Madgwick
Dependents: IMU_ethernet IMU_serial_test IMU_serial
MadgwickAHRS.cpp@2:11ffe983c3f8, 2016-10-06 (annotated)
- Committer:
- rctaduio
- Date:
- Thu Oct 06 17:34:56 2016 +0000
- Revision:
- 2:11ffe983c3f8
- Parent:
- 1:189289643d44
- Child:
- 3:689b64501b7d
adding comments and stuff;
Who changed what in which revision?
User | Revision | Line number | New contents of line |
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rctaduio | 0:2ed6ce16f06f | 1 | //===================================================================================================== |
rctaduio | 0:2ed6ce16f06f | 2 | // MadgwickAHRS.c |
rctaduio | 0:2ed6ce16f06f | 3 | //===================================================================================================== |
rctaduio | 0:2ed6ce16f06f | 4 | // |
rctaduio | 0:2ed6ce16f06f | 5 | // Implementation of Madgwick's IMU and AHRS algorithms. |
rctaduio | 0:2ed6ce16f06f | 6 | // See: http://www.x-io.co.uk/node/8#open_source_ahrs_and_imu_algorithms |
rctaduio | 0:2ed6ce16f06f | 7 | // |
rctaduio | 0:2ed6ce16f06f | 8 | // Date Author Notes |
rctaduio | 0:2ed6ce16f06f | 9 | // 29/09/2011 SOH Madgwick Initial release |
rctaduio | 0:2ed6ce16f06f | 10 | // 02/10/2011 SOH Madgwick Optimised for reduced CPU load |
rctaduio | 0:2ed6ce16f06f | 11 | // 19/02/2012 SOH Madgwick Magnetometer measurement is normalised |
rctaduio | 0:2ed6ce16f06f | 12 | // |
rctaduio | 0:2ed6ce16f06f | 13 | //===================================================================================================== |
rctaduio | 0:2ed6ce16f06f | 14 | |
rctaduio | 0:2ed6ce16f06f | 15 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 16 | // Header files |
rctaduio | 0:2ed6ce16f06f | 17 | |
rctaduio | 0:2ed6ce16f06f | 18 | #include "MadgwickAHRS.h" |
rctaduio | 0:2ed6ce16f06f | 19 | #include <math.h> |
rctaduio | 0:2ed6ce16f06f | 20 | |
rctaduio | 0:2ed6ce16f06f | 21 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 22 | // Definitions |
rctaduio | 0:2ed6ce16f06f | 23 | |
rctaduio | 0:2ed6ce16f06f | 24 | #define sampleFreq 28.0f // sample frequency in Hz |
rctaduio | 0:2ed6ce16f06f | 25 | #define betaDef 0.9f // 2 * proportional gain |
rctaduio | 0:2ed6ce16f06f | 26 | |
rctaduio | 0:2ed6ce16f06f | 27 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 28 | // Variable definitions |
rctaduio | 0:2ed6ce16f06f | 29 | |
rctaduio | 0:2ed6ce16f06f | 30 | volatile float beta = betaDef; // 2 * proportional gain (Kp) |
rctaduio | 1:189289643d44 | 31 | //volatile float q0 = 1.0f, q1 = 0.0f, q2 = 0.0f, q3 = 0.0f; // quaternion of sensor frame relative to auxiliary frame |
rctaduio | 0:2ed6ce16f06f | 32 | |
rctaduio | 0:2ed6ce16f06f | 33 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 34 | // Function declarations |
rctaduio | 0:2ed6ce16f06f | 35 | |
rctaduio | 0:2ed6ce16f06f | 36 | float invSqrt(float x); |
rctaduio | 0:2ed6ce16f06f | 37 | |
rctaduio | 0:2ed6ce16f06f | 38 | //==================================================================================================== |
rctaduio | 0:2ed6ce16f06f | 39 | // Functions |
rctaduio | 0:2ed6ce16f06f | 40 | |
