Bug 1452 - Decouple math functionality to 'com.jogamp.math' to be toolkit agnostic (PMVMatrix, Matrix4f, Vec4f, ..)

Math functionality (PMVMatrix, Matrix4f, Vec4f, ..)
- shall be used toolkit agnostic, e.g. independent from OpenGL
- shall be reused within our upcoming Vulkan implementation
- may also move outside of JOGL, i.e. GlueGen or within its own package to be reused for other purposed.

The 'com.jogamp.opengl.util.PMVMatrix' currently also used to feed in GLUniformData
via the toolkit agnostic SyncAction and SyncBuffer
shall also be split to a toolkit agnostic variant.

An OpenGL PMVMatrix specialization implementing GLMatrixFunc can still exist,
being derived from the toolkit agnostic base implementation.

+++

Initial commit .. compile clean, passing most unit tests.

1 files changed, 274 insertions, 0 deletions

diff --git a/src/jogl/classes/com/jogamp/math/DoubleUtil.java b/src/jogl/classes/com/jogamp/math/DoubleUtil.java
new file mode 100644
index 000000000..e9ccceb10
--- /dev/null
+++ b/src/jogl/classes/com/jogamp/math/DoubleUtil.java
@@ -0,0 +1,274 @@
+/**
+ * Copyright 2010-2023 JogAmp Community. All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without modification, are
+ * permitted provided that the following conditions are met:
+ *
+ *    1. Redistributions of source code must retain the above copyright notice, this list of
+ *       conditions and the following disclaimer.
+ *
+ *    2. Redistributions in binary form must reproduce the above copyright notice, this list
+ *       of conditions and the following disclaimer in the documentation and/or other materials
+ *       provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY JogAmp Community ``AS IS'' AND ANY EXPRESS OR IMPLIED
+ * WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL JogAmp Community OR
+ * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+ * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
+ * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
+ * ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ * NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
+ * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * The views and conclusions contained in the software and documentation are those of the
+ * authors and should not be interpreted as representing official policies, either expressed
+ * or implied, of JogAmp Community.
+ */
+package com.jogamp.math;
+
+/**
+ * Basic Double math utility functions.
+ */
+public final class DoubleUtil {
+  //
+  // Scalar Ops
+  //
+
+  @SuppressWarnings("unused")
+  private static void calculateMachineEpsilonDouble() {
+      final long t0;
+      double machEps = 1.0;
+      int i=0;
+      do {
+          machEps /= 2.0;
+          i++;
+      } while (1.0 + (machEps / 2.0) != 1.0);
+      machEpsilon = machEps;
+  }
+  private static volatile boolean machEpsilonAvail = false;
+  private static double machEpsilon = 0f;
+
+  /**
+   * Return computed machine Epsilon value.
+   * <p>
+   * The machine Epsilon value is computed once.
+   * </p>
+   * @see #EPSILON
+   */
+  public static double getMachineEpsilon() {
+      if( !machEpsilonAvail ) {
+          synchronized(DoubleUtil.class) {
+              if( !machEpsilonAvail ) {
+                  machEpsilonAvail = true;
+                  calculateMachineEpsilonDouble();
+              }
+          }
+      }
+      return machEpsilon;
+  }
+
+  public static final double E = 2.7182818284590452354;
+
+  /** The value PI, i.e. 180 degrees in radians. */
+  public static final double PI = 3.14159265358979323846;
+
+  /** The value 2PI, i.e. 360 degrees in radians. */
+  public static final double TWO_PI = 2.0 * PI;
+
+  /** The value PI/2, i.e. 90 degrees in radians. */
+  public static final double HALF_PI = PI / 2.0;
+
+  /** The value PI/4, i.e. 45 degrees in radians. */
+  public static final double QUARTER_PI = PI / 4.0;
+
+  /** The value PI^2. */
+  public final static double SQUARED_PI = PI * PI;
+
+  /** Converts arc-degree to radians */
+  public static double adegToRad(final double arc_degree) {
+      return arc_degree * PI / 180.0;
+  }
+
+  /** Converts radians to arc-degree */
+  public static double radToADeg(final double rad) {
+      return rad * 180.0 / PI;
+  }
+
+  /**
+   * Epsilon for floating point {@value}, as once computed via {@link #getMachineEpsilon()} on an AMD-64 CPU.
+   * <p>
+   * Definition of machine epsilon guarantees that:
+   * <pre>
+   *        1.0 + EPSILON != 1.0
+   * </pre>
+   * In other words: <i>machEps</i> is the maximum relative error of the chosen rounding procedure.
+   * </p>
+   * <p>
+   * A number can be considered zero if it is in the range (or in the set):
+   * <pre>
+   *    <b>MaybeZeroSet</b> e ]-<i>machEps</i> .. <i>machEps</i>[  <i>(exclusive)</i>
+   * </pre>
+   * While comparing floating point values, <i>machEps</i> allows to clip the relative error:
