src/f32-vsigmoid/sse-lut64-p2-div.c.in

// 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.

$assert BATCH_TILE % 4 == 0
$assert BATCH_TILE >= 4
$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
$SSE_HEADER = {2: "emmintrin.h", 4: "smmintrin.h"}[SSE]
#include <assert.h>

#include <${SSE_HEADER}>

#include <xnnpack/common.h>
#include <xnnpack/vunary.h>


extern XNN_INTERNAL const float xnn_table_exp2minus_k_over_64[64];

$ISA = {2: "sse2", 4: "sse41"}[SSE]
void xnn_f32_vsigmoid_ukernel__${ISA}_lut64_p2_div_x${BATCH_TILE}(
    size_t n,
    const float* x,
    float* y,
    const void* params) XNN_DISABLE_TSAN
{
  assert(n % sizeof(float) == 0);

  const __m128 vsign_mask = _mm_set1_ps(-0.0f);
  const __m128 vmagic_bias = _mm_set1_ps(0x1.800000p17f);
  const __m128 vlog2e = _mm_set1_ps(0x1.715476p0f);
  const __m128i vindex_mask = _mm_set1_epi32(INT32_C(0x3F));
  const __m128 vminus_ln2_hi = _mm_set1_ps(-0x1.630000p-1f);
  const __m128 vminus_ln2_lo = _mm_set1_ps(0x1.BD0106p-13f);
  const __m128 vc2 = _mm_set1_ps(0x1.FFFF0Ap-2f);
  const __m128 vone = _mm_set1_ps(1.0f);
  const __m128 vdenorm_cutoff = _mm_set1_ps(-0x1.5D589Ep+6f);

  $if BATCH_TILE > 4:
    for (; n >= ${BATCH_TILE} * sizeof(float); n -= ${BATCH_TILE} * sizeof(float)) {
      const __m128 vx${ABC[0:4]} = _mm_loadu_ps(x);
      $for N in range(4, BATCH_TILE, 4):
        const __m128 vx${ABC[N:N+4]} = _mm_loadu_ps(x + ${N});
      x += ${BATCH_TILE};

      $for N in range(0, BATCH_TILE, 4):
        const __m128 vz${ABC[N:N+4]} = _mm_or_ps(vx${ABC[N:N+4]}, vsign_mask);

      $for N in range(0, BATCH_TILE, 4):
        __m128 vn${ABC[N:N+4]} = _mm_add_ps(_mm_mul_ps(vz${ABC[N:N+4]}, vlog2e), vmagic_bias);

      $for N in range(0, BATCH_TILE, 4):
        const __m128i ve${ABC[N:N+4]} = _mm_slli_epi32(_mm_castps_si128(vn${ABC[N:N+4]}), 17);

      $for N in range(0, BATCH_TILE, 4):
        const __m128i vidx${ABC[N:N+4]} = _mm_slli_epi32(_mm_and_si128(_mm_castps_si128(vn${ABC[N:N+4]}), vindex_mask), 2);