rctaduio | 0:2ed6ce16f06f | 41 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 42 | // AHRS algorithm update |
rctaduio | 0:2ed6ce16f06f | 43 | |
rctaduio | 2:11ffe983c3f8 | 44 | void MadgwickAHRSupdate(float gx, float gy, float gz, float ax, float ay, float az, float mx, float my, float mz) |
rctaduio | 2:11ffe983c3f8 | 45 | { |
rctaduio | 0:2ed6ce16f06f | 46 | float recipNorm; |
rctaduio | 0:2ed6ce16f06f | 47 | float s0, s1, s2, s3; |
rctaduio | 0:2ed6ce16f06f | 48 | float qDot1, qDot2, qDot3, qDot4; |
rctaduio | 0:2ed6ce16f06f | 49 | float hx, hy; |
rctaduio | 0:2ed6ce16f06f | 50 | 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; |
rctaduio | 0:2ed6ce16f06f | 51 | |
rctaduio | 0:2ed6ce16f06f | 52 | // Use IMU algorithm if magnetometer measurement invalid (avoids NaN in magnetometer normalisation) |
rctaduio | 0:2ed6ce16f06f | 53 | if((mx == 0.0f) && (my == 0.0f) && (mz == 0.0f)) { |
rctaduio | 0:2ed6ce16f06f | 54 | MadgwickAHRSupdateIMU(gx, gy, gz, ax, ay, az); |
rctaduio | 0:2ed6ce16f06f | 55 | return; |
rctaduio | 0:2ed6ce16f06f | 56 | } |
rctaduio | 0:2ed6ce16f06f | 57 | |
rctaduio | 0:2ed6ce16f06f | 58 | // Rate of change of quaternion from gyroscope |
rctaduio | 0:2ed6ce16f06f | 59 | qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); |
rctaduio | 0:2ed6ce16f06f | 60 | qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); |
rctaduio | 0:2ed6ce16f06f | 61 | qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); |
rctaduio | 0:2ed6ce16f06f | 62 | qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); |
rctaduio | 0:2ed6ce16f06f | 63 | |
rctaduio | 0:2ed6ce16f06f | 64 | // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) |
rctaduio | 0:2ed6ce16f06f | 65 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { |
rctaduio | 0:2ed6ce16f06f | 66 | |
rctaduio | 0:2ed6ce16f06f | 67 | // Normalise accelerometer measurement |
rctaduio | 0:2ed6ce16f06f | 68 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); |
rctaduio | 0:2ed6ce16f06f | 69 | ax *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 70 | ay *= recipNorm; |
rctaduio | 2:11ffe983c3f8 | 71 | az *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 72 | |
rctaduio | 0:2ed6ce16f06f | 73 | // Normalise magnetometer measurement |
rctaduio | 0:2ed6ce16f06f | 74 | recipNorm = invSqrt(mx * mx + my * my + mz * mz); |
rctaduio | 0:2ed6ce16f06f | 75 | mx *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 76 | my *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 77 | mz *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 78 | |
rctaduio | 0:2ed6ce16f06f | 79 | // Auxiliary variables to avoid repeated arithmetic |
rctaduio | 0:2ed6ce16f06f | 80 | _2q0mx = 2.0f * q0 * mx; |
rctaduio | 0:2ed6ce16f06f | 81 | _2q0my = 2.0f * q0 * my; |
rctaduio | 0:2ed6ce16f06f | 82 | _2q0mz = 2.0f * q0 * mz; |
rctaduio | 0:2ed6ce16f06f | 83 | _2q1mx = 2.0f * q1 * mx; |
rctaduio | 0:2ed6ce16f06f | 84 | _2q0 = 2.0f * q0; |
rctaduio | 0:2ed6ce16f06f | 85 | _2q1 = 2.0f * q1; |
rctaduio | 0:2ed6ce16f06f | 86 | _2q2 = 2.0f * q2; |
rctaduio | 0:2ed6ce16f06f | 87 | _2q3 = 2.0f * q3; |
rctaduio | 0:2ed6ce16f06f | 88 | _2q0q2 = 2.0f * q0 * q2; |
