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// Copyright 2020 Google LLC
//
// This source code is licensed under the BSD-style license found in the
// LICENSE file in the root directory of this source tree.
#include <assert.h>
#include <stddef.h>
#include <arm_neon.h>
#include <xnnpack/math.h>
#include <xnnpack/math-stubs.h>
void xnn_math_f32_sqrt__neon_nr2rsqrts(
size_t n,
const float* input,
float* output)
{
assert(n % (4 * sizeof(float)) == 0);
for (; n != 0; n -= 4 * sizeof(float)) {
const float32x4_t vx = vld1q_f32(input); input += 4;
// Initial approximation
float32x4_t vrsqrtx = vrsqrteq_f32(vx);
// Netwon-Raphson iteration: rsqrt_x <- rsqrt_x * ((3 - x * (rsqrt_x * rsqrt_x)) / 2)
// Note: x * (rsqrt_x * rsqrt_x) for the first iteration and (x * rsqrt_x) * rsqrt_x for the second improves accuracy
// Note: vrsqrtsq_f32(x, y) := (3 - x * y) / 2
vrsqrtx = vmulq_f32(vrsqrtx, vrsqrtsq_f32(vx, vmulq_f32(vrsqrtx, vrsqrtx)));
vrsqrtx = vmulq_f32(vrsqrtx, vrsqrtsq_f32(vmulq_f32(vrsqrtx, vx), vrsqrtx));
// Reconstruct sqrt(x) = rsqrt(x) * x
const float32x4_t vy = vmulq_f32(vrsqrtx, vx);
vst1q_f32(output, vy); output += 4;
}
}