Add 'third_party/abseil_cpp/' from commit '768eb2ca2857342673fcd462792ce04b8bac3fa3' r/781

git-subtree-dir: third_party/abseil_cpp
git-subtree-mainline: ffb2ae54beb5796cd408fbe15d2d2da09ff37adf
git-subtree-split: 768eb2ca2857342673fcd462792ce04b8bac3fa3

1 files changed, 804 insertions, 0 deletions

diff --git a/third_party/abseil_cpp/absl/random/internal/nanobenchmark.cc b/third_party/abseil_cpp/absl/random/internal/nanobenchmark.cc
new file mode 100644
index 000000000000..c9181813f7f0
--- /dev/null
+++ b/third_party/abseil_cpp/absl/random/internal/nanobenchmark.cc
@@ -0,0 +1,804 @@
+// Copyright 2017 Google Inc. All Rights Reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+#include "absl/random/internal/nanobenchmark.h"
+
+#include <sys/types.h>
+
+#include <algorithm>  // sort
+#include <atomic>
+#include <cstddef>
+#include <cstdint>
+#include <cstdlib>
+#include <cstring>  // memcpy
+#include <limits>
+#include <string>
+#include <utility>
+#include <vector>
+
+#include "absl/base/attributes.h"
+#include "absl/base/internal/raw_logging.h"
+#include "absl/random/internal/platform.h"
+#include "absl/random/internal/randen_engine.h"
+
+// OS
+#if defined(_WIN32) || defined(_WIN64)
+#define ABSL_OS_WIN
+#include <windows.h>  // NOLINT
+
+#elif defined(__ANDROID__)
+#define ABSL_OS_ANDROID
+
+#elif defined(__linux__)
+#define ABSL_OS_LINUX
+#include <sched.h>        // NOLINT
+#include <sys/syscall.h>  // NOLINT
+#endif
+
+#if defined(ABSL_ARCH_X86_64) && !defined(ABSL_OS_WIN)
+#include <cpuid.h>  // NOLINT
+#endif
+
+// __ppc_get_timebase_freq
+#if defined(ABSL_ARCH_PPC)
+#include <sys/platform/ppc.h>  // NOLINT
+#endif
+
+// clock_gettime
+#if defined(ABSL_ARCH_ARM) || defined(ABSL_ARCH_AARCH64)
+#include <time.h>  // NOLINT
+#endif
+
+// ABSL_RANDOM_INTERNAL_ATTRIBUTE_NEVER_INLINE prevents inlining of the method.
+#if ABSL_HAVE_ATTRIBUTE(noinline) || (defined(__GNUC__) && !defined(__clang__))
+#define ABSL_RANDOM_INTERNAL_ATTRIBUTE_NEVER_INLINE __attribute__((noinline))
+#elif defined(_MSC_VER)
+#define ABSL_RANDOM_INTERNAL_ATTRIBUTE_NEVER_INLINE __declspec(noinline)
+#else
+#define ABSL_RANDOM_INTERNAL_ATTRIBUTE_NEVER_INLINE
+#endif
+
+namespace absl {
+ABSL_NAMESPACE_BEGIN
+namespace random_internal_nanobenchmark {
+namespace {
+
+// For code folding.
+namespace platform {
+#if defined(ABSL_ARCH_X86_64)
+
+// TODO(janwas): Merge with the one in randen_hwaes.cc?
+void Cpuid(const uint32_t level, const uint32_t count,
+           uint32_t* ABSL_RANDOM_INTERNAL_RESTRICT abcd) {
+#if defined(ABSL_OS_WIN)
+  int regs[4];
+  __cpuidex(regs, level, count);
+  for (int i = 0; i < 4; ++i) {
+    abcd[i] = regs[i];
+  }
+#else
+  uint32_t a, b, c, d;
+  __cpuid_count(level, count, a, b, c, d);
+  abcd[0] = a;
+  abcd[1] = b;
+  abcd[2] = c;
+  abcd[3] = d;
+#endif
+}
+
+std::string BrandString() {
+  char brand_string[49];
+  uint32_t abcd[4];
+
+  // Check if brand string is supported (it is on all reasonable Intel/AMD)
+  Cpuid(0x80000000U, 0, abcd);
+  if (abcd[0] < 0x80000004U) {
+    return std::string();
+  }
+
+  for (int i = 0; i < 3; ++i) {
+    Cpuid(0x80000002U + i, 0, abcd);
+    memcpy(brand_string + i * 16, &abcd, sizeof(abcd));
+  }
+  brand_string[48] = 0;
+  return brand_string;
+}
+
+// Returns the frequency quoted inside the brand string. This does not
+// account for throttling nor Turbo Boost.
