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background-position: left; width: 550px; min-height: 105px; _height: 105px; background-repeat: no-repeat; '> <div class='titlewrapper' style='background: transparent'> <h1 class='title' style='background: transparent; border-width: 0px'> <a href='http://www.righto.com/'> Ken Shirriff's blog </a> </h1> </div> <div class='descriptionwrapper'> <p class='description'><span>Computer history, restoring vintage computers, IC reverse engineering, and whatever</span></p> </div> </div> </div></div> </div> </div> <div class='header-cap-bottom cap-bottom'> <div class='cap-left'></div> <div class='cap-right'></div> </div> </div> </header> <div class='tabs-outer'> <div class='tabs-cap-top cap-top'> <div class='cap-left'></div> <div class='cap-right'></div> </div> <div class='fauxborder-left tabs-fauxborder-left'> <div class='fauxborder-right tabs-fauxborder-right'></div> <div class='region-inner tabs-inner'> <div class='tabs no-items section' id='crosscol'></div> <div class='tabs no-items section' id='crosscol-overflow'></div> </div> </div> <div class='tabs-cap-bottom cap-bottom'> <div class='cap-left'></div> <div class='cap-right'></div> </div> </div> <div class='main-outer'> <div class='main-cap-top cap-top'> <div class='cap-left'></div> <div class='cap-right'></div> </div> <div class='fauxborder-left main-fauxborder-left'> <div class='fauxborder-right main-fauxborder-right'></div> <div class='region-inner main-inner'> <div class='columns fauxcolumns'> <div class='fauxcolumn-outer fauxcolumn-center-outer'> <div class='cap-top'> <div class='cap-left'></div> <div class='cap-right'></div> </div> <div class='fauxborder-left'> <div class='fauxborder-right'></div> <div class='fauxcolumn-inner'> </div> </div> <div class='cap-bottom'> <div class='cap-left'></div> <div class='cap-right'></div> </div> </div> <div class='fauxcolumn-outer fauxcolumn-left-outer'> <div class='cap-top'> <div class='cap-left'></div> <div class='cap-right'></div> </div> <div class='fauxborder-left'> <div class='fauxborder-right'></div> <div class='fauxcolumn-inner'> </div> </div> <div class='cap-bottom'> <div class='cap-left'></div> <div class='cap-right'></div> </div> </div> <div class='fauxcolumn-outer fauxcolumn-right-outer'> <div class='cap-top'> <div class='cap-left'></div> <div class='cap-right'></div> </div> <div class='fauxborder-left'> <div class='fauxborder-right'></div> <div class='fauxcolumn-inner'> </div> </div> <div class='cap-bottom'> <div class='cap-left'></div> <div class='cap-right'></div> </div> </div>  <div class='columns-inner'> <div class='column-center-outer'> <div class='column-center-inner'> <div class='main section' id='main'><div class='widget Blog' data-version='1' id='Blog1'> <div class='blog-posts hfeed'> <div class='status-msg-wrap'> <div class='status-msg-body'> Showing posts with label <b>386</b>. <a href="http://www.righto.com/">Show all posts</a> </div> <div class='status-msg-border'> <div class='status-msg-bg'> <div class='status-msg-hidden'>Showing posts with label <b>386</b>. <a href="http://www.righto.com/">Show all posts</a></div> </div> </div> </div> <div style='clear: both;'></div> <div class="date-outer"> <div class="date-posts"> <div class='post-outer'> <div class='post hentry' itemprop='blogPost' itemscope='itemscope' itemtype='http://schema.org/BlogPosting'> <meta content='https://static.righto.com/images/386-stdcell/386-apr-w600.jpg' itemprop='image_url'/> <meta content='6264947694886887540' itemprop='blogId'/> <meta content='7582473692859841880' itemprop='postId'/> <a name='7582473692859841880'></a> <h3 class='post-title entry-title' itemprop='name'> <a href='http://www.righto.com/2024/01/intel-386-standard-cells.html'>Reverse engineering standard cell logic in the Intel 386 processor</a> </h3> <div class='post-header'> <div class='post-header-line-1'></div> </div> <div class='post-body entry-content' id='post-body-7582473692859841880' itemprop='description articleBody'> The 386 processor (1985) was Intel's most complex processor at the time, with 285,000 transistors. Intel had scheduled 50 person-years to design the processor, but it was falling behind schedule. The design team decided to automate chunks of the layout, developing "automatic place and route" software.<span id="fnref:oral-history"><a class="ref" href="#fn:oral-history">1</a></span> This was a risky decision since if the software couldn't create a dense enough layout, the chip couldn't be manufactured. But in the end, the 386 finished ahead of schedule, an almost unheard-of accomplishment.</p> <p>In this article, I take a close look at the "standard cells" used in the 386, the logic blocks that were arranged and wired by software. Reverse-engineering these circuits shows how standard cells implement logic gates, latches, and other components with CMOS transistors. Modern integrated circuits still use standard cells, much smaller now, of course, but built from the same principles.