1 /* 2 $License: 3 Copyright (C) 2011-2012 InvenSense Corporation, All Rights Reserved. 4 See included License.txt for License information. 5 $ 6 */ 7 8 /******************************************************************************* 9 * 10 * $Id:$ 11 * 12 ******************************************************************************/ 13 14 /** 15 * @defgroup ML_MATH_FUNC ml_math_func 16 * @brief Motion Library - Math Functions 17 * Common math functions the Motion Library 18 * 19 * @{ 20 * @file ml_math_func.c 21 * @brief Math Functions. 22 */ 23 24 #include "mlmath.h" 25 #include "ml_math_func.h" 26 #include "mlinclude.h" 27 #include <string.h> 28 29 /** @internal 30 * Does the cross product of compass by gravity, then converts that 31 * to the world frame using the quaternion, then computes the angle that 32 * is made. 33 * 34 * @param[in] compass Compass Vector (Body Frame), length 3 35 * @param[in] grav Gravity Vector (Body Frame), length 3 36 * @param[in] quat Quaternion, Length 4 37 * @return Angle Cross Product makes after quaternion rotation. 38 */ 39 float inv_compass_angle(const long *compass, const long *grav, const float *quat) 40 { 41 float cgcross[4], q1[4], q2[4], qi[4]; 42 float angW; 43 44 // Compass cross Gravity 45 cgcross[0] = 0.f; 46 cgcross[1] = (float)compass[1] * grav[2] - (float)compass[2] * grav[1]; 47 cgcross[2] = (float)compass[2] * grav[0] - (float)compass[0] * grav[2]; 48 cgcross[3] = (float)compass[0] * grav[1] - (float)compass[1] * grav[0]; 49 50 // Now convert cross product into world frame 51 inv_q_multf(quat, cgcross, q1); 52 inv_q_invertf(quat, qi); 53 inv_q_multf(q1, qi, q2); 54 55 // Protect against atan2 of 0,0 56 if ((q2[2] == 0.f) && (q2[1] == 0.f)) 57 return 0.f; 58 59 // This is the unfiltered heading correction 60 angW = -atan2f(q2[2], q2[1]); 61 return angW; 62 } 63 64 /** 65 * @brief The gyro data magnitude squared : 66 * (1 degree per second)^2 = 2^6 = 2^GYRO_MAG_SQR_SHIFT. 67 * @param[in] gyro Gyro data scaled with 1 dps = 2^16 68 * @return the computed magnitude squared output of the gyroscope. 69 */ 70 unsigned long inv_get_gyro_sum_of_sqr(const long *gyro) 71 { 72 unsigned long gmag = 0; 73 long temp; 74 int kk; 75 76 for (kk = 0; kk < 3; ++kk) { 77 temp = gyro[kk] >> (16 - (GYRO_MAG_SQR_SHIFT / 2)); 78 gmag += temp * temp; 79 } 80 81 return gmag; 82 } 83 84 /** Performs a multiply and shift by 29. These are good functions to write in assembly on 85 * with devices with small memory where you want to get rid of the long long which some 86 * assemblers don't handle well 87 * @param[in] a 88 * @param[in] b 89 * @return ((long long)a*b)>>29 90 */ 91 long inv_q29_mult(long a, long b) 92 { 93 #ifdef UMPL_ELIMINATE_64BIT 94 long result; 95 result = (long)((float)a * b / (1L << 29)); 96 return result; 97 #else 98 long long temp; 99 long result; 100 temp = (long long)a * b; 101 result = (long)(temp >> 29); 102 return result; 103 #endif 104 } 105 106 /** Performs a multiply and shift by 30. These are good functions to write in assembly on 107 * with devices with small memory where you want to get rid of the long long which some 108 * assemblers don't handle well 109 * @param[in] a 110 * @param[in] b 111 * @return ((long long)a*b)>>30 112 */ 113 long inv_q30_mult(long a, long b) 114 { 115 #ifdef UMPL_ELIMINATE_64BIT 116 long result; 117 result = (long)((float)a * b / (1L << 30)); 118 return result; 119 #else 120 long long temp; 121 long result; 122 temp = (long long)a * b; 123 result = (long)(temp >> 30); 124 return result; 125 #endif 126 } 127 128 #ifndef UMPL_ELIMINATE_64BIT 129 long inv_q30_div(long a, long b) 130 { 131 long long temp; 132 long result; 133 temp = (((long long)a) << 30) / b; 134 result = (long)temp; 135 return result; 136 } 137 #endif 138 139 /** Performs a multiply and shift by shift. These are good functions to write 140 * in assembly on with devices with small memory where you want to get rid of 141 * the long long which some assemblers don't handle well 142 * @param[in] a First multicand 143 * @param[in] b Second multicand 144 * @param[in] shift Shift amount after multiplying 145 * @return ((long long)a*b)<<shift 146 */ 147 #ifndef UMPL_ELIMINATE_64BIT 148 long inv_q_shift_mult(long a, long b, int shift) 149 { 150 long result; 151 result = (long)(((long long)a * b) >> shift); 152 return result; 153 } 154 #endif 155 156 /** Performs a fixed point quaternion multiply. 