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Add FMA optimization for SSE2 implementation of asin, acos and atan in x86 targets. (#4620)
tags/20230517
Kenji Mouri
GitHub
3 years ago
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GPG Key ID: 4AEE18F83AFDEB23
1 changed files with 78 additions and 89 deletions
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+78 -89src/layer/x86/sse_mathfun.h
+ 78
- 89
src/layer/x86/sse_mathfun.h
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| @@ -883,39 +883,37 @@ static NCNN_FORCEINLINE __m128 asin_ps(__m128 x) | |||
| square_of_input_approx, square_of_input_approx); | |||
| // TODO: Need more explanations. | |||
| // x1 = ((magic_a4 * fourth_power_of_input_approx) + magic_a2); | |||
| // x2 = ((magic_a5 * fourth_power_of_input_approx) + magic_a3); | |||
| // x3 = ((x1 * fourth_power_of_input_approx) + magic_a0); | |||
| // x1 = ((fourth_power_of_input_approx * magic_a4) + magic_a2); | |||
| // x2 = ((fourth_power_of_input_approx * magic_a5) + magic_a3); | |||
| // x3 = ((fourth_power_of_input_approx * x1) + magic_a0); | |||
| // x4 = ((fourth_power_of_input_approx * x2) + magic_a1); | |||
| // output_approx = (x3 + (square_of_input_approx * x4)); | |||
| __m128 output_approx = _mm_add_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps(magic_a4, fourth_power_of_input_approx), | |||
| magic_a2), | |||
| fourth_power_of_input_approx), | |||
| magic_a0), | |||
| _mm_mul_ps( | |||
| square_of_input_approx, | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_add_ps( | |||
| _mm_mul_ps(magic_a5, fourth_power_of_input_approx), | |||
| magic_a3)), | |||
| magic_a1))); | |||
| // output_approx = ((square_of_input_approx * x4) + x3); | |||
| __m128 output_approx = _mm_comp_fmadd_ps( | |||
| square_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a5, | |||
| magic_a3), | |||
| magic_a1), | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a4, | |||
| magic_a2), | |||
| magic_a0)); | |||
| // TODO: Need more explanations. | |||
| // x1 = ((0.5 * PI) * is_big_input); | |||
| // x2 = (output_approx * input_approx); | |||
| // x3 = (1.0f - (3.0f * is_big_input)); | |||
| // final_approx = (x1 + (x2 * x3)); | |||
| __m128 final_approx = _mm_add_ps( | |||
| _mm_mul_ps(magic_half_pi, is_big_input), | |||
| _mm_mul_ps( | |||
| _mm_mul_ps(output_approx, input_approx), | |||
| _mm_sub_ps(magic_one, _mm_mul_ps(magic_three, is_big_input)))); | |||
| // x3 = (-(3.0f * is_big_input) + 1.0f); | |||
| // final_approx = ((x2 * x3) + x1); | |||
| __m128 final_approx = _mm_comp_fmadd_ps( | |||
| _mm_mul_ps(output_approx, input_approx), | |||
| _mm_comp_fnmadd_ps(magic_three, is_big_input, magic_one), | |||
| _mm_mul_ps(magic_half_pi, is_big_input)); | |||
| // return (final_approx || negative_mask); | |||
| return _mm_or_ps(final_approx, negative_mask); | |||
| @@ -966,28 +964,27 @@ static NCNN_FORCEINLINE __m128 acos_ps(__m128 x) | |||
| square_of_input_approx, square_of_input_approx); | |||
| // TODO: Need more explanations. | |||
| // x1 = ((magic_a4 * fourth_power_of_input_approx) + magic_a2); | |||
| // x2 = ((magic_a5 * fourth_power_of_input_approx) + magic_a3); | |||
| // x3 = ((x1 * fourth_power_of_input_approx) + magic_a0); | |||
| // x1 = ((fourth_power_of_input_approx * magic_a4) + magic_a2); | |||
| // x2 = ((fourth_power_of_input_approx * magic_a5) + magic_a3); | |||