</p> <p>The photo below shows the 386 die with the automatic-place-and-route regions highlighted in red. These blocks of unstructured logic have cells arranged in rows, giving them a characteristic striped appearance. In comparison, functional blocks such as the datapath on the left and the microcode ROM in the lower right were designed manually to optimize density and performance, giving them a more solid appearance. As for other features on the chip, the black circles around the border are bond wire connections that go to the chip's external pins. The chip has two metal layers, a small number by modern standards, but a jump from the single metal layer of earlier processors such as the 286. The metal appears white in larger areas, but purplish where circuitry underneath roughens its surface. For the most part, the underlying silicon and the polysilicon wiring on top are obscured by the metal layers.</p> <p><a href="https://static.righto.com/images/386-stdcell/386-apr.jpg"><img alt="Die photo of the 386 processor with standard-cell logic highlighted in red." class="hilite" height="636" src="https://static.righto.com/images/386-stdcell/386-apr-w600.jpg" title="Die photo of the 386 processor with standard-cell logic highlighted in red." width="600" /></a><div class="cite">Die photo of the 386 processor with standard-cell logic highlighted in red.</div></p> <p>Early processors in the 1970s were usually designed by manually laying out every transistor individually, fitting transistors together like puzzle pieces to optimize their layout. While this was tedious, it resulted in a highly dense layout. Federico Faggin, designer of the popular Z80 processor, <a href="https://archive.computerhistory.org/resources/text/Oral_History/Zilog_Z80/102658073.05.01.pdf#page=20">describes</a> finding that the last few transistors wouldn't fit, so he had to erase three weeks of work and start over. The closeup of the resulting Z80 layout below shows that each transistor has a different, complex shape, optimized to pack the transistors as tightly as possible.<span id="fnref:regularity"><a class="ref" href="#fn:regularity">2</a></span></p> <p><a href="https://static.righto.com/images/386-stdcell/z80.jpg"><img alt="A closeup of transistors in the Zilog Z80 processor (1976). This chip is NMOS, not CMOS, which provides more layout flexibility. The metal and polysilicon layers have been removed to expose the underlying silicon. The lighter stripes over active silicon indicate where the polysilicon gates were. I think this photo is from the Visual 6502 project but I'm not sure." class="hilite" height="377" src="https://static.righto.com/images/386-stdcell/z80-w350.jpg" title="A closeup of transistors in the Zilog Z80 processor (1976). This chip is NMOS, not CMOS, which provides more layout flexibility. The metal and polysilicon layers have been removed to expose the underlying silicon. The lighter stripes over active silicon indicate where the polysilicon gates were. I think this photo is from the Visual 6502 project but I'm not sure." width="350" /></a><div class="cite">A closeup of transistors in the Zilog Z80 processor (1976). This chip is NMOS, not CMOS, which provides more layout flexibility. The metal and polysilicon layers have been removed to expose the underlying silicon. The lighter stripes over active silicon indicate where the polysilicon gates were. I think this photo is from the Visual 6502 project but I'm not sure.</div></p>  <p>Standard-cell logic is an alternative that is much easier than manual layout.<span id="fnref:gate-arrays"><a class="ref" href="#fn:gate-arrays">3</a></span> The idea is to create a standard library of blocks (cells) to implement each type of gate, flip-flop, and other low-level component. To use a particular circuit, instead of arranging each transistor, you use the standard design. Each cell has a fixed height but the width varies as needed, so the standard cells can be arranged in rows. For example, the die photo below three cells in a row: a latch, a high-current inverter, and a second latch. This region has 24 transistors in total with PMOS above and NMOS below. Compare the orderly arrangement of these transistors with the Z80 transistors above.</p> <p><a href="https://static.righto.com/images/386-stdcell/cells.jpg"><img alt="Some standard cell circuitry in the 386. I removed the metal and polysilicon to show the underlying silicon. The irregular blotches are oxide that wasn't fully removed, and can be ignored." class="hilite" height="128" src="https://static.righto.com/images/386-stdcell/cells-w350.jpg" title="Some standard cell circuitry in the 386. I removed the metal and polysilicon to show the underlying silicon. The irregular blotches are oxide that wasn't fully removed, and can be ignored." width="350" /></a><div class="cite">Some standard cell circuitry in the 386. I removed the metal and polysilicon to show the underlying silicon. The irregular blotches are oxide that wasn't fully removed, and can be ignored.