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// Math overloads for simd -*- C++ -*- // Copyright (C) 2020-2021 Free Software Foundation, Inc. // // This file is part of the GNU ISO C++ Library. This library is free // software; you can redistribute it and/or modify it under the // terms of the GNU General Public License as published by the // Free Software Foundation; either version 3, or (at your option) // any later version. // This library is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // Under Section 7 of GPL version 3, you are granted additional // permissions described in the GCC Runtime Library Exception, version // 3.1, as published by the Free Software Foundation. // You should have received a copy of the GNU General Public License and // a copy of the GCC Runtime Library Exception along with this program; // see the files COPYING3 and COPYING.RUNTIME respectively. If not, see // <http://www.gnu.org/licenses/>. #ifndef _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_ #define _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_ #if __cplusplus >= 201703L #include <utility> #include <iomanip> _GLIBCXX_SIMD_BEGIN_NAMESPACE template <typename _Tp, typename _V> using _Samesize = fixed_size_simd<_Tp, _V::size()>; // _Math_return_type {{{ template <typename _DoubleR, typename _Tp, typename _Abi> struct _Math_return_type; template <typename _DoubleR, typename _Tp, typename _Abi> using _Math_return_type_t = typename _Math_return_type<_DoubleR, _Tp, _Abi>::type; template <typename _Tp, typename _Abi> struct _Math_return_type<double, _Tp, _Abi> { using type = simd<_Tp, _Abi>; }; template <typename _Tp, typename _Abi> struct _Math_return_type<bool, _Tp, _Abi> { using type = simd_mask<_Tp, _Abi>; }; template <typename _DoubleR, typename _Tp, typename _Abi> struct _Math_return_type { using type = fixed_size_simd<_DoubleR, simd_size_v<_Tp, _Abi>>; }; //}}} // _GLIBCXX_SIMD_MATH_CALL_ {{{ #define _GLIBCXX_SIMD_MATH_CALL_(__name) \ template <typename _Tp, typename _Abi, typename..., \ typename _R = _Math_return_type_t< \ decltype(std::__name(declval<double>())), _Tp, _Abi>> \ enable_if_t<is_floating_point_v<_Tp>, _R> \ __name(simd<_Tp, _Abi> __x) \ { return {__private_init, _Abi::_SimdImpl::_S_##__name(__data(__x))}; } // }}} //_Extra_argument_type{{{ template <typename _Up, typename _Tp, typename _Abi> struct _Extra_argument_type; template <typename _Tp, typename _Abi> struct _Extra_argument_type<_Tp*, _Tp, _Abi> { using type = simd<_Tp, _Abi>*; static constexpr double* declval(); static constexpr bool __needs_temporary_scalar = true; _GLIBCXX_SIMD_INTRINSIC static constexpr auto _S_data(type __x) { return &__data(*__x); } }; template <typename _Up, typename _Tp, typename _Abi> struct _Extra_argument_type<_Up*, _Tp, _Abi> { static_assert(is_integral_v<_Up>); using type = fixed_size_simd<_Up, simd_size_v<_Tp, _Abi>>*; static constexpr _Up* declval(); static constexpr bool __needs_temporary_scalar = true; _GLIBCXX_SIMD_INTRINSIC static constexpr auto _S_data(type __x) { return &__data(*__x); } }; template <typename _Tp, typename _Abi> struct _Extra_argument_type<_Tp, _Tp, _Abi> { using type = simd<_Tp, _Abi>; static constexpr double declval(); static constexpr bool __needs_temporary_scalar = false; _GLIBCXX_SIMD_INTRINSIC static constexpr decltype(auto) _S_data(const type& __x) { return __data(__x); } }; template <typename _Up, typename _Tp, typename _Abi> struct _Extra_argument_type { static_assert(is_integral_v<_Up>); using type = fixed_size_simd<_Up, simd_size_v<_Tp, _Abi>>; static constexpr _Up declval(); static constexpr bool __needs_temporary_scalar = false; _GLIBCXX_SIMD_INTRINSIC static constexpr decltype(auto) _S_data(const type& __x) { return __data(__x); } }; //}}} // _GLIBCXX_SIMD_MATH_CALL2_ {{{ #define _GLIBCXX_SIMD_MATH_CALL2_(__name, arg2_) \ template < \ typename _Tp, typename _Abi, typename..., \ typename _Arg2 = _Extra_argument_type<arg2_, _Tp, _Abi>, \ typename _R = _Math_return_type_t< \ decltype(std::__name(declval<double>(), _Arg2::declval())), _Tp, _Abi>> \ enable_if_t<is_floating_point_v<_Tp>, _R> \ __name(const simd<_Tp, _Abi>& __x, const typename _Arg2::type& __y) \ { \ return {__private_init, \ _Abi::_SimdImpl::_S_##__name(__data(__x), _Arg2::_S_data(__y))}; \ } \ template <typename _Up, typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC _Math_return_type_t< \ decltype(std::__name( \ declval<double>(), \ declval<enable_if_t< \ conjunction_v< \ is_same<arg2_, _Tp>, \ negation<is_same<__remove_cvref_t<_Up>, simd<_Tp, _Abi>>>, \ is_convertible<_Up, simd<_Tp, _Abi>>, is_floating_point<_Tp>>, \ double>>())), \ _Tp, _Abi> \ __name(_Up&& __xx, const simd<_Tp, _Abi>& __yy) \ { return __name(simd<_Tp, _Abi>(static_cast<_Up&&>(__xx)), __yy); } // }}} // _GLIBCXX_SIMD_MATH_CALL3_ {{{ #define _GLIBCXX_SIMD_MATH_CALL3_(__name, arg2_, arg3_) \ template <typename _Tp, typename _Abi, typename..., \ typename _Arg2 = _Extra_argument_type<arg2_, _Tp, _Abi>, \ typename _Arg3 = _Extra_argument_type<arg3_, _Tp, _Abi>, \ typename _R = _Math_return_type_t< \ decltype(std::__name(declval<double>(), _Arg2::declval(), \ _Arg3::declval())), \ _Tp, _Abi>> \ enable_if_t<is_floating_point_v<_Tp>, _R> \ __name(const simd<_Tp, _Abi>& __x, const typename _Arg2::type& __y, \ const typename _Arg3::type& __z) \ { \ return {__private_init, \ _Abi::_SimdImpl::_S_##__name(__data(__x), _Arg2::_S_data(__y), \ _Arg3::_S_data(__z))}; \ } \ template < \ typename _T0, typename _T1, typename _T2, typename..., \ typename _U0 = __remove_cvref_t<_T0>, \ typename _U1 = __remove_cvref_t<_T1>, \ typename _U2 = __remove_cvref_t<_T2>, \ typename _Simd = conditional_t<is_simd_v<_U1>, _U1, _U2>, \ typename = enable_if_t<conjunction_v< \ is_simd<_Simd>, is_convertible<_T0&&, _Simd>, \ is_convertible<_T1&&, _Simd>, is_convertible<_T2&&, _Simd>, \ negation<conjunction< \ is_simd<_U0>, is_floating_point<__value_type_or_identity_t<_U0>>>>>>> \ _GLIBCXX_SIMD_INTRINSIC decltype(__name(declval<const _Simd&>(), \ declval<const _Simd&>(), \ declval<const _Simd&>())) \ __name(_T0&& __xx, _T1&& __yy, _T2&& __zz) \ { \ return __name(_Simd(static_cast<_T0&&>(__xx)), \ _Simd(static_cast<_T1&&>(__yy)), \ _Simd(static_cast<_T2&&>(__zz))); \ } // }}} // __cosSeries {{{ template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE static simd<float, _Abi> __cosSeries(const simd<float, _Abi>& __x) { const simd<float, _Abi> __x2 = __x * __x; simd<float, _Abi> __y; __y = 0x1.ap-16f; // 1/8! __y = __y * __x2 - 0x1.6c1p-10f; // -1/6! __y = __y * __x2 + 0x1.555556p-5f; // 1/4! return __y * (__x2 * __x2) - .5f * __x2 + 1.f; } template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE static simd<double, _Abi> __cosSeries(const simd<double, _Abi>& __x) { const simd<double, _Abi> __x2 = __x * __x; simd<double, _Abi> __y; __y = 0x1.AC00000000000p-45; // 1/16! __y = __y * __x2 - 0x1.9394000000000p-37; // -1/14! __y = __y * __x2 + 0x1.1EED8C0000000p-29; // 1/12! __y = __y * __x2 - 0x1.27E4FB7400000p-22; // -1/10! __y = __y * __x2 + 0x1.A01A01A018000p-16; // 1/8! __y = __y * __x2 - 0x1.6C16C16C16C00p-10; // -1/6! __y = __y * __x2 + 0x1.5555555555554p-5; // 1/4! return (__y * __x2 - .5f) * __x2 + 1.f; } // }}} // __sinSeries {{{ template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE static simd<float, _Abi> __sinSeries(const simd<float, _Abi>& __x) { const simd<float, _Abi> __x2 = __x * __x; simd<float, _Abi> __y; __y = -0x1.9CC000p-13f; // -1/7! __y = __y * __x2 + 0x1.111100p-7f; // 1/5! __y = __y * __x2 - 0x1.555556p-3f; // -1/3! return __y * (__x2 * __x) + __x; } template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE static simd<double, _Abi> __sinSeries(const simd<double, _Abi>& __x) { // __x = [0, 0.7854 = pi/4] // __x² = [0, 0.6169 = pi²/8] const simd<double, _Abi> __x2 = __x * __x; simd<double, _Abi> __y; __y = -0x1.ACF0000000000p-41; // -1/15! __y = __y * __x2 + 0x1.6124400000000p-33; // 1/13! __y = __y * __x2 - 0x1.AE64567000000p-26; // -1/11! __y = __y * __x2 + 0x1.71DE3A5540000p-19; // 1/9! __y = __y * __x2 - 0x1.A01A01A01A000p-13; // -1/7! __y = __y * __x2 + 0x1.1111111111110p-7; // 1/5! __y = __y * __x2 - 0x1.5555555555555p-3; // -1/3! return __y * (__x2 * __x) + __x; } // }}} // __zero_low_bits {{{ template <int _Bits, typename _Tp, typename _Abi> _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> __zero_low_bits(simd<_Tp, _Abi> __x) { const simd<_Tp, _Abi> __bitmask = __bit_cast<_Tp>(~make_unsigned_t<__int_for_sizeof_t<_Tp>>() << _Bits); return {__private_init, _Abi::_SimdImpl::_S_bit_and(__data(__x), __data(__bitmask))}; } // }}} // __fold_input {{{ /**@internal * Fold @p x into [-¼π, ¼π] and remember the quadrant it came from: * quadrant 0: [-¼π, ¼π] * quadrant 1: [ ¼π, ¾π] * quadrant 2: [ ¾π, 1¼π] * quadrant 3: [1¼π, 1¾π] * * The algorithm determines `y` as the multiple `x - y * ¼π = [-¼π, ¼π]`. Using * a bitmask, `y` is reduced to `quadrant`. `y` can be calculated as * ``` * y = trunc(x / ¼π); * y += fmod(y, 2); * ``` * This can be simplified by moving the (implicit) division by 2 into the * truncation expression. The `+= fmod` effect can the be achieved by using * rounding instead of truncation: `y = round(x / ½π) * 2`. If precision allows, * `2/π * x` is better (faster). */ template <typename _Tp, typename _Abi> struct _Folded { simd<_Tp, _Abi> _M_x; rebind_simd_t<int, simd<_Tp, _Abi>> _M_quadrant; }; namespace __math_float { inline constexpr float __pi_over_4 = 0x1.921FB6p-1f; // π/4 inline constexpr float __2_over_pi = 0x1.45F306p-1f; // 2/π inline constexpr float __pi_2_5bits0 = 0x1.921fc0p0f; // π/2, 5 0-bits (least significant) inline constexpr float __pi_2_5bits0_rem = -0x1.5777a6p-21f; // π/2 - __pi_2_5bits0 } // namespace __math_float namespace __math_double { inline constexpr double __pi_over_4 = 0x1.921fb54442d18p-1; // π/4 inline constexpr double __2_over_pi = 0x1.45F306DC9C883p-1; // 2/π inline constexpr double __pi_2 = 0x1.921fb54442d18p0; // π/2 } // namespace __math_double template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE _Folded<float, _Abi> __fold_input(const simd<float, _Abi>& __x) { using _V = simd<float, _Abi>; using _IV = rebind_simd_t<int, _V>; using namespace __math_float; _Folded<float, _Abi> __r; __r._M_x = abs(__x); #if 0 // zero most mantissa bits: constexpr float __1_over_pi = 0x1.45F306p-2f; // 1/π const auto __y = (__r._M_x * __1_over_pi + 0x1.8p23f) - 0x1.8p23f; // split π into 4 parts, the first three with 13 trailing zeros (to make the // following multiplications precise): constexpr float __pi0 = 0x1.920000p1f; constexpr float __pi1 = 0x1.fb4000p-11f; constexpr float __pi2 = 0x1.444000p-23f; constexpr float __pi3 = 0x1.68c234p-38f; __r._M_x - __y*__pi0 - __y*__pi1 - __y*__pi2 - __y*__pi3 #else if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__r._M_x < __pi_over_4))) __r._M_quadrant = 0; else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__r._M_x < 6 * __pi_over_4))) { const _V __y = nearbyint(__r._M_x * __2_over_pi); __r._M_quadrant = static_simd_cast<_IV>(__y) & 3; // __y mod 4 __r._M_x -= __y * __pi_2_5bits0; __r._M_x -= __y * __pi_2_5bits0_rem; } else { using __math_double::__2_over_pi; using __math_double::__pi_2; using _VD = rebind_simd_t<double, _V>; _VD __xd = static_simd_cast<_VD>(__r._M_x); _VD __y = nearbyint(__xd * __2_over_pi); __r._M_quadrant = static_simd_cast<_IV>(__y) & 3; // = __y mod 4 __r._M_x = static_simd_cast<_V>(__xd - __y * __pi_2); } #endif return __r; } template <typename _Abi> _GLIBCXX_SIMD_ALWAYS_INLINE _Folded<double, _Abi> __fold_input(const simd<double, _Abi>& __x) { using _V = simd<double, _Abi>; using _IV = rebind_simd_t<int, _V>; using namespace __math_double; _Folded<double, _Abi> __r; __r._M_x = abs(__x); if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__r._M_x < __pi_over_4))) { __r._M_quadrant = 0; return __r; } const _V __y = nearbyint(__r._M_x / (2 * __pi_over_4)); __r._M_quadrant = static_simd_cast<_IV>(__y) & 3; if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__r._M_x < 1025 * __pi_over_4))) { // x - y * pi/2, y uses no more than 11 