Revert "Simplification and refactoring of the AudioBuffer code"

This reverts commit 81c0cf287c8514cb1cd6f3baca484d668c6eb128.

Reason for revert: internal test failures

Original change's description:
> Simplification and refactoring of the AudioBuffer code
> 
> This CL performs a major refactoring and simplification
> of the AudioBuffer code that.
> -Removes 7 of the 9 internal buffers of the AudioBuffer.
> -Avoids the implicit copying required to keep the
>  internal buffers in sync.
> -Removes all code relating to handling of fixed-point
>  sample data in the AudioBuffer.
> -Changes the naming of the class methods to reflect
>  that only floating point is handled.
> -Corrects some bugs in the code.
> -Extends the handling of internal downmixing to be
>  more generic.
> 
> Bug: webrtc:10882
> Change-Id: I12c8af156fbe366b154744a0a1b3d926bf7be572
> Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/149828
> Commit-Queue: Per Ã…hgren <peah@webrtc.org>
> Reviewed-by: Gustaf Ullberg <gustaf@webrtc.org>
> Cr-Commit-Position: refs/heads/master@{#28928}

TBR=gustaf@webrtc.org,peah@webrtc.org

Change-Id: I2729e3ad24b3a9b40b368b84cb565c859e79b51e
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Bug: webrtc:10882
Reviewed-on: https://webrtc-review.googlesource.com/c/src/+/150084
Reviewed-by: Steve Anton <steveanton@webrtc.org>
Commit-Queue: Steve Anton <steveanton@webrtc.org>
Cr-Commit-Position: refs/heads/master@{#28931}
diff --git a/modules/audio_processing/audio_buffer.cc b/modules/audio_processing/audio_buffer.cc
index e1d5b3a..32668fa 100644
--- a/modules/audio_processing/audio_buffer.cc
+++ b/modules/audio_processing/audio_buffer.cc
@@ -23,169 +23,183 @@
 namespace webrtc {
 namespace {
 
-constexpr size_t kSamplesPer32kHzChannel = 320;
-constexpr size_t kSamplesPer48kHzChannel = 480;
-constexpr size_t kSamplesPer192kHzChannel = 1920;
-constexpr size_t kMaxSamplesPerChannel = kSamplesPer192kHzChannel;
+const size_t kSamplesPer16kHzChannel = 160;
+const size_t kSamplesPer32kHzChannel = 320;
+const size_t kSamplesPer48kHzChannel = 480;
 
-size_t NumBandsFromFramesPerChannel(size_t num_frames) {
-  if (num_frames == kSamplesPer32kHzChannel) {
-    return 2;
+size_t NumBandsFromSamplesPerChannel(size_t num_frames) {
+  size_t num_bands = 1;
+  if (num_frames == kSamplesPer32kHzChannel ||
+      num_frames == kSamplesPer48kHzChannel) {
+    num_bands = rtc::CheckedDivExact(num_frames, kSamplesPer16kHzChannel);
   }
-  if (num_frames == kSamplesPer48kHzChannel) {
-    return 3;
-  }
-  return 1;
+  return num_bands;
 }
 
