| 0,0 → 1,153 |
|---|
| #include "91x_lib.h" |
| #include "mymath.h" |
| #include <math.h> |
| |
| // discrete mathematics |
| |
| // sinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
| const s16 sinlookup[91] = {0, 143, 286, 429, 571, 714, 856, 998, 1140, 1282, 1423, 1563, 1703, 1843, 1982, 2120, 2258, 2395, 2531, 2667, 2802, 2936, 3069, 3201, 3332, 3462, 3591, 3719, 3846, 3972, 4096, 4219, 4341, 4462, 4581, 4699, 4815, 4930, 5043, 5155, 5266, 5374, 5482, 5587, 5691, 5793, 5893, 5991, 6088, 6183, 6275, 6366, 6455, 6542, 6627, 6710, 6791, 6870, 6947, 7022, 7094, 7165, 7233, 7299, 7363, 7424, 7484, 7541, 7595, 7648, 7698, 7746, 7791, 7834, 7875, 7913, 7949, 7982, 8013, 8041, 8068, 8091, 8112, 8131, 8147, 8161, 8172, 8181, 8187, 8191, 8192}; |
| //0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 38 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 |
| const s16 arccos64[65] = {90,89,88,87,86, 85, 84, 83, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 51, 50, 49, 48, 47, 45, 44, 43, 41, 40, 39, 37, 36, 34, 32, 31, 29, 27, 25, 23, 20, 18, 14, 10, 0}; |
| |
| s16 c_sin_8192(s16 angle) |
| { |
| s8 m, n; |
| s16 sinus; |
| |
| // avoid negative angles |
| if (angle < 0) |
| { |
| m = -1; |
| angle = -angle; |
| } |
| else m = +1; |
| |
| // fold angle to interval 0 to 359 |
| angle %= 360; |
| |
| // check quadrant |
| if (angle <= 90) n = 1; // first quadrant |
| else if ((angle > 90) && (angle <= 180)) {angle = 180 - angle; n = 1;} // second quadrant |
| else if ((angle > 180) && (angle <= 270)) {angle = angle - 180; n = -1;} // third quadrant |
| else {angle = 360 - angle; n = -1;} //fourth quadrant |
| // get lookup value |
| sinus = sinlookup[angle]; |
| // calculate sinus value |
| return (sinus * m * n); |
| } |
| |
| s16 c_arccos2(s32 a, s32 b) |
| { |
| if(a>b) return(0); |
| return(arccos64[64 * a / b]); |
| } |
| |
| // cosinus with argument in degree at an angular resolution of 1 degree and a discretisation of 13 bit. |
| s16 c_cos_8192(s16 angle) |
| { |
| return (c_sin_8192(90 - angle)); |
| } |
| |
| // higher resolution angle in deg is arg/div |
| s16 c_sin_8192_res(s16 arg, s16 div) |
| { |
| s16 angle, rest; |
| s32 tmp; |
| |
| angle = arg/div; |
| rest = arg%div; |
| |
| if(rest>0) |
| { |
| tmp = (div-rest)*(s32)c_sin_8192(angle); |
| tmp += rest * (s32)c_sin_8192(angle+1); |
| tmp /= div; |
| return(tmp); |
| } |
| else if(rest<0) |
| { |
| tmp = (div+rest)*(s32)c_sin_8192(angle); |
| tmp -= rest * (s32)c_sin_8192(angle-1); |
| tmp /= div; |
| return(tmp); |
| } |
| else |
| { |
| return(c_sin_8192(angle)); |
| } |
| |
| } |
| |
| s16 c_cos_8192_res(s16 arg, s16 div) |
| { |
| return(c_sin_8192_res(90*div - arg, div)); |
| } |
| |
| |
| // integer based atan2 that returns angle in counts of 1/546.13° |
| s32 c_atan2_546(s32 y, s32 x) |
| { |
| s32 qx, qy, q; |
| |
| if( x < 0) qx = -x; |
| else qx = x; |
| if( y < 0) qy = -y; |
| else qy = y; |
| if(qy <= qx) |
| { // scale down to avoid overflow in quadratic interpolation |
| while(qy > (1<<15)) |
| { |
| qy/=2; |
| qx/=2; |
| } |
| // calculate the quatratic interpolation |
| q = (((qy<<13)/qx)*qy)/qx; |
| q = (qy<<15)/qx-q; |
| } |
| else |
| { // scale down to avoid overflow in quadratic interpolation |
| while(qx>(1<<15)) |
| { |
| qy/=2; |
| qx/=2; |
| } |
| // calculate the quatratic interpolation |
| q = (((qx<<13)/qy)*qx)/qy; |
| q = (qx<<15)/qy-q; |
| q = 2*((1<<15)-(1<<13)) - q; |
| } |
| if(y < 0) |
| { |
| if(x < 0) q = q - 4*((1<<15)-(1<<13)); |
| else q = -q; |
| } |
| else if( x < 0) q = 4*((1<<15)-(1<<13)) - q; |
| return(q); |
| } |
| |
| |
| |
| // retuns the largest integer whose square is less than or equal to the |
| u32 isqrt(u32 value) |
| { |
| u32 rem = 0, root =0, idx; |
| |
| for(idx = 0; idx < 16; idx++) |
| { |
| root <<= 1; |
| |
| rem = ((rem << 2) + (value >> 30)); |
| value <<= 2; |
| root++; |
| if(root <= rem) |
| { |
| rem -= root; |
| root++; |
| } |
| else |
| { |
| root--; |
| } |
| } |
| return(root >> 1); |
| } |