1 // Copyright 2020 Google LLC
2 //
3 // This source code is licensed under the BSD-style license found in the
4 // LICENSE file in the root directory of this source tree.
5
6 #include <assert.h>
7 #include <stddef.h>
8
9 #include <arm_neon.h>
10
11 #include <xnnpack/math.h>
12 #include <xnnpack/math-stubs.h>
13
14
xnn_math_f32_sqrt__neon_nr3rsqrts(size_t n,const float * input,float * output)15 void xnn_math_f32_sqrt__neon_nr3rsqrts(
16 size_t n,
17 const float* input,
18 float* output)
19 {
20 assert(n % (4 * sizeof(float)) == 0);
21
22 for (; n != 0; n -= 4 * sizeof(float)) {
23 const float32x4_t vx = vld1q_f32(input); input += 4;
24
25 // Initial approximation
26 float32x4_t vrsqrtx = vrsqrteq_f32(vx);
27
28 // Netwon-Raphson iteration: rsqrt_x <- rsqrt_x * ((3 - x * rsqrt_x * rsqrt_x) / 2)
29 // Note: x * (rsqrt_x * rsqrt_x) for the first iteration and (x * rsqrt_x) * rsqrt_x for the next two improves accuracy
30 // Note: vrsqrtsq_f32(x, y) := (3 - x * y) / 2
31 vrsqrtx = vmulq_f32(vrsqrtx, vrsqrtsq_f32(vx, vmulq_f32(vrsqrtx, vrsqrtx)));
32 vrsqrtx = vmulq_f32(vrsqrtx, vrsqrtsq_f32(vmulq_f32(vrsqrtx, vx), vrsqrtx));
33 vrsqrtx = vmulq_f32(vrsqrtx, vrsqrtsq_f32(vmulq_f32(vrsqrtx, vx), vrsqrtx));
34
35 // Reconstruct sqrt(x) = rsqrt(x) * x
36 const float32x4_t vy = vmulq_f32(vrsqrtx, vx);
37
38 vst1q_f32(output, vy); output += 4;
39 }
40 }
41