rctaduio | 0:2ed6ce16f06f | 89 | _2q2q3 = 2.0f * q2 * q3; |
rctaduio | 0:2ed6ce16f06f | 90 | q0q0 = q0 * q0; |
rctaduio | 0:2ed6ce16f06f | 91 | q0q1 = q0 * q1; |
rctaduio | 0:2ed6ce16f06f | 92 | q0q2 = q0 * q2; |
rctaduio | 0:2ed6ce16f06f | 93 | q0q3 = q0 * q3; |
rctaduio | 0:2ed6ce16f06f | 94 | q1q1 = q1 * q1; |
rctaduio | 0:2ed6ce16f06f | 95 | q1q2 = q1 * q2; |
rctaduio | 0:2ed6ce16f06f | 96 | q1q3 = q1 * q3; |
rctaduio | 0:2ed6ce16f06f | 97 | q2q2 = q2 * q2; |
rctaduio | 0:2ed6ce16f06f | 98 | q2q3 = q2 * q3; |
rctaduio | 0:2ed6ce16f06f | 99 | q3q3 = q3 * q3; |
rctaduio | 0:2ed6ce16f06f | 100 | |
rctaduio | 0:2ed6ce16f06f | 101 | // Reference direction of Earth's magnetic field |
rctaduio | 0:2ed6ce16f06f | 102 | hx = mx * q0q0 - _2q0my * q3 + _2q0mz * q2 + mx * q1q1 + _2q1 * my * q2 + _2q1 * mz * q3 - mx * q2q2 - mx * q3q3; |
rctaduio | 0:2ed6ce16f06f | 103 | hy = _2q0mx * q3 + my * q0q0 - _2q0mz * q1 + _2q1mx * q2 - my * q1q1 + my * q2q2 + _2q2 * mz * q3 - my * q3q3; |
rctaduio | 0:2ed6ce16f06f | 104 | _2bx = sqrt(hx * hx + hy * hy); |
rctaduio | 0:2ed6ce16f06f | 105 | _2bz = -_2q0mx * q2 + _2q0my * q1 + mz * q0q0 + _2q1mx * q3 - mz * q1q1 + _2q2 * my * q3 - mz * q2q2 + mz * q3q3; |
rctaduio | 0:2ed6ce16f06f | 106 | _4bx = 2.0f * _2bx; |
rctaduio | 0:2ed6ce16f06f | 107 | _4bz = 2.0f * _2bz; |
rctaduio | 0:2ed6ce16f06f | 108 | |
rctaduio | 0:2ed6ce16f06f | 109 | // Gradient decent algorithm corrective step |
rctaduio | 0:2ed6ce16f06f | 110 | 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); |
rctaduio | 0:2ed6ce16f06f | 111 | 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); |
rctaduio | 0:2ed6ce16f06f | 112 | 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); |
rctaduio | 0:2ed6ce16f06f | 113 | 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); |
rctaduio | 0:2ed6ce16f06f | 114 | recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude |
rctaduio | 0:2ed6ce16f06f | 115 | s0 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 116 | s1 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 117 | s2 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 118 | s3 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 119 | |
rctaduio | 0:2ed6ce16f06f | 120 | // Apply feedback step |
rctaduio | 0:2ed6ce16f06f | 121 | qDot1 -= beta * s0; |
rctaduio | 0:2ed6ce16f06f | 122 | qDot2 -= beta * s1; |
rctaduio | 0:2ed6ce16f06f | 123 | qDot3 -= beta * s2; |
rctaduio | 0:2ed6ce16f06f | 124 | qDot4 -= beta * s3; |
rctaduio | 0:2ed6ce16f06f | 125 | } |
rctaduio | 0:2ed6ce16f06f | 126 | |
rctaduio | 0:2ed6ce16f06f | 127 | // Integrate rate of change of quaternion to yield quaternion |
rctaduio | 0:2ed6ce16f06f | 128 | q0 += qDot1 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 129 | q1 += qDot2 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 130 | q2 += qDot3 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 131 | q3 += qDot4 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 132 | |
rctaduio | 0:2ed6ce16f06f | 133 | // Normalise quaternion |
rctaduio | 0:2ed6ce16f06f | 134 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); |
