\subsection{Types and Units}All math in diskmodel is performed using integer arithmetic.  Anglesidentified as points on a circle divided into discrete units.  Time isrepresented as multiples of some very small time base.  Diskmodelexports the types \texttt{dm\_time\_t} and \texttt{dm\_angle\_t} torepresent these quantities.  Diskmodel exports functions\texttt{dm\_time\_itod}, \texttt{dm\_time\_dtoi} (likewise for angles)for converting between doubles and the native format.  The timefunction converts to and from milliseconds; the angle functionconverts to and from a fraction of a circle.  \texttt{dm\_time\_t} and\texttt{dm\_angle\_t} should be regarded as opaque and may change overtime.  Diskmodel is sector-size agnostic in that it assumes thatsectors are some fixed size but does not make any assumption aboutwhat that size is.\subsubsection{Three Zero Angles}When considering the angular offset of a sector on a track, there areat least three plausible candidates for a ``zero'' angle.  The firstis ``absolute'' zero which is the same on every track on the disk.For various reasons, this zero may not coincide with a sectorboundary on a track.  This motivates the second 0 which we will referto as $0_t$ (t for ``track'') which is the angular offset of the firstsector boundary past 0 on a track.  Because of skews and defects, thelowest lbn on the track may not lie at $0_t$.  We call the angle ofthe lowest sector on the track $0_l$ (l for ``logical'' or ``lbn'').\subsubsection{Two Zero Sectors}Similarly, when numbering the sectors on a track, it is reasonable tocall either the sector at $0_t$ or the one at $0_l$ ``sector 0.''$0_t$ corresponds to directly to the physical location of sectors on atrack whereas $0_l$ corresponds to logical layout.  Diskmodel works inboth systems and the following function descriptions identify whichnumbering a given function uses.\subsubsection{Example}Consider a disk with 100 sectors per track, 2 heads, a head switchskew of 10 sectors and a cylinder switch skew of 20 sectors. $(x,y,z)$denotes cylinder $x$, head $y$ and sector $z$.\\\begin{tabular}{l|l|l}LBN & $0_l$ PBN & $0_t$ PBN \\\cline{1-3}0 & (0,0,0) & (0,0,0) \\\multicolumn{3}{c}{$\vdots$} \\99 & (0,0,99) & (0,0,99) \\100 &  (0,1,0) & (0,1,10) \\101 &  (0,1,1) & (0,1,11) \\\multicolumn{3}{c}{$\vdots$} \\189 & (0,1,89) & (0,1,99) \\190 & (0,1,90) & (0,1,0) \\191 & (0,1,91) & (0,1,1) \\199 & (0,1,99) & (0,1,9) \\\end{tabular}\\Note that a sector is $3.6$ degrees wide.\\\begin{tabular}{l|l|l}Cylinder & Head & $0_l$ angle \\\cline{1-3}0 & 0 & 0 degrees \\0 & 1 & 36 degrees \\1 & 0 & 72 degrees \\1 & 1 & 108 degrees \\2 & 0 & 180 degrees \\\end{tabular}