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volk_32f_invsqrt_32f.h
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/* -*- c++ -*- */
/*
* Copyright 2013, 2014 Free Software Foundation, Inc.
* Copyright 2026 Magnus Lundmark <magnuslundmark@gmail.com>
*
* This file is part of VOLK
*
* SPDX-License-Identifier: LGPL-3.0-or-later
*/
#ifndef INCLUDED_volk_32f_invsqrt_32f_a_H
#define INCLUDED_volk_32f_invsqrt_32f_a_H
#include <math.h>
#include <volk/volk_common.h>
#ifdef LV_HAVE_GENERIC
static inline void volk_32f_invsqrt_32f_generic(float* cVector,
const float* aVector,
unsigned int num_points)
{
for (unsigned int number = 0; number < num_points; number++) {
cVector[number] = sqrtf(1.0f / aVector[number]);
}
}
#endif /* LV_HAVE_GENERIC */
#ifdef LV_HAVE_GENERIC
static inline void volk_32f_invsqrt_32f_recip_sqrt(float* cVector,
const float* aVector,
unsigned int num_points)
{
for (unsigned int number = 0; number < num_points; number++) {
cVector[number] = 1.0f / sqrtf(aVector[number]);
}
}
#endif /* LV_HAVE_GENERIC */
#ifdef LV_HAVE_GENERIC
static inline void volk_32f_invsqrt_32f_Q_rsqrt(float* cVector,
const float* aVector,
unsigned int num_points)
{
// The famous fast inverse square root from Quake III Arena
union {
float f;
uint32_t u;
} conv, result;
for (unsigned int number = 0; number < num_points; number++) {
float a = aVector[number];
float xhalf = 0.5f * a;
conv.f = a;
uint32_t input_bits = conv.u; // Save original bits for edge case detection
conv.u = 0x5f3759df - (conv.u >> 1); // The magic (note: use unsigned for shift)
float x = conv.f;
x = x * (1.5f - xhalf * x * x); // Newton-Raphson iteration 1
x = x * (1.5f - xhalf * x * x);
x = x * (1.5f - xhalf * x * x);
// Branchless special case handling
result.f = x;
uint32_t is_positive = (uint32_t)(-(int32_t)(a > 0.0f));
uint32_t is_zero = (uint32_t)(-(int32_t)(input_bits == 0x00000000));
uint32_t is_inf = (uint32_t)(-(int32_t)(input_bits == 0x7F800000));
uint32_t is_normal_pos = is_positive & ~is_inf;
result.u = (result.u & is_normal_pos) | // Normal positive: keep result
(0x7F800000u & is_zero) | // +0 → +Inf
(0x7FC00000u & ~is_positive & ~is_zero); // Negative/NaN → NaN
// Note: +Inf → 0 is handled implicitly (all terms are 0 when is_inf)
cVector[number] = result.f;
}
}
#endif /* LV_HAVE_GENERIC */
#ifdef LV_HAVE_SSE
#include <volk/volk_sse_intrinsics.h>
#include <xmmintrin.h>
static inline void
volk_32f_invsqrt_32f_a_sse(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int quarterPoints = num_points / 4;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < quarterPoints; number++) {
__m128 aVal = _mm_load_ps(aPtr);
__m128 cVal = _mm_rsqrt_nr_ps(aVal);
_mm_store_ps(cPtr, cVal);
aPtr += 4;
cPtr += 4;
}
number = quarterPoints * 4;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_SSE */
#ifdef LV_HAVE_AVX
#include <immintrin.h>
#include <volk/volk_avx_intrinsics.h>
static inline void
volk_32f_invsqrt_32f_a_avx(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int eighthPoints = num_points / 8;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < eighthPoints; number++) {
__m256 aVal = _mm256_load_ps(aPtr);
__m256 cVal = _mm256_rsqrt_nr_ps(aVal);
_mm256_store_ps(cPtr, cVal);
aPtr += 8;
cPtr += 8;