      #if XNN_ARCH_X86_64
        $for N in range(0, BATCH_TILE, 4):
          const uint64_t vidx${ABC[N:N+2]} = (uint64_t) _mm_cvtsi128_si64(vidx${ABC[N:N+4]});
          $if SSE >= 4:
            const uint64_t vidx${ABC[N+2:N+4]} = (uint64_t) _mm_extract_epi64(vidx${ABC[N:N+4]}, 1);
          $else:
            const uint64_t vidx${ABC[N+2:N+4]} = (uint64_t) _mm_cvtsi128_si64(_mm_unpackhi_epi64(vidx${ABC[N:N+4]}, vidx${ABC[N:N+4]}));
          const __m128i vl${ABC[N]}   = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx${ABC[N:N+2]})));
          const __m128i vl${ABC[N+2]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx${ABC[N+2:N+4]})));
          $if SSE >= 4:
            const __m128i vl${ABC[N:N+2]} = _mm_insert_epi32(vl${ABC[N]}, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx${ABC[N:N+2]} >> 32))), 1);
          $else:
            const __m128i vl${ABC[N+1]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx${ABC[N:N+2]} >> 32))));
            const __m128i vl${ABC[N:N+2]} = _mm_unpacklo_epi32(vl${ABC[N]}, vl${ABC[N+1]});
          $if SSE >= 4:
            const __m128i vl${ABC[N+2:N+4]} = _mm_insert_epi32(vl${ABC[N+2]}, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx${ABC[N+2:N+4]} >> 32))), 1);
          $else:
            const __m128i vl${ABC[N+3]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx${ABC[N+2:N+4]} >> 32))));
            const __m128i vl${ABC[N+2:N+4]} = _mm_unpacklo_epi32(vl${ABC[N+2]}, vl${ABC[N+3]});
          const __m128i vl${ABC[N:N+4]} = _mm_unpacklo_epi64(vl${ABC[N:N+2]}, vl${ABC[N+2:N+4]});
      #else  // !XNN_ARCH_X86_64
        $for N in range(0, BATCH_TILE, 4):
          const uint32_t vidx${ABC[N]} = (uint32_t) _mm_cvtsi128_si32(vidx${ABC[N:N+4]});
          const uint32_t vidx${ABC[N+1]} = (uint32_t) _mm_extract_epi16(vidx${ABC[N:N+4]}, 2);
          const uint32_t vidx${ABC[N+2]} = (uint32_t) _mm_extract_epi16(vidx${ABC[N:N+4]}, 4);
          const uint32_t vidx${ABC[N+3]} = (uint32_t) _mm_extract_epi16(vidx${ABC[N:N+4]}, 6);
          const __m128i vl${ABC[N]}   = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N]})));
          const __m128i vl${ABC[N+2]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N+2]})));
          $if SSE >= 4:
            const __m128i vl${ABC[N:N+2]} = _mm_insert_epi32(vl${ABC[N]}, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N+1]})), 1);
          $else:
            const __m128i vl${ABC[N+1]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N+1]})));
            const __m128i vl${ABC[N:N+2]} = _mm_unpacklo_epi32(vl${ABC[N]}, vl${ABC[N+1]});
          $if SSE >= 4:
            const __m128i vl${ABC[N+2:N+4]} = _mm_insert_epi32(vl${ABC[N+2]}, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N+3]})), 1);
          $else:
            const __m128i vl${ABC[N+3]} = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + vidx${ABC[N+3]})));
            const __m128i vl${ABC[N+2:N+4]} = _mm_unpacklo_epi32(vl${ABC[N+2]}, vl${ABC[N+3]});
          const __m128i vl${ABC[N:N+4]} = _mm_unpacklo_epi64(vl${ABC[N:N+2]}, vl${ABC[N+2:N+4]});
      #endif  // XNN_ARCH_X86_64

      $for N in range(0, BATCH_TILE, 4):
        const __m128 vs${ABC[N:N+4]} = _mm_castsi128_ps(_mm_add_epi32(vl${ABC[N:N+4]}, ve${ABC[N:N+4]}));

      $for N in range(0, BATCH_TILE, 4):
        vn${ABC[N:N+4]} = _mm_sub_ps(vn${ABC[N:N+4]}, vmagic_bias);

      $for N in range(0, BATCH_TILE, 4):
        __m128 vt${ABC[N:N+4]} = _mm_add_ps(vz${ABC[N:N+4]}, _mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_hi));

      $for N in range(0, BATCH_TILE, 4):
        vt${ABC[N:N+4]} = _mm_add_ps(vt${ABC[N:N+4]}, _mm_mul_ps(vn${ABC[N:N+4]}, vminus_ln2_lo));

      $for N in range(0, BATCH_TILE, 4):
        __m128 vp${ABC[N:N+4]} = _mm_mul_ps(vt${ABC[N:N+4]}, vc2);

      $for N in range(0, BATCH_TILE, 4):
        vp${ABC[N:N+4]} = _mm_add_ps(vt${ABC[N:N+4]}, _mm_mul_ps(vp${ABC[N:N+4]}, vt${ABC[N:N+4]}));

      $for N in range(0, BATCH_TILE, 4):
        const __m128 vy${ABC[N:N+4]} = _mm_add_ps(vs${ABC[N:N+4]}, _mm_mul_ps(vs${ABC[N:N+4]}, vp${ABC[N:N+4]}));

      $for N in range(0, BATCH_TILE, 4):
        __m128 vf${ABC[N:N+4]} = _mm_div_ps(vy${ABC[N:N+4]}, _mm_add_ps(vy${ABC[N:N+4]}, vone));

      $for N in range(0, BATCH_TILE, 4):
        vf${ABC[N:N+4]} = _mm_andnot_ps(_mm_cmplt_ps(vz${ABC[N:N+4]}, vdenorm_cutoff), vf${ABC[N:N+4]});

