src/f32-raddstoreexpminusmax/avx2-p5.c.in

// Copyright 2019 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 ELEMENTS_TILE % 8 == 0
$assert ELEMENTS_TILE >= 8
$SIMD_TILE = ELEMENTS_TILE // 8
$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
#include <assert.h>

#include <immintrin.h>

#include <xnnpack/raddstoreexpminusmax.h>


static const int32_t mask_table[14] = {-1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0};

void xnn_f32_raddstoreexpminusmax_ukernel__avx2_p5_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}(
    size_t elements,
    const float* input,
    float* output,
    float* sum,
    float max)
{
  assert(elements % sizeof(float) == 0);

  const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
  // The smallest x for which expf(x) is normalized.
  const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep6f);
  const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
  const __m256 vminus_ln2_hi = _mm256_set1_ps(-0x1.62E43p-1f);
  const __m256 vminus_ln2_lo = _mm256_set1_ps(0x1.05C61p-29f);

  const __m256 vc1 = _mm256_set1_ps(0x1.FFFFF6p-1f);
  const __m256 vc2 = _mm256_set1_ps(0x1.FFFDC6p-2f);
  const __m256 vc3 = _mm256_set1_ps(0x1.555A80p-3f);
  const __m256 vc4 = _mm256_set1_ps(0x1.573A1Ap-5f);
  const __m256 vc5 = _mm256_set1_ps(0x1.0F9F9Cp-7f);

  const __m256 vi_max = _mm256_set1_ps(max);

  $for K in range(ACCUMULATORS):
    __m256 vacc${K} = _mm256_setzero_ps();
  for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) {
    // Load ${ELEMENTS_TILE} (${SIMD_TILE}x8) inputs at a time.
    const __m256 vi0 = _mm256_loadu_ps(input);
    $for N in range(1, SIMD_TILE):
      const __m256 vi${N} = _mm256_loadu_ps(input + ${N * 8});
    input += ${ELEMENTS_TILE};

    // Subtract maximum input x := i - i_max. This implies x <= 0.
    $for N in range(SIMD_TILE):
      const __m256 vx${N} = _mm256_sub_ps(vi${N}, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    $for N in range(SIMD_TILE):
      __m256 vn${N} = _mm256_fmadd_ps(vx${N}, vlog2e, vmagic_bias);

    // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
    // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
    $for N in range(SIMD_TILE):
      const __m256 vs${N} = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn${N}), 23));

    // Subtract the large number back to get final elements := round(x / log(2)).
    $for N in range(SIMD_TILE):
      vn${N} = _mm256_sub_ps(vn${N}, vmagic_bias);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    $for N in range(SIMD_TILE):
      __m256 vt${N} = _mm256_fmadd_ps(vn${N}, vminus_ln2_hi, vx${N});

    $for N in range(SIMD_TILE):
      vt${N} = _mm256_fmadd_ps(vn${N}, vminus_ln2_lo, vt${N});

    // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
    $for N in range(SIMD_TILE):
      __m256 vp${N} = _mm256_fmadd_ps(vc5, vt${N}, vc4);

    $for N in range(SIMD_TILE):
      vp${N} = _mm256_fmadd_ps(vp${N}, vt${N}, vc3);

    $for N in range(SIMD_TILE):
      vp${N} = _mm256_fmadd_ps(vp${N}, vt${N}, vc2);

    $for N in range(SIMD_TILE):
      vp${N} = _mm256_fmadd_ps(vp${N}, vt${N}, vc1);

    // Reconstruct the final f value:
    //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
    //     = s + (t * s) * p
    $for N in range(SIMD_TILE):
      vt${N} = _mm256_mul_ps(vt${N}, vs${N});

    $for N in range(SIMD_TILE):
      __m256 vf${N} = _mm256_fmadd_ps(vt${N}, vp${N}, vs${N});

    // For inputs below zero cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    $for N in range(SIMD_TILE):
      vf${N} = _mm256_andnot_ps(_mm256_cmp_ps(vx${N}, vdenorm_cutoff, _CMP_LT_OS), vf${N});

    // Store ${ELEMENTS_TILE} (${SIMD_TILE}x8) outputs at a time.
    _mm256_storeu_ps(output, vf0);
    $for N in range(1, SIMD_TILE):
      _mm256_storeu_ps(output + ${N * 8}, vf${N});
    output += ${ELEMENTS_TILE};

