math.h

Go to the documentation of this file.

/* -*- c++ -*- */
/*
 * Copyright 2003,2005,2008,2013,2018 Free Software Foundation, Inc.
 *
 * This file is part of GNU Radio
 *
 * GNU Radio is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 3, or (at your option)
 * any later version.
 *
 * GNU Radio is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with GNU Radio; see the file COPYING.  If not, write to
 * the Free Software Foundation, Inc., 51 Franklin Street,
 * Boston, MA 02110-1301, USA.
 */

/*
 * 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 (2 * GR_M_PI)                  /* 2*pi */
#define GR_M_SQRT2 1.41421356237309504880         /* sqrt(2) */


namespace gr {

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)
{
    float x1 = fabsf(x + clip);
    float x2 = fabsf(x - clip);
    x1 -= x2;
    return 0.5 * x1;
}

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_ */