## GEN03

GEN03 — Generates a stored function table by evaluating a polynomial.

## Description

This subroutine generates a stored function table by evaluating a polynomial in x over a fixed interval and with specified coefficients.

## Syntax

`f  #  time  size  3  xval1  xval2  c0  c1  c2  ...  cn`

## Initialization

size -- number of points in the table. Must be a power of 2 or a power-of-2 plus 1.

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.

## Examples

Here is a simple example of the GEN03 routine. It uses the files gen03.csd. It fills 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. Here is its diagram:

Diagram of the waveform generated by GEN03.

Example 553. A simple example of the GEN03 routine.

```<CsoundSynthesizer>
<CsOptions>
; Select audio/midi flags here according to platform
; Audio out   Audio in
; For Non-realtime ouput leave only the line below:
; -o gen03.wav -W ;;; for file output any platform
</CsOptions>
<CsInstruments>

; Initialize the global variables.
sr = 44100
kr = 4410
ksmps = 10
nchnls = 1

; Instrument #1.
instr 1
; Create an index over the length of our entire note.
kcps init 1/p3
kndx phasor kcps

; Read Table #1 with our index.
ifn = 1
ixmode = 1
kamp table kndx, ifn, ixmode

; Create a sine wave, use the Table #1 values to control
; the amplitude.
a1 oscil kamp*30000, 440, 2
out a1
endin

</CsInstruments>
<CsScore>

; Table #1: a polynomial function (using GEN03).
f 1 0 1025 3 -1 1 5 4 3 2 2 1
; Table #2, a sine wave.
f 2 0 16384 10 1

; Play Instrument #1 for 2 seconds.
i 1 0 2
e

</CsScore>
</CsoundSynthesizer>
```