src/f32-raddstoreexpminusmax/gen/scalar-p5-x4-acc2.c

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

#include <assert.h>

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

#include <fp16/bitcasts.h>


void xnn_f32_raddstoreexpminusmax_ukernel__scalar_p5_x4_acc2(
    size_t elements,
    const float* input,
    float* output,
    float* sum,
    float vi_max)
{
  assert(elements % sizeof(float) == 0);

  const float vmagic_bias = 0x1.8000FEp23f;
  // The smallest x for which expf(x) is normalized.
  const float vdenorm_cutoff = -0x1.5D589Ep6f;
  const float vlog2e = 0x1.715476p+0f;
  // Last 7 bits are zeroes
  const float vminus_ln2_hi = -0x1.62E400p-1f;
  const float vminus_ln2_lo = -0x1.7F7D1Cp-20f;

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

  float vacc0 = 0.0f;
  float vacc1 = 0.0f;
  for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
    // Load 4 inputs at a time.
    const float vi0 = input[0];
    const float vi1 = input[1];
    const float vi2 = input[2];
    const float vi3 = input[3];
    input += 4;

    // Subtract maximum input x := i - i_max. This implies x <= 0.
    const float vx0 = vi0 - vi_max;
    const float vx1 = vi1 - vi_max;
    const float vx2 = vi2 - vi_max;
    const float vx3 = vi3 - vi_max;

    // Compute reduced argument n := round(x / log(2)).
    // We do it by adding a large number (magic bias) to the product x * (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 outside of [-87.336540, 0.0] underflow expf(x)
    // anyway. We fixup the result for such inputs at the very end of the algorithm.
    float vn0 = vx0 * vlog2e + vmagic_bias;
    float vn1 = vx1 * vlog2e + vmagic_bias;
    float vn2 = vx2 * vlog2e + vmagic_bias;
    float vn3 = vx3 * 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 <= x <= 0.0, and -126 <= n <= 0 accordingly.
    const float vs0 = fp32_from_bits(fp32_to_bits(vn0) << 23);
    const float vs1 = fp32_from_bits(fp32_to_bits(vn1) << 23);
    const float vs2 = fp32_from_bits(fp32_to_bits(vn2) << 23);
    const float vs3 = fp32_from_bits(fp32_to_bits(vn3) << 23);

    // Subtract the large number back to get final n := round(x / log(2)).
    vn0 -= vmagic_bias;
    vn1 -= vmagic_bias;
    vn2 -= vmagic_bias;
    vn3 -= vmagic_bias;

    // Compute reduced argument t := x - n * log(2).
    // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
    float vt0 = vn0 * vminus_ln2_hi + vx0;
    float vt1 = vn1 * vminus_ln2_hi + vx1;
    float vt2 = vn2 * vminus_ln2_hi + vx2;
    float vt3 = vn3 * vminus_ln2_hi + vx3;

    vt0 = vn0 * vminus_ln2_lo + vt0;
    vt1 = vn1 * vminus_ln2_lo + vt1;
    vt2 = vn2 * vminus_ln2_lo + vt2;
    vt3 = vn3 * vminus_ln2_lo + vt3;

    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
    float vp0 = vc5 * vt0 + vc4;
    float vp1 = vc5 * vt1 + vc4;
    float vp2 = vc5 * vt2 + vc4;
    float vp3 = vc5 * vt3 + vc4;

    vp0 = vp0 * vt0 + vc3;
    vp1 = vp1 * vt1 + vc3;
    vp2 = vp2 * vt2 + vc3;
    vp3 = vp3 * vt3 + vc3;

    vp0 = vp0 * vt0 + vc2;
    vp1 = vp1 * vt1 + vc2;
    vp2 = vp2 * vt2 + vc2;
    vp3 = vp3 * vt3 + vc2;

    vp0 = vp0 * vt0 + vc1;
    vp1 = vp1 * vt1 + vc1;
    vp2 = vp2 * vt2 + vc1;
    vp3 = vp3 * vt3 + 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
    vt0 *= vs0;
    vt1 *= vs1;
    vt2 *= vs2;
    vt3 *= vs3;

    float vf0 = vt0 * vp0 + vs0;
    float vf1 = vt1 * vp1 + vs1;
    float vf2 = vt2 * vp2 + vs2;
    float vf3 = vt3 * vp3 + vs3;

    // For inputs below denormal cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    if XNN_UNPREDICTABLE(vx0 < vdenorm_cutoff) {
      vf0 = 0.0f;
    }
    if XNN_UNPREDICTABLE(vx1 < vdenorm_cutoff) {
      vf1 = 0.0f;
    }
    if XNN_UNPREDICTABLE(vx2 < vdenorm_cutoff) {
      vf2 = 0.0f;
    }
    if XNN_UNPREDICTABLE(vx3 < vdenorm_cutoff) {
      vf3 = 0.0f;
    }

    // Store 4 outputs at a time.
    output[0] = vf0;
    output[1] = vf1;
    output[2] = vf2;
    output[3] = vf3;
    output += 4;

    // Accumulate computed exponents.
    vacc0 += vf0;
    vacc1 += vf1;
    vacc0 += vf2;
    vacc1 += vf3;
  }
  // Add up all accumulators to vacc0
  vacc0 += vacc1;

  float vacc = vacc0;
  for (; elements >= sizeof(float); elements -= sizeof(float)) {
    // Load 1 input at a time.
    const float vi = *input++;

    // Subtract maximum input x := i - i_max. This implies x <= 0.
    const float vx = vi - vi_max;

    // Compute reduced argument n := round(x / log(2)).
    // We do it by adding a large number (magic bias) to the product x * (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 outside of [-87.336540, 0.0] underflow expf(x)
    // anyway. We fixup the result for such inputs at the very end of the algorithm.
    float vn = vx * 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 <= x <= 0.0, and -126 <= n <= 0 accordingly.
    const float vs = fp32_from_bits(fp32_to_bits(vn) << 23);

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

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

    // Compute degree-5 polynomial approximation for exp(t) on [-log(2)/2, log(2)/2].
    float vp = vc5 * vt + vc4;
    vp = vp * vt + vc3;
    vp = vp * vt + vc2;
    vp = 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 *= vs;
    float vf = vt * vp + vs;

    // For inputs below denormal cutoff, replace output with +0.0f.
    // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
    if XNN_UNPREDICTABLE(vx < vdenorm_cutoff) {
      vf = 0.0f;
    }

    // Store 1 output at a time.
    *output++ = vf;

    // Accumulate computed exponents.
    vacc += vf;
  }
  *sum = vacc;
}