157 * @param[in] q1 First Quaternion Multicand, length 4. 1.0 scaled 158 * to 2^30 159 * @param[in] q2 Second Quaternion Multicand, length 4. 1.0 scaled 160 * to 2^30 161 * @param[out] qProd Product after quaternion multiply. Length 4. 162 * 1.0 scaled to 2^30. 163 */ 164 void inv_q_mult(const long *q1, const long *q2, long *qProd) 165 { 166 INVENSENSE_FUNC_START; 167 qProd[0] = inv_q30_mult(q1[0], q2[0]) - inv_q30_mult(q1[1], q2[1]) - 168 inv_q30_mult(q1[2], q2[2]) - inv_q30_mult(q1[3], q2[3]); 169 170 qProd[1] = inv_q30_mult(q1[0], q2[1]) + inv_q30_mult(q1[1], q2[0]) + 171 inv_q30_mult(q1[2], q2[3]) - inv_q30_mult(q1[3], q2[2]); 172 173 qProd[2] = inv_q30_mult(q1[0], q2[2]) - inv_q30_mult(q1[1], q2[3]) + 174 inv_q30_mult(q1[2], q2[0]) + inv_q30_mult(q1[3], q2[1]); 175 176 qProd[3] = inv_q30_mult(q1[0], q2[3]) + inv_q30_mult(q1[1], q2[2]) - 177 inv_q30_mult(q1[2], q2[1]) + inv_q30_mult(q1[3], q2[0]); 178 } 179 180 /** Performs a fixed point quaternion addition. 181 * @param[in] q1 First Quaternion term, length 4. 1.0 scaled 182 * to 2^30 183 * @param[in] q2 Second Quaternion term, length 4. 1.0 scaled 184 * to 2^30 185 * @param[out] qSum Sum after quaternion summation. Length 4. 186 * 1.0 scaled to 2^30. 187 */ 188 void inv_q_add(long *q1, long *q2, long *qSum) 189 { 190 INVENSENSE_FUNC_START; 191 qSum[0] = q1[0] + q2[0]; 192 qSum[1] = q1[1] + q2[1]; 193 qSum[2] = q1[2] + q2[2]; 194 qSum[3] = q1[3] + q2[3]; 195 } 196 197 void inv_vector_normalize(long *vec, int length) 198 { 199 INVENSENSE_FUNC_START; 200 double normSF = 0; 201 int ii; 202 for (ii = 0; ii < length; ii++) { 203 normSF += 204 inv_q30_to_double(vec[ii]) * inv_q30_to_double(vec[ii]); 205 } 206 if (normSF > 0) { 207 normSF = 1 / sqrt(normSF); 208 for (ii = 0; ii < length; ii++) { 209 vec[ii] = (int)((double)vec[ii] * normSF); 210 } 211 } else { 212 vec[0] = 1073741824L; 213 for (ii = 1; ii < length; ii++) { 214 vec[ii] = 0; 215 } 216 } 217 } 218 219 void inv_q_normalize(long *q) 220 { 221 INVENSENSE_FUNC_START; 222 inv_vector_normalize(q, 4); 223 } 224 225 void inv_q_invert(const long *q, long *qInverted) 226 { 227 INVENSENSE_FUNC_START; 228 qInverted[0] = q[0]; 229 qInverted[1] = -q[1]; 230 qInverted[2] = -q[2]; 231 qInverted[3] = -q[3]; 232 } 233 234 double quaternion_to_rotation_angle(const long *quat) { 235 double quat0 = (double )quat[0] / 1073741824; 236 if (quat0 > 1.0f) { 237 quat0 = 1.0; 238 } else if (quat0 < -1.0f) { 239 quat0 = -1.0; 240 } 241 242 return acos(quat0)*2*180/M_PI; 243 } 244 245 /** Rotates a 3-element vector by Rotation defined by Q 246 */ 247 void inv_q_rotate(const long *q, const long *in, long *out) 248 { 249 long q_temp1[4], q_temp2[4]; 250 long in4[4], out4[4]; 251 252 // Fixme optimize 253 in4[0] = 0; 254 memcpy(&in4[1], in, 3 * sizeof(long)); 255 inv_q_mult(q, in4, q_temp1); 256 inv_q_invert(q, q_temp2); 257 inv_q_mult(q_temp1, q_temp2, out4); 258 memcpy(out, &out4[1], 3 * sizeof(long)); 259 } 260 261 void inv_q_multf(const float *q1, const float *q2, float *qProd) 262 { 263 INVENSENSE_FUNC_START; 264 qProd[0] = 265 (q1[0] * q2[0] - q1[1] * q2[1] - q1[2] * q2[2] - q1[3] * q2[3]); 266 qProd[1] = 267 (q1[0] * q2[1] + q1[1] * q2[0] + q1[2] * q2[3] - q1[3] * q2[2]); 268 qProd[2] = 269 (q1[0] * q2[2] - q1[1] * q2[3] + q1[2] * q2[0] + q1[3] * q2[1]); 270 qProd[3] = 271 (q1[0] * q2[3] + q1[1] * q2[2] - q1[2] * q2[1] + q1[3] * q2[0]); 272 } 273 274 void inv_q_addf(const float *q1, const float *q2, float *qSum) 275 { 276 INVENSENSE_FUNC_START; 277 qSum[0] = q1[0] + q2[0]; 278 qSum[1] = q1[1] + q2[1]; 279 qSum[2] = q1[2] + q2[2]; 280 qSum[3] = q1[3] + q2[3]; 281 } 282 283 void inv_q_normalizef(float *q) 284 { 285 INVENSENSE_FUNC_START; 286 float normSF = 0; 287 float xHalf = 0; 288 normSF = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 289 