volk_32f_atan_32f.h

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/* -*- c++ -*- */
/*
 * Copyright 2014 Free Software Foundation, Inc.
 * Copyright 2023, 2024 Magnus Lundmark <magnuslundmark@gmail.com>
 *
 * This file is part of VOLK
 *
 * SPDX-License-Identifier: LGPL-3.0-or-later
 */

#include <math.h>
 
#ifndef INCLUDED_volk_32f_atan_32f_a_H
#define INCLUDED_volk_32f_atan_32f_a_H
 
#ifdef LV_HAVE_GENERIC
static inline void
volk_32f_atan_32f_generic(float* out, const float* in, unsigned int num_points)
{
    for (unsigned int number = 0; number < num_points; number++) {
        *out++ = atanf(*in++);
    }
}
#endif /* LV_HAVE_GENERIC */
 
#ifdef LV_HAVE_GENERIC
static inline void
volk_32f_atan_32f_polynomial(float* out, const float* in, unsigned int num_points)
{
    for (unsigned int number = 0; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_GENERIC */
 
#if LV_HAVE_AVX512F && LV_HAVE_AVX512DQ
#include <immintrin.h>
#include <volk/volk_avx512_intrinsics.h>
static inline void
volk_32f_atan_32f_a_avx512dq(float* out, const float* in, unsigned int num_points)
{
    const __m512 one = _mm512_set1_ps(1.f);
    const __m512 pi_over_2 = _mm512_set1_ps(0x1.921fb6p0f);
    const __m512 abs_mask = _mm512_castsi512_ps(_mm512_set1_epi32(0x7FFFFFFF));
    const __m512 sign_mask = _mm512_castsi512_ps(_mm512_set1_epi32(0x80000000));
 
    const unsigned int sixteenth_points = num_points / 16;
 
    for (unsigned int number = 0; number < sixteenth_points; number++) {
        __m512 x = _mm512_load_ps(in);
        in += 16;
        __mmask16 swap_mask =
            _mm512_cmp_ps_mask(_mm512_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m512 x_star = _mm512_mask_blend_ps(swap_mask, x, _mm512_rcp14_ps(x));
        __m512 result = _mm512_arctan_poly_avx512(x_star);
        __m512 term = _mm512_and_ps(x_star, sign_mask);
        term = _mm512_or_ps(pi_over_2, term);
        term = _mm512_sub_ps(term, result);
        result = _mm512_mask_blend_ps(swap_mask, result, term);
        _mm512_store_ps(out, result);
        out += 16;
    }
 
    for (unsigned int number = sixteenth_points * 16; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX512F && LV_HAVE_AVX512DQ for aligned */
 
#if LV_HAVE_AVX2 && LV_HAVE_FMA
#include <immintrin.h>
#include <volk/volk_avx2_fma_intrinsics.h>
static inline void
volk_32f_atan_32f_a_avx2_fma(float* out, const float* in, unsigned int num_points)
{
    const __m256 one = _mm256_set1_ps(1.f);
    const __m256 pi_over_2 = _mm256_set1_ps(0x1.921fb6p0f);
    const __m256 abs_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x7FFFFFFF));
    const __m256 sign_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x80000000));
 
    const unsigned int eighth_points = num_points / 8;
 
    for (unsigned int number = 0; number < eighth_points; number++) {
        __m256 x = _mm256_load_ps(in);
        in += 8;
        __m256 swap_mask = _mm256_cmp_ps(_mm256_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m256 x_star = _mm256_blendv_ps(x, _mm256_rcp_ps(x), swap_mask);
        __m256 result = _mm256_arctan_poly_avx2_fma(x_star);
        __m256 term = _mm256_and_ps(x_star, sign_mask);
        term = _mm256_or_ps(pi_over_2, term);
        term = _mm256_sub_ps(term, result);
        result = _mm256_blendv_ps(result, term, swap_mask);
        _mm256_store_ps(out, result);
        out += 8;
    }
 
    for (unsigned int number = eighth_points * 8; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX2 && LV_HAVE_FMA for aligned */
 
