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182 lines
No EOL
8.6 KiB
C++
182 lines
No EOL
8.6 KiB
C++
#include "math.h"
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#include <cmath>
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namespace dsp
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{
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/***************************************************************************/
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/* Constant definitions */
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/***************************************************************************/
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#define TAN_MAP_RES 0.003921569 /* (smallest non-zero value in table) */
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#define RAD_PER_DEG 0.017453293
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#define TAN_MAP_SIZE 255
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/* arctangents from 0 to pi/4 radians */
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static float fast_atan_table[257] = {
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0.000000e+00, 3.921549e-03, 7.842976e-03, 1.176416e-02, 1.568499e-02, 1.960533e-02,
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2.352507e-02, 2.744409e-02, 3.136226e-02, 3.527947e-02, 3.919560e-02, 4.311053e-02,
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4.702413e-02, 5.093629e-02, 5.484690e-02, 5.875582e-02, 6.266295e-02, 6.656816e-02,
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7.047134e-02, 7.437238e-02, 7.827114e-02, 8.216752e-02, 8.606141e-02, 8.995267e-02,
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9.384121e-02, 9.772691e-02, 1.016096e-01, 1.054893e-01, 1.093658e-01, 1.132390e-01,
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1.171087e-01, 1.209750e-01, 1.248376e-01, 1.286965e-01, 1.325515e-01, 1.364026e-01,
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1.402496e-01, 1.440924e-01, 1.479310e-01, 1.517652e-01, 1.555948e-01, 1.594199e-01,
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1.632403e-01, 1.670559e-01, 1.708665e-01, 1.746722e-01, 1.784728e-01, 1.822681e-01,
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1.860582e-01, 1.898428e-01, 1.936220e-01, 1.973956e-01, 2.011634e-01, 2.049255e-01,
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2.086818e-01, 2.124320e-01, 2.161762e-01, 2.199143e-01, 2.236461e-01, 2.273716e-01,
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2.310907e-01, 2.348033e-01, 2.385093e-01, 2.422086e-01, 2.459012e-01, 2.495869e-01,
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2.532658e-01, 2.569376e-01, 2.606024e-01, 2.642600e-01, 2.679104e-01, 2.715535e-01,
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2.751892e-01, 2.788175e-01, 2.824383e-01, 2.860514e-01, 2.896569e-01, 2.932547e-01,
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2.968447e-01, 3.004268e-01, 3.040009e-01, 3.075671e-01, 3.111252e-01, 3.146752e-01,
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3.182170e-01, 3.217506e-01, 3.252758e-01, 3.287927e-01, 3.323012e-01, 3.358012e-01,
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3.392926e-01, 3.427755e-01, 3.462497e-01, 3.497153e-01, 3.531721e-01, 3.566201e-01,
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3.600593e-01, 3.634896e-01, 3.669110e-01, 3.703234e-01, 3.737268e-01, 3.771211e-01,
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3.805064e-01, 3.838825e-01, 3.872494e-01, 3.906070e-01, 3.939555e-01, 3.972946e-01,
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4.006244e-01, 4.039448e-01, 4.072558e-01, 4.105574e-01, 4.138496e-01, 4.171322e-01,
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4.204054e-01, 4.236689e-01, 4.269229e-01, 4.301673e-01, 4.334021e-01, 4.366272e-01,
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4.398426e-01, 4.430483e-01, 4.462443e-01, 4.494306e-01, 4.526070e-01, 4.557738e-01,
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4.589307e-01, 4.620778e-01, 4.652150e-01, 4.683424e-01, 4.714600e-01, 4.745676e-01,
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4.776654e-01, 4.807532e-01, 4.838312e-01, 4.868992e-01, 4.899573e-01, 4.930055e-01,
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4.960437e-01, 4.990719e-01, 5.020902e-01, 5.050985e-01, 5.080968e-01, 5.110852e-01,
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5.140636e-01, 5.170320e-01, 5.199904e-01, 5.229388e-01, 5.258772e-01, 5.288056e-01,
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5.317241e-01, 5.346325e-01, 5.375310e-01, 5.404195e-01, 5.432980e-01, 5.461666e-01,
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5.490251e-01, 5.518738e-01, 5.547124e-01, 5.575411e-01, 5.603599e-01, 5.631687e-01,
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5.659676e-01, 5.687566e-01, 5.715357e-01, 5.743048e-01, 5.770641e-01, 5.798135e-01,
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5.825531e-01, 5.852828e-01, 5.880026e-01, 5.907126e-01, 5.934128e-01, 5.961032e-01,
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5.987839e-01, 6.014547e-01, 6.041158e-01, 6.067672e-01, 6.094088e-01, 6.120407e-01,
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6.146630e-01, 6.172755e-01, 6.198784e-01, 6.224717e-01, 6.250554e-01, 6.276294e-01,
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6.301939e-01, 6.327488e-01, 6.352942e-01, 6.378301e-01, 6.403565e-01, 6.428734e-01,
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6.453808e-01, 6.478788e-01, 6.503674e-01, 6.528466e-01, 6.553165e-01, 6.577770e-01,
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6.602282e-01, 6.626701e-01, 6.651027e-01, 6.675261e-01, 6.699402e-01, 6.723452e-01,
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6.747409e-01, 6.771276e-01, 6.795051e-01, 6.818735e-01, 6.842328e-01, 6.865831e-01,
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6.889244e-01, 6.912567e-01, 6.935800e-01, 6.958943e-01, 6.981998e-01, 7.004964e-01,
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7.027841e-01, 7.050630e-01, 7.073330e-01, 7.095943e-01, 7.118469e-01, 7.140907e-01,
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7.163258e-01, 7.185523e-01, 7.207701e-01, 7.229794e-01, 7.251800e-01, 7.273721e-01,
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7.295557e-01, 7.317307e-01, 7.338974e-01, 7.360555e-01, 7.382053e-01, 7.403467e-01,
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7.424797e-01, 7.446045e-01, 7.467209e-01, 7.488291e-01, 7.509291e-01, 7.530208e-01,
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7.551044e-01, 7.571798e-01, 7.592472e-01, 7.613064e-01, 7.633576e-01, 7.654008e-01,
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7.674360e-01, 7.694633e-01, 7.714826e-01, 7.734940e-01, 7.754975e-01, 7.774932e-01,
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7.794811e-01, 7.814612e-01, 7.834335e-01, 7.853982e-01, 7.853982e-01};
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/*****************************************************************************
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Function: Arc tangent
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Syntax: angle = fast_atan2(y, x);
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float y y component of input vector
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float x x component of input vector
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float angle angle of vector (x, y) in radians
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Description: This function calculates the angle of the vector (x,y)
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based on a table lookup and linear interpolation. The table uses a
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256 point table covering -45 to +45 degrees and uses symmetry to
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determine the final angle value in the range of -180 to 180
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degrees. Note that this function uses the small angle approximation