}
number = eighthPoints * 8;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX */
#ifdef LV_HAVE_AVX2
#include <immintrin.h>
#include <volk/volk_avx2_intrinsics.h>
static inline void
volk_32f_invsqrt_32f_a_avx2(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int eighthPoints = num_points / 8;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < eighthPoints; number++) {
__m256 aVal = _mm256_load_ps(aPtr);
__m256 cVal = _mm256_rsqrt_nr_avx2(aVal);
_mm256_store_ps(cPtr, cVal);
aPtr += 8;
cPtr += 8;
}
number = eighthPoints * 8;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX2 */
#ifdef LV_HAVE_AVX512F
#include <immintrin.h>
#include <volk/volk_avx512_intrinsics.h>
static inline void volk_32f_invsqrt_32f_a_avx512f(float* cVector,
const float* aVector,
unsigned int num_points)
{
unsigned int number = 0;
const unsigned int sixteenthPoints = num_points / 16;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < sixteenthPoints; number++) {
__m512 aVal = _mm512_load_ps(aPtr);
__m512 cVal = _mm512_rsqrt_nr_ps(aVal);
_mm512_store_ps(cPtr, cVal);
aPtr += 16;
cPtr += 16;
}
number = sixteenthPoints * 16;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX512F */
#ifdef LV_HAVE_SSE
#include <volk/volk_sse_intrinsics.h>
#include <xmmintrin.h>
static inline void
volk_32f_invsqrt_32f_u_sse(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int quarterPoints = num_points / 4;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < quarterPoints; number++) {
__m128 aVal = _mm_loadu_ps(aPtr);
__m128 cVal = _mm_rsqrt_nr_ps(aVal);
_mm_storeu_ps(cPtr, cVal);
aPtr += 4;
cPtr += 4;
}
number = quarterPoints * 4;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_SSE */
#ifdef LV_HAVE_AVX
#include <immintrin.h>
#include <volk/volk_avx_intrinsics.h>
static inline void
volk_32f_invsqrt_32f_u_avx(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int eighthPoints = num_points / 8;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < eighthPoints; number++) {
__m256 aVal = _mm256_loadu_ps(aPtr);
__m256 cVal = _mm256_rsqrt_nr_ps(aVal);
_mm256_storeu_ps(cPtr, cVal);
aPtr += 8;
cPtr += 8;
}
number = eighthPoints * 8;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX */
#ifdef LV_HAVE_AVX2
#include <immintrin.h>
#include <volk/volk_avx2_intrinsics.h>
static inline void
volk_32f_invsqrt_32f_u_avx2(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number = 0;
const unsigned int eighthPoints = num_points / 8;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < eighthPoints; number++) {
__m256 aVal = _mm256_loadu_ps(aPtr);
__m256 cVal = _mm256_rsqrt_nr_avx2(aVal);
_mm256_storeu_ps(cPtr, cVal);
aPtr += 8;
cPtr += 8;
}
number = eighthPoints * 8;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX2 */
#ifdef LV_HAVE_AVX512F
#include <immintrin.h>
#include <volk/volk_avx512_intrinsics.h>
static inline void volk_32f_invsqrt_32f_u_avx512f(float* cVector,
const float* aVector,
unsigned int num_points)
{
unsigned int number = 0;
const unsigned int sixteenthPoints = num_points / 16;
float* cPtr = cVector;
const float* aPtr = aVector;
for (; number < sixteenthPoints; number++) {
__m512 aVal = _mm512_loadu_ps(aPtr);
__m512 cVal = _mm512_rsqrt_nr_ps(aVal);
_mm512_storeu_ps(cPtr, cVal);
