src/f32-raddexpminusmax/avx512f-p5-scalef.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 % 16 == 0
$assert ELEMENTS_TILE >= 16
$SIMD_TILE = ELEMENTS_TILE // 16
$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
#include <assert.h>

#include <immintrin.h>

#include <xnnpack/intrinsics-polyfill.h>
#include <xnnpack/raddexpminusmax.h>


void xnn_f32_raddexpminusmax_ukernel__avx512f_p5_scalef_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}(
    size_t elements,
    const float* input,
    float* sum,
    float max)
{
  assert(elements % sizeof(float) == 0);

  const __m512 vlog2e = _mm512_set1_ps(0x1.715476p+0f);
  const __m512 vminus_ln2_hi = _mm512_set1_ps(-0x1.62E43p-1f);
  const __m512 vminus_ln2_lo = _mm512_set1_ps(0x1.05C61p-29f);

  const __m512 vc0 = _mm512_set1_ps(1.0f);
  const __m512 vc1 = _mm512_set1_ps(0x1.FFFFF6p-1f);
  const __m512 vc2 = _mm512_set1_ps(0x1.FFFDC6p-2f);
  const __m512 vc3 = _mm512_set1_ps(0x1.555A80p-3f);
  const __m512 vc4 = _mm512_set1_ps(0x1.573A1Ap-5f);
  const __m512 vc5 = _mm512_set1_ps(0x1.0F9F9Cp-7f);

  const __m512 vi_max = _mm512_set1_ps(max);

  $for K in range(ACCUMULATORS):
    __m512 vacc${K} = _mm512_setzero_ps();
  for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) {
    // Load ${ELEMENTS_TILE} (${SIMD_TILE}x16) inputs at a time.
    const __m512 vi0 = _mm512_loadu_ps(input);
    $for N in range(1, SIMD_TILE):
      const __m512 vi${N} = _mm512_loadu_ps(input + ${N * 16});
    input += ${ELEMENTS_TILE};

    // Subtract maximum input x := i - i_max.
    $for N in range(SIMD_TILE):
      const __m512 vx${N} = _mm512_sub_ps(vi${N}, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    $for N in range(SIMD_TILE):
      const __m512 vn${N} = _mm512_roundscale_ps(_mm512_mul_ps(vx${N}, vlog2e), 0);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    $for N in range(SIMD_TILE):
      __m512 vt${N} = _mm512_fmadd_ps(vn${N}, vminus_ln2_hi, vx${N});

    $for N in range(SIMD_TILE):
      vt${N} = _mm512_fmadd_ps(vn${N}, vminus_ln2_lo, vt${N});

    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
    $for N in range(SIMD_TILE):
      __m512 vp${N} = _mm512_fmadd_ps(vc5, vt${N}, vc4);

    $for N in range(SIMD_TILE):
      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc3);

    $for N in range(SIMD_TILE):
      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc2);

    $for N in range(SIMD_TILE):
      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc1);

    $for N in range(SIMD_TILE):
      vp${N} = _mm512_fmadd_ps(vp${N}, vt${N}, vc0);

    // Reconstruct the final f value:
    //   f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = 2**elements * p
    $for N in range(SIMD_TILE):
      const __m512 vf${N} = _mm512_scalef_ps(vp${N}, vn${N});

    // Accumulate computed exponents.
    $for N in range(SIMD_TILE):
      vacc${N % ACCUMULATORS} = _mm512_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} = _mm512_add_ps(vacc${A}, vacc${A + ACC_SLICE});
      $ACC_SLICE *= 2

  __m512 vacc = vacc0;
  for (; elements >= 16 * sizeof(float); elements -= 16 * sizeof(float)) {
    // Load 16 inputs at a time.
    const __m512 vi = _mm512_loadu_ps(input);
    input += 16;

    // Subtract maximum input x := i - i_max.
    const __m512 vx = _mm512_sub_ps(vi, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
    vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);

    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
    __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
    vp = _mm512_fmadd_ps(vp, vt, vc3);
    vp = _mm512_fmadd_ps(vp, vt, vc2);
    vp = _mm512_fmadd_ps(vp, vt, vc1);
    vp = _mm512_fmadd_ps(vp, vt, vc0);

    // Reconstruct the final f value:
    //   f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = 2**elements * p
    const __m512 vf = _mm512_scalef_ps(vp, vn);

    // Accumulate computed exponents.
    vacc = _mm512_add_ps(vacc, vf);
  }
  if (elements != 0) {
    // Prepare mask for valid 32-bit elements (depends on elements).
    elements >>= 2 /* log2(sizeof(float)) */;
    const __mmask16 vmask = _cvtu32_mask16((uint16_t) ((uint32_t) (UINT32_C(1) << elements) - UINT32_C(1)));

    // Load up to 15 inputs at a time.
    const __m512 vi = _mm512_maskz_loadu_ps(vmask, input);

    // Subtract maximum input x := i - i_max.
    const __m512 vx = _mm512_sub_ps(vi, vi_max);

    // Compute reduced argument elements := round(x / log(2)).
    const __m512 vn = _mm512_roundscale_ps(_mm512_mul_ps(vx, vlog2e), 0);

    // Compute reduced argument t := x - elements * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    __m512 vt = _mm512_fmadd_ps(vn, vminus_ln2_hi, vx);
    vt = _mm512_fmadd_ps(vn, vminus_ln2_lo, vt);

    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
    __m512 vp = _mm512_fmadd_ps(vc5, vt, vc4);
    vp = _mm512_fmadd_ps(vp, vt, vc3);
    vp = _mm512_fmadd_ps(vp, vt, vc2);
    vp = _mm512_fmadd_ps(vp, vt, vc1);
    vp = _mm512_fmadd_ps(vp, vt, vc0);

    // Reconstruct the final f value:
    //   f = 2**elements * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
    //     = 2**elements * p
    const __m512 vf = _mm512_scalef_ps(vp, vn);

    // Accumulate computed exponents.
    vacc = _mm512_mask_add_ps(vacc, vmask, vacc, vf);
  }
  *sum = _mm512_reduce_add_ps(vacc);
}