+double NominalClockRate() {
+  const std::string& brand_string = BrandString();
+  // Brand strings include the maximum configured frequency. These prefixes are
+  // defined by Intel CPUID documentation.
+  const char* prefixes[3] = {"MHz", "GHz", "THz"};
+  const double multipliers[3] = {1E6, 1E9, 1E12};
+  for (size_t i = 0; i < 3; ++i) {
+    const size_t pos_prefix = brand_string.find(prefixes[i]);
+    if (pos_prefix != std::string::npos) {
+      const size_t pos_space = brand_string.rfind(' ', pos_prefix - 1);
+      if (pos_space != std::string::npos) {
+        const std::string digits =
+            brand_string.substr(pos_space + 1, pos_prefix - pos_space - 1);
+        return std::stod(digits) * multipliers[i];
+      }
+    }
+  }
+
+  return 0.0;
+}
+
+#endif  // ABSL_ARCH_X86_64
+}  // namespace platform
+
+// Prevents the compiler from eliding the computations that led to "output".
+template <class T>
+inline void PreventElision(T&& output) {
+#ifndef ABSL_OS_WIN
+  // Works by indicating to the compiler that "output" is being read and
+  // modified. The +r constraint avoids unnecessary writes to memory, but only
+  // works for built-in types (typically FuncOutput).
+  asm volatile("" : "+r"(output) : : "memory");
+#else
+  // MSVC does not support inline assembly anymore (and never supported GCC's
+  // RTL constraints). Self-assignment with #pragma optimize("off") might be
+  // expected to prevent elision, but it does not with MSVC 2015. Type-punning
+  // with volatile pointers generates inefficient code on MSVC 2017.
+  static std::atomic<T> dummy(T{});
+  dummy.store(output, std::memory_order_relaxed);
+#endif
+}
+
+namespace timer {
+
+// Start/Stop return absolute timestamps and must be placed immediately before
+// and after the region to measure. We provide separate Start/Stop functions
+// because they use different fences.
+//
+// Background: RDTSC is not 'serializing'; earlier instructions may complete
+// after it, and/or later instructions may complete before it. 'Fences' ensure
+// regions' elapsed times are independent of such reordering. The only
+// documented unprivileged serializing instruction is CPUID, which acts as a
+// full fence (no reordering across it in either direction). Unfortunately
+// the latency of CPUID varies wildly (perhaps made worse by not initializing
+// its EAX input). Because it cannot reliably be deducted from the region's
+// elapsed time, it must not be included in the region to measure (i.e.
+// between the two RDTSC).
+//
+// The newer RDTSCP is sometimes described as serializing, but it actually
+// only serves as a half-fence with release semantics. Although all
+// instructions in the region will complete before the final timestamp is
+// captured, subsequent instructions may leak into the region and increase the
+// elapsed time. Inserting another fence after the final RDTSCP would prevent
+// such reordering without affecting the measured region.
+//
+// Fortunately, such a fence exists. The LFENCE instruction is only documented
+// to delay later loads until earlier loads are visible. However, Intel's
+// reference manual says it acts as a full fence (waiting until all earlier
+// instructions have completed, and delaying later instructions until it
+// completes). AMD assigns the same behavior to MFENCE.
+//
+// We need a fence before the initial RDTSC to prevent earlier instructions
+// from leaking into the region, and arguably another after RDTSC to avoid
+// region instructions from completing before the timestamp is recorded.
