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Copy pathmandelbrot-explicit-simd-thr.cc
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mandelbrot-explicit-simd-thr.cc
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#include "common.inc"
#include <x86intrin.h>
#include "simd_emu.hh"
inline __m512d _mm512_log2_pd(__m512d x) /* log2(x) for eight positive doubles */
{
constexpr int mantissa_bits = 52, exponent_bias = 1022;
__m512d half = _mm512_set1_pd(0.5);
__m512i e = _mm512_srli_epi64(_mm512_castpd_si512(x), mantissa_bits);
__m512i m = _mm512_and_si512(_mm512_castpd_si512(x), _mm512_set1_epi64((1ull << mantissa_bits)-1));
x = _mm512_or_pd(half, _mm512_castsi512_pd(m));
__mmask8 lt = _mm512_cmp_pd_mask(x, _mm512_set1_pd(1/std::sqrt(2.)), _MM_CMPINT_LT);
__m512d ltid = _mm512_castsi512_pd(_mm512_mask_mov_epi64(_mm512_set1_epi64(0), lt, _mm512_set1_epi64(-1)));
__m512i lti = _mm512_castpd_si512(ltid);
__m512d dbl_e = _mm512_sub_pd(_mm512_cvtepi64_pd(_mm512_add_epi64(e,lti)), _mm512_set1_pd(exponent_bias));
__m512d z = _mm512_sub_pd(x, _mm512_add_pd(half, _mm512_andnot_pd(ltid, half)));
__m512d y = _mm512_fmadd_pd(half, _mm512_sub_pd(x, _mm512_and_pd(ltid, half)), half);
x = _mm512_div_pd(z, y);
z = _mm512_mul_pd(x, x);
__m512d u = _mm512_add_pd(z, _mm512_set1_pd(-3.56722798512324312549E1));
__m512d t = _mm512_set1_pd(-7.89580278884799154124E-1);
u = _mm512_fmadd_pd(u, z, _mm512_set1_pd(3.12093766372244180303E2));
t = _mm512_fmadd_pd(t, z, _mm512_set1_pd(1.63866645699558079767E1));
u = _mm512_fmadd_pd(u, z, _mm512_set1_pd(-7.69691943550460008604E2));
t = _mm512_fmadd_pd(t, z, _mm512_set1_pd(-6.41409952958715622951E1));
y = _mm512_fmadd_pd(z, _mm512_div_pd(t, u), _mm512_add_pd(half,half));
return _mm512_fmadd_pd(x, _mm512_mul_pd(y, _mm512_set1_pd(std::log2(std::exp(1.)))), dbl_e);
}
__m256i to256(__mmask8 c)
{ return _mm256_mask_mov_epi32(_mm256_set1_epi32(-1), c, _mm256_setzero_si256()); }
__m512d ifelse(__m256i c, __m512d ok, __m512d nok)
{ return _mm512_mask_mov_pd(nok, _mm256_cmp_epi32_mask(c, _mm256_setzero_si256(), _MM_CMPINT_NE), ok); }
template<bool WithMoment>
__m512d Iterate(__m512d zr, __m512d zi)
{
const double escape_radius_squared = ESCAPE_RADIUS_SQUARED;
const int maxiter = MAXITER;
__m512d cr = zr, sr = cr;
__m512d ci = zi, si = ci;
__m512d dist = _mm512_set1_pd(0.0), limit = _mm512_set1_pd(escape_radius_squared);
__m256i one = _mm256_set1_epi32(1), zero = _mm256_setzero_si256();
__m512d i2 = _mm512_mul_pd(ci,ci), r2 = _mm512_mul_pd(cr,cr);
__m256i notescaped = to256(_mm512_kand(
_mm512_cmp_pd_mask(
