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| 1 | +//***************************************************************************** |
| 2 | +// Copyright (c) 2025, Intel Corporation |
| 3 | +// All rights reserved. |
| 4 | +// |
| 5 | +// Redistribution and use in source and binary forms, with or without |
| 6 | +// modification, are permitted provided that the following conditions are met: |
| 7 | +// - Redistributions of source code must retain the above copyright notice, |
| 8 | +// this list of conditions and the following disclaimer. |
| 9 | +// - Redistributions in binary form must reproduce the above copyright notice, |
| 10 | +// this list of conditions and the following disclaimer in the documentation |
| 11 | +// and/or other materials provided with the distribution. |
| 12 | +// - Neither the name of the copyright holder nor the names of its contributors |
| 13 | +// may be used to endorse or promote products derived from this software |
| 14 | +// without specific prior written permission. |
| 15 | +// |
| 16 | +// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" |
| 17 | +// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 18 | +// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 19 | +// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE |
| 20 | +// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
| 21 | +// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
| 22 | +// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
| 23 | +// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
| 24 | +// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 25 | +// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF |
| 26 | +// THE POSSIBILITY OF SUCH DAMAGE. |
| 27 | +//***************************************************************************** |
| 28 | + |
| 29 | +#pragma once |
| 30 | + |
| 31 | +#include <limits> |
| 32 | +#include <sycl/sycl.hpp> |
| 33 | + |
| 34 | +namespace dpnp::kernels::erfs::impl |
| 35 | +{ |
| 36 | +template <typename Tp> |
| 37 | +inline Tp polevl(Tp x, const Tp *coeff, int i) |
| 38 | +{ |
| 39 | + Tp p = *coeff++; |
| 40 | + |
| 41 | + do { |
| 42 | + p = p * x + *coeff++; |
| 43 | + } while (--i); |
| 44 | + return p; |
| 45 | +} |
| 46 | + |
| 47 | +template <typename Tp> |
| 48 | +inline Tp p1evl(Tp x, const Tp *coeff, int i) |
| 49 | +{ |
| 50 | + Tp p = x + *coeff++; |
| 51 | + |
| 52 | + while (--i) { |
| 53 | + p = p * x + *coeff++; |
| 54 | + } |
| 55 | + return p; |
| 56 | +} |
| 57 | + |
| 58 | +template <typename Tp> |
| 59 | +inline Tp ndtri(Tp y0) |
| 60 | +{ |
| 61 | + Tp y; |
| 62 | + int code = 1; |
| 63 | + |
| 64 | + if (y0 == 0.0) { |
| 65 | + return -std::numeric_limits<Tp>::infinity(); |
| 66 | + } |
| 67 | + else if (y0 == 1.0) { |
| 68 | + return std::numeric_limits<Tp>::infinity(); |
| 69 | + } |
| 70 | + else if (y0 < 0.0 || y0 > 1.0) { |
| 71 | + return std::numeric_limits<Tp>::quiet_NaN(); |
| 72 | + } |
| 73 | + |
| 74 | + // exp(-2) |
| 75 | + constexpr Tp exp_minus2 = 0.13533528323661269189399949497248L; |
| 76 | + if (y0 > (1.0 - exp_minus2)) { |
| 77 | + y = 1.0 - y0; |
| 78 | + code = 0; |
| 79 | + } |
| 80 | + else { |
| 81 | + y = y0; |
| 82 | + } |
| 83 | + |
| 84 | + if (y > exp_minus2) { |
| 85 | + // sqrt(2*pi) |
| 86 | + constexpr Tp root_2_pi = 2.50662827463100050241576528481105L; |
| 87 | + |
| 88 | + // approximation for 0 <= |y - 0.5| <= 3/8 |
| 89 | + constexpr Tp p[] = { |
| 90 | + -5.99633501014107895267E1, 9.80010754185999661536E1, |
| 91 | + -5.66762857469070293439E1, 1.39312609387279679503E1, |
| 92 | + -1.23916583867381258016E0, |
| 93 | + }; |
| 94 | + constexpr Tp q[] = { |
| 95 | + 1.95448858338141759834E0, 4.67627912898881538453E0, |
| 96 | + 8.63602421390890590575E1, -2.25462687854119370527E2, |
| 97 | + 2.00260212380060660359E2, -8.20372256168333339912E1, |
| 98 | + 1.59056225126211695515E1, -1.18331621121330003142E0, |
| 99 | + }; |
| 100 | + |
| 101 | + y -= 0.5; |
| 102 | + Tp y2 = y * y; |
| 103 | + Tp x = y + y * (y2 * polevl(y2, p, 4) / p1evl(y2, q, 8)); |
| 104 | + return x * root_2_pi; |
| 105 | + } |
| 106 | + |
| 107 | + Tp x = sycl::sqrt(-2.0 * sycl::log(y)); |
