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volk_avx_intrinsics.h
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/* -*- c++ -*- */
/*
* Copyright 2015 Free Software Foundation, Inc.
* Copyright 2023-2026 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 AVX intrinsics.
* They should be used in VOLK kernels to avoid copy-pasta.
*/
#ifndef INCLUDE_VOLK_VOLK_AVX_INTRINSICS_H_
#define INCLUDE_VOLK_VOLK_AVX_INTRINSICS_H_
#include <immintrin.h>
/*
* Newton-Raphson refined reciprocal square root: 1/sqrt(a)
* One iteration doubles precision from ~12-bit to ~24-bit
* x1 = x0 * (1.5 - 0.5 * a * x0^2)
* Handles edge cases: +0 → +Inf, +Inf → 0
*/
static inline __m256 _mm256_rsqrt_nr_ps(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
// Blend: use x0 where a == +0 or a == +Inf, else use x1
// AVX-only: use SSE2 integer compare, then reconstruct AVX mask
__m128i a_lo = _mm256_castsi256_si128(_mm256_castps_si256(a));
__m128i a_hi = _mm_castps_si128(_mm256_extractf128_ps(a, 1));
__m128i zero_si = _mm_setzero_si128();
__m128i inf_si = _mm_set1_epi32(0x7F800000);
__m128i zero_mask_lo = _mm_cmpeq_epi32(a_lo, zero_si);
__m128i zero_mask_hi = _mm_cmpeq_epi32(a_hi, zero_si);
__m128i inf_mask_lo = _mm_cmpeq_epi32(a_lo, inf_si);
__m128i inf_mask_hi = _mm_cmpeq_epi32(a_hi, inf_si);
__m128 mask_lo = _mm_castsi128_ps(_mm_or_si128(zero_mask_lo, inf_mask_lo));
__m128 mask_hi = _mm_castsi128_ps(_mm_or_si128(zero_mask_hi, inf_mask_hi));
__m256 special_mask =
_mm256_insertf128_ps(_mm256_castps128_ps256(mask_lo), mask_hi, 1);
return _mm256_blendv_ps(x1, x0, special_mask);
}
/*
* Approximate arctan(x) via polynomial expansion
* on the interval [-1, 1]
*
* Maximum relative error ~6.5e-7
* Polynomial evaluated via Horner's method
*/
static inline __m256 _mm256_arctan_poly_avx(const __m256 x)
{
const __m256 a1 = _mm256_set1_ps(+0x1.ffffeap-1f);
const __m256 a3 = _mm256_set1_ps(-0x1.55437p-2f);
const __m256 a5 = _mm256_set1_ps(+0x1.972be6p-3f);
const __m256 a7 = _mm256_set1_ps(-0x1.1436ap-3f);
const __m256 a9 = _mm256_set1_ps(+0x1.5785aap-4f);
const __m256 a11 = _mm256_set1_ps(-0x1.2f3004p-5f);
const __m256 a13 = _mm256_set1_ps(+0x1.01a37cp-7f);
const __m256 x_times_x = _mm256_mul_ps(x, x);
__m256 arctan;
arctan = a13;
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a11);
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a9);
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a7);
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a5);
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a3);
arctan = _mm256_mul_ps(x_times_x, arctan);
arctan = _mm256_add_ps(arctan, a1);
arctan = _mm256_mul_ps(x, arctan);
return arctan;
}
/*
* Approximate arcsin(x) via polynomial expansion
* P(u) such that asin(x) = x * P(x^2) on |x| <= 0.5
*
* Maximum relative error ~1.5e-6
* Polynomial evaluated via Horner's method
*/
static inline __m256 _mm256_arcsin_poly_avx(const __m256 x)
{
const __m256 c0 = _mm256_set1_ps(0x1.ffffcep-1f);
const __m256 c1 = _mm256_set1_ps(0x1.55b648p-3f);
const __m256 c2 = _mm256_set1_ps(0x1.24d192p-4f);
const __m256 c3 = _mm256_set1_ps(0x1.0a788p-4f);
const __m256 u = _mm256_mul_ps(x, x);
__m256 p = c3;
p = _mm256_mul_ps(u, p);
p = _mm256_add_ps(p, c2);
p = _mm256_mul_ps(u, p);
p = _mm256_add_ps(p, c1);
p = _mm256_mul_ps(u, p);
p = _mm256_add_ps(p, c0);
return _mm256_mul_ps(x, p);
}
static inline __m256 _mm256_complexmul_ps(__m256 x, __m256 y)
{
__m256 yl, yh, tmp1, tmp2;
yl = _mm256_moveldup_ps(y); // Load yl with cr,cr,dr,dr ...
yh = _mm256_movehdup_ps(y); // Load yh with ci,ci,di,di ...
tmp1 = _mm256_mul_ps(x, yl); // tmp1 = ar*cr,ai*cr,br*dr,bi*dr ...
x = _mm256_shuffle_ps(x, x, 0xB1); // Re-arrange x to be ai,ar,bi,br ...
