sample_pdf CUDA and C++ implementations.

Summary: Implement the sample_pdf function from the NeRF project as compiled operators.. The binary search (in searchsorted) is replaced with a low tech linear search, but this is not a problem for the envisaged numbers of bins.

Reviewed By: gkioxari

Differential Revision: D26312535

fbshipit-source-id: df1c3119cd63d944380ed1b2657b6ad81d743e49

pytorch3d/csrc/ext.cpp

@@ -26,6 +26,7 @@
 #include "point_mesh/point_mesh_cuda.h"
 #include "rasterize_meshes/rasterize_meshes.h"
 #include "rasterize_points/rasterize_points.h"
+#include "sample_pdf/sample_pdf.h"
 
 PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
   m.def("face_areas_normals_forward", &FaceAreasNormalsForward);
@@ -83,6 +84,9 @@ PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
   m.def("point_face_array_dist_forward", &PointFaceArrayDistanceForward);
   m.def("point_face_array_dist_backward", &PointFaceArrayDistanceBackward);
 
+  // Sample PDF
+  m.def("sample_pdf", &SamplePdf);
+
   // Pulsar.
 #ifdef PULSAR_LOGGING_ENABLED
   c10::ShowLogInfoToStderr();

pytorch3d/csrc/sample_pdf/sample_pdf.cu

+/*
+ * Copyright (c) Facebook, Inc. and its affiliates.
+ * All rights reserved.
+ *
+ * This source code is licensed under the BSD-style license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#include <ATen/ATen.h>
+#include <ATen/cuda/CUDAContext.h>
+#include <c10/cuda/CUDAGuard.h>
+
+// There is no intermediate memory, so no reason not to have blocksize=32.
+// 256 is a reasonable number of blocks.
+
+// DESIGN
+// We exploit the fact that n_samples is not tiny.
+// A chunk of work is T*blocksize many samples from
+// a single batch elememt.
+// For each batch element there will be
+// chunks_per_batch = 1 + (n_samples-1)/(T*blocksize) of them.
+// The number of potential chunks to do is
+// n_chunks = chunks_per_batch * n_batches.
+// These chunks are divided among the gridSize-many blocks.
+// In block b, we work on chunks b, b+gridSize, b+2*gridSize etc .
+// In chunk i, we work on batch_element i/chunks_per_batch
+// on samples starting from (i%chunks_per_batch) * (T*blocksize)
+
+// BEGIN HYPOTHETICAL
+// Another option (not implemented) if batch_size was always large
+// would be as follows.
+
+// A chunk of work is S samples from each of blocksize-many
+// batch elements.
+// For each batch element there will be
+// chunks_per_batch = (1+(n_samples-1)/S) of them.
+// The number of potential chunks to do is
+// n_chunks = chunks_per_batch * (1+(n_batches-1)/blocksize)
+// These chunks are divided among the gridSize-many blocks.
+// In block b, we work on chunks b, b+gridSize, b+2*gridSize etc .
+// In chunk i, we work on samples starting from S*(i%chunks_per_batch)
+// on batch elements starting from blocksize*(i/chunks_per_batch).
+// END HYPOTHETICAL
+
+__global__ void SamplePdfCudaKernel(
+    const float* __restrict__ bins,
+    const float* __restrict__ weights,
+    float* __restrict__ outputs,
+    float eps,
+    const int T,
+    const int64_t batch_size,
+    const int64_t n_bins,
+    const int64_t n_samples) {
+  const int64_t chunks_per_batch = 1 + (n_samples - 1) / (T * blockDim.x);
+  const int64_t n_chunks = chunks_per_batch * batch_size;
+
+  for (int64_t i_chunk = blockIdx.x; i_chunk < n_chunks; i_chunk += gridDim.x) {
+    // Loop over the chunks.
+    int64_t i_batch_element = i_chunk / chunks_per_batch;
+    int64_t sample_start = (i_chunk % chunks_per_batch) * (T * blockDim.x);
+    const float* const weight_startp = weights + n_bins * i_batch_element;
+    const float* const bin_startp = bins + (1 + n_bins) * i_batch_element;