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for values close to zero. This routine calculates the arc tangent
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with an average error of +/- 3.56e-5 degrees (6.21e-7 radians).
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*****************************************************************************/
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/* From GNU Radio */
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float fast_atan2f(float y, float x)
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{
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float x_abs, y_abs, z;
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float alpha, angle, base_angle;
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int index;
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/* normalize to +/- 45 degree range */
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y_abs = fabsf(y);
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x_abs = fabsf(x);
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/* don't divide by zero! */
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if (!((y_abs > 0.0f) || (x_abs > 0.0f)))
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return 0.0;
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if (y_abs < x_abs)
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z = y_abs / x_abs;
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else
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z = x_abs / y_abs;
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/* when ratio approaches the table resolution, the angle is */
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/* best approximated with the argument itself... */
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if (z < TAN_MAP_RES)
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base_angle = z;
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else
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{
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/* find index and interpolation value */
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alpha = z * (float)TAN_MAP_SIZE;
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index = ((int)alpha) & 0xff;
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alpha -= (float)index;
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/* determine base angle based on quadrant and */
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/* add or subtract table value from base angle based on quadrant */
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base_angle = fast_atan_table[index];
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base_angle += (fast_atan_table[index + 1] - fast_atan_table[index]) * alpha;
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}
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if (x_abs > y_abs)
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{ /* -45 -> 45 or 135 -> 225 */
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if (x >= 0.0)
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{ /* -45 -> 45 */
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if (y >= 0.0)
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angle = base_angle; /* 0 -> 45, angle OK */
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else
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angle = -base_angle; /* -45 -> 0, angle = -angle */
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}
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else
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{ /* 135 -> 180 or 180 -> -135 */
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angle = 3.14159265358979323846;
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if (y >= 0.0)
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angle -= base_angle; /* 135 -> 180, angle = 180 - angle */
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else
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angle = base_angle - angle; /* 180 -> -135, angle = angle - 180 */
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}
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}
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else
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{ /* 45 -> 135 or -135 -> -45 */
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if (y >= 0.0)
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{ /* 45 -> 135 */
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angle = 1.57079632679489661923;
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if (x >= 0.0)
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angle -= base_angle; /* 45 -> 90, angle = 90 - angle */
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else
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angle += base_angle; /* 90 -> 135, angle = 90 + angle */
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}
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else
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{ /* -135 -> -45 */
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angle = -1.57079632679489661923;
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if (x >= 0.0)
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angle += base_angle; /* -90 -> -45, angle = -90 + angle */
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else
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angle -= base_angle; /* -135 -> -90, angle = -90 - angle */
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}
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}
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#ifdef ZERO_TO_TWOPI
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if (angle < 0)
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return (angle + TWOPI);
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else
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return (angle);
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#else
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return (angle);
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#endif
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}
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// Both of those are from https://stackoverflow.com/questions/11261170/c-and-maths-fast-approximation-of-a-trigonometric-function
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// This gave a bit better results than the Babylonian method.
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float fast_cos(float x)
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{
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float x8, x4, x2;
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x2 = x * x;
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x4 = x2 * x2;
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x8 = x4 * x4;
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return (-2.7236370439787708e-7 * x2 + 2.4799852696610628e-5) * x8 +
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(-1.3888885054799695e-3 * x2 + 4.1666666636943683e-2) * x4 +
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(-4.9999999999963024e-1 * x2 + 1.0000000000000000e+0);
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}
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float fast_sin(float x)
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{
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float x4, x2;
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x2 = x * x;
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x4 = x2 * x2;
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return ((2.7181216275479732e-6 * x2 - 1.9839312269456257e-4) * x4 +
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(8.3333293048425631e-3 * x2 - 1.6666666640797048e-1)) *
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x2 * x +
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x;
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}
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} // namespace libdsp
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