Vectorized Class — pytorch Architecture
Architecture documentation for the Vectorized class in vec512_complex_double.h from the pytorch codebase.
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Source Code
aten/src/ATen/cpu/vec/vec512/vec512_complex_double.h lines 25–475
template <>
class Vectorized<c10::complex<double>> {
private:
__m512d values;
static constexpr __m512i zero_vector{0, 0, 0, 0, 0, 0, 0, 0};
public:
using value_type = c10::complex<double>;
using size_type = int;
static constexpr size_type size() {
return 4;
}
Vectorized() {
values = _mm512_setzero_pd();
}
Vectorized(__m512d v) : values(v) {}
Vectorized(c10::complex<double> val) {
double real_value = val.real();
double imag_value = val.imag();
values = _mm512_setr_pd(
real_value,
imag_value,
real_value,
imag_value,
real_value,
imag_value,
real_value,
imag_value);
}
Vectorized(
c10::complex<double> val1,
c10::complex<double> val2,
c10::complex<double> val3,
c10::complex<double> val4) {
values = _mm512_setr_pd(
val1.real(),
val1.imag(),
val2.real(),
val2.imag(),
val3.real(),
val3.imag(),
val4.real(),
val4.imag());
}
operator __m512d() const {
return values;
}
template <int64_t mask>
static Vectorized<c10::complex<double>> blend(
const Vectorized<c10::complex<double>>& a,
const Vectorized<c10::complex<double>>& b) {
// convert c10::complex<V> index mask to V index mask: xy -> xxyy
// NOLINTNEXTLINE(clang-diagnostic-warning)
switch (mask) {
case 0:
return a;
case 1:
return _mm512_mask_blend_pd(
0x03, a.values, b.values); // b0000 0001 = b0000 0011
case 2:
return _mm512_mask_blend_pd(
0x0C, a.values, b.values); // b0000 0010 = b0000 1100
case 3:
return _mm512_mask_blend_pd(
0x0F, a.values, b.values); // b0000 0011 = b0000 1111
case 4:
return _mm512_mask_blend_pd(
0x30, a.values, b.values); // b0000 0100 = b0011 0000
case 5:
return _mm512_mask_blend_pd(
0x33, a.values, b.values); // b0000 0101 = b0011 0011
case 6:
return _mm512_mask_blend_pd(
0x3C, a.values, b.values); // b0000 0110 = b0011 1100
case 7:
return _mm512_mask_blend_pd(
0x3F, a.values, b.values); // b0000 0111 = b0011 1111
case 8:
return _mm512_mask_blend_pd(
0xC0, a.values, b.values); // b0000 1000 = b1100 0000
case 9:
return _mm512_mask_blend_pd(
0xC3, a.values, b.values); // b0000 1001 = b1100 0011
case 10:
return _mm512_mask_blend_pd(
0xCC, a.values, b.values); // b0000 1010 = b1100 1100
case 11:
return _mm512_mask_blend_pd(
0xCF, a.values, b.values); // b0000 1011 = b1100 1111
case 12:
return _mm512_mask_blend_pd(
0xF0, a.values, b.values); // b0000 1100 = b1111 0000
case 13:
return _mm512_mask_blend_pd(
0xF3, a.values, b.values); // b0000 1101 = b1111 0011
case 14:
return _mm512_mask_blend_pd(
0xFC, a.values, b.values); // b0000 1110 = b1111 1100
case 15:
return _mm512_mask_blend_pd(
0xFF, a.values, b.values); // b0000 1111 = b1111 1111
}
return b;
}
static Vectorized<c10::complex<double>> blendv(
const Vectorized<c10::complex<double>>& a,
const Vectorized<c10::complex<double>>& b,
const Vectorized<c10::complex<double>>& mask) {
// convert c10::complex<V> index mask to V index mask: xy -> xxyy
auto mask_ = _mm512_unpacklo_pd(mask.values, mask.values);
auto all_ones = _mm512_set1_epi64(0xFFFFFFFFFFFFFFFF);
auto mmask = _mm512_cmp_epi64_mask(
_mm512_castpd_si512(mask_), all_ones, _MM_CMPINT_EQ);
return _mm512_mask_blend_pd(mmask, a.values, b.values);
}
template <typename step_t>
static Vectorized<c10::complex<double>> arange(
c10::complex<double> base = 0.,
step_t step = static_cast<step_t>(1)) {
return Vectorized<c10::complex<double>>(
base,
base + c10::complex<double>(1) * step,
base + c10::complex<double>(2) * step,
base + c10::complex<double>(3) * step);
}
static Vectorized<c10::complex<double>> set(
const Vectorized<c10::complex<double>>& a,
const Vectorized<c10::complex<double>>& b,
int64_t count = size()) {
switch (count) {
case 0:
return a;
case 1:
return blend<1>(a, b);
case 2:
return blend<3>(a, b);
case 3:
return blend<7>(a, b);
}
return b;
}
static Vectorized<c10::complex<double>> loadu(
const void* ptr,
int64_t count = size()) {
if (count == size())
return _mm512_loadu_pd(reinterpret_cast<const double*>(ptr));
__at_align__ double tmp_values[2 * size()];
// Ensure uninitialized memory does not change the output value See
// https://github.com/pytorch/pytorch/issues/32502 for more details. We do
// not initialize arrays to zero using "={0}" because gcc would compile it
// to two instructions while a loop would be compiled to one instruction.