 }  // namespace
 
-AudioBuffer::AudioBuffer(size_t input_rate,
-                         size_t input_num_channels,
-                         size_t buffer_rate,
-                         size_t buffer_num_channels,
-                         size_t output_rate)
-    : input_num_frames_(
-          rtc::CheckedDivExact(static_cast<int>(input_rate), 100)),
-      input_num_channels_(input_num_channels),
-      buffer_num_frames_(
-          rtc::CheckedDivExact(static_cast<int>(buffer_rate), 100)),
-      buffer_num_channels_(buffer_num_channels),
-      output_num_frames_(
-          rtc::CheckedDivExact(static_cast<int>(output_rate), 100)),
-      num_channels_(buffer_num_channels),
-      num_bands_(NumBandsFromFramesPerChannel(buffer_num_frames_)),
-      num_split_frames_(rtc::CheckedDivExact(buffer_num_frames_, num_bands_)),
-      data_(new ChannelBuffer<float>(buffer_num_frames_, buffer_num_channels_)),
-      output_buffer_(
-          new ChannelBuffer<float>(output_num_frames_, num_channels_)) {
+AudioBuffer::AudioBuffer(size_t input_num_frames,
+                         size_t num_input_channels,
+                         size_t process_num_frames,
+                         size_t num_process_channels,
+                         size_t output_num_frames)
+    : input_num_frames_(input_num_frames),
+      num_input_channels_(num_input_channels),
+      proc_num_frames_(process_num_frames),
+      num_proc_channels_(num_process_channels),
+      output_num_frames_(output_num_frames),
+      num_channels_(num_process_channels),
+      num_bands_(NumBandsFromSamplesPerChannel(proc_num_frames_)),
+      num_split_frames_(rtc::CheckedDivExact(proc_num_frames_, num_bands_)),
+      data_(new IFChannelBuffer(proc_num_frames_, num_proc_channels_)),
+      output_buffer_(new IFChannelBuffer(output_num_frames_, num_channels_)) {
   RTC_DCHECK_GT(input_num_frames_, 0);
-  RTC_DCHECK_GT(buffer_num_frames_, 0);
+  RTC_DCHECK_GT(proc_num_frames_, 0);
   RTC_DCHECK_GT(output_num_frames_, 0);
-  RTC_DCHECK_GT(input_num_channels_, 0);
-  RTC_DCHECK_GT(buffer_num_channels_, 0);
-  RTC_DCHECK_LE(buffer_num_channels_, input_num_channels_);
+  RTC_DCHECK_GT(num_input_channels_, 0);
+  RTC_DCHECK_GT(num_proc_channels_, 0);
+  RTC_DCHECK_LE(num_proc_channels_, num_input_channels_);
 
-  const bool input_resampling_needed = input_num_frames_ != buffer_num_frames_;
-  const bool output_resampling_needed =
-      output_num_frames_ != buffer_num_frames_;
-  if (input_resampling_needed) {
-    for (size_t i = 0; i < buffer_num_channels_; ++i) {
-      input_resamplers_.push_back(std::unique_ptr<PushSincResampler>(
-          new PushSincResampler(input_num_frames_, buffer_num_frames_)));
+  if (input_num_frames_ != proc_num_frames_ ||
+      output_num_frames_ != proc_num_frames_) {
+    // Create an intermediate buffer for resampling.
+    process_buffer_.reset(
+        new ChannelBuffer<float>(proc_num_frames_, num_proc_channels_));
+
+    if (input_num_frames_ != proc_num_frames_) {
+      for (size_t i = 0; i < num_proc_channels_; ++i) {
+        input_resamplers_.push_back(std::unique_ptr<PushSincResampler>(
+            new PushSincResampler(input_num_frames_, proc_num_frames_)));
+      }
     }
-  }
 
-  if (output_resampling_needed) {
-    for (size_t i = 0; i < buffer_num_channels_; ++i) {
-      output_resamplers_.push_back(std::unique_ptr<PushSincResampler>(
-          new PushSincResampler(buffer_num_frames_, output_num_frames_)));
+    if (output_num_frames_ != proc_num_frames_) {
+      for (size_t i = 0; i < num_proc_channels_; ++i) {
+        output_resamplers_.push_back(std::unique_ptr<PushSincResampler>(
+            new PushSincResampler(proc_num_frames_, output_num_frames_)));
+      }
     }
   }
 
   if (num_bands_ > 1) {
-    split_data_.reset(new ChannelBuffer<float>(
-        buffer_num_frames_, buffer_num_channels_, num_bands_));
-    splitting_filter_.reset(new SplittingFilter(
-        buffer_num_channels_, num_bands_, buffer_num_frames_));
+    split_data_.reset(
+        new IFChannelBuffer(proc_num_frames_, num_proc_channels_, num_bands_));
+    splitting_filter_.reset(
+        new SplittingFilter(num_proc_channels_, num_bands_, proc_num_frames_));
   }
 }
 
