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技术宅的结界»论坛 › 计算机技术 › 技巧探讨 › 【嵌入式】【定点数】适合嵌入式使用的查表法三角函数实 ...
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【嵌入式】【定点数】适合嵌入式使用的查表法三角函数实现

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发表于 2025-12-10 20:50:02 | 显示全部楼层 |阅读模式

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查表法 Sin Cos 三角函数

虽然 STM32H750 支持浮点数，也支持浮点数的 sin() cos() 三角函数计算，但是它们实在是太慢了，最慢要 900ms，稍微优化一下也有 100ms，而如果你需要不是很精确但是一定要很快速的三角函数，这里我用查表法实现了周期为 1024 的快速正弦、余弦代码，其返回值结果范围在 -1024 到 1024 之间的闭区间，每秒应该能计算上十万、百万次（理论结果，未经验证）。

特性

  • 无整数除法。
  • 无求余。
  • 以 1024 为一个周期。
  • 支持负数 x。
  • 返回值结果范围在 -1024 到 1024 之间的闭区间。
  • 计算成本约等于：一到三次条件分支判断，五次以内的加减法，一次按位与运算，一次查表，一次整数乘法。
#include <stdint.h>

const uint16_t CosTable[] =
{
    1024,1024,1024,1024,1024,1024,1023,1023,1023,1022,1022,1022,1021,1021,1020,1020,
    1019,1018,1018,1017,1016,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,
    1004,1003,1002,1000,999,998,996,995,993,992,990,989,987,985,983,982,
    980,978,976,974,972,970,968,966,964,962,960,958,955,953,951,948,
    946,944,941,939,936,934,931,928,926,923,920,917,915,912,909,906,
    903,900,897,894,891,888,885,882,878,875,872,868,865,862,858,855,
    851,848,844,841,837,834,830,826,822,819,815,811,807,803,799,796,
    792,788,784,779,775,771,767,763,759,755,750,746,742,737,733,729,
    724,720,715,711,706,702,697,692,688,683,678,674,669,664,659,654,
    650,645,640,635,630,625,620,615,610,605,600,595,590,584,579,574,
    569,564,558,553,548,543,537,532,526,521,516,510,505,499,494,488,
    483,477,472,466,460,455,449,443,438,432,426,421,415,409,403,398,
    392,386,380,374,369,363,357,351,345,339,333,327,321,315,309,303,
    297,291,285,279,273,267,261,255,249,243,237,230,224,218,212,206,
    200,194,187,181,175,169,163,156,150,144,138,132,125,119,113,107,
    100,94,88,82,75,69,63,57,50,44,38,31,25,19,13,6,
    0,
};

int16_t FastCos(int x)
{
    int sign = 1;
    if (x < 0) x = 1 - x;
    x &= 1023;
    if (x > 512)
    {
        x -= 512;
        sign = -1;
    }
    if (x <= 256) return CosTable[x] * sign;
    return -CosTable[512 - x] * sign;
}

int16_t FastSin(int x)
{
    int sign = 1;
    if (x < 0) x = 1 - x;
    x &= 1023;
    if (x > 512)
    {
        x -= 512;
        sign = -1;
    }
    if (x <= 256) return CosTable[256 - x] * sign;
    return CosTable[x - 256] * sign;
}

计算结果例

FastSin

测试代码：

for (int i = 0; i < 1024; i++)
{
    printf("%d,", FastSin(i));
    if (i % 16 == 15) printf("\n");
}

