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volk_avx2_intrinsics.h
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/* -*- c++ -*- */
/*
* Copyright 2015 Free Software Foundation, Inc.
* Copyright 2023 Magnus Lundmark <magnuslundmark@gmail.com>
*
* This file is part of VOLK
*
* SPDX-License-Identifier: LGPL-3.0-or-later
*/
/*
* This file is intended to hold AVX2 intrinsics of intrinsics.
* They should be used in VOLK kernels to avoid copy-paste.
*/
#ifndef INCLUDE_VOLK_VOLK_AVX2_INTRINSICS_H_
#define INCLUDE_VOLK_VOLK_AVX2_INTRINSICS_H_
#include "volk/volk_avx_intrinsics.h"
#include <immintrin.h>
/*
* Newton-Raphson refined reciprocal square root: 1/sqrt(a)
* AVX2 version with native 256-bit integer operations for edge case handling
* Handles edge cases: +0 → +Inf, +Inf → 0
*/
static inline __m256 _mm256_rsqrt_nr_avx2(const __m256 a)
{
const __m256 HALF = _mm256_set1_ps(0.5f);
const __m256 THREE_HALFS = _mm256_set1_ps(1.5f);
const __m256 x0 = _mm256_rsqrt_ps(a); // +Inf for +0, 0 for +Inf
// Newton-Raphson: x1 = x0 * (1.5 - 0.5 * a * x0^2)
__m256 x1 = _mm256_mul_ps(
x0,
_mm256_sub_ps(THREE_HALFS,
_mm256_mul_ps(HALF, _mm256_mul_ps(_mm256_mul_ps(x0, x0), a))));
// For +0 and +Inf inputs, x0 is correct but NR produces NaN due to Inf*0
// AVX2: native 256-bit integer compare
__m256i a_si = _mm256_castps_si256(a);
__m256i zero_mask = _mm256_cmpeq_epi32(a_si, _mm256_setzero_si256());
__m256i inf_mask = _mm256_cmpeq_epi32(a_si, _mm256_set1_epi32(0x7F800000));
__m256 special_mask = _mm256_castsi256_ps(_mm256_or_si256(zero_mask, inf_mask));
return _mm256_blendv_ps(x1, x0, special_mask);
}
static inline __m256 _mm256_real(const __m256 z1, const __m256 z2)
{
const __m256i permute_mask = _mm256_set_epi32(7, 6, 3, 2, 5, 4, 1, 0);
__m256 r = _mm256_shuffle_ps(z1, z2, _MM_SHUFFLE(2, 0, 2, 0));
return _mm256_permutevar8x32_ps(r, permute_mask);
}
static inline __m256 _mm256_imag(const __m256 z1, const __m256 z2)
{
const __m256i permute_mask = _mm256_set_epi32(7, 6, 3, 2, 5, 4, 1, 0);
__m256 i = _mm256_shuffle_ps(z1, z2, _MM_SHUFFLE(3, 1, 3, 1));
return _mm256_permutevar8x32_ps(i, permute_mask);
}
static inline __m256 _mm256_polar_sign_mask_avx2(__m128i fbits)
{
const __m128i zeros = _mm_set1_epi8(0x00);
const __m128i sign_extract = _mm_set1_epi8(0x80);
const __m256i shuffle_mask = _mm256_setr_epi8(0xff,
0xff,
0xff,
0x00,
0xff,
0xff,
0xff,
0x01,
0xff,
0xff,
0xff,
0x02,
0xff,
0xff,
0xff,
0x03,
0xff,
0xff,
0xff,
0x04,
0xff,
0xff,
0xff,
0x05,
0xff,
0xff,
0xff,
0x06,
0xff,
0xff,
0xff,
0x07);
__m256i sign_bits = _mm256_setzero_si256();
fbits = _mm_cmpgt_epi8(fbits, zeros);
fbits = _mm_and_si128(fbits, sign_extract);
sign_bits = _mm256_insertf128_si256(sign_bits, fbits, 0);
sign_bits = _mm256_insertf128_si256(sign_bits, fbits, 1);
sign_bits = _mm256_shuffle_epi8(sign_bits, shuffle_mask);
return _mm256_castsi256_ps(sign_bits);
}
static inline __m256
_mm256_polar_fsign_add_llrs_avx2(__m256 src0, __m256 src1, __m128i fbits)
{
// prepare sign mask for correct +-
__m256 sign_mask = _mm256_polar_sign_mask_avx2(fbits);
__m256 llr0, llr1;
_mm256_polar_deinterleave(&llr0, &llr1, src0, src1);
// calculate result
llr0 = _mm256_xor_ps(llr0, sign_mask);