</div></p> <p>The space between rows is used as a "wiring channel" that holds the wiring between the cells. The photo below zooms out to show four rows of standard cells (the dark bands) and the wiring in between. The 386 uses three layers for this wiring: polysilicon and the upper metal layer (M2) for vertical segments and the lower metal layer (M1) for horizontal segments.</p> <p><a href="https://static.righto.com/images/386-stdcell/standard-cell.jpg"><img alt="Some standard-cell logic in the 386 processor." class="hilite" height="398" src="https://static.righto.com/images/386-stdcell/standard-cell-w600.jpg" title="Some standard-cell logic in the 386 processor." width="600" /></a><div class="cite">Some standard-cell logic in the 386 processor.</div></p> <p>To summarize, with standard cell logic, the cells are obtained from the standard cell library as needed, defining the transistor layout and the wiring inside the cell. However, the locations of each cell (placing) need to be determined, as well as how to arrange the wiring (routing). As will be seen, placing and routing the cells can be done manually or automatically.</p>  <h2>Use of standard cells in the 386</h2> <p>Fairly late in the design process, the 386 team decided to use automatic place and route for parts of the chip. By using automatic place and route, 2,254 gates (consisting of over 10,000 devices) were placed and routed in seven weeks. (These numbers are from a paper "Automatic Place and Route Used on the 80386", co-written by Pat Gelsinger, now the CEO of Intel. I refer to this paper multiple times, so I'll call it <em>APR386</em> for convenience.<span id="fnref:apr386"><a class="ref" href="#fn:apr386">4</a></span>) Automatic place and route was not only faster, but it avoided the errors that crept in when layout was performed manually.<span id="fnref:compaction"><a class="ref" href="#fn:compaction">5</a></span></p> <p>The "place" part of automatic place and route consists of determining the arrangement of the standard cells into rows to minimize the distance between connected cells. Running long wires between cells wastes space on the die, since you end up with a lot of unnecessary metal wiring. But more importantly, long paths have higher resistance, slowing down the signals. Placement is a difficult optimization problem that is <a href="https://dl.acm.org/doi/10.1145/103724.103725">NP-complete</a>. Moreover, the task was made more complicated by weighting paths by importance and electrical characteristics, classifying signals as "normal", "fast", or "critical". Paths were also weighted to encourage the use of the thicker M2 metal layer rather than the lower M1 layer.</p> <p>The 386 team solved the placement problem with a program called Timberwolf, developed by a Berkeley grad student. As one member of the 386 team <a href="https://dl.acm.org/doi/10.1145/103724.103725">said</a>, "If management had known that we were using a tool by some grad student as a key part of the methodology, they would never have let us use it." Timberwolf used a simulated annealing algorithm, based on a simulated temperature that decreased over time. The idea is to randomly move cells around, trying to find better positions, but gradually tighten up the moves as the "temperature" drops. At the end, the result is close to optimal. The purpose of the temperature is to avoid getting stuck in a local minimum by allowing "bad" changes at the beginning, but then tightening up the changes as the algorithm progresses.</p> <p>Once the cells were placed in their positions, the second step was "routing", generating the layout of all the wiring. A suitable commercial router was not available in 1984, so Intel developed its own. As routing is a difficult problem (also NP-complete), they took an iterative heuristic approach, repeatedly routing until they found the smallest channel height that would work. (Thus, the wiring channels are different sizes as needed.) Then they checked the R-C timing of all the signals to find any signals that were too slow. Designers could boost the size of the associated drivers (using the variety of available standard cells) and try the routing again.</p> <h2>Brief CMOS overview</h2> <p>The 386 was the first processor in Intel's x86 line to be built with a technology called CMOS instead of using NMOS. Modern processors are all built from CMOS because CMOS uses much less power than NMOS. CMOS is more complicated to construct, though, because it uses two types of transistors—NMOS and PMOS—so early processors were typically NMOS. But by the mid-1980s, the advantages of switching to CMOS were compelling.</p> <p>The diagram below shows how an NMOS transistor is constructed. The transistor can be considered a switch between the source and drain, controlled by the gate. The source and drain regions (green) consist of silicon doped with impurities to change its semiconductor properties, forming N+ silicon. The gate consists of a layer of polysilicon (red), separated from the silicon by a very thin insulating oxide layer. Whenever polysilicon crosses active silicon, a transistor is formed. A PMOS transistor has similar construction except it swaps the N-type and P-type silicon, consisting of P+ regions in a substrate of N silicon.