+++ /dev/null
-// Default texts for the math documentator of the Faust compiler.
-// Copyright (C) 2009 GRAME, Centre National de Creation Musicale
-// Karim Barkati
-
-// Remark:
-// double quotes are useful to visualize spaces and tabulations
-// at the beginning or at the end of strings.
-
-
-
-// Metadatas section.
-
-:name "name"
-:author "author"
-:copyright "copyright"
-:license "license"
-:version "version"
-
-
-// Notice section.
-
-: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."
-
-: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})."
-
-: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."
-
-: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."
-
-:faustdocdir "The \texttt{\faustdocdir/} directory may also include the following subdirectories:"
-"\begin{itemize}"
-" \item \texttt{cpp/} for Faust compiled code; "
-" \item \texttt{pdf/} which contains this document; "
-" \item \texttt{src/} for all Faust sources used (even libraries); "
-" \item \texttt{svg/} for block diagrams, encoded using the Scalable Vector Graphics format (\textsf{http://www.w3.org/Graphics/SVG/});"
-" \item \texttt{tex/} for the \LaTeX\ source of this document."
-"\end{itemize}"
-
-:foreignfun ""ff" prefix in some function name stands for C++ "foreign function"."
-
-:intcast
-"$\forall \, x \in \mathbb{R}$, "
-" \begin{displaymath}"
-" \mathrm{int}(x) ="
-" \left\{\begin{array}{cl}"
-" \lfloor x \rfloor & \mbox{if \,} x > 0 \\"
-" \lceil x \rceil & \mbox{if \,} x < 0 \\"
-" 0 & \mbox{if \,} x = 0 \\"
-" \end{array}\right.."
-" \end{displaymath}"
-
-:operators "This document uses the following integer operations:"
-:optabtitle "\emph{operation} & \emph{name} & \emph{semantics} \\"
-:intplus "$i \oplus j$ & integer addition & $\mathrm{normalize}(i+j), \mathrm{~in~} \mathbb{Z}$ \\"
-:intminus "$i \ominus j$ & integer substraction & $\mathrm{normalize}(i-j), \mathrm{~in~} \mathbb{Z}$ \\"
-:intmult "$i \odot j$ & integer multiplication & $\mathrm{normalize}(i \cdot j), \mathrm{~in~} \mathbb{Z}$ \\"
-:intdiv "$i \oslash j$ & integer division & $\mathrm{normalize}(\mathrm{int}(i/j)), \mathrm{~in~} \mathbb{Q}$ \\"
-
-: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 "
-"$$\mathrm{normalize}(i) = i - N\cdot\mathrm{sign}(i) \cdot \left\lfloor \frac{|i|+N/2+(\mathrm{sign}(i)\!-\!1)/2}{N} \right\rfloor , $$"
-" where $N = 2^n$ and $\mathrm{sign}(i) = 0 \mathrm{\ if\ } i=0 \mathrm{\ and\ } i / |i| \mathrm{\ otherwise}.$"
-"Unary integer operations are defined likewise."
-
-
-// Auto-documentation section.
-
-: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."
-
-:autoeqntitle "\section{Mathematical definition of \texttt{process}}"
-"\label{equation}"
-:autoeqntext "The \emph{\faustprogname} program evaluates the signal transformer denoted by \texttt{process}, which is mathematically defined as follows:"
-
-:autodgmtitle "\section{Block diagram of \texttt{process}}"
-"\label{diagram}"
-:autodgmtext "The block diagram of \texttt{process} is shown on Figure\,\ref{figure1} (page\,\pageref{figure1})."
-
-:autontctitle "\section{Notice}"
-"\label{notice}"
-:autontctext "This document was generated using Faust version \faustversion\ on \faustdocdate."
-
-:autolsttitle1 "\section{Faust code listing}"
-"\label{listing}"
-:autolsttext1 "This section provides the listing of the Faust code used to generate this document."
-
-:autolsttitle2 "\section{Faust code listings}"
-"\label{listing}"
-:autolsttext2 "This section provides the listings of the Faust code used to generate this document, including dependencies."
-
-
-// Titles for each type of formulas.
-
-:inputsigtitle1 "Input signal"
-:inputsigtitle2 "Input signals"
-:outputsigtitle1 "Output signal"
-:outputsigtitle2 "Output signals"
-:constsigtitle1 "Constant"
-:constsigtitle2 "Constants"
-:uisigtitle1 "User-interface input signal"
-:uisigtitle2 "User-interface input signals"
-:intermedsigtitle1 "Intermediate signal"
-:intermedsigtitle2 "Intermediate signals"
-
-:lateqcomment "% Set of Faust formulas (corresponding to an <equation> tag)."
-:emptyformulafield "none"
-:defaultvalue "default value"
-:suchthat "such that"
-:and "and"
-:for "for"
-:rootlevel "(at root level)"
-
-:dgmcaption "Block diagram of"
projects / Faustine.git / blobdiff