    // Accumulate computed exponents.
    $for N in range(SIMD_TILE):
      vacc${N % ACCUMULATORS} = _mm256_add_ps(vacc${N % ACCUMULATORS}, vf${N});
  }
  $if ACCUMULATORS > 1:
    // Add up all accumulators to vacc0
    $ACC_SLICE = 1
    $while ACC_SLICE < ACCUMULATORS:
      $for A in range(0, ACCUMULATORS, ACC_SLICE * 2):
        $if A + ACC_SLICE < ACCUMULATORS:
          vacc${A} = _mm256_add_ps(vacc${A}, vacc${A + ACC_SLICE});
      $ACC_SLICE *= 2

  __m256 vacc = vacc0;
  for (; elements >= 8 * sizeof(float); elements -= 8 * sizeof(float)) {
    // Load 8 inputs at a time.
    const __m256 vi = _mm256_loadu_ps(input);
    input += 8;

    // Subtract maximum input x := i - i_max. This implies x <= 0.
    const __m256 vx = _mm256_sub_ps(vi, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);

    // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
    // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
    const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

    // Subtract the large number back to get final elements := round(x / log(2)).
    vn = _mm256_sub_ps(vn, vmagic_bias);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
    vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

    // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
    __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
    vp = _mm256_fmadd_ps(vp, vt, vc3);
    vp = _mm256_fmadd_ps(vp, vt, vc2);
    vp = _mm256_fmadd_ps(vp, vt, vc1);

    // Reconstruct the final f value:
    //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
    //     = s + (t * s) * p
    vt = _mm256_mul_ps(vt, vs);
    __m256 vf = _mm256_fmadd_ps(vt, vp, vs);

    // For inputs below zero cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);

    // Store 8 outputs at a time.
    _mm256_storeu_ps(output, vf);
    output += 8;

    // Accumulate computed exponents.
    vacc = _mm256_add_ps(vacc, vf);
  }
  if (elements != 0) {
    assert(elements >= 1 * sizeof(float));
    assert(elements <= 7 * sizeof(float));
    const __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - elements));

    // Load up to 7 inputs at a time.
    const __m256 vi = _mm256_maskload_ps(input, vmask);

    // Subtract maximum input x := i - i_max. This implies x <= 0.
    const __m256 vx = _mm256_sub_ps(vi, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    __m256 vn = _mm256_fmadd_ps(vx, vlog2e, vmagic_bias);

    // Create a floating-point number s (scale) such that s == 2**elements for inputs which don't cause underflow, i.e.
    // -87.33642 <= x <= 0.0, and -126 <= elements <= 0 accordingly.
    const __m256 vs = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn), 23));

    // Subtract the large number back to get final elements := round(x / log(2)).
    vn = _mm256_sub_ps(vn, vmagic_bias);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2_hi, vx);
    vt = _mm256_fmadd_ps(vn, vminus_ln2_lo, vt);

    // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
    __m256 vp = _mm256_fmadd_ps(vc5, vt, vc4);
    vp = _mm256_fmadd_ps(vp, vt, vc3);
    vp = _mm256_fmadd_ps(vp, vt, vc2);
    vp = _mm256_fmadd_ps(vp, vt, vc1);

    // Reconstruct the final f value:
    //   f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
    //     = s + (t * s) * p
    vt = _mm256_mul_ps(vt, vs);
    __m256 vf = _mm256_fmadd_ps(vt, vp, vs);

    // For inputs below zero cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    vf = _mm256_andnot_ps(_mm256_cmp_ps(vx, vdenorm_cutoff, _CMP_LT_OS), vf);

    // Store up to 7 outputs at a time.
    _mm256_maskstore_ps(output, vmask, vf);

    // Accumulate computed exponents. And addend with mask to leave unmasked 32-bit lanes unchanged.
    vacc = _mm256_add_ps(vacc, _mm256_and_ps(vf, _mm256_castsi256_ps(vmask)));
  }
  // Reduce 8 elements in the SIMD register
  __m128 vacc_lo = _mm_add_ps(_mm256_castps256_ps128(vacc), _mm256_extractf128_ps(vacc, 1));
  vacc_lo = _mm_add_ps(vacc_lo, _mm_movehl_ps(vacc_lo, vacc_lo));
  vacc_lo = _mm_add_ss(vacc_lo, _mm_movehdup_ps(vacc_lo));
  _mm_store_ss(sum, vacc_lo);
  _mm256_zeroupper();
}