+// When surrounded by fences, the additional RDTSCP half-fence provides no
+// benefit, so the initial timestamp can be recorded via RDTSC, which has
+// lower overhead than RDTSCP because it does not read TSC_AUX. In summary,
+// we define Start = LFENCE/RDTSC/LFENCE; Stop = RDTSCP/LFENCE.
+//
+// Using Start+Start leads to higher variance and overhead than Stop+Stop.
+// However, Stop+Stop includes an LFENCE in the region measurements, which
+// adds a delay dependent on earlier loads. The combination of Start+Stop
+// is faster than Start+Start and more consistent than Stop+Stop because
+// the first LFENCE already delayed subsequent loads before the measured
+// region. This combination seems not to have been considered in prior work:
+// http://akaros.cs.berkeley.edu/lxr/akaros/kern/arch/x86/rdtsc_test.c
+//
+// Note: performance counters can measure 'exact' instructions-retired or
+// (unhalted) cycle counts. The RDPMC instruction is not serializing and also
+// requires fences. Unfortunately, it is not accessible on all OSes and we
+// prefer to avoid kernel-mode drivers. Performance counters are also affected
+// by several under/over-count errata, so we use the TSC instead.
+
+// Returns a 64-bit timestamp in unit of 'ticks'; to convert to seconds,
+// divide by InvariantTicksPerSecond.
+inline uint64_t Start64() {
+  uint64_t t;
+#if defined(ABSL_ARCH_PPC)
+  asm volatile("mfspr %0, %1" : "=r"(t) : "i"(268));
+#elif defined(ABSL_ARCH_X86_64)
+#if defined(ABSL_OS_WIN)
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+  t = __rdtsc();
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+#else
+  asm volatile(
+      "lfence\n\t"
+      "rdtsc\n\t"
+      "shl $32, %%rdx\n\t"
+      "or %%rdx, %0\n\t"
+      "lfence"
+      : "=a"(t)
+      :
+      // "memory" avoids reordering. rdx = TSC >> 32.
+      // "cc" = flags modified by SHL.
+      : "rdx", "memory", "cc");
+#endif
+#else
+  // Fall back to OS - unsure how to reliably query cntvct_el0 frequency.
+  timespec ts;
+  clock_gettime(CLOCK_REALTIME, &ts);
+  t = ts.tv_sec * 1000000000LL + ts.tv_nsec;
+#endif
+  return t;
+}
+
+inline uint64_t Stop64() {
+  uint64_t t;
+#if defined(ABSL_ARCH_X86_64)
+#if defined(ABSL_OS_WIN)
+  _ReadWriteBarrier();
+  unsigned aux;
+  t = __rdtscp(&aux);
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+#else
+  // Use inline asm because __rdtscp generates code to store TSC_AUX (ecx).
+  asm volatile(
+      "rdtscp\n\t"
+      "shl $32, %%rdx\n\t"
+      "or %%rdx, %0\n\t"
+      "lfence"
+      : "=a"(t)
+      :
+      // "memory" avoids reordering. rcx = TSC_AUX. rdx = TSC >> 32.
+      // "cc" = flags modified by SHL.
+      : "rcx", "rdx", "memory", "cc");
+#endif
+#else
+  t = Start64();
+#endif
+  return t;
+}
+
+// Returns a 32-bit timestamp with about 4 cycles less overhead than
+// Start64. Only suitable for measuring very short regions because the
+// timestamp overflows about once a second.
+inline uint32_t Start32() {
+  uint32_t t;
+#if defined(ABSL_ARCH_X86_64)
+#if defined(ABSL_OS_WIN)
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+  t = static_cast<uint32_t>(__rdtsc());
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+#else
+  asm volatile(
+      "lfence\n\t"
+      "rdtsc\n\t"
+      "lfence"
+      : "=a"(t)
+      :
+      // "memory" avoids reordering. rdx = TSC >> 32.
+      : "rdx", "memory");
+#endif
+#else
+  t = static_cast<uint32_t>(Start64());
+#endif
+  return t;
+}
+
+inline uint32_t Stop32() {
+  uint32_t t;
+#if defined(ABSL_ARCH_X86_64)
+#if defined(ABSL_OS_WIN)
+  _ReadWriteBarrier();
+  unsigned aux;
+  t = static_cast<uint32_t>(__rdtscp(&aux));
+  _ReadWriteBarrier();
+  _mm_lfence();
+  _ReadWriteBarrier();
+#else
+  // Use inline asm because __rdtscp generates code to store TSC_AUX (ecx).
