package org.j4me.util;
/**
* Implements the methods which are in the standard J2SE's <code>Math</code> class,
* but are not in in J2ME's.
* <p>
* The following methods are still missing from the implementation:
* <ul>
* <li><code>public static double exp (double a)</code>
* <li><code>public static double log (double a)</code>
* <li><code>public static double pow (double a, double b)</code>
* <li><code>public static double random ()</code>
* <li><code>public static double rint()</code>
* </ul>
*
* @see java.lang.Math
*/
public final class MathFunc
{
/**
* Constant for PI divided by 2.
*/
private static final double PIover2 = Math.PI / 2;
/**
* Constant for PI divided by 4.
*/
private static final double PIover4 = Math.PI / 4;
/**
* Constant for PI divided by 6.
*/
private static final double PIover6 = Math.PI / 6;
/**
* Constant for PI divided by 12.
*/
private static final double PIover12 = Math.PI / 12;
/**
* Constant used in the <code>atan</code> calculation.
*/
private static final double ATAN_CONSTANT = 1.732050807569;
/**
* Returns the arc cosine of an angle, in the range of 0.0 through <code>Math.PI</code>.
* Special case:
* <ul>
* <li>If the argument is <code>NaN</code> or its absolute value is greater than 1,
* then the result is <code>NaN</code>.
* </ul>
*
* @param a - the value whose arc cosine is to be returned.
* @return the arc cosine of the argument.
*/
public static double acos (double a)
{
// Special case.
if ( Double.isNaN(a) || Math.abs(a) > 1.0 )
{
return Double.NaN;
}
// Calculate the arc cosine.
double aSquared = a * a;
double arcCosine = atan2( Math.sqrt(1 - aSquared), a );
return arcCosine;
}
/**
* Returns the arc sine of an angle, in the range of <code>-Math.PI/2</code> through
* <code>Math.PI/2</code>. Special cases:
* <ul>
* <li>If the argument is <code>NaN</code> or its absolute value is greater than 1,
* then the result is <code>NaN</code>.
* <li>If the argument is zero, then the result is a zero with the same sign
* as the argument.
* </ul>
*
* @param a - the value whose arc sine is to be returned.
* @return the arc sine of the argument.
*/
public static double asin (double a)
{
// Special cases.
if ( Double.isNaN(a) || Math.abs(a) > 1.0 )
{
return Double.NaN;
}
if ( a == 0.0 )
{
return a;
}
// Calculate the arc sine.
double aSquared = a * a;
double arcSine = atan2( a, Math.sqrt(1 - aSquared) );
return arcSine;
}
/**
* Returns the arc tangent of an angle, in the range of <code>-Math.PI/2</code>
* through <code>Math.PI/2</code>. Special cases:
* <ul>
* <li>If the argument is <code>NaN</code>, then the result is <code>NaN</code>.
* <li>If the argument is zero, then the result is a zero with the same
* sign as the argument.
* </ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a - the value whose arc tangent is to be returned.
* @return the arc tangent of the argument.
*/
public static double atan (double a)
{
// Special cases.
if ( Double.isNaN(a) )
{
return Double.NaN;
}
if ( a == 0.0 )
{
return a;
}
// Compute the arc tangent.
boolean negative = false;
boolean greaterThanOne = false;
int i = 0;
if ( a < 0.0 )
{
a = -a;
negative = true;
}
if ( a > 1.0 )
{
a = 1.0 / a;
greaterThanOne = true;
}
double t;
for ( ; a > PIover12; a *= t )
{
i++;
t = a + ATAN_CONSTANT;
t = 1.0 / t;
a *= ATAN_CONSTANT;
a--;
}
double aSquared = a * a;
double arcTangent = aSquared + 1.4087812;
arcTangent = 0.55913709 / arcTangent;
arcTangent += 0.60310578999999997;
arcTangent -= 0.051604539999999997 * aSquared;
arcTangent *= a;
for ( ; i > 0; i-- )
{
arcTangent += PIover6;
}
if ( greaterThanOne )
{
arcTangent = PIover2 - arcTangent;
}
if ( negative )
{
arcTangent = -arcTangent;
}
return arcTangent;
}
/**
* Converts rectangular coordinates (x, y) to polar (r, <i>theta</i>). This method
* computes the phase <i>theta</i> by computing an arc tangent of y/x in the range
* of <i>-pi</i> to <i>pi</i>. Special cases:
* <ul>
* <li>If either argument is <code>NaN</code>, then the result is <code>NaN</code>.
* <li>If the first argument is positive zero and the second argument is
* positive, or the first argument is positive and finite and the second
* argument is positive infinity, then the result is positive zero.
* <li>If the first argument is negative zero and the second argument is
* positive, or the first argument is negative and finite and the second
* argument is positive infinity, then the result is negative zero.
* <li>If the first argument is positive zero and the second argument is
* negative, or the first argument is positive and finite and the second
* argument is negative infinity, then the result is the <code>double</code> value
* closest to <i>pi</i>.
* <li>If the first argument is negative zero and the second argument is
* negative, or the first argument is negative and finite and the second
* argument is negative infinity, then the result is the <code>double</code> value
* closest to <i>-pi</i>.
* <li>If the first argument is positive and the second argument is positive
* zero or negative zero, or the first argument is positive infinity and
* the second argument is finite, then the result is the <code>double</code> value
* closest to <i>pi</i>/2.