| 108 | + Tp x0 = x - sycl::log(x) / x; |
| 109 | + Tp z = 1.0 / x; |
| 110 | + |
| 111 | + Tp x1; |
| 112 | + if (x < 8.0) { |
| 113 | + // approximation for 2 <= sqrt(-2*log(y)) < 8 |
| 114 | + constexpr Tp p[] = { |
| 115 | + 4.05544892305962419923E0, 3.15251094599893866154E1, |
| 116 | + 5.71628192246421288162E1, 4.40805073893200834700E1, |
| 117 | + 1.46849561928858024014E1, 2.18663306850790267539E0, |
| 118 | + -1.40256079171354495875E-1, -3.50424626827848203418E-2, |
| 119 | + -8.57456785154685413611E-4, |
| 120 | + }; |
| 121 | + |
| 122 | + constexpr Tp q[] = { |
| 123 | + 1.57799883256466749731E1, 4.53907635128879210584E1, |
| 124 | + 4.13172038254672030440E1, 1.50425385692907503408E1, |
| 125 | + 2.50464946208309415979E0, -1.42182922854787788574E-1, |
| 126 | + -3.80806407691578277194E-2, -9.33259480895457427372E-4, |
| 127 | + }; |
| 128 | + |
| 129 | + x1 = z * polevl(z, p, 8) / p1evl(z, q, 8); |
| 130 | + } |
| 131 | + else { |
| 132 | + // approximation for 8 <= sqrt(-2*log(y)) < 64 |
| 133 | + constexpr Tp p[] = { |
| 134 | + 3.23774891776946035970E0, 6.91522889068984211695E0, |
| 135 | + 3.93881025292474443415E0, 1.33303460815807542389E0, |
| 136 | + 2.01485389549179081538E-1, 1.23716634817820021358E-2, |
| 137 | + 3.01581553508235416007E-4, 2.65806974686737550832E-6, |
| 138 | + 6.23974539184983293730E-9, |
| 139 | + }; |
| 140 | + |
| 141 | + constexpr Tp q[] = { |
| 142 | + 6.02427039364742014255E0, 3.67983563856160859403E0, |
| 143 | + 1.37702099489081330271E0, 2.16236993594496635890E-1, |
| 144 | + 1.34204006088543189037E-2, 3.28014464682127739104E-4, |
| 145 | + 2.89247864745380683936E-6, 6.79019408009981274425E-9, |
| 146 | + }; |
| 147 | + |
| 148 | + x1 = z * polevl(z, p, 8) / p1evl(z, q, 8); |
| 149 | + } |
| 150 | + |
| 151 | + x = x0 - x1; |
| 152 | + if (code != 0) { |
| 153 | + x = -x; |
| 154 | + } |
| 155 | + return x; |
| 156 | +} |
| 157 | + |
| 158 | +template <typename Tp> |
| 159 | +inline Tp erfinv(Tp y) |
| 160 | +{ |
| 161 | + static_assert(std::is_floating_point_v<Tp>, |
| 162 | + "erfinv requires a floating-point type"); |
| 163 | + |
| 164 | + constexpr Tp lower = -1; |
| 165 | + constexpr Tp upper = 1; |
| 166 | + |
| 167 | + constexpr Tp thresh = 1e-7; |
| 168 | + |
| 169 | + // For small arguments, use the Taylor expansion. |
| 170 | + // Otherwise, y + 1 loses precision for |y| << 1. |
| 171 | + if ((-thresh < y) && (y < thresh)) { |
| 172 | + // 2/sqrt(pi) |
| 173 | + constexpr Tp inv_sqrtpi = 1.1283791670955125738961589031215452L; |
| 174 | + return y / inv_sqrtpi; |
| 175 | + } |
| 176 | + |
| 177 | + if ((lower < y) && (y < upper)) { |
| 178 | + // 1/sqrt(2) |
| 179 | + constexpr Tp one_div_root_2 = 0.7071067811865475244008443621048490L; |
| 180 | + return ndtri(0.5 * (y + 1)) * one_div_root_2; |
| 181 | + } |
| 182 | + else if (y == lower) { |
| 183 | + return -std::numeric_limits<Tp>::infinity(); |
| 184 | + } |
| 185 | + else if (y == upper) { |
| 186 | + return std::numeric_limits<Tp>::infinity(); |
| 187 | + } |
| 188 | + else if (sycl::isnan(y)) { |
| 189 | + return y; |
| 190 | + } |
| 191 | + return std::numeric_limits<Tp>::quiet_NaN(); |
| 192 | +} |
| 193 | + |
| 194 | +template <typename Tp> |
| 195 | +inline Tp erfcinv(Tp y) |
| 196 | +{ |
| 197 | + static_assert(std::is_floating_point_v<Tp>, |
| 198 | + "erfcinv requires a floating-point type"); |
| 199 | + |
| 200 | + constexpr Tp lower = 0; |
| 201 | + constexpr Tp upper = 2; |
| 202 | + |
| 203 | + if ((lower < y) && (y < upper)) { |
| 204 | + // 1/sqrt(2) |
| 205 | + constexpr Tp one_div_root_2 = 0.7071067811865475244008443621048490L; |
| 206 | + return -ndtri(0.5 * y) * one_div_root_2; |
| 207 | + } |
| 208 | + else if (y == lower) { |
| 209 | + return std::numeric_limits<Tp>::infinity(); |
| 210 | + } |
| 211 | + else if (y == upper) { |
| 212 | + return -std::numeric_limits<Tp>::infinity(); |
| 213 | + } |
| 214 | + else if (sycl::isnan(y)) { |
| 215 | + return y; |
| 216 | + } |
| 217 | + return std::numeric_limits<Tp>::quiet_NaN(); |
| 218 | +} |
| 219 | +} // namespace dpnp::kernels::erfs::impl |
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