+  asm volatile(
+      "rdtscp\n\t"
+      "lfence"
+      : "=a"(t)
+      :
+      // "memory" avoids reordering. rcx = TSC_AUX. rdx = TSC >> 32.
+      : "rcx", "rdx", "memory");
+#endif
+#else
+  t = static_cast<uint32_t>(Stop64());
+#endif
+  return t;
+}
+
+}  // namespace timer
+
+namespace robust_statistics {
+
+// Sorts integral values in ascending order (e.g. for Mode). About 3x faster
+// than std::sort for input distributions with very few unique values.
+template <class T>
+void CountingSort(T* values, size_t num_values) {
+  // Unique values and their frequency (similar to flat_map).
+  using Unique = std::pair<T, int>;
+  std::vector<Unique> unique;
+  for (size_t i = 0; i < num_values; ++i) {
+    const T value = values[i];
+    const auto pos =
+        std::find_if(unique.begin(), unique.end(),
+                     [value](const Unique u) { return u.first == value; });
+    if (pos == unique.end()) {
+      unique.push_back(std::make_pair(value, 1));
+    } else {
+      ++pos->second;
+    }
+  }
+
+  // Sort in ascending order of value (pair.first).
+  std::sort(unique.begin(), unique.end());
+
+  // Write that many copies of each unique value to the array.
+  T* ABSL_RANDOM_INTERNAL_RESTRICT p = values;
+  for (const auto& value_count : unique) {
+    std::fill(p, p + value_count.second, value_count.first);
+    p += value_count.second;
+  }
+  ABSL_RAW_CHECK(p == values + num_values, "Did not produce enough output");
+}
+
+// @return i in [idx_begin, idx_begin + half_count) that minimizes
+// sorted[i + half_count] - sorted[i].
+template <typename T>
+size_t MinRange(const T* const ABSL_RANDOM_INTERNAL_RESTRICT sorted,
+                const size_t idx_begin, const size_t half_count) {
+  T min_range = (std::numeric_limits<T>::max)();
+  size_t min_idx = 0;
+
+  for (size_t idx = idx_begin; idx < idx_begin + half_count; ++idx) {
+    ABSL_RAW_CHECK(sorted[idx] <= sorted[idx + half_count], "Not sorted");
+    const T range = sorted[idx + half_count] - sorted[idx];
+    if (range < min_range) {
+      min_range = range;
+      min_idx = idx;
+    }
+  }
+
+  return min_idx;
+}
+
+// Returns an estimate of the mode by calling MinRange on successively
+// halved intervals. "sorted" must be in ascending order. This is the
+// Half Sample Mode estimator proposed by Bickel in "On a fast, robust
+// estimator of the mode", with complexity O(N log N). The mode is less
+// affected by outliers in highly-skewed distributions than the median.
+// The averaging operation below assumes "T" is an unsigned integer type.
+template <typename T>
+T ModeOfSorted(const T* const ABSL_RANDOM_INTERNAL_RESTRICT sorted,
+               const size_t num_values) {
+  size_t idx_begin = 0;
+  size_t half_count = num_values / 2;
+  while (half_count > 1) {
+    idx_begin = MinRange(sorted, idx_begin, half_count);
+    half_count >>= 1;
+  }
+
+  const T x = sorted[idx_begin + 0];
+  if (half_count == 0) {
+    return x;
+  }
+  ABSL_RAW_CHECK(half_count == 1, "Should stop at half_count=1");
+  const T average = (x + sorted[idx_begin + 1] + 1) / 2;
+  return average;
+}
+
+// Returns the mode. Side effect: sorts "values".
+template <typename T>
+T Mode(T* values, const size_t num_values) {
+  CountingSort(values, num_values);
+  return ModeOfSorted(values, num_values);
+}
+
+template <typename T, size_t N>
+T Mode(T (&values)[N]) {
+  return Mode(&values[0], N);
+}
+
+// Returns the median value. Side effect: sorts "values".