_mm512_fmadd_pd(i2,
_mm512_fmadd_pd(i2, _mm512_set1_pd(8),
_mm512_fmadd_pd(r2, _mm512_set1_pd(16), _mm512_set1_pd(-3))),
_mm512_fmadd_pd(r2, _mm512_fmadd_pd(r2, _mm512_set1_pd(8), _mm512_set1_pd(-3)), cr)),
_mm512_set1_pd(3./32), _MM_CMPINT_GE),
_mm512_cmp_pd_mask(
_mm512_fmadd_pd(_mm512_add_pd(cr,_mm512_set1_pd(1)),_mm512_add_pd(cr,_mm512_set1_pd(1)), i2),
_mm512_set1_pd(1./16), _MM_CMPINT_GE)));
__m256i iter = _mm256_and_si256(_mm256_set1_epi32(maxiter), notescaped);
while(!_mm256_testz_si256(notescaped, notescaped))
{
dist = ifelse(notescaped, _mm512_fmadd_pd(cr,cr, i2), dist);
notescaped = _mm256_and_si256(notescaped,
_mm256_andnot_si256(_mm256_cmpeq_epi32(iter, zero),
to256(_mm512_cmp_pd_mask(dist, limit, _MM_CMPINT_LT))));
iter = _mm256_add_epi32(iter, notescaped);
ci = _mm512_fmadd_pd(_mm512_mul_pd(cr, ci), _mm512_set1_pd(2), zi);
cr = _mm512_fmadd_pd(cr,cr, _mm512_sub_pd(zr, i2));
i2 = _mm512_mul_pd(ci,ci);
if(WithMoment)
{
__m256i moment = _mm256_cmpeq_epi32(_mm256_and_si256(iter, _mm256_sub_epi32(iter, one)), zero);
iter = _mm256_andnot_si256(to256(_mm512_kand(_mm512_cmp_pd_mask(cr,sr,_MM_CMPINT_EQ),
_mm512_cmp_pd_mask(ci,si,_MM_CMPINT_EQ))), iter);
sr = ifelse(moment, cr, sr);
si = ifelse(moment, ci, si);
}
}
return _mm512_castsi512_pd(_mm512_andnot_si512(_mm512_cvtepi32_epi64(_mm256_cmpeq_epi32(iter, zero)), _mm512_castpd_si512(
_mm512_mul_pd(_mm512_set1_pd(4/std::log2(std::exp(1.))),
_mm512_log2_pd(_mm512_add_pd(_mm512_cvtepi32_pd(_mm256_sub_epi32(_mm256_set1_epi32(maxiter), iter)),
_mm512_sub_pd(_mm512_set1_pd(1),
_mm512_log2_pd(_mm512_mul_pd(_mm512_log2_pd(dist),
_mm512_set1_pd(0.5))))))))));
}
inline __m256d _mm256_log2_pd(__m256d x) /* log2(x) for four positive doubles */
{
constexpr int mantissa_bits = 52, exponent_bias = 1022;
__m256d half = _mm256_set1_pd(0.5);
__m256i e = _mm256_srli_epi64(_mm256_castpd_si256(x), mantissa_bits);
__m256i m = _mm256_and_si256(_mm256_castpd_si256(x), _mm256_set1_epi64x((1ull << mantissa_bits)-1));
x = _mm256_or_pd(half, _mm256_castsi256_pd(m));
__m256d ltid = _mm256_cmp_pd(x, _mm256_set1_pd(1/std::sqrt(2.)), _CMP_LT_OQ);
__m256i lti = _mm256_castpd_si256(ltid);
__m256d dbl_e = _mm256_sub_pd(_mm256_cvtepi64_pd(_mm256_add_epi64(e,lti)), _mm256_set1_pd(exponent_bias));
__m256d z = _mm256_sub_pd(x, _mm256_add_pd(half, _mm256_andnot_pd(ltid, half)));
__m256d y = _mm256_fmadd_pd(half, _mm256_sub_pd(x, _mm256_and_pd(ltid, half)), half);
x = _mm256_div_pd(z, y);
z = _mm256_mul_pd(x, x);
__m256d u = _mm256_add_pd(z, _mm256_set1_pd(-3.56722798256324312549E1));
__m256d t = _mm256_set1_pd(-7.89580278884799154124E-1);
u = _mm256_fmadd_pd(u, z, _mm256_set1_pd(3.12093766372244180303E2));