 AudioBuffer::~AudioBuffer() {}
 
-void AudioBuffer::set_downmixing_to_specific_channel(size_t channel) {
-  downmix_by_averaging_ = false;
-  RTC_DCHECK_GT(input_num_channels_, channel);
-  channel_for_downmixing_ = std::min(channel, input_num_channels_ - 1);
-}
-
-void AudioBuffer::set_downmixing_by_averaging() {
-  downmix_by_averaging_ = true;
-}
-
 void AudioBuffer::CopyFrom(const float* const* data,
                            const StreamConfig& stream_config) {
   RTC_DCHECK_EQ(stream_config.num_frames(), input_num_frames_);
-  RTC_DCHECK_EQ(stream_config.num_channels(), input_num_channels_);
-  RestoreNumChannels();
-  const bool downmix_needed = input_num_channels_ > 1 && num_channels_ == 1;
+  RTC_DCHECK_EQ(stream_config.num_channels(), num_input_channels_);
+  InitForNewData();
+  // Initialized lazily because there's a different condition in
+  // DeinterleaveFrom.
+  const bool need_to_downmix =
+      num_input_channels_ > 1 && num_proc_channels_ == 1;
+  if (need_to_downmix && !input_buffer_) {
+    input_buffer_.reset(
+        new IFChannelBuffer(input_num_frames_, num_proc_channels_));
+  }
 
-  const bool resampling_needed = input_num_frames_ != buffer_num_frames_;
+  // Downmix.
+  const float* const* data_ptr = data;
+  if (need_to_downmix) {
+    DownmixToMono<float, float>(data, input_num_frames_, num_input_channels_,
+                                input_buffer_->fbuf()->channels()[0]);
+    data_ptr = input_buffer_->fbuf_const()->channels();
+  }
 
-  if (downmix_needed) {
-    RTC_DCHECK_GT(kMaxSamplesPerChannel, input_num_frames_);
-
-    std::array<float, kMaxSamplesPerChannel> downmix;
-    if (downmix_by_averaging_) {
-      const float kOneByNumChannels = 1.f / input_num_channels_;
-      for (size_t i = 0; i < input_num_frames_; ++i) {
-        float value = data[0][i];
-        for (size_t j = 1; j < input_num_channels_; ++j) {
-          value += data[j][i];
-        }
-        downmix[i] = value * kOneByNumChannels;
-      }
+  // Resample.
+  if (input_num_frames_ != proc_num_frames_) {
+    for (size_t i = 0; i < num_proc_channels_; ++i) {
+      input_resamplers_[i]->Resample(data_ptr[i], input_num_frames_,
+                                     process_buffer_->channels()[i],
+                                     proc_num_frames_);
     }
-    const float* downmixed_data =
-        downmix_by_averaging_ ? downmix.data() : data[channel_for_downmixing_];
+    data_ptr = process_buffer_->channels();
+  }
 
-    if (resampling_needed) {
-      input_resamplers_[0]->Resample(downmixed_data, input_num_frames_,
-                                     data_->channels()[0], buffer_num_frames_);
-    }
-    const float* data_to_convert =
-        resampling_needed ? data_->channels()[0] : downmixed_data;
-    FloatToFloatS16(data_to_convert, buffer_num_frames_, data_->channels()[0]);
-  } else {
-    if (resampling_needed) {
-      for (size_t i = 0; i < num_channels_; ++i) {
-        input_resamplers_[i]->Resample(data[i], input_num_frames_,
-                                       data_->channels()[i],
-                                       buffer_num_frames_);
-        FloatToFloatS16(data_->channels()[i], buffer_num_frames_,
-                        data_->channels()[i]);
-      }
-    } else {
-      for (size_t i = 0; i < num_channels_; ++i) {
-        FloatToFloatS16(data[i], buffer_num_frames_, data_->channels()[i]);
-      }
-    }
+  // Convert to the S16 range.
+  for (size_t i = 0; i < num_proc_channels_; ++i) {
+    FloatToFloatS16(data_ptr[i], proc_num_frames_,
+                    data_->fbuf()->channels()[i]);
   }
 }
 
 void AudioBuffer::CopyTo(const StreamConfig& stream_config,
                          float* const* data) {
   RTC_DCHECK_EQ(stream_config.num_frames(), output_num_frames_);
+  RTC_DCHECK(stream_config.num_channels() == num_channels_ ||
+             num_channels_ == 1);
 