+template <typename T>
+T Median(T* values, const size_t num_values) {
+  ABSL_RAW_CHECK(num_values != 0, "Empty input");
+  std::sort(values, values + num_values);
+  const size_t half = num_values / 2;
+  // Odd count: return middle
+  if (num_values % 2) {
+    return values[half];
+  }
+  // Even count: return average of middle two.
+  return (values[half] + values[half - 1] + 1) / 2;
+}
+
+// Returns a robust measure of variability.
+template <typename T>
+T MedianAbsoluteDeviation(const T* values, const size_t num_values,
+                          const T median) {
+  ABSL_RAW_CHECK(num_values != 0, "Empty input");
+  std::vector<T> abs_deviations;
+  abs_deviations.reserve(num_values);
+  for (size_t i = 0; i < num_values; ++i) {
+    const int64_t abs = std::abs(int64_t(values[i]) - int64_t(median));
+    abs_deviations.push_back(static_cast<T>(abs));
+  }
+  return Median(abs_deviations.data(), num_values);
+}
+
+}  // namespace robust_statistics
+
+// Ticks := platform-specific timer values (CPU cycles on x86). Must be
+// unsigned to guarantee wraparound on overflow. 32 bit timers are faster to
+// read than 64 bit.
+using Ticks = uint32_t;
+
+// Returns timer overhead / minimum measurable difference.
+Ticks TimerResolution() {
+  // Nested loop avoids exceeding stack/L1 capacity.
+  Ticks repetitions[Params::kTimerSamples];
+  for (size_t rep = 0; rep < Params::kTimerSamples; ++rep) {
+    Ticks samples[Params::kTimerSamples];
+    for (size_t i = 0; i < Params::kTimerSamples; ++i) {
+      const Ticks t0 = timer::Start32();
+      const Ticks t1 = timer::Stop32();
+      samples[i] = t1 - t0;
+    }
+    repetitions[rep] = robust_statistics::Mode(samples);
+  }
+  return robust_statistics::Mode(repetitions);
+}
+
+static const Ticks timer_resolution = TimerResolution();
+
+// Estimates the expected value of "lambda" values with a variable number of
+// samples until the variability "rel_mad" is less than "max_rel_mad".
+template <class Lambda>
+Ticks SampleUntilStable(const double max_rel_mad, double* rel_mad,
+                        const Params& p, const Lambda& lambda) {
+  auto measure_duration = [&lambda]() -> Ticks {
+    const Ticks t0 = timer::Start32();
+    lambda();
+    const Ticks t1 = timer::Stop32();
+    return t1 - t0;
+  };
+
+  // Choose initial samples_per_eval based on a single estimated duration.
+  Ticks est = measure_duration();
+  static const double ticks_per_second = InvariantTicksPerSecond();
+  const size_t ticks_per_eval = ticks_per_second * p.seconds_per_eval;
+  size_t samples_per_eval = ticks_per_eval / est;
+  samples_per_eval = (std::max)(samples_per_eval, p.min_samples_per_eval);
+
+  std::vector<Ticks> samples;
+  samples.reserve(1 + samples_per_eval);
+  samples.push_back(est);
+
+  // Percentage is too strict for tiny differences, so also allow a small
+  // absolute "median absolute deviation".
+  const Ticks max_abs_mad = (timer_resolution + 99) / 100;
+  *rel_mad = 0.0;  // ensure initialized
+
+  for (size_t eval = 0; eval < p.max_evals; ++eval, samples_per_eval *= 2) {
+    samples.reserve(samples.size() + samples_per_eval);
+    for (size_t i = 0; i < samples_per_eval; ++i) {
+      const Ticks r = measure_duration();
+      samples.push_back(r);
+    }
+
+    if (samples.size() >= p.min_mode_samples) {
+      est = robust_statistics::Mode(samples.data(), samples.size());
+    } else {
+      // For "few" (depends also on the variance) samples, Median is safer.
+      est = robust_statistics::Median(samples.data(), samples.size());
+    }
+    ABSL_RAW_CHECK(est != 0, "Estimator returned zero duration");
+
+    // Median absolute deviation (mad) is a robust measure of 'variability'.