__m256 dst = _mm256_add_ps(llr0, llr1);
return dst;
}
static inline __m256 _mm256_magnitudesquared_ps_avx2(const __m256 cplxValue0,
const __m256 cplxValue1)
{
const __m256i idx = _mm256_set_epi32(7, 6, 3, 2, 5, 4, 1, 0);
const __m256 squared0 = _mm256_mul_ps(cplxValue0, cplxValue0); // Square the values
const __m256 squared1 = _mm256_mul_ps(cplxValue1, cplxValue1); // Square the Values
const __m256 complex_result = _mm256_hadd_ps(squared0, squared1);
return _mm256_permutevar8x32_ps(complex_result, idx);
}
static inline __m256 _mm256_scaled_norm_dist_ps_avx2(const __m256 symbols0,
const __m256 symbols1,
const __m256 points0,
const __m256 points1,
const __m256 scalar)
{
/*
* Calculate: |y - x|^2 * SNR_lin
* Consider 'symbolsX' and 'pointsX' to be complex float
* 'symbolsX' are 'y' and 'pointsX' are 'x'
*/
const __m256 diff0 = _mm256_sub_ps(symbols0, points0);
const __m256 diff1 = _mm256_sub_ps(symbols1, points1);
const __m256 norms = _mm256_magnitudesquared_ps_avx2(diff0, diff1);
return _mm256_mul_ps(norms, scalar);
}
/*
* The function below vectorizes the inner loop of the following code:
*
* float max_values[8] = {0.f};
* unsigned max_indices[8] = {0};
* unsigned current_indices[8] = {0, 1, 2, 3, 4, 5, 6, 7};
* for (unsigned i = 0; i < num_points / 8; ++i) {
* for (unsigned j = 0; j < 8; ++j) {
* float abs_squared = real(src0) * real(src0) + imag(src0) * imag(src1)
* bool compare = abs_squared > max_values[j];
* max_values[j] = compare ? abs_squared : max_values[j];
* max_indices[j] = compare ? current_indices[j] : max_indices[j]
* current_indices[j] += 8; // update for next outer loop iteration
* ++src0;
* }
* }
*/
static inline void vector_32fc_index_max_variant0(__m256 in0,
__m256 in1,
__m256* max_values,
__m256i* max_indices,
__m256i* current_indices,
__m256i indices_increment)
{
in0 = _mm256_mul_ps(in0, in0);
in1 = _mm256_mul_ps(in1, in1);
/*
* Given the vectors a = (a_7, a_6, …, a_1, a_0) and b = (b_7, b_6, …, b_1, b_0)
* hadd_ps(a, b) computes
* (b_7 + b_6,
* b_5 + b_4,
* ---------
* a_7 + b_6,
* a_5 + a_4,
* ---------
* b_3 + b_2,
* b_1 + b_0,
* ---------
* a_3 + a_2,
* a_1 + a_0).
* The result is the squared absolute value of complex numbers at index
* offsets (7, 6, 3, 2, 5, 4, 1, 0). This must be the initial value of
* current_indices!
*/
__m256 abs_squared = _mm256_hadd_ps(in0, in1);
/*
* Compare the recently computed squared absolute values with the
* previously determined maximum values. cmp_ps(a, b) determines
* a > b ? 0xFFFFFFFF for each element in the vectors =>
* compare_mask = abs_squared > max_values ? 0xFFFFFFFF : 0
*
* If either operand is NaN, 0 is returned as an “ordered” comparision is
* used => the blend operation will select the value from *max_values.
*/
__m256 compare_mask = _mm256_cmp_ps(abs_squared, *max_values, _CMP_GT_OS);
/* Select maximum by blending. This is the only line which differs from variant1 */
*max_values = _mm256_blendv_ps(*max_values, abs_squared, compare_mask);
/*
* Updates indices: blendv_ps(a, b, mask) determines mask ? b : a for
* each element in the vectors =>
* max_indices = compare_mask ? current_indices : max_indices
*
* Note: The casting of data types is required to make the compiler happy
* and does not change values.