      $if SSE >= 4:
        $for N in range(0, BATCH_TILE, 4):
          vf${ABC[N:N+4]} = _mm_blendv_ps(_mm_sub_ps(vone, vf${ABC[N:N+4]}), vf${ABC[N:N+4]}, vx${ABC[N:N+4]});
      $else:
        $for N in range(0, BATCH_TILE, 4):
          const __m128 vm${ABC[N:N+4]} = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx${ABC[N:N+4]})));

        $for N in range(0, BATCH_TILE, 4):
          vf${ABC[N:N+4]} = _mm_or_ps(_mm_and_ps(vf${ABC[N:N+4]}, vm${ABC[N:N+4]}), _mm_andnot_ps(vm${ABC[N:N+4]}, _mm_sub_ps(vone, vf${ABC[N:N+4]})));

      _mm_storeu_ps(y, vf${ABC[0:4]});
      $for N in range(4, BATCH_TILE, 4):
        _mm_storeu_ps(y + ${N}, vf${ABC[N:N+4]});
      y += ${BATCH_TILE};
    }
  for (; n >= 4 * sizeof(float); n -= 4 * sizeof(float)) {
    const __m128 vx = _mm_loadu_ps(x);
    x += 4;

    const __m128 vz = _mm_or_ps(vx, vsign_mask);

    __m128 vn = _mm_add_ps(_mm_mul_ps(vz, vlog2e), vmagic_bias);
    const __m128i ve = _mm_slli_epi32(_mm_castps_si128(vn), 17);

    const __m128i vidx = _mm_slli_epi32(_mm_and_si128(_mm_castps_si128(vn), vindex_mask), 2);
    #if XNN_ARCH_X86_64
      const uint64_t vidx_lo = (uint64_t) _mm_cvtsi128_si64(vidx);
      $if SSE >= 4:
        const uint64_t vidx_hi = (uint64_t) _mm_extract_epi64(vidx, 1);
      $else:
        const uint64_t vidx_hi = (uint64_t) _mm_cvtsi128_si64(_mm_unpackhi_epi64(vidx, vidx));
      const __m128i vl_ll   = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx_lo)));
      const __m128i vl_hl = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx_hi)));
      $if SSE >= 4:
        const __m128i vl_lo = _mm_insert_epi32(vl_ll, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_lo >> 32))), 1);
      $else:
        const __m128i vl_lh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_lo >> 32))));
        const __m128i vl_lo = _mm_unpacklo_epi32(vl_ll, vl_lh);
      $if SSE >= 4:
        const __m128i vl_hi = _mm_insert_epi32(vl_hl, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_hi >> 32))), 1);
      $else:
        const __m128i vl_hh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_hi >> 32))));
        const __m128i vl_hi = _mm_unpacklo_epi32(vl_hl, vl_hh);
    #else  // !XNN_ARCH_X86_64
      const __m128i vl_ll = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_cvtsi128_si32(vidx))));
      const __m128i vl_hl = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 4))));
      $if SSE >= 4:
        const __m128i vl_lo = _mm_insert_epi32(vl_ll, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 2))), 1);
      $else:
        const __m128i vl_lh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 2))));
        const __m128i vl_lo = _mm_unpacklo_epi32(vl_ll, vl_lh);
      $if SSE >= 4:
        const __m128i vl_hi = _mm_insert_epi32(vl_hl, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 6))), 1);
      $else:
        const __m128i vl_hh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 6))));
        const __m128i vl_hi = _mm_unpacklo_epi32(vl_hl, vl_hh);
    #endif  // XNN_ARCH_X86_64
    const __m128i vl = _mm_unpacklo_epi64(vl_lo, vl_hi);

    const __m128 vs = _mm_castsi128_ps(_mm_add_epi32(vl, ve));
    vn = _mm_sub_ps(vn, vmagic_bias);

    __m128 vt = _mm_add_ps(vz, _mm_mul_ps(vn, vminus_ln2_hi));
    vt = _mm_add_ps(vt, _mm_mul_ps(vn, vminus_ln2_lo));

    __m128 vp = _mm_mul_ps(vt, vc2);
    vp = _mm_add_ps(vt, _mm_mul_ps(vp, vt));

    const __m128 vy = _mm_add_ps(vs, _mm_mul_ps(vs, vp));

    __m128 vf = _mm_div_ps(vy, _mm_add_ps(vy, vone));
    vf = _mm_andnot_ps(_mm_cmplt_ps(vz, vdenorm_cutoff), vf);
    $if SSE >= 4:
      vf = _mm_blendv_ps(_mm_sub_ps(vone, vf), vf, vx);
    $else:
      const __m128 vm = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx)));
      vf = _mm_or_ps(_mm_and_ps(vf, vm), _mm_andnot_ps(vm, _mm_sub_ps(vone, vf)));