+
+    // Each chunk looks at a single batch element, so we do the preprocessing
+    // which depends on the batch element, namely finding the total weight.
+    // Idenntical work is being done in sync here by every thread of the block.
+    float total_weight = eps;
+    for (int64_t i_bin = 0; i_bin < n_bins; ++i_bin) {
+      total_weight += weight_startp[i_bin];
+    }
+
+    float* const output_startp =
+        outputs + n_samples * i_batch_element + sample_start;
+
+    for (int t = 0; t < T; ++t) {
+      // Loop over T, which is the number of samples each thread makes within
+      // the chunk.
+      const int64_t i_sample_within_chunk = threadIdx.x + t * blockDim.x;
+      if (sample_start + i_sample_within_chunk >= n_samples) {
+        // Some threads need to exit early because the sample they would
+        // make is unwanted.
+        continue;
+      }
+      // output_startp[i_sample_within_chunk] contains the quantile we (i.e.
+      // this thread) are calcvulating.
+      float uniform = total_weight * output_startp[i_sample_within_chunk];
+      int64_t i_bin = 0;
+      // We find the bin containing the quantile by walking along the weights.
+      // This loop must be thread dependent. I.e. the whole warp will wait until
+      // every thread has found the bin for its quantile.
+      // It may be best to write it differently.
+      while (i_bin + 1 < n_bins && uniform > weight_startp[i_bin]) {
+        uniform -= weight_startp[i_bin];
+        ++i_bin;
+      }
+
+      // Now we know which bin to look in, we use linear interpolation
+      // to find the location of the quantile within the bin, and
+      // write the answer back.
+      float bin_start = bin_startp[i_bin];
+      float bin_end = bin_startp[i_bin + 1];
+      float bin_weight = weight_startp[i_bin];
+      float output_value = bin_start;
+      if (uniform > bin_weight) {
+        output_value = bin_end;
+      } else if (bin_weight > eps) {
+        output_value += (uniform / bin_weight) * (bin_end - bin_start);
+      }
+      output_startp[i_sample_within_chunk] = output_value;
+    }
+  }
+}
+
+void SamplePdfCuda(
+    const at::Tensor& bins,
+    const at::Tensor& weights,
+    const at::Tensor& outputs,
+    float eps) {
+  // Check inputs are on the same device
+  at::TensorArg bins_t{bins, "bins", 1}, weights_t{weights, "weights", 2},
+      outputs_t{outputs, "outputs", 3};
+  at::CheckedFrom c = "SamplePdfCuda";
+  at::checkAllSameGPU(c, {bins_t, weights_t, outputs_t});
+  at::checkAllSameType(c, {bins_t, weights_t, outputs_t});
+
+  // Set the device for the kernel launch based on the device of the input
+  at::cuda::CUDAGuard device_guard(bins.device());
+  cudaStream_t stream = at::cuda::getCurrentCUDAStream();
+
+  const int64_t batch_size = bins.size(0);
+  const int64_t n_bins = weights.size(1);
+  const int64_t n_samples = outputs.size(1);
+
+  const int64_t threads = 32;
+  const int64_t T = n_samples <= threads ? 1 : 2;
+  const int64_t chunks_per_batch = 1 + (n_samples - 1) / (T * threads);
+  const int64_t n_chunks = chunks_per_batch * batch_size;
+
+  const int64_t max_blocks = 1024;
+  const int64_t blocks = n_chunks < max_blocks ? n_chunks : max_blocks;
+
+  SamplePdfCudaKernel<<<blocks, threads, 0, stream>>>(
+      bins.contiguous().data_ptr<float>(),
+      weights.contiguous().data_ptr<float>(),
+      outputs.data_ptr<float>(), // Checked contiguous in header file.
+      eps,
+      T,
+      batch_size,
+      n_bins,
+      n_samples);
+
+  AT_CUDA_CHECK(cudaGetLastError());
+}