输出：

0,6,13,19,25,31,38,44,50,57,63,69,75,82,88,94,
100,107,113,119,125,132,138,144,150,156,163,169,175,181,187,194,
200,206,212,218,224,230,237,243,249,255,261,267,273,279,285,291,
297,303,309,315,321,327,333,339,345,351,357,363,369,374,380,386,
392,398,403,409,415,421,426,432,438,443,449,455,460,466,472,477,
483,488,494,499,505,510,516,521,526,532,537,543,548,553,558,564,
569,574,579,584,590,595,600,605,610,615,620,625,630,635,640,645,
650,654,659,664,669,674,678,683,688,692,697,702,706,711,715,720,
724,729,733,737,742,746,750,755,759,763,767,771,775,779,784,788,
792,796,799,803,807,811,815,819,822,826,830,834,837,841,844,848,
851,855,858,862,865,868,872,875,878,882,885,888,891,894,897,900,
903,906,909,912,915,917,920,923,926,928,931,934,936,939,941,944,
946,948,951,953,955,958,960,962,964,966,968,970,972,974,976,978,
980,982,983,985,987,989,990,992,993,995,996,998,999,1000,1002,1003,
1004,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1016,1017,1018,1018,
1019,1020,1020,1021,1021,1022,1022,1022,1023,1023,1023,1024,1024,1024,1024,1024,
1024,1024,1024,1024,1024,1024,1023,1023,1023,1022,1022,1022,1021,1021,1020,1020,
1019,1018,1018,1017,1016,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,
1004,1003,1002,1000,999,998,996,995,993,992,990,989,987,985,983,982,
980,978,976,974,972,970,968,966,964,962,960,958,955,953,951,948,
946,944,941,939,936,934,931,928,926,923,920,917,915,912,909,906,
903,900,897,894,891,888,885,882,878,875,872,868,865,862,858,855,
851,848,844,841,837,834,830,826,822,819,815,811,807,803,799,796,
792,788,784,779,775,771,767,763,759,755,750,746,742,737,733,729,
724,720,715,711,706,702,697,692,688,683,678,674,669,664,659,654,
650,645,640,635,630,625,620,615,610,605,600,595,590,584,579,574,
569,564,558,553,548,543,537,532,526,521,516,510,505,499,494,488,
483,477,472,466,460,455,449,443,438,432,426,421,415,409,403,398,
392,386,380,374,369,363,357,351,345,339,333,327,321,315,309,303,
297,291,285,279,273,267,261,255,249,243,237,230,224,218,212,206,
200,194,187,181,175,169,163,156,150,144,138,132,125,119,113,107,
100,94,88,82,75,69,63,57,50,44,38,31,25,19,13,6,
0,-6,-13,-19,-25,-31,-38,-44,-50,-57,-63,-69,-75,-82,-88,-94,
-100,-107,-113,-119,-125,-132,-138,-144,-150,-156,-163,-169,-175,-181,-187,-194,
-200,-206,-212,-218,-224,-230,-237,-243,-249,-255,-261,-267,-273,-279,-285,-291,
-297,-303,-309,-315,-321,-327,-333,-339,-345,-351,-357,-363,-369,-374,-380,-386,
-392,-398,-403,-409,-415,-421,-426,-432,-438,-443,-449,-455,-460,-466,-472,-477,
-483,-488,-494,-499,-505,-510,-516,-521,-526,-532,-537,-543,-548,-553,-558,-564,
-569,-574,-579,-584,-590,-595,-600,-605,-610,-615,-620,-625,-630,-635,-640,-645,
-650,-654,-659,-664,-669,-674,-678,-683,-688,-692,-697,-702,-706,-711,-715,-720,
-724,-729,-733,-737,-742,-746,-750,-755,-759,-763,-767,-771,-775,-779,-784,-788,
-792,-796,-799,-803,-807,-811,-815,-819,-822,-826,-830,-834,-837,-841,-844,-848,
-851,-855,-858,-862,-865,-868,-872,-875,-878,-882,-885,-888,-891,-894,-897,-900,
-903,-906,-909,-912,-915,-917,-920,-923,-926,-928,-931,-934,-936,-939,-941,-944,
-946,-948,-951,-953,-955,-958,-960,-962,-964,-966,-968,-970,-972,-974,-976,-978,
-980,-982,-983,-985,-987,-989,-990,-992,-993,-995,-996,-998,-999,-1000,-1002,-1003,
-1004,-1006,-1007,-1008,-1009,-1010,-1011,-1012,-1013,-1014,-1015,-1016,-1016,-1017,-1018,-1018,
-1019,-1020,-1020,-1021,-1021,-1022,-1022,-1022,-1023,-1023,-1023,-1024,-1024,-1024,-1024,-1024,
-1024,-1024,-1024,-1024,-1024,-1024,-1023,-1023,-1023,-1022,-1022,-1022,-1021,-1021,-1020,-1020,
-1019,-1018,-1018,-1017,-1016,-1016,-1015,-1014,-1013,-1012,-1011,-1010,-1009,-1008,-1007,-1006,
-1004,-1003,-1002,-1000,-999,-998,-996,-995,-993,-992,-990,-989,-987,-985,-983,-982,
-980,-978,-976,-974,-972,-970,-968,-966,-964,-962,-960,-958,-955,-953,-951,-948,
-946,-944,-941,-939,-936,-934,-931,-928,-926,-923,-920,-917,-915,-912,-909,-906,
-903,-900,-897,-894,-891,-888,-885,-882,-878,-875,-872,-868,-865,-862,-858,-855,
-851,-848,-844,-841,-837,-834,-830,-826,-822,-819,-815,-811,-807,-803,-799,-796,
-792,-788,-784,-779,-775,-771,-767,-763,-759,-755,-750,-746,-742,-737,-733,-729,
-724,-720,-715,-711,-706,-702,-697,-692,-688,-683,-678,-674,-669,-664,-659,-654,
-650,-645,-640,-635,-630,-625,-620,-615,-610,-605,-600,-595,-590,-584,-579,-574,
-569,-564,-558,-553,-548,-543,-537,-532,-526,-521,-516,-510,-505,-499,-494,-488,
-483,-477,-472,-466,-460,-455,-449,-443,-438,-432,-426,-421,-415,-409,-403,-398,
-392,-386,-380,-374,-369,-363,-357,-351,-345,-339,-333,-327,-321,-315,-309,-303,
-297,-291,-285,-279,-273,-267,-261,-255,-249,-243,-237,-230,-224,-218,-212,-206,
-200,-194,-187,-181,-175,-169,-163,-156,-150,-144,-138,-132,-125,-119,-113,-107,
-100,-94,-88,-82,-75,-69,-63,-57,-50,-44,-38,-31,-25,-19,-13,-6,

