// Auto-generated file. Do not edit!
//   Template: src/f32-vlog/rational-3-3.c.in
//   Generator: tools/xngen
//
// Copyright 2024 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 <stddef.h>

#include "xnnpack/simd/f32-avx512f.h"

#include "xnnpack/common.h"
#include "xnnpack/microparams.h"
#include "xnnpack/vunary.h"

// Define some mathematical constants in case they are not provided by `math.h`.
#ifndef M_LN2
#define M_LN2 0.69314718055994531
#endif  // M_LN2

// Extracts the exponent of the input `a` as a `float` value.
#ifndef HAVE_XNN_SIGNED_GETEXP_F32
#define HAVE_XNN_SIGNED_GETEXP_F32
static XNN_INLINE xnn_simd_f32_t xnn_signed_getexp_f32(xnn_simd_f32_t a) {
  // Create a mask of the zeros in the input.
  __mmask16 zero_mask = _mm512_cmp_ps_mask(a, _mm512_setzero_ps(), _CMP_EQ_OQ);

  // Create a mask of the negative inputs.
  __mmask16 neg_mask = _mm512_cmp_ps_mask(a, _mm512_setzero_ps(), _CMP_LT_OQ);

  // Extract the exponent.
  __m512 res = _mm512_getexp_ps(a);

  // Set the zero inputs to `-Inf` and the negative inputs to `NaN`.
  res = _mm512_castsi512_ps(_mm512_mask_set1_epi32(
      _mm512_castps_si512(res), zero_mask, 0xFF800000 /*Inf*/));
  res = _mm512_castsi512_ps(_mm512_mask_set1_epi32(
      _mm512_castps_si512(res), neg_mask, 0x7FC00001 /*NaN*/));

  return res;
}
#endif  // HAVE_XNN_SIGNED_GETEXP_F32


void xnn_f32_vlog_ukernel__avx512f_rational_3_3_nr_u16(
    size_t batch,
    const float* input,
    float* output,
    const struct xnn_f32_default_params unused_params[restrict XNN_MIN_ELEMENTS(1)])
{
  assert(batch != 0);
  assert(batch % sizeof(float) == 0);
  assert(input != NULL);
  assert(output != NULL);
  assert(xnn_simd_size_f32 == 16);

  // Some useful constants.
  XNN_SIMD_CONST_F32(vone, 1.0f);
  XNN_SIMD_CONST_F32(vln2, M_LN2);
  XNN_SIMD_CONST_F32_FROM_INT32(vmantissa_bits_mask, 0x007FFFFFUL);

  // Note that these two values are not _exactly_ `(float)M_SQRT2` and
  // `(float)M_SQRT1_2`, but are instead chosen such that their product is
  // exactly `1.0f` when evaluated in `float` precision.
  XNN_SIMD_CONST_F32(vsqrt2, 1.4142134190e+00);
  XNN_SIMD_CONST_F32(vsqrt1_2, 7.0710688829e-01);

  // The monomial coefficients of the numerator polynomial.
  // XNN_SIMD_CONST_F32(valpha_0, 0.0f);
  // XNN_SIMD_CONST_F32(valpha_1, 1.0f);
  // XNN_SIMD_CONST_F32(valpha_2, 1.0f);
  XNN_SIMD_CONST_F32(valpha_3, 1.824996918440e-01);

  // The monomial coefficients of the denominator polynomial.
  // XNN_SIMD_CONST_F32(vbeta_0, 1.0f);
  XNN_SIMD_CONST_F32(vbeta_1, 1.5f);
  XNN_SIMD_CONST_F32(vbeta_2, 0.599170029163);
  XNN_SIMD_CONST_F32(vbeta_3, 0.049584995955);

  // Constant needed for the Newton-Raphson iteration of the reciprocal.
  XNN_SIMD_CONST_F32(vtwo, 2.0f);

  for (; batch >= xnn_simd_bytes_f32; batch -= xnn_simd_bytes_f32) {
    xnn_simd_f32_t vx = xnn_loadu_f32(input);
    input += xnn_simd_size_f32;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx = xnn_mul_f32(vx, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);

