math.hpp

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//
// Copyright 2014-2015 Ettus Research LLC
// Copyright 2018 Ettus Research, a National Instruments Company
//
// SPDX-License-Identifier: GPL-3.0-or-later
//
 
#pragma once
 
#include <uhd/config.hpp>
#include <uhd/exception.hpp>
#include <stdint.h>
#include <boost/numeric/conversion/bounds.hpp>
#include <cmath>
#if BOOST_VERSION >= 106700
#    include <boost/integer/common_factor.hpp>
// "bmint" for "boost math integer"
namespace _bmint = boost::integer;
#else
#    include <boost/math/common_factor.hpp>
namespace _bmint = boost::math;
#endif
 
 
namespace uhd {
 
namespace math {
 
static const double PI = 3.14159265358979323846;
 
static const float SINGLE_PRECISION_EPSILON  = 1.19e-7f;
static const double DOUBLE_PRECISION_EPSILON = 2.22e-16;
 
//
// Note that this is a UHD/USRP-specific constant. In UHD, frequencies are on
// the order of 1e9 (GHz) or below. We will declare frequencies as equal if they
// are within a millihertz.  For the purpose of
// comparing frequencies, we "lose" 9 decimal places for the integer
// component of the frequency, so we choose this epsilon value for floating
// point comparison of frequencies.
static constexpr double FREQ_COMPARE_EPSILON = 1e-12;
 
namespace fp_compare {
 
template <typename float_t>
class fp_compare_epsilon
{
public:
    UHD_INLINE fp_compare_epsilon(float_t value);
    UHD_INLINE fp_compare_epsilon(float_t value, float_t epsilon);
    UHD_INLINE fp_compare_epsilon(const fp_compare_epsilon<float_t>& copy);
    UHD_INLINE ~fp_compare_epsilon();
    UHD_INLINE void operator=(const fp_compare_epsilon& copy);
 
    float_t _value;
    float_t _epsilon;
};
 
/* A Note on Floating Point Equality with Epsilons
 *
 * There are obviously a lot of strategies for defining floating point
 * equality, and in the end it all comes down to the domain at hand. UHD's
 * floating-point-with-epsilon comparison algorithm is based on the method
 * presented in Knuth's "The Art of Computer Science" called "close enough
 * with tolerance epsilon".
 *
 *      [(|u - v| / |u|) <= e] || [(|u - v| / |v|) <= e]
 *
 * UHD's modification to this algorithm is using the denominator's epsilon
 * value (since each float_t object has its own epsilon) for each
 * comparison.
 */
 
template <typename float_t>
UHD_INLINE bool operator==(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator!=(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<=(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>=(
    fp_compare_epsilon<float_t> lhs, fp_compare_epsilon<float_t> rhs);
 
/* If these operators are used with floats, we rely on type promotion to
 * double. */
template <typename float_t>
UHD_INLINE bool operator==(fp_compare_epsilon<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator!=(fp_compare_epsilon<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator<(fp_compare_epsilon<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator<=(fp_compare_epsilon<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator>(fp_compare_epsilon<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator>=(fp_compare_epsilon<float_t> lhs, double rhs);
 
template <typename float_t>
UHD_INLINE bool operator==(double lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator!=(double lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<(double lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<=(double lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>(double lhs, fp_compare_epsilon<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>=(double lhs, fp_compare_epsilon<float_t> rhs);
 
class freq_compare_epsilon : public fp_compare_epsilon<double>
{
public:
    UHD_INLINE freq_compare_epsilon(double value)
        : fp_compare_epsilon<double>(value, FREQ_COMPARE_EPSILON)
    {
    }
 
    UHD_INLINE freq_compare_epsilon(const freq_compare_epsilon& copy)
        : fp_compare_epsilon<double>(copy)
    {
    }
};
 
 
} // namespace fp_compare
 
 
static const float SINGLE_PRECISION_DELTA  = 1e-3f;
static const double DOUBLE_PRECISION_DELTA = 1e-5;
 
static const double FREQ_COMPARISON_DELTA_HZ = 0.1;
 
 
namespace fp_compare {
 
template <typename float_t>
class fp_compare_delta
{
public:
    UHD_INLINE fp_compare_delta(float_t value);
    UHD_INLINE fp_compare_delta(float_t value, float_t delta);
    UHD_INLINE fp_compare_delta(const fp_compare_delta<float_t>& copy);
    UHD_INLINE ~fp_compare_delta();
    UHD_INLINE void operator=(const fp_compare_delta& copy);
 
    float_t _value;
    float_t _delta;
};
 
template <typename float_t>
UHD_INLINE bool operator==(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator!=(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<=(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>=(fp_compare_delta<float_t> lhs, fp_compare_delta<float_t> rhs);
 
/* If these operators are used with floats, we rely on type promotion to
 * double. */
template <typename float_t>
UHD_INLINE bool operator==(fp_compare_delta<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator!=(fp_compare_delta<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator<(fp_compare_delta<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator<=(fp_compare_delta<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator>(fp_compare_delta<float_t> lhs, double rhs);
template <typename float_t>
UHD_INLINE bool operator>=(fp_compare_delta<float_t> lhs, double rhs);
 
template <typename float_t>
UHD_INLINE bool operator==(double lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator!=(double lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<(double lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator<=(double lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>(double lhs, fp_compare_delta<float_t> rhs);
template <typename float_t>
UHD_INLINE bool operator>=(double lhs, fp_compare_delta<float_t> rhs);
 
} // namespace fp_compare
 
UHD_INLINE bool frequencies_are_equal(double lhs, double rhs)
{
    return (fp_compare::fp_compare_delta<double>(lhs, FREQ_COMPARISON_DELTA_HZ)
            == fp_compare::fp_compare_delta<double>(rhs, FREQ_COMPARISON_DELTA_HZ));
}
 
inline double dB_to_lin(const double dB_val)
{
    return std::pow(10, (dB_val) / 10.0);
}
 
inline double lin_to_dB(const double val)
{
    return 10 * std::log10(val);
}
 
 
template <typename IntegerType>
inline IntegerType lcm(IntegerType x, IntegerType y)
{
    // Note: _bmint is defined conditionally at the top of the file
    return _bmint::lcm<IntegerType>(x, y);
}
 
template <typename IntegerType>
inline IntegerType gcd(IntegerType x, IntegerType y)
{
    // Note: _bmint is defined conditionally at the top of the file
    return _bmint::gcd<IntegerType>(x, y);
}
 
//
// Note: This is equivalent to the Boost.Math version, but without the
// dependency.
//
// Returns +1 for positive arguments, -1 for negative arguments, and 0 if x is
// zero.
template <typename T>
inline constexpr int sign(T x)
{
    // Note: If T is unsigned, then this will compile with a warning. Should
    // we need that, expand the template logic.
    return (T(0) < x) - (x < T(0));
}
 
// Nyquist zone.
//
// Examples:
// - Just above the sampling rate:
//   wrap_frequency(250e6, 200e6) == 50e6
// - Just outside the Nyquist zone:
//   wrap_frequency(120e6, 200e6) == -80e6
// - Also works for negative frequencies:
//   wrap_frequency(-250e6, 200e6) == -50e6
inline double wrap_frequency(const double requested_freq, const double rate)
{
    double freq = std::fmod(requested_freq, rate);
    if (std::abs(freq) > rate / 2.0)
        freq -= uhd::math::sign(freq) * rate;
    return freq;
}
 
} // namespace math
} // namespace uhd
 
#include <uhd/utils/fp_compare_delta.ipp>
#include <uhd/utils/fp_compare_epsilon.ipp>