How do I generate a fixed-waveform table in C?

Question

What is the most efficient way to generate a signed float array of arbitrary length containing the amplitude (represented from 1 to -1) of a sine wave in C?

Answer 1

If you want no runtime overhead, write yourself a little program that prints out all your values as a C array declaration/initialization, and then #include that file into your program.

Answer 2

As Carl Smotricz pointed out in his answer, you can easily write a simple C program to build a hard-coded array for you.

The following code would do the trick:

int main(int argc, char * argv[])
{
    const int tableSize = 10;
    const char * fileName = "sin_table.txt";

    int x;
    FILE * file;

    file = fopen(fileName, "w");
    if (file == NULL) { printf("unable to open file\n"); return -1; }

    fprintf(file, "float sin_table[%d] =\n{\n ", tableSize);
    for (x = 0; x < tableSize; x++)
    {
        fprintf(file, "\t%f,\n", sinf(x*2*pi/tableSize));
    }
    fprintf(file, "};\n");

    fclose(file);
    return 0;
}

And the output would look like this:

float sin_table[10] =
{
    0.000000,
    0.587785,
    0.951057,
    0.951056,
    0.587785,
    -0.000000,
    -0.587785,
    -0.951057,
    -0.951056,
    -0.587785,
};

Answer 3

If you want something very fast use a table (as already suggested).

Another approach is to simulate a little sine-oscillator and use it to generate your data-array.

Here is an example how to do this:

int main (int argc, char **args)
{
  int i;

  float data[1024];
  float angle = 2.0f * 3.14 / 1024;

  // start of the sine-wave:
  float sinval = 0;
  float cosval = 1;

  // rotation per iteration
  float delta_sin = sinf(angle);
  float delta_cos = cosf(angle);

  for (i=0; i<1024; i++)
  {
    // store current value:
    data[i] = sinval;

    // update the oscillator:
    float s = sinval * delta_cos - cosval * delta_sin;
    float c = sinval * delta_sin + cosval * delta_cos;
    sinval = s;
    cosval = c;
  }
}

The trick behind this is, that we start with a fixed point in 2D-space, stored in 9sinval, cosval). Furthermore I precompute the parameters for a single rotation in (delta_cos, delta_sin).

All I do in the loop is to rotate the point 1024 times with the fixed rotation. This creates a sin/cos pair per iteration. (note: it's the same as a complex multiplication).

This method becomes unstable sooner or later and is not as exact as calling sin/cos in the loop.

So it's not a good idea to create huge tables with it, but if you can live with a slight error and smallish tables up to ten thousand elements it's quite usable. To get around that issue you could change the type to double, do proper rounding or re-normalize the result every n iterations.

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Edit: Just tested the code with double and 1e9 iterations. Works for me. I have a slight drift in the phase, but the results are still more exact than using single precision sinf/cosf.