    // Normalize `x` to an exponent of zero.
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_storeu_f32(output, vy);
    output += xnn_simd_size_f32;
  }
  if XNN_UNLIKELY(batch != 0) {
    xnn_simd_f32_t vx = xnn_load_tail_f32(input, batch >> XNN_LOG2_SIZEOF_FLOAT);

    // See the loop above for comments.
    vx = xnn_mul_f32(vx, vsqrt2);
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_store_tail_f32(output, vy, batch >> XNN_LOG2_SIZEOF_FLOAT);
  }
}

void xnn_f32_vlog_ukernel__avx512f_rational_3_3_nr_u32(
    size_t batch,
    const float* input,
    float* output,
    const struct xnn_f32_default_params unused_params[restrict XNN_MIN_ELEMENTS(1)])
{
  assert(batch != 0);
  assert(batch % sizeof(float) == 0);
  assert(input != NULL);
  assert(output != NULL);
  assert(xnn_simd_size_f32 == 16);

  // Some useful constants.
  XNN_SIMD_CONST_F32(vone, 1.0f);
  XNN_SIMD_CONST_F32(vln2, M_LN2);
  XNN_SIMD_CONST_F32_FROM_INT32(vmantissa_bits_mask, 0x007FFFFFUL);

  // Note that these two values are not _exactly_ `(float)M_SQRT2` and
  // `(float)M_SQRT1_2`, but are instead chosen such that their product is
  // exactly `1.0f` when evaluated in `float` precision.
  XNN_SIMD_CONST_F32(vsqrt2, 1.4142134190e+00);
  XNN_SIMD_CONST_F32(vsqrt1_2, 7.0710688829e-01);

  // The monomial coefficients of the numerator polynomial.
  // XNN_SIMD_CONST_F32(valpha_0, 0.0f);
  // XNN_SIMD_CONST_F32(valpha_1, 1.0f);
  // XNN_SIMD_CONST_F32(valpha_2, 1.0f);
  XNN_SIMD_CONST_F32(valpha_3, 1.824996918440e-01);

  // The monomial coefficients of the denominator polynomial.
  // XNN_SIMD_CONST_F32(vbeta_0, 1.0f);
  XNN_SIMD_CONST_F32(vbeta_1, 1.5f);
  XNN_SIMD_CONST_F32(vbeta_2, 0.599170029163);
  XNN_SIMD_CONST_F32(vbeta_3, 0.049584995955);

  // Constant needed for the Newton-Raphson iteration of the reciprocal.
  XNN_SIMD_CONST_F32(vtwo, 2.0f);

  for (; batch >= 32 * sizeof(float); batch -= 32 * sizeof(float)) {
    xnn_simd_f32_t vx_0 = xnn_loadu_f32(input);
    xnn_simd_f32_t vx_1 = xnn_loadu_f32(input + 1 * xnn_simd_size_f32);
    input += 32;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx_0 = xnn_mul_f32(vx_0, vsqrt2);
    vx_1 = xnn_mul_f32(vx_1, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp_0 = xnn_signed_getexp_f32(vx_0);
    const xnn_simd_f32_t vexp_1 = xnn_signed_getexp_f32(vx_1);