if (normSF < 2) { 290 xHalf = 0.5f * normSF; 291 normSF = normSF * (1.5f - xHalf * normSF * normSF); 292 normSF = normSF * (1.5f - xHalf * normSF * normSF); 293 normSF = normSF * (1.5f - xHalf * normSF * normSF); 294 normSF = normSF * (1.5f - xHalf * normSF * normSF); 295 q[0] *= normSF; 296 q[1] *= normSF; 297 q[2] *= normSF; 298 q[3] *= normSF; 299 } else { 300 q[0] = 1.0; 301 q[1] = 0.0; 302 q[2] = 0.0; 303 q[3] = 0.0; 304 } 305 normSF = (q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 306 } 307 308 /** Performs a length 4 vector normalization with a square root. 309 * @param[in,out] q vector to normalize. Returns [1,0,0,0] is magnitude is zero. 310 */ 311 void inv_q_norm4(float *q) 312 { 313 float mag; 314 mag = sqrtf(q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3]); 315 if (mag) { 316 q[0] /= mag; 317 q[1] /= mag; 318 q[2] /= mag; 319 q[3] /= mag; 320 } else { 321 q[0] = 1.f; 322 q[1] = 0.f; 323 q[2] = 0.f; 324 q[3] = 0.f; 325 } 326 } 327 328 void inv_q_invertf(const float *q, float *qInverted) 329 { 330 INVENSENSE_FUNC_START; 331 qInverted[0] = q[0]; 332 qInverted[1] = -q[1]; 333 qInverted[2] = -q[2]; 334 qInverted[3] = -q[3]; 335 } 336 337 /** 338 * Converts a quaternion to a rotation matrix. 339 * @param[in] quat 4-element quaternion in fixed point. One is 2^30. 340 * @param[out] rot Rotation matrix in fixed point. One is 2^30. The 341 * First 3 elements of the rotation matrix, represent 342 * the first row of the matrix. Rotation matrix multiplied 343 * by a 3 element column vector transform a vector from Body 344 * to World. 345 */ 346 void inv_quaternion_to_rotation(const long *quat, long *rot) 347 { 348 rot[0] = 349 inv_q29_mult(quat[1], quat[1]) + inv_q29_mult(quat[0], 350 quat[0]) - 351 1073741824L; 352 rot[1] = 353 inv_q29_mult(quat[1], quat[2]) - inv_q29_mult(quat[3], quat[0]); 354 rot[2] = 355 inv_q29_mult(quat[1], quat[3]) + inv_q29_mult(quat[2], quat[0]); 356 rot[3] = 357 inv_q29_mult(quat[1], quat[2]) + inv_q29_mult(quat[3], quat[0]); 358 rot[4] = 359 inv_q29_mult(quat[2], quat[2]) + inv_q29_mult(quat[0], 360 quat[0]) - 361 1073741824L; 362 rot[5] = 363 inv_q29_mult(quat[2], quat[3]) - inv_q29_mult(quat[1], quat[0]); 364 rot[6] = 365 inv_q29_mult(quat[1], quat[3]) - inv_q29_mult(quat[2], quat[0]); 366 rot[7] = 367 inv_q29_mult(quat[2], quat[3]) + inv_q29_mult(quat[1], quat[0]); 368 rot[8] = 369 inv_q29_mult(quat[3], quat[3]) + inv_q29_mult(quat[0], 370 quat[0]) - 371 1073741824L; 372 } 373 374 /** 375 * Converts a quaternion to a rotation vector. A rotation vector is 376 * a method to represent a 4-element quaternion vector in 3-elements. 377 * To get the quaternion from the 3-elements, The last 3-elements of 378 * the quaternion will be the given rotation vector. The first element 379 * of the quaternion will be the positive value that will be required 380 * to make the magnitude of the quaternion 1.0 or 2^30 in fixed point units. 381 * @param[in] quat 4-element quaternion in fixed point. One is 2^30. 382 * @param[out] rot Rotation vector in fixed point. One is 2^30. 383 */ 384 void inv_quaternion_to_rotation_vector(const long *quat, long *rot) 385 { 386 rot[0] = quat[1]; 387 rot[1] = quat[2]; 388 rot[2] = quat[3]; 389 390 if (quat[0] < 0.0) { 391 rot[0] = -rot[0]; 392 rot[1] = -rot[1]; 393 rot[2] = -rot[2]; 394 } 395 } 396 397 /** Converts a 32-bit long to a big endian byte stream */ 398 unsigned char *inv_int32_to_big8(long x, unsigned char *big8) 399 { 400 big8[0] = (unsigned char)((x >> 24) & 0xff); 401 big8[1] = (unsigned char)((x >> 16) & 0xff); 402 big8[2] = (unsigned char)((x >> 8) & 0xff); 403 big8[3] = (unsigned char)(x & 0xff); 404 return big8; 405 } 406 407 /** Converts a big endian byte stream into a 32-bit long */ 408 long inv_big8_to_int32(const unsigned char *big8) 409 { 410 long x; 411 x = ((long)big8[0] << 24) | ((long)big8[1] << 16) | ((long)big8[2] << 8) 412 | ((long)big8[3]); 413 return x; 414 } 415 416 /** Converts a big endian byte stream into a 16-bit integer (short) */ 417 short inv_big8_to_int16(const unsigned char *big8) 418 { 419 short x; 420 x = ((short)big8[0] << 