</p> <p><a href="https://static.righto.com/images/386-stdcell/mosfet-n.jpg"><img alt="Diagram showing the structure of an NMOS transistor." class="hilite" height="231" src="https://static.righto.com/images/386-stdcell/mosfet-n-w400.jpg" title="Diagram showing the structure of an NMOS transistor." width="400" /></a><div class="cite">Diagram showing the structure of an NMOS transistor.</div></p> <p>The NMOS and PMOS transistors are opposite in their construction and operation. An NMOS transistor turns on when the gate is high, while a PMOS transistor turns on when the gate is low. An NMOS transistor is best at pulling its output low, while a PMOS transistor is best at pulling its output high. In a CMOS circuit, the transistors work as a team, pulling the output high or low as needed; this is the "Complementary" in CMOS. (The behavior of MOS transistors is complicated, so this description is simplified, just enough to understand digital circuits.)</p> <p>One complication is that NMOS transistors are built on P-type silicon, while PMOS transistors are built on N-type silicon. Since the silicon die itself is N silicon, the NMOS transistors need to be surrounded by a tub or well of P silicon.<span id="fnref:tub"><a class="ref" href="#fn:tub">6</a></span> The cross-section diagram below shows how the NMOS transistor on the left is embedded in a well of P-type silicon.</p> <p><a href="https://static.righto.com/images/386-stdcell/cmos-cross-section.jpg"><img alt="Simplified structure of the CMOS circuits." class="hilite" height="217" src="https://static.righto.com/images/386-stdcell/cmos-cross-section-w500.jpg" title="Simplified structure of the CMOS circuits." width="500" /></a><div class="cite">Simplified structure of the CMOS circuits.</div></p> <p>For proper operation, the silicon that surrounds transistors needs to be connected to the appropriate voltage through "tap" contacts.<span id="fnref:tap"><a class="ref" href="#fn:tap">7</a></span> For PMOS transistors, the substrate is connected to power through the taps, while for NMOS transistors the well region is connected to ground through the taps. The chip needs to have enough taps to keep the voltage from fluctuating too much; each standard cell typically has a positive tap and a ground tap.</p> <p>The actual structure of the integrated circuit is much more three-dimensional than the diagram above, due to the thickness of the various layers. The diagram below is a more accurate cross-section. The 386 has two layers of metal: the lower metal layer (M1) in blue and the upper metal layer (M2) in purple. Polysilicon is colored red, while the insulating oxide layers are gray.</p> <p><a href="https://static.righto.com/images/386-stdcell/cross-section.jpg"><img alt="Cross-section of CHMOS III transistors. From A double layer metal CHMOS III technology, image colorized by me." class="hilite" height="259" src="https://static.righto.com/images/386-stdcell/cross-section-w600.jpg" title="Cross-section of CHMOS III transistors. From A double layer metal CHMOS III technology, image colorized by me." width="600" /></a><div class="cite">Cross-section of CHMOS III transistors. From <a href="https://www.semanticscholar.org/paper/A-double-layer-metal-CHMOS-III-technology-Smith-Sery/7f1eb575d0c029300c946166f43f46558b4ba1b0">A double layer metal CHMOS III technology</a>, image colorized by me.</div></p> <p>This complicated three-dimensional structure makes it harder to interpret the microscope images. Moreover, the two metal layers obscure the circuitry underneath. I have removed various layers with acids for die photos, but even so, the images are harder to interpret than those of simpler chips. If the die photos look confusing, don't be surprised.</p> <p>A logic gate in CMOS is constructed from NMOS and PMOS transistors working together. The schematic below shows a NAND gate with two PMOS transistors in parallel above and two NMOS transistors in series below. If both inputs are high, the two NMOS transistors turn on, pulling the output low. If either input is low, a PMOS transistor turns on, pulling the output high. (Recall that NMOS and PMOS are opposites: a high voltage turns an NMOS transistor on while a low voltage turns a PMOS transistor on.) Thus, the CMOS circuit below produces the desired output for the NAND function.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand.jpg"><img alt="A CMOS NAND gate." class="hilite" height="269" src="https://static.righto.com/images/386-stdcell/nand-w200.jpg" title="A CMOS NAND gate." width="200" /></a><div class="cite">A CMOS NAND gate.</div></p> <p>The diagram below shows how this NAND gate is implemented in the 386 as a standard cell.