    // Normalize `x` to an exponent of zero.
    vx_0 = xnn_or_f32(xnn_and_f32(vx_0, vmantissa_bits_mask), vone);
    vx_1 = xnn_or_f32(xnn_and_f32(vx_1, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx_0 = xnn_sub_f32(xnn_mul_f32(vx_0, vsqrt1_2), vone);
    vx_1 = xnn_sub_f32(xnn_mul_f32(vx_1, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp_0 = xnn_fmadd_f32(vx_0, valpha_3, vone);
    xnn_simd_f32_t vp_1 = xnn_fmadd_f32(vx_1, valpha_3, vone);
    vp_0 = xnn_fmadd_f32(vx_0, vp_0, vone);
    vp_1 = xnn_fmadd_f32(vx_1, vp_1, vone);
    vp_0 = xnn_mul_f32(vx_0, vp_0);
    vp_1 = xnn_mul_f32(vx_1, vp_1);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq_0 = xnn_fmadd_f32(vx_0, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_1 = xnn_fmadd_f32(vx_1, vbeta_3, vbeta_2);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vbeta_1);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vbeta_1);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vone);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq_0 = xnn_rcp_f32(vq_0);
    xnn_simd_f32_t vrq_1 = xnn_rcp_f32(vq_1);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq_0 = xnn_mul_f32(vrq_0, xnn_fnmadd_f32(vrq_0, vq_0, vtwo));
      vrq_1 = xnn_mul_f32(vrq_1, xnn_fnmadd_f32(vrq_1, vq_1, vtwo));
    }
    xnn_simd_f32_t vy_0 = xnn_mul_f32(vp_0, vrq_0);
    xnn_simd_f32_t vy_1 = xnn_mul_f32(vp_1, vrq_1);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy_0 = xnn_fmadd_f32(vexp_0, vln2, vy_0);
    vy_1 = xnn_fmadd_f32(vexp_1, vln2, vy_1);

    xnn_storeu_f32(output, vy_0);
    xnn_storeu_f32(output + 1 * xnn_simd_size_f32, vy_1);
    output += 32;
  }
  for (; batch >= xnn_simd_bytes_f32; batch -= xnn_simd_bytes_f32) {
    xnn_simd_f32_t vx = xnn_loadu_f32(input);
    input += xnn_simd_size_f32;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx = xnn_mul_f32(vx, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);

    // Normalize `x` to an exponent of zero.
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_storeu_f32(output, vy);
    output += xnn_simd_size_f32;
  }
  if XNN_UNLIKELY(batch != 0) {
    xnn_simd_f32_t vx = xnn_load_tail_f32(input, batch >> XNN_LOG2_SIZEOF_FLOAT);

    // See the loop above for comments.
    vx = xnn_mul_f32(vx, vsqrt2);
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_store_tail_f32(output, vy, batch >> XNN_LOG2_SIZEOF_FLOAT);
  }
}

void xnn_f32_vlog_ukernel__avx512f_rational_3_3_nr_u48(
    size_t batch,
    const float* input,
    float* output,
    const struct xnn_f32_default_params unused_params[restrict XNN_MIN_ELEMENTS(1)])
{
  assert(batch != 0);
  assert(batch % sizeof(float) == 0);
  assert(input != NULL);
  assert(output != NULL);
  assert(xnn_simd_size_f32 == 16);

  // Some useful constants.
  XNN_SIMD_CONST_F32(vone, 1.0f);
  XNN_SIMD_CONST_F32(vln2, M_LN2);
  XNN_SIMD_CONST_F32_FROM_INT32(vmantissa_bits_mask, 0x007FFFFFUL);

  // Note that these two values are not _exactly_ `(float)M_SQRT2` and
  // `(float)M_SQRT1_2`, but are instead chosen such that their product is
  // exactly `1.0f` when evaluated in `float` precision.
  XNN_SIMD_CONST_F32(vsqrt2, 1.4142134190e+00);
  XNN_SIMD_CONST_F32(vsqrt1_2, 7.0710688829e-01);

  // The monomial coefficients of the numerator polynomial.
  // XNN_SIMD_CONST_F32(valpha_0, 0.0f);
  // XNN_SIMD_CONST_F32(valpha_1, 1.0f);
  // XNN_SIMD_CONST_F32(valpha_2, 1.0f);
  XNN_SIMD_CONST_F32(valpha_3, 1.824996918440e-01);

  // The monomial coefficients of the denominator polynomial.
  // XNN_SIMD_CONST_F32(vbeta_0, 1.0f);
  XNN_SIMD_CONST_F32(vbeta_1, 1.5f);
  XNN_SIMD_CONST_F32(vbeta_2, 0.599170029163);
  XNN_SIMD_CONST_F32(vbeta_3, 0.049584995955);