aPtr += 16;
cPtr += 16;
}
number = sixteenthPoints * 16;
for (; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_AVX512F */
#ifdef LV_HAVE_NEON
#include <arm_neon.h>
#include <volk/volk_neon_intrinsics.h>
static inline void
volk_32f_invsqrt_32f_neon(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number;
const unsigned int quarter_points = num_points / 4;
float* cPtr = cVector;
const float* aPtr = aVector;
for (number = 0; number < quarter_points; ++number) {
float32x4_t a_val = vld1q_f32(aPtr);
float32x4_t c_val = _vinvsqrtq_f32(a_val);
vst1q_f32(cPtr, c_val);
aPtr += 4;
cPtr += 4;
}
for (number = quarter_points * 4; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_NEON */
#ifdef LV_HAVE_NEONV8
#include <arm_neon.h>
static inline void
volk_32f_invsqrt_32f_neonv8(float* cVector, const float* aVector, unsigned int num_points)
{
unsigned int number;
const unsigned int quarter_points = num_points / 4;
float* cPtr = cVector;
const float* aPtr = aVector;
// Process 4 elements at a time (1 vector)
for (number = 0; number < quarter_points; ++number) {
float32x4_t a = vld1q_f32(aPtr);
float32x4_t x0 = vrsqrteq_f32(a); // +Inf for +0, 0 for +Inf
// Two Newton-Raphson iterations for float32 accuracy
float32x4_t x1 = vmulq_f32(x0, vrsqrtsq_f32(vmulq_f32(a, x0), x0));
x1 = vmulq_f32(x1, vrsqrtsq_f32(vmulq_f32(a, x1), x1));
// 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
uint32x4_t a_bits = vreinterpretq_u32_f32(a);
uint32x4_t zero_mask = vceqq_u32(a_bits, vdupq_n_u32(0x00000000));
uint32x4_t inf_mask = vceqq_u32(a_bits, vdupq_n_u32(0x7F800000));
uint32x4_t special_mask = vorrq_u32(zero_mask, inf_mask);
vst1q_f32(cPtr, vbslq_f32(special_mask, x0, x1));
aPtr += 4;
cPtr += 4;
}
for (number = quarter_points * 4; number < num_points; number++) {
*cPtr++ = 1.0f / sqrtf(*aPtr++);
}
}
#endif /* LV_HAVE_NEONV8 */
#ifdef LV_HAVE_RVV
#include <riscv_vector.h>
static inline void
volk_32f_invsqrt_32f_rvv(float* cVector, const float* aVector, unsigned int num_points)
{
size_t n = num_points;
for (size_t vl; n > 0; n -= vl, aVector += vl, cVector += vl) {
vl = __riscv_vsetvl_e32m8(n);
vfloat32m8_t a = __riscv_vle32_v_f32m8(aVector, vl);
vfloat32m8_t half = __riscv_vfmv_v_f_f32m8(0.5f, vl);
vfloat32m8_t three_halfs = __riscv_vfmv_v_f_f32m8(1.5f, vl);
// Initial estimate (~7-bit precision): +Inf for +0, 0 for +Inf
vfloat32m8_t x0 = __riscv_vfrsqrt7(a, vl);
// Two Newton-Raphson iterations: x = x * (1.5 - 0.5 * a * x * x)
vfloat32m8_t half_a = __riscv_vfmul(half, a, vl);
vfloat32m8_t x1 = __riscv_vfmul(
x0, __riscv_vfnmsac(three_halfs, half_a, __riscv_vfmul(x0, x0, vl), vl), vl);
x1 = __riscv_vfmul(
x1, __riscv_vfnmsac(three_halfs, half_a, __riscv_vfmul(x1, x1, vl), vl), vl);
// 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
vuint32m8_t a_bits = __riscv_vreinterpret_v_f32m8_u32m8(a);
vbool4_t zero_mask = __riscv_vmseq_vx_u32m8_b4(a_bits, 0x00000000, vl);
vbool4_t inf_mask = __riscv_vmseq_vx_u32m8_b4(a_bits, 0x7F800000, vl);
vbool4_t special_mask = __riscv_vmor_mm_b4(zero_mask, inf_mask, vl);
vfloat32m8_t result = __riscv_vmerge_vvm_f32m8(x1, x0, special_mask, vl);
__riscv_vse32(cVector, result, vl);
}
}
#endif /*LV_HAVE_RVV*/
#endif /* INCLUDED_volk_32f_invsqrt_32f_a_H */