for (const auto i : c10::irange(2 * size())) {
tmp_values[i] = 0.0;
}
std::memcpy(
tmp_values,
reinterpret_cast<const double*>(ptr),
count * sizeof(c10::complex<double>));
return _mm512_load_pd(tmp_values);
}
void store(void* ptr, int count = size()) const {
if (count == size()) {
_mm512_storeu_pd(reinterpret_cast<double*>(ptr), values);
} else if (count > 0) {
double tmp_values[2 * size()];
_mm512_storeu_pd(reinterpret_cast<double*>(tmp_values), values);
std::memcpy(ptr, tmp_values, count * sizeof(c10::complex<double>));
}
}
const c10::complex<double>& operator[](int idx) const = delete;
c10::complex<double>& operator[](int idx) = delete;
Vectorized<c10::complex<double>> map(
c10::complex<double> (*const f)(const c10::complex<double>&)) const {
__at_align__ c10::complex<double> tmp[size()];
store(tmp);
for (const auto i : c10::irange(size())) {
tmp[i] = f(tmp[i]);
}
return loadu(tmp);
}
// AVX512 doesn't have horizontal add & horizontal sub instructions.
// TODO: hadd_pd() & hsub_pd() may have scope for improvement.
static inline __m512d hadd_pd(__m512d a, __m512d b) {
__m512i idx1 = _mm512_set_epi64(14, 6, 12, 4, 10, 2, 8, 0);
__m512i idx2 = _mm512_set_epi64(15, 7, 13, 5, 11, 3, 9, 1);
return _mm512_add_pd(
_mm512_mask_permutex2var_pd(a, 0xff, idx1, b),
_mm512_mask_permutex2var_pd(a, 0xff, idx2, b));
}
static inline __m512d hsub_pd(__m512d a, __m512d b) {
__m512i idx1 = _mm512_set_epi64(14, 6, 12, 4, 10, 2, 8, 0);
__m512i idx2 = _mm512_set_epi64(15, 7, 13, 5, 11, 3, 9, 1);
return _mm512_sub_pd(
_mm512_mask_permutex2var_pd(a, 0xff, idx1, b),
_mm512_mask_permutex2var_pd(a, 0xff, idx2, b));
}
__m512d abs_2_() const {
auto val_2 = _mm512_mul_pd(values, values); // a*a b*b
return hadd_pd(val_2, val_2); // a*a+b*b a*a+b*b
}
__m512d abs_() const {
auto real = _mm512_movedup_pd(values); // real real
// movehdup_pd does not exist...
