Export of internal Abseil changes.

--
7a6ff16a85beb730c172d5d25cf1b5e1be885c56 by Laramie Leavitt <lar@google.com>:

Internal change.

PiperOrigin-RevId: 254454546

--
ff8f9bafaefc26d451f576ea4a06d150aed63f6f by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254451562

--
deefc5b651b479ce36f0b4ef203e119c0c8936f2 by CJ Johnson <johnsoncj@google.com>:

Account for subtracting unsigned values from the size of InlinedVector

PiperOrigin-RevId: 254450625

--
3c677316a27bcadc17e41957c809ca472d5fef14 by Andy Soffer <asoffer@google.com>:

Add C++17's std::make_from_tuple to absl/utility/utility.h

PiperOrigin-RevId: 254411573

--
4ee3536a918830eeec402a28fc31a62c7c90b940 by CJ Johnson <johnsoncj@google.com>:

Adds benchmark for the rest of the InlinedVector public API

PiperOrigin-RevId: 254408378

--
e5a21a00700ee83498ff1efbf649169756463ee4 by CJ Johnson <johnsoncj@google.com>:

Updates the definition of InlinedVector::shrink_to_fit() to be exception safe and adds exception safety tests for it.

PiperOrigin-RevId: 254401387

--
2ea82e72b86d82d78b4e4712a63a55981b53c64b by Laramie Leavitt <lar@google.com>:

Use absl::InsecureBitGen in place of std::mt19937
in tests absl/random/...distribution_test.cc

PiperOrigin-RevId: 254289444

--
fa099e02c413a7ffda732415e8105cad26a90337 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254286334

--
ce34b7f36933b30cfa35b9c9a5697a792b5666e4 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254273059

--
6f9c473da7c2090c2e85a37c5f00622e8a912a89 by Jorg Brown <jorg@google.com>:

Change absl::container_internal::CompressedTuple to instantiate its
internal Storage class with the name of the type it's holding, rather
than the name of the Tuple.  This is not an externally-visible change,
other than less compiler memory is used and less debug information is
generated.

PiperOrigin-RevId: 254269285

--
8bd3c186bf2fc0c55d8a2dd6f28a5327502c9fba by Andy Soffer <asoffer@google.com>:

Adding short-hand IntervalClosed for IntervalClosedClosed and IntervalOpen for
IntervalOpenOpen.

PiperOrigin-RevId: 254252419

--
ea957f99b6a04fccd42aa05605605f3b44b1ecfd by Abseil Team <absl-team@google.com>:

Do not directly use __SIZEOF_INT128__.

In order to avoid linker errors when building with clang-cl (__fixunsdfti, __udivti3 and __fixunssfti are undefined), this CL uses ABSL_HAVE_INTRINSIC_INT128 which is not defined for clang-cl.

PiperOrigin-RevId: 254250739

--
89ab385cd26b34d64130bce856253aaba96d2345 by Andy Soffer <asoffer@google.com>:

Internal changes

PiperOrigin-RevId: 254242321

--
cffc793d93eca6d6bdf7de733847b6ab4a255ae9 by CJ Johnson <johnsoncj@google.com>:

Adds benchmark for InlinedVector::reserve(size_type)

PiperOrigin-RevId: 254199226

--
c90c7a9fa3c8f0c9d5114036979548b055ea2f2a by Gennadiy Rozental <rogeeff@google.com>:

Import of CCTZ from GitHub.

PiperOrigin-RevId: 254072387

--
c4c388beae016c9570ab54ffa1d52660e4a85b7b by Laramie Leavitt <lar@google.com>:

Internal cleanup.

PiperOrigin-RevId: 254062381

--
d3c992e221cc74e5372d0c8fa410170b6a43c062 by Tom Manshreck <shreck@google.com>:

Update distributions.h to Abseil standards

PiperOrigin-RevId: 254054946

--
d15ad0035c34ef11b14fadc5a4a2d3ec415f5518 by CJ Johnson <johnsoncj@google.com>:

Removes functions with only one caller from the implementation details of InlinedVector by manually inlining the definitions

PiperOrigin-RevId: 254005427

--
2f37e807efc3a8ef1f4b539bdd379917d4151520 by Andy Soffer <asoffer@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253999861

--
24ed1694b6430791d781ed533a8f8ccf6cac5856 by CJ Johnson <johnsoncj@google.com>:

Updates the definition of InlinedVector::assign(...)/InlinedVector::operator=(...) to new, exception-safe implementations with exception safety tests to boot

PiperOrigin-RevId: 253993691

--
5613d95f5a7e34a535cfaeadce801441e990843e by CJ Johnson <johnsoncj@google.com>:

Adds benchmarks for InlinedVector::shrink_to_fit()

PiperOrigin-RevId: 253989647

--
2a96ddfdac40bbb8cb6a7f1aeab90917067c6e63 by Abseil Team <absl-team@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253927497

--
bf1aff8fc9ffa921ad74643e9525ecf25b0d8dc1 by Andy Soffer <asoffer@google.com>:

Initial release of Abseil Random

PiperOrigin-RevId: 253920512

--
bfc03f4a3dcda3cf3a4b84bdb84cda24e3394f41 by Laramie Leavitt <lar@google.com>:

Internal change.