<span id="fnref:nand-layout"><a class="ref" href="#fn:nand-layout">9</a></span> A lot is going on in this cell, but it boils down to four transistors, as in the schematic above. The yellow region is the P-type silicon that forms the two PMOS transistors; the transistor gates are where the polysilicon (red) crosses the yellow region.<span id="fnref:colors"><a class="ref" href="#fn:colors">8</a></span> (The middle yellow region is the drain for both transistors; there is no discrete boundary between the transistors.) Likewise, the two NMOS transistors are at the bottom, where the polysilicon (red) crosses the active silicon (green). The blue lines indicate the metal wiring for the cell. I thinned these lines to make the diagram clearer; in the actual cell, the metal lines are as thick as they can be without touching, so they cover most of the cell. The black circles are contacts, connections between the metal and the silicon or polysilicon. Finally, the well taps are the opposite type of silicon, connected to the underlying silicon well or substrate to keep it at the proper voltage.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-cell.jpg"><img alt="A standard cell for NAND in the 386." class="hilite" height="428" src="https://static.righto.com/images/386-stdcell/nand-cell-w400.jpg" title="A standard cell for NAND in the 386." width="400" /></a><div class="cite">A standard cell for NAND in the 386.</div></p> <p>Wiring to a cell's inputs and output takes place at the top or bottom of the cell, with wiring in the channels between rows of cells. The polysilicon input and output lines are thickened at the top and bottom of the cell to allow connections to the cell. The wiring between cells can be done with either polysilicon or metal. Typically the upper metal layer (M2) is used for vertical wiring, while the lower metal layer (M1) is used for horizontal runs. Since each standard cell only uses M1, vertical wiring (M2) can pass over cells. Moreover, a cell's output can also use a vertical metal wire (M2) rather than the polysilicon shown. The point is that there is a lot of flexibility in how the system can route wires between the cells. The power and ground wires (M1) are horizontal so they can run from cell to cell and a whole row can be powered from the ends.</p> <p>The photo below shows this NAND cell with the metal layers removed by acid, leaving the silicon and the polysilicon. You can match the features in the photo with the diagram above. The polysilicon appears green due to thin-film effects. At the bottom, two polysilicon lines are connected to the inputs.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-poly.jpg"><img alt="Die photo of the NAND standard cell with the metal layers removed. The image isn't as clear as I would like, but it was very difficult to remove the metal without destroying the polysilicon." class="hilite" height="357" src="https://static.righto.com/images/386-stdcell/nand-poly-w180.jpg" title="Die photo of the NAND standard cell with the metal layers removed. The image isn't as clear as I would like, but it was very difficult to remove the metal without destroying the polysilicon." width="180" /></a><div class="cite">Die photo of the NAND standard cell with the metal layers removed. The image isn't as clear as I would like, but it was very difficult to remove the metal without destroying the polysilicon.</div></p> <p>The photo below shows how the cell appears in the original die. The two metal layers are visible, but they hide the polysilicon and silicon underneath. The vertical metal stripes are the upper (M2) wiring while the lower metal wiring (M1) makes up the standard cell. It is hard to distinguish the two metal layers, which makes interpretation of the images difficult. Note that the metal wiring is wide, almost completely covering the cell, with small gaps between wires. The contacts are visible as dark circles. Is hard to recognize the standard cells from the bare die, as the contact pattern is the only distinguishing feature.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-metal.jpg"><img alt="Die photo of the NAND standard cell showing the metal layer." class="hilite" height="391" src="https://static.righto.com/images/386-stdcell/nand-metal-w180.jpg" title="Die photo of the NAND standard cell showing the metal layer." width="180" /></a><div class="cite">Die photo of the NAND standard cell showing the metal layer.</div></p> <p>One of the interesting features of the 386's standard cell library is that each type of logic gate is available in multiple drive strengths. That is, cells are available with small transistors, large transistors, or multiple transistors in parallel. Because the wiring and the transistor gates have capacitance, a delay occurs when changing state. Bigger transistors produce more current, so they can switch the values on a wire faster. But there are two disadvantages to bigger transistors. First, they take up more space on the die. But more importantly, bigger transistors have bigger gates with more capacitance, so their inputs take longer to switch. (In other words, increasing the transistor size speeds up the output but slows the input, so overall performance could end up worse.) Thus, the sizes of transistors need to be carefully balanced to achieve optimum performance.