pytorch3d/csrc/sample_pdf/sample_pdf.h

+/*
+ * Copyright (c) Facebook, Inc. and its affiliates.
+ * All rights reserved.
+ *
+ * This source code is licensed under the BSD-style license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#pragma once
+#include <torch/extension.h>
+#include <cstdio>
+#include <tuple>
+#include "utils/pytorch3d_cutils.h"
+
+// ****************************************************************************
+// *                          SamplePdf                                       *
+// ****************************************************************************
+
+//  Samples a probability density functions defined by bin edges `bins` and
+//  the non-negative per-bin probabilities `weights`.
+
+//  Args:
+//      bins: FloatTensor of shape `(batch_size, n_bins+1)` denoting the edges
+//      of the sampling bins.
+
+//      weights: FloatTensor of shape `(batch_size, n_bins)` containing
+//      non-negative numbers representing the probability of sampling the
+//      corresponding bin.
+
+//      uniforms: The quantiles to draw, FloatTensor of shape
+//      `(batch_size, n_samples)`.
+
+//      outputs: On call, this contains the quantiles to draw. It is overwritten
+//              with the drawn samples. FloatTensor of shape
+//              `(batch_size, n_samples), where `n_samples are drawn from each
+//               distribution.
+
+//      eps: A constant preventing division by zero in case empty bins are
+//      present.
+
+//  Not differentiable
+
+#ifdef WITH_CUDA
+void SamplePdfCuda(
+    const torch::Tensor& bins,
+    const torch::Tensor& weights,
+    const torch::Tensor& outputs,
+    float eps);
+#endif
+
+void SamplePdfCpu(
+    const torch::Tensor& bins,
+    const torch::Tensor& weights,
+    const torch::Tensor& outputs,
+    float eps);
+
+inline void SamplePdf(
+    const torch::Tensor& bins,
+    const torch::Tensor& weights,
+    const torch::Tensor& outputs,
+    float eps) {
+  if (bins.is_cuda()) {
+#ifdef WITH_CUDA
+    CHECK_CUDA(weights);
+    CHECK_CONTIGUOUS_CUDA(outputs);
+    SamplePdfCuda(bins, weights, outputs, eps);
+    return;
+#else
+    AT_ERROR("Not compiled with GPU support.");
+#endif
+  }
+  CHECK_CONTIGUOUS(outputs);
+  SamplePdfCpu(bins, weights, outputs, eps);
+}

pytorch3d/csrc/sample_pdf/sample_pdf_cpu.cpp

+/*
+ * Copyright (c) Facebook, Inc. and its affiliates.
+ * All rights reserved.
+ *
+ * This source code is licensed under the BSD-style license found in the
+ * LICENSE file in the root directory of this source tree.
+ */
+
+#include <torch/extension.h>
+#include <algorithm>
+#include <thread>
+#include <vector>
+
+// If the number of bins is the typical 64, it is
+// quicker to use binary search than linear scan.
+// With more bins, it is more important.
+// There is no equivalent CUDA implementation yet.
+#define USE_BINARY_SEARCH
+
+namespace {
+// This worker function does the job of SamplePdf but only on
+// batch elements in [start_batch, end_batch).
+void SamplePdfCpu_worker(
+    const torch::Tensor& bins,
+    const torch::Tensor& weights,
+    const torch::Tensor& outputs,
+    float eps,
+    int64_t start_batch,
+    int64_t end_batch) {
+  const int64_t n_bins = weights.size(1);
+  const int64_t n_samples = outputs.size(1);
+
+  auto bins_a = bins.accessor<float, 2>();
+  auto weights_a = weights.accessor<float, 2>();
+  float* __restrict__ output_p =
+      outputs.data_ptr<float>() + start_batch * n_samples;
+
+#ifdef USE_BINARY_SEARCH
+  std::vector<float> partial_sums(n_bins);
+#endif
+
+  for (int64_t i_batch_elt = start_batch; i_batch_elt < end_batch;
+       ++i_batch_elt) {
+    auto bin_a = bins_a[i_batch_elt];
+    auto weight_a = weights_a[i_batch_elt];
+
+    // Here we do the work which has to be done once per batch element.
+    // i.e. (1) finding the total weight. (2) If using binary search,
+    // precompute the partial sums of the weights.
+
+    float total_weight = 0;
+    for (int64_t i_bin = 0; i_bin < n_bins; ++i_bin) {
+      total_weight += weight_a[i_bin];
+#ifdef USE_BINARY_SEARCH
+      partial_sums[i_bin] = total_weight;
+#endif
+    }
+    total_weight += eps;
+
+    for (int64_t i_sample = 0; i_sample < n_samples; ++i_sample) {
+      // Here we are taking a single random quantile (which is stored
+      // in *output_p) and using it to make a single sample, which we
+      // write back to the same location. First we find which bin
+      // the quantile lives in, either by binary search in the
+      // precomputed partial sums, or by scanning through the weights.
+
+      float uniform = total_weight * *output_p;
+#ifdef USE_BINARY_SEARCH
+      int64_t i_bin = std::lower_bound(
+                          partial_sums.begin(), --partial_sums.end(), uniform) -
+          partial_sums.begin();
+      if (i_bin > 0) {
+        uniform -= partial_sums[i_bin - 1];
+      }
+#else
+      int64_t i_bin = 0;
+      while (i_bin + 1 < n_bins && uniform > weight_a[i_bin]) {
+        uniform -= weight_a[i_bin];
+        ++i_bin;
+      }
+#endif
+
+      // Now i_bin identifies the bin the quantile lives in, we use
+      // straight line interpolation to find the position of the
+      // quantile within the bin, and write it to *output_p.
+
+      float bin_start = bin_a[i_bin];
+      float bin_end = bin_a[i_bin + 1];
+      float bin_weight = weight_a[i_bin];
+      float output_value = bin_start;
+      if (uniform > bin_weight) {
+        output_value = bin_end;
+      } else if (bin_weight > eps) {
+        output_value += (uniform / bin_weight) * (bin_end - bin_start);
+      }
+      *output_p = output_value;
+      ++output_p;
+    }
+  }
+}
+
+} // anonymous namespace
+
+void SamplePdfCpu(
+    const torch::Tensor& bins,
+    const torch::Tensor& weights,
+    const torch::Tensor& outputs,
+    float eps) {
+  const int64_t batch_size = bins.size(0);
+  const int64_t max_threads = std::min(4, at::get_num_threads());
+  const int64_t n_threads = std::min(max_threads, batch_size);
+  if (batch_size == 0) {
+    return;
+  }
+
+  // SamplePdfCpu_worker does the work of this function. We send separate ranges
+  // of batch elements to that function in nThreads-1 separate threads.
+
+  std::vector<std::thread> threads;
+  threads.reserve(n_threads - 1);
+  const int64_t batch_elements_per_thread = 1 + (batch_size - 1) / n_threads;
+  int64_t start_batch = 0;
+  for (int iThread = 0; iThread < n_threads - 1; ++iThread) {
+    threads.emplace_back(
+        SamplePdfCpu_worker,
+        bins,
+        weights,
+        outputs,
+        eps,
+        start_batch,
+        start_batch + batch_elements_per_thread);
+    start_batch += batch_elements_per_thread;
+  }
+
+  // The remaining batch elements are calculated in this threads. If nThreads is
+  // 1 then all the work happens in this line.
+  SamplePdfCpu_worker(bins, weights, outputs, eps, start_batch, batch_size);
+  for (auto&& thread : threads) {
+    thread.join();
+  }
+}

