快速FloatSin函数

就是一个快速实现求 float 的 Sin 函数。

#ifdef _MSC_VER 
typedef __int32 int32_t; 
#else 
#include <stdint.h> 
#endif 
 
inline int32_t fast_round(double x) { 
#ifndef NO_FAST_TRUNCATE 
 
 const double MAGIC_ROUND = 6755399441055744.0; /* https://stereopsis.com/sree/fpu2006.html */ 
 
 union { 
    double d; 
    
    struct { 
        #ifdef BIG_ENDIAN 
        int32_t hw; 
        int32_t lw; 
        #else 
        int32_t lw; 
        int32_t hw; 
        #endif 
    }; 
 } fast_trunc; 
 
 fast_trunc.d = x; 
 fast_trunc.d += MAGIC_ROUND; 
 
 return fast_trunc.lw; 
 
#else 
 
 if (x < 0) { 
    return (int32_t)(x - 0.5); 
 } 
 else { 
    return (int32_t)(x + 0.5); 
 } 
 
#endif 
} 
 
const double PI = 3.14159265358979323846264338327950288; 
const double INVPI = 0.31830988618379067153776752674502872; 
const double A = 0.00735246819687011731341356165096815; 
const double B = -0.16528911397014738207016302002888890; 
const double C = 0.99969198629596757779830113868360584; 
// sin 516ms 
// fast_sin1 257ms 
// 有部分误差 
inline double fast_sin1(double x) { 
 
 int32_t k; 
 double x2; 
 
 // 查询 x 在[PI/2, -PI/2] 的偏移 
 k = fast_round(INVPI * x); 
 
 // 调整 x 进入[PI/2, -PI/2] 
 x -= k * PI; 
 
 // 计算sin 
 x2 = x * x; 
 x = x*(C + x2*(B + A*x2)); 
 
 // 纠正负值 
 if (k % 2) x = -x; 
 
 return x; 
} 
//泰勒函数逼近 
 
//查表法的误差如下 
// 91 x 2 bytes ==> 182 bytes 
unsigned int isinTable16[] = { 
 0, 1144, 2287, 3430, 4571, 5712, 6850, 7987, 9121, 10252, 11380, 
 12505, 13625, 14742, 15854, 16962, 18064, 19161, 20251, 21336, 22414, 
 23486, 24550, 25607, 26655, 27696, 28729, 29752, 30767, 31772, 32768, 
 
 33753, 34728, 35693, 36647, 37589, 38521, 39440, 40347, 41243, 42125, 
 42995, 43851, 44695, 45524, 46340, 47142, 47929, 48702, 49460, 50203, 
 50930, 51642, 52339, 53019, 53683, 54331, 54962, 55577, 56174, 56755, 
 
 57318, 57864, 58392, 58902, 59395, 59869, 60325, 60763, 61182, 61583, 
 61965, 62327, 62671, 62996, 63302, 63588, 63855, 64103, 64331, 64539, 
 64728, 64897, 65047, 65176, 65286, 65375, 65445, 65495, 65525, 65535, 
}; 
 
float fast_sin4(float f) 
{ 
 long x = f + 0.5; 
 bool pos = true; 
 if (x < 0) 
 { 
 x = -x; 
 pos = !pos; 
 } 
 if (x >= 360) x %= 360; 
 if (x > 180) 
 { 
 x -= 180; 
 pos = !pos; 
 } 
 if (x > 90) x = 180 - x;; 
 if (pos) return isinTable16[x] * 0.0000152590219; // 1/65535.0 
 return isinTable16[x] * -0.0000152590219; 
}