+//=====================================================================================================\r
+// MadgwickAHRS.c\r
+//=====================================================================================================\r
+//\r
+// Implementation of Madgwick's IMU and AHRS algorithms.\r
+// See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms\r
+//\r
+// Date Author Notes\r
+// 29/09/2011 SOH Madgwick Initial release\r
+// 02/10/2011 SOH Madgwick Optimised for reduced CPU load\r
+// 19/02/2012 SOH Madgwick Magnetometer measurement is normalised\r
+//\r
+//=====================================================================================================\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// Header files\r
+\r
+#include "MadgwickAHRS.h"\r
+#include <math.h>\r
+\r
+#include <f32.h>\r
+\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// Definitions\r
+\r
+//#define sampleFreq 512.0f // sample frequency in Hz\r
+//#define sampleFreq 46.0f // sample frequency in Hz\r
+#define sampleFreq 85.0f // sample frequency in Hz\r
+#define betaDef 0.1f // 2 * proportional gain\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// Variable definitions\r
+\r
+volatile float beta = betaDef; // 2 * proportional gain (Kp)\r
+volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame\r
+\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// Function declarations\r
+\r
+float invSqrt(float x);\r
+\r
+//====================================================================================================\r
+// Functions\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// AHRS algorithm update\r
+\r
+void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) {\r
+ float recipNorm;\r
+ float s0, s1, s2, s3;\r
+ float qDot1, qDot2, qDot3, qDot4;\r
+ float hx, hy;\r
+ float _2q0mx, _2q0my, _2q0mz, _2q1mx, _2bx, _2bz, _4bx, _4bz, _2q0, _2q1, _2q2, _2q3, _2q0q2, _2q2q3, q0q0, q0q1, q0q2, q0q3, q1q1, q1q2, q1q3, q2q2, q2q3, q3q3;\r
+\r
+ // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation)\r
+ if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) {\r
+ MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az);\r
+ return;\r
+ }\r
+\r
+ // Rate of change of quaternion from gyroscope\r
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);\r
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);\r
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);\r
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);\r
+\r
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)\r
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {\r
+\r
+ // Normalise accelerometer measurement\r
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);\r
+ ax *= recipNorm;\r
+ ay *= recipNorm;\r
+ az *= recipNorm;\r
+\r
+ // Normalise magnetometer measurement\r
+ recipNorm = invSqrt(mx * mx + my * my + mz * mz);\r
+ mx *= recipNorm;\r
+ my *= recipNorm;\r
+ mz *= recipNorm;\r
+\r
+ // Auxiliary variables to avoid repeated arithmetic\r
+ _2q0mx = 2.0f * q0 * mx;\r
+ _2q0my = 2.0f * q0 * my;\r
+ _2q0mz = 2.0f * q0 * mz;\r
+ _2q1mx = 2.0f * q1 * mx;\r