<span id="fnref:logical-effort"><a class="ref" href="#fn:logical-effort">10</a></span> With a variety of sizes in the standard cell library, designers can make the best choices.</p> <p>The image below shows a small NAND gate. The design is the same as the one described earlier, but the transistors are much smaller. (Note that there is one row of metal contacts instead of two or three.) The transistor gates are about half as wide (measured vertically) so the NAND gate will produce about half the output current.<span id="fnref:gates"><a class="ref" href="#fn:gates">11</a></span></p> <p><a href="https://static.righto.com/images/386-stdcell/nand-small.jpg"><img alt="Die photo of a small NAND standard cell with the metal removed." class="hilite" height="334" src="https://static.righto.com/images/386-stdcell/nand-small-w154.jpg" title="Die photo of a small NAND standard cell with the metal removed." width="154" /></a><div class="cite">Die photo of a small NAND standard cell with the metal removed.</div></p> <p>Since the standard cells are all the same height, the maximum size of a transistor is limited. To provide a larger drive strength, multiple transistors can be used in parallel. The NAND gate below uses 8 transistors, four PMOS and four NMOS, providing twice as much current.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-large.jpg"><img alt="A large NAND gate as it appears on the die, with the metal removed. The left side is slightly obscured by some remaining oxide." class="hilite" height="361" src="https://static.righto.com/images/386-stdcell/nand-large-w240.jpg" title="A large NAND gate as it appears on the die, with the metal removed. The left side is slightly obscured by some remaining oxide." width="240" /></a><div class="cite">A large NAND gate as it appears on the die, with the metal removed. The left side is slightly obscured by some remaining oxide.</div></p> <p>The diagram below shows the structure of the large NAND gate, essentially two NAND gates in parallel. Note that input 1 must be provided separately to both halves by the routing outside the cell. Input 2, on the other hand, only needs to be supplied to the cell once, since it is wired to both halves inside the cell.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-large-diagram.jpg"><img alt="A diagram showing the structure of the large NAND gate." class="hilite" height="421" src="https://static.righto.com/images/386-stdcell/nand-large-diagram-w400.jpg" title="A diagram showing the structure of the large NAND gate." width="400" /></a><div class="cite">A diagram showing the structure of the large NAND gate.</div></p> <p>Inverters are also available in a variety of drive strengths, from very small to very large, as shown below. The inverter on the left uses the smallest transistors, while the inverter on the right not only uses large transistors but is constructed from six inverters in parallel. One polysilicon input controls all the transistors.</p> <p><a href="https://static.righto.com/images/386-stdcell/inverters.jpg"><img alt="A small inverter and a large inverter." class="hilite" height="320" src="https://static.righto.com/images/386-stdcell/inverters-w460.jpg" title="A small inverter and a large inverter." width="460" /></a><div class="cite">A small inverter and a large inverter.</div></p> <p>A more complex standard cell is XOR. The diagram below shows an XOR cell with large drive current. (There are smaller XOR cells). As with the large NAND gate, the PMOS transistors are doubled up for more current. The multiple input connections are handled by the routing outside the cell. Since the NMOS transistors don't need to be doubled up, there is a lot of unused space in the lower part of the cell. The extra space is used for a very large tap contact, consisting of 24 contacts to ground the well.</p> <p><a href="https://static.righto.com/images/386-stdcell/xor-diagram.jpg"><img alt="The structure of an XOR cell with large drive current." class="hilite" height="372" src="https://static.righto.com/images/386-stdcell/xor-diagram-w600.jpg" title="The structure of an XOR cell with large drive current." width="600" /></a><div class="cite">The structure of an XOR cell with large drive current.</div></p> <p>XOR is a difficult gate to build with CMOS. The cell above implements it by combining a NOR gate and an AND-NOR gate, as shown below. You can verify that if both inputs are 0 or both inputs are 1, the output is forced low as desired. In the layout above, the NOR gate is on the left, while the AND-NOR gate has the AND part on the right. A metal wire down the center connects the NOR output to the AND-NOR input. The need for two sub-gates is another reason why the XOR cell is so large.