f32-sigmoid/gen/avx2-rr1-p5-nr2fma-x16.c

// Auto-generated file. Do not edit!
//   Template: src/f32-sigmoid/avx2-p5.c.in
//   Generator: tools/xngen
//
// 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.

#include <assert.h>

#include <immintrin.h>

#include <xnnpack/common.h>
#include <xnnpack/vunary.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_sigmoid_ukernel__avx2_rr1_p5_nr2fma_x16(
    size_t n,
    const float* x,
    float* y,
    const void* params)
{
  assert(n % sizeof(float) == 0);

  const __m256 vmagic_bias = _mm256_set1_ps(0x1.8000FEp23f);
  // The smallest x for which sigmoidf(x) is normalized.
  // This number is also the smallest x for which expf(x) is normalized.
  const __m256 vdenorm_cutoff = _mm256_set1_ps(-0x1.5D589Ep+6f);
  const __m256 vlog2e = _mm256_set1_ps(0x1.715476p+0f);
  const __m256 vminus_ln2 = _mm256_set1_ps(-0x1.62E43p-1f);
  const __m256 vone = _mm256_set1_ps(1.0f);
  const __m256 vsign_mask = _mm256_set1_ps(-0.0f);

  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);

  for (; n >= 16 * sizeof(float); n -= 16 * sizeof(float)) {
    const __m256 vx0 = _mm256_loadu_ps(x);
    const __m256 vx1 = _mm256_loadu_ps(x + 8);
    x += 16;

    // General structure of the algorithm:
    //           / exp(x) / (1 + exp(x)) if x <= 0
    //   f[x] :=
    //           \ 1 - f[-x] if x >= 0
    //
    // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
    // then replace result with 1 - f[z] if x >= 0.
    const __m256 vz0 = _mm256_or_ps(vx0, vsign_mask);
    const __m256 vz1 = _mm256_or_ps(vx1, vsign_mask);

    // Compute reduced argument n := round(z / log(2)).
    // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
    // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
    // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
    // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
    // the algorithm.
    __m256 vn0 = _mm256_fmadd_ps(vz0, vlog2e, vmagic_bias);
    __m256 vn1 = _mm256_fmadd_ps(vz1, vlog2e, vmagic_bias);

    // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
    // -87.33642 <= z <= 0.0, and -126 <= n <= 0 accordingly.
    const __m256 vs0 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn0), 23));
    const __m256 vs1 = _mm256_castsi256_ps(_mm256_slli_epi32(_mm256_castps_si256(vn1), 23));

    // Subtract the large number back to get final n := round(z / log(2)).
    vn0 = _mm256_sub_ps(vn0, vmagic_bias);
    vn1 = _mm256_sub_ps(vn1, vmagic_bias);

    // Compute reduced argument t := z - n * log(2).
    __m256 vt0 = _mm256_fmadd_ps(vn0, vminus_ln2, vz0);
    __m256 vt1 = _mm256_fmadd_ps(vn1, vminus_ln2, vz1);

    // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
    __m256 vp0 = _mm256_fmadd_ps(vc5, vt0, vc4);
    __m256 vp1 = _mm256_fmadd_ps(vc5, vt1, vc4);

    vp0 = _mm256_fmadd_ps(vp0, vt0, vc3);
    vp1 = _mm256_fmadd_ps(vp1, vt1, vc3);

    vp0 = _mm256_fmadd_ps(vp0, vt0, vc2);
    vp1 = _mm256_fmadd_ps(vp1, vt1, vc2);

    vp0 = _mm256_fmadd_ps(vp0, vt0, vc1);
    vp1 = _mm256_fmadd_ps(vp1, vt1, vc1);

    // Reconstruct the exp(z) value:
    //   e = 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
    vt0 = _mm256_mul_ps(vt0, vs0);
    vt1 = _mm256_mul_ps(vt1, vs1);

    const __m256 ve0 = _mm256_fmadd_ps(vt0, vp0, vs0);
    const __m256 ve1 = _mm256_fmadd_ps(vt1, vp1, vs1);

    // Denominator of the sigmoid fraction: 1.0 + exp(z)
    const __m256 vd0 = _mm256_add_ps(ve0, vone);
    const __m256 vd1 = _mm256_add_ps(ve1, vone);

    // Use Newton-Raphson method to compute reciprocal of denominator.
    // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
    // Thus the reciprocal of the denominator never overflows.
    __m256 vr0 = _mm256_rcp_ps(vd0);
    __m256 vr1 = _mm256_rcp_ps(vd1);

    vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0);
    vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1);

    vr0 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr0, vd0, vone), vr0, vr0);
    vr1 = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr1, vd1, vone), vr1, vr1);

    // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
    __m256 vf0 = _mm256_mul_ps(ve0, vr0);
    __m256 vf1 = _mm256_mul_ps(ve1, vr1);

    // For inputs below denormal cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    vf0 = _mm256_andnot_ps(_mm256_cmp_ps(vz0, vdenorm_cutoff, _CMP_LT_OS), vf0);
    vf1 = _mm256_andnot_ps(_mm256_cmp_ps(vz1, vdenorm_cutoff, _CMP_LT_OS), vf1);

    // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
    vf0 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf0), vf0, vx0);
    vf1 = _mm256_blendv_ps(_mm256_sub_ps(vone, vf1), vf1, vx1);

    _mm256_storeu_ps(y, vf0);
    _mm256_storeu_ps(y + 8, vf1);
    y += 16;
  }
  for (; n >= 8 * sizeof(float); n -= 8 * sizeof(float)) {
    const __m256 vx = _mm256_loadu_ps(x);
    x += 8;

    // General structure of the algorithm:
    //           / exp(x) / (1 + exp(x)) if x <= 0
    //   f[x] :=
    //           \ 1 - f[-x] if x >= 0
    //
    // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
    // then replace result with 1 - f[z] if x >= 0.
    const __m256 vz = _mm256_or_ps(vx, vsign_mask);

    // Compute reduced argument n := round(z / log(2)).
    // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
    // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
    // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
    // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
    // the algorithm.
    __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

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

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

    // Compute reduced argument t := z - n * log(2).
    __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);

    // 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 exp(z) value:
    //   e = 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);
    const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

    // Denominator of the sigmoid fraction: 1.0 + exp(z)
    const __m256 vd = _mm256_add_ps(ve, vone);

    // Use Newton-Raphson method to compute reciprocal of denominator.
    // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
    // Thus the reciprocal of the denominator never overflows.
    __m256 vr = _mm256_rcp_ps(vd);
    vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
    vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

    // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
    __m256 vf = _mm256_mul_ps(ve, vr);

    // For inputs below denormal 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(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

    // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
    vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

    _mm256_storeu_ps(y, vf);
    y += 8;
  }
  if XNN_UNLIKELY(n != 0) {
    assert(n >= 1 * sizeof(float));
    assert(n <= 7 * sizeof(float));
    __m256i vmask = _mm256_loadu_si256((const __m256i*) ((uintptr_t) &mask_table[7] - n));

    const __m256 vx = _mm256_maskload_ps(x, vmask);

    // General structure of the algorithm:
    //           / exp(x) / (1 + exp(x)) if x <= 0
    //   f[x] :=
    //           \ 1 - f[-x] if x >= 0
    //
    // First we compute f[z] := exp(z) / (1 + exp(z)) where z = -abs(x),
    // then replace result with 1 - f[z] if x >= 0.
    const __m256 vz = _mm256_or_ps(vx, vsign_mask);

    // Compute reduced argument n := round(z / log(2)).
    // We do it by adding a large number (magic bias) to the product z * (1/log(2)), which cause rounding of the result
    // to an integer, then subtracing the large number back. The trick with adding large number is valid only within
    // certain bounds (|x| <= 2**22), but thats ok, because inputs x outside of [-87.336544, 17.328678] (i.e. z outsize
    // [0, 87.336544]) underflow or saturate sigmoidf(x) anyway. We fixup the result for such inputs at the very end of
    // the algorithm.
    __m256 vn = _mm256_fmadd_ps(vz, vlog2e, vmagic_bias);

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

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

    // Compute reduced argument t := z - n * log(2).
    __m256 vt = _mm256_fmadd_ps(vn, vminus_ln2, vz);

    // 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 exp(z) value:
    //   e = 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);
    const __m256 ve = _mm256_fmadd_ps(vt, vp, vs);

    // Denominator of the sigmoid fraction: 1.0 + exp(z)
    const __m256 vd = _mm256_add_ps(ve, vone);

    // Use Newton-Raphson method to compute reciprocal of denominator.
    // Note: 1 < d <= 2, because z >= 0.0 and 0 < exp(-z) <= 1.0.
    // Thus the reciprocal of the denominator never overflows.
    __m256 vr = _mm256_rcp_ps(vd);
    vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);
    vr = _mm256_fmadd_ps(_mm256_fnmadd_ps(vr, vd, vone), vr, vr);

    // Reconstruct sigmoid(z) = exp(z) * recip(1.0 + exp(z))
    __m256 vf = _mm256_mul_ps(ve, vr);

    // For inputs below denormal 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(vz, vdenorm_cutoff, _CMP_LT_OS), vf);

    // Reconstruct sigmoid(x) = x < 0 ? sigmoid(z) : 1.0 - sigmoid(z)
    vf = _mm256_blendv_ps(_mm256_sub_ps(vone, vf), vf, vx);

    // _mm256_maskstore_ps(y, vmask, vf) could be used here, but triggers msan failures (probably an msan bug).
    __m128 vf_lo = _mm256_castps256_ps128(vf);
    if (n & (4 * sizeof(float))) {
      _mm_storeu_ps(y, vf_lo);
      vf_lo = _mm256_extractf128_ps(vf, 1);
      y += 4;
    }
    if (n & (2 * sizeof(float))) {
      _mm_storel_pi((__m64*) y, vf_lo);
      vf_lo = _mm_movehl_ps(vf_lo, vf_lo);
      y += 2;
    }
    if (n & (1 * sizeof(float))) {
      _mm_store_ss(y, vf_lo);
    }
  }
}