mantissa bits __r._M_x -= __y * 0x1.921FB54443000p0; __r._M_x -= __y * -0x1.73DCB3B39A000p-43; __r._M_x -= __y * 0x1.45C06E0E68948p-86; } else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__y <= 0x1.0p30))) { // x - y * pi/2, y uses no more than 29 mantissa bits __r._M_x -= __y * 0x1.921FB40000000p0; __r._M_x -= __y * 0x1.4442D00000000p-24; __r._M_x -= __y * 0x1.8469898CC5170p-48; } else { // x - y * pi/2, y may require all mantissa bits const _V __y_hi = __zero_low_bits<26>(__y); const _V __y_lo = __y - __y_hi; const auto __pi_2_1 = 0x1.921FB50000000p0; const auto __pi_2_2 = 0x1.110B460000000p-26; const auto __pi_2_3 = 0x1.1A62630000000p-54; const auto __pi_2_4 = 0x1.8A2E03707344Ap-81; __r._M_x = __r._M_x - __y_hi * __pi_2_1 - max(__y_hi * __pi_2_2, __y_lo * __pi_2_1) - min(__y_hi * __pi_2_2, __y_lo * __pi_2_1) - max(__y_hi * __pi_2_3, __y_lo * __pi_2_2) - min(__y_hi * __pi_2_3, __y_lo * __pi_2_2) - max(__y * __pi_2_4, __y_lo * __pi_2_3) - min(__y * __pi_2_4, __y_lo * __pi_2_3); } return __r; } // }}} // __extract_exponent_as_int {{{ template <typename _Tp, typename _Abi> rebind_simd_t<int, simd<_Tp, _Abi>> __extract_exponent_as_int(const simd<_Tp, _Abi>& __v) { using _Vp = simd<_Tp, _Abi>; using _Up = make_unsigned_t<__int_for_sizeof_t<_Tp>>; using namespace std::experimental::__float_bitwise_operators; const _Vp __exponent_mask = __infinity_v<_Tp>; // 0x7f800000 or 0x7ff0000000000000 return static_simd_cast<rebind_simd_t<int, _Vp>>( __bit_cast<rebind_simd_t<_Up, _Vp>>(__v & __exponent_mask) >> (__digits_v<_Tp> - 1)); } // }}} // __impl_or_fallback {{{ template <typename ImplFun, typename FallbackFun, typename... _Args> _GLIBCXX_SIMD_INTRINSIC auto __impl_or_fallback_dispatch(int, ImplFun&& __impl_fun, FallbackFun&&, _Args&&... __args) -> decltype(__impl_fun(static_cast<_Args&&>(__args)...)) { return __impl_fun(static_cast<_Args&&>(__args)...); } template <typename ImplFun, typename FallbackFun, typename... _Args> inline auto __impl_or_fallback_dispatch(float, ImplFun&&, FallbackFun&& __fallback_fun, _Args&&... __args) -> decltype(__fallback_fun(static_cast<_Args&&>(__args)...)) { return __fallback_fun(static_cast<_Args&&>(__args)...); } template <typename... _Args> _GLIBCXX_SIMD_INTRINSIC auto __impl_or_fallback(_Args&&... __args) { return __impl_or_fallback_dispatch(int(), static_cast<_Args&&>(__args)...); } //}}} // trigonometric functions {{{ _GLIBCXX_SIMD_MATH_CALL_(acos) _GLIBCXX_SIMD_MATH_CALL_(asin) _GLIBCXX_SIMD_MATH_CALL_(atan) _GLIBCXX_SIMD_MATH_CALL2_(atan2, _Tp) /* * algorithm for sine and cosine: * * The result can be calculated with sine or cosine depending on the π/4 section * the input is in. sine ≈ __x + __x³ cosine ≈ 1 - __x² * * sine: * Map -__x to __x and invert the output * Extend precision of __x - n * π/4 by calculating * ((__x - n * p1) - n * p2) - n * p3 (p1 + p2 + p3 = π/4) * * Calculate Taylor series with tuned coefficients. * Fix sign. */ // cos{{{ template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> cos(const simd<_Tp, _Abi>& __x) { using _V = simd<_Tp, _Abi>; if constexpr (__is_scalar_abi<_Abi>() || __is_fixed_size_abi_v<_Abi>) return {__private_init, _Abi::_SimdImpl::_S_cos(__data(__x))}; else { if constexpr (is_same_v<_Tp, float>) if (_GLIBCXX_SIMD_IS_UNLIKELY(any_of(abs(__x) >= 393382))) return static_simd_cast<_V>( cos(static_simd_cast<rebind_simd_t<double, _V>>(__x))); const auto __f = __fold_input(__x); // quadrant | effect // 0 | cosSeries, + // 1 | sinSeries, - // 2 | cosSeries, - // 3 | sinSeries, + using namespace std::experimental::__float_bitwise_operators; const _V __sign_flip = _V(-0.f) & static_simd_cast<_V>((1 + __f._M_quadrant) << 30); const auto __need_cos = (__f._M_quadrant & 1) == 0; if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__need_cos))) return __sign_flip ^ __cosSeries(__f._M_x); else if (_GLIBCXX_SIMD_IS_UNLIKELY(none_of(__need_cos))) return __sign_flip ^ __sinSeries(__f._M_x); else // some_of(__need_cos) { _V __r = __sinSeries(__f._M_x); where(__need_cos.__cvt(), __r) = __cosSeries(__f._M_x); return __r ^ __sign_flip; } } } template <typename _Tp> _GLIBCXX_SIMD_ALWAYS_INLINE enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, simd_abi::scalar>> cos(simd<_Tp, simd_abi::scalar> __x) { return std::cos(__data(__x)); } //}}} // sin{{{ template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> sin(const simd<_Tp, _Abi>& __x) { using _V = simd<_Tp, _Abi>; if constexpr (__is_scalar_abi<_Abi>() || __is_fixed_size_abi_v<_Abi>) return {__private_init, _Abi::_SimdImpl::_S_sin(__data(__x))}; else { if constexpr (is_same_v<_Tp, float>) if (_GLIBCXX_SIMD_IS_UNLIKELY(any_of(abs(__x) >= 527449))) return static_simd_cast<_V>( sin(static_simd_cast<rebind_simd_t<double, _V>>(__x))); const auto __f = __fold_input(__x); // quadrant | effect // 0 | sinSeries // 1 | cosSeries // 2 | sinSeries, sign flip // 3 | cosSeries, sign flip using namespace std::experimental::__float_bitwise_operators; const auto __sign_flip = (__x ^ static_simd_cast<_V>(1 - __f._M_quadrant)) & _V(_Tp(-0.)); const auto __need_sin = (__f._M_quadrant & 1) == 0; if (_GLIBCXX_SIMD_IS_UNLIKELY(all_of(__need_sin))) return __sign_flip ^ __sinSeries(__f._M_x); else if (_GLIBCXX_SIMD_IS_UNLIKELY(none_of(__need_sin))) return __sign_flip ^ __cosSeries(__f._M_x); else // some_of(__need_sin) { _V __r = __cosSeries(__f._M_x); where(__need_sin.