8) | ((short)big8[1]); 421 return x; 422 } 423 424 /** Converts a little endian byte stream into a 16-bit integer (short) */ 425 short inv_little8_to_int16(const unsigned char *little8) 426 { 427 short x; 428 x = ((short)little8[1] << 8) | ((short)little8[0]); 429 return x; 430 } 431 432 /** Converts a 16-bit short to a big endian byte stream */ 433 unsigned char *inv_int16_to_big8(short x, unsigned char *big8) 434 { 435 big8[0] = (unsigned char)((x >> 8) & 0xff); 436 big8[1] = (unsigned char)(x & 0xff); 437 return big8; 438 } 439 440 void inv_matrix_det_inc(float *a, float *b, int *n, int x, int y) 441 { 442 int k, l, i, j; 443 for (i = 0, k = 0; i < *n; i++, k++) { 444 for (j = 0, l = 0; j < *n; j++, l++) { 445 if (i == x) 446 i++; 447 if (j == y) 448 j++; 449 *(b + 6 * k + l) = *(a + 6 * i + j); 450 } 451 } 452 *n = *n - 1; 453 } 454 455 void inv_matrix_det_incd(double *a, double *b, int *n, int x, int y) 456 { 457 int k, l, i, j; 458 for (i = 0, k = 0; i < *n; i++, k++) { 459 for (j = 0, l = 0; j < *n; j++, l++) { 460 if (i == x) 461 i++; 462 if (j == y) 463 j++; 464 *(b + 6 * k + l) = *(a + 6 * i + j); 465 } 466 } 467 *n = *n - 1; 468 } 469 470 float inv_matrix_det(float *p, int *n) 471 { 472 float d[6][6], sum = 0; 473 int i, j, m; 474 m = *n; 475 if (*n == 2) 476 return (*p ** (p + 7) - *(p + 1) ** (p + 6)); 477 for (i = 0, j = 0; j < m; j++) { 478 *n = m; 479 inv_matrix_det_inc(p, &d[0][0], n, i, j); 480 sum = 481 sum + *(p + 6 * i + j) * SIGNM(i + 482 j) * 483 inv_matrix_det(&d[0][0], n); 484 } 485 486 return (sum); 487 } 488 489 double inv_matrix_detd(double *p, int *n) 490 { 491 double d[6][6], sum = 0; 492 int i, j, m; 493 m = *n; 494 if (*n == 2) 495 return (*p ** (p + 7) - *(p + 1) ** (p + 6)); 496 for (i = 0, j = 0; j < m; j++) { 497 *n = m; 498 inv_matrix_det_incd(p, &d[0][0], n, i, j); 499 sum = 500 sum + *(p + 6 * i + j) * SIGNM(i + 501 j) * 502 inv_matrix_detd(&d[0][0], n); 503 } 504 505 return (sum); 506 } 507 508 /** Wraps angle from (-M_PI,M_PI] 509 * @param[in] ang Angle in radians to wrap 510 * @return Wrapped angle from (-M_PI,M_PI] 511 */ 512 float inv_wrap_angle(float ang) 513 { 514 if (ang > M_PI) 515 return ang - 2 * (float)M_PI; 516 else if (ang <= -(float)M_PI) 517 return ang + 2 * (float)M_PI; 518 else 519 return ang; 520 } 521 522 /** Finds the minimum angle difference ang1-ang2 such that difference 523 * is between [-M_PI,M_PI] 524 * @param[in] ang1 525 * @param[in] ang2 526 * @return angle difference ang1-ang2 527 */ 528 float inv_angle_diff(float ang1, float ang2) 529 { 530 float d; 531 ang1 = inv_wrap_angle(ang1); 532 ang2 = inv_wrap_angle(ang2); 533 d = ang1 - ang2; 534 if (d > M_PI) 535 d -= 2 * (float)M_PI; 536 else if (d < -(float)M_PI) 537 d += 2 * (float)M_PI; 538 return d; 539 } 540 541 /** bernstein hash, derived from public domain source */ 542 uint32_t inv_checksum(const unsigned char *str, int len) 543 { 544 uint32_t hash = 5381; 545 int i, c; 546 547 for (i = 0; i < len; i++) { 548 c = *(str + i); 549 hash = ((hash << 5) + hash) + c; /* hash * 33 + c */ 550 } 551 552 return hash; 553 } 554 555 static unsigned short inv_row_2_scale(const signed char *row) 556 { 557 unsigned short b; 558 559 if (row[0] > 0) 560 b = 0; 561 else if (row[0] < 0) 562 b = 4; 563 else if (row[1] > 0) 564 b = 1; 565 else if (row[1] < 0) 566 b = 5; 567 else if (row[2] > 0) 568 b = 2; 569 else if (row[2] < 0) 570 b = 6; 571 else 572 b = 7; // error 573 return b; 574 } 575 576 577 /** Converts an orientation matrix made up of 0,+1,and -1 to a scalar representation. 578 * @param[in] mtx Orientation matrix to convert to a scalar. 