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 <xmmintrin.h>
10
11 #include <xnnpack/math.h>
12 #include <xnnpack/math-stubs.h>
13
14
xnn_math_f32_sqrt__sse_hh1mac(size_t n,const float * input,float * output)15 void xnn_math_f32_sqrt__sse_hh1mac(
16 size_t n,
17 const float* input,
18 float* output)
19 {
20 assert(n % (4 * sizeof(float)) == 0);
21
22 const __m128 vc1875 = _mm_set1_ps(1.875f);
23 const __m128 vc0375 = _mm_set1_ps(0.375f);
24 const __m128 vc1250 = _mm_set1_ps(1.250f);
25 for (; n != 0; n -= 4 * sizeof(float)) {
26 const __m128 vx = _mm_load_ps(input);
27 input += 4;
28
29 // Initial approximation
30 __m128 vrsqrtx = _mm_rsqrt_ps(vx);
31
32 // Householder (order 2) iteration:
33 // rsqrt_x <- rsqrt_x * (1.875 + t * (0.375 * t - 1.25)) where t = x * rsqrt_x * rsqrt_x
34 // Note: half_x * (rsqrt_x * rsqrt_x) is less accurate than (half_x * rsqrt_x) * rsqrt_x
35 const __m128 vt = _mm_mul_ps(_mm_mul_ps(vx, vrsqrtx), vrsqrtx);
36 vrsqrtx = _mm_mul_ps(vrsqrtx, _mm_add_ps(_mm_mul_ps(vt, _mm_sub_ps(_mm_mul_ps(vt, vc0375), vc1250)), vc1875));
37
38 // Reconstruct sqrt(x) = rsqrt(x) * x
39 const __m128 vy = _mm_mul_ps(vrsqrtx, vx);
40
41 _mm_store_ps(output, vy);
42 output += 4;
43 }
44 }
45