constants.hpp

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//
// Copyright (c) 2021-2023, University of Colorado Denver. All rights reserved.
//
// This file is part of <T>LAPACK.
// <T>LAPACK is free software: you can redistribute it and/or modify it under
// the terms of the BSD 3-Clause license. See the accompanying LICENSE file.
 
#ifndef TLAPACK_CONSTANTS_HH
#define TLAPACK_CONSTANTS_HH
 
#include <limits>
#include <type_traits>
 
#include "tlapack/base/utils.hpp"
 
namespace tlapack {
 
// -----------------------------------------------------------------------------
// Macros to compute scaling constants
 
template <TLAPACK_REAL real_t>
constexpr real_t ulp() noexcept
{
    return std::numeric_limits<real_t>::epsilon();
}
 
template <TLAPACK_REAL real_t>
constexpr real_t uroundoff() noexcept
{
    return ulp<real_t>() * std::numeric_limits<real_t>::round_error();
}
 
template <typename real_t>
int digits() noexcept
{
    return std::numeric_limits<real_t>::digits;
}
 
template <TLAPACK_REAL real_t>
constexpr real_t safe_min() noexcept
{
    const int fradix = std::numeric_limits<real_t>::radix;
    const int expm = std::numeric_limits<real_t>::min_exponent;
    const int expM = std::numeric_limits<real_t>::max_exponent;
 
    return pow(fradix, real_t(max(expm - 1, 1 - expM)));
}
 
template <TLAPACK_REAL real_t>
constexpr real_t safe_max() noexcept
{
    return real_t(1) / safe_min<real_t>();
}
 
template <TLAPACK_REAL real_t>
constexpr real_t blue_min() noexcept
{
    const real_t half(0.5);
    const int fradix = std::numeric_limits<real_t>::radix;
    const int expm = std::numeric_limits<real_t>::min_exponent;
 
    return pow(fradix, ceil(half * real_t(expm - 1)));
}
 
template <TLAPACK_REAL real_t>
constexpr real_t blue_max() noexcept
{
    const real_t half(0.5);
    const int fradix = std::numeric_limits<real_t>::radix;
    const int expM = std::numeric_limits<real_t>::max_exponent;
    const int t = digits<real_t>();
 
    return pow(fradix, floor(half * real_t(expM - t + 1)));
}
 
template <TLAPACK_REAL real_t>
constexpr real_t blue_scalingMin() noexcept
{
    const real_t half(0.5);
    const int fradix = std::numeric_limits<real_t>::radix;
    const int expm = std::numeric_limits<real_t>::min_exponent;
    const int t = digits<real_t>();
 
    return pow(fradix, -floor(half * real_t(expm - t)));
}
 
template <TLAPACK_REAL real_t>
constexpr real_t blue_scalingMax() noexcept
{
    const real_t half(0.5);
    const int fradix = std::numeric_limits<real_t>::radix;
    const int expM = std::numeric_limits<real_t>::max_exponent;
    const int t = digits<real_t>();
 
    return pow(fradix, -ceil(half * real_t(expM + t - 1)));
}
 
}  // namespace tlapack
 
#endif  // TLAPACK_CONSTANTS_HH