| 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 | |||
| 15 | namespace plf | ||
| 16 | { | ||
| 17 | |||
| 18 | template<typename Options> | ||
| 19 | struct exp_t : plf::elementwise_callable<exp_t, eve::exp_t, Options, raw_option, pedantic_option> | ||
| 20 | { | ||
| 21 | 6598 | template<concepts::polyfloat_like Z> POLYFLOAT_ABI constexpr Z operator()(Z z) const noexcept | |
| 22 | { | ||
| 23 | 6598 | return POLYFLOAT_CALL(z); | |
| 24 | } | ||
| 25 | |||
| 26 | 6572 | POLYFLOAT_CALLABLE_OBJECT(exp_t, exp_); | |
| 27 | }; | ||
| 28 | //====================================================================================================================== | ||
| 29 | //! @addtogroup math | ||
| 30 | //! @{ | ||
| 31 | //! @var exp | ||
| 32 | //! @brief return the exponential value. | ||
| 33 | //! | ||
| 34 | //! @groupheader{Header file} | ||
| 35 | //! | ||
| 36 | //! @code | ||
| 37 | //! #include <polyfloat/core.hpp> | ||
| 38 | //! @endcode | ||
| 39 | //! | ||
| 40 | //! @groupheader{Callable Signatures} | ||
| 41 | //! | ||
| 42 | //! @code | ||
| 43 | //! namespace polyfloat | ||
| 44 | //! { | ||
| 45 | //! template<polyfloat::concepts::polyfloat_like T> constexpr auto exp(T z) noexcept; | ||
| 46 | //! } | ||
| 47 | //! @endcode | ||
| 48 | //! | ||
| 49 | //! **Parameters** | ||
| 50 | //! | ||
| 51 | //! * `z`: Value to process. | ||
| 52 | //! | ||
| 53 | //! **Return value** | ||
| 54 | //! | ||
| 55 | //! Returns the exponential of z. | ||
| 56 | //! | ||
| 57 | //! @groupheader{Example} | ||
| 58 | //! | ||
| 59 | //! @godbolt{doc/math/exp.cpp} | ||
| 60 | //====================================================================================================================== | ||
| 61 | |||
| 62 | inline constexpr auto exp = eve::functor<exp_t>; | ||
| 63 | //====================================================================================================================== | ||
| 64 | //! @} | ||
| 65 | //====================================================================================================================== | ||
| 66 | } | ||
| 67 | |||
| 68 | namespace plf::_ | ||
| 69 | { | ||
| 70 | |||
| 71 | 6572 | template<typename T, eve::callable_options O> constexpr auto exp_(POLYFLOAT_DELAY(), O const&, T xx) noexcept | |
| 72 | { | ||
| 73 | using u_t = eve::underlying_type_t<T>; | ||
| 74 | 6572 | auto negative = plf::is_ltz(xx); | |
| 75 | 6572 | auto nan = plf::is_nan(xx); | |
| 76 | 6572 | auto out_of_range = plf::is_greater(plf::abs(xx), plf::maxlog(eve::as<u_t>())); | |
| 77 | 6572 | xx = plf::if_else(out_of_range, inf, xx); | |
| 78 | 6572 | auto x = plf::if_else(out_of_range || nan, zero, xx); | |
| 79 | |||
| 80 | 6572 | constexpr int shift = dimension_v<T> == 2 ? -6 : -16; | |
| 81 | 6572 | constexpr u_t p = 1ul << (-shift); | |
| 82 | 6572 | auto e = plf::euler(eve::as<eve::element_type_t<T>>()); | |
| 83 | 6572 | auto n = plf::hi(nearest(x)); | |
| 84 | 6572 | auto xf = x - n; | |
| 85 | 6572 | xf = plf::ldexp(xf, shift); | |
| 86 | // PadeApproximant[Exp[x], {x, 0, {10,10}}] | ||
| 87 | auto nn = | ||
| 88 | 26288 | (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf + 110) + 5940) + 205920) + 5045040) + 90810720) + | |
| 89 | 6572 | 1210809600) + | |
| 90 | 6572 | 11762150400) + | |
| 91 | 6572 | 79394515200) + | |
| 92 | 6572 | 335221286400) + | |
| 93 | 6572 | 670442572800); | |
| 94 | auto dd = | ||
| 95 | 26288 | (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf * (xf - 110) + 5940) - 205920) + 5045040) - 90810720) + | |
| 96 | 6572 | 1210809600) - | |
| 97 | 6572 | 11762150400) + | |
| 98 | 6572 | 79394515200) - | |
| 99 | 6572 | 335221286400) + | |
| 100 | 6572 | 670442572800); | |
| 101 | 6572 | auto nod = if_else(nn == dd, eve::one, nn / dd); | |
| 102 | 6572 | auto r = pown(e, n) * pown(nod, p); | |
| 103 | 6572 | r = if_else(out_of_range, if_else(negative, eve::zero, plf::inf(eve::as<T>())), r); | |
| 104 | 6572 | r = if_else(nan, xx, r); | |
| 105 | |||
| 106 | 6572 | return r; | |
| 107 | } | ||
| 108 | } | ||
| 109 |