+    const Ticks abs_mad = robust_statistics::MedianAbsoluteDeviation(
+        samples.data(), samples.size(), est);
+    *rel_mad = static_cast<double>(static_cast<int>(abs_mad)) / est;
+
+    if (*rel_mad <= max_rel_mad || abs_mad <= max_abs_mad) {
+      if (p.verbose) {
+        ABSL_RAW_LOG(INFO,
+                     "%6zu samples => %5u (abs_mad=%4u, rel_mad=%4.2f%%)\n",
+                     samples.size(), est, abs_mad, *rel_mad * 100.0);
+      }
+      return est;
+    }
+  }
+
+  if (p.verbose) {
+    ABSL_RAW_LOG(WARNING,
+                 "rel_mad=%4.2f%% still exceeds %4.2f%% after %6zu samples.\n",
+                 *rel_mad * 100.0, max_rel_mad * 100.0, samples.size());
+  }
+  return est;
+}
+
+using InputVec = std::vector<FuncInput>;
+
+// Returns vector of unique input values.
+InputVec UniqueInputs(const FuncInput* inputs, const size_t num_inputs) {
+  InputVec unique(inputs, inputs + num_inputs);
+  std::sort(unique.begin(), unique.end());
+  unique.erase(std::unique(unique.begin(), unique.end()), unique.end());
+  return unique;
+}
+
+// Returns how often we need to call func for sufficient precision, or zero
+// on failure (e.g. the elapsed time is too long for a 32-bit tick count).
+size_t NumSkip(const Func func, const void* arg, const InputVec& unique,
+               const Params& p) {
+  // Min elapsed ticks for any input.
+  Ticks min_duration = ~0u;
+
+  for (const FuncInput input : unique) {
+    // Make sure a 32-bit timer is sufficient.
+    const uint64_t t0 = timer::Start64();
+    PreventElision(func(arg, input));
+    const uint64_t t1 = timer::Stop64();
+    const uint64_t elapsed = t1 - t0;
+    if (elapsed >= (1ULL << 30)) {
+      ABSL_RAW_LOG(WARNING,
+                   "Measurement failed: need 64-bit timer for input=%zu\n",
+                   static_cast<size_t>(input));
+      return 0;
+    }
+
+    double rel_mad;
+    const Ticks total = SampleUntilStable(
+        p.target_rel_mad, &rel_mad, p,
+        [func, arg, input]() { PreventElision(func(arg, input)); });
+    min_duration = (std::min)(min_duration, total - timer_resolution);
+  }
+
+  // Number of repetitions required to reach the target resolution.
+  const size_t max_skip = p.precision_divisor;
+  // Number of repetitions given the estimated duration.
+  const size_t num_skip =
+      min_duration == 0 ? 0 : (max_skip + min_duration - 1) / min_duration;
+  if (p.verbose) {
+    ABSL_RAW_LOG(INFO, "res=%u max_skip=%zu min_dur=%u num_skip=%zu\n",
+                 timer_resolution, max_skip, min_duration, num_skip);
+  }
+  return num_skip;
+}
+
+// Replicates inputs until we can omit "num_skip" occurrences of an input.
+InputVec ReplicateInputs(const FuncInput* inputs, const size_t num_inputs,
+                         const size_t num_unique, const size_t num_skip,
+                         const Params& p) {
+  InputVec full;
+  if (num_unique == 1) {
+    full.assign(p.subset_ratio * num_skip, inputs[0]);
+    return full;
+  }
+
+  full.reserve(p.subset_ratio * num_skip * num_inputs);
+  for (size_t i = 0; i < p.subset_ratio * num_skip; ++i) {
+    full.insert(full.end(), inputs, inputs + num_inputs);
+  }
+  absl::random_internal::randen_engine<uint32_t> rng;
+  std::shuffle(full.begin(), full.end(), rng);
+  return full;
+}
+
+// Copies the "full" to "subset" in the same order, but with "num_skip"
+// randomly selected occurrences of "input_to_skip" removed.