rctaduio | 0:2ed6ce16f06f | 135 | q0 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 136 | q1 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 137 | q2 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 138 | q3 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 139 | } |
rctaduio | 0:2ed6ce16f06f | 140 | |
rctaduio | 0:2ed6ce16f06f | 141 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 142 | // IMU algorithm update |
rctaduio | 0:2ed6ce16f06f | 143 | |
rctaduio | 2:11ffe983c3f8 | 144 | void MadgwickAHRSupdateIMU(float gx, float gy, float gz, float ax, float ay, float az) |
rctaduio | 2:11ffe983c3f8 | 145 | { |
rctaduio | 0:2ed6ce16f06f | 146 | float recipNorm; |
rctaduio | 0:2ed6ce16f06f | 147 | float s0, s1, s2, s3; |
rctaduio | 0:2ed6ce16f06f | 148 | float qDot1, qDot2, qDot3, qDot4; |
rctaduio | 0:2ed6ce16f06f | 149 | float _2q0, _2q1, _2q2, _2q3, _4q0, _4q1, _4q2 ,_8q1, _8q2, q0q0, q1q1, q2q2, q3q3; |
rctaduio | 0:2ed6ce16f06f | 150 | |
rctaduio | 0:2ed6ce16f06f | 151 | // Rate of change of quaternion from gyroscope |
rctaduio | 0:2ed6ce16f06f | 152 | qDot1 = 0.5f * (-q1 * gx - q2 * gy - q3 * gz); |
rctaduio | 0:2ed6ce16f06f | 153 | qDot2 = 0.5f * (q0 * gx + q2 * gz - q3 * gy); |
rctaduio | 0:2ed6ce16f06f | 154 | qDot3 = 0.5f * (q0 * gy - q1 * gz + q3 * gx); |
rctaduio | 0:2ed6ce16f06f | 155 | qDot4 = 0.5f * (q0 * gz + q1 * gy - q2 * gx); |
rctaduio | 0:2ed6ce16f06f | 156 | |
rctaduio | 0:2ed6ce16f06f | 157 | // Compute feedback only if accelerometer measurement valid (avoids NaN in accelerometer normalisation) |
rctaduio | 0:2ed6ce16f06f | 158 | if(!((ax == 0.0f) && (ay == 0.0f) && (az == 0.0f))) { |
rctaduio | 0:2ed6ce16f06f | 159 | |
rctaduio | 0:2ed6ce16f06f | 160 | // Normalise accelerometer measurement |
rctaduio | 0:2ed6ce16f06f | 161 | recipNorm = invSqrt(ax * ax + ay * ay + az * az); |
rctaduio | 0:2ed6ce16f06f | 162 | ax *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 163 | ay *= recipNorm; |
rctaduio | 2:11ffe983c3f8 | 164 | az *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 165 | |
rctaduio | 0:2ed6ce16f06f | 166 | // Auxiliary variables to avoid repeated arithmetic |
rctaduio | 0:2ed6ce16f06f | 167 | _2q0 = 2.0f * q0; |
rctaduio | 0:2ed6ce16f06f | 168 | _2q1 = 2.0f * q1; |
rctaduio | 0:2ed6ce16f06f | 169 | _2q2 = 2.0f * q2; |
rctaduio | 0:2ed6ce16f06f | 170 | _2q3 = 2.0f * q3; |
rctaduio | 0:2ed6ce16f06f | 171 | _4q0 = 4.0f * q0; |
rctaduio | 0:2ed6ce16f06f | 172 | _4q1 = 4.0f * q1; |
rctaduio | 0:2ed6ce16f06f | 173 | _4q2 = 4.0f * q2; |
rctaduio | 0:2ed6ce16f06f | 174 | _8q1 = 8.0f * q1; |
rctaduio | 0:2ed6ce16f06f | 175 | _8q2 = 8.0f * q2; |
rctaduio | 0:2ed6ce16f06f | 176 | q0q0 = q0 * q0; |
rctaduio | 0:2ed6ce16f06f | 177 | q1q1 = q1 * q1; |
rctaduio | 0:2ed6ce16f06f | 178 | q2q2 = q2 * q2; |
rctaduio | 0:2ed6ce16f06f | 179 | q3q3 = q3 * q3; |
rctaduio | 0:2ed6ce16f06f | 180 | |
rctaduio | 0:2ed6ce16f06f | 181 | // Gradient decent algorithm corrective step |
rctaduio | 0:2ed6ce16f06f | 182 | s0 = _4q0 * q2q2 + _2q2 * ax + _4q0 * q1q1 - _2q1 * ay; |
rctaduio | 0:2ed6ce16f06f | 183 | s1 = _4q1 * q3q3 - _2q3 * ax + 4.0f * q0q0 * q1 - _2q0 * ay - _4q1 + _8q1 * q1q1 + _8q1 * q2q2 + _4q1 * az; |
