/* Vector Extensions - Mandelbrot "Succesfully programmed the dishwasher and debugged the pump this week..." - javidx9 License (OLC-3) ~~~~~~~~~~~~~~~ Copyright 2018-2020 OneLoneCoder.com Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions or derivations of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions or derivative works in binary form must reproduce the above copyright notice. This list of conditions and the following disclaimer must be reproduced in the documentation and/or other materials provided with the distribution. 3. Neither the name of the copyright holder nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. 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Relevant Video: https://youtu.be/x9Scb5Mku1g Links ~~~~~ YouTube: https://www.youtube.com/javidx9 https://www.youtube.com/javidx9extra Discord: https://discord.gg/WhwHUMV Twitter: https://www.twitter.com/javidx9 Twitch: https://www.twitch.tv/javidx9 GitHub: https://www.github.com/onelonecoder Patreon: https://www.patreon.com/javidx9 Homepage: https://www.onelonecoder.com Community Blog: https://community.onelonecoder.com Author ~~~~~~ David Barr, aka javidx9, ŠOneLoneCoder 2018, 2019, 2020 */ // NOTE: THIS PROGRAM CANNOT BE EXCUTED - IT IS INTENDED AS A GUIDE // TO THIS VIDEO: https://youtu.be/x9Scb5Mku1g // Method 4) - Use AVX2 Vector co-processor to handle 4 fractal locations at once void CreateFractalIntrinsics(const olc::vi2d& pix_tl, const olc::vi2d& pix_br, const olc::vd2d& frac_tl, const olc::vd2d& frac_br, const int iterations) { double x_scale = (frac_br.x - frac_tl.x) / (double(pix_br.x) - double(pix_tl.x)); double y_scale = (frac_br.y - frac_tl.y) / (double(pix_br.y) - double(pix_tl.y)); double y_pos = frac_tl.y; int y_offset = 0; int row_size = ScreenWidth(); int x, y; // 64-bit "double" registers __m256d _a, _b, _two, _four, _mask1; __m256d _zr, _zi, _zr2, _zi2, _cr, _ci; __m256d _x_pos_offsets, _x_pos, _x_scale, _x_jump; // 64-bit "integer" registers __m256i _one, _c, _n, _iterations, _mask2; // Expand constants into vectors of constants // one = |(int)1|(int)1|(int)1|(int)1| _one = _mm256_set1_epi64x(1); // two = |2.0|2.0|2.0|2.0| _two = _mm256_set1_pd(2.0); // four = |4.0|4.0|4.0|4.0| _four = _mm256_set1_pd(4.0); // iterations = |iterations|iterations|iterations|iterations| _iterations = _mm256_set1_epi64x(iterations); _x_scale = _mm256_set1_pd(x_scale); _x_jump = _mm256_set1_pd(x_scale * 4); _x_pos_offsets = _mm256_set_pd(0, 1, 2, 3); _x_pos_offsets = _mm256_mul_pd(_x_pos_offsets, _x_scale); for (y = pix_tl.y; y < pix_br.y; y++) { // Reset x_position _a = _mm256_set1_pd(frac_tl.x); _x_pos = _mm256_add_pd(_a, _x_pos_offsets); _ci = _mm256_set1_pd(y_pos); for (x = pix_tl.x; x < pix_br.x; x += 4) { _cr = _x_pos; // Zreal = 0 _zr = _mm256_setzero_pd(); // Zimag = 0 _zi = _mm256_setzero_pd(); // nIterations = 0 _n = _mm256_setzero_si256(); repeat: // Normal: z = (z * z) + c; // Manual: a = zr * zr - zi * zi + cr; // b = zr * zi * 2.0 + ci; // zr = a; // zi = b; // zr^2 = zr * zr _zr2 = _mm256_mul_pd(_zr, _zr); // zr * zr // zi^2 = zi * zi _zi2 = _mm256_mul_pd(_zi, _zi); // zi * zi // a = zr^2 - zi^2 _a = _mm256_sub_pd(_zr2, _zi2); // a = (zr * zr) - (zi * zi) // a = a + cr _a = _mm256_add_pd(_a, _cr); // a = ((zr * zr) - (zi * zi)) + cr // b = zr * zi _b = _mm256_mul_pd(_zr, _zi); // b = zr * zi // b = b * 2.0 + ci // b = b * |2.0|2.0|2.0|2.0| + ci _b = _mm256_fmadd_pd(_b, _two, _ci); // b = (zr * zi) * 2.0 + ci // zr = a _zr = _a; // zr = a // zi = b _zi = _b; // zr = b // Normal: while (abs(z) < 2.0 && n < iterations) // Manual: while ((zr * zr + zi * zi) < 4.0 && n < iterations) // a = zr^2 + zi^2 _a = _mm256_add_pd(_zr2, _zi2); // a = (zr * zr) + (zi * zi) // m1 = if (a < 4.0) // m1 = |if(a[3] < 4.0)|if(a[2] < 4.0)|if(a[1] < 4.0)|if(a[0] < 4.0)| // m1 = |111111...11111|000000...00000|111111...11111|000000...00000| // m1 = |11...11|00...00|11...11|00...00| <- Shortened to reduce typing :P _mask1 = _mm256_cmp_pd(_a, _four, _CMP_LT_OQ); // m2 = if (iterations > n) // m2 = |00...00|11...11|11...11|00...00| _mask2 = _mm256_cmpgt_epi64(_iterations, _n); // m2 = m2 AND m1 = if(a < 4.0 && iterations > n) // // m2 = |00...00|11...11|11...11|00...00| // m1 = AND|11...11|00...00|11...11|00...00| // m2 = |00...00|00...00|11...11|00...00| _mask2 = _mm256_and_si256(_mask2, _mm256_castpd_si256(_mask1)); // c = |(int)1|(int)1|(int)1|(int)1| AND m2 // // c = |00...01|00...01|00...01|00...01| // m2 = AND|00...00|00...00|11...11|00...00| // c = |00...00|00...00|00...01|00...00| // // c = |(int)0|(int)0|(int)1|(int)0| _c = _mm256_and_si256(_one, _mask2); // n = n + c // n = |00...24|00...13|00...08|00...21| // c = +|00...00|00...00|00...01|00...00| // n = |00...24|00...13|00...09|00...21| (Increment only applied to 'enabled' element) _n = _mm256_add_epi64(_n, _c); // if ((zr * zr + zi * zi) < 4.0 && n < iterations) goto repeat // i.e. if our mask has any elements that are 1 // |00...00|00...00|11...11|00...00| // | 0 | 0 | 1 | 0 | = 0b0010 = 2 // so... if (2 > 0) goto repeat if (_mm256_movemask_pd(_mm256_castsi256_pd(_mask2)) > 0) goto repeat; // Tight loop has finished, all 4 pixels have been evaluated. Increment // fractal space x positions for next 4 pixels // x_pos = x_pos + x_jump _x_pos = _mm256_add_pd(_x_pos, _x_jump); // Unpack our 4x64-bit Integer Vector into normal 32-bit Integers // and write into memory at correct location. Note, depending on // how you structure the memory, and the types you use, this step // may not be required. If I was working with 64-bit integers I // could choose to just write the vector entirely, saving this // truncation at the expense of 2x the memory required #if defined(__linux__) // Intrinsics are not cross platform! pFractal[y_offset + x + 0] = int(_n[3]); pFractal[y_offset + x + 1] = int(_n[2]); pFractal[y_offset + x + 2] = int(_n[1]); pFractal[y_offset + x + 3] = int(_n[0]); #endif #if defined(_WIN32) pFractal[y_offset + x + 0] = int(_n.m256i_i64[3]); pFractal[y_offset + x + 1] = int(_n.m256i_i64[2]); pFractal[y_offset + x + 2] = int(_n.m256i_i64[1]); pFractal[y_offset + x + 3] = int(_n.m256i_i64[0]); #endif } y_pos += y_scale; y_offset += row_size; } }