579 * @return Description of orientation matrix. The lowest 2 bits (0 and 1) represent the column the one is on for the 580 * first row, with the bit number 2 being the sign. The next 2 bits (3 and 4) represent 581 * the column the one is on for the second row with bit number 5 being the sign. 582 * The next 2 bits (6 and 7) represent the column the one is on for the third row with 583 * bit number 8 being the sign. In binary the identity matrix would therefor be: 584 * 010_001_000 or 0x88 in hex. 585 */ 586 unsigned short inv_orientation_matrix_to_scalar(const signed char *mtx) 587 { 588 589 unsigned short scalar; 590 591 /* 592 XYZ 010_001_000 Identity Matrix 593 XZY 001_010_000 594 YXZ 010_000_001 595 YZX 000_010_001 596 ZXY 001_000_010 597 ZYX 000_001_010 598 */ 599 600 scalar = inv_row_2_scale(mtx); 601 scalar |= inv_row_2_scale(mtx + 3) << 3; 602 scalar |= inv_row_2_scale(mtx + 6) << 6; 603 604 605 return scalar; 606 } 607 608 /** Uses the scalar orientation value to convert from chip frame to body frame 609 * @param[in] orientation A scalar that represent how to go from chip to body frame 610 * @param[in] input Input vector, length 3 611 * @param[out] output Output vector, length 3 612 */ 613 void inv_convert_to_body(unsigned short orientation, const long *input, long *output) 614 { 615 output[0] = input[orientation & 0x03] * SIGNSET(orientation & 0x004); 616 output[1] = input[(orientation>>3) & 0x03] * SIGNSET(orientation & 0x020); 617 output[2] = input[(orientation>>6) & 0x03] * SIGNSET(orientation & 0x100); 618 } 619 620 /** Uses the scalar orientation value to convert from body frame to chip frame 621 * @param[in] orientation A scalar that represent how to go from chip to body frame 622 * @param[in] input Input vector, length 3 623 * @param[out] output Output vector, length 3 624 */ 625 void inv_convert_to_chip(unsigned short orientation, const long *input, long *output) 626 { 627 output[orientation & 0x03] = input[0] * SIGNSET(orientation & 0x004); 628 output[(orientation>>3) & 0x03] = input[1] * SIGNSET(orientation & 0x020); 629 output[(orientation>>6) & 0x03] = input[2] * SIGNSET(orientation & 0x100); 630 } 631 632 633 /** Uses the scalar orientation value to convert from chip frame to body frame and 634 * apply appropriate scaling. 635 * @param[in] orientation A scalar that represent how to go from chip to body frame 636 * @param[in] sensitivity Sensitivity scale 637 * @param[in] input Input vector, length 3 638 * @param[out] output Output vector, length 3 639 */ 640 void inv_convert_to_body_with_scale(unsigned short orientation, long sensitivity, const long *input, long *output) 641 { 642 output[0] = inv_q30_mult(input[orientation & 0x03] * 643 SIGNSET(orientation & 0x004), sensitivity); 644 output[1] = inv_q30_mult(input[(orientation>>3) & 0x03] * 645 SIGNSET(orientation & 0x020), sensitivity); 646 output[2] = inv_q30_mult(input[(orientation>>6) & 0x03] * 647 SIGNSET(orientation & 0x100), sensitivity); 648 } 649 650 /** find a norm for a vector 651 * @param[in] a vector [3x1] 652 * @param[out] output the norm of the input vector 653 */ 654 double inv_vector_norm(const float *x) 655 { 656 return sqrt(x[0]*x[0]+x[1]*x[1]+x[2]*x[2]); 657 } 658 659 void inv_init_biquad_filter(inv_biquad_filter_t *pFilter, float *pBiquadCoeff) { 660 int i; 661 // initial state to zero 662 pFilter->state[0] = 0; 663 pFilter->state[1] = 0; 664 665 // set up coefficients 666 for (i=0; i<5; i++) { 667 pFilter->c[i] = pBiquadCoeff[i]; 668 } 669 } 670 671 void inv_calc_state_to_match_output(inv_biquad_filter_t *pFilter, float input) 672 { 673 pFilter->input = input; 674 pFilter->output = input; 675 pFilter->state[0] = input / (1 + pFilter->c[2] + pFilter->c[3]); 676 pFilter->state[1] = pFilter->state[0]; 677 } 678 679 float inv_biquad_filter_process(inv_biquad_filter_t *pFilter, float input) { 680 float stateZero; 681 682 pFilter->input = input; 683 // calculate the new state; 684 stateZero = pFilter->input - pFilter->c[2]*pFilter->state[0] 685 - pFilter->c[3]*pFilter->state[1]; 686 687 pFilter->output = stateZero + pFilter->c[0]*pFilter->state[0] 688 + pFilter->c[1]*pFilter->state[1]; 689 690 // update the output and state 691 pFilter->output = pFilter->output * pFilter->c[4]; 692 pFilter->state[1] = pFilter->state[0]; 693 pFilter->state[0] = stateZero; 694 return pFilter->output; 695 } 696 697 void inv_get_cross_product_vec(float *cgcross, float compass[3], float grav[3]) { 698 699 cgcross[0] = (float)compass[1] * grav[2] - (float)compass[2] * grav[1]; 700 cgcross[1] = (float)compass[2] * grav[0] - (float)compass[0] * grav[2]; 