interpretor/preprocessor/faust-0.9.47mr3/architecture/mathdoctexts-en.txt

   1 // Default texts for the math documentator of the Faust compiler.
   2 // Copyright (C) 2009 GRAME, Centre National de Creation Musicale
   3 // Karim Barkati
   4
   5 // Remark:
   6 // double quotes are useful to visualize spaces and tabulations
   7 // at the beginning or at the end of strings.
   8
   9
  10
  11 // Metadatas section.
  12
  13 :name           "name"
  14 :author         "author"
  15 :copyright      "copyright"
  16 :license        "license"
  17 :version        "version"
  18
  19
  20 // Notice section.
  21
  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."
  23
  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})."
  25
  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."
  27
  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."
  29
  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}"
  38
  39 :foreignfun             ""ff" prefix in some function name stands for C++ "foreign function"."
  40
  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}"
  51
  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 & $\mathrm{normalize}(\mathrm{int}(i/j)), \mathrm{~in~} \mathbb{Q}$ \\"
  58
  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."
  63
  64
  65 // Auto-documentation section.
  66
  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."
  68
  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:"
  72
  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})."
  76
  77 :autontctitle   "\section{Notice}"
  78 "\label{notice}"
  79 :autontctext    "This document was generated using Faust version \faustversion\ on \faustdocdate."
  80
  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."
  84
  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."
  88
  89
  90 // Titles for each type of formulas.
  91
  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"
 102
 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)"
 110
 111 :dgmcaption                     "Block diagram of"