1 // Default texts for the math documentator of the Faust compiler.
2 // Copyright (C) 2009 GRAME, Centre National de Creation Musicale
3 // Karim Barkati
5 // Remark:
6 // double quotes are useful to visualize spaces and tabulations
7 // at the beginning or at the end of strings.
13 :name "name"
14 :author "author"
17 :version "version"
20 // Notice section.
22 :faustapply "The value of a Faust program is the result of applying the signal transformer denoted by the expression to which the \texttt{process} identifier is bound to input signals, running at the $f_S$ sampling frequency."
24 :faustpresentation "Faust (\emph{Functional Audio Stream}) is a functional programming language designed for synchronous real-time signal processing and synthesis applications. A Faust program is a set of bindings of identifiers to expressions that denote signal transformers. A signal $s$ in $S$ is a function mapping\footnote{Faust assumes that $\forall \, s \in S, \forall \, t \in \mathbb{Z}, s(t) = 0 \mathrm{\ when\ } t < 0$.} times $t \in \mathbb{Z}$ to values $s(t) \in \mathbb{R}$, while a signal transformer is a function from $S^n$ to $S^m$, where $n,m\in \mathbb{N}$. See the Faust manual for additional information (\textsf{http://faust.grame.fr})."
26 :causality "Every mathematical formula derived from a Faust expression is assumed, in this document, to having been normalized (in an implementation-depen\-dent manner) by the Faust compiler."
28 :blockdiagrams "A block diagram is a graphical representation of the Faust binding of an identifier I to an expression E; each graph is put in a box labeled by I. Subexpressions of E are recursively displayed as long as the whole picture fits in one page."
30 :faustdocdir "The \texttt{\faustdocdir/} directory may also include the following subdirectories:"
31 "\begin{itemize}"
32 " \item \texttt{cpp/} for Faust compiled code; "
33 " \item \texttt{pdf/} which contains this document; "
34 " \item \texttt{src/} for all Faust sources used (even libraries); "
35 " \item \texttt{svg/} for block diagrams, encoded using the Scalable Vector Graphics format (\textsf{http://www.w3.org/Graphics/SVG/});"
36 " \item \texttt{tex/} for the \LaTeX\ source of this document."
37 "\end{itemize}"
39 :foreignfun ""ff" prefix in some function name stands for C++ "foreign function"."
41 :intcast
42 "$\forall \, x \in \mathbb{R}$, "
43 " \begin{displaymath}"
44 " \mathrm{int}(x) ="
45 " \left\{\begin{array}{cl}"
46 " \lfloor x \rfloor & \mbox{if \,} x > 0 \\"
47 " \lceil x \rceil & \mbox{if \,} x < 0 \\"
48 " 0 & \mbox{if \,} x = 0 \\"
49 " \end{array}\right.."
50 " \end{displaymath}"
52 :operators "This document uses the following integer operations:"
53 :optabtitle "\emph{operation} & \emph{name} & \emph{semantics} \\"
54 :intplus "$i \oplus j$ & integer addition & $\mathrm{normalize}(i+j), \mathrm{~in~} \mathbb{Z}$ \\"
55 :intminus "$i \ominus j$ & integer substraction & $\mathrm{normalize}(i-j), \mathrm{~in~} \mathbb{Z}$ \\"
56 :intmult "$i \odot j$ & integer multiplication & $\mathrm{normalize}(i \cdot j), \mathrm{~in~} \mathbb{Z}$ \\"
57 :intdiv "$i \oslash j$ & integer division & $\mathrm{normalize}(\mathrm{int}(i/j)), \mathrm{~in~} \mathbb{Q}$ \\"
59 :integerops "Integer operations in Faust are inspired by the semantics of operations on the n-bit two's complement representation of integer numbers; they are internal composition laws on the subset $[\,-2^{n-1}, 2^{n-1}\!-\!1\,]$ of $\mathbb{Z}$, with $n = 32$. For any integer binary operation $\times$ on $\mathbb{Z}$, the $\otimes$ operation is defined as: $i \otimes j = \mathrm{normalize}(i \times j)$, with "
60 "$$\mathrm{normalize}(i) = i - N\cdot\mathrm{sign}(i) \cdot \left\lfloor \frac{|i|+N/2+(\mathrm{sign}(i)\!-\!1)/2}{N} \right\rfloor ,$$"
61 " where $N = 2^n$ and $\mathrm{sign}(i) = 0 \mathrm{\ if\ } i=0 \mathrm{\ and\ } i / |i| \mathrm{\ otherwise}.$"
62 "Unary integer operations are defined likewise."
65 // Auto-documentation section.
67 :thisdoc "This document provides a mathematical description of the Faust program text stored in the \texttt{\faustfilename} file. See the notice in Section\,\ref{notice} (page\,\pageref{notice}) for details."
69 :autoeqntitle "\section{Mathematical definition of \texttt{process}}"
70 "\label{equation}"
71 :autoeqntext "The \emph{\faustprogname} program evaluates the signal transformer denoted by \texttt{process}, which is mathematically defined as follows:"
73 :autodgmtitle "\section{Block diagram of \texttt{process}}"
74 "\label{diagram}"
75 :autodgmtext "The block diagram of \texttt{process} is shown on Figure\,\ref{figure1} (page\,\pageref{figure1})."
77 :autontctitle "\section{Notice}"
78 "\label{notice}"
79 :autontctext "This document was generated using Faust version \faustversion\ on \faustdocdate."
81 :autolsttitle1 "\section{Faust code listing}"
82 "\label{listing}"
83 :autolsttext1 "This section provides the listing of the Faust code used to generate this document."
85 :autolsttitle2 "\section{Faust code listings}"
86 "\label{listing}"
87 :autolsttext2 "This section provides the listings of the Faust code used to generate this document, including dependencies."
90 // Titles for each type of formulas.
92 :inputsigtitle1 "Input signal"
93 :inputsigtitle2 "Input signals"
94 :outputsigtitle1 "Output signal"
95 :outputsigtitle2 "Output signals"
96 :constsigtitle1 "Constant"
97 :constsigtitle2 "Constants"
98 :uisigtitle1 "User-interface input signal"
99 :uisigtitle2 "User-interface input signals"
100 :intermedsigtitle1 "Intermediate signal"
101 :intermedsigtitle2 "Intermediate signals"
103 :lateqcomment "% Set of Faust formulas (corresponding to an <equation> tag)."
104 :emptyformulafield "none"
105 :defaultvalue "default value"
106 :suchthat "such that"
107 :and "and"
108 :for "for"
109 :rootlevel "(at root level)"
111 :dgmcaption "Block diagram of"