__cvt(), __r) = __sinSeries(__f._M_x); return __sign_flip ^ __r; } } } template <typename _Tp> _GLIBCXX_SIMD_ALWAYS_INLINE enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, simd_abi::scalar>> sin(simd<_Tp, simd_abi::scalar> __x) { return std::sin(__data(__x)); } //}}} _GLIBCXX_SIMD_MATH_CALL_(tan) _GLIBCXX_SIMD_MATH_CALL_(acosh) _GLIBCXX_SIMD_MATH_CALL_(asinh) _GLIBCXX_SIMD_MATH_CALL_(atanh) _GLIBCXX_SIMD_MATH_CALL_(cosh) _GLIBCXX_SIMD_MATH_CALL_(sinh) _GLIBCXX_SIMD_MATH_CALL_(tanh) // }}} // exponential functions {{{ _GLIBCXX_SIMD_MATH_CALL_(exp) _GLIBCXX_SIMD_MATH_CALL_(exp2) _GLIBCXX_SIMD_MATH_CALL_(expm1) // }}} // frexp {{{ #if _GLIBCXX_SIMD_X86INTRIN template <typename _Tp, size_t _Np> _SimdWrapper<_Tp, _Np> __getexp(_SimdWrapper<_Tp, _Np> __x) { if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>()) return __auto_bitcast(_mm_getexp_ps(__to_intrin(__x))); else if constexpr (__have_avx512f && __is_sse_ps<_Tp, _Np>()) return __auto_bitcast(_mm512_getexp_ps(__auto_bitcast(__to_intrin(__x)))); else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>()) return _mm_getexp_pd(__x); else if constexpr (__have_avx512f && __is_sse_pd<_Tp, _Np>()) return __lo128(_mm512_getexp_pd(__auto_bitcast(__x))); else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>()) return _mm256_getexp_ps(__x); else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>()) return __lo256(_mm512_getexp_ps(__auto_bitcast(__x))); else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>()) return _mm256_getexp_pd(__x); else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>()) return __lo256(_mm512_getexp_pd(__auto_bitcast(__x))); else if constexpr (__is_avx512_ps<_Tp, _Np>()) return _mm512_getexp_ps(__x); else if constexpr (__is_avx512_pd<_Tp, _Np>()) return _mm512_getexp_pd(__x); else __assert_unreachable<_Tp>(); } template <typename _Tp, size_t _Np> _SimdWrapper<_Tp, _Np> __getmant_avx512(_SimdWrapper<_Tp, _Np> __x) { if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>()) return __auto_bitcast(_mm_getmant_ps(__to_intrin(__x), _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)); else if constexpr (__have_avx512f && __is_sse_ps<_Tp, _Np>()) return __auto_bitcast(_mm512_getmant_ps(__auto_bitcast(__to_intrin(__x)), _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)); else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>()) return _mm_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src); else if constexpr (__have_avx512f && __is_sse_pd<_Tp, _Np>()) return __lo128(_mm512_getmant_pd(__auto_bitcast(__x), _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)); else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>()) return _mm256_getmant_ps(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src); else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>()) return __lo256(_mm512_getmant_ps(__auto_bitcast(__x), _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)); else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>()) return _mm256_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src); else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>()) return __lo256(_mm512_getmant_pd(__auto_bitcast(__x), _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src)); else if constexpr (__is_avx512_ps<_Tp, _Np>()) return _mm512_getmant_ps(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src); else if constexpr (__is_avx512_pd<_Tp, _Np>()) return _mm512_getmant_pd(__x, _MM_MANT_NORM_p5_1, _MM_MANT_SIGN_src); else __assert_unreachable<_Tp>(); } #endif // _GLIBCXX_SIMD_X86INTRIN /** * splits @p __v into exponent and mantissa, the sign is kept with the mantissa * * The return value will be in the range [0.5, 1.0[ * The @p __e value will be an integer defining the power-of-two exponent */ template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> frexp(const simd<_Tp, _Abi>& __x, _Samesize<int, simd<_Tp, _Abi>>* __exp) { if constexpr (simd_size_v<_Tp, _Abi> == 1) { int __tmp; const auto __r = std::frexp(__x[0], &__tmp); (*__exp)[0] = __tmp; return __r; } else if constexpr (__is_fixed_size_abi_v<_Abi>) { return {__private_init, _Abi::_SimdImpl::_S_frexp(__data(__x), __data(*__exp))}; #if _GLIBCXX_SIMD_X86INTRIN } else if constexpr (__have_avx512f) { constexpr size_t _Np = simd_size_v<_Tp, _Abi>; constexpr size_t _NI = _Np < 4 ? 4 : _Np; const auto __v = __data(__x); const auto __isnonzero = _Abi::_SimdImpl::_S_isnonzerovalue_mask(__v._M_data); const _SimdWrapper<int, _NI> __exp_plus1 = 1 + __convert<_SimdWrapper<int, _NI>>(__getexp(__v))._M_data; const _SimdWrapper<int, _Np> __e = __wrapper_bitcast<int, _Np>( _Abi::_CommonImpl::_S_blend(_SimdWrapper<bool, _NI>(__isnonzero), _SimdWrapper<int, _NI>(), __exp_plus1)); simd_abi::deduce_t<int, _Np>::_CommonImpl::_S_store(__e, __exp); return {__private_init, _Abi::_CommonImpl::_S_blend(_SimdWrapper<bool, _Np>( __isnonzero), __v, __getmant_avx512(__v))}; #endif // _GLIBCXX_SIMD_X86INTRIN } else { // fallback implementation static_assert(sizeof(_Tp) == 4 || sizeof(_Tp) == 8); using _V = simd<_Tp, _Abi>; using _IV = rebind_simd_t<int, _V>; using namespace std::experimental::__proposed; using namespace std::experimental::__float_bitwise_operators; constexpr int __exp_adjust = sizeof(_Tp) == 4 ? 0x7e : 0x3fe; constexpr int __exp_offset = sizeof(_Tp) == 4 ? 0x70 : 0x200; constexpr _Tp __subnorm_scale = sizeof(_Tp) == 4 ? 0x1p112 : 0x1p512; _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __exponent_mask = __infinity_v<_Tp>; // 0x7f800000 or 0x7ff0000000000000 _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __p5_1_exponent = -(2 - __epsilon_v<_Tp>) / 2; // 0xbf7fffff or 0xbfefffffffffffff _V __mant = __p5_1_exponent & (__exponent_mask | __x); // +/-[.5, 1) const _IV __exponent_bits = __extract_exponent_as_int(__x); if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x)))) { *__exp = simd_cast<_Samesize<int, _V>>(__exponent_bits - __exp_adjust); return __mant; } #if __FINITE_MATH_ONLY__ // at least one element of __x is 0 or subnormal, the rest is normal // (inf and NaN are excluded by -ffinite-math-only) const auto __iszero_inf_nan = __x == 0; #else const auto __as_int = __bit_cast<rebind_simd_t<__int_for_sizeof_t<_Tp>, _V>>(abs(__x)); const auto __inf = __bit_cast<rebind_simd_t<__int_for_sizeof_t<_Tp>, _V>>( _V(__infinity_v<_Tp>)); const auto __iszero_inf_nan = static_simd_cast<typename _V::mask_type>( __as_int == 0 || __as_int >= __inf); #endif const _V __scaled_subnormal = __x * __subnorm_scale; const _V __mant_subnormal = __p5_1_exponent & (__exponent_mask | __scaled_subnormal); where(!isnormal(__x), __mant) = __mant_subnormal; where(__iszero_inf_nan, __mant) = __x; _IV __e = __extract_exponent_as_int(__scaled_subnormal); using _MaskType = typename conditional_t<sizeof(typename _V::value_type) == sizeof(int), _V, _IV>::mask_type; const _MaskType __value_isnormal = isnormal(__x).