*/
*max_indices =
_mm256_castps_si256(_mm256_blendv_ps(_mm256_castsi256_ps(*max_indices),
_mm256_castsi256_ps(*current_indices),
compare_mask));
/* compute indices of complex numbers which will be loaded in the next iteration */
*current_indices = _mm256_add_epi32(*current_indices, indices_increment);
}
/* See _variant0 for details */
static inline void vector_32fc_index_max_variant1(__m256 in0,
__m256 in1,
__m256* max_values,
__m256i* max_indices,
__m256i* current_indices,
__m256i indices_increment)
{
in0 = _mm256_mul_ps(in0, in0);
in1 = _mm256_mul_ps(in1, in1);
__m256 abs_squared = _mm256_hadd_ps(in0, in1);
__m256 compare_mask = _mm256_cmp_ps(abs_squared, *max_values, _CMP_GT_OS);
/*
* This is the only line which differs from variant0. Using maxps instead of
* blendvps is faster on Intel CPUs (on the ones tested with).
*
* Note: The order of arguments matters if a NaN is encountered in which
* case the value of the second argument is selected. This is consistent
* with the “ordered” comparision and the blend operation: The comparision
* returns false if a NaN is encountered and the blend operation
* consequently selects the value from max_indices.
*/
*max_values = _mm256_max_ps(abs_squared, *max_values);
*max_indices =
_mm256_castps_si256(_mm256_blendv_ps(_mm256_castsi256_ps(*max_indices),
_mm256_castsi256_ps(*current_indices),
compare_mask));
*current_indices = _mm256_add_epi32(*current_indices, indices_increment);
}
/*
* The function below vectorizes the inner loop of the following code:
*
* float min_values[8] = {FLT_MAX};
* unsigned min_indices[8] = {0};
* unsigned current_indices[8] = {0, 1, 2, 3, 4, 5, 6, 7};
* for (unsigned i = 0; i < num_points / 8; ++i) {
* for (unsigned j = 0; j < 8; ++j) {
* float abs_squared = real(src0) * real(src0) + imag(src0) * imag(src1)
* bool compare = abs_squared < min_values[j];
* min_values[j] = compare ? abs_squared : min_values[j];
* min_indices[j] = compare ? current_indices[j] : min_indices[j]
* current_indices[j] += 8; // update for next outer loop iteration
* ++src0;
* }
* }
*/
static inline void vector_32fc_index_min_variant0(__m256 in0,
__m256 in1,
__m256* min_values,
__m256i* min_indices,
__m256i* current_indices,
__m256i indices_increment)
{
in0 = _mm256_mul_ps(in0, in0);
in1 = _mm256_mul_ps(in1, in1);
/*
* Given the vectors a = (a_7, a_6, …, a_1, a_0) and b = (b_7, b_6, …, b_1, b_0)
* hadd_ps(a, b) computes
* (b_7 + b_6,
* b_5 + b_4,
* ---------
* a_7 + b_6,
* a_5 + a_4,
* ---------
* b_3 + b_2,
* b_1 + b_0,
* ---------
* a_3 + a_2,
* a_1 + a_0).
* The result is the squared absolute value of complex numbers at index
* offsets (7, 6, 3, 2, 5, 4, 1, 0). This must be the initial value of
* current_indices!
*/
__m256 abs_squared = _mm256_hadd_ps(in0, in1);
/*
* Compare the recently computed squared absolute values with the
* previously determined minimum values. cmp_ps(a, b) determines
* a < b ? 0xFFFFFFFF for each element in the vectors =>
* compare_mask = abs_squared < min_values ? 0xFFFFFFFF : 0
*
* If either operand is NaN, 0 is returned as an “ordered” comparision is
* used => the blend operation will select the value from *min_values.
*/
__m256 compare_mask = _mm256_cmp_ps(abs_squared, *min_values, _CMP_LT_OS);
/* Select minimum by blending. This is the only line which differs from variant1 */
*min_values = _mm256_blendv_ps(*min_values, abs_squared, compare_mask);
/*
* Updates indices: blendv_ps(a, b, mask) determines mask ? b : a for
* each element in the vectors =>
* min_indices = compare_mask ? current_indices : min_indices
*
* Note: The casting of data types is required to make the compiler happy
* and does not change values.
*/
*min_indices =
_mm256_castps_si256(_mm256_blendv_ps(_mm256_castsi256_ps(*min_indices),
_mm256_castsi256_ps(*current_indices),
compare_mask));
/* compute indices of complex numbers which will be loaded in the next iteration */
*current_indices = _mm256_add_epi32(*current_indices, indices_increment);
}
/* See _variant0 for details */
static inline void vector_32fc_index_min_variant1(__m256 in0,
__m256 in1,
__m256* min_values,
__m256i* min_indices,
__m256i* current_indices,
__m256i indices_increment)
{
in0 = _mm256_mul_ps(in0, in0);
in1 = _mm256_mul_ps(in1, in1);
__m256 abs_squared = _mm256_hadd_ps(in0, in1);
__m256 compare_mask = _mm256_cmp_ps(abs_squared, *min_values, _CMP_LT_OS);
/*
* This is the only line which differs from variant0. Using maxps instead of
* blendvps is faster on Intel CPUs (on the ones tested with).
