Posted by Stephen Booth on August 01, 2005 at 02:09 PM PDT #

Most of the time I really enjoy reading Gosling's blogs, but this one is different. There are natural mathematical reasons why sin/cos are defined with periods of 2*PI. It wasn't that a bunch of people sat around and said, "How can we define these functions so that we can confuse everyone." If you redefine them differently, then much of the rest of mathematics dealing with these functions changes, including the simple fact that the derivative of the sine function is cosine function.

If you want a different period, it is certainly reasonable to add new functions to the MATH API, but just don't use them to replace the standard trig functions that have stood the test of time and that everyone has learned in school for many, many years (before you were born).

Posted by John Moore on August 02, 2005 at 03:59 AM PDT #

Posted by Ranjit Mathew on August 04, 2005 at 10:38 PM PDT #

I agree. 8087 designers were not very smart implementing things using radians. They should have used, say, binadians (define: 2**X binadians = 2*PI radians). Then shifting to [-PI/4,PI/4] would be a piece of cake and things should be faster and more accurate.

Anyway the problem is making computer maths look like real maths. Accuracy is important, but correctness is much more important in computer maths. After all you want to be sure that that huge set of Java (Fortran/C/C++) files are really solving your equations.

That's what we need in Fortress. And, yes, Fortress should use binadians internally, but should also let us use radians in our source code.

Posted by Antonio on August 11, 2005 at 01:26 AM PDT #

package fasttrig;

import static fasttrig.Time.*;
import static java.lang.Math.*;

public class Main {
    private static final int nLoops = 10000000;
    private static final int sinScale = 100;
    private static final int[] sinTable = new int[ sinScale ];
    static {
        for ( int i = 0; i < sinScale; i++ ) {
            sinTable[ i ] = (int)(sin( i * PI / sinScale ) * sinScale);
        }
    }
    public static final Timable accurate = new Timable() {
        public double time() {
            double sum = 0;
            for ( int i = 0; i < nLoops; i++ ) {
                sum += sin( i * PI / nLoops );
            }
            return sum;
        }
        public String toString() {
            return "Math.sin";
        }
    };
    public static final Timable fast = new Timable() {
        public double time() {
            double sum = 0;
            for ( int i = 0; i < nLoops; i++ ) {
                final int index = i * sinScale / nLoops;
                final int sinApprox = sinTable[ index ];
                sum += (double)sinApprox / sinScale;
            }
            return sum;
        }
        public String toString() {
            return "Table";
        }
    };
    public static void main( final String[] notUsed ) {
        time( accurate );
        time( fast );
    }
}

Test Math.sin, run 0, time taken 2504 ms, result 6366197.723675204
Test Math.sin, run 1, time taken 2493 ms, result 6366197.723675204
Test Table, run 0, time taken 301 ms, result 6314000.000286256
Test Table, run 1, time taken 290 ms, result 6314000.000286256

Posted by Howard Lovatt on August 15, 2005 at 07:59 PM PDT #

Posted by 1 on August 20, 2005 at 11:07 AM PDT #

Posted by 84.218.62.105 on August 29, 2005 at 12:55 PM PDT #

Posted by mary on September 07, 2005 at 02:14 PM PDT #

Posted by Antonio on September 17, 2005 at 09:54 AM PDT #

Posted by thiyagu on September 20, 2005 at 08:46 AM PDT #

Posted by George Colpitts on October 03, 2006 at 01:25 PM PDT #

http://www.0120128888.com/
http://www.wonder-up.net/
http://www.akasaka-hisyo.com/
http://www.ran-s.jp/
http://www.tokyo-living.com/jp.html
http://www.firstep.jp/
http://www.tb-k.com/
http://www.kw-ai.com/

Posted by sasasas on July 22, 2009 at 10:41 PM PDT #