normal_distribution.hpp

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//============================================================================
// MCKL/include/mckl/random/normal_distribution.hpp
//----------------------------------------------------------------------------
// MCKL: Monte Carlo Kernel Library
//----------------------------------------------------------------------------
// Copyright (c) 2013-2018, Yan Zhou
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
//   Redistributions of source code must retain the above copyright notice,
//   this list of conditions and the following disclaimer.
//
//   Redistributions in binary form must reproduce the above copyright notice,
//   this list of conditions and the following disclaimer in the documentation
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//============================================================================

#ifndef MCKL_RANDOM_NORMAL_DISTRIBUTION_HPP
#define MCKL_RANDOM_NORMAL_DISTRIBUTION_HPP

#include <mckl/random/internal/common.hpp>
#include <mckl/internal/cblas.hpp>
#include <mckl/random/u01_distribution.hpp>
#include <mckl/random/uniform_real_distribution.hpp>

namespace mckl {

namespace internal {

template <typename RealType>
inline bool normal_distribution_check_param(RealType, RealType stddev)
{
    return stddev > 0;
}

template <std::size_t K, typename RealType, typename RNGType>
inline void normal_distribution_impl(
    RNGType &rng, std::size_t n, RealType *r, RealType mean, RealType stddev)
{
    alignas(MCKL_ALIGNMENT) std::array<RealType, K / 2> s;
    const std::size_t nu = n / 2;
    RealType *const u1 = r;
    RealType *const u2 = r + nu;
    u01_oc_distribution(rng, n, r);
    log(nu, u1, s.data());
    mul(nu, static_cast<RealType>(-2), s.data(), s.data());
    sqrt(nu, s.data(), s.data());
    mul(nu, const_pi_2<RealType>(), u2, u2);
    sincos(nu, u2, u1, u2);
    MCKL_PUSH_CLANG_WARNING("-Wfloat-equal")
    MCKL_PUSH_INTEL_WARNING(1572) // floating-point comparison
    if (stddev != 1) {
        mul(nu, stddev, s.data(), s.data());
    }
    if (mean != 0) {
        muladd(nu, s.data(), u1, mean, u1);
        muladd(nu, s.data(), u2, mean, u2);
    } else {
        mul(nu, s.data(), u1, u1);
        mul(nu, s.data(), u2, u2);
    }
    MCKL_POP_CLANG_WARNING
    MCKL_POP_INTEL_WARNING
}

} // namespace internal

template <typename RealType, typename RNGType>
inline void normal_distribution(
    RNGType &rng, std::size_t n, RealType *r, RealType mean, RealType stddev)
{
    const std::size_t k = BufferSize<RealType>::value;
    const std::size_t m = n / k;
    const std::size_t l = n % k;
    for (std::size_t i = 0; i != m; ++i, r += k) {
        internal::normal_distribution_impl<k>(rng, k, r, mean, stddev);
    }
    internal::normal_distribution_impl<k>(rng, l, r, mean, stddev);
    if (n % 2 != 0) {
        U01OCDistribution<RealType> u01;
        RealType u = u01(rng);
        RealType v = u01(rng);
        r[l - 1] = mean +
            stddev * std::sqrt(-2 * std::log(u)) *
                std::cos(const_pi_2<RealType>() * v);
    }
}

template <typename RealType, typename RNGType>
inline void normal_distribution(RNGType &rng, std::size_t n, RealType *r,
    const typename NormalDistribution<RealType>::param_type &param)
{
    normal_distribution(rng, n, r, param.mean(), param.stddev());
}

MCKL_PUSH_CLANG_WARNING("-Wpadded")
template <typename RealType>
class NormalDistribution
{
    MCKL_DEFINE_RANDOM_DISTRIBUTION_ASSERT_REAL_TYPE(Normal)
    MCKL_DEFINE_RANDOM_DISTRIBUTION_2(
        Normal, normal, RealType, result_type, mean, 0, result_type, stddev, 1)
    MCKL_DEFINE_RANDOM_DISTRIBUTION_MEMBER_2(result_type, v_, bool, saved_)

  public:
    result_type min() const
    {
        return std::numeric_limits<result_type>::lowest();
    }

    result_type max() const { return std::numeric_limits<result_type>::max(); }

    void reset()
    {
        v_ = 0;
        saved_ = false;
    }

  private:
    template <typename RNGType>
    result_type generate(RNGType &rng, const param_type &param)
    {
        result_type z = 0;
        if (saved_) {
            z = v_;
            saved_ = false;
        } else {
            U01OCDistribution<RealType> u01;
            result_type u1 = std::sqrt(-2 * std::log(u01(rng)));
            result_type u2 = const_pi_2<result_type>() * u01(rng);
            z = u1 * std::cos(u2);
            v_ = u1 * std::sin(u2);
            saved_ = true;
        }

        return param.mean() + param.stddev() * z;
    }
}; // class NormalDistribution
MCKL_POP_CLANG_WARNING

MCKL_DEFINE_RANDOM_DISTRIBUTION_RAND(Normal, RealType)

} // namespace mckl

#endif // MCKL_RANDOM_NORMAL_DISTRIBUTION_HPP