+ _2q0 = 2.0f * q0;\r
+ _2q1 = 2.0f * q1;\r
+ _2q2 = 2.0f * q2;\r
+ _2q3 = 2.0f * q3;\r
+ _2q0q2 = 2.0f * q0 * q2;\r
+ _2q2q3 = 2.0f * q2 * q3;\r
+ q0q0 = q0 * q0;\r
+ q0q1 = q0 * q1;\r
+ q0q2 = q0 * q2;\r
+ q0q3 = q0 * q3;\r
+ q1q1 = q1 * q1;\r
+ q1q2 = q1 * q2;\r
+ q1q3 = q1 * q3;\r
+ q2q2 = q2 * q2;\r
+ q2q3 = q2 * q3;\r
+ q3q3 = q3 * q3;\r
+\r
+ // Reference direction of Earth's magnetic field\r
+ hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3;\r
+ hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3;\r
+ _2bx = sqrt(hx * hx + hy * hy);\r
+ _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3;\r
+ _4bx = 2.0f * _2bx;\r
+ _4bz = 2.0f * _2bz;\r
+\r
+ // Gradient decent algorithm corrective step\r
+ s0 = -_2q2 * (2.0f * q1q3 - _2q0q2 - ax) + _2q1 * (2.0f * q0q1 + _2q2q3 - ay) - _2bz * q2 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q3 + _2bz * q1) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q2 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);\r
+ s1 = _2q3 * (2.0f * q1q3 - _2q0q2 - ax) + _2q0 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q1 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + _2bz * q3 * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q2 + _2bz * q0) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q3 - _4bz * q1) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);\r
+ s2 = -_2q0 * (2.0f * q1q3 - _2q0q2 - ax) + _2q3 * (2.0f * q0q1 + _2q2q3 - ay) - 4.0f * q2 * (1 - 2.0f * q1q1 - 2.0f * q2q2 - az) + (-_4bx * q2 - _2bz * q0) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (_2bx * q1 + _2bz * q3) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + (_2bx * q0 - _4bz * q2) * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);\r
+ s3 = _2q1 * (2.0f * q1q3 - _2q0q2 - ax) + _2q2 * (2.0f * q0q1 + _2q2q3 - ay) + (-_4bx * q3 + _2bz * q1) * (_2bx * (0.5f - q2q2 - q3q3) + _2bz * (q1q3 - q0q2) - mx) + (-_2bx * q0 + _2bz * q2) * (_2bx * (q1q2 - q0q3) + _2bz * (q0q1 + q2q3) - my) + _2bx * q1 * (_2bx * (q0q2 + q1q3) + _2bz * (0.5f - q1q1 - q2q2) - mz);\r
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude\r
+ s0 *= recipNorm;\r
+ s1 *= recipNorm;\r
+ s2 *= recipNorm;\r
+ s3 *= recipNorm;\r
+\r
+ // Apply feedback step\r
+ qDot1 -= beta * s0;\r
+ qDot2 -= beta * s1;\r
+ qDot3 -= beta * s2;\r
+ qDot4 -= beta * s3;\r
+ }\r
+\r
+ // Integrate rate of change of quaternion to yield quaternion\r
+ q0 += qDot1 * (1.0f / sampleFreq);\r
+ q1 += qDot2 * (1.0f / sampleFreq);\r
+ q2 += qDot3 * (1.0f / sampleFreq);\r
+ q3 += qDot4 * (1.0f / sampleFreq);\r
+\r
+ // Normalise quaternion\r
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);\r
+ q0 *= recipNorm;\r
+ q1 *= recipNorm;\r
+ q2 *= recipNorm;\r
+ q3 *= recipNorm;\r
+}\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// IMU algorithm update\r
+\r
+void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) {\r
+ float recipNorm;\r
+ float s0, s1, s2, s3;\r
+ float qDot1, qDot2, qDot3, qDot4;\r
+ float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3;\r
+\r
+ // Rate of change of quaternion from gyroscope\r
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);\r
