// 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.

$assert BATCH_TILE % 4 == 0
$assert BATCH_TILE >= 4
$SIMD_TILE = BATCH_TILE // 4
$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
#include <assert.h>

#include <xmmintrin.h>

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

// In the following, we first compute the _reciprocal_ square root of an input
// `a` and then multiply it with `a` to produce the square root.
//
// We compute the reciprocal square root using a single Newton-Raphson step on
// the equation $x^{-2} - a$, which expands to:
//
//  $$x_{k+1} = 0.5 * x_k * (3.0 - a * x_k^2)$$
//
// So we do the following steps:
//
//  1. t0 = x_k
//  2. t1 = t0 * t0   (x_k^2)
//  3. t2 = a * t1    (a * x_k^2)
//  4. t3 = 3.0 - t2  (3.0 - a * x_k^2)
//  5. t4 = 0.5 * t0  (0.5 * x_k)
//  6. t5 = t3 * t4   (0.5 * x_k * (3.0 - a * x_k^2))
//  7. y = a * t5     (a * a^{-1/2})
//
// Where $x_k$ is the original 14-bit approximation and `t5` contains the final
// 24-bit approximation $x_{k+1}$.


void xnn_f32_vsqrt_ukernel__sse_rsqrt_u${BATCH_TILE}(
    size_t batch,
    const float* input,
    float* output,
    const struct xnn_f32_default_params params[restrict XNN_MIN_ELEMENTS(1)]) XNN_OOB_READS
{
  assert(batch != 0);
  assert(batch % sizeof(float) == 0);
  assert(input != NULL);
  assert(output != NULL);

  // Constants for the Newton-Raphson iteration.
  const __m128 vthree = _mm_set1_ps(3.0f);
  const __m128 vhalf = _mm_set1_ps(0.5f);

  $if BATCH_TILE > 4:
    for (; batch >= ${BATCH_TILE} * sizeof(float); batch -= ${BATCH_TILE} * sizeof(float)) {
      const __m128 vx${ABC[0]} = _mm_loadu_ps(input);
      $for N in range(1, SIMD_TILE):
        const __m128 vx${ABC[N]} = _mm_loadu_ps(input + ${N * 4});
      input += ${BATCH_TILE};

      // Create a mask of the +/-0 inputs, which will be flushed to zero later.
      $for N in range(SIMD_TILE):
        const __m128 vmask${ABC[N]} = _mm_cmpeq_ps(vx${ABC[N]}, _mm_setzero_ps());

      // Generate the initial 12-bit approximation.
      $for N in range(SIMD_TILE):
        const __m128 vt0_${ABC[N]} = _mm_rsqrt_ps(vx${ABC[N]});

      // Do a single Newton-Raphson step as described above.
      $for N in range(SIMD_TILE):
        const __m128 vt1_${ABC[N]} = _mm_mul_ps(vt0_${ABC[N]}, vt0_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vt2_${ABC[N]} = _mm_mul_ps(vx${ABC[N]}, vt1_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vt3_${ABC[N]} = _mm_sub_ps(vthree, vt2_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vt4_${ABC[N]} = _mm_mul_ps(vhalf, vt0_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vt5_${ABC[N]} = _mm_mul_ps(vt3_${ABC[N]}, vt4_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vt6_${ABC[N]} = _mm_andnot_ps(vmask${ABC[N]}, vt5_${ABC[N]});
      $for N in range(SIMD_TILE):
        const __m128 vy${ABC[N]} = _mm_mul_ps(vx${ABC[N]}, vt6_${ABC[N]});

      // Store the results.
      _mm_storeu_ps(output, vy${ABC[0]});
      $for N in range(1, SIMD_TILE):
        _mm_storeu_ps(output + ${N * 4}, vy${ABC[N]});
      output += ${BATCH_TILE};
    }
  for (; batch >= 4 * sizeof(float); batch -= 4 * sizeof(float)) {
    const __m128 vx = _mm_loadu_ps(input);
    input += 4;

    // Generate the initial 12-bit approximation.
    const __m128 vt0 = _mm_rsqrt_ps(vx);

    // Create a mask of the +/-0 inputs, which will be flushed to zero later.
    const __m128 vmask = _mm_cmpeq_ps(vx, _mm_setzero_ps());

    // Do a single Newton-Raphson step as described above.
    const __m128 vt1 = _mm_mul_ps(vt0, vt0);
    const __m128 vt2 = _mm_mul_ps(vx, vt1);
    const __m128 vt3 = _mm_sub_ps(vthree, vt2);
    const __m128 vt4 = _mm_mul_ps(vhalf, vt0);
    const __m128 vt5 = _mm_mul_ps(vt3, vt4);
    const __m128 vt6 = _mm_andnot_ps(vmask, vt5);
    const __m128 vy = _mm_mul_ps(vx, vt6);
    _mm_storeu_ps(output, vy);
    output += 4;
  }
  if XNN_UNLIKELY(batch != 0) {
    const __m128 vx = _mm_loadu_ps(input);
    // Generate the initial 12-bit approximation.
    const __m128 vt0 = _mm_rsqrt_ps(vx);

    // Create a mask of the +/-0 inputs, which will be flushed to zero later.
    const __m128 vmask = _mm_cmpeq_ps(vx, _mm_setzero_ps());

    // Do a single Newton-Raphson step as described above.
    const __m128 vt1 = _mm_mul_ps(vt0, vt0);
    const __m128 vt2 = _mm_mul_ps(vx, vt1);
    const __m128 vt3 = _mm_sub_ps(vthree, vt2);
    const __m128 vt4 = _mm_mul_ps(vhalf, vt0);
    const __m128 vt5 = _mm_mul_ps(vt3, vt4);
    const __m128 vt6 = _mm_andnot_ps(vmask, vt5);
    __m128 vy = _mm_mul_ps(vx, vt6);

    if (batch & (2 * sizeof(float))) {
      _mm_storel_pi((__m64*) output, vy);
      vy = _mm_movehl_ps(vy, vy);
      output += 2;
    }
    if (batch & (1 * sizeof(float))) {
      _mm_store_ss(output, vy);
    }
  }
}