+   * <pre>
+   *    boolean isZero    = afloat < EPSILON;
+   *    boolean isNotZero = afloat >= EPSILON;
+   *
+   *    boolean isEqual    = abs(bfloat - afloat) < EPSILON;
+   *    boolean isNotEqual = abs(bfloat - afloat) >= EPSILON;
+   * </pre>
+   * </p>
+   * @see #isEqual(float, float, float)
+   * @see #isZero(float, float)
+   */
+  public static final double EPSILON = 2.220446049250313E-16;
+
+  /**
+   * Inversion Epsilon, used with equals method to determine if two inverted matrices are close enough to be considered equal.
+   * <p>
+   * Using {@value}, which is ~100 times {@link DoubleUtil#EPSILON}.
+   * </p>
+   */
+  public static final double INV_DEVIANCE = 1.0E-8f; // EPSILON == 1.1920929E-7f; double ALLOWED_DEVIANCE: 1.0E-8f
+
+  /**
+   * Return true if both values are equal w/o regarding an epsilon.
+   * <p>
+   * Implementation considers following corner cases:
+   * <ul>
+   *    <li>NaN == NaN</li>
+   *    <li>+Inf == +Inf</li>
+   *    <li>-Inf == -Inf</li>
+   * </ul>
+   * </p>
+   * @see #isEqual(float, float, float)
+   */
+  public static boolean isEqualRaw(final double a, final double b) {
+      // Values are equal (Inf, Nan .. )
+      return Double.doubleToLongBits(a) == Double.doubleToLongBits(b);
+  }
+
+  /**
+   * Return true if both values are equal, i.e. their absolute delta < <code>epsilon</code>.
+   * <p>
+   * Implementation considers following corner cases:
+   * <ul>
+   *    <li>NaN == NaN</li>
+   *    <li>+Inf == +Inf</li>
+   *    <li>-Inf == -Inf</li>
+   * </ul>
+   * </p>
+   * @see #EPSILON
+   */
+  public static boolean isEqual(final double a, final double b, final double epsilon) {
+      if ( Math.abs(a - b) < epsilon ) {
+          return true;
+      } else {
+          // Values are equal (Inf, Nan .. )
+          return Double.doubleToLongBits(a) == Double.doubleToLongBits(b);
+      }
+  }
+
+  /**
+   * Return true if both values are equal, i.e. their absolute delta < {@link #EPSILON}.
+   * <p>
+   * Implementation considers following corner cases:
+   * <ul>
+   *    <li>NaN == NaN</li>
+   *    <li>+Inf == +Inf</li>
+   *    <li>-Inf == -Inf</li>
+   * </ul>
+   * </p>
+   * @see #EPSILON
+   */
+  public static boolean isEqual(final double a, final double b) {
+      if ( Math.abs(a - b) < EPSILON ) {
+          return true;
+      } else {
+          // Values are equal (Inf, Nan .. )
+          return Double.doubleToLongBits(a) == Double.doubleToLongBits(b);
+      }
+  }
+
+  /**
+   * Return true if both values are equal, i.e. their absolute delta < {@link #EPSILON}.
+   * <p>
+   * Implementation does not consider corner cases like {@link #isEqual(float, float, float)}.
+   * </p>
+   * @see #EPSILON
+   */
+  public static boolean isEqual2(final double a, final double b) {
+      return Math.abs(a - b) < EPSILON;
+  }
+
+  /**
+   * Return true if both values are equal w/o regarding an epsilon.
+   * <p>
+   * Implementation considers following corner cases:
+   * <ul>
+   *    <li>NaN == NaN</li>
+   *    <li>+Inf == +Inf</li>
+   *    <li>-Inf == -Inf</li>
+   *    <li>NaN > 0</li>
+   *    <li>+Inf > -Inf</li>
+   * </ul>
+   * </p>
+   * @see #compare(float, float, float)
+   */
+  public static int compare(final double a, final double b) {
+      if (a < b) {
+          return -1; // Neither is NaN, a is smaller
+      }
+      if (a > b) {
+          return 1;  // Neither is NaN, a is larger
+      }
+      final long aBits = Double.doubleToLongBits(a);
+      final long bBits = Double.doubleToLongBits(b);
+      if( aBits == bBits ) {
+          return 0;  // Values are equal (Inf, Nan .. )
+      } else if( aBits < bBits ) {
+          return -1; // (-0.0,  0.0) or (!NaN,  NaN)
+      } else {
+          return 1;  // ( 0.0, -0.0) or ( NaN, !NaN)
+      }
+  }
+
+  /**
+   * Return true if both values are equal, i.e. their absolute delta < <code>epsilon</code>.
+   * <p>
+   * Implementation considers following corner cases:
+   * <ul>
+   *    <li>NaN == NaN</li>
+   *    <li>+Inf == +Inf</li>
+   *    <li>-Inf == -Inf</li>
+   *    <li>NaN > 0</li>
+   *    <li>+Inf > -Inf</li>
+   * </ul>
+   * </p>
+   * @see #EPSILON
+   */
+  public static int compare(final double a, final double b, final double epsilon) {
+      if ( Math.abs(a - b) < epsilon ) {
+          return 0;
+      } else {
+          return compare(a, b);
+      }
+  }
+
+  /**
+   * Return true if value is zero, i.e. it's absolute value < <code>epsilon</code>.
+   * @see #EPSILON
+   */
+  public static boolean isZero(final double a, final double epsilon) {
+      return Math.abs(a) < epsilon;
+  }
+
+  /**
+   * Return true if value is zero, i.e. it's absolute value < {@link #EPSILON}.
+   * @see #EPSILON
+   */
+  public static boolean isZero(final double a) {
+      return Math.abs(a) < EPSILON;
+  }
+
+}
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