701 cgcross[2] = (float)compass[0] * grav[1] - (float)compass[1] * grav[0]; 702 } 703 704 void mlMatrixVectorMult(long matrix[9], const long vecIn[3], long *vecOut) { 705 // matrix format 706 // [ 0 3 6; 707 // 1 4 7; 708 // 2 5 8] 709 710 // vector format: [0 1 2]^T; 711 int i, j; 712 long temp; 713 714 for (i=0; i<3; i++) { 715 temp = 0; 716 for (j=0; j<3; j++) { 717 temp += inv_q30_mult(matrix[i+j*3], vecIn[j]); 718 } 719 vecOut[i] = temp; 720 } 721 } 722 723 //============== 1/sqrt(x), 1/x, sqrt(x) Functions ================================ 724 725 /** Calculates 1/square-root of a fixed-point number (30 bit mantissa, positive): Q1.30 726 * Input must be a positive scaled (2^30) integer 727 * The number is scaled to lie between a range in which a Newton-Raphson 728 * iteration works best. Corresponding square root of the power of two is returned. 729 * Caller must scale final result by 2^rempow (while avoiding overflow). 730 * @param[in] x0, length 1 731 * @param[out] rempow, length 1 732 * @return scaledSquareRoot on success or zero. 733 */ 734 long inv_inverse_sqrt(long x0, int*rempow) 735 { 736 //% Inverse sqrt NR in the neighborhood of 1.3>x>=0.65 737 //% x(k+1) = x(k)*(3 - x0*x(k)^2) 738 739 //% Seed equals 1. Works best in this region. 740 //xx0 = int32(1*2^30); 741 742 long oneoversqrt2, oneandhalf, x0_2; 743 unsigned long xx; 744 int pow2, sq2scale, nr_iters; 745 //long upscale, sqrt_upscale, upsclimit; 746 //long downscale, sqrt_downscale, downsclimit; 747 748 // Precompute some constants for efficiency 749 //% int32(2^30*1/sqrt(2)) 750 oneoversqrt2=759250125L; 751 //% int32(1.5*2^30); 752 oneandhalf=1610612736L; 753 754 //// Further scaling into optimal region saves one or more NR iterations. Maps into region (.9, 1.1) 755 //// int32(0.9/log(2)*2^30) 756 //upscale = 1394173804L; 757 //// int32(sqrt(0.9/log(2))*2^30) 758 //sqrt_upscale = 1223512453L; 759 // // int32(1.1*log(2)/.9*2^30) 760 //upsclimit = 909652478L; 761 //// int32(1.1/log(4)*2^30) 762 //downscale = 851995103L; 763 //// int32(sqrt(1.1/log(4))*2^30) 764 //sqrt_downscale = 956463682L; 765 // // int32(0.9*log(4)/1.1*2^30) 766 //downsclimit = 1217881829L; 767 768 nr_iters = test_limits_and_scale(&x0, &pow2); 769 770 sq2scale=pow2%2; // Find remainder. Is it even or odd? 771 772 773 // Further scaling to decrease NR iterations 774 // With the mapping below, 89% of calculations will require 2 NR iterations or less. 775 // TBD 776 777 778 x0_2 = x0 >>1; // This scaling incorporates factor of 2 in NR iteration below. 779 // Initial condition starts at 1: xx=(1L<<30); 780 // First iteration is simple: Instead of initializing xx=1, assign to result of first iteration: 781 // xx= (3/2-x0/2); 782 //% NR formula: xx=xx*(3/2-x0*xx*xx/2); = xx*(1.5 - (x0/2)*xx*xx) 783 // Initialize NR (first iteration). Note we are starting with xx=1, so the first iteration becomes an initialization. 784 xx = oneandhalf - x0_2; 785 if ( nr_iters>=2 ) { 786 // Second NR iteration 787 xx = inv_q30_mult( xx, ( oneandhalf - inv_q30_mult(x0_2, inv_q30_mult(xx,xx) ) ) ); 788 if ( nr_iters==3 ) { 789 // Third NR iteration. 790 xx = inv_q30_mult( xx, ( oneandhalf - inv_q30_mult(x0_2, inv_q30_mult(xx,xx) ) ) ); 791 // Fourth NR iteration: Not needed due to single precision. 792 } 793 } 794 if (sq2scale) { 795 *rempow = (pow2>>1) + 1; // Account for sqrt(2) in denominator, note we multiply if s2scale is true 796 return (inv_q30_mult(xx,oneoversqrt2)); 797 } 798 else { 799 *rempow = pow2>>1; 800 return xx; 801 } 802 } 803 804 805 /** Calculates square-root of a fixed-point number (30 bit mantissa, positive) 806 * Input must be a positive scaled (2^30) integer 807 * The number is scaled to lie between a range in which a Newton-Raphson 808 * iteration works best. 809 * @param[in] x0, length 1 810 * @return scaledSquareRoot on success or zero. **/ 811 long inv_fast_sqrt(long x0) 812 { 813 814 //% Square-Root with NR in the neighborhood of 1.3>x>=0.65 (log(2) <= x <= log(4) ) 815 // Two-variable NR iteration: 816 // Initialize: a=x; c=x-1; 817 // 1st Newton Step: a=a-a*c/2; ( or: a = x - x*(x-1)/2 ) 818 // Iterate: c = c*c*(c-3)/4 819 // a = a - a*c/2 --> reevaluating c at this step gives error of approximation 820 821 //% Seed equals 1. Works best in this region. 