t = _mm256_fmadd_pd(t, z, _mm256_set1_pd(1.63866645699558079767E1));
u = _mm256_fmadd_pd(u, z, _mm256_set1_pd(-7.69691943550460008604E2));
t = _mm256_fmadd_pd(t, z, _mm256_set1_pd(-6.41409952958715622951E1));
y = _mm256_fmadd_pd(z, _mm256_div_pd(t, u), _mm256_add_pd(half,half));
return _mm256_fmadd_pd(x, _mm256_mul_pd(y, _mm256_set1_pd(std::log2(std::exp(1.)))), dbl_e);
}
__m128i to128(__m256d v)
{ __m256i c = _mm256_castpd_si256(v); return _mm_packs_epi16(extract128(c,0), extract128(c,1)); }
__m256d ifelse(__m256i c, __m256d ok, __m256d nok) { return _mm256_blendv_pd(nok, ok, _mm256_castsi256_pd(c)); }
__m256d ifelse(__m128i c, __m256d ok, __m256d nok) { return ifelse(_mm256_cvtepi32_epi64(c), ok, nok); }
template<bool WithMoment>
__m256d Iterate(__m256d zr, __m256d zi)
{
const double escape_radius_squared = ESCAPE_RADIUS_SQUARED;
const int maxiter = MAXITER;
__m256d cr = zr, sr = cr;
__m256d ci = zi, si = ci;
__m256d dist = _mm256_set1_pd(0.0), limit = _mm256_set1_pd(escape_radius_squared);
__m128i one = _mm_set1_epi32(1), zero = _mm_setzero_si128();
__m256d i2 = _mm256_mul_pd(ci,ci), r2 = _mm256_mul_pd(cr,cr);
__m128i notescaped = to128(_mm256_and_pd(
_mm256_cmp_pd(
_mm256_fmadd_pd(i2,
_mm256_fmadd_pd(i2, _mm256_set1_pd(8),
_mm256_fmadd_pd(r2, _mm256_set1_pd(16), _mm256_set1_pd(-3))),
_mm256_fmadd_pd(r2, _mm256_fmadd_pd(r2, _mm256_set1_pd(8), _mm256_set1_pd(-3)), cr)),
_mm256_set1_pd(3./32), _CMP_GE_OQ),
_mm256_cmp_pd(
_mm256_fmadd_pd(_mm256_add_pd(cr,_mm256_set1_pd(1)),_mm256_add_pd(cr,_mm256_set1_pd(1)), i2),
_mm256_set1_pd(1./16), _CMP_GE_OQ)));
__m128i iter = _mm_and_si128(_mm_set1_epi32(maxiter), notescaped);
while(!_mm_testz_si128(notescaped, notescaped))
{
dist = ifelse(notescaped, _mm256_fmadd_pd(cr,cr, i2), dist);
notescaped = _mm_and_si128(notescaped,
_mm_andnot_si128(_mm_cmpeq_epi32(iter, zero),
to128(_mm256_cmp_pd(dist, limit, _CMP_LT_OQ))));
iter = _mm_add_epi32(iter, notescaped);
ci = _mm256_fmadd_pd(_mm256_mul_pd(cr, ci), _mm256_set1_pd(2), zi);
cr = _mm256_fmadd_pd(cr,cr, _mm256_sub_pd(zr, i2));
i2 = _mm256_mul_pd(ci,ci);
if(WithMoment)
{
__m128i moment = _mm_cmpeq_epi32(_mm_and_si128(iter, _mm_sub_epi32(iter, one)), zero);
iter = _mm_andnot_si128(to128(_mm256_and_pd(_mm256_cmp_pd(cr,sr,_CMP_EQ_OQ),
_mm256_cmp_pd(ci,si,_CMP_EQ_OQ))), iter);
sr = ifelse(moment, cr, sr);
si = ifelse(moment, ci, si);
}
}
return _mm256_castsi256_pd(_mm256_andnot_si256(_mm256_cvtepi32_epi64(_mm_cmpeq_epi32(iter, zero)), _mm256_castpd_si256(