pytorch3d/renderer/implicit/sample_pdf.py

@@ -6,6 +6,62 @@
 
 
 import torch
+from pytorch3d import _C
+
+
+def sample_pdf(
+    bins: torch.Tensor,
+    weights: torch.Tensor,
+    n_samples: int,
+    det: bool = False,
+    eps: float = 1e-5,
+) -> torch.Tensor:
+    """
+    Samples probability density functions defined by bin edges `bins` and
+    the non-negative per-bin probabilities `weights`.
+
+    Args:
+        bins: Tensor of shape `(..., n_bins+1)` denoting the edges of the sampling bins.
+        weights: Tensor of shape `(..., n_bins)` containing non-negative numbers
+            representing the probability of sampling the corresponding bin.
+        n_samples: The number of samples to draw from each set of bins.
+        det: If `False`, the sampling is random. `True` yields deterministic
+            uniformly-spaced sampling from the inverse cumulative density function.
+        eps: A constant preventing division by zero in case empty bins are present.
+
+    Returns:
+        samples: Tensor of shape `(..., n_samples)` containing `n_samples` samples
+            drawn from each probability distribution.
+
+    Refs:
+        [1] https://github.com/bmild/nerf/blob/55d8b00244d7b5178f4d003526ab6667683c9da9/run_nerf_helpers.py#L183  # noqa E501
+    """
+    if torch.is_grad_enabled() and (bins.requires_grad or weights.requires_grad):
+        raise NotImplementedError("sample_pdf differentiability.")
+    if weights.min() <= -eps:
+        raise ValueError("Negative weights provided.")
+    batch_shape = bins.shape[:-1]
+    n_bins = weights.shape[-1]
+    if n_bins + 1 != bins.shape[-1] or weights.shape[:-1] != batch_shape:
+        shapes = f"{bins.shape}{weights.shape}"
+        raise ValueError("Inconsistent shapes of bins and weights: " + shapes)
+    output_shape = batch_shape + (n_samples,)
+
+    if det:
+        u = torch.linspace(0.0, 1.0, n_samples, device=bins.device, dtype=torch.float32)
+        output = u.expand(output_shape).contiguous()
+    else:
+        output = torch.rand(output_shape, dtype=torch.float32, device=bins.device)
+
+    # pyre-fixme[16]: Module `pytorch3d` has no attribute `_C`.
+    _C.sample_pdf(
+        bins.reshape(-1, n_bins + 1),
+        weights.reshape(-1, n_bins),
+        output.reshape(-1, n_samples),
+        eps,
+    )
+
+    return output
 
