src/qs8-requantization/fp32-sse2.c

// Copyright (c) Facebook, Inc. and its affiliates.
// All rights reserved.
//
// 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 <stdint.h>
#include <stddef.h>

#include <emmintrin.h>

#include <xnnpack/requantization-stubs.h>


void xnn_qs8_requantize_fp32__sse2(
    size_t n,
    const int32_t* input,
    float scale,
    int8_t zero_point,
    int8_t qmin,
    int8_t qmax,
    int8_t* output)
{
  assert(n % 16 == 0);
  assert(scale < 1.0f);
  assert(scale >= 0x1.0p-32f);

  const __m128 vscale = _mm_set1_ps(scale);
  const __m128i vzero_point = _mm_set1_epi16((short) (uint16_t) zero_point);
  const __m128i vqmin = _mm_set1_epi8((char) qmin);
  const __m128i vqmax = _mm_set1_epi8((char) qmax);
  for (; n != 0; n -= 16) {
    const __m128i x = _mm_loadu_si128((const __m128i*) input);
    const __m128i y = _mm_loadu_si128((const __m128i*) (input + 4));
    const __m128i z = _mm_loadu_si128((const __m128i*) (input + 8));
    const __m128i w = _mm_loadu_si128((const __m128i*) (input + 12));
    input += 16;

    // Convert int32_t input to FP32 and multiply by FP32 scale.
    // Both operations involve statistically unbiased roundings (with default MXCSR rounding mode):
    // - Large int32_t values can't be exactly represented as FP32. CVTDQ2PS instruction on x86 would round it
    //   according to nearest FP32 value with ties to even (assuming default MXCSR rounding mode).
    // - Product of two FP32 values is generally not exactly representation as an FP32 value, and will be rounded
    //   to nearest FP32 value with ties to even with default MXCSR rounding mode.
    const __m128 x_scaled = _mm_mul_ps(_mm_cvtepi32_ps(x), vscale);
    const __m128 y_scaled = _mm_mul_ps(_mm_cvtepi32_ps(y), vscale);
    const __m128 z_scaled = _mm_mul_ps(_mm_cvtepi32_ps(z), vscale);
    const __m128 w_scaled = _mm_mul_ps(_mm_cvtepi32_ps(w), vscale);

    // Convert scaled FP32 result to int32_t using CVTPS2DQ instruction from x86 SSE2. CVTPS2DQ instruction rounds
    // result according to nearest FP32 value with ties to even (assuming default MXCSR rounding mode).
    // However, when conversion overflows, it produces INT32_MIN as a result. For large positive inputs the result
    // of conversion can become negative, which affects the final requantization result. Note that on x86 SSE2 we
    // have e.g. int32_t(float(INT32_MAX)) == INT32_MIN! This happens because float(INT32_MAX) rounds to 2**31,
    // which overflows int32_t when it is converted back to integer.
    //
    // Thankfully, we can prove that overflow never happens in this requantization scheme. The largest positive
    // input is INT32_MAX (2**31 - 1), which turns into 2**31 when converted to float. The largest scale value
    // is 0x1.FFFFFEp-1. When multiplied together, the result is 2147483520 (compare to INT32_MAX = 2147483647),
    // which fits into int32_t without overflow.
    const __m128i x_rounded = _mm_cvtps_epi32(x_scaled);
    const __m128i y_rounded = _mm_cvtps_epi32(y_scaled);
    const __m128i z_rounded = _mm_cvtps_epi32(z_scaled);
    const __m128i w_rounded = _mm_cvtps_epi32(w_scaled);

    // Standard final sequence on x86 SSE2:
    // - Pack to int16_t and saturate
    // - Add zero point
    // - Clamp between qmin and qmax
    // - Pack to int8_t and saturate
    const __m128i xy_packed = _mm_adds_epi16(_mm_packs_epi32(x_rounded, y_rounded), vzero_point);
    const __m128i zw_packed = _mm_adds_epi16(_mm_packs_epi32(z_rounded, w_rounded), vzero_point);
    const __m128i xy_clamped = _mm_max_epi16(_mm_min_epi16(xy_packed, vqmax), vqmin);
    const __m128i zw_clamped = _mm_max_epi16(_mm_min_epi16(zw_packed, vqmax), vqmin);
    const __m128i xyzw_clamped = _mm_packs_epi16(xy_clamped, zw_clamped);

    // 4x CVTDQ2PS
    // 4x MULPS
    // 4x CVTPS2DQ
    // 2x PACKSSDW
    // 2x PADDSW
    // 2x PMAXSW
    // 2x PMINSW
    // 1x PACKSSWB
    // ---------------------
    // 21 instructions total

    _mm_storeu_si128((__m128i*) output, xyzw_clamped);
    output += 16;
  }
}