__cvt(); where(__value_isnormal.__cvt(), __e) = __exponent_bits; static_assert(sizeof(_IV) == sizeof(__value_isnormal)); const _IV __offset = (__bit_cast<_IV>(__value_isnormal) & _IV(__exp_adjust)) | (__bit_cast<_IV>(static_simd_cast<_MaskType>(__exponent_bits == 0) & static_simd_cast<_MaskType>(__x != 0)) & _IV(__exp_adjust + __exp_offset)); *__exp = simd_cast<_Samesize<int, _V>>(__e - __offset); return __mant; } } // }}} _GLIBCXX_SIMD_MATH_CALL2_(ldexp, int) _GLIBCXX_SIMD_MATH_CALL_(ilogb) // logarithms {{{ _GLIBCXX_SIMD_MATH_CALL_(log) _GLIBCXX_SIMD_MATH_CALL_(log10) _GLIBCXX_SIMD_MATH_CALL_(log1p) _GLIBCXX_SIMD_MATH_CALL_(log2) //}}} // logb{{{ template <typename _Tp, typename _Abi> enable_if_t<is_floating_point<_Tp>::value, simd<_Tp, _Abi>> logb(const simd<_Tp, _Abi>& __x) { constexpr size_t _Np = simd_size_v<_Tp, _Abi>; if constexpr (_Np == 1) return std::logb(__x[0]); else if constexpr (__is_fixed_size_abi_v<_Abi>) { return {__private_init, __data(__x)._M_apply_per_chunk([](auto __impl, auto __xx) { using _V = typename decltype(__impl)::simd_type; return __data( std::experimental::logb(_V(__private_init, __xx))); })}; } #if _GLIBCXX_SIMD_X86INTRIN // {{{ else if constexpr (__have_avx512vl && __is_sse_ps<_Tp, _Np>()) return {__private_init, __auto_bitcast(_mm_getexp_ps(__to_intrin(__as_vector(__x))))}; else if constexpr (__have_avx512vl && __is_sse_pd<_Tp, _Np>()) return {__private_init, _mm_getexp_pd(__data(__x))}; else if constexpr (__have_avx512vl && __is_avx_ps<_Tp, _Np>()) return {__private_init, _mm256_getexp_ps(__data(__x))}; else if constexpr (__have_avx512vl && __is_avx_pd<_Tp, _Np>()) return {__private_init, _mm256_getexp_pd(__data(__x))}; else if constexpr (__have_avx512f && __is_avx_ps<_Tp, _Np>()) return {__private_init, __lo256(_mm512_getexp_ps(__auto_bitcast(__data(__x))))}; else if constexpr (__have_avx512f && __is_avx_pd<_Tp, _Np>()) return {__private_init, __lo256(_mm512_getexp_pd(__auto_bitcast(__data(__x))))}; else if constexpr (__is_avx512_ps<_Tp, _Np>()) return {__private_init, _mm512_getexp_ps(__data(__x))}; else if constexpr (__is_avx512_pd<_Tp, _Np>()) return {__private_init, _mm512_getexp_pd(__data(__x))}; #endif // _GLIBCXX_SIMD_X86INTRIN }}} else { using _V = simd<_Tp, _Abi>; using namespace std::experimental::__proposed; auto __is_normal = isnormal(__x); // work on abs(__x) to reflect the return value on Linux for negative // inputs (domain-error => implementation-defined value is returned) const _V abs_x = abs(__x); // __exponent(__x) returns the exponent value (bias removed) as // simd<_Up> with integral _Up auto&& __exponent = [](const _V& __v) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { using namespace std::experimental::__proposed; using _IV = rebind_simd_t< conditional_t<sizeof(_Tp) == sizeof(_LLong), _LLong, int>, _V>; return (__bit_cast<_IV>(__v) >> (__digits_v<_Tp> - 1)) - (__max_exponent_v<_Tp> - 1); }; _V __r = static_simd_cast<_V>(__exponent(abs_x)); if (_GLIBCXX_SIMD_IS_LIKELY(all_of(__is_normal))) // without corner cases (nan, inf, subnormal, zero) we have our // answer: return __r; const auto __is_zero = __x == 0; const auto __is_nan = isnan(__x); const auto __is_inf = isinf(__x); where(__is_zero, __r) = -__infinity_v<_Tp>; where(__is_nan, __r) = __x; where(__is_inf, __r) = __infinity_v<_Tp>; __is_normal |= __is_zero || __is_nan || __is_inf; if (all_of(__is_normal)) // at this point everything but subnormals is handled return __r; // subnormals repeat the exponent extraction after multiplication of the // input with __a floating point value that has 112 (0x70) in its exponent // (not too big for sp and large enough for dp) const _V __scaled = abs_x * _Tp(0x1p112); _V __scaled_exp = static_simd_cast<_V>(__exponent(__scaled) - 112); where(__is_normal, __scaled_exp) = __r; return __scaled_exp; } } //}}} template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> modf(const simd<_Tp, _Abi>& __x, simd<_Tp, _Abi>* __iptr) { if constexpr (__is_scalar_abi<_Abi>() || (__is_fixed_size_abi_v< _Abi> && simd_size_v<_Tp, _Abi> == 1)) { _Tp __tmp; _Tp __r = std::modf(__x[0], &__tmp); __iptr[0] = __tmp; return __r; } else { const auto __integral = trunc(__x); *__iptr = __integral; auto __r = __x - __integral; #if !__FINITE_MATH_ONLY__ where(isinf(__x), __r) = _Tp(); #endif return copysign(__r, __x); } } _GLIBCXX_SIMD_MATH_CALL2_(scalbn, int) _GLIBCXX_SIMD_MATH_CALL2_(scalbln, long) _GLIBCXX_SIMD_MATH_CALL_(cbrt) _GLIBCXX_SIMD_MATH_CALL_(abs) _GLIBCXX_SIMD_MATH_CALL_(fabs) // [parallel.simd.math] only asks for is_floating_point_v<_Tp> and forgot to // allow signed integral _Tp template <typename _Tp, typename _Abi> enable_if_t<!is_floating_point_v<_Tp> && is_signed_v<_Tp>, simd<_Tp, _Abi>> abs(const simd<_Tp, _Abi>& __x) { return {__private_init, _Abi::_SimdImpl::_S_abs(__data(__x))}; } template <typename _Tp, typename _Abi> enable_if_t<!is_floating_point_v<_Tp> && is_signed_v<_Tp>, simd<_Tp, _Abi>> fabs(const simd<_Tp, _Abi>& __x) { return {__private_init, _Abi::_SimdImpl::_S_abs(__data(__x))}; } // the following are overloads for functions in <cstdlib> and not covered by // [parallel.simd.math]. I don't see much value in making them work, though /* template <typename _Abi> simd<long, _Abi> labs(const simd<long, _Abi> &__x) { return {__private_init, _Abi::_SimdImpl::abs(__data(__x))}; } template <typename _Abi> simd<long long, _Abi> llabs(const simd<long long, _Abi> &__x) { return {__private_init, _Abi::_SimdImpl::abs(__data(__x))}; } */ #define _GLIBCXX_SIMD_CVTING2(_NAME) \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y) \ { \ return _NAME(__x, __y); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y) \ { \ return _NAME(__x, __y); \ } #define _GLIBCXX_SIMD_CVTING3(_NAME) \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y, \ const simd<_Tp, _Abi>& __z) \ { \ return _NAME(__x, __y, __z); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y, \ const simd<_Tp, _Abi>& __z) \ { \ return _NAME(__x, __y, __z); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y, \ const __type_identity_t<simd<_Tp, _Abi>>& __z) \ { \ return _NAME(__x, __y, __z); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const simd<_Tp, _Abi>& __x, const __type_identity_t<simd<_Tp, _Abi>>& __y, \ const __type_identity_t<simd<_Tp, _Abi>>& __z) \ { \ return _NAME(__x, __y, __z); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const __type_identity_t<simd<_Tp, _Abi>>& __x, const simd<_Tp, _Abi>& __y, \ const __type_identity_t<simd<_Tp, _Abi>>& __z) \ { \ return _NAME(__x, __y, __z); \ } \ \ template <typename _Tp, typename _Abi> \ _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> _NAME( \ const __type_identity_t<simd<_Tp, _Abi>>& __x, \ const __type_identity_t<simd<_Tp, _Abi>>& __y, const simd<_Tp, _Abi>& __z) \ { \ return _NAME(__x, __y, __z); \ } template <typename _R, typename _ToApply, typename _Tp, typename... _Tps> _GLIBCXX_SIMD_INTRINSIC _R __fixed_size_apply(_ToApply&& __apply, const _Tp& __arg0, const _Tps&... __args) { return {__private_init, __data(__arg0)._M_apply_per_chunk( [&](auto __impl, const auto&... __inner) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { using _V = typename decltype(__impl)::simd_type; return __data(__apply(_V(__private_init, __inner)...)); }, __data(__args)...)}; } template <typename _VV> __remove_cvref_t<_VV> __hypot(_VV __x, _VV __y) { using _V = __remove_cvref_t<_VV>; using _Tp = typename _V::value_type; if constexpr (_V::size() == 1) return std::hypot(_Tp(__x[0]), _Tp(__y[0])); else if constexpr (__is_fixed_size_abi_v<typename _V::abi_type>) { return __fixed_size_apply<_V>([](auto __a, auto __b) { return hypot(__a, __b); }, __x, __y); } else { // A simple solution for _Tp == float would be to cast to double and // simply calculate sqrt(x²+y²) as it can't over-/underflow anymore with // dp. It still needs the Annex F fixups though and isn't faster on // Skylake-AVX512 (not even for SSE and AVX vectors, and really bad for // AVX-512). using namespace __float_bitwise_operators; _V __absx = abs(__x); // no error _V __absy = abs(__y); // no error _V __hi = max(__absx, __absy); // no error _V __lo = min(__absy, __absx); // no error // round __hi down to the next power-of-2: _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __inf(__infinity_v<_Tp>); #ifndef __FAST_MATH__ if constexpr (__have_neon && !__have_neon_a32) { // With ARMv7 NEON, we have no subnormals and must use slightly // different strategy const _V __hi_exp = __hi & __inf; _V __scale_back = __hi_exp; // For large exponents (max & max/2) the inversion comes too close // to subnormals. Subtract 3 from the exponent: where(__hi_exp > 1, __scale_back) = __hi_exp * _Tp(0.125); // Invert and adjust for the off-by-one error of inversion via xor: const _V __scale = (__scale_back ^ __inf) * _Tp(.5); const _V __h1 = __hi * __scale; const _V __l1 = __lo * __scale; _V __r = __scale_back * sqrt(__h1 * __h1 + __l1 * __l1); // Fix up hypot(0, 0) to not be NaN: where(__hi == 0, __r) = 0; return __r; } #endif #ifdef __FAST_MATH__ // With fast-math, ignore precision of subnormals and inputs from // __finite_max_v/2 to __finite_max_v. This removes all // branching/masking. if constexpr (true) #else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x)) && all_of(isnormal(__y)))) #endif { const _V __hi_exp = __hi & __inf; //((__hi + __hi) & __inf) ^ __inf almost works for computing //__scale, // except when (__hi + __hi) & __inf == __inf, in which case __scale // becomes 0 (should be min/2 instead) and thus loses the // information from __lo. #ifdef __FAST_MATH__ using _Ip = __int_for_sizeof_t<_Tp>; using _IV = rebind_simd_t<_Ip, _V>; const auto __as_int = __bit_cast<_IV>(__hi_exp); const _V __scale = __bit_cast<_V>(2 * __bit_cast<_Ip>(_Tp(1)) - __as_int); #else const _V __scale = (__hi_exp ^ __inf) * _Tp(.5); #endif _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __mant_mask = __norm_min_v<_Tp> - __denorm_min_v<_Tp>; const _V __h1 = (__hi & __mant_mask) | _V(1); const _V __l1 = __lo * __scale; return __hi_exp * sqrt(__h1 * __h1 + __l1 * __l1); } else { // slower path to support subnormals // if __hi is subnormal, avoid scaling by inf & final mul by 0 // (which yields NaN) by using min() _V __scale = _V(1 / __norm_min_v<_Tp>); // invert exponent w/o error and w/o using the slow divider unit: // xor inverts the exponent but off by 1. Multiplication with .5 // adjusts for the discrepancy. where(__hi >= __norm_min_v<_Tp>, __scale) = ((__hi & __inf) ^ __inf) * _Tp(.5); // adjust final exponent for subnormal inputs _V __hi_exp = __norm_min_v<_Tp>; where(__hi >= __norm_min_v<_Tp>, __hi_exp) = __hi & __inf; // no error _V __h1 = __hi * __scale; // no error _V __l1 = __lo * __scale; // no error // sqrt(x²+y²) = e*sqrt((x/e)²+(y/e)²): // this ensures no overflow in the argument to sqrt _V __r = __hi_exp * sqrt(__h1 * __h1 + __l1 * __l1); #ifdef __STDC_IEC_559__ // fixup for Annex F requirements // the naive fixup goes like this: // // where(__l1 == 0, __r) = __hi; // where(isunordered(__x, __y), __r) = __quiet_NaN_v<_Tp>; // where(isinf(__absx) || isinf(__absy), __r) = __inf; // // The fixup can be prepared in parallel with the sqrt, requiring a // single blend step after hi_exp * sqrt, reducing latency and // throughput: _V __fixup = __hi; // __lo == 0 where(isunordered(__x, __y), __fixup) = __quiet_NaN_v<_Tp>; where(isinf(__absx) || isinf(__absy), __fixup) = __inf; where(!