*
* Note: The order of arguments matters if a NaN is encountered in which
* case the value of the second argument is selected. This is consistent
* with the “ordered” comparision and the blend operation: The comparision
* returns false if a NaN is encountered and the blend operation
* consequently selects the value from min_indices.
*/
*min_values = _mm256_min_ps(abs_squared, *min_values);
*min_indices =
_mm256_castps_si256(_mm256_blendv_ps(_mm256_castsi256_ps(*min_indices),
_mm256_castsi256_ps(*current_indices),
compare_mask));
*current_indices = _mm256_add_epi32(*current_indices, indices_increment);
}
/*
* Approximate sin(x) via polynomial expansion
* on the interval [-pi/4, pi/4]
*
* Maximum absolute error ~7.3e-9
* sin(x) = x + x^3 * (s1 + x^2 * (s2 + x^2 * s3))
*/
static inline __m256 _mm256_sin_poly_avx2(const __m256 x)
{
const __m256 s1 = _mm256_set1_ps(-0x1.555552p-3f);
const __m256 s2 = _mm256_set1_ps(+0x1.110be2p-7f);
const __m256 s3 = _mm256_set1_ps(-0x1.9ab22ap-13f);
const __m256 x2 = _mm256_mul_ps(x, x);
const __m256 x3 = _mm256_mul_ps(x2, x);
__m256 poly = _mm256_add_ps(_mm256_mul_ps(x2, s3), s2);
poly = _mm256_add_ps(_mm256_mul_ps(x2, poly), s1);
return _mm256_add_ps(_mm256_mul_ps(x3, poly), x);
}
/*
* Approximate cos(x) via polynomial expansion
* on the interval [-pi/4, pi/4]
*
* Maximum absolute error ~1.1e-7
* cos(x) = 1 + x^2 * (c1 + x^2 * (c2 + x^2 * c3))
*/
static inline __m256 _mm256_cos_poly_avx2(const __m256 x)
{
const __m256 c1 = _mm256_set1_ps(-0x1.fffff4p-2f);
const __m256 c2 = _mm256_set1_ps(+0x1.554a46p-5f);
const __m256 c3 = _mm256_set1_ps(-0x1.661be2p-10f);
const __m256 one = _mm256_set1_ps(1.0f);
const __m256 x2 = _mm256_mul_ps(x, x);
__m256 poly = _mm256_add_ps(_mm256_mul_ps(x2, c3), c2);
poly = _mm256_add_ps(_mm256_mul_ps(x2, poly), c1);
return _mm256_add_ps(_mm256_mul_ps(x2, poly), one);
}
/*
* Polynomial coefficients for log2(x)/(x-1) on [1, 2]
* Generated with Sollya: remez(log2(x)/(x-1), 6, [1+1b-20, 2])
* Max error: ~1.55e-6
*
* Usage: log2(x) ≈ poly(x) * (x - 1) for x ∈ [1, 2]
* Polynomial evaluated via Horner's method
*/
static inline __m256 _mm256_log2_poly_avx2(const __m256 x)
{
const __m256 c0 = _mm256_set1_ps(+0x1.a8a726p+1f);
const __m256 c1 = _mm256_set1_ps(-0x1.0b7f7ep+2f);
const __m256 c2 = _mm256_set1_ps(+0x1.05d9ccp+2f);
const __m256 c3 = _mm256_set1_ps(-0x1.4d476cp+1f);
const __m256 c4 = _mm256_set1_ps(+0x1.04fc3ap+0f);
const __m256 c5 = _mm256_set1_ps(-0x1.c97982p-3f);
const __m256 c6 = _mm256_set1_ps(+0x1.57aa42p-6f);
// Horner's method: c0 + x*(c1 + x*(c2 + ...))
__m256 poly = c6;
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c5);
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c4);
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c3);
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c2);
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c1);
poly = _mm256_add_ps(_mm256_mul_ps(poly, x), c0);
return poly;
}
#endif /* INCLUDE_VOLK_VOLK_AVX2_INTRINSICS_H_ */