src/qu8-requantization/gemmlowp-scalar.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 <fp16/bitcasts.h>

#include <xnnpack/math.h>
#include <xnnpack/requantization-stubs.h>


void xnn_qu8_requantize_gemmlowp__scalar(
    size_t n,
    const int32_t* input,
    float scale,
    uint8_t zero_point,
    uint8_t qmin,
    uint8_t qmax,
    uint8_t* output)
{
  assert(n % 4 == 0);
  assert(scale < 1.0f);
  assert(scale >= 0x1.0p-32f);

  // Compute requantization parameters.
  const uint32_t scale_bits = fp32_to_bits(scale);

  // Multiplier is in [0x40000000, 0x7FFFFF80] range.
  const int32_t multiplier = (int32_t)(((scale_bits & UINT32_C(0x007FFFFF)) | UINT32_C(0x00800000)) << 7);
  assert(multiplier >= INT32_C(0x40000000));
  assert(multiplier <= INT32_C(0x7FFFFF80));

  // Shift is in [0, 31] range.
  const int32_t shift = 127 + 31 - 32 - (fp32_to_bits(scale) >> 23);
  assert(shift >= 0);
  assert(shift < 32);

  const int64_t q31rounding = INT64_C(0x40000000);
  const int32_t remainder_mask = (int32_t) ((UINT32_C(1) << shift) - UINT32_C(1));
  const int32_t threshold = (int32_t) ((uint32_t) remainder_mask >> 1);
  const int32_t smin = (int32_t) (uint32_t) qmin - (int32_t) (uint32_t) zero_point;
  const int32_t smax = (int32_t) (uint32_t) qmax - (int32_t) (uint32_t) zero_point;
  for (; n != 0; n -= 4) {
    const int32_t x = input[0];
    const int32_t y = input[1];
    const int32_t z = input[2];
    const int32_t w = input[3];
    input += 4;

    // Compute full 64-bit product of signed 32-bit factors.
    //
    // Note: multiplier can be treated as either signed or unsigned.
    const int64_t x_product = (int64_t) x * (int64_t) multiplier;
    const int64_t y_product = (int64_t) y * (int64_t) multiplier;
    const int64_t z_product = (int64_t) z * (int64_t) multiplier;
    const int64_t w_product = (int64_t) w * (int64_t) multiplier;

    // Get the Q31 multiplication result by extracting bits 31-62 of the product, with rounding up.
    // Add rounding value (0x40000000) and then shift right by 31 bits and extract the low 32-bit word.
    // Note: casts to unsigned types are needed to avoid undefined behavior.
    // Given the multiplier range, the result of Q31 multiplication is in [-2147483520, 2147483519] range.
    const int32_t x_q31product = (int32_t) (uint32_t) ((uint64_t) (x_product + q31rounding) >> 31);
    const int32_t y_q31product = (int32_t) (uint32_t) ((uint64_t) (y_product + q31rounding) >> 31);
    const int32_t z_q31product = (int32_t) (uint32_t) ((uint64_t) (z_product + q31rounding) >> 31);
    const int32_t w_q31product = (int32_t) (uint32_t) ((uint64_t) (w_product + q31rounding) >> 31);

    // Arithmetically shift the adjusted product right with rounding.
    // Rounding is performed towards closest integer, with midpoints rounded away from zero.
    //
    // Shift with correct rounding could be efficiently implemented by pre-adding rounding constant, but with input in
    // [-2147483520, 2147483519] range and rounding constant up to 2**30 we can't rule out overflow. This limitation
    // leaves us with 3 options:
    // 1. Extend input to 64-bit signed integer, perform addition and shift on 64-bit integers, then truncate result
    //    to 32 bits.
    // 2. Detect overflow and handle this situation separately. Note that overflow is possible only when input is
    //    positive, and even when addition of a rounding constant overflows 32-bit signed integer, it still doesn't
    //    overflow 32-bit unsigned integer. Thus, in case of signed overflow, we can compute the result using unsigned
    //    arithmetics, specifically using logical shift right instead of arithmetic shift right.
    // 3. Performs arithmetic shift as is, which will produce division result rounded down. Then compute remainder of
    //    this division by a power of 2, and adjust the result. Result needs adjustment (increment by 1) when
    //     - input is positive, shift is non-zero, and remainder >= 2**(shift - 1), e.g. 10 >> 2 needs adjustment
    //     - input is negative, shift is non-zero, and remainder > 2**(shift - 1), e.g. -10 >> 2 doesn't need adjustment
    //    These conditions can be generalized as
    //        remainder + (input <= 0) > 2**(shift - 1)
    //    or equivalently
    //        remainder - (input < 0) > ((2**shift - 1) >> 1)
    //    When shift is 0, remainder is 0 as well, the last condition is always false, and no adjustment is done.
    //
    // Among these options, option 3 is the most performant across the board, although option 1 is promising for 64-bit
    // instruction sets.
    const int32_t x_remainder = (x_q31product & remainder_mask) - (int32_t) (x_q31product < 0);
    const int32_t y_remainder = (y_q31product & remainder_mask) - (int32_t) (y_q31product < 0);
    const int32_t z_remainder = (z_q31product & remainder_mask) - (int32_t) (z_q31product < 0);
    const int32_t w_remainder = (w_q31product & remainder_mask) - (int32_t) (w_q31product < 0);

    const int32_t x_scaled = asr_s32(x_q31product, shift) + (int32_t) (x_remainder > threshold);
    const int32_t y_scaled = asr_s32(y_q31product, shift) + (int32_t) (y_remainder > threshold);
    const int32_t z_scaled = asr_s32(z_q31product, shift) + (int32_t) (z_remainder > threshold);
    const int32_t w_scaled = asr_s32(w_q31product, shift) + (int32_t) (w_remainder > threshold);

    // Clamp scaled value with zero point between (qmin - zero point) and (qmax - zero point).
    const int32_t x_clamped = math_min_s32(math_max_s32(x_scaled, smin), smax);
    const int32_t y_clamped = math_min_s32(math_max_s32(y_scaled, smin), smax);
    const int32_t z_clamped = math_min_s32(math_max_s32(z_scaled, smin), smax);
    const int32_t w_clamped = math_min_s32(math_max_s32(w_scaled, smin), smax);

    // Add zero point to clamped value.
    // The result is guaranteed to be in [qmin, qmax] range.
    //
    // This addition can not be safely done before clamping, because scaled values are in [-2147483520, 2147483519]
    // range, so addition of zero point (which can be up to 255) can overflow signed 32-bit integer.
    const int32_t x_biased = x_clamped + zero_point;
    const int32_t y_biased = y_clamped + zero_point;
    const int32_t z_biased = z_clamped + zero_point;
    const int32_t w_biased = w_clamped + zero_point;

    output[0] = (uint8_t) x_biased;
    output[1] = (uint8_t) y_biased;
    output[2] = (uint8_t) z_biased;
    output[3] = (uint8_t) w_biased;
    output += 4;
  }
}