Sine function

[Owkmann]

Can someone give me a rough idea how a value is obtained for a trigonometric
function like Math.Sin? What is the algorithm? I'm finding that putting a
large number in this function ( > 8000 ) really slows things down. Why is
that?

Thanks,

Owkmann

 

[John Liu]

Sin(360) = Sin(0).

do this.

Sin( largeNumber % 360 );

 

[Bruce Wood]

First of all, Math.Sin takes its argument in radians, not degrees, so
360 is the wrong denominator.

Second, the argument is a double, for which there is no modulo
operator, even if you could get a reasonably accurate value for 2p.
Not even Math.DivRem provides an overload for doubles.

 

[John Liu]

Trust me to reply without thinking the logic through.

The angle is measured in radians, so it shouldn't be 360, but 2 pi.

Disclaimer:
Untested code.

jliu
johnliu.net

 

[John Liu]

And Bruce's right. % or DivRem won't work.

I found double Math.IEEERemainder(double x, doubly y) though.

So the idea should be:

Math.Sin( Math.IEEERemainder( largeNumber, 2* Math.PI ));

Disclaimer:
Untested code.

jliu
johnliu.net

 

[Gabriel Magaña]

Jeez, instead of criticizing you could have been a little more helpful.

Math.Sin(Math.IEEERemainder(LargeNum, 6.28318))

Should do the trick. (Hint: provide a more accurate number of the number of
radians in a full circle to get a better answer).

 

[Gabriel Magaña]

Math.Sin(Math.IEEERemainder(LargeNum, 6.28318))

Actually to get a better number for this, you could use

Math.Sin(Math.IEEERemainder(LargeNum, (double)360 / (double)2 / Math.PI))

But that assumes the compiler is smart enough to not evaluate the equation
every time (or better yet, evaluate it at compile time)... It might be a
safe assumption to make these days, but just to make sure you might want to
turn that into a constant.

 

[John Liu]

Tried this in snippet compiler, because I was worried about the error.
DateTime start = DateTime.Now;
WL("Math.Sin(10000) = {0}", Math.Sin(10000));
TimeSpan ts = DateTime.Now - start;
WL("Time Taken: {0}", ts);

DateTime start2 = DateTime.Now;
WL("Math.Sin(Math.IEEERemainder(10000, 2*Math.PI)) = {0}",
Math.Sin(Math.IEEERemainder(10000, 2*Math.PI)));
TimeSpan ts2 = DateTime.Now - start2;
WL("Time Taken: {0}", ts2);
RL();

Out:
Math.Sin(10000) = -0.305614388888252
Time Taken: 00:00:00
Math.Sin(Math.IEEERemainder(10000, 2*Math.PI)) = -0.305614388888028
Time Taken: 00:00:00

Math.Sin(1000000) = -0.349993502171292
Time Taken: 00:00:00
Math.Sin(Math.IEEERemainder(1000000, 2*Math.PI)) = -0.349993502093929
Time Taken: 00:00:00

There seems to be a increasing error as the number gets bigger. The
error may be too high to be acceptable in your situation.

I'm not seeing this slowness problem though. May be I need to run it
1000 times.

jliu
johnliu.net

 

[Gabriel Magaña]

Yup, a classical case of magnified errors due to scale vs precision... It
would be much smarter to get the number down to 0 >= x >= 360 before calling
the sine function...

 

[Owkmann]

I'm not seeing this slowness problem though. May be I need to run it

1000 times.

jliu
johnliu.net

Yah. 16384 times (2^14).

public static double[] SineWave(double frequency, double phase, double
magnitude, int N_samples, double SampleRate)
{
const double PI = Math.PI;
double[] Xreal = new double[N_samples]; // N_samples = 16384; Gets really
slow
double Freq = frequency;
double Phase = phase;
double Mag = magnitude;
double Sample_Rate = SampleRate;
double Operand = 2 * PI * Freq * 1 / Sample_Rate + Phase;

for (int i = 0; i < N_samples; i++)
{
// This equation returns an array of doubles that simulate
// an A/D sampling a sine wave at a given sample rate

Xreal = Mag * Math.Sin(Operand * i);
}
return Xreal;
}

That's why I was wondering how Math.Sin calculates its number.

There's got to be an easier way!

Owkmann

 

[Bruce Wood]

Jeez, instead of criticizing you could have been a little more helpful.

Math.Sin(Math.IEEERemainder(LargeNum, 6.28318))

Should do the trick.

I wasn't more helpful because I didn't know about IEEERemainder().