/*
Vector Extensions - Mandelbrot
"Succesfully programmed the dishwasher and debugged the pump this week..." - javidx9
License (OLC-3)
~~~~~~~~~~~~~~~
Copyright 2018-2020 OneLoneCoder.com
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Relevant Video: https://youtu.be/x9Scb5Mku1g
Links
~~~~~
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Author
~~~~~~
David Barr, aka javidx9, �OneLoneCoder 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;
}
}