f # time size 3 xval1 xval2 c0 c1 c2 . . . cn
xval1, xval2 - left and right values of the x interval over which the polynomial is defined (xval1 < xval2). These will produce the 1st stored value and the (power-of-2 plus l)th stored value respectively in the generated function table.
c0, c1, c2, ... cn - coefficients of the nth-order polynomial
c0 + c1x + c2x2 + . . . + cnxn
Coefficients may be positive or negative real numbers; a zero denotes a missing term in the polynomial. The coefficient list begins in p7, providing a current upper limit of 144 terms.
Note:
The defined segment [fn(xval1),fn(xval2)] is evenly distributed. Thus a 512-point table over the interval [-1,1] will have its origin at location 257 (at the start of the 2nd half). Provided the extended guard point is requested, both fn(-1) and fn(1) will exist in the table.
GEN03 is useful in conjunction with table or tablei for audio waveshaping (sound modification by non-linear distortion). Coefficients to produce a particular formant from a sinusoidal lookup index of known amplitude can be determined at preprocessing time using algorithms such as Chebyshev formulae. See also GEN13.
Example: f 1 0 1025 3 -1 1 5 4 3 2 2 1
This calls GEN03 to fill a table with a 4th order polynomial function over the x-interval -1 to 1. The origin will be at the offset position 512. The function is post-normalized.