-  const bool resampling_needed = output_num_frames_ != buffer_num_frames_;
-  if (resampling_needed) {
+  // Convert to the float range.
+  float* const* data_ptr = data;
+  if (output_num_frames_ != proc_num_frames_) {
+    // Convert to an intermediate buffer for subsequent resampling.
+    data_ptr = process_buffer_->channels();
+  }
+  for (size_t i = 0; i < num_channels_; ++i) {
+    FloatS16ToFloat(data_->fbuf()->channels()[i], proc_num_frames_,
+                    data_ptr[i]);
+  }
+
+  // Resample.
+  if (output_num_frames_ != proc_num_frames_) {
     for (size_t i = 0; i < num_channels_; ++i) {
-      FloatS16ToFloat(data_->channels()[i], buffer_num_frames_,
-                      data_->channels()[i]);
-      output_resamplers_[i]->Resample(data_->channels()[i], buffer_num_frames_,
-                                      data[i], output_num_frames_);
-    }
-  } else {
-    for (size_t i = 0; i < num_channels_; ++i) {
-      FloatS16ToFloat(data_->channels()[i], buffer_num_frames_, data[i]);
+      output_resamplers_[i]->Resample(data_ptr[i], proc_num_frames_, data[i],
+                                      output_num_frames_);
     }
   }
 
+  // Upmix.
   for (size_t i = num_channels_; i < stream_config.num_channels(); ++i) {
     memcpy(data[i], data[0], output_num_frames_ * sizeof(**data));
   }
 }
 
-void AudioBuffer::RestoreNumChannels() {
-  num_channels_ = buffer_num_channels_;
-  data_->set_num_channels(buffer_num_channels_);
+void AudioBuffer::InitForNewData() {
+  num_channels_ = num_proc_channels_;
+  data_->set_num_channels(num_proc_channels_);
   if (split_data_.get()) {
-    split_data_->set_num_channels(buffer_num_channels_);
+    split_data_->set_num_channels(num_proc_channels_);
   }
 }
 
+const float* const* AudioBuffer::split_channels_const_f(Band band) const {
+  if (split_data_.get()) {
+    return split_data_->fbuf_const()->channels(band);
+  } else {
+    return band == kBand0To8kHz ? data_->fbuf_const()->channels() : nullptr;
+  }
+}
+
+const float* const* AudioBuffer::channels_const_f() const {
+  return data_->fbuf_const()->channels();
+}
+
+float* const* AudioBuffer::channels_f() {
+  return data_->fbuf()->channels();
+}
+
+const float* const* AudioBuffer::split_bands_const_f(size_t channel) const {
+  return split_data_.get() ? split_data_->fbuf_const()->bands(channel)
+                           : data_->fbuf_const()->bands(channel);
+}
+
+float* const* AudioBuffer::split_bands_f(size_t channel) {
+  return split_data_.get() ? split_data_->fbuf()->bands(channel)
+                           : data_->fbuf()->bands(channel);
+}
+
+size_t AudioBuffer::num_channels() const {
+  return num_channels_;
+}
+
 void AudioBuffer::set_num_channels(size_t num_channels) {
-  RTC_DCHECK_GE(buffer_num_channels_, num_channels);
   num_channels_ = num_channels;
   data_->set_num_channels(num_channels);
   if (split_data_.get()) {
@@ -193,140 +207,78 @@
   }
 }
 
+size_t AudioBuffer::num_frames() const {
+  return proc_num_frames_;
+}
+
+size_t AudioBuffer::num_frames_per_band() const {
+  return num_split_frames_;
+}
+
+size_t AudioBuffer::num_bands() const {
+  return num_bands_;
+}
+
 // The resampler is only for supporting 48kHz to 16kHz in the reverse stream.
-void AudioBuffer::CopyFrom(const AudioFrame* frame) {
-  RTC_DCHECK_EQ(frame->num_channels_, input_num_channels_);
+void AudioBuffer::DeinterleaveFrom(const AudioFrame* frame) {
+  RTC_DCHECK_EQ(frame->num_channels_, num_input_channels_);
   RTC_DCHECK_EQ(frame->samples_per_channel_, input_num_frames_);
-  RestoreNumChannels();
+  InitForNewData();
+  // Initialized lazily because there's a different condition in CopyFrom.
+  if ((input_num_frames_ != proc_num_frames_) && !input_buffer_) {
+    input_buffer_.reset(
+        new IFChannelBuffer(input_num_frames_, num_proc_channels_));
+  }
 