#if LV_HAVE_AVX
#include <immintrin.h>
#include <volk/volk_avx_intrinsics.h>
static inline void
volk_32f_atan_32f_a_avx2(float* out, const float* in, unsigned int num_points)
{
    const __m256 one = _mm256_set1_ps(1.f);
    const __m256 pi_over_2 = _mm256_set1_ps(0x1.921fb6p0f);
    const __m256 abs_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x7FFFFFFF));
    const __m256 sign_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x80000000));
 
    const unsigned int eighth_points = num_points / 8;
 
    for (unsigned int number = 0; number < eighth_points; number++) {
        __m256 x = _mm256_load_ps(in);
        in += 8;
        __m256 swap_mask = _mm256_cmp_ps(_mm256_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m256 x_star = _mm256_blendv_ps(x, _mm256_rcp_ps(x), swap_mask);
        __m256 result = _mm256_arctan_poly_avx(x_star);
        __m256 term = _mm256_and_ps(x_star, sign_mask);
        term = _mm256_or_ps(pi_over_2, term);
        term = _mm256_sub_ps(term, result);
        result = _mm256_blendv_ps(result, term, swap_mask);
        _mm256_store_ps(out, result);
        out += 8;
    }
 
    for (unsigned int number = eighth_points * 8; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX for aligned */
 
#ifdef LV_HAVE_SSE4_1
#include <smmintrin.h>
#include <volk/volk_sse_intrinsics.h>
static inline void
volk_32f_atan_32f_a_sse4_1(float* out, const float* in, unsigned int num_points)
{
    const __m128 one = _mm_set1_ps(1.f);
    const __m128 pi_over_2 = _mm_set1_ps(0x1.921fb6p0f);
    const __m128 abs_mask = _mm_castsi128_ps(_mm_set1_epi32(0x7FFFFFFF));
    const __m128 sign_mask = _mm_castsi128_ps(_mm_set1_epi32(0x80000000));
 
    const unsigned int quarter_points = num_points / 4;
 
    for (unsigned int number = 0; number < quarter_points; number++) {
        __m128 x = _mm_load_ps(in);
        in += 4;
        __m128 swap_mask = _mm_cmpgt_ps(_mm_and_ps(x, abs_mask), one);
        __m128 x_star = _mm_blendv_ps(x, _mm_rcp_ps(x), swap_mask);
        __m128 result = _mm_arctan_poly_sse(x_star);
        __m128 term = _mm_and_ps(x_star, sign_mask);
        term = _mm_or_ps(pi_over_2, term);
        term = _mm_sub_ps(term, result);
        result = _mm_blendv_ps(result, term, swap_mask);
        _mm_store_ps(out, result);
        out += 4;
    }
 
    for (unsigned int number = quarter_points * 4; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_SSE4_1 for aligned */
 
#ifdef LV_HAVE_NEON
#include <arm_neon.h>
#include <volk/volk_neon_intrinsics.h>
static inline void
volk_32f_atan_32f_neon(float* out, const float* in, unsigned int num_points)
{
    const float32x4_t one = vdupq_n_f32(1.f);
    const float32x4_t pi_over_2 = vdupq_n_f32(0x1.921fb6p0f);
    const uint32x4_t sign_mask = vdupq_n_u32(0x80000000);
 
    const unsigned int quarter_points = num_points / 4;
 
    for (unsigned int number = 0; number < quarter_points; number++) {
        float32x4_t x = vld1q_f32(in);
        in += 4;
 
        // swap_mask = |x| > 1
        float32x4_t abs_x = vabsq_f32(x);
        uint32x4_t swap_mask = vcgtq_f32(abs_x, one);
 
        // x_star = swap_mask ? 1/x : x
        float32x4_t x_star = vbslq_f32(swap_mask, _vinvq_f32(x), x);
 
        // Compute arctan polynomial
        float32x4_t result = _varctan_poly_f32(x_star);
 