auto imag = _mm512_permute_pd(values, 0xff); // imag imag
return Sleef_hypotd8_u05(real, imag); // abs abs
}
Vectorized<c10::complex<double>> abs() const {
const __m512d real_mask = _mm512_castsi512_pd(_mm512_setr_epi64(
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000));
return _mm512_and_pd(abs_(), real_mask); // abs 0
}
__m512d angle_() const {
// angle = atan2(b/a)
auto b_a = _mm512_permute_pd(values, 0x55); // b a
return Sleef_atan2d8_u10(values, b_a); // 90-angle angle
}
Vectorized<c10::complex<double>> angle() const {
const __m512d real_mask = _mm512_castsi512_pd(_mm512_setr_epi64(
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000));
auto angle = _mm512_permute_pd(angle_(), 0x55); // angle 90-angle
return _mm512_and_pd(angle, real_mask); // angle 0
}
Vectorized<c10::complex<double>> sgn() const {
auto abs = abs_();
auto zero = _mm512_setzero_pd();
auto mask = _mm512_cmp_pd_mask(abs, zero, _CMP_EQ_OQ);
auto div = _mm512_div_pd(values, abs);
return _mm512_mask_blend_pd(mask, div, zero);
}
__m512d real_() const {
const __m512d real_mask = _mm512_castsi512_pd(_mm512_setr_epi64(
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000));
return _mm512_and_pd(values, real_mask);
}
Vectorized<c10::complex<double>> real() const {
return real_();
}
__m512d imag_() const {
const __m512d imag_mask = _mm512_castsi512_pd(_mm512_setr_epi64(
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF,
0x0000000000000000,
0xFFFFFFFFFFFFFFFF));
return _mm512_and_pd(values, imag_mask);
}
Vectorized<c10::complex<double>> imag() const {
return _mm512_permute_pd(imag_(), 0x55); // b a
}
__m512d conj_() const {
const __m512d sign_mask =
_mm512_setr_pd(0.0, -0.0, 0.0, -0.0, 0.0, -0.0, 0.0, -0.0);
return _mm512_xor_pd(values, sign_mask); // a -b
}
Vectorized<c10::complex<double>> conj() const {
return conj_();
}
Vectorized<c10::complex<double>> log() const {
// Most trigonomic ops use the log() op to improve complex number
// performance.
return map(std::log);
}
Vectorized<c10::complex<double>> log2() const {
const __m512d log2_ = _mm512_set1_pd(std::log(2));
return _mm512_div_pd(log(), log2_);
}
Vectorized<c10::complex<double>> log10() const {
const __m512d log10_ = _mm512_set1_pd(std::log(10));
return _mm512_div_pd(log(), log10_);
}
Vectorized<c10::complex<double>> log1p() const {
return map(std::log1p);
}
Vectorized<c10::complex<double>> asin() const {
// TODO: The vectorized implementation requires special handling for the
// case where real number/imag number is 0/Inf/NaN.
// // asin(x)
// // = -i*ln(iz + sqrt(1 -z^2))
// // = -i*ln((ai - b) + sqrt(1 - (a + bi)*(a + bi)))
// // = -i*ln((-b + ai) + sqrt(1 - (a**2 - b**2) - 2*abi))
// const __m512d one = _mm512_set1_pd(1);
// auto conj = conj_();
// auto b_a = _mm512_permute_pd(conj, 0x55); //-b a
// auto ab = _mm512_mul_pd(conj, b_a); //-ab
// -ab auto im = _mm512_add_pd(ab, ab); //-2ab -2ab
// auto val_2 = _mm512_mul_pd(values, values); // a*a
// b*b auto re = hsub_pd(val_2, _mm512_permute_pd(val_2, 0x55)); // a*a-b*b
// b*b-a*a re = _mm512_sub_pd(one, re);
// auto root = Vectorized(_mm512_mask_blend_pd(0xAA, re, im)).sqrt();
// //sqrt(re + i*im) auto ln = Vectorized(_mm512_add_pd(b_a, root)).log();
// //ln(iz + sqrt()) return Vectorized(_mm512_permute_pd(ln.values,
// 0x55)).conj(); //-i*ln()
return map(std::asin);
}
Vectorized<c10::complex<double>> acos() const {
// acos(x) = pi/2 - asin(x)
constexpr auto pi_2d = c10::pi<double> / 2;
const __m512d pi_2 =
_mm512_setr_pd(pi_2d, 0.0, pi_2d, 0.0, pi_2d, 0.0, pi_2d, 0.0);
return _mm512_sub_pd(pi_2, asin());
}
Vectorized<c10::complex<double>> atan() const;
Vectorized<c10::complex<double>> atanh() const {
return map(std::atanh);
}
Vectorized<c10::complex<double>> exp() const {
// TODO: The vectorized implementation requires special handling for the
// case where real number/imag number is 0/Inf/NaN.
