| 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/math/pow_abs.hpp> | ||
| 15 | #include <polyfloat/module/math/log_abs.hpp> | ||
| 16 | |||
| 17 | namespace plf | ||
| 18 | { | ||
| 19 | |||
| 20 | template<typename Options> | ||
| 21 | struct powm1_t : plf::elementwise_callable<powm1_t, eve::powm1_t, Options, raw_option, pedantic_option> | ||
| 22 | { | ||
| 23 | template<concepts::polyfloat_like Z1, concepts::polyfloat_like Z2> | ||
| 24 | 28 | POLYFLOAT_ABI constexpr as_polyfloat_like_t<Z1, Z2> operator()(Z1 z1, Z2 z2) const noexcept | |
| 25 | { | ||
| 26 | 28 | return POLYFLOAT_CALL(z1, z2); | |
| 27 | } | ||
| 28 | |||
| 29 | 18 | POLYFLOAT_CALLABLE_OBJECT(powm1_t, powm1_); | |
| 30 | }; | ||
| 31 | //====================================================================================================================== | ||
| 32 | //! @addtogroup math | ||
| 33 | //! @{ | ||
| 34 | //! @var powm1 | ||
| 35 | //! @brief return \f$x^y-1\f$. | ||
| 36 | //! | ||
| 37 | //! @groupheader{Header file} | ||
| 38 | //! | ||
| 39 | //! @code | ||
| 40 | //! #include <polyfloat/math.hpp> | ||
| 41 | //! @endcode | ||
| 42 | //! | ||
| 43 | //! @groupheader{Callable Signatures} | ||
| 44 | //! | ||
| 45 | //! @code | ||
| 46 | //! namespace polyfloat | ||
| 47 | //! { | ||
| 48 | //! // Regular overload | ||
| 49 | //! constexpr auto powm1(auto x, auto y) noexcept; // 1 | ||
| 50 | //! | ||
| 51 | //! // Lanes masking | ||
| 52 | //! constexpr auto powm1[conditional_expr c](auto x, auto y) noexcept; // 2 | ||
| 53 | //! constexpr auto powm1[logical_value auto m](auto x, auto y) noexcept; // 2 | ||
| 54 | //! | ||
| 55 | //! // Semantic options | ||
| 56 | //! constexpr auto powm1[raw]( auto x, auto y) noexcept; // 3 | ||
| 57 | //! } | ||
| 58 | //! @endcode | ||
| 59 | //! | ||
| 60 | //! **Parameters** | ||
| 61 | //! | ||
| 62 | //! * `z`: Value to process. | ||
| 63 | //! | ||
| 64 | //! **Return value** | ||
| 65 | //! | ||
| 66 | //! 1. Returns the [elementwise](@ref glossary_elementwise) power minus one, with good accuracy, | ||
| 67 | //! even when `y` is very small, or when `x` is close to 1. | ||
| 68 | //! 2. [The operation is performed conditionally](@ref conditional) | ||
| 69 | //! 3. faster but less accurate call. | ||
| 70 | //! | ||
| 71 | //! @groupheader{Example} | ||
| 72 | //! | ||
| 73 | //! @godbolt{doc/math/powm1.cpp} | ||
| 74 | //====================================================================================================================== | ||
| 75 | |||
| 76 | inline constexpr auto powm1 = eve::functor<powm1_t>; | ||
| 77 | //====================================================================================================================== | ||
| 78 | //! @} | ||
| 79 | //====================================================================================================================== | ||
| 80 | } | ||
| 81 | |||
| 82 | namespace plf::_ | ||
| 83 | { | ||
| 84 | |||
| 85 | template<typename T, typename U, eve::callable_options O> | ||
| 86 | 18 | constexpr auto powm1_(POLYFLOAT_DELAY(), O const& o, T a, U b) noexcept | |
| 87 | { | ||
| 88 | using r_t = as_polyfloat_like_t<T, U>; | ||
| 89 | if constexpr (O::contains(raw)) | ||
| 90 | { | ||
| 91 | return plf::dec(plf::pow[o](a, b)); | ||
| 92 | } | ||
| 93 | else | ||
| 94 | { | ||
| 95 | using e_t = eve::element_type_t<r_t>; | ||
| 96 | 18 | auto cvt = [](auto a) { return plf::convert(a, eve::as<e_t>()); }; | |
| 97 | 18 | auto x = cvt(a); | |
| 98 | 18 | auto y = cvt(b); | |
| 99 | 18 | auto r = plf::dec(plf::pow(x, y)); | |
| 100 | 18 | auto test = (plf::abs(y * plf::dec(x)) < r_t(0.5) || (plf::abs(y) < r_t(0.2))); | |
| 101 |
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18 | if (eve::any(test)) |
| 102 | { | ||
| 103 | // We don't have any good/quick approximation for log(x) * y | ||
| 104 | // so just try it and see: | ||
| 105 | 10 | auto l = y * plf::log_abs(x); | |
| 106 | 10 | auto tmp0 = plf::expm1(l); | |
| 107 | 10 | auto tmp1 = plf::minus[plf::is_ltz(x) && plf::is_odd(x)](tmp0); | |
| 108 | 10 | return plf::if_else(l < T(0.5), tmp1, r); | |
| 109 | } | ||
| 110 | 8 | else return r; | |
| 111 | } | ||
| 112 | } | ||
| 113 | } | ||
| 114 |