        // If swapped: result = sign(x_star)*pi/2 - result
        uint32x4_t x_star_sign = vandq_u32(vreinterpretq_u32_f32(x_star), sign_mask);
        float32x4_t term = vreinterpretq_f32_u32(
            vorrq_u32(vreinterpretq_u32_f32(pi_over_2), x_star_sign));
        term = vsubq_f32(term, result);
        result = vbslq_f32(swap_mask, term, result);
 
        vst1q_f32(out, result);
        out += 4;
    }
 
    for (unsigned int number = quarter_points * 4; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_NEON */
 
#ifdef LV_HAVE_NEONV8
#include <arm_neon.h>
#include <volk/volk_neon_intrinsics.h>
/* ARMv8 NEON with FMA and 2x unrolling for better ILP */
static inline void
volk_32f_atan_32f_neonv8(float* out, const float* in, unsigned int num_points)
{
    const float32x4_t one = vdupq_n_f32(1.f);
    const float32x4_t pi_over_2 = vdupq_n_f32(0x1.921fb6p0f);
    const uint32x4_t sign_mask = vdupq_n_u32(0x80000000);
 
    const unsigned int eighth_points = num_points / 8;
 
    for (unsigned int number = 0; number < eighth_points; number++) {
        /* Load 8 floats */
        float32x4_t x0 = vld1q_f32(in);
        float32x4_t x1 = vld1q_f32(in + 4);
        in += 8;
 
        /* Process first 4 */
        float32x4_t abs_x0 = vabsq_f32(x0);
        uint32x4_t swap_mask0 = vcgtq_f32(abs_x0, one);
        float32x4_t x_star0 = vbslq_f32(swap_mask0, _vinvq_f32(x0), x0);
        float32x4_t result0 = _varctan_poly_neonv8(x_star0);
        uint32x4_t x_star_sign0 = vandq_u32(vreinterpretq_u32_f32(x_star0), sign_mask);
        float32x4_t term0 = vreinterpretq_f32_u32(
            vorrq_u32(vreinterpretq_u32_f32(pi_over_2), x_star_sign0));
        term0 = vsubq_f32(term0, result0);
        result0 = vbslq_f32(swap_mask0, term0, result0);
 
        /* Process second 4 */
        float32x4_t abs_x1 = vabsq_f32(x1);
        uint32x4_t swap_mask1 = vcgtq_f32(abs_x1, one);
        float32x4_t x_star1 = vbslq_f32(swap_mask1, _vinvq_f32(x1), x1);
        float32x4_t result1 = _varctan_poly_neonv8(x_star1);
        uint32x4_t x_star_sign1 = vandq_u32(vreinterpretq_u32_f32(x_star1), sign_mask);
        float32x4_t term1 = vreinterpretq_f32_u32(
            vorrq_u32(vreinterpretq_u32_f32(pi_over_2), x_star_sign1));
        term1 = vsubq_f32(term1, result1);
        result1 = vbslq_f32(swap_mask1, term1, result1);
 
        vst1q_f32(out, result0);
        vst1q_f32(out + 4, result1);
        out += 8;
    }
 
    for (unsigned int number = eighth_points * 8; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_NEONV8 */
 
#endif /* INCLUDED_volk_32f_atan_32f_a_H */
 
#ifndef INCLUDED_volk_32f_atan_32f_u_H
#define INCLUDED_volk_32f_atan_32f_u_H
 
#if LV_HAVE_AVX512F && LV_HAVE_AVX512DQ
#include <immintrin.h>
#include <volk/volk_avx512_intrinsics.h>
static inline void
volk_32f_atan_32f_u_avx512dq(float* out, const float* in, unsigned int num_points)
{
    const __m512 one = _mm512_set1_ps(1.f);
    const __m512 pi_over_2 = _mm512_set1_ps(0x1.921fb6p0f);
    const __m512 abs_mask = _mm512_castsi512_ps(_mm512_set1_epi32(0x7FFFFFFF));
    const __m512 sign_mask = _mm512_castsi512_ps(_mm512_set1_epi32(0x80000000));
 
    const unsigned int sixteenth_points = num_points / 16;
 
