\paragraph{Function Tables} \seclabel{function-table} Each function table must have a unique integer ID (\type{Table}), creation time (usually 0), size (which must be a power of 2), and a {\tt Normalize} flag. Most tables in CSound are normalized, i.e.\ rescaled to a maximum absolute value of 1. The normalization process can be skipped by setting the {\tt Normalize} flag to {\tt False}. Such a table may be desirable to generate a control or modifying signal, but is not very useful for audio signal generation. Tables are simply arrays of floating point values. The values stored in the table are calculated by one of CSound's predefined \keyword{generating routines}, represented by the type {\tt Generator.T}: \begin{haskelllisting}

    > module Haskore.Interface.CSound.Generator where
    >
    > import Haskore.Interface.CSound (Time)
    > import Haskore.General.Utility
    >    (flattenTuples2, flattenTuples3, flattenTuples4)
    >
    > data T = Routine Number [Parameter]
    >        | SoundFile SFName SkipTime ChanNum
    >      deriving Show
    >
    > type SFName    = String
    > type SkipTime  = Time
    > type ChanNum   = Float
    > type Number    = Int
    > type Parameter = Float

\end{haskelllisting} {\tt Routine n args} refers to CSound's generating routine $n$ (an integer), called with floating point arguments {\tt args}. There is only one generating routine (called \refgen{01}) in CSound that takes an argument type other than floating point, and thus we represent this using the special constructor {\tt SoundFile}, whose functionality will be described shortly. Knowing which of CSound's generating routines to use and with what arguments can be a daunting task. The newest version of CSound (version 4.01) provides 23 different generating routines, and each one of them assigns special meanings to its arguments. To avoid having to reference routines using integer ids, the following functions are defined for the most often-used generating routines. A brief discussion of each routine is also included. For a full description of these and other routines, refer to the CSound manual or consult the following webpage: \url{http://www.leeds.ac.uk/music/Man/Csound/Function/GENS.html}. The user familiar with CSound is free to write helper functions like the ones below to capture other generating routines. \genparagraph{01} Transfers data from a soundfile into a function table. Recall that the size of the function table in CSound must be a power of two. If the soundfile is larger than the table size, reading stops when the table is full; if it is smaller, then the table is padded with zeros. One exception is allowed: if the file is of type AIFF and the table size is set to zero, the size of the function table is allocated dynamically as the number of points in the soundfile. The table is then unusable by normal oscillators, but can be used by a special {\tt SampOsc} constructor (discussed in \secref{orchestra-file}). The first argument passed to the \refgen{01} subroutine is a string containing the name of the source file. The second argument is skip time, which is the number of seconds into the file that the reading begins. Finally there is an argument for the channel number, with 0 meaning read all channels. \refgen{01} is represented in Haskore as {\tt SoundFile SFName SkipTime ChanNum}, as discussed earlier. To make the use of {\tt SoundFile} consistent with the use of other functions to be described shortly, we define a simple equivalent: \begin{haskelllisting}

    > soundFile :: SFName -> SkipTime -> ChanNum -> T
    > soundFile = SoundFile

\end{haskelllisting} \genparagraph{02} Transfers data from its argument fields directly into the function table. We represent its functionality as follows: \begin{haskelllisting}

    > tableValues :: [Parameter] -> T
    > tableValues gas = Routine 2 gas

\end{haskelllisting} \genparagraph{03} Fills the table by evaluating a polynomial over a specified interval and with given coefficients. For example, calling \refgen{03} with an interval of $(-1,1)$ and coefficients 5, 4, 3, 2, 0, 1 will generate values of the function $5+4x+3x^2+2x^3+x^5$ over the interval $-1$ to $1$. The number of values generated is equal to the size of the table. Let's express this by the following function: \begin{haskelllisting}

    > polynomial :: Interval -> Coefficients -> T
    > polynomial (x1,x2) cfs = Routine 3 (x1:x2:cfs)
    >
    > type Interval     = (Float, Float)
    > type Coefficients = [Float]

\end{haskelllisting} \genparagraph{05} Constructs a table from segments of exponential curves. The first argument is the starting point. The meaning of the subsequent arguments alternates between the length of a segment in samples, and the endpoint of the segment. The endpoint of one segment is the starting point of the next. The sum of all the segment lengths normally equals the size of the table: if it is less the table is padded with zeros, if it is more, only the first \type{TableSize} locations will be stored in the table. \begin{haskelllisting}

    > exponential1 :: StartPt -> [(SegLength, EndPt)] -> T
    > exponential1 sp xs = Routine 5 (sp : flattenTuples2 xs)
    >
    > type StartPt   = Float
    > type SegLength = Float
    > type EndPt     = Float

\end{haskelllisting} \genparagraph{25} Similar to \refgen{05} in that it produces segments of exponential curves, but instead of representing the lengths of segments and their endpoints, its arguments represent $(x,y)$ coordinates in the table, and the subroutine produces curves between successive locations. The $x$-coordinates must be in increasing order. \begin{haskelllisting}

    > exponential2 :: [Point] -> T
    > exponential2 pts = Routine 25 (flattenTuples2 pts)
    >
    > type Point = (Float,Float)