+void FillSubset(const InputVec& full, const FuncInput input_to_skip,
+                const size_t num_skip, InputVec* subset) {
+  const size_t count = std::count(full.begin(), full.end(), input_to_skip);
+  // Generate num_skip random indices: which occurrence to skip.
+  std::vector<uint32_t> omit;
+  // Replacement for std::iota, not yet available in MSVC builds.
+  omit.reserve(count);
+  for (size_t i = 0; i < count; ++i) {
+    omit.push_back(i);
+  }
+  // omit[] is the same on every call, but that's OK because they identify the
+  // Nth instance of input_to_skip, so the position within full[] differs.
+  absl::random_internal::randen_engine<uint32_t> rng;
+  std::shuffle(omit.begin(), omit.end(), rng);
+  omit.resize(num_skip);
+  std::sort(omit.begin(), omit.end());
+
+  uint32_t occurrence = ~0u;  // 0 after preincrement
+  size_t idx_omit = 0;        // cursor within omit[]
+  size_t idx_subset = 0;      // cursor within *subset
+  for (const FuncInput next : full) {
+    if (next == input_to_skip) {
+      ++occurrence;
+      // Haven't removed enough already
+      if (idx_omit < num_skip) {
+        // This one is up for removal
+        if (occurrence == omit[idx_omit]) {
+          ++idx_omit;
+          continue;
+        }
+      }
+    }
+    if (idx_subset < subset->size()) {
+      (*subset)[idx_subset++] = next;
+    }
+  }
+  ABSL_RAW_CHECK(idx_subset == subset->size(), "idx_subset not at end");
+  ABSL_RAW_CHECK(idx_omit == omit.size(), "idx_omit not at end");
+  ABSL_RAW_CHECK(occurrence == count - 1, "occurrence not at end");
+}
+
+// Returns total ticks elapsed for all inputs.
+Ticks TotalDuration(const Func func, const void* arg, const InputVec* inputs,
+                    const Params& p, double* max_rel_mad) {
+  double rel_mad;
+  const Ticks duration =
+      SampleUntilStable(p.target_rel_mad, &rel_mad, p, [func, arg, inputs]() {
+        for (const FuncInput input : *inputs) {
+          PreventElision(func(arg, input));
+        }
+      });
+  *max_rel_mad = (std::max)(*max_rel_mad, rel_mad);
+  return duration;
+}
+
+// (Nearly) empty Func for measuring timer overhead/resolution.
+ABSL_RANDOM_INTERNAL_ATTRIBUTE_NEVER_INLINE FuncOutput
+EmptyFunc(const void* arg, const FuncInput input) {
+  return input;
+}
+
+// Returns overhead of accessing inputs[] and calling a function; this will
+// be deducted from future TotalDuration return values.
+Ticks Overhead(const void* arg, const InputVec* inputs, const Params& p) {
+  double rel_mad;
+  // Zero tolerance because repeatability is crucial and EmptyFunc is fast.
+  return SampleUntilStable(0.0, &rel_mad, p, [arg, inputs]() {
+    for (const FuncInput input : *inputs) {
+      PreventElision(EmptyFunc(arg, input));
+    }
+  });
+}
+
+}  // namespace
+
+void PinThreadToCPU(int cpu) {
+  // We might migrate to another CPU before pinning below, but at least cpu
+  // will be one of the CPUs on which this thread ran.
+#if defined(ABSL_OS_WIN)
+  if (cpu < 0) {
+    cpu = static_cast<int>(GetCurrentProcessorNumber());
+    ABSL_RAW_CHECK(cpu >= 0, "PinThreadToCPU detect failed");
+    if (cpu >= 64) {
+      // NOTE: On wine, at least, GetCurrentProcessorNumber() sometimes returns
+      // a value > 64, which is out of range. When this happens, log a message
+      // and don't set a cpu affinity.
+      ABSL_RAW_LOG(ERROR, "Invalid CPU number: %d", cpu);
+      return;
+    }
+  } else if (cpu >= 64) {
+    // User specified an explicit CPU affinity > the valid range.