    _mm_storeu_ps(y, vf);
    y += 4;
  }
  if XNN_UNLIKELY(n != 0) {
    const __m128 vx = _mm_loadu_ps(x);

    const __m128 vz = _mm_or_ps(vx, vsign_mask);

    __m128 vn = _mm_add_ps(_mm_mul_ps(vz, vlog2e), vmagic_bias);
    const __m128i ve = _mm_slli_epi32(_mm_castps_si128(vn), 17);

    const __m128i vidx = _mm_slli_epi32(_mm_and_si128(_mm_castps_si128(vn), vindex_mask), 2);
    #if XNN_ARCH_X86_64
      const uint64_t vidx_lo = (uint64_t) _mm_cvtsi128_si64(vidx);
      $if SSE >= 4:
        const uint64_t vidx_hi = (uint64_t) _mm_extract_epi64(vidx, 1);
      $else:
        const uint64_t vidx_hi = (uint64_t) _mm_cvtsi128_si64(_mm_unpackhi_epi64(vidx, vidx));
      const __m128i vl_ll   = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx_lo)));
      const __m128i vl_hl = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) vidx_hi)));
      $if SSE >= 4:
        const __m128i vl_lo = _mm_insert_epi32(vl_ll, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_lo >> 32))), 1);
      $else:
        const __m128i vl_lh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_lo >> 32))));
        const __m128i vl_lo = _mm_unpacklo_epi32(vl_ll, vl_lh);
      $if SSE >= 4:
        const __m128i vl_hi = _mm_insert_epi32(vl_hl, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_hi >> 32))), 1);
      $else:
        const __m128i vl_hh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) (vidx_hi >> 32))));
        const __m128i vl_hi = _mm_unpacklo_epi32(vl_hl, vl_hh);
    #else  // !XNN_ARCH_X86_64
      const __m128i vl_ll = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_cvtsi128_si32(vidx))));
      const __m128i vl_hl = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 4))));
      $if SSE >= 4:
        const __m128i vl_lo = _mm_insert_epi32(vl_ll, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 2))), 1);
      $else:
        const __m128i vl_lh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 2))));
        const __m128i vl_lo = _mm_unpacklo_epi32(vl_ll, vl_lh);
      $if SSE >= 4:
        const __m128i vl_hi = _mm_insert_epi32(vl_hl, *((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 6))), 1);
      $else:
        const __m128i vl_hh = _mm_cvtsi32_si128(*((const int*) ((uintptr_t) xnn_table_exp2minus_k_over_64 + (uint32_t) _mm_extract_epi16(vidx, 6))));
        const __m128i vl_hi = _mm_unpacklo_epi32(vl_hl, vl_hh);
    #endif  // XNN_ARCH_X86_64
    const __m128i vl = _mm_unpacklo_epi64(vl_lo, vl_hi);

    const __m128 vs = _mm_castsi128_ps(_mm_add_epi32(vl, ve));
    vn = _mm_sub_ps(vn, vmagic_bias);

    __m128 vt = _mm_add_ps(vz, _mm_mul_ps(vn, vminus_ln2_hi));
    vt = _mm_add_ps(vt, _mm_mul_ps(vn, vminus_ln2_lo));

    __m128 vp = _mm_mul_ps(vt, vc2);
    vp = _mm_add_ps(vt, _mm_mul_ps(vp, vt));

    const __m128 vy = _mm_add_ps(vs, _mm_mul_ps(vs, vp));

    __m128 vf = _mm_div_ps(vy, _mm_add_ps(vy, vone));
    vf = _mm_andnot_ps(_mm_cmplt_ps(vz, vdenorm_cutoff), vf);
    $if SSE >= 4:
      vf = _mm_blendv_ps(_mm_sub_ps(vone, vf), vf, vx);
    $else:
      const __m128 vm = _mm_castsi128_ps(_mm_cmpgt_epi32(_mm_setzero_si128(), _mm_castps_si128(vx)));
      vf = _mm_or_ps(_mm_and_ps(vf, vm), _mm_andnot_ps(vm, _mm_sub_ps(vone, vf)));

    if (n & (2 * sizeof(float))) {
      _mm_storel_pi((__m64*) y, vf);
      vf = _mm_movehl_ps(vf, vf);
      y += 2;
    }
    if (n & (1 * sizeof(float))) {
      _mm_store_ss(y, vf);
    }
  }
}