\end{haskelllisting} \genparagraph{06} Generates a table from segments of cubic polynomial functions, spanning three points at a time. We define a function {\tt cubic} with two arguments: a starting position and a list of segment length (in number of samples) and segment endpoint pairs. The endpoint of one segment is the starting point of the next. The meaning of the segment endpoint alternates between a local minimum/maximum and point of inflexion. Whether a point is a maximum or a minimum is determined by its relation to the next point of inflexion. Also note that for two successive minima or maxima, the inflexion points will be jagged, whereas for alternating maxima and minima, they will be smooth. The slope of the two segments is independent at the point of inflection and will likely vary. The starting point is a local minimum or maximum (if the following point is greater than the starting point, then the starting point is a minimum, otherwise it is a maximum). The first pair of numbers will in essence indicate the position of the first inflexion point in $(x,y)$ coordinates. The folowing pair will determine the next local minimum/maximum, followed by the second point of inflexion, etc. \begin{haskelllisting}

    > cubic ::  StartPt -> [(SegLength, EndPt)] -> T
    > cubic sp pts = Routine 6 (sp : flattenTuples2 pts)

\end{haskelllisting} \genparagraph{07} Similar to \refgen{05}, except that it generates straight lines instead of exponential curve segments. All other issues discussed about \refgen{05} also apply to \refgen{07}. We represent it as: \begin{haskelllisting}

    > lineSeg1 :: StartPt -> [(SegLength, EndPt)] -> T
    > lineSeg1 sp pts = Routine 7 (sp : flattenTuples2 pts)

\end{haskelllisting} \genparagraph{27} As with \refgen{05} and \refgen{25}, produces straight line segments between points whose locations are given as $(x,y)$ coordinates, rather than a list of segment length, endpoint pairs. \begin{haskelllisting}

    > lineSeg2 :: [Point] -> T
    > lineSeg2 pts = Routine 27 (flattenTuples2 pts)

\end{haskelllisting} \genparagraph{08} Produces a smooth piecewise cubic spline curve through the specified points. Neighboring segments have the same slope at the common points, and it is that of a parabola through that point and its two neighbors. The slope is zero at the ends. \begin{haskelllisting}

    > cubicSpline :: StartPt -> [(SegLength, EndPt)] -> T
    > cubicSpline sp pts = Routine 8 (sp : flattenTuples2 pts)

\end{haskelllisting} \genparagraph{10} Produces a composite sinusoid. It takes a list of relative strengths of harmonic partials 1, 2, 3, etc. Partials not required should be given strength of zero. \begin{haskelllisting}

    > compSine1 :: [PStrength] -> T
    > compSine1 pss = Routine 10 pss
    >
    > type PStrength = Float

\end{haskelllisting} \genparagraph{09} Also produces a composite sinusoid, but requires three arguments to specify each contributing partial. The arguments specify the partial number, which doesn't have to be an integer (i.e.\ inharmonic partials are allowed), the relative partial strength, and the initial phase offset of each partial, expressed in degrees. \begin{haskelllisting}

    > compSine2 :: [(PNum, PStrength, PhaseOffset)] -> T
    > compSine2 args = Routine 9 (flattenTuples3 args)
    >
    > type PNum = Float
    > type PhaseOffset = Float

\end{haskelllisting} \genparagraph{19} Provides all of the functionality of \refgen{09}, but in addition a DC offset must be specified for each partial. The DC offset is a vertical displacement, so that a value of 2 will lift a 2-strength partial from range $[-2,2]$ to range $[0,4]$ before further scaling. \begin{haskelllisting}

    > compSine3 :: [(PNum, PStrength, PhaseOffset, DCOffset)] -> T
    > compSine3 args = Routine 19 (flattenTuples4 args)
    >
    > type DCOffset = Float

\end{haskelllisting} \genparagraph{11} Produces an additive set of harmonic cosine partials, similar to \refgen{10}. We will represent it by a function that takes three arguments: the number of harmonics present, the lowest harmonic present, and a multiplier in an exponential series of harmonics amplitudes (if the $x$'th harmonic has strength coefficient of $A$, then the $(x+n)$'th harmonic will have a strength of $A*(r^n)$, where $r$ is the multiplier). \begin{haskelllisting}

    > cosineHarms :: NHarms -> LowestHarm -> Mult -> T
    > cosineHarms n l m = Routine 11 [fromIntegral n, fromIntegral l, m]
    >
    > type NHarms = Int
    > type LowestHarm = Int
    > type Mult = Float

\end{haskelllisting} \genparagraph{21} Produces tables having selected random distributions. \begin{haskelllisting}

    > randomTable :: RandDist -> T
    > randomTable rd = Routine 21 [fromIntegral (fromEnum rd + 1)]
    >
    > data RandDist =
    >        Uniform
    >      | Linear
    >      | Triangular
    >      | Expon
    >      | BiExpon
    >      | Gaussian
    >      | Cauchy
    >      | PosCauchy
    >    deriving (Eq, Ord, Enum, Show)

\end{haskelllisting} \begin{haskelllisting}

    > toStatementWords :: T -> [String]
    > toStatementWords (Routine gn gas)     = show gn : map show gas
    > toStatementWords (SoundFile nm st cn) = ["1", nm, show st, "0", show cn]

\end{haskelllisting}