Author: sebb
Date: Tue Sep 6 23:33:54 2011
New Revision: 1165929
URL: http://svn.apache.org/viewvc?rev=1165929&view=rev
Log:
More docn of algorithms and magic numbers
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/FastMath.java
Modified:
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/FastMath.java
URL:
http://svn.apache.org/viewvc/commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/FastMath.java?rev=1165929&r1=1165928&r2=1165929&view=diff
==============================================================================
---
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/FastMath.java
(original)
+++
commons/proper/math/trunk/src/main/java/org/apache/commons/math/util/FastMath.java
Tue Sep 6 23:33:54 2011
@@ -5161,7 +5161,7 @@ public class FastMath {
private static final int FACT_LEN = 20;
- /** Factorial table, for Taylor series expansions. */
+ /** Factorial table, for Taylor series expansions. 0!, 1!, 2!, ... 19! */
private static final double FACT[] = new double[]
{
+1.0d,
@@ -6267,7 +6267,8 @@ public class FastMath {
{-0.16624879837036133, -2.6033824355191673E-8}
};
- private static final int SINE_TABLE_LEN = 14; // MAGIC NUMBER
+ /** Sine, Cosine, Tangent tables are for 0, 1/8, 2/8, ... 13/8 = PI/2
approx. */
+ private static final int SINE_TABLE_LEN = 14;
/** Sine table (high bits). */
private static final double SINE_TABLE_A[] =
@@ -8069,9 +8070,11 @@ public class FastMath {
}
/**
- * For x between 0 and pi/4 compute sine.
+ * For x between 0 and pi/4 compute sine using Taylor expansion:
+ * sin(x) = x - x^3/3! + x^5/5! - x^7/7! ...
* @param x number from which sine is requested
* @param result placeholder where to put the result in extended precision
+ * (may be null)
* @return sin(x)
*/
private static double slowSin(final double x, final double result[]) {
@@ -8082,18 +8085,18 @@ public class FastMath {
split(x, xs);
ys[0] = ys[1] = 0.0;
- for (int i = 19; i >= 0; i--) {
+ for (int i = FACT_LEN-1; i >= 0; i--) {
splitMult(xs, ys, as);
ys[0] = as[0]; ys[1] = as[1];
- if ( (i & 1) == 0) {
+ if ( (i & 1) == 0) { // Ignore even numbers
continue;
}
split(FACT[i], as);
splitReciprocal(as, facts);
- if ( (i & 2) != 0 ) {
+ if ( (i & 2) != 0 ) { // alternate terms are negative
facts[0] = -facts[0];
facts[1] = -facts[1];
}
@@ -8111,9 +8114,11 @@ public class FastMath {
}
/**
- * For x between 0 and pi/4 compute cosine
+ * For x between 0 and pi/4 compute cosine using Talor series
+ * cos(x) = 1 - x^2/2! + x^4/4! ...
* @param x number from which cosine is requested
* @param result placeholder where to put the result in extended precision
+ * (may be null)
* @return cos(x)
*/
private static double slowCos(final double x, final double result[]) {
@@ -8125,18 +8130,18 @@ public class FastMath {
split(x, xs);
ys[0] = ys[1] = 0.0;
- for (int i = 19; i >= 0; i--) {
+ for (int i = FACT_LEN-1; i >= 0; i--) {
splitMult(xs, ys, as);
ys[0] = as[0]; ys[1] = as[1];
- if ( (i & 1) != 0) {
+ if ( (i & 1) != 0) { // skip odd entries
continue;
}
split(FACT[i], as);
splitReciprocal(as, facts);
- if ( (i & 2) != 0 ) {
+ if ( (i & 2) != 0 ) { // alternate terms are negative
facts[0] = -facts[0];
facts[1] = -facts[1];
}
@@ -8172,7 +8177,7 @@ public class FastMath {
}
/* Use angle addition formula to complete table to 13/8, just beyond
pi/2 */
- for (int i = 7; i < 14; i++) {
+ for (int i = 7; i < SINE_TABLE_LEN; i++) {
double xs[] = new double[2];
double ys[] = new double[2];
double as[] = new double[2];
@@ -8228,7 +8233,7 @@ public class FastMath {
}
/* Compute tangent = sine/cosine */
- for (int i = 0; i < 14; i++) {
+ for (int i = 0; i < SINE_TABLE_LEN; i++) {
double xs[] = new double[2];
double ys[] = new double[2];
double as[] = new double[2];