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);\r
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);\r
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);\r
+\r
+\r
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)\r
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {\r
+\r
+ // Normalise accelerometer measurement\r
+ recipNorm = invSqrt(ax * ax + ay * ay + az * az);\r
+ ax *= recipNorm;\r
+ ay *= recipNorm;\r
+ az *= recipNorm;\r
+\r
+ // Auxiliary variables to avoid repeated arithmetic\r
+ _2q0 = 2.0f * q0;\r
+ _2q1 = 2.0f * q1;\r
+ _2q2 = 2.0f * q2;\r
+ _2q3 = 2.0f * q3;\r
+ _4q0 = 4.0f * q0;\r
+ _4q1 = 4.0f * q1;\r
+ _4q2 = 4.0f * q2;\r
+ _8q1 = 8.0f * q1;\r
+ _8q2 = 8.0f * q2;\r
+ q0q0 = q0 * q0;\r
+ q1q1 = q1 * q1;\r
+ q2q2 = q2 * q2;\r
+ q3q3 = q3 * q3;\r
+\r
+\r
+ // Gradient decent algorithm corrective step\r
+ s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;\r
+ s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;\r
+ s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;\r
+ s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;\r
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude\r
+\r
+\r
+\r
+ s0 *= recipNorm;\r
+ s1 *= recipNorm;\r
+ s2 *= recipNorm;\r
+ s3 *= recipNorm;\r
+\r
+\r
+ // Apply feedback step\r
+ qDot1 -= beta * s0;\r
+ qDot2 -= beta * s1;\r
+ qDot3 -= beta * s2;\r
+ qDot4 -= beta * s3;\r
+ }\r
+\r
+ // Integrate rate of change of quaternion to yield quaternion\r
+ q0 += qDot1 * (1.0f / sampleFreq);\r
+ q1 += qDot2 * (1.0f / sampleFreq);\r
+ q2 += qDot3 * (1.0f / sampleFreq);\r
+ q3 += qDot4 * (1.0f / sampleFreq);\r
+\r
+\r
+ // Normalise quaternion\r
+ recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);\r
+ q0 *= recipNorm;\r
+ q1 *= recipNorm;\r
+ q2 *= recipNorm;\r
+ q3 *= recipNorm;\r
+\r
+ //printf("%+3.3f\t%+3.3f\t%+3.3f\r\n", q0, q1, q2);\r
+\r
+}\r
+\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// IMU algorithm update\r
+\r
+f32 f_q0;\r
+f32 f_q1;\r
+f32 f_q2;\r
+f32 f_q3;\r
+\r
+\r
+void Mad_f32_init()\r
+{\r
+ f_q0 = f32_from_double((double)1.0);\r
+ f_q1 = f32_from_double((double)0.0);\r
+ f_q2 = f32_from_double((double)0.0);\r
+ f_q3 = f32_from_double((double)0.0);\r
+\r
+}\r
+void MadgwickAHRSupdateIMU_f32(float gx, float gy, float gz, float ax, float ay, float az) {\r
+ f32 f_recipNorm;\r
+ f32 f_s0, f_s1, f_s2, f_s3;\r
+ f32 f_qDot1, f_qDot2, f_qDot3, f_qDot4;\r
+ f32 f__2q0, f__2q1, f__2q2, f__2q3, f__4q0, f__4q1, f__4q2 ,f__8q1, f__8q2, f_q0q0, f_q1q1, f_q2q2, f_q3q3;\r
+\r
+ f32 f_gx, f_gy, f_gz;\r
+ f32 f_ax, f_ay, f_az;\r
+\r
+ f32 f_beta;\r
+ f32 f_sampleFreq;\r
+\r
+\r
+ f_gx = f32_from_double((double)gx);\r
+ f_gy = f32_from_double((double)gy);\r
+ f_gz = f32_from_double((double)gz);\r
+\r
+ f_ax = f32_from_double((double)ax);\r
+ f_ay = f32_from_double((double)ay);\r
+ f_az = f32_from_double((double)az);\r
+\r
+ f_beta = f32_from_double((double)beta);\r
+ f_sampleFreq = f32_from_double((double)sampleFreq);\r
+\r
+\r
+ // Rate of change of quaternion from gyroscope\r
+ /*\r
+ qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz);\r
+ qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy);\r
+ qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx);\r
+ qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx);\r
+ */\r
+\r
+ f_qDot1 = f32_mul(f32_sub(f32_sub(f32_neg(f32_mul(f_gx, f_q1)), f32_mul(f_gy, f_q2)), f32_mul(f_gz, f_q3)), f32_from_double(0.5));\r
+ f_qDot2 = f32_mul(f32_sub(f32_add(f32_mul(f_gx, f_q0), f32_mul(f_gz, f_q2)), f32_mul(f_gy, f_q3)), f32_from_double(0.5));\r
+ f_qDot3 = f32_mul(f32_add(f32_mul(f_gx, f_q3), f32_sub(f32_mul(f_gy, f_q0), f32_mul(f_gz, f_q1))), f32_from_double(0.5));\r
+ f_qDot4 = f32_mul(f32_sub(f32_add(f32_mul(f_gy, f_q1), f32_mul(f_gz, f_q0)), f32_mul(f_gx, f_q2)), f32_from_double(0.5));\r
+\r
+\r
+\r
+\r
+ // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation)\r
+ if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) {\r
+\r
+ // Normalise accelerometer measurement\r
+ //recipNorm = invSqrt(ax * ax + ay * ay + az * az);\r
+ f_recipNorm = f32_inv(f32_sqrt((f32_add(f32_mul(f_ax, f_ax), f32_add(f32_mul(f_ay, f_ay), f32_mul(f_az, f_az))))));\r
+ /*\r
+ ax *= recipNorm;\r
+ ay *= recipNorm;\r
+ az *= recipNorm;\r
+ */\r
+\r
+ f_ax = f32_mul(f_ax, f_recipNorm);\r
+ f_ay = f32_mul(f_ay, f_recipNorm);\r
+ f_az = f32_mul(f_az, f_recipNorm);\r
+\r
+ // Auxiliary variables to avoid repeated arithmetic\r
+\r
+ /*\r
+ _2q0 = 2.0f * q0;\r
+ _2q1 = 2.0f * q1;\r
+ _2q2 = 2.0f * q2;\r
+ _2q3 = 2.0f * q3;\r
+ _4q0 = 4.0f * q0;\r
+ _4q1 = 4.0f * q1;\r
+ _4q2 = 4.0f * q2;\r
+ _8q1 = 8.0f * q1;\r
+ _8q2 = 8.0f * q2;\r
+ q0q0 = q0 * q0;\r
+ q1q1 = q1 * q1;\r
+ q2q2 = q2 * q2;\r
+ q3q3 = q3 * q3;\r
+ */\r
+\r
+ f__2q0 = f32_mul(f32_from_double(2.0f), f_q0);\r
+ f__2q1 = f32_mul(f32_from_double(2.0f), f_q1);\r
+ f__2q2 = f32_mul(f32_from_double(2.0f), f_q2);\r
+ f__2q3 = f32_mul(f32_from_double(2.0f), f_q3);\r
+ f__4q0 = f32_mul(f32_from_double(4.0f), f_q0);\r
+ f__4q1 = f32_mul(f32_from_double(4.0f), f_q1);\r
+ f__4q2 = f32_mul(f32_from_double(4.0f), f_q2);\r
+ f__8q1 = f32_mul(f32_from_double(8.0f), f_q1);\r
+ f__8q2 = f32_mul(f32_from_double(8.0f), f_q2);\r
+ f_q0q0 = f32_mul(f_q0, f_q0);\r
+ f_q1q1 = f32_mul(f_q1, f_q1);\r
+ f_q2q2 = f32_mul(f_q2, f_q2);\r
+ f_q3q3 = f32_mul(f_q3, f_q3);\r
+\r
+\r
+ // Gradient decent algorithm corrective step\r
+\r
+ /*\r
+ s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay;\r
+ s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az;\r
+ s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az;\r
+ s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay;\r
+ recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude\r
+ */\r
+\r
+ f_s0 = f32_sub(f32_add(f32_mul(f__2q2, f_ax), f32_add(f32_mul(f__4q0, f_q1q1), f32_mul(f__4q0, f_q2q2))), f32_mul(f__2q1, f_ay));\r
+ f_s1 = f32_add(f32_mul(f__4q1, f_az), f32_add(f32_mul(f__8q1, f_q1q1), f32_add(f32_mul(f__8q1, f_q2q2), f32_sub(f32_sub(f32_add(f32_mul(f_q0q0, f32_mul(f_q1, f32_from_double(4.0f))), f32_sub(f32_mul(f__4q1, f_q3q3), f32_mul(f__2q3, f_ax))), f32_mul(f__2q0, f_ay)), f__4q1))));\r