  // Constant needed for the Newton-Raphson iteration of the reciprocal.
  XNN_SIMD_CONST_F32(vtwo, 2.0f);

  for (; batch >= 48 * sizeof(float); batch -= 48 * sizeof(float)) {
    xnn_simd_f32_t vx_0 = xnn_loadu_f32(input);
    xnn_simd_f32_t vx_1 = xnn_loadu_f32(input + 1 * xnn_simd_size_f32);
    xnn_simd_f32_t vx_2 = xnn_loadu_f32(input + 2 * xnn_simd_size_f32);
    input += 48;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx_0 = xnn_mul_f32(vx_0, vsqrt2);
    vx_1 = xnn_mul_f32(vx_1, vsqrt2);
    vx_2 = xnn_mul_f32(vx_2, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp_0 = xnn_signed_getexp_f32(vx_0);
    const xnn_simd_f32_t vexp_1 = xnn_signed_getexp_f32(vx_1);
    const xnn_simd_f32_t vexp_2 = xnn_signed_getexp_f32(vx_2);

    // Normalize `x` to an exponent of zero.
    vx_0 = xnn_or_f32(xnn_and_f32(vx_0, vmantissa_bits_mask), vone);
    vx_1 = xnn_or_f32(xnn_and_f32(vx_1, vmantissa_bits_mask), vone);
    vx_2 = xnn_or_f32(xnn_and_f32(vx_2, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx_0 = xnn_sub_f32(xnn_mul_f32(vx_0, vsqrt1_2), vone);
    vx_1 = xnn_sub_f32(xnn_mul_f32(vx_1, vsqrt1_2), vone);
    vx_2 = xnn_sub_f32(xnn_mul_f32(vx_2, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp_0 = xnn_fmadd_f32(vx_0, valpha_3, vone);
    xnn_simd_f32_t vp_1 = xnn_fmadd_f32(vx_1, valpha_3, vone);
    xnn_simd_f32_t vp_2 = xnn_fmadd_f32(vx_2, valpha_3, vone);
    vp_0 = xnn_fmadd_f32(vx_0, vp_0, vone);
    vp_1 = xnn_fmadd_f32(vx_1, vp_1, vone);
    vp_2 = xnn_fmadd_f32(vx_2, vp_2, vone);
    vp_0 = xnn_mul_f32(vx_0, vp_0);
    vp_1 = xnn_mul_f32(vx_1, vp_1);
    vp_2 = xnn_mul_f32(vx_2, vp_2);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq_0 = xnn_fmadd_f32(vx_0, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_1 = xnn_fmadd_f32(vx_1, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_2 = xnn_fmadd_f32(vx_2, vbeta_3, vbeta_2);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vbeta_1);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vbeta_1);
    vq_2 = xnn_fmadd_f32(vx_2, vq_2, vbeta_1);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vone);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vone);
    vq_2 = xnn_fmadd_f32(vx_2, vq_2, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq_0 = xnn_rcp_f32(vq_0);
    xnn_simd_f32_t vrq_1 = xnn_rcp_f32(vq_1);
    xnn_simd_f32_t vrq_2 = xnn_rcp_f32(vq_2);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq_0 = xnn_mul_f32(vrq_0, xnn_fnmadd_f32(vrq_0, vq_0, vtwo));
      vrq_1 = xnn_mul_f32(vrq_1, xnn_fnmadd_f32(vrq_1, vq_1, vtwo));
      vrq_2 = xnn_mul_f32(vrq_2, xnn_fnmadd_f32(vrq_2, vq_2, vtwo));
    }
    xnn_simd_f32_t vy_0 = xnn_mul_f32(vp_0, vrq_0);
    xnn_simd_f32_t vy_1 = xnn_mul_f32(vp_1, vrq_1);
    xnn_simd_f32_t vy_2 = xnn_mul_f32(vp_2, vrq_2);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy_0 = xnn_fmadd_f32(vexp_0, vln2, vy_0);
    vy_1 = xnn_fmadd_f32(vexp_1, vln2, vy_1);
    vy_2 = xnn_fmadd_f32(vexp_2, vln2, vy_2);

    xnn_storeu_f32(output, vy_0);
    xnn_storeu_f32(output + 1 * xnn_simd_size_f32, vy_1);
    xnn_storeu_f32(output + 2 * xnn_simd_size_f32, vy_2);
    output += 48;
  }
  for (; batch >= xnn_simd_bytes_f32; batch -= xnn_simd_bytes_f32) {
    xnn_simd_f32_t vx = xnn_loadu_f32(input);
    input += xnn_simd_size_f32;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx = xnn_mul_f32(vx, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);