822 //xx0 = int32(1*2^30); 823 824 long sqrt2, oneoversqrt2, one_pt5; 825 long xx, cc; 826 int pow2, sq2scale, nr_iters; 827 828 // Return if input is zero. Negative should really error out. 829 if (x0 <= 0L) { 830 return 0L; 831 } 832 833 sqrt2 =1518500250L; 834 oneoversqrt2=759250125L; 835 one_pt5=1610612736L; 836 837 nr_iters = test_limits_and_scale(&x0, &pow2); 838 839 sq2scale = 0; 840 if (pow2 > 0) 841 sq2scale=pow2%2; // Find remainder. Is it even or odd? 842 pow2 = pow2-sq2scale; // Now pow2 is even. Note we are adding because result is scaled with sqrt(2) 843 844 // Sqrt 1st NR iteration 845 cc = x0 - (1L<<30); 846 xx = x0 - (inv_q30_mult(x0, cc)>>1); 847 if ( nr_iters>=2 ) { 848 // Sqrt second NR iteration 849 // cc = cc*cc*(cc-3)/4; = cc*cc*(cc/2 - 3/2)/2; 850 // cc = ( cc*cc*((cc>>1) - onePt5) ) >> 1 851 cc = inv_q30_mult( cc, inv_q30_mult(cc, (cc>>1) - one_pt5) ) >> 1; 852 xx = xx - (inv_q30_mult(xx, cc)>>1); 853 if ( nr_iters==3 ) { 854 // Sqrt third NR iteration 855 cc = inv_q30_mult( cc, inv_q30_mult(cc, (cc>>1) - one_pt5) ) >> 1; 856 xx = xx - (inv_q30_mult(xx, cc)>>1); 857 } 858 } 859 if (sq2scale) 860 xx = inv_q30_mult(xx,oneoversqrt2); 861 // Scale the number with the half of the power of 2 scaling 862 if (pow2>0) 863 xx = (xx >> (pow2>>1)); 864 else if (pow2 == -1) 865 xx = inv_q30_mult(xx,sqrt2); 866 return xx; 867 } 868 869 /** Calculates 1/x of a fixed-point number (30 bit mantissa) 870 * Input must be a scaled (2^30) integer (+/-) 871 * The number is scaled to lie between a range in which a Newton-Raphson 872 * iteration works best. Corresponding multiplier power of two is returned. 873 * Caller must scale final result by 2^pow (while avoiding overflow). 874 * @param[in] x, length 1 875 * @param[out] pow, length 1 876 * @return scaledOneOverX on success or zero. 877 */ 878 long inv_one_over_x(long x0, int*pow) 879 { 880 //% NR for 1/x in the neighborhood of log(2) => x => log(4) 881 //% y(k+1)=y(k)*(2 x0*y(k)) 882 //% with y(0) = 1 as the starting value for NR 883 884 long two, xx; 885 int numberwasnegative, nr_iters, did_upscale, did_downscale; 886 887 long upscale, downscale, upsclimit, downsclimit; 888 889 *pow = 0; 890 // Return if input is zero. 891 if (x0 == 0L) { 892 return 0L; 893 } 894 895 // This is really (2^31-1), i.e. 1.99999... . 896 // Approximation error is 1e-9. Note 2^31 will overflow to sign bit, so it can't be used here. 897 two = 2147483647L; 898 899 // int32(0.92/log(2)*2^30) 900 upscale = 1425155444L; 901 // int32(1.08/upscale*2^30) 902 upsclimit = 873697834L; 903 904 // int32(1.08/log(4)*2^30) 905 downscale = 836504283L; 906 // int32(0.92/downscale*2^30) 907 downsclimit = 1268000423L; 908 909 // Algorithm is intended to work with positive numbers only. Change sign: 910 numberwasnegative = 0; 911 if (x0 < 0L) { 912 numberwasnegative = 1; 913 x0 = -x0; 914 } 915 916 nr_iters = test_limits_and_scale(&x0, pow); 917 918 did_upscale=0; 919 did_downscale=0; 920 // Pre-scaling to reduce NR iterations and improve accuracy: 921 if (x0<=upsclimit) { 922 x0 = inv_q30_mult(x0, upscale); 923 did_upscale = 1; 924 // The scaling ALWAYS leaves the number in the 2-NR iterations region: 925 nr_iters = 2; 926 // Is x0 in the single NR iteration region (0.994, 1.006) ? 927 if (x0 > 1067299373 && x0 < 1080184275) 928 nr_iters = 1; 929 } else if (x0>=downsclimit) { 930 x0 = inv_q30_mult(x0, downscale); 931 did_downscale = 1; 932 // The scaling ALWAYS leaves the number in the 2-NR iterations region: 933 nr_iters = 2; 934 // Is x0 in the single NR iteration region (0.994, 1.006) ? 935 if (x0 > 1067299373 && x0 < 1080184275) 936 nr_iters = 1; 937 } 938 939 xx = (two - x0) + 1; // Note 2 will overflow so the computation (2-x) is done with "two" == (2^30-1) 940 // First NR iteration 941 xx = inv_q30_mult( xx, (two - inv_q30_mult(x0, xx)) + 1 ); 942 if ( nr_iters>=2 ) { 943 // Second NR iteration 944 xx = inv_q30_mult( xx, (two - inv_q30_mult(x0, xx)) + 1 ); 945 if ( nr_iters==3 ) { 946 // THird NR iteration. 