+ f_s2 = f32_add(f32_mul(f__4q2, f_az), f32_add(f32_mul(f__8q2, f_q1q1), f32_add(f32_mul(f__8q2, f_q2q2), f32_sub(f32_sub(f32_add(f32_mul(f__2q0, f_ax), f32_add(f32_mul(f__4q2, f_q3q3), f32_mul(f_q0q0, f32_mul(f_q2, f32_from_double(4.0))))), f32_mul(f__2q3, f_ay)), f__4q2))));\r
+ f_s3 = f32_sub(f32_add(f32_mul(f_q2q2, f32_mul(f_q3, f32_from_double(4.0))), f32_sub(f32_mul(f_q1q1, f32_mul(f_q3, f32_from_double(4.0))), f32_mul(f__2q1, f_ax))), f32_mul(f__2q2, f_ay));\r
+ f_recipNorm = f32_inv(f32_sqrt(f32_add(f32_mul(f_s0, f_s0), f32_add(f32_mul(f_s1, f_s1), f32_add(f32_mul(f_s2, f_s2), f32_mul(f_s3, f_s3))))));\r
+\r
+ /*\r
+ s0 *= recipNorm;\r
+ s1 *= recipNorm;\r
+ s2 *= recipNorm;\r
+ s3 *= recipNorm;\r
+ */\r
+\r
+ f_s0 = f32_mul(f_s0, f_recipNorm);\r
+ f_s1 = f32_mul(f_s1, f_recipNorm);\r
+ f_s2 = f32_mul(f_s2, f_recipNorm);\r
+ f_s3 = f32_mul(f_s3, f_recipNorm);\r
+\r
+\r
+ // Apply feedback step\r
+\r
+ /*\r
+ qDot1 -= beta * s0;\r
+ qDot2 -= beta * s1;\r
+ qDot3 -= beta * s2;\r
+ qDot4 -= beta * s3;\r
+ */\r
+\r
+ f_qDot1 = f32_sub(f_qDot1, f32_mul(f_beta, f_s0));\r
+ f_qDot2 = f32_sub(f_qDot2, f32_mul(f_beta, f_s1));\r
+ f_qDot3 = f32_sub(f_qDot3, f32_mul(f_beta, f_s2));\r
+ f_qDot4 = f32_sub(f_qDot4, f32_mul(f_beta, f_s3));\r
+\r
+ }\r
+\r
+ // Integrate rate of change of quaternion to yield quaternion\r
+\r
+ /*\r
+ q0 += qDot1 * (1.0f / sampleFreq);\r
+ q1 += qDot2 * (1.0f / sampleFreq);\r
+ q2 += qDot3 * (1.0f / sampleFreq);\r
+ q3 += qDot4 * (1.0f / sampleFreq);\r
+ */\r
+\r
+ f_q0 = f32_add(f_q0, f32_mul(f_qDot1, f32_inv(f_sampleFreq)));\r
+ f_q1 = f32_add(f_q1, f32_mul(f_qDot2, f32_inv(f_sampleFreq)));\r
+ f_q2 = f32_add(f_q2, f32_mul(f_qDot3, f32_inv(f_sampleFreq)));\r
+ f_q3 = f32_add(f_q3, f32_mul(f_qDot4, f32_inv(f_sampleFreq)));\r
+\r
+ // Normalise quaternion\r
+ //recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3);\r
+\r
+ f_recipNorm = f32_inv(f32_sqrt(f32_add(f32_mul(f_q0, f_q0), f32_add(f32_mul(f_q1, f_q1), f32_add(f32_mul(f_q2, f_q2), f32_mul(f_q3, f_q3))))));\r
+\r
+ /*\r
+ q0 *= recipNorm;\r
+ q1 *= recipNorm;\r
+ q2 *= recipNorm;\r
+ q3 *= recipNorm;\r
+ */\r
+\r
+ f_q0 = f32_mul(f_q0, f_recipNorm);\r
+ f_q1 = f32_mul(f_q1, f_recipNorm);\r
+ f_q2 = f32_mul(f_q2, f_recipNorm);\r
+ f_q3 = f32_mul(f_q3, f_recipNorm);\r
+\r
+\r
+ q0 = f32_to_double(f_q0);\r
+ q1 = f32_to_double(f_q1);\r
+ q2 = f32_to_double(f_q2);\r
+ q3 = f32_to_double(f_q3);\r
+\r
+ //printf("%+3.3f\t%+3.3f\t%+3.3f\r\n", q0, q1, q2);\r
+\r
+}\r
+\r
+\r
+//---------------------------------------------------------------------------------------------------\r
+// Fast inverse square-root\r
+// See: http://en.wikipedia.org/wiki/Fast_inverse_square_root\r
+/*\r
+float invSqrt(float x) {\r
+ float halfx = 0.5f * x;\r
+ float y = x;\r
+ long i = *(long*)&y;\r
+ i = 0x5f3759df - (i>>1);\r
+ y = *(float*)&i;\r
+ y = y * (1.5f - (halfx * y * y));\r
+ return y;\r
+}\r
+*/\r
+float invSqrt(float x) {\r
+ return 1.0f / sqrtf(x);\r
+}\r
+//====================================================================================================\r
+// END OF CODE\r
+//====================================================================================================\r