FastCos

测试代码：

for (int i = 0; i < 1024; i++)
{
    printf("%d,", FastCos(i));
    if (i % 16 == 15) printf("\n");
}

输出：

1024,1024,1024,1024,1024,1024,1023,1023,1023,1022,1022,1022,1021,1021,1020,1020,
1019,1018,1018,1017,1016,1016,1015,1014,1013,1012,1011,1010,1009,1008,1007,1006,
1004,1003,1002,1000,999,998,996,995,993,992,990,989,987,985,983,982,
980,978,976,974,972,970,968,966,964,962,960,958,955,953,951,948,
946,944,941,939,936,934,931,928,926,923,920,917,915,912,909,906,
903,900,897,894,891,888,885,882,878,875,872,868,865,862,858,855,
851,848,844,841,837,834,830,826,822,819,815,811,807,803,799,796,
792,788,784,779,775,771,767,763,759,755,750,746,742,737,733,729,
724,720,715,711,706,702,697,692,688,683,678,674,669,664,659,654,
650,645,640,635,630,625,620,615,610,605,600,595,590,584,579,574,
569,564,558,553,548,543,537,532,526,521,516,510,505,499,494,488,
483,477,472,466,460,455,449,443,438,432,426,421,415,409,403,398,
392,386,380,374,369,363,357,351,345,339,333,327,321,315,309,303,
297,291,285,279,273,267,261,255,249,243,237,230,224,218,212,206,
200,194,187,181,175,169,163,156,150,144,138,132,125,119,113,107,
100,94,88,82,75,69,63,57,50,44,38,31,25,19,13,6,
0,-6,-13,-19,-25,-31,-38,-44,-50,-57,-63,-69,-75,-82,-88,-94,
-100,-107,-113,-119,-125,-132,-138,-144,-150,-156,-163,-169,-175,-181,-187,-194,
-200,-206,-212,-218,-224,-230,-237,-243,-249,-255,-261,-267,-273,-279,-285,-291,
-297,-303,-309,-315,-321,-327,-333,-339,-345,-351,-357,-363,-369,-374,-380,-386,
-392,-398,-403,-409,-415,-421,-426,-432,-438,-443,-449,-455,-460,-466,-472,-477,
-483,-488,-494,-499,-505,-510,-516,-521,-526,-532,-537,-543,-548,-553,-558,-564,
-569,-574,-579,-584,-590,-595,-600,-605,-610,-615,-620,-625,-630,-635,-640,-645,
-650,-654,-659,-664,-669,-674,-678,-683,-688,-692,-697,-702,-706,-711,-715,-720,
-724,-729,-733,-737,-742,-746,-750,-755,-759,-763,-767,-771,-775,-779,-784,-788,
-792,-796,-799,-803,-807,-811,-815,-819,-822,-826,-830,-834,-837,-841,-844,-848,
-851,-855,-858,-862,-865,-868,-872,-875,-878,-882,-885,-888,-891,-894,-897,-900,
-903,-906,-909,-912,-915,-917,-920,-923,-926,-928,-931,-934,-936,-939,-941,-944,
-946,-948,-951,-953,-955,-958,-960,-962,-964,-966,-968,-970,-972,-974,-976,-978,
-980,-982,-983,-985,-987,-989,-990,-992,-993,-995,-996,-998,-999,-1000,-1002,-1003,
-1004,-1006,-1007,-1008,-1009,-1010,-1011,-1012,-1013,-1014,-1015,-1016,-1016,-1017,-1018,-1018,
-1019,-1020,-1020,-1021,-1021,-1022,-1022,-1022,-1023,-1023,-1023,-1024,-1024,-1024,-1024,-1024,