tmp2 = _mm256_mul_ps(x, yh); // tmp2 = ai*ci,ar*ci,bi*di,br*di
// ar*cr-ai*ci, ai*cr+ar*ci, br*dr-bi*di, bi*dr+br*di
return _mm256_addsub_ps(tmp1, tmp2);
}
static inline __m256 _mm256_conjugate_ps(__m256 x)
{
const __m256 conjugator = _mm256_setr_ps(0, -0.f, 0, -0.f, 0, -0.f, 0, -0.f);
return _mm256_xor_ps(x, conjugator); // conjugate y
}
static inline __m256 _mm256_complexconjugatemul_ps(const __m256 x, const __m256 y)
{
const __m256 nswap = _mm256_permute_ps(x, 0xb1);
const __m256 dreal = _mm256_moveldup_ps(y);
const __m256 dimag = _mm256_movehdup_ps(y);
const __m256 conjugator = _mm256_setr_ps(0, -0.f, 0, -0.f, 0, -0.f, 0, -0.f);
const __m256 dimagconj = _mm256_xor_ps(dimag, conjugator);
const __m256 multreal = _mm256_mul_ps(x, dreal);
const __m256 multimag = _mm256_mul_ps(nswap, dimagconj);
return _mm256_add_ps(multreal, multimag);
}
static inline __m256 _mm256_normalize_ps(__m256 val)
{
__m256 tmp1 = _mm256_mul_ps(val, val);
tmp1 = _mm256_hadd_ps(tmp1, tmp1);
tmp1 = _mm256_shuffle_ps(tmp1, tmp1, _MM_SHUFFLE(3, 1, 2, 0)); // equals 0xD8
tmp1 = _mm256_sqrt_ps(tmp1);
return _mm256_div_ps(val, tmp1);
}
static inline __m256 _mm256_magnitudesquared_ps(__m256 cplxValue1, __m256 cplxValue2)
{
__m256 complex1, complex2;
cplxValue1 = _mm256_mul_ps(cplxValue1, cplxValue1); // Square the values
cplxValue2 = _mm256_mul_ps(cplxValue2, cplxValue2); // Square the Values
complex1 = _mm256_permute2f128_ps(cplxValue1, cplxValue2, 0x20);
complex2 = _mm256_permute2f128_ps(cplxValue1, cplxValue2, 0x31);
return _mm256_hadd_ps(complex1, complex2); // Add the I2 and Q2 values
}
static inline __m256 _mm256_magnitude_ps(__m256 cplxValue1, __m256 cplxValue2)
{
return _mm256_sqrt_ps(_mm256_magnitudesquared_ps(cplxValue1, cplxValue2));
}
static inline __m256 _mm256_scaled_norm_dist_ps(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(diff0, diff1);
return _mm256_mul_ps(norms, scalar);
}
static inline __m256 _mm256_polar_sign_mask(__m128i fbits)
{
__m256 sign_mask_dummy = _mm256_setzero_ps();
const __m128i zeros = _mm_set1_epi8(0x00);
const __m128i sign_extract = _mm_set1_epi8(0x80);
const __m128i shuffle_mask0 = _mm_setr_epi8(0xff,
0xff,
0xff,
0x00,
0xff,
0xff,
0xff,
0x01,
0xff,
0xff,
0xff,
0x02,
0xff,
0xff,
0xff,
0x03);
const __m128i shuffle_mask1 = _mm_setr_epi8(0xff,
0xff,
0xff,
0x04,
0xff,
0xff,
0xff,
0x05,
0xff,
0xff,
0xff,
0x06,
0xff,
0xff,
0xff,
0x07);
fbits = _mm_cmpgt_epi8(fbits, zeros);
fbits = _mm_and_si128(fbits, sign_extract);
__m128i sign_bits0 = _mm_shuffle_epi8(fbits, shuffle_mask0);
__m128i sign_bits1 = _mm_shuffle_epi8(fbits, shuffle_mask1);
__m256 sign_mask =
_mm256_insertf128_ps(sign_mask_dummy, _mm_castsi128_ps(sign_bits0), 0x0);
return _mm256_insertf128_ps(sign_mask, _mm_castsi128_ps(sign_bits1), 0x1);
// This is the desired function call. Though it seems to be missing in GCC.
// Compare: https://www.intel.com/content/www/us/en/docs/intrinsics-guide/index.html
// return _mm256_set_m128(_mm_castsi128_ps(sign_bits1),
// _mm_castsi128_ps(sign_bits0));
}
static inline void
_mm256_polar_deinterleave(__m256* llr0, __m256* llr1, __m256 src0, __m256 src1)
{
// deinterleave values
__m256 part0 = _mm256_permute2f128_ps(src0, src1, 0x20);
__m256 part1 = _mm256_permute2f128_ps(src0, src1, 0x31);
*llr0 = _mm256_shuffle_ps(part0, part1, 0x88);
*llr1 = _mm256_shuffle_ps(part0, part1, 0xdd);
}
static inline __m256 _mm256_polar_minsum_llrs(__m256 src0, __m256 src1)
{
const __m256 sign_mask = _mm256_set1_ps(-0.0f);
const __m256 abs_mask =
_mm256_andnot_ps(sign_mask, _mm256_castsi256_ps(_mm256_set1_epi8(0xff)));
__m256 llr0, llr1;
_mm256_polar_deinterleave(&llr0, &llr1, src0, src1);
// calculate result
__m256 sign =
_mm256_xor_ps(_mm256_and_ps(llr0, sign_mask), _mm256_and_ps(llr1, sign_mask));
__m256 dst =
_mm256_min_ps(_mm256_and_ps(llr0, abs_mask), _mm256_and_ps(llr1, abs_mask));
return _mm256_or_ps(dst, sign);
}
static inline __m256 _mm256_polar_fsign_add_llrs(__m256 src0, __m256 src1, __m128i fbits)
{
// prepare sign mask for correct +-
__m256 sign_mask = _mm256_polar_sign_mask(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_accumulate_square_sum_ps(
__m256 sq_acc, __m256 acc, __m256 val, __m256 rec, __m256 aux)
{
aux = _mm256_mul_ps(aux, val);
aux = _mm256_sub_ps(aux, acc);
aux = _mm256_mul_ps(aux, aux);
aux = _mm256_mul_ps(aux, rec);
return _mm256_add_ps(sq_acc, aux);
}
/*
* 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_avx(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_AVX_INTRINSICS_H_ */