| // x3 = ((fourth_power_of_input_approx * x1) + magic_a0); | |||
| // x4 = ((fourth_power_of_input_approx * x2) + magic_a1); | |||
| // output_approx = (x3 + (square_of_input_approx * x4)); | |||
| __m128 output_approx = _mm_add_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps(magic_a4, fourth_power_of_input_approx), | |||
| magic_a2), | |||
| fourth_power_of_input_approx), | |||
| magic_a0), | |||
| _mm_mul_ps( | |||
| square_of_input_approx, | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_add_ps( | |||
| _mm_mul_ps(magic_a5, fourth_power_of_input_approx), | |||
| magic_a3)), | |||
| magic_a1))); | |||
| // output_approx = ((square_of_input_approx * x4) + x3); | |||
| __m128 output_approx = _mm_comp_fmadd_ps( | |||
| square_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a5, | |||
| magic_a3), | |||
| magic_a1), | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a4, | |||
| magic_a2), | |||
| magic_a0)); | |||
| // TODO: Need more explanations. | |||
| // x1 = (output_approx * input_approx); | |||
| @@ -1058,46 +1055,38 @@ static NCNN_FORCEINLINE __m128 atan_ps(__m128 x) | |||
| square_of_input_approx, square_of_input_approx); | |||
| // TODO: Need more explanations. | |||
| // x1 = ((magic_a7 * fourth_power_of_input_approx) + magic_a5); | |||
| // x2 = ((magic_a8 * fourth_power_of_input_approx) + magic_a6); | |||
| // x3 = ((x1 * fourth_power_of_input_approx) + magic_a3); | |||
| // x4 = ((x2 * fourth_power_of_input_approx) + magic_a4); | |||
| // x5 = ((x3 * fourth_power_of_input_approx) + magic_a1); | |||
| // x6 = ((x4 * fourth_power_of_input_approx) + magic_a2); | |||
| // x7 = ((x6 * fourth_power_of_input_approx) + magic_a0); | |||
| // output_approx = ((x5 * square_of_input_approx) + x7); | |||
| __m128 output_approx = _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| magic_a7, | |||
| fourth_power_of_input_approx), | |||
| magic_a5), | |||
| fourth_power_of_input_approx), | |||
| magic_a3), | |||
| fourth_power_of_input_approx), | |||
| magic_a1), | |||
| square_of_input_approx), | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| _mm_add_ps( | |||
| _mm_mul_ps( | |||
| magic_a8, | |||
| fourth_power_of_input_approx), | |||
| magic_a6), | |||
| fourth_power_of_input_approx), | |||
| magic_a4), | |||
| fourth_power_of_input_approx), | |||
| magic_a2), | |||
| fourth_power_of_input_approx), | |||
| // x1 = ((fourth_power_of_input_approx * magic_a7) + magic_a5); | |||
| // x2 = ((fourth_power_of_input_approx * magic_a8) + magic_a6); | |||
| // x3 = ((fourth_power_of_input_approx * x1) + magic_a3); | |||
| // x4 = ((fourth_power_of_input_approx * x2) + magic_a4); | |||
| // x5 = ((fourth_power_of_input_approx * x3) + magic_a1); | |||
| // x6 = ((fourth_power_of_input_approx * x4) + magic_a2); | |||
| // x7 = ((fourth_power_of_input_approx * x6) + magic_a0); | |||
| // output_approx = ((square_of_input_approx * x5) + x7); | |||
| __m128 output_approx = _mm_comp_fmadd_ps( | |||
| square_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a7, | |||
| magic_a5), | |||
| magic_a3), | |||
| magic_a1), | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| _mm_comp_fmadd_ps( | |||
| fourth_power_of_input_approx, | |||
| magic_a8, | |||
| magic_a6), | |||
| magic_a4), | |||
| magic_a2), | |||
| magic_a0)); | |||
| // TODO: Need more explanations. | |||