| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | //====================================================================================================================== | ||
| 2 | /* | ||
| 3 | POLYFLOAT - Extended precision floating points | ||
| 4 | Copyright : POLYFLOAT Contributors & Maintainers | ||
| 5 | SPDX-License-Identifier: BSL-1.0 | ||
| 6 | */ | ||
| 7 | //====================================================================================================================== | ||
| 8 | #pragma once | ||
| 9 | |||
| 10 | #include <polyfloat/details/callable.hpp> | ||
| 11 | #include <polyfloat/types/concepts.hpp> | ||
| 12 | #include <polyfloat/types/traits.hpp> | ||
| 13 | #include <type_traits> | ||
| 14 | #include <polyfloat/module/core/two_split.hpp> | ||
| 15 | #include <polyfloat/module/core/is_not_finite.hpp> | ||
| 16 | #include <polyfloat/module/core/if_else.hpp> | ||
| 17 | |||
| 18 | namespace plf | ||
| 19 | { | ||
| 20 | |||
| 21 | template<typename Options> | ||
| 22 | struct dekker_prod_t : eve::strict_tuple_callable<dekker_prod_t, Options, raw_option, pedantic_option> | ||
| 23 | { | ||
| 24 | template<concepts::polyfloat_like T0, concepts::polyfloat_like T1> | ||
| 25 | POLYFLOAT_ABI typename eve::zipped<plf::as_polyfloat_like_t<T0, T1>, plf::as_polyfloat_like_t<T0, T1>> constexpr | ||
| 26 | 13985 | operator()(T0 t0, T1 t1) const noexcept | |
| 27 | { | ||
| 28 | 13985 | return POLYFLOAT_CALL(t0, t1); | |
| 29 | } | ||
| 30 | |||
| 31 | 13985 | POLYFLOAT_CALLABLE_OBJECT(dekker_prod_t, dekker_prod_); | |
| 32 | }; | ||
| 33 | //================================================================================================ | ||
| 34 | //! @addtogroup core_accuracy | ||
| 35 | //! @{ | ||
| 36 | //! @var dekker_prod | ||
| 37 | //! @brief Computes the pair consisting of the | ||
| 38 | //! product and its resulting rounding error without using fma. | ||
| 39 | //! | ||
| 40 | //! @groupheader{Header file} | ||
| 41 | //! | ||
| 42 | //! @code | ||
| 43 | //! #include <eve/module/core.hpp> | ||
| 44 | //! @endcode | ||
| 45 | //! | ||
| 46 | //! @groupheader{Callable Signatures} | ||
| 47 | //! | ||
| 48 | //! @code | ||
| 49 | //! namespace eve | ||
| 50 | //! { | ||
| 51 | //! // Regular overload | ||
| 52 | //! constexpr auto dekker_prod( auto x, auto y) noexcept; // 1 | ||
| 53 | //! // Semantic options | ||
| 54 | //! constexpr auto dekker_prod[pedantic](auto x, auto y) noexcept; // 2 | ||
| 55 | //! } | ||
| 56 | //! @endcode | ||
| 57 | //! | ||
| 58 | //! **Parameters** | ||
| 59 | //! | ||
| 60 | //! * `x`, `y`: polyfloat arguments](@ref eve::floating_value) of same dimension. | ||
| 61 | //! | ||
| 62 | //! **Return value** | ||
| 63 | //! | ||
| 64 | //! Computes [elementwise](@ref glossary_elementwise) a pair of values `[a,e]` such that: | ||
| 65 | //! * `a` is `x+y` | ||
| 66 | //! * `e` is a value such that `a`\f$\oplus\f$`e` is equal to `x`\f$\oplus\f$`y`, | ||
| 67 | //! where \f$\oplus\f$ adds its dekker parameters with infinite precision. | ||
| 68 | //! | ||
| 69 | //! The algorithm depends on the overload: | ||
| 70 | //! | ||
| 71 | //! 1. Dekker algorithm. | ||
| 72 | //! 2. Handles overflow. | ||
| 73 | //! | ||
| 74 | //! @groupheader{External references} | ||
| 75 | //! * [On the Computation of Correctly-Rounded Sums](https://www.vinc17.net/research/papers/rr_ccrsums2.pdf) | ||
| 76 | //! | ||
| 77 | //! @groupheader{Example} | ||
| 78 | //! @godbolt_todo{doc/core/core/dekker_prod.cpp} | ||
| 79 | //================================================================================================ | ||
| 80 | inline constexpr auto dekker_prod = eve::functor<dekker_prod_t>; | ||
| 81 | //================================================================================================ | ||
| 82 | //! @} | ||
| 83 | //================================================================================================ | ||
| 84 | |||
| 85 | namespace _ | ||
| 86 | { | ||
| 87 | template<typename T0, typename T1, eve::callable_options O> | ||
| 88 | 13985 | constexpr auto dekker_prod_(POLYFLOAT_DELAY(), O const&, T0 aa, T1 bb) noexcept | |
| 89 | { | ||
| 90 | using r_t = plf::as_polyfloat_like_t<T0, T1>; | ||
| 91 | 14084 | auto cvt = [](auto a) { return plf::convert(a, eve::as_element<r_t>{}); }; | |
| 92 | 13985 | auto a = cvt(aa); | |
| 93 | 13985 | auto b = cvt(bb); | |
| 94 | 27442 | auto [ah, al] = two_split(a); | |
| 95 | 27442 | auto [bh, bl] = two_split(b); | |
| 96 | 13985 | auto abh = a * b; | |
| 97 | 13985 | auto abl = ah * bh - abh; | |
| 98 | 13985 | abl += ah * bl; | |
| 99 | 13985 | abl += al * bh; | |
| 100 | 13985 | abl += al * bl; | |
| 101 | 13985 | if constexpr (eve::platform::supports_invalids) abl = plf::if_else(plf::is_not_finite(abh), eve::zero, abl); | |
| 102 | 13985 | return eve::zip(abh, abl); | |
| 103 | } | ||
| 104 | } | ||
| 105 | } | ||
| 106 |