-  const bool resampling_required = input_num_frames_ != buffer_num_frames_;
-
-  const int16_t* interleaved = frame->data();
-  if (num_channels_ == 1) {
-    if (input_num_channels_ == 1) {
-      if (resampling_required) {
-        std::array<float, kMaxSamplesPerChannel> float_buffer;
-        S16ToFloatS16(interleaved, input_num_frames_, float_buffer.data());
-        input_resamplers_[0]->Resample(float_buffer.data(), input_num_frames_,
-                                       data_->channels()[0],
-                                       buffer_num_frames_);
-      } else {
-        S16ToFloatS16(interleaved, input_num_frames_, data_->channels()[0]);
-      }
-    } else {
-      std::array<float, kMaxSamplesPerChannel> float_buffer;
-      float* downmixed_data =
-          resampling_required ? float_buffer.data() : data_->channels()[0];
-      if (downmix_by_averaging_) {
-        for (size_t j = 0, k = 0; j < input_num_frames_; ++j) {
-          int32_t sum = 0;
-          for (size_t i = 0; i < input_num_channels_; ++i, ++k) {
-            sum += interleaved[k];
-          }
-          downmixed_data[j] = sum / static_cast<int16_t>(input_num_channels_);
-        }
-      } else {
-        for (size_t j = 0, k = channel_for_downmixing_; j < input_num_frames_;
-             ++j, k += input_num_channels_) {
-          downmixed_data[j] = interleaved[k];
-        }
-      }
-
-      if (resampling_required) {
-        input_resamplers_[0]->Resample(downmixed_data, input_num_frames_,
-                                       data_->channels()[0],
-                                       buffer_num_frames_);
-      }
-    }
+  int16_t* const* deinterleaved;
+  if (input_num_frames_ == proc_num_frames_) {
+    deinterleaved = data_->ibuf()->channels();
   } else {
-    auto deinterleave_channel = [](size_t channel, size_t num_channels,
-                                   size_t samples_per_channel, const int16_t* x,
-                                   float* y) {
-      for (size_t j = 0, k = channel; j < samples_per_channel;
-           ++j, k += num_channels) {
-        y[j] = x[k];
-      }
-    };
+    deinterleaved = input_buffer_->ibuf()->channels();
+  }
+  // TODO(yujo): handle muted frames more efficiently.
+  if (num_proc_channels_ == 1) {
+    // Downmix and deinterleave simultaneously.
+    DownmixInterleavedToMono(frame->data(), input_num_frames_,
+                             num_input_channels_, deinterleaved[0]);
+  } else {
+    RTC_DCHECK_EQ(num_proc_channels_, num_input_channels_);
+    Deinterleave(frame->data(), input_num_frames_, num_proc_channels_,
+                 deinterleaved);
+  }
 
-    if (resampling_required) {
-      std::array<float, kMaxSamplesPerChannel> float_buffer;
-      for (size_t i = 0; i < num_channels_; ++i) {
-        deinterleave_channel(i, num_channels_, input_num_frames_, interleaved,
-                             float_buffer.data());
-        input_resamplers_[i]->Resample(float_buffer.data(), input_num_frames_,
-                                       data_->channels()[i],
-                                       buffer_num_frames_);
-      }
-    } else {
-      for (size_t i = 0; i < num_channels_; ++i) {
-        deinterleave_channel(i, num_channels_, input_num_frames_, interleaved,
-                             data_->channels()[i]);
-      }
+  // Resample.
+  if (input_num_frames_ != proc_num_frames_) {
+    for (size_t i = 0; i < num_proc_channels_; ++i) {
+      input_resamplers_[i]->Resample(
+          input_buffer_->fbuf_const()->channels()[i], input_num_frames_,
+          data_->fbuf()->channels()[i], proc_num_frames_);
     }
   }
 }
 
-void AudioBuffer::CopyTo(AudioFrame* frame) const {
+void AudioBuffer::InterleaveTo(AudioFrame* frame) const {
   RTC_DCHECK(frame->num_channels_ == num_channels_ || num_channels_ == 1);
   RTC_DCHECK_EQ(frame->samples_per_channel_, output_num_frames_);
 