    // Normalize `x` to an exponent of zero.
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_storeu_f32(output, vy);
    output += xnn_simd_size_f32;
  }
  if XNN_UNLIKELY(batch != 0) {
    xnn_simd_f32_t vx = xnn_load_tail_f32(input, batch >> XNN_LOG2_SIZEOF_FLOAT);

    // See the loop above for comments.
    vx = xnn_mul_f32(vx, vsqrt2);
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_store_tail_f32(output, vy, batch >> XNN_LOG2_SIZEOF_FLOAT);
  }
}

void xnn_f32_vlog_ukernel__avx512f_rational_3_3_nr_u64(
    size_t batch,
    const float* input,
    float* output,
    const struct xnn_f32_default_params unused_params[restrict XNN_MIN_ELEMENTS(1)])
{
  assert(batch != 0);
  assert(batch % sizeof(float) == 0);
  assert(input != NULL);
  assert(output != NULL);
  assert(xnn_simd_size_f32 == 16);

  // Some useful constants.
  XNN_SIMD_CONST_F32(vone, 1.0f);
  XNN_SIMD_CONST_F32(vln2, M_LN2);
  XNN_SIMD_CONST_F32_FROM_INT32(vmantissa_bits_mask, 0x007FFFFFUL);

  // Note that these two values are not _exactly_ `(float)M_SQRT2` and
  // `(float)M_SQRT1_2`, but are instead chosen such that their product is
  // exactly `1.0f` when evaluated in `float` precision.
  XNN_SIMD_CONST_F32(vsqrt2, 1.4142134190e+00);
  XNN_SIMD_CONST_F32(vsqrt1_2, 7.0710688829e-01);

  // The monomial coefficients of the numerator polynomial.
  // XNN_SIMD_CONST_F32(valpha_0, 0.0f);
  // XNN_SIMD_CONST_F32(valpha_1, 1.0f);
  // XNN_SIMD_CONST_F32(valpha_2, 1.0f);
  XNN_SIMD_CONST_F32(valpha_3, 1.824996918440e-01);

  // The monomial coefficients of the denominator polynomial.
  // XNN_SIMD_CONST_F32(vbeta_0, 1.0f);
  XNN_SIMD_CONST_F32(vbeta_1, 1.5f);
  XNN_SIMD_CONST_F32(vbeta_2, 0.599170029163);
  XNN_SIMD_CONST_F32(vbeta_3, 0.049584995955);

  // Constant needed for the Newton-Raphson iteration of the reciprocal.
  XNN_SIMD_CONST_F32(vtwo, 2.0f);

  for (; batch >= 64 * sizeof(float); batch -= 64 * sizeof(float)) {
    xnn_simd_f32_t vx_0 = xnn_loadu_f32(input);
    xnn_simd_f32_t vx_1 = xnn_loadu_f32(input + 1 * xnn_simd_size_f32);
    xnn_simd_f32_t vx_2 = xnn_loadu_f32(input + 2 * xnn_simd_size_f32);
    xnn_simd_f32_t vx_3 = xnn_loadu_f32(input + 3 * xnn_simd_size_f32);
    input += 64;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx_0 = xnn_mul_f32(vx_0, vsqrt2);
    vx_1 = xnn_mul_f32(vx_1, vsqrt2);
    vx_2 = xnn_mul_f32(vx_2, vsqrt2);
    vx_3 = xnn_mul_f32(vx_3, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp_0 = xnn_signed_getexp_f32(vx_0);
    const xnn_simd_f32_t vexp_1 = xnn_signed_getexp_f32(vx_1);
    const xnn_simd_f32_t vexp_2 = xnn_signed_getexp_f32(vx_2);
    const xnn_simd_f32_t vexp_3 = xnn_signed_getexp_f32(vx_3);

