[wpimath] Move math functionality into new wpimath library (#2629)

The wpimath library is a new library designed to separate the reusable math functionality
from the common utility library (wpiutil) and the hardware-dependent library (wpilibc/j).

Package names / include file names were NOT changed to minimize breakage.  In a future year
it would be good to revamp these for a more uniform user experience and to reduce the risk
of accidental naming conflicts.

While theoretically all of this functionality could be placed into wpiutil, several pieces
of this library (e.g. DARE) are very time-consuming to compile, so it's nice to avoid this
expense for users who only want cscore or ntcore.  It also allows for easy future separation
of build tasks vs number of workers on memory-constrained machines.

This moves the following functionality from wpiutil into wpimath:
- Eigen
- ejml
- Drake
- DARE
- wpiutil.math package (Matrix etc)
- units

And the following functionality from wpilibc/j into wpimath:
- Geometry
- Kinematics
- Spline
- Trajectory
- LinearFilter
- MedianFilter
- Feed-forward controllers

wpimath/src/main/native/include/frc/trajectory/TrapezoidProfile.h

@@ -0,0 +1,159 @@
+/*----------------------------------------------------------------------------*/
+/* Copyright (c) 2019-2020 FIRST. All Rights Reserved.                        */
+/* Open Source Software - may be modified and shared by FRC teams. The code   */
+/* must be accompanied by the FIRST BSD license file in the root directory of */
+/* the project.                                                               */
+/*----------------------------------------------------------------------------*/
+
+#pragma once
+
+#include "math/MathShared.h"
+#include "units/time.h"
+
+namespace frc {
+
+/**
+ * A trapezoid-shaped velocity profile.
+ *
+ * While this class can be used for a profiled movement from start to finish,
+ * the intended usage is to filter a reference's dynamics based on trapezoidal
+ * velocity constraints. To compute the reference obeying this constraint, do
+ * the following.
+ *
+ * Initialization:
+ * @code{.cpp}
+ * TrapezoidalMotionProfile::Constraints constraints{kMaxV, kMaxA};
+ * double previousProfiledReference = initialReference;
+ * @endcode
+ *
+ * Run on update:
+ * @code{.cpp}
+ * TrapezoidalMotionProfile profile{constraints, unprofiledReference,
+ *                                  previousProfiledReference};
+ * previousProfiledReference = profile.Calculate(timeSincePreviousUpdate);
+ * @endcode
+ *
+ * where `unprofiledReference` is free to change between calls. Note that when
+ * the unprofiled reference is within the constraints, `Calculate()` returns the
+ * unprofiled reference unchanged.
+ *
+ * Otherwise, a timer can be started to provide monotonic values for
+ * `Calculate()` and to determine when the profile has completed via
+ * `IsFinished()`.
+ */
+template <class Distance>
+class TrapezoidProfile {
+ public:
+  using Distance_t = units::unit_t<Distance>;
+  using Velocity =
+      units::compound_unit<Distance, units::inverse<units::seconds>>;
+  using Velocity_t = units::unit_t<Velocity>;
+  using Acceleration =
+      units::compound_unit<Velocity, units::inverse<units::seconds>>;
+  using Acceleration_t = units::unit_t<Acceleration>;
+
+  class Constraints {
+   public:
+    Constraints() {
+      wpi::math::MathSharedStore::ReportUsage(
+          wpi::math::MathUsageId::kTrajectory_TrapezoidProfile, 1);
+    }
+    Constraints(Velocity_t maxVelocity_, Acceleration_t maxAcceleration_)
+        : maxVelocity{maxVelocity_}, maxAcceleration{maxAcceleration_} {
+      wpi::math::MathSharedStore::ReportUsage(
+          wpi::math::MathUsageId::kTrajectory_TrapezoidProfile, 1);
+    }
+    Velocity_t maxVelocity{0};
+    Acceleration_t maxAcceleration{0};
+  };
+
+  class State {
+   public:
+    Distance_t position{0};
+    Velocity_t velocity{0};
+    bool operator==(const State& rhs) const {
+      return position == rhs.position && velocity == rhs.velocity;
+    }
+    bool operator!=(const State& rhs) const { return !(*this == rhs); }
+  };
+
+  /**
+   * Construct a TrapezoidProfile.
+   *
+   * @param constraints The constraints on the profile, like maximum velocity.
+   * @param goal        The desired state when the profile is complete.
+   * @param initial     The initial state (usually the current state).
+   */
+  TrapezoidProfile(Constraints constraints, State goal,
+                   State initial = State{Distance_t(0), Velocity_t(0)});
+
+  TrapezoidProfile(const TrapezoidProfile&) = default;
+  TrapezoidProfile& operator=(const TrapezoidProfile&) = default;
+  TrapezoidProfile(TrapezoidProfile&&) = default;
+  TrapezoidProfile& operator=(TrapezoidProfile&&) = default;
+
+  /**
+   * Calculate the correct position and velocity for the profile at a time t
+   * where the beginning of the profile was at time t = 0.
+   *
+   * @param t The time since the beginning of the profile.
+   */
+  State Calculate(units::second_t t) const;
+
+  /**
+   * Returns the time left until a target distance in the profile is reached.
+   *
+   * @param target The target distance.
+   */
+  units::second_t TimeLeftUntil(Distance_t target) const;
+
+  /**
+   * Returns the total time the profile takes to reach the goal.
+   */
+  units::second_t TotalTime() const { return m_endDeccel; }
+
+  /**
+   * Returns true if the profile has reached the goal.
+   *
+   * The profile has reached the goal if the time since the profile started
+   * has exceeded the profile's total time.
+   *
+   * @param t The time since the beginning of the profile.
+   */
+  bool IsFinished(units::second_t t) const { return t >= TotalTime(); }
+
+ private:
+  /**
+   * Returns true if the profile inverted.
+   *
+   * The profile is inverted if goal position is less than the initial position.
+   *
+   * @param initial The initial state (usually the current state).
+   * @param goal    The desired state when the profile is complete.
+   */
+  static bool ShouldFlipAcceleration(const State& initial, const State& goal) {
+    return initial.position > goal.position;
+  }
+
+  // Flip the sign of the velocity and position if the profile is inverted
+  State Direct(const State& in) const {
+    State result = in;
+    result.position *= m_direction;
+    result.velocity *= m_direction;
+    return result;
+  }
+
+  // The direction of the profile, either 1 for forwards or -1 for inverted
+  int m_direction;
+
+  Constraints m_constraints;
+  State m_initial;
+  State m_goal;
+
+  units::second_t m_endAccel;
+  units::second_t m_endFullSpeed;
+  units::second_t m_endDeccel;
+};
+}  // namespace frc
+
+#include "TrapezoidProfile.inc"