PiperOrigin-RevId: 253886486

--
05036cfcc078ca7c5f581a00dfb0daed568cbb69 by Eric Fiselier <ericwf@google.com>:

Don't include `winsock2.h` because it drags in `windows.h` and friends,
and they define awful macros like OPAQUE, ERROR, and more. This has the
potential to break abseil users.

Instead we only forward declare `timeval` and require Windows users
include `winsock2.h` themselves. This is both inconsistent and poor QoI, but so
including 'windows.h' is bad too.

PiperOrigin-RevId: 253852615
GitOrigin-RevId: 7a6ff16a85beb730c172d5d25cf1b5e1be885c56
Change-Id: Icd6aff87da26f29ec8915da856f051129987cef6

1 files changed, 230 insertions, 0 deletions

diff --git a/absl/random/internal/chi_square.cc b/absl/random/internal/chi_square.cc
new file mode 100644
index 000000000000..c0acc9477883
--- /dev/null
+++ b/absl/random/internal/chi_square.cc
@@ -0,0 +1,230 @@
+// Copyright 2017 The Abseil Authors.
+//
+// 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/chi_square.h"
+
+#include <cmath>
+
+#include "absl/random/internal/distribution_test_util.h"
+
+namespace absl {
+namespace random_internal {
+namespace {
+
+#if defined(__EMSCRIPTEN__)
+// Workaround __EMSCRIPTEN__ error: llvm_fma_f64 not found.
+inline double fma(double x, double y, double z) {
+  return (x * y) + z;
+}
+#endif
+
+// Use Horner's method to evaluate a polynomial.
+template <typename T, unsigned N>
+inline T EvaluatePolynomial(T x, const T (&poly)[N]) {
+#if !defined(__EMSCRIPTEN__)
+  using std::fma;
+#endif
+  T p = poly[N - 1];
+  for (unsigned i = 2; i <= N; i++) {
+    p = fma(p, x, poly[N - i]);
+  }
+  return p;
+}
+
+static constexpr int kLargeDOF = 150;
+
+// Returns the probability of a normal z-value.
+//
+// Adapted from the POZ function in:
+//     Ibbetson D, Algorithm 209
+//     Collected Algorithms of the CACM 1963 p. 616
+//
+double POZ(double z) {
+  static constexpr double kP1[] = {
+      0.797884560593,  -0.531923007300, 0.319152932694,
+      -0.151968751364, 0.059054035642,  -0.019198292004,
+      0.005198775019,  -0.001075204047, 0.000124818987,
+  };
+  static constexpr double kP2[] = {
+      0.999936657524,  0.000535310849,  -0.002141268741, 0.005353579108,
+      -0.009279453341, 0.011630447319,  -0.010557625006, 0.006549791214,
+      -0.002034254874, -0.000794620820, 0.001390604284,  -0.000676904986,
+      -0.000019538132, 0.000152529290,  -0.000045255659,
+  };
+
+  const double kZMax = 6.0;  // Maximum meaningful z-value.
+  if (z == 0.0) {
+    return 0.5;
+  }
+  double x;
+  double y = 0.5 * std::fabs(z);
+  if (y >= (kZMax * 0.5)) {
+    x = 1.0;
+  } else if (y < 1.0) {
+    double w = y * y;
+    x = EvaluatePolynomial(w, kP1) * y * 2.0;
+  } else {
+    y -= 2.0;
+    x = EvaluatePolynomial(y, kP2);
+  }
+  return z > 0.0 ? ((x + 1.0) * 0.5) : ((1.0 - x) * 0.5);
+}
+
+// Approximates the survival function of the normal distribution.
+//
+// Algorithm 26.2.18, from:
+// [Abramowitz and Stegun, Handbook of Mathematical Functions,p.932]
+// http://people.math.sfu.ca/~cbm/aands/abramowitz_and_stegun.pdf
+//
+double normal_survival(double z) {
+  // Maybe replace with the alternate formulation.
+  // 0.5 * erfc((x - mean)/(sqrt(2) * sigma))
+  static constexpr double kR[] = {
+      1.0, 0.196854, 0.115194, 0.000344, 0.019527,
+  };
+  double r = EvaluatePolynomial(z, kR);
+  r *= r;
+  return 0.5 / (r * r);
+}
+
+}  // namespace
+
+// Calculates the critical chi-square value given degrees-of-freedom and a
+// p-value, usually using bisection. Also known by the name CRITCHI.
+double ChiSquareValue(int dof, double p) {
+  static constexpr double kChiEpsilon =
+      0.000001;  // Accuracy of the approximation.
+  static constexpr double kChiMax =
+      99999.0;  // Maximum chi-squared value.
+
+  const double p_value = 1.0 - p;
+  if (dof < 1 || p_value > 1.0) {