    // Normalize `x` to an exponent of zero.
    vx_0 = xnn_or_f32(xnn_and_f32(vx_0, vmantissa_bits_mask), vone);
    vx_1 = xnn_or_f32(xnn_and_f32(vx_1, vmantissa_bits_mask), vone);
    vx_2 = xnn_or_f32(xnn_and_f32(vx_2, vmantissa_bits_mask), vone);
    vx_3 = xnn_or_f32(xnn_and_f32(vx_3, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx_0 = xnn_sub_f32(xnn_mul_f32(vx_0, vsqrt1_2), vone);
    vx_1 = xnn_sub_f32(xnn_mul_f32(vx_1, vsqrt1_2), vone);
    vx_2 = xnn_sub_f32(xnn_mul_f32(vx_2, vsqrt1_2), vone);
    vx_3 = xnn_sub_f32(xnn_mul_f32(vx_3, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp_0 = xnn_fmadd_f32(vx_0, valpha_3, vone);
    xnn_simd_f32_t vp_1 = xnn_fmadd_f32(vx_1, valpha_3, vone);
    xnn_simd_f32_t vp_2 = xnn_fmadd_f32(vx_2, valpha_3, vone);
    xnn_simd_f32_t vp_3 = xnn_fmadd_f32(vx_3, valpha_3, vone);
    vp_0 = xnn_fmadd_f32(vx_0, vp_0, vone);
    vp_1 = xnn_fmadd_f32(vx_1, vp_1, vone);
    vp_2 = xnn_fmadd_f32(vx_2, vp_2, vone);
    vp_3 = xnn_fmadd_f32(vx_3, vp_3, vone);
    vp_0 = xnn_mul_f32(vx_0, vp_0);
    vp_1 = xnn_mul_f32(vx_1, vp_1);
    vp_2 = xnn_mul_f32(vx_2, vp_2);
    vp_3 = xnn_mul_f32(vx_3, vp_3);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq_0 = xnn_fmadd_f32(vx_0, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_1 = xnn_fmadd_f32(vx_1, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_2 = xnn_fmadd_f32(vx_2, vbeta_3, vbeta_2);
    xnn_simd_f32_t vq_3 = xnn_fmadd_f32(vx_3, vbeta_3, vbeta_2);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vbeta_1);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vbeta_1);
    vq_2 = xnn_fmadd_f32(vx_2, vq_2, vbeta_1);
    vq_3 = xnn_fmadd_f32(vx_3, vq_3, vbeta_1);
    vq_0 = xnn_fmadd_f32(vx_0, vq_0, vone);
    vq_1 = xnn_fmadd_f32(vx_1, vq_1, vone);
    vq_2 = xnn_fmadd_f32(vx_2, vq_2, vone);
    vq_3 = xnn_fmadd_f32(vx_3, vq_3, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq_0 = xnn_rcp_f32(vq_0);
    xnn_simd_f32_t vrq_1 = xnn_rcp_f32(vq_1);
    xnn_simd_f32_t vrq_2 = xnn_rcp_f32(vq_2);
    xnn_simd_f32_t vrq_3 = xnn_rcp_f32(vq_3);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq_0 = xnn_mul_f32(vrq_0, xnn_fnmadd_f32(vrq_0, vq_0, vtwo));
      vrq_1 = xnn_mul_f32(vrq_1, xnn_fnmadd_f32(vrq_1, vq_1, vtwo));
      vrq_2 = xnn_mul_f32(vrq_2, xnn_fnmadd_f32(vrq_2, vq_2, vtwo));
      vrq_3 = xnn_mul_f32(vrq_3, xnn_fnmadd_f32(vrq_3, vq_3, vtwo));
    }
    xnn_simd_f32_t vy_0 = xnn_mul_f32(vp_0, vrq_0);
    xnn_simd_f32_t vy_1 = xnn_mul_f32(vp_1, vrq_1);
    xnn_simd_f32_t vy_2 = xnn_mul_f32(vp_2, vrq_2);
    xnn_simd_f32_t vy_3 = xnn_mul_f32(vp_3, vrq_3);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy_0 = xnn_fmadd_f32(vexp_0, vln2, vy_0);
    vy_1 = xnn_fmadd_f32(vexp_1, vln2, vy_1);
    vy_2 = xnn_fmadd_f32(vexp_2, vln2, vy_2);
    vy_3 = xnn_fmadd_f32(vexp_3, vln2, vy_3);