+    ABSL_RAW_LOG(FATAL, "Invalid CPU number: %d", cpu);
+  }
+  const DWORD_PTR prev = SetThreadAffinityMask(GetCurrentThread(), 1ULL << cpu);
+  ABSL_RAW_CHECK(prev != 0, "SetAffinity failed");
+#elif defined(ABSL_OS_LINUX) && !defined(ABSL_OS_ANDROID)
+  if (cpu < 0) {
+    cpu = sched_getcpu();
+    ABSL_RAW_CHECK(cpu >= 0, "PinThreadToCPU detect failed");
+  }
+  const pid_t pid = 0;  // current thread
+  cpu_set_t set;
+  CPU_ZERO(&set);
+  CPU_SET(cpu, &set);
+  const int err = sched_setaffinity(pid, sizeof(set), &set);
+  ABSL_RAW_CHECK(err == 0, "SetAffinity failed");
+#endif
+}
+
+// Returns tick rate. Invariant means the tick counter frequency is independent
+// of CPU throttling or sleep. May be expensive, caller should cache the result.
+double InvariantTicksPerSecond() {
+#if defined(ABSL_ARCH_PPC)
+  return __ppc_get_timebase_freq();
+#elif defined(ABSL_ARCH_X86_64)
+  // We assume the TSC is invariant; it is on all recent Intel/AMD CPUs.
+  return platform::NominalClockRate();
+#else
+  // Fall back to clock_gettime nanoseconds.
+  return 1E9;
+#endif
+}
+
+size_t MeasureImpl(const Func func, const void* arg, const size_t num_skip,
+                   const InputVec& unique, const InputVec& full,
+                   const Params& p, Result* results) {
+  const float mul = 1.0f / static_cast<int>(num_skip);
+
+  InputVec subset(full.size() - num_skip);
+  const Ticks overhead = Overhead(arg, &full, p);
+  const Ticks overhead_skip = Overhead(arg, &subset, p);
+  if (overhead < overhead_skip) {
+    ABSL_RAW_LOG(WARNING, "Measurement failed: overhead %u < %u\n", overhead,
+                 overhead_skip);
+    return 0;
+  }
+
+  if (p.verbose) {
+    ABSL_RAW_LOG(INFO, "#inputs=%5zu,%5zu overhead=%5u,%5u\n", full.size(),
+                 subset.size(), overhead, overhead_skip);
+  }
+
+  double max_rel_mad = 0.0;
+  const Ticks total = TotalDuration(func, arg, &full, p, &max_rel_mad);
+
+  for (size_t i = 0; i < unique.size(); ++i) {
+    FillSubset(full, unique[i], num_skip, &subset);
+    const Ticks total_skip = TotalDuration(func, arg, &subset, p, &max_rel_mad);
+
+    if (total < total_skip) {
+      ABSL_RAW_LOG(WARNING, "Measurement failed: total %u < %u\n", total,
+                   total_skip);
+      return 0;
+    }
+
+    const Ticks duration = (total - overhead) - (total_skip - overhead_skip);
+    results[i].input = unique[i];
+    results[i].ticks = duration * mul;
+    results[i].variability = max_rel_mad;
+  }
+
+  return unique.size();
+}
+
+size_t Measure(const Func func, const void* arg, const FuncInput* inputs,
+               const size_t num_inputs, Result* results, const Params& p) {
+  ABSL_RAW_CHECK(num_inputs != 0, "No inputs");
+
+  const InputVec unique = UniqueInputs(inputs, num_inputs);
+  const size_t num_skip = NumSkip(func, arg, unique, p);  // never 0
+  if (num_skip == 0) return 0;  // NumSkip already printed error message
+
+  const InputVec full =
+      ReplicateInputs(inputs, num_inputs, unique.size(), num_skip, p);
+
+  // MeasureImpl may fail up to p.max_measure_retries times.
+  for (size_t i = 0; i < p.max_measure_retries; i++) {
+    auto result = MeasureImpl(func, arg, num_skip, unique, full, p, results);
+    if (result != 0) {
+      return result;
+    }
+  }
+  // All retries failed. (Unusual)
+  return 0;
+}
+
+}  // namespace random_internal_nanobenchmark
+ABSL_NAMESPACE_END
+}  // namespace absl