+    return 0.0;
+  }
+
+  if (dof > kLargeDOF) {
+    // For large degrees of freedom, use the normal approximation by
+    //     Wilson, E. B. and Hilferty, M. M. (1931)
+    //                     chi^2 - mean
+    //                Z = --------------
+    //                        stddev
+    const double z = InverseNormalSurvival(p_value);
+    const double mean = 1 - 2.0 / (9 * dof);
+    const double variance = 2.0 / (9 * dof);
+    // Cannot use this method if the variance is 0.
+    if (variance != 0) {
+      return std::pow(z * std::sqrt(variance) + mean, 3.0) * dof;
+    }
+  }
+
+  if (p_value <= 0.0) return kChiMax;
+
+  // Otherwise search for the p value by bisection
+  double min_chisq = 0.0;
+  double max_chisq = kChiMax;
+  double current = dof / std::sqrt(p_value);
+  while ((max_chisq - min_chisq) > kChiEpsilon) {
+    if (ChiSquarePValue(current, dof) < p_value) {
+      max_chisq = current;
+    } else {
+      min_chisq = current;
+    }
+    current = (max_chisq + min_chisq) * 0.5;
+  }
+  return current;
+}
+
+// Calculates the p-value (probability) of a given chi-square value
+// and degrees of freedom.
+//
+// Adapted from the POCHISQ function from:
+//     Hill, I. D. and Pike, M. C.  Algorithm 299
+//     Collected Algorithms of the CACM 1963 p. 243
+//
+double ChiSquarePValue(double chi_square, int dof) {
+  static constexpr double kLogSqrtPi =
+      0.5723649429247000870717135;  // Log[Sqrt[Pi]]
+  static constexpr double kInverseSqrtPi =
+      0.5641895835477562869480795;  // 1/(Sqrt[Pi])
+
+  // For large degrees of freedom, use the normal approximation by
+  //     Wilson, E. B. and Hilferty, M. M. (1931)
+  // Via Wikipedia:
+  //   By the Central Limit Theorem, because the chi-square distribution is the
+  //   sum of k independent random variables with finite mean and variance, it
+  //   converges to a normal distribution for large k.
+  if (dof > kLargeDOF) {
+    // Re-scale everything.
+    const double chi_square_scaled = std::pow(chi_square / dof, 1.0 / 3);
+    const double mean = 1 - 2.0 / (9 * dof);
+    const double variance = 2.0 / (9 * dof);
+    // If variance is 0, this method cannot be used.
+    if (variance != 0) {
+      const double z = (chi_square_scaled - mean) / std::sqrt(variance);
+      if (z > 0) {
+        return normal_survival(z);
+      } else if (z < 0) {
+        return 1.0 - normal_survival(-z);
+      } else {
+        return 0.5;
+      }
+    }
+  }
+
+  // The chi square function is >= 0 for any degrees of freedom.
+  // In other words, probability that the chi square function >= 0 is 1.
+  if (chi_square <= 0.0) return 1.0;
+
+  // If the degrees of freedom is zero, the chi square function is always 0 by
+  // definition. In other words, the probability that the chi square function
+  // is > 0 is zero (chi square values <= 0 have been filtered above).
+  if (dof < 1) return 0;
+
+  auto capped_exp = [](double x) { return x < -20 ? 0.0 : std::exp(x); };
+  static constexpr double kBigX = 20;
+
+  double a = 0.5 * chi_square;
+  const bool even = !(dof & 1);  // True if dof is an even number.
+  const double y = capped_exp(-a);
+  double s = even ? y : (2.0 * POZ(-std::sqrt(chi_square)));
+
+  if (dof <= 2) {
+    return s;
+  }
+
+  chi_square = 0.5 * (dof - 1.0);
+  double z = (even ? 1.0 : 0.5);
+  if (a > kBigX) {
+    double e = (even ? 0.0 : kLogSqrtPi);
+    double c = std::log(a);
+    while (z <= chi_square) {
+      e = std::log(z) + e;
+      s += capped_exp(c * z - a - e);
+      z += 1.0;
+    }
+    return s;
+  }
+
+  double e = (even ? 1.0 : (kInverseSqrtPi / std::sqrt(a)));
+  double c = 0.0;
+  while (z <= chi_square) {
+    e = e * (a / z);
+    c = c + e;
+    z += 1.0;
+  }
+  return c * y + s;
+}
+
+}  // namespace random_internal
+}  // namespace absl