 
 def sample_pdf_python(
@@ -16,6 +72,12 @@ def sample_pdf_python(
     eps: float = 1e-5,
 ) -> torch.Tensor:
     """
+    This is a pure python implementation of the `sample_pdf` function.
+    It may be faster than sample_pdf when the number of bins is very large,
+    because it behaves as O(batchsize * [n_bins + log(n_bins) * n_samples] )
+    whereas sample_pdf  behaves as O(batchsize * n_bins * n_samples).
+    For 64 bins sample_pdf is much faster.
+
     Samples probability density functions defined by bin edges `bins` and
     the non-negative per-bin probabilities `weights`.
 

tests/bm_sample_pdf.py

@@ -12,7 +12,7 @@ from test_sample_pdf import TestSamplePDF
 
 def bm_sample_pdf() -> None:
 
-    backends = ["python_cuda", "python_cpu"]
+    backends = ["python_cuda", "cuda", "python_cpu", "cpu"]
 
     kwargs_list = []
     sample_counts = [64]

tests/test_sample_pdf.py

@@ -5,10 +5,11 @@
 # LICENSE file in the root directory of this source tree.
 
 import unittest
+from itertools import product
 
 import torch
 from common_testing import TestCaseMixin
-from pytorch3d.renderer.implicit.sample_pdf import sample_pdf_python
+from pytorch3d.renderer.implicit.sample_pdf import sample_pdf, sample_pdf_python
 
 
 class TestSamplePDF(TestCaseMixin, unittest.TestCase):
@@ -23,9 +24,59 @@ class TestSamplePDF(TestCaseMixin, unittest.TestCase):
         calc = torch.linspace(17, 18, 100).expand(5, -1)
         self.assertClose(output, calc)
 
+    def test_simple_det(self):
+        for n_bins, n_samples, batch in product(
+            [7, 20], [2, 7, 31, 32, 33], [(), (1, 4), (31,), (32,), (33,)]
+        ):
+            weights = torch.rand(size=(batch + (n_bins,)))
+            bins = torch.cumsum(torch.rand(size=(batch + (n_bins + 1,))), dim=-1)
+            python = sample_pdf_python(bins, weights, n_samples, det=True)
+
+            cpp = sample_pdf(bins, weights, n_samples, det=True)
+            self.assertClose(cpp, python, atol=2e-3)
+
+            nthreads = torch.get_num_threads()
+            torch.set_num_threads(1)
+            cpp_singlethread = sample_pdf(bins, weights, n_samples, det=True)
+            self.assertClose(cpp_singlethread, python, atol=2e-3)
+            torch.set_num_threads(nthreads)
+
+            device = torch.device("cuda:0")
+            cuda = sample_pdf(
+                bins.to(device), weights.to(device), n_samples, det=True
+            ).cpu()
+
+            self.assertClose(cuda, python, atol=2e-3)
+
+    def test_rand_cpu(self):
+        n_bins, n_samples, batch_size = 11, 17, 9
+        weights = torch.rand(size=(batch_size, n_bins))
+        bins = torch.cumsum(torch.rand(size=(batch_size, n_bins + 1)), dim=-1)
+        torch.manual_seed(1)
+        python = sample_pdf_python(bins, weights, n_samples)
+        torch.manual_seed(1)
+        cpp = sample_pdf(bins, weights, n_samples)
+
+        self.assertClose(cpp, python, atol=2e-3)
+
+    def test_rand_nogap(self):
+        # Case where random is actually deterministic
+        weights = torch.FloatTensor([0, 10, 0])
+        bins = torch.FloatTensor([0, 10, 10, 25])
+        n_samples = 8
+        predicted = torch.full((n_samples,), 10.0)
+        python = sample_pdf_python(bins, weights, n_samples)
+        self.assertClose(python, predicted)
+        cpp = sample_pdf(bins, weights, n_samples)
+        self.assertClose(cpp, predicted)
+
+        device = torch.device("cuda:0")
+        cuda = sample_pdf(bins.to(device), weights.to(device), n_samples).cpu()
+        self.assertClose(cuda, predicted)
+
     @staticmethod
     def bm_fn(*, backend: str, n_samples, batch_size, n_bins):
-        f = sample_pdf_python
+        f = sample_pdf_python if "python" in backend else sample_pdf
         weights = torch.rand(size=(batch_size, n_bins))
         bins = torch.cumsum(torch.rand(size=(batch_size, n_bins + 1)), dim=-1)