947 xx = inv_q30_mult( xx, (two - inv_q30_mult(x0, xx)) + 1 ); 948 // Fourth NR iteration: Not needed due to single precision. 949 } 950 } 951 952 // Post-scaling 953 if (did_upscale) 954 xx = inv_q30_mult( xx, upscale); 955 else if (did_downscale) 956 xx = inv_q30_mult( xx, downscale); 957 958 if (numberwasnegative) 959 xx = -xx; 960 return xx; 961 } 962 963 /** Auxiliary function used by inv_OneOverX(), inv_fastSquareRoot(), inv_inverseSqrt(). 964 * Finds the range of the argument, determines the optimal number of Newton-Raphson 965 * iterations and . Corresponding square root of the power of two is returned. 966 * Restrictions: Number is represented as Q1.30. 967 * Number is betweeen the range 2<x<=0 968 * @param[in] x, length 1 969 * @param[out] pow, length 1 970 * @return # of NR iterations, x0 scaled between log(2) and log(4) and 2^N scaling (N=pow) 971 */ 972 int test_limits_and_scale(long *x0, int *pow) 973 { 974 long lowerlimit, upperlimit, oneiterlothr, oneiterhithr, zeroiterlothr, zeroiterhithr; 975 976 // Lower Limit: ll = int32(log(2)*2^30); 977 lowerlimit = 744261118L; 978 //Upper Limit ul = int32(log(4)*2^30); 979 upperlimit = 1488522236L; 980 // int32(0.9*2^30) 981 oneiterlothr = 966367642L; 982 // int32(1.1*2^30) 983 oneiterhithr = 1181116006L; 984 // int32(0.99*2^30) 985 zeroiterlothr=1063004406L; 986 //int32(1.01*2^30) 987 zeroiterhithr=1084479242L; 988 989 // Scale number such that Newton Raphson iteration works best: 990 // Find the power of two scaling that leaves the number in the optimal range, 991 // ll <= number <= ul. Note odd powers have special scaling further below 992 if (*x0 > upperlimit) { 993 // Halving the number will push it in the optimal range since largest value is 2 994 *x0 = *x0>>1; 995 *pow=-1; 996 } else if (*x0 < lowerlimit) { 997 // Find position of highest bit, counting from left, and scale number 998 *pow=get_highest_bit_position((unsigned long*)x0); 999 if (*x0 >= upperlimit) { 1000 // Halving the number will push it in the optimal range 1001 *x0 = *x0>>1; 1002 *pow=*pow-1; 1003 } 1004 else if (*x0 < lowerlimit) { 1005 // Doubling the number will push it in the optimal range 1006 *x0 = *x0<<1; 1007 *pow=*pow+1; 1008 } 1009 } else { 1010 *pow = 0; 1011 } 1012 1013 if ( *x0<oneiterlothr || *x0>oneiterhithr ) 1014 return 3; // 3 NR iterations 1015 if ( *x0<zeroiterlothr || *x0>zeroiterhithr ) 1016 return 2; // 2 NR iteration 1017 1018 return 1; // 1 NR iteration 1019 } 1020 1021 /** Auxiliary function used by testLimitsAndScale() 1022 * Find the highest nonzero bit in an unsigned 32 bit integer: 1023 * @param[in] value, length 1. 1024 * @return highes bit position. 1025 **/int get_highest_bit_position(unsigned long *value) 1026 { 1027 int position; 1028 position = 0; 1029 if (*value == 0) return 0; 1030 1031 if ((*value & 0xFFFF0000) == 0) { 1032 position += 16; 1033 *value=*value<<16; 1034 } 1035 if ((*value & 0xFF000000) == 0) { 1036 position += 8; 1037 *value=*value<<8; 1038 } 1039 if ((*value & 0xF0000000) == 0) { 1040 position += 4; 1041 *value=*value<<4; 1042 } 1043 if ((*value & 0xC0000000) == 0) { 1044 position += 2; 1045 *value=*value<<2; 1046 } 1047 1048 // If we got too far into sign bit, shift back. Note we are using an 1049 // unsigned long here, so right shift is going to shift all the bits. 1050 if ((*value & 0x80000000)) { 1051 position -= 1; 1052 *value=*value>>1; 1053 } 1054 return position; 1055 } 1056 1057 /* compute real part of quaternion, element[0] 1058 @param[in] inQuat, 3 elements gyro quaternion 1059 @param[out] outquat, 4 elements gyro quaternion 1060 */ 1061 int inv_compute_scalar_part(const long * inQuat, long* outQuat) 1062 { 1063 long scalarPart = 0; 1064 1065 scalarPart = inv_fast_sqrt((1L<<30) - inv_q30_mult(inQuat[0], inQuat[0]) 1066 - inv_q30_mult(inQuat[1], inQuat[1]) 1067 - inv_q30_mult(inQuat[2], inQuat[2]) ); 1068 outQuat[0] = scalarPart; 1069 outQuat[1] = inQuat[0]; 1070 outQuat[2] = inQuat[1]; 1071 outQuat[3] = inQuat[2]; 1072 1073 return 0; 1074 } 1075 /** 1076 * @} 1077 */ 1078