rctaduio | 0:2ed6ce16f06f | 184 | s2 = 4.0f * q0q0 * q2 + _2q0 * ax + _4q2 * q3q3 - _2q3 * ay - _4q2 + _8q2 * q1q1 + _8q2 * q2q2 + _4q2 * az; |
rctaduio | 0:2ed6ce16f06f | 185 | s3 = 4.0f * q1q1 * q3 - _2q1 * ax + 4.0f * q2q2 * q3 - _2q2 * ay; |
rctaduio | 0:2ed6ce16f06f | 186 | recipNorm = invSqrt(s0 * s0 + s1 * s1 + s2 * s2 + s3 * s3); // normalise step magnitude |
rctaduio | 0:2ed6ce16f06f | 187 | s0 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 188 | s1 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 189 | s2 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 190 | s3 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 191 | |
rctaduio | 0:2ed6ce16f06f | 192 | // Apply feedback step |
rctaduio | 0:2ed6ce16f06f | 193 | qDot1 -= beta * s0; |
rctaduio | 0:2ed6ce16f06f | 194 | qDot2 -= beta * s1; |
rctaduio | 0:2ed6ce16f06f | 195 | qDot3 -= beta * s2; |
rctaduio | 0:2ed6ce16f06f | 196 | qDot4 -= beta * s3; |
rctaduio | 0:2ed6ce16f06f | 197 | } |
rctaduio | 0:2ed6ce16f06f | 198 | |
rctaduio | 0:2ed6ce16f06f | 199 | // Integrate rate of change of quaternion to yield quaternion |
rctaduio | 0:2ed6ce16f06f | 200 | q0 += qDot1 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 201 | q1 += qDot2 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 202 | q2 += qDot3 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 203 | q3 += qDot4 * (1.0f / sampleFreq); |
rctaduio | 0:2ed6ce16f06f | 204 | |
rctaduio | 0:2ed6ce16f06f | 205 | // Normalise quaternion |
rctaduio | 0:2ed6ce16f06f | 206 | recipNorm = invSqrt(q0 * q0 + q1 * q1 + q2 * q2 + q3 * q3); |
rctaduio | 0:2ed6ce16f06f | 207 | q0 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 208 | q1 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 209 | q2 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 210 | q3 *= recipNorm; |
rctaduio | 0:2ed6ce16f06f | 211 | } |
rctaduio | 0:2ed6ce16f06f | 212 | |
rctaduio | 0:2ed6ce16f06f | 213 | //--------------------------------------------------------------------------------------------------- |
rctaduio | 0:2ed6ce16f06f | 214 | // Fast inverse square-root |
rctaduio | 0:2ed6ce16f06f | 215 | // See: http://en.wikipedia.org/wiki/Fast_inverse_square_root |
rctaduio | 0:2ed6ce16f06f | 216 | |
rctaduio | 2:11ffe983c3f8 | 217 | float invSqrt(float x) |
rctaduio | 2:11ffe983c3f8 | 218 | { |
rctaduio | 0:2ed6ce16f06f | 219 | float halfx = 0.5f * x; |
rctaduio | 0:2ed6ce16f06f | 220 | float y = x; |
rctaduio | 0:2ed6ce16f06f | 221 | long i = *(long*)&y; |
rctaduio | 0:2ed6ce16f06f | 222 | i = 0x5f3759df - (i>>1); |
rctaduio | 0:2ed6ce16f06f | 223 | y = *(float*)&i; |
rctaduio | 0:2ed6ce16f06f | 224 | y = y * (1.5f - (halfx * y * y)); |
rctaduio | 0:2ed6ce16f06f | 225 | return y; |
rctaduio | 0:2ed6ce16f06f | 226 | } |
rctaduio | 0:2ed6ce16f06f | 227 | |
rctaduio | 0:2ed6ce16f06f | 228 | //==================================================================================================== |
rctaduio | 0:2ed6ce16f06f | 229 | // END OF CODE |
rctaduio | 0:2ed6ce16f06f | 230 | //==================================================================================================== |