |
| -972;487;160;337 |
| -971;486;163;344 |
| -970;485;166;351 |
| -969;484;169;358 |
| -968;483;172;365 |
| -967;482;175;372 |
| -966;481;178;379 |
| -965;479;181;386 |
| -964;478;184;394 |
| -963;477;187;401 |
| -962;476;190;408 |
| -961;475;193;415 |
| -960;474;195;423 |
| -959;473;198;430 |
| -958;471;201;437 |
| -957;470;204;445 |
| -956;469;207;452 |
| -955;468;210;460 |
| -954;466;213;467 |
| -953;465;216;475 |
| -952;464;218;482 |
| -951;462;221;490 |
| -950;461;224;498 |
| -949;460;227;506 |
| -948;458;230;513 |
| -947;457;233;521 |
| -946;455;235;529 |
| -945;454;238;537 |
| -944;453;241;545 |
| -943;451;244;553 |
| -942;450;246;561 |
| -941;448;249;569 |
| -940;447;252;578 |
| -939;445;255;586 |
| -938;443;257;594 |
| -937;442;260;603 |
| -936;440;263;611 |
| -935;439;265;620 |
| -934;437;268;628 |
| -933;435;271;637 |
| -932;434;273;645 |
| -931;432;276;654 |
| -930;430;279;663 |
| -929;429;281;672 |
| -928;427;284;681 |
| -927;425;287;690 |
| -926;423;289;699 |
| -925;422;292;708 |
| -924;420;294;718 |
| -923;418;297;727 |
| -922;416;299;736 |
| -921;414;302;746 |
| -920;413;305;756 |
| -919;411;307;765 |
| -918;409;310;775 |
| -917;407;312;785 |
| -916;405;315;795 |
| -915;403;317;805 |
| -914;401;319;815 |
| -913;399;322;825 |
| -912;397;324;836 |
| -911;395;327;846 |
| -910;393;329;857 |
| -909;391;332;867 |
| -908;389;334;878 |
| -907;387;336;889 |
| -906;385;339;900 |
| -905;383;341;911 |
| -904;381;343;923 |
| -903;379;346;934 |
| -902;377;348;945 |
| -901;375;350;957 |
| -900;372;353;969 |
| -899;370;355;981 |
| -898;368;357;993 |
| -897;366;359;1005 |
| -896;364;362;1017 |
| -895;362;364;1030 |
| -894;359;366;1042 |
| -893;357;368;1055 |
| -892;355;370;1068 |
| -891;353;372;1081 |
| -890;350;375;1095 |
| -889;348;377;1108 |
| -888;346;379;1122 |
| -887;343;381;1136 |
| -886;341;383;1150 |
| -885;339;385;1164 |
| -884;336;387;1178 |
| -883;334;389;1193 |
| -882;332;391;1208 |
| -881;329;393;1223 |
| -880;327;395;1238 |
| -879;324;397;1253 |
| -878;322;399;1269 |
| -877;319;401;1285 |
| -876;317;403;1301 |
| -875;315;405;1318 |
| -874;312;407;1335 |
| -873;310;409;1352 |
| -872;307;411;1369 |
| -871;305;413;1386 |
| -870;302;414;1404 |
| -869;299;416;1423 |
| -868;297;418;1441 |
| -867;294;420;1460 |
| -866;292;422;1479 |
| -865;289;423;1498 |
| -864;287;425;1518 |
| -863;284;427;1538 |
| -862;281;429;1559 |
| -861;279;430;1580 |
| -860;276;432;1601 |
| -859;273;434;1623 |
| -858;271;435;1645 |
| -857;268;437;1668 |
| -856;265;439;1691 |
| -855;263;440;1714 |
| -854;260;442;1738 |
| -853;257;443;1763 |
| -852;255;445;1788 |
| -851;252;447;1813 |
| -850;249;448;1839 |
| -849;246;450;1866 |
| -848;244;451;1893 |
| -847;241;453;1922 |
| -846;238;454;1950 |
| -845;235;455;1980 |
| -844;233;457;2009 |
| -843;230;458;2040 |
| -842;227;460;2072 |
| -841;224;461;2104 |
| -840;221;462;2137 |
| -839;218;464;2171 |
| -838;216;465;2206 |
| -837;213;466;2242 |
| -836;210;468;2278 |
| -835;207;469;2316 |