_mm256_mul_pd(_mm256_set1_pd(4/std::log2(std::exp(1.))),
_mm256_log2_pd(_mm256_add_pd(_mm256_cvtepi32_pd(_mm_sub_epi32(_mm_set1_epi32(maxiter), iter)),
_mm256_sub_pd(_mm256_set1_pd(1),
_mm256_log2_pd(_mm256_mul_pd(_mm256_log2_pd(dist),
_mm256_set1_pd(0.5))))))))));
}
int main()
{
bool NeedMoment = true;
MAINLOOP_START(1);
while(MAINLOOP_GET_CONDITION())
{
std::vector<unsigned> pixels (Xres * Yres);
double zr, zi, xscale, yscale; MAINLOOP_SET_COORDINATES();
#if defined(__AVX2__) || defined(__AVX512F__)
constexpr unsigned N=8;
#else
constexpr unsigned N=4;
#endif
switch(N)
{
case 4:
{
unsigned n_zeroes = 0;
#pragma omp parallel for schedule(dynamic) reduction(+:n_zeroes)
for(unsigned y=0; y<Yres; ++y)
{
__m128i num_zeroes = _mm_setzero_si128();
__m256d i = _mm256_set1_pd( zi+yscale*int(y-Yres/2) );
for(unsigned x=0; x<Xres/N*N; x += N)
{
__m256d r = _mm256_fmadd_pd(_mm256_set1_pd(xscale), _mm256_add_pd(_mm256_set_pd(3,2,1,0),
_mm256_set1_pd(int(x-Xres/2))),
_mm256_set1_pd(zr));
__m256d results = NeedMoment ? Iterate<true>(r,i) : Iterate<false>(r,i);
num_zeroes = _mm_sub_epi32(num_zeroes, to128(_mm256_cmp_pd(results, _mm256_setzero_pd(), _CMP_EQ_OQ)));
for(unsigned n=0; n<N; ++n) { pixels[y*Xres + x+n] = Color(x+n,y, results[n]); }
}
num_zeroes = _mm_add_epi32(num_zeroes, _mm_srli_si128(num_zeroes, 8)); // 0+2, 1+3, 2, 3
num_zeroes = _mm_hadd_epi32(num_zeroes, num_zeroes); // 0+2+1+3, ...
n_zeroes += _mm_extract_epi32(num_zeroes,0);
}
NeedMoment = n_zeroes >= int(Xres*Yres/1024);
break;
}
case 8:
{
unsigned n_zeroes = 0;
#pragma omp parallel for schedule(dynamic) reduction(+:n_zeroes)
for(unsigned y=0; y<Yres; ++y)
{
__m256i num_zeroes = _mm256_setzero_si256();
__m512d i = _mm512_set1_pd( zi+yscale*int(y-Yres/2) );
for(unsigned x=0; x<Xres/N*N; x += N)
{
__m512d r = _mm512_fmadd_pd(_mm512_set1_pd(xscale), _mm512_add_pd(_mm512_set_pd(7,6,5,4,3,2,1,0),
_mm512_set1_pd(int(x-Xres/2))),
_mm512_set1_pd(zr));
__m512d results = NeedMoment ? Iterate<true>(r,i) : Iterate<false>(r,i);
num_zeroes = _mm256_sub_epi32(num_zeroes, to256(_mm512_cmp_pd_mask(results, _mm512_setzero_pd(), _MM_CMPINT_EQ)));
for(unsigned n=0; n<N; ++n) { pixels[y*Xres + x+n] = Color(x+n,y, results[n]); }
}
__m128i z128 = _mm_add_epi32(extract128(num_zeroes,0), extract128(num_zeroes,1)); // 0+4, 1+5, 2+6, 3+7
z128 = _mm_add_epi32(z128, _mm_srli_si128(z128, 8)); // 0+4+2+6, 1+5+3+7, 2+6, 3+7
z128 = _mm_hadd_epi32(z128, z128); // 0+4+2+6+1+5+3+7, ...
n_zeroes += _mm_extract_epi32(z128,0);
}
NeedMoment = n_zeroes >= int(Xres*Yres/1024);
break;
}
}
MAINLOOP_PUT_RESULT(pixels);
}
MAINLOOP_FINISH();
}