</p> <p><a href="https://static.righto.com/images/386-stdcell/xor-schematic.jpg"><img alt="Schematic of the XOR cell." class="hilite" height="124" src="https://static.righto.com/images/386-stdcell/xor-schematic-w400.jpg" title="Schematic of the XOR cell." width="400" /></a><div class="cite">Schematic of the XOR cell.</div></p> <p>I'll describe one more cell, the latch, which holds one bit and is controlled by a clock signal. Latches are heavily used in the 386 whenever a signal needs to be remembered or a circuit needs to be synchronous. The 386 has multiple types of standard cell latches including latches with set or reset controls and latches with different drive strengths. Moreover, two latches can be combined to form an edge-triggered flip-flop standard cell.</p> <p>The schematic below shows the basic latch circuit, the most common type in the 386. On the right, two inverters form a loop. This loop can stably hold a 0 or 1 value. On the left, a PMOS transistor and an NMOS transistor form a transmission gate. If the clock is high, both transistors will turn on and pass the input through. If the clock is low, both transistors will turn off and block the input. The trick to the latch is that one inverter is weak, producing just a small current. The consequence is that the input can overpower the inverter output, causing the inverter loop to switch to the input value. The result is that when the clock is high, the latch will pass the input value through to the output. But when the clock is low, the latch will hold its previous value. (The output is inverted with respect to the input, which is slightly inconvenient but reduces the size of the latch.)</p> <p><a href="https://static.righto.com/images/386-stdcell/latch-schematic.jpg"><img alt="Schematic of a latch." class="hilite" height="171" src="https://static.righto.com/images/386-stdcell/latch-schematic-w350.jpg" title="Schematic of a latch." width="350" /></a><div class="cite">Schematic of a latch.</div></p> <p>The standard cell layout of the latch (below) is complicated, but it corresponds to the schematic. At the left are the PMOS and NMOS transistors that form the transmission gate. In the center is the weak inverter, with its output to the left. The weak transistors are in the middle; they are overlapped by a thick polysilicon region, creating a long gate that produces a low current.<span id="fnref:current"><a class="ref" href="#fn:current">12</a></span> At the right is the inverter that drives the output. The layout of this circuit is clever, designed to make the latch as compact as possible. For example, the two inverters share power and ground connections. Notice how the two clock lines pass from top to bottom through gaps in the active silicon so each line only forms one transistor. Finally, the metal line in the center connects the transmission gate outputs and the weak inverter output to the other inverter's input, but asymmetrically at the top so the two inverters don't collide.</p> <p><a href="https://static.righto.com/images/386-stdcell/latch-diagram.jpg"><img alt="The standard cell layout of a latch." class="hilite" height="428" src="https://static.righto.com/images/386-stdcell/latch-diagram-w550.jpg" title="The standard cell layout of a latch." width="550" /></a><div class="cite">The standard cell layout of a latch.</div></p> <p>To summarize, I examined many (but not all) of the standard cells in the 386 and found about 70 different types of cells. These included the typical logic gates with various drive strengths: inverters, buffers, XOR, XNOR, AND-NOR, and 3- and 4-input logic gates. There are also transmission gates including ones that default high or low, as well as multiplexers built from transmission gates. I found a few cells that were surprising such as dual inverters and a combination 3-input and 2-input NAND gate. I suspect these consist of two standard cells that were merged together, since they seem too specialized to be part of a standard cell library.</p> <p>The APR386 paper showed six of the standard cells in the 386 with the diagram below. The small and large inverters are the same as the ones described above, as is the NAND gate NA2B. The latch is similar to the one described above, but with larger transistors. The APR386 paper also showed a block of standard cells, which I was able to locate in the 386.<span id="fnref:cell-block"><a class="ref" href="#fn:cell-block">13</a></span></p> <p><a href="https://static.righto.com/images/386-stdcell/paper-cells.jpg"><img alt="Examples of standard cells, from APR386. The numbers are not defined but may indicate input and output capacitance. (Click for a larger version.)" class="hilite" height="228" src="https://static.righto.com/images/386-stdcell/paper-cells-w800.jpg" title="Examples of standard cells, from APR386. The numbers are not defined but may indicate input and output capacitance. (Click for a larger version.)" width="800" /></a><div class="cite">Examples of standard cells, from APR386. The numbers are not defined but may indicate input and output capacitance. (Click for a larger version.)