* <li>If the first argument is negative and the second argument is positive
* zero or negative zero, or the first argument is negative infinity and
* the second argument is finite, then the result is the <code>double</code> value
* closest to <i>-pi</i>/2.
* <li>If both arguments are positive infinity, then the result is the double
* value closest to <i>pi</i>/4.
* <li>If the first argument is positive infinity and the second argument is
* negative infinity, then the result is the double value closest to 3*<i>pi</i>/4.
* <li>If the first argument is negative infinity and the second argument is
* positive infinity, then the result is the double value closest to -<i>pi</i>/4.
* <li>If both arguments are negative infinity, then the result is the double
* value closest to -3*<i>pi</i>/4.
* </ul>
* <p>
* A result must be within 2 ulps of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param y - the ordinate coordinate
* @param x - the abscissa coordinate
* @return the <i>theta</i> component of the point (r, <i>theta</i>) in polar
* coordinates that corresponds to the point (x, y) in Cartesian coordinates.
*/
public static double atan2 (double y, double x)
{
// Special cases.
if ( Double.isNaN(y) || Double.isNaN(x) )
{
return Double.NaN;
}
else if ( Double.isInfinite(y) )
{
if ( y > 0.0 ) // Positive infinity
{
if ( Double.isInfinite(x) )
{
if ( x > 0.0 )
{
return PIover4;
}
else
{
return 3.0 * PIover4;
}
}
else if ( x != 0.0 )
{
return PIover2;
}
}
else // Negative infinity
{
if ( Double.isInfinite(x) )
{
if ( x > 0.0 )
{
return -PIover4;
}
else
{
return -3.0 * PIover4;
}
}
else if ( x != 0.0 )
{
return -PIover2;
}
}
}
else if ( y == 0.0 )
{
if ( x > 0.0 )
{
return y;
}
else if ( x < 0.0 )
{
return Math.PI;
}
}
else if ( Double.isInfinite(x) )
{
if ( x > 0.0 ) // Positive infinity
{
if ( y > 0.0 )
{
return 0.0;
}
else if ( y < 0.0 )
{
return -0.0;
}
}
else // Negative infinity
{
if ( y > 0.0 )
{
return Math.PI;
}
else if ( y < 0.0 )
{
return -Math.PI;
}
}
}
else if ( x == 0.0 )
{
if ( y > 0.0 )
{
return PIover2;
}
else if ( y < 0.0 )
{
return -PIover2;
}
}
// Implementation a simple version ported from a PASCAL implementation:
// http://everything2.com/index.pl?node_id=1008481
double arcTangent;
// Use arctan() avoiding division by zero.
if ( Math.abs(x) > Math.abs(y) )
{
arcTangent = atan(y / x);
}
else
{
arcTangent = atan(x / y); // -PI/4 <= a <= PI/4
if ( arcTangent < 0 )
{
arcTangent = -PIover2 - arcTangent; // a is negative, so we're adding
}
else
{
arcTangent = PIover2 - arcTangent;
}
}
// Adjust result to be from [-PI, PI]
if ( x < 0 )
{
if ( y < 0 )
{
arcTangent = arcTangent - Math.PI;
}
else
{
arcTangent = arcTangent + Math.PI;
}
}
return arcTangent;
}
/**
* Returns the closest <code>int</code> to the argument. The
* result is rounded to an integer by adding 1/2, taking the
* floor of the result, and casting the result to type <code>int</code>.
* In other words, the result is equal to the value of the expression:
* <p>
* <pre>(int)Math.floor(a + 0.5f)</pre>
* <p>
* Special cases:
* <ul>
* <li>If the argument is NaN, the result is 0.
* <li>If the argument is negative infinity or any value less than or
* equal to the value of <code>Integer.MIN_VALUE</code>, the result is
* equal to the value of <code>Integer.MIN_VALUE</code>.
* <li>If the argument is positive infinity or any value greater than or
* equal to the value of <code>Integer.MAX_VALUE</code>, the result is
* equal to the value of <code>Integer.MAX_VALUE</code>.
* </ul>
*
* @param a - a floating-point value to be rounded to an integer.
* @return the value of the argument rounded to the nearest <code>int</code> value.
*/
public static int round (float a)
{
return (int)Math.floor( a + 0.5f );
}
/**
* Returns the closest <code>long</code> to the argument. The result
* is rounded to an integer by adding 1/2, taking the floor of the
* result, and casting the result to type <code>long</code>. In other
* words, the result is equal to the value of the expression:
* <p>
* <pre>(long)Math.floor(a + 0.5d)</pre>
* <p>
* Special cases:
* <ul>
* <li>If the argument is NaN, the result is 0.
* <li>If the argument is negative infinity or any value less than or
* equal to the value of <code>Long.MIN_VALUE</code>, the result is
* equal to the value of <code>Long.MIN_VALUE</code>.
* <li>If the argument is positive infinity or any value greater than or
* equal to the value of <code>Long.MAX_VALUE</code>, the result is
* equal to the value of <code>Long.MAX_VALUE</code>.
* </ul>
*
* @param a - a floating-point value to be rounded to a <code>long</code>.
* @return the value of the argument rounded to the nearest <code>long</code> value.
*/
public static long round (double a)
{
return (long)Math.floor( a + 0.5 );
}
}