(__lo == 0 || isunordered(__x, __y) || (isinf(__absx) || isinf(__absy))), __fixup) = __r; __r = __fixup; #endif return __r; } } } template <typename _Tp, typename _Abi> _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> hypot(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y) { return __hypot<conditional_t<__is_fixed_size_abi_v<_Abi>, const simd<_Tp, _Abi>&, simd<_Tp, _Abi>>>(__x, __y); } _GLIBCXX_SIMD_CVTING2(hypot) template <typename _VV> __remove_cvref_t<_VV> __hypot(_VV __x, _VV __y, _VV __z) { using _V = __remove_cvref_t<_VV>; using _Abi = typename _V::abi_type; using _Tp = typename _V::value_type; /* FIXME: enable after PR77776 is resolved if constexpr (_V::size() == 1) return std::hypot(_Tp(__x[0]), _Tp(__y[0]), _Tp(__z[0])); else */ if constexpr (__is_fixed_size_abi_v<_Abi> && _V::size() > 1) { return __fixed_size_apply<simd<_Tp, _Abi>>( [](auto __a, auto __b, auto __c) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return hypot(__a, __b, __c); }, __x, __y, __z); } else { using namespace __float_bitwise_operators; const _V __absx = abs(__x); // no error const _V __absy = abs(__y); // no error const _V __absz = abs(__z); // no error _V __hi = max(max(__absx, __absy), __absz); // no error _V __l0 = min(__absz, max(__absx, __absy)); // no error _V __l1 = min(__absy, __absx); // no error if constexpr (__digits_v<_Tp> == 64 && __max_exponent_v<_Tp> == 0x4000 && __min_exponent_v<_Tp> == -0x3FFD && _V::size() == 1) { // Seems like x87 fp80, where bit 63 is always 1 unless subnormal or // NaN. In this case the bit-tricks don't work, they require IEC559 // binary32 or binary64 format. #ifdef __STDC_IEC_559__ // fixup for Annex F requirements if (isinf(__absx[0]) || isinf(__absy[0]) || isinf(__absz[0])) return __infinity_v<_Tp>; else if (isunordered(__absx[0], __absy[0] + __absz[0])) return __quiet_NaN_v<_Tp>; else if (__l0[0] == 0 && __l1[0] == 0) return __hi; #endif _V __hi_exp = __hi; const _ULLong __tmp = 0x8000'0000'0000'0000ull; __builtin_memcpy(&__data(__hi_exp), &__tmp, 8); const _V __scale = 1 / __hi_exp; __hi *= __scale; __l0 *= __scale; __l1 *= __scale; return __hi_exp * sqrt((__l0 * __l0 + __l1 * __l1) + __hi * __hi); } else { // round __hi down to the next power-of-2: _GLIBCXX_SIMD_USE_CONSTEXPR_API _V __inf(__infinity_v<_Tp>); #ifndef __FAST_MATH__ if constexpr (_V::size() > 1 && __have_neon && !__have_neon_a32) { // With ARMv7 NEON, we have no subnormals and must use slightly // different strategy const _V __hi_exp = __hi & __inf; _V __scale_back = __hi_exp; // For large exponents (max & max/2) the inversion comes too // close to subnormals. Subtract 3 from the exponent: where(__hi_exp > 1, __scale_back) = __hi_exp * _Tp(0.125); // Invert and adjust for the off-by-one error of inversion via // xor: const _V __scale = (__scale_back ^ __inf) * _Tp(.5); const _V __h1 = __hi * __scale; __l0 *= __scale; __l1 *= __scale; _V __lo = __l0 * __l0 + __l1 * __l1; // add the two smaller values first asm("" : "+m"(__lo)); _V __r = __scale_back * sqrt(__h1 * __h1 + __lo); // Fix up hypot(0, 0, 0) to not be NaN: where(__hi == 0, __r) = 0; return __r; } #endif #ifdef __FAST_MATH__ // With fast-math, ignore precision of subnormals and inputs from // __finite_max_v/2 to __finite_max_v. This removes all // branching/masking. if constexpr (true) #else if (_GLIBCXX_SIMD_IS_LIKELY(all_of(isnormal(__x)) && all_of(isnormal(__y)) && all_of(isnormal(__z)))) #endif { const _V __hi_exp = __hi & __inf; //((__hi + __hi) & __inf) ^ __inf almost works for computing //__scale, except when (__hi + __hi) & __inf == __inf, in which // case __scale // becomes 0 (should be min/2 instead) and thus loses the // information from __lo. #ifdef __FAST_MATH__ using _Ip = __int_for_sizeof_t<_Tp>; using _IV = rebind_simd_t<_Ip, _V>; const auto __as_int = __bit_cast<_IV>(__hi_exp); const _V __scale = __bit_cast<_V>(2 * __bit_cast<_Ip>(_Tp(1)) - __as_int); #else const _V __scale = (__hi_exp ^ __inf) * _Tp(.5); #endif constexpr _Tp __mant_mask = __norm_min_v<_Tp> - __denorm_min_v<_Tp>; const _V __h1 = (__hi & _V(__mant_mask)) | _V(1); __l0 *= __scale; __l1 *= __scale; const _V __lo = __l0 * __l0 + __l1 * __l1; // add the two smaller values first return __hi_exp * sqrt(__lo + __h1 * __h1); } else { // slower path to support subnormals // if __hi is subnormal, avoid scaling by inf & final mul by 0 // (which yields NaN) by using min() _V __scale = _V(1 / __norm_min_v<_Tp>); // invert exponent w/o error and w/o using the slow divider // unit: xor inverts the exponent but off by 1. Multiplication // with .5 adjusts for the discrepancy. where(__hi >= __norm_min_v<_Tp>, __scale) = ((__hi & __inf) ^ __inf) * _Tp(.5); // adjust final exponent for subnormal inputs _V __hi_exp = __norm_min_v<_Tp>; where(__hi >= __norm_min_v<_Tp>, __hi_exp) = __hi & __inf; // no error _V __h1 = __hi * __scale; // no error __l0 *= __scale; // no error __l1 *= __scale; // no error _V __lo = __l0 * __l0 + __l1 * __l1; // add the two smaller values first _V __r = __hi_exp * sqrt(__lo + __h1 * __h1); #ifdef __STDC_IEC_559__ // fixup for Annex F requirements _V __fixup = __hi; // __lo == 0 // where(__lo == 0, __fixup) = __hi; where(isunordered(__x, __y + __z), __fixup) = __quiet_NaN_v<_Tp>; where(isinf(__absx) || isinf(__absy) || isinf(__absz), __fixup) = __inf; // Instead of __lo == 0, the following could depend on __h1² == // __h1² + __lo (i.e. __hi is so much larger than the other two // inputs that the result is exactly __hi). While this may // improve precision, it is likely to reduce efficiency if the // ISA has FMAs (because __h1² + __lo is an FMA, but the // intermediate // __h1² must be kept) where(!