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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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22e86402f7
commit
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1 changed files with 78 additions and 89 deletions
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    -89
      src/layer/x86/sse_mathfun.h

+ 78
- 89
src/layer/x86/sse_mathfun.h View File

@@ -883,39 +883,37 @@ static NCNN_FORCEINLINE __m128 asin_ps(__m128 x)
square_of_input_approx, square_of_input_approx); square_of_input_approx, square_of_input_approx);


// TODO: Need more explanations. // 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); // 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. // TODO: Need more explanations.
// x1 = ((0.5 * PI) * is_big_input); // x1 = ((0.5 * PI) * is_big_input);
// x2 = (output_approx * input_approx); // 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 (final_approx || negative_mask);
return _mm_or_ps(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); square_of_input_approx, square_of_input_approx);


// TODO: Need more explanations. // 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); // 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. // TODO: Need more explanations.
// x1 = (output_approx * input_approx); // 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); square_of_input_approx, square_of_input_approx);


// TODO: Need more explanations. // 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)); magic_a0));


// TODO: Need more explanations. // TODO: Need more explanations.


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