    for (unsigned int number = 0; number < sixteenth_points; number++) {
        __m512 x = _mm512_loadu_ps(in);
        in += 16;
        __mmask16 swap_mask =
            _mm512_cmp_ps_mask(_mm512_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m512 x_star = _mm512_mask_blend_ps(swap_mask, x, _mm512_rcp14_ps(x));
        __m512 result = _mm512_arctan_poly_avx512(x_star);
        __m512 term = _mm512_and_ps(x_star, sign_mask);
        term = _mm512_or_ps(pi_over_2, term);
        term = _mm512_sub_ps(term, result);
        result = _mm512_mask_blend_ps(swap_mask, result, term);
        _mm512_storeu_ps(out, result);
        out += 16;
    }
 
    for (unsigned int number = sixteenth_points * 16; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX512F && LV_HAVE_AVX512DQ for unaligned */
 
#if LV_HAVE_AVX2 && LV_HAVE_FMA
#include <immintrin.h>
static inline void
volk_32f_atan_32f_u_avx2_fma(float* out, const float* in, unsigned int num_points)
{
    const __m256 one = _mm256_set1_ps(1.f);
    const __m256 pi_over_2 = _mm256_set1_ps(0x1.921fb6p0f);
    const __m256 abs_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x7FFFFFFF));
    const __m256 sign_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x80000000));
 
    const unsigned int eighth_points = num_points / 8;
 
    for (unsigned int number = 0; number < eighth_points; number++) {
        __m256 x = _mm256_loadu_ps(in);
        in += 8;
        __m256 swap_mask = _mm256_cmp_ps(_mm256_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m256 x_star = _mm256_blendv_ps(x, _mm256_rcp_ps(x), swap_mask);
        __m256 result = _mm256_arctan_poly_avx2_fma(x_star);
        __m256 term = _mm256_and_ps(x_star, sign_mask);
        term = _mm256_or_ps(pi_over_2, term);
        term = _mm256_sub_ps(term, result);
        result = _mm256_blendv_ps(result, term, swap_mask);
        _mm256_storeu_ps(out, result);
        out += 8;
    }
 
    for (unsigned int number = eighth_points * 8; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX2 && LV_HAVE_FMA for unaligned */
 
#if LV_HAVE_AVX
#include <immintrin.h>
static inline void
volk_32f_atan_32f_u_avx2(float* out, const float* in, unsigned int num_points)
{
    const __m256 one = _mm256_set1_ps(1.f);
    const __m256 pi_over_2 = _mm256_set1_ps(0x1.921fb6p0f);
    const __m256 abs_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x7FFFFFFF));
    const __m256 sign_mask = _mm256_castsi256_ps(_mm256_set1_epi32(0x80000000));
 
    const unsigned int eighth_points = num_points / 8;
 
    for (unsigned int number = 0; number < eighth_points; number++) {
        __m256 x = _mm256_loadu_ps(in);
        in += 8;
        __m256 swap_mask = _mm256_cmp_ps(_mm256_and_ps(x, abs_mask), one, _CMP_GT_OS);
        __m256 x_star = _mm256_blendv_ps(x, _mm256_rcp_ps(x), swap_mask);
        __m256 result = _mm256_arctan_poly_avx(x_star);
        __m256 term = _mm256_and_ps(x_star, sign_mask);
        term = _mm256_or_ps(pi_over_2, term);
        term = _mm256_sub_ps(term, result);
        result = _mm256_blendv_ps(result, term, swap_mask);
        _mm256_storeu_ps(out, result);
        out += 8;
    }
 
    for (unsigned int number = eighth_points * 8; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_AVX for unaligned */
 
