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/* -*- c++ -*- */
/*
* Copyright 2003,2005,2008,2013,2018 Free Software Foundation, Inc.
*
* This file is part of GNU Radio
*
* SPDX-License-Identifier: GPL-3.0-or-later
*
*/
/*
* mathematical odds and ends.
*/
#ifndef _GR_MATH_H_
#define _GR_MATH_H_
#include <gnuradio/api.h>
#include <gnuradio/gr_complex.h>
#include <cmath>
/*
* \brief Define commonly used mathematical constants
* \ingroup misc
*
* Mathematical constants are neither defined in the C standard
* nor the C++ standard. For -std=c{++}11 M_LOG2E and M_SQRT2 won't
* compile. GR_M_PI actually works with C++ but is defined here for the sake
* of consistency.
*/
#define GR_M_LOG2E 1.4426950408889634074 /* log_2 e */
#define GR_M_PI 3.14159265358979323846 /* pi */
#define GR_M_PI_4 0.78539816339744830961566084582 /* pi/4 */
#define GR_M_TWOPI 6.28318530717958647692 /* 2*pi */
#define GR_M_SQRT2 1.41421356237309504880 /* sqrt(2) */
#define GR_M_ONE_OVER_2PI 0.15915494309189533577 /* 1 / (2*pi) */
#define GR_M_MINUS_TWO_PI -6.28318530717958647692 /* - 2*pi */
namespace gr {
static inline void
fast_cc_multiply(gr_complex& out, const gr_complex cc1, const gr_complex cc2)
{
// The built-in complex.h multiply has significant NaN/INF checking that
// considerably slows down performance. While on some compilers the
// -fcx-limit-range flag can be used, this fast function makes the math consistent
// in terms of performance for the Costas loop.
float o_r, o_i;
o_r = (cc1.real() * cc2.real()) - (cc1.imag() * cc2.imag());
o_i = (cc1.real() * cc2.imag()) + (cc1.imag() * cc2.real());
out.real(o_r);
out.imag(o_i);
}
static inline bool is_power_of_2(long x) { return x != 0 && (x & (x - 1)) == 0; }
/*!
* \brief Fast arc tangent using table lookup and linear interpolation
* \ingroup misc
*
* \param y component of input vector
* \param x component of input vector
* \returns float angle angle of vector (x, y) in radians
*
* This function calculates the angle of the vector (x,y) based on a
* table lookup and linear interpolation. The table uses a 256 point
* table covering -45 to +45 degrees and uses symmetry to determine
* the final angle value in the range of -180 to 180 degrees. Note
* that this function uses the small angle approximation for values
* close to zero. This routine calculates the arc tangent with an
* average error of +/- 0.045 degrees.
*/
GR_RUNTIME_API float fast_atan2f(float y, float x);
static inline float fast_atan2f(gr_complex z) { return fast_atan2f(z.imag(), z.real()); }
/* This bounds x by +/- clip without a branch */
static inline float branchless_clip(float x, float clip)
{
return 0.5 * (std::abs(x + clip) - std::abs(x - clip));
}
static inline float clip(float x, float clip)
{
float y = x;
if (x > clip)
y = clip;
else if (x < -clip)
y = -clip;
return y;
}
// Slicer Functions
static inline unsigned int binary_slicer(float x)
{
if (x >= 0)
return 1;
else
return 0;
}
static inline unsigned int quad_45deg_slicer(float r, float i)
{
unsigned int ret = 0;
if ((r >= 0) && (i >= 0))
ret = 0;
else if ((r < 0) && (i >= 0))
ret = 1;
else if ((r < 0) && (i < 0))
ret = 2;
else
ret = 3;
return ret;
}
static inline unsigned int quad_0deg_slicer(float r, float i)
{
unsigned int ret = 0;
if (fabsf(r) > fabsf(i)) {
if (r > 0)
ret = 0;
else
ret = 2;
} else {
if (i > 0)
ret = 1;
else
ret = 3;
}
return ret;
}
static inline unsigned int quad_45deg_slicer(gr_complex x)
{
return quad_45deg_slicer(x.real(), x.imag());
}
static inline unsigned int quad_0deg_slicer(gr_complex x)
{
return quad_0deg_slicer(x.real(), x.imag());
}
// Branchless Slicer Functions
static inline unsigned int branchless_binary_slicer(float x) { return (x >= 0); }
static inline unsigned int branchless_quad_0deg_slicer(float r, float i)
{
unsigned int ret = 0;
ret = (fabsf(r) > fabsf(i)) * (((r < 0) << 0x1)); // either 0 (00) or 2 (10)
ret |= (fabsf(i) > fabsf(r)) * (((i < 0) << 0x1) | 0x1); // either 1 (01) or 3 (11)
return ret;
}
static inline unsigned int branchless_quad_0deg_slicer(gr_complex x)
{
return branchless_quad_0deg_slicer(x.real(), x.imag());
}
static inline unsigned int branchless_quad_45deg_slicer(float r, float i)
{
char ret = (r <= 0);
ret |= ((i <= 0) << 1);
return (ret ^ ((ret & 0x2) >> 0x1));
}
static inline unsigned int branchless_quad_45deg_slicer(gr_complex x)
{
return branchless_quad_45deg_slicer(x.real(), x.imag());
}
/*!
* \param x any value
* \param pow2 must be a power of 2
* \returns \p x rounded down to a multiple of \p pow2.
*/
static inline size_t p2_round_down(size_t x, size_t pow2) { return x & -pow2; }
/*!
* \param x any value
* \param pow2 must be a power of 2
* \returns \p x rounded up to a multiple of \p pow2.
*/
static inline size_t p2_round_up(size_t x, size_t pow2)
{
return p2_round_down(x + pow2 - 1, pow2);
}
/*!
* \param x any value
* \param pow2 must be a power of 2
* \returns \p x modulo \p pow2.
*/
static inline size_t p2_modulo(size_t x, size_t pow2) { return x & (pow2 - 1); }
/*!
* \param x any value
* \param pow2 must be a power of 2
* \returns \p pow2 - (\p x modulo \p pow2).
*/
static inline size_t p2_modulo_neg(size_t x, size_t pow2)
{
return pow2 - p2_modulo(x, pow2);
}
} /* namespace gr */
#endif /* _GR_MATH_H_ */
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