| -834;204;470;2355 |
| -833;201;471;2395 |
| -832;198;473;2436 |
| -831;195;474;2478 |
| -830;193;475;2522 |
| -829;190;476;2566 |
| -828;187;477;2613 |
| -827;184;478;2661 |
| -826;181;479;2710 |
| -825;178;481;2761 |
| -824;175;482;2813 |
| -823;172;483;2868 |
| -822;169;484;2924 |
| -821;166;485;2983 |
| -820;163;486;3043 |
| -819;160;487;3106 |
| -818;157;488;3171 |
| -817;154;489;3238 |
| -816;151;489;3308 |
| -815;148;490;3381 |
| -814;145;491;3458 |
| -813;142;492;3537 |
| -812;139;493;3620 |
| -811;136;494;3707 |
| -810;133;495;3796 |
| -809;130;495;3891 |
| -808;127;496;3990 |
| -807;124;497;4094 |
| -806;121;498;4203 |
| -805;118;498;4318 |
| -804;115;499;4439 |
| -803;112;500;4567 |
| -802;109;500;4701 |
| -801;106;501;4843 |
| -800;102;502;4993 |
| -799;99;502;5154 |
| -798;96;503;5325 |
| -797;93;503;5507 |
| -796;90;504;5699 |
| -795;87;504;5907 |
| -794;84;505;6129 |
| -793;81;505;6371 |
| -792;78;506;6630 |
| -791;75;506;6909 |
| -790;72;507;7215 |
| -789;68;507;7545 |
| -788;65;508;7909 |
| -787;62;508;8310 |
| -786;59;508;8753 |
| -785;56;509;9238 |
| -784;53;509;9786 |
| -783;50;509;10401 |
| -782;47;510;11106 |
| -781;43;510;11902 |
| -780;40;510;12820 |
| -779;37;510;13890 |
| -778;34;511;15154 |
| -777;31;511;16684 |
| -776;28;511;18536 |
| -775;25;511;20846 |
| -774;21;511;23847 |
| -773;18;511;27809 |
| -772;15;511;33410 |
| -771;12;511;41726 |
| -770;9;511;55731 |
| -769;6;511;83463 |
| -768;3;512;167772 |
| -767;-4;512;-167772 |
| -766;-7;511;-83463 |
| -765;-10;511;-55731 |
| -764;-13;511;-41726 |
| -763;-16;511;-33410 |
| -762;-19;511;-27809 |
| -761;-22;511;-23847 |
| -760;-26;511;-20846 |
| -759;-29;511;-18536 |
| -758;-32;511;-16684 |
| -757;-35;511;-15154 |
| -756;-38;510;-13890 |
| -755;-41;510;-12820 |
| -754;-44;510;-11902 |
| -753;-48;510;-11106 |
| -752;-51;509;-10401 |
| -751;-54;509;-9786 |
| -750;-57;509;-9238 |
| -749;-60;508;-8753 |
| -748;-63;508;-8310 |
| -747;-66;508;-7909 |
| -746;-69;507;-7545 |
| -745;-73;507;-7215 |
| -744;-76;506;-6909 |
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| <title>Filter Factory - sin, cos, tan functions diagram</title> |
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| <h1>FilterFactory - sin,cos,tan functions diagram</h1> |
| <a href="function_cos.html">Go to cos function</a> / <a href="function_sin.html"> |
| Go to sin function</a> / <a href="function_tan.html">Go to tan function</a></p> |
| <p align="center"><img src="sincostan.png" width="50%"></p> |
| <p align="center"> |
| <a href="sincostan.xlsx">XLSX</a> | |
| <a href="sincostan.csv">CSV</a> | |
| <a href="sincostan.svg">SVG</a> | |
| <a href="sincostan.png">PNG</a> | |
| <a href="sincostan.c">C source</a> |
| </p> |
| <p><i>Note: The diagram in the Filter Factory Programming Guide by Werner D. Streidt has a diagram that shows that tan(x) is bounded and will not reach infinity. This is not correct!</i></p> |
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