(__lo == 0 || isunordered(__x, __y + __z) || isinf(__absx) || isinf(__absy) || isinf(__absz)), __fixup) = __r; __r = __fixup; #endif return __r; } } } } template <typename _Tp, typename _Abi> _GLIBCXX_SIMD_INTRINSIC simd<_Tp, _Abi> hypot(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y, const simd<_Tp, _Abi>& __z) { return __hypot<conditional_t<__is_fixed_size_abi_v<_Abi>, const simd<_Tp, _Abi>&, simd<_Tp, _Abi>>>(__x, __y, __z); } _GLIBCXX_SIMD_CVTING3(hypot) _GLIBCXX_SIMD_MATH_CALL2_(pow, _Tp) _GLIBCXX_SIMD_MATH_CALL_(sqrt) _GLIBCXX_SIMD_MATH_CALL_(erf) _GLIBCXX_SIMD_MATH_CALL_(erfc) _GLIBCXX_SIMD_MATH_CALL_(lgamma) _GLIBCXX_SIMD_MATH_CALL_(tgamma) _GLIBCXX_SIMD_MATH_CALL_(ceil) _GLIBCXX_SIMD_MATH_CALL_(floor) _GLIBCXX_SIMD_MATH_CALL_(nearbyint) _GLIBCXX_SIMD_MATH_CALL_(rint) _GLIBCXX_SIMD_MATH_CALL_(lrint) _GLIBCXX_SIMD_MATH_CALL_(llrint) _GLIBCXX_SIMD_MATH_CALL_(round) _GLIBCXX_SIMD_MATH_CALL_(lround) _GLIBCXX_SIMD_MATH_CALL_(llround) _GLIBCXX_SIMD_MATH_CALL_(trunc) _GLIBCXX_SIMD_MATH_CALL2_(fmod, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(remainder, _Tp) _GLIBCXX_SIMD_MATH_CALL3_(remquo, _Tp, int*) template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> copysign(const simd<_Tp, _Abi>& __x, const simd<_Tp, _Abi>& __y) { if constexpr (simd_size_v<_Tp, _Abi> == 1) return std::copysign(__x[0], __y[0]); else if constexpr (is_same_v<_Tp, long double> && sizeof(_Tp) == 12) // Remove this case once __bit_cast is implemented via __builtin_bit_cast. // It is necessary, because __signmask below cannot be computed at compile // time. return simd<_Tp, _Abi>( [&](auto __i) { return std::copysign(__x[__i], __y[__i]); }); else { using _V = simd<_Tp, _Abi>; using namespace std::experimental::__float_bitwise_operators; _GLIBCXX_SIMD_USE_CONSTEXPR_API auto __signmask = _V(1) ^ _V(-1); return (__x & (__x ^ __signmask)) | (__y & __signmask); } } _GLIBCXX_SIMD_MATH_CALL2_(nextafter, _Tp) // not covered in [parallel.simd.math]: // _GLIBCXX_SIMD_MATH_CALL2_(nexttoward, long double) _GLIBCXX_SIMD_MATH_CALL2_(fdim, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(fmax, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(fmin, _Tp) _GLIBCXX_SIMD_MATH_CALL3_(fma, _Tp, _Tp) _GLIBCXX_SIMD_MATH_CALL_(fpclassify) _GLIBCXX_SIMD_MATH_CALL_(isfinite) // isnan and isinf require special treatment because old glibc may declare // `int isinf(double)`. template <typename _Tp, typename _Abi, typename..., typename _R = _Math_return_type_t<bool, _Tp, _Abi>> enable_if_t<is_floating_point_v<_Tp>, _R> isinf(simd<_Tp, _Abi> __x) { return {__private_init, _Abi::_SimdImpl::_S_isinf(__data(__x))}; } template <typename _Tp, typename _Abi, typename..., typename _R = _Math_return_type_t<bool, _Tp, _Abi>> enable_if_t<is_floating_point_v<_Tp>, _R> isnan(simd<_Tp, _Abi> __x) { return {__private_init, _Abi::_SimdImpl::_S_isnan(__data(__x))}; } _GLIBCXX_SIMD_MATH_CALL_(isnormal) template <typename..., typename _Tp, typename _Abi> simd_mask<_Tp, _Abi> signbit(simd<_Tp, _Abi> __x) { if constexpr (is_integral_v<_Tp>) { if constexpr (is_unsigned_v<_Tp>) return simd_mask<_Tp, _Abi>{}; // false else return __x < 0; } else return {__private_init, _Abi::_SimdImpl::_S_signbit(__data(__x))}; } _GLIBCXX_SIMD_MATH_CALL2_(isgreater, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(isgreaterequal, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(isless, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(islessequal, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(islessgreater, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(isunordered, _Tp) /* not covered in [parallel.simd.math] template <typename _Abi> __doublev<_Abi> nan(const char* tagp); template <typename _Abi> __floatv<_Abi> nanf(const char* tagp); template <typename _Abi> __ldoublev<_Abi> nanl(const char* tagp); template <typename _V> struct simd_div_t { _V quot, rem; }; template <typename _Abi> simd_div_t<_SCharv<_Abi>> div(_SCharv<_Abi> numer, _SCharv<_Abi> denom); template <typename _Abi> simd_div_t<__shortv<_Abi>> div(__shortv<_Abi> numer, __shortv<_Abi> denom); template <typename _Abi> simd_div_t<__intv<_Abi>> div(__intv<_Abi> numer, __intv<_Abi> denom); template <typename _Abi> simd_div_t<__longv<_Abi>> div(__longv<_Abi> numer, __longv<_Abi> denom); template <typename _Abi> simd_div_t<__llongv<_Abi>> div(__llongv<_Abi> numer, __llongv<_Abi> denom); */ // special math {{{ template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> assoc_laguerre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::assoc_laguerre(__n[__i], __m[__i], __x[__i]); }); } template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> assoc_legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::assoc_legendre(__n[__i], __m[__i], __x[__i]); }); } _GLIBCXX_SIMD_MATH_CALL2_(beta, _Tp) _GLIBCXX_SIMD_MATH_CALL_(comp_ellint_1) _GLIBCXX_SIMD_MATH_CALL_(comp_ellint_2) _GLIBCXX_SIMD_MATH_CALL2_(comp_ellint_3, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_i, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_j, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(cyl_bessel_k, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(cyl_neumann, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(ellint_1, _Tp) _GLIBCXX_SIMD_MATH_CALL2_(ellint_2, _Tp) _GLIBCXX_SIMD_MATH_CALL3_(ellint_3, _Tp, _Tp) _GLIBCXX_SIMD_MATH_CALL_(expint) template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> hermite(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::hermite(__n[__i], __x[__i]); }); } template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> laguerre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::laguerre(__n[__i], __x[__i]); }); } template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::legendre(__n[__i], __x[__i]); }); } _GLIBCXX_SIMD_MATH_CALL_(riemann_zeta) template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> sph_bessel(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::sph_bessel(__n[__i], __x[__i]); }); } template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> sph_legendre(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __l, const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __m, const simd<_Tp, _Abi>& theta) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::assoc_legendre(__l[__i], __m[__i], theta[__i]); }); } template <typename _Tp, typename _Abi> enable_if_t<is_floating_point_v<_Tp>, simd<_Tp, _Abi>> sph_neumann(const fixed_size_simd<unsigned, simd_size_v<_Tp, _Abi>>& __n, const simd<_Tp, _Abi>& __x) { return simd<_Tp, _Abi>([&](auto __i) _GLIBCXX_SIMD_ALWAYS_INLINE_LAMBDA { return std::sph_neumann(__n[__i], __x[__i]); }); } // }}} #undef _GLIBCXX_SIMD_MATH_CALL_ #undef _GLIBCXX_SIMD_MATH_CALL2_ #undef _GLIBCXX_SIMD_MATH_CALL3_ _GLIBCXX_SIMD_END_NAMESPACE #endif // __cplusplus >= 201703L #endif // _GLIBCXX_EXPERIMENTAL_SIMD_MATH_H_ // vim: foldmethod=marker sw=2 ts=8 noet sts=2
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