    xnn_storeu_f32(output, vy_0);
    xnn_storeu_f32(output + 1 * xnn_simd_size_f32, vy_1);
    xnn_storeu_f32(output + 2 * xnn_simd_size_f32, vy_2);
    xnn_storeu_f32(output + 3 * xnn_simd_size_f32, vy_3);
    output += 64;
  }
  for (; batch >= xnn_simd_bytes_f32; batch -= xnn_simd_bytes_f32) {
    xnn_simd_f32_t vx = xnn_loadu_f32(input);
    input += xnn_simd_size_f32;

    // Scale `x` with `sqrt(2)` so that the exponent is rounded up.
    vx = xnn_mul_f32(vx, vsqrt2);

    // Extract the exponent.
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);

    // Normalize `x` to an exponent of zero.
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);

    // Scale `x` back with `1/sqrt(2)` to move its range from `[1.0, 2.0)` to
    // `[sqrt(1/2), sqrt(2))`, and further subtract `1.0` so that it is around
    // zero, i.e. `[sqrt(1/2) - 1, sqrt(2) - 1)`, or `[−0.29289, 0.4142136)`.
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);

    // In the following, we use a 3/2-degree rational polynomial to
    // approximate the (shifted) `log(x + 1)` on the (shifted) interval
    // `[sqrt(1/2) - 1, sqrt(2) - 1)`. The shifted interval is chosen so that
    // `f(0) = 0`.

    // Evaluate the numerator polynomial p.
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);

    // Evaluate the denominator polynomial q.
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);

    // Divide the numerator by the denominator.
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);

    // Put it all together, i.e. `log(x) = `log(2)*exp + y`.
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_storeu_f32(output, vy);
    output += xnn_simd_size_f32;
  }
  if XNN_UNLIKELY(batch != 0) {
    xnn_simd_f32_t vx = xnn_load_tail_f32(input, batch >> XNN_LOG2_SIZEOF_FLOAT);

    // See the loop above for comments.
    vx = xnn_mul_f32(vx, vsqrt2);
    const xnn_simd_f32_t vexp = xnn_signed_getexp_f32(vx);
    vx = xnn_or_f32(xnn_and_f32(vx, vmantissa_bits_mask), vone);
    vx = xnn_sub_f32(xnn_mul_f32(vx, vsqrt1_2), vone);
    xnn_simd_f32_t vp = xnn_fmadd_f32(vx, valpha_3, vone);
    vp = xnn_fmadd_f32(vx, vp, vone);
    vp = xnn_mul_f32(vx, vp);
    xnn_simd_f32_t vq = xnn_fmadd_f32(vx, vbeta_3, vbeta_2);
    vq = xnn_fmadd_f32(vx, vq, vbeta_1);
    vq = xnn_fmadd_f32(vx, vq, vone);
    xnn_simd_f32_t vrq = xnn_rcp_f32(vq);
    for (size_t iter = 0; iter < XNN_SIMD_NUM_RCP_ITER_F32; iter++) {
      vrq = xnn_mul_f32(vrq, xnn_fnmadd_f32(vrq, vq, vtwo));
    }
    xnn_simd_f32_t vy = xnn_mul_f32(vp, vrq);
    vy = xnn_fmadd_f32(vexp, vln2, vy);

    xnn_store_tail_f32(output, vy, batch >> XNN_LOG2_SIZEOF_FLOAT);
  }
}