-1024,-1024,-1024,-1024,-1024,-1024,-1023,-1023,-1023,-1022,-1022,-1022,-1021,-1021,-1020,-1020,
-1019,-1018,-1018,-1017,-1016,-1016,-1015,-1014,-1013,-1012,-1011,-1010,-1009,-1008,-1007,-1006,
-1004,-1003,-1002,-1000,-999,-998,-996,-995,-993,-992,-990,-989,-987,-985,-983,-982,
-980,-978,-976,-974,-972,-970,-968,-966,-964,-962,-960,-958,-955,-953,-951,-948,
-946,-944,-941,-939,-936,-934,-931,-928,-926,-923,-920,-917,-915,-912,-909,-906,
-903,-900,-897,-894,-891,-888,-885,-882,-878,-875,-872,-868,-865,-862,-858,-855,
-851,-848,-844,-841,-837,-834,-830,-826,-822,-819,-815,-811,-807,-803,-799,-796,
-792,-788,-784,-779,-775,-771,-767,-763,-759,-755,-750,-746,-742,-737,-733,-729,
-724,-720,-715,-711,-706,-702,-697,-692,-688,-683,-678,-674,-669,-664,-659,-654,
-650,-645,-640,-635,-630,-625,-620,-615,-610,-605,-600,-595,-590,-584,-579,-574,
-569,-564,-558,-553,-548,-543,-537,-532,-526,-521,-516,-510,-505,-499,-494,-488,
-483,-477,-472,-466,-460,-455,-449,-443,-438,-432,-426,-421,-415,-409,-403,-398,
-392,-386,-380,-374,-369,-363,-357,-351,-345,-339,-333,-327,-321,-315,-309,-303,
-297,-291,-285,-279,-273,-267,-261,-255,-249,-243,-237,-230,-224,-218,-212,-206,
-200,-194,-187,-181,-175,-169,-163,-156,-150,-144,-138,-132,-125,-119,-113,-107,
-100,-94,-88,-82,-75,-69,-63,-57,-50,-44,-38,-31,-25,-19,-13,-6,
0,6,13,19,25,31,38,44,50,57,63,69,75,82,88,94,
100,107,113,119,125,132,138,144,150,156,163,169,175,181,187,194,
200,206,212,218,224,230,237,243,249,255,261,267,273,279,285,291,
297,303,309,315,321,327,333,339,345,351,357,363,369,374,380,386,
392,398,403,409,415,421,426,432,438,443,449,455,460,466,472,477,
483,488,494,499,505,510,516,521,526,532,537,543,548,553,558,564,
569,574,579,584,590,595,600,605,610,615,620,625,630,635,640,645,
650,654,659,664,669,674,678,683,688,692,697,702,706,711,715,720,
724,729,733,737,742,746,750,755,759,763,767,771,775,779,784,788,
792,796,799,803,807,811,815,819,822,826,830,834,837,841,844,848,
851,855,858,862,865,868,872,875,878,882,885,888,891,894,897,900,
903,906,909,912,915,917,920,923,926,928,931,934,936,939,941,944,
946,948,951,953,955,958,960,962,964,966,968,970,972,974,976,978,
980,982,983,985,987,989,990,992,993,995,996,998,999,1000,1002,1003,
1004,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1016,1017,1018,1018,
1019,1020,1020,1021,1021,1022,1022,1022,1023,1023,1023,1024,1024,1024,1024,1024,

负数x

负数x 我也测过了，没有任何问题，请您放心。如果不放心，可以自己去 Godbolt 测试。

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