-  const bool resampling_required = buffer_num_frames_ != output_num_frames_;
-
-  int16_t* interleaved = frame->mutable_data();
-  if (num_channels_ == 1) {
-    std::array<float, kMaxSamplesPerChannel> float_buffer;
-
-    if (resampling_required) {
-      output_resamplers_[0]->Resample(data_->channels()[0], buffer_num_frames_,
-                                      float_buffer.data(), output_num_frames_);
+  // Resample if necessary.
+  IFChannelBuffer* data_ptr = data_.get();
+  if (proc_num_frames_ != output_num_frames_) {
+    for (size_t i = 0; i < num_channels_; ++i) {
+      output_resamplers_[i]->Resample(
+          data_->fbuf()->channels()[i], proc_num_frames_,
+          output_buffer_->fbuf()->channels()[i], output_num_frames_);
     }
-    const float* deinterleaved =
-        resampling_required ? float_buffer.data() : data_->channels()[0];
+    data_ptr = output_buffer_.get();
+  }
 
-    if (frame->num_channels_ == 1) {
-      for (size_t j = 0; j < output_num_frames_; ++j) {
-        interleaved[j] = FloatS16ToS16(deinterleaved[j]);
-      }
-    } else {
-      for (size_t i = 0, k = 0; i < output_num_frames_; ++i) {
-        float tmp = FloatS16ToS16(deinterleaved[i]);
-        for (size_t j = 0; j < frame->num_channels_; ++j, ++k) {
-          interleaved[k] = tmp;
-        }
-      }
-    }
+  // TODO(yujo): handle muted frames more efficiently.
+  if (frame->num_channels_ == num_channels_) {
+    Interleave(data_ptr->ibuf()->channels(), output_num_frames_, num_channels_,
+               frame->mutable_data());
   } else {
-    auto interleave_channel = [](size_t channel, size_t num_channels,
-                                 size_t samples_per_channel, const float* x,
-                                 int16_t* y) {
-      for (size_t k = 0, j = channel; k < samples_per_channel;
-           ++k, j += num_channels) {
-        y[j] = FloatS16ToS16(x[k]);
-      }
-    };
-
-    if (resampling_required) {
-      for (size_t i = 0; i < num_channels_; ++i) {
-        std::array<float, kMaxSamplesPerChannel> float_buffer;
-        output_resamplers_[i]->Resample(data_->channels()[i],
-                                        buffer_num_frames_, float_buffer.data(),
-                                        output_num_frames_);
-        interleave_channel(i, frame->num_channels_, output_num_frames_,
-                           float_buffer.data(), interleaved);
-      }
-    } else {
-      for (size_t i = 0; i < num_channels_; ++i) {
-        interleave_channel(i, frame->num_channels_, output_num_frames_,
-                           data_->channels()[i], interleaved);
-      }
-    }
-
-    for (size_t i = num_channels_; i < frame->num_channels_; ++i) {
-      for (size_t j = 0, k = i, n = num_channels_; j < output_num_frames_;
-           ++j, k += frame->num_channels_, n += frame->num_channels_) {
-        interleaved[k] = interleaved[n];
-      }
-    }
+    UpmixMonoToInterleaved(data_ptr->ibuf()->channels()[0], output_num_frames_,
+                           frame->num_channels_, frame->mutable_data());
   }
 }
 
@@ -338,11 +290,10 @@
   splitting_filter_->Synthesis(split_data_.get(), data_.get());
 }
 
-void AudioBuffer::ExportSplitChannelData(size_t channel,
+void AudioBuffer::CopySplitChannelDataTo(size_t channel,
                                          int16_t* const* split_band_data) {
   for (size_t k = 0; k < num_bands(); ++k) {
-    const float* band_data = split_bands(channel)[k];
-
+    const float* band_data = split_bands_f(channel)[k];
     RTC_DCHECK(split_band_data[k]);
     RTC_DCHECK(band_data);
     for (size_t i = 0; i < num_frames_per_band(); ++i) {
@@ -351,11 +302,11 @@
   }
 }
 
-void AudioBuffer::ImportSplitChannelData(
+void AudioBuffer::CopySplitChannelDataFrom(
     size_t channel,
     const int16_t* const* split_band_data) {
   for (size_t k = 0; k < num_bands(); ++k) {
-    float* band_data = split_bands(channel)[k];
+    float* band_data = split_bands_f(channel)[k];
     RTC_DCHECK(split_band_data[k]);
     RTC_DCHECK(band_data);
     for (size_t i = 0; i < num_frames_per_band(); ++i) {