</div></p>  <h2>Intel's standard cell line</h2> <p>Intel productized its standard cells around 1986 as a 1.5 碌m library using Intel's CMOS technology (called CHMOS III).<span id="fnref:handbook"><a class="ref" href="#fn:handbook">14</a></span> Although the library had over 100 cell types, it was very limited compared to the cells used inside the 386. The library included logic gates, flip-flops, and latches as well as scalable registers, counters, and adders. Most gates only came in one drive strength. Even inverters only came in "normal" and "high" drive strength. I assume these cells are the same as the ones used in the 386, but I don't have proof. The library also included larger devices such as a cell-compatible 80C51 microcontroller and PC peripheral chips such as the 8259 programmable interrupt controller and the 8254 programmable interval timer. I think these were re-implemented using standard cells.</p> <p>Intel later produced a 1.0 碌m library using CHMOS IV, for use "both by ASIC customers and Intel's internal chip designers." This library had a larger collection of drive strengths. The 1.0 碌m library included the 80C186 and associated peripheral chips.</p>  <h2>Layout techniques in the 386</h2> <p>In this section, I'll look at the active silicon regions, making the cells themselves more visible. In the photos below, I dissolved the metal and polysilicon, leaving the active silicon. (Ignore the irregular greenish shapes; these are oxide that wasn't fully removed.)</p> <p>The photo below shows the silicon for three rows of standard cells using automatic place and route. You can see the wide variety of standard cell widths, but the height of the cells is constant. The transistor gates are visible as the darker vertical stripes across the silicon. You may be able to spot the latch in each row, distinguished by the long, narrow transistors of the weak inverters.</p> <p><a href="https://static.righto.com/images/386-stdcell/silicon1.jpg"><img alt="Three rows of standard cells that were automatically placed and routed." class="hilite" height="399" src="https://static.righto.com/images/386-stdcell/silicon1-w236.jpg" title="Three rows of standard cells that were automatically placed and routed." width="236" /></a><div class="cite">Three rows of standard cells that were automatically placed and routed.</div></p> <p>In the first row, the larger PMOS transistors are on top, while the smaller NMOS transistors are below. This pattern alternates from row to row, so the second row has the NMOS transistors on top and the third row has the PMOS transistors on top. The height of the wiring channel between the cells is variable, made as small as possible while fitting the wiring.</p> <p>The 386 also contains regions of standard cells that were apparently manually placed and routed, as shown in the photo below. Using standard cells avoids the effort of laying out each transistor, so it is still easier than a fully custom layout. These cells are in rows, but the rows are now double rows with channels in between. The density is higher, but routing the wires becomes more challenging.</p> <p><a href="https://static.righto.com/images/386-stdcell/silicon2.jpg"><img alt="Three rows of standard cells that were manually placed and routed." class="hilite" height="410" src="https://static.righto.com/images/386-stdcell/silicon2-w347.jpg" title="Three rows of standard cells that were manually placed and routed." width="347" /></a><div class="cite">Three rows of standard cells that were manually placed and routed.</div></p> <p>For critical circuitry such as the datapath, the layout of each transistor was optimized. The register file, for example, has a very dense layout as shown below. As you can see, the density is much higher than in the previous photos. (The three photos are at the same scale.) Transistors are packed together with very little wasted space. This makes the layout difficult since there is little room for wiring. For this particular circuit, the lower metal layer (M1) runs vertically with signals for each bit while the upper metal layer (M2) runs horizontally for power, ground, and control signals.<span id="fnref:regs"><a class="ref" href="#fn:regs">15</a></span></p> <p><a href="https://static.righto.com/images/386-stdcell/silicon3.jpg"><img alt="Three rows of standard cells that were manually placed and routed." class="hilite" height="288" src="https://static.righto.com/images/386-stdcell/silicon3-w400.jpg" title="Three rows of standard cells that were manually placed and routed." width="400" /></a><div class="cite">Three rows of standard cells that were manually placed and routed.</div></p> <p>The point of this is that the 386 uses a variety of different design techniques, from dense manual layout to much faster automated layout. Different techniques were used for different parts of the chip, based on how important it was to optimize. For example, circuits in the datapath were typically repeated 32 times, once for each bit, so manual effort was worthwhile. The most critical