// //exp(a + bi)
// // = exp(a)*(cos(b) + sin(b)i)
// auto exp = Sleef_expd8_u10(values); //exp(a) exp(b) exp =
// _mm512_mask_blend_pd(0xAA, exp, _mm512_permute_pd(exp, 0x55)); //exp(a)
// exp(a)
// auto sin_cos = Sleef_sincosd8_u10(values); //[sin(a), cos(a)] [sin(b),
// cos(b)] auto cos_sin = _mm512_mask_blend_pd(0xAA,
// _mm512_permute_pd(sin_cos.y, 0x55),
// sin_cos.x); //cos(b)
// sin(b)
// return _mm512_mul_pd(exp, cos_sin);
return map(std::exp);
}
Vectorized<c10::complex<double>> exp2() const {
// Use identity 2**x = exp(log(2) * x)
const __m512d ln_2 = _mm512_set1_pd(c10::ln_2<double>);
Vectorized<c10::complex<double>> scaled_values =
_mm512_mul_pd(values, ln_2);
return scaled_values.exp();
}
Vectorized<c10::complex<double>> expm1() const {
return map(std::expm1);
}
Vectorized<c10::complex<double>> sin() const {
return map(std::sin);
}
Vectorized<c10::complex<double>> sinh() const {
return map(std::sinh);
}
Vectorized<c10::complex<double>> cos() const {
return map(std::cos);
}
Vectorized<c10::complex<double>> cosh() const {
return map(std::cosh);
}
Vectorized<c10::complex<double>> ceil() const {
return _mm512_ceil_pd(values);
}
Vectorized<c10::complex<double>> floor() const {
return _mm512_floor_pd(values);
}
Vectorized<c10::complex<double>> neg() const {
auto zero = _mm512_setzero_pd();
return _mm512_sub_pd(zero, values);
}
Vectorized<c10::complex<double>> round() const {
return _mm512_roundscale_pd(
values, (_MM_FROUND_TO_NEAREST_INT | _MM_FROUND_NO_EXC));
}
Vectorized<c10::complex<double>> tan() const {
return map(std::tan);
}
Vectorized<c10::complex<double>> tanh() const {
return map(std::tanh);
}
Vectorized<c10::complex<double>> trunc() const {
return _mm512_roundscale_pd(
values, (_MM_FROUND_TO_ZERO | _MM_FROUND_NO_EXC));
}
Vectorized<c10::complex<double>> sqrt() const {
return map(std::sqrt);
}
Vectorized<c10::complex<double>> reciprocal() const;
Vectorized<c10::complex<double>> rsqrt() const {
return sqrt().reciprocal();
}
Vectorized<c10::complex<double>> pow(
const Vectorized<c10::complex<double>>& exp) const {
__at_align__ c10::complex<double> x_tmp[size()];
__at_align__ c10::complex<double> y_tmp[size()];
store(x_tmp);
exp.store(y_tmp);
for (const auto i : c10::irange(size())) {
x_tmp[i] = std::pow(x_tmp[i], y_tmp[i]);
}
return loadu(x_tmp);
}
// Comparison using the _CMP_**_OQ predicate.
// `O`: get false if an operand is NaN
// `Q`: do not raise if an operand is NaN
Vectorized<c10::complex<double>> operator==(
const Vectorized<c10::complex<double>>& other) const {
auto mask = _mm512_cmp_pd_mask(values, other.values, _CMP_EQ_OQ);
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(zero_vector, mask, 0xFFFFFFFFFFFFFFFF));
}
Vectorized<c10::complex<double>> operator!=(
const Vectorized<c10::complex<double>>& other) const {
auto mask = _mm512_cmp_pd_mask(values, other.values, _CMP_NEQ_UQ);
return _mm512_castsi512_pd(
_mm512_mask_set1_epi64(zero_vector, mask, 0xFFFFFFFFFFFFFFFF));
}
Vectorized<c10::complex<double>> operator<(
const Vectorized<c10::complex<double>>& other [[maybe_unused]]) const {
TORCH_CHECK(false, "not supported for complex numbers");
}
Vectorized<c10::complex<double>> operator<=(
const Vectorized<c10::complex<double>>& other [[maybe_unused]]) const {
TORCH_CHECK(false, "not supported for complex numbers");
}
Vectorized<c10::complex<double>> operator>(
const Vectorized<c10::complex<double>>& other [[maybe_unused]]) const {
TORCH_CHECK(false, "not supported for complex numbers");
}
Vectorized<c10::complex<double>> operator>=(
const Vectorized<c10::complex<double>>& other [[maybe_unused]]) const {
TORCH_CHECK(false, "not supported for complex numbers");
}
Vectorized<c10::complex<double>> eq(
const Vectorized<c10::complex<double>>& other) const;
Vectorized<c10::complex<double>> ne(
const Vectorized<c10::complex<double>>& other) const;
};Source
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