#ifdef LV_HAVE_SSE4_1
#include <smmintrin.h>
#include <volk/volk_sse_intrinsics.h>
static inline void
volk_32f_atan_32f_u_sse4_1(float* out, const float* in, unsigned int num_points)
{
    const __m128 one = _mm_set1_ps(1.f);
    const __m128 pi_over_2 = _mm_set1_ps(0x1.921fb6p0f);
    const __m128 abs_mask = _mm_castsi128_ps(_mm_set1_epi32(0x7FFFFFFF));
    const __m128 sign_mask = _mm_castsi128_ps(_mm_set1_epi32(0x80000000));
 
    const unsigned int quarter_points = num_points / 4;
 
    for (unsigned int number = 0; number < quarter_points; number++) {
        __m128 x = _mm_loadu_ps(in);
        in += 4;
        __m128 swap_mask = _mm_cmpgt_ps(_mm_and_ps(x, abs_mask), one);
        __m128 x_star = _mm_blendv_ps(x, _mm_rcp_ps(x), swap_mask);
        __m128 result = _mm_arctan_poly_sse(x_star);
        __m128 term = _mm_and_ps(x_star, sign_mask);
        term = _mm_or_ps(pi_over_2, term);
        term = _mm_sub_ps(term, result);
        result = _mm_blendv_ps(result, term, swap_mask);
        _mm_storeu_ps(out, result);
        out += 4;
    }
 
    for (unsigned int number = quarter_points * 4; number < num_points; number++) {
        *out++ = volk_arctan(*in++);
    }
}
#endif /* LV_HAVE_SSE4_1 for unaligned */
 
#ifdef LV_HAVE_RVV
#include <riscv_vector.h>
 
static inline void
volk_32f_atan_32f_rvv(float* out, const float* in, unsigned int num_points)
{
    size_t vlmax = __riscv_vsetvlmax_e32m2();
 
    const vfloat32m2_t cpio2 = __riscv_vfmv_v_f_f32m2(1.5707964f, vlmax);
    const vfloat32m2_t cf1 = __riscv_vfmv_v_f_f32m2(1.0f, vlmax);
    const vfloat32m2_t c1 = __riscv_vfmv_v_f_f32m2(+0x1.ffffeap-1f, vlmax);
    const vfloat32m2_t c3 = __riscv_vfmv_v_f_f32m2(-0x1.55437p-2f, vlmax);
    const vfloat32m2_t c5 = __riscv_vfmv_v_f_f32m2(+0x1.972be6p-3f, vlmax);
    const vfloat32m2_t c7 = __riscv_vfmv_v_f_f32m2(-0x1.1436ap-3f, vlmax);
    const vfloat32m2_t c9 = __riscv_vfmv_v_f_f32m2(+0x1.5785aap-4f, vlmax);
    const vfloat32m2_t c11 = __riscv_vfmv_v_f_f32m2(-0x1.2f3004p-5f, vlmax);
    const vfloat32m2_t c13 = __riscv_vfmv_v_f_f32m2(+0x1.01a37cp-7f, vlmax);
 
    size_t n = num_points;
    for (size_t vl; n > 0; n -= vl, in += vl, out += vl) {
        vl = __riscv_vsetvl_e32m2(n);
        vfloat32m2_t v = __riscv_vle32_v_f32m2(in, vl);
        vbool16_t mswap = __riscv_vmfgt(__riscv_vfabs(v, vl), cf1, vl);
        vfloat32m2_t x = __riscv_vfdiv_mu(mswap, v, cf1, v, vl);
        vfloat32m2_t xx = __riscv_vfmul(x, x, vl);
        vfloat32m2_t p = c13;
        p = __riscv_vfmadd(p, xx, c11, vl);
        p = __riscv_vfmadd(p, xx, c9, vl);
        p = __riscv_vfmadd(p, xx, c7, vl);
        p = __riscv_vfmadd(p, xx, c5, vl);
        p = __riscv_vfmadd(p, xx, c3, vl);
        p = __riscv_vfmadd(p, xx, c1, vl);
        p = __riscv_vfmul(p, x, vl);
 
        vfloat32m2_t t = __riscv_vfsub(__riscv_vfsgnj(cpio2, x, vl), p, vl);
        p = __riscv_vmerge(p, t, mswap, vl);
 
        __riscv_vse32(out, p, vl);
    }
}
#endif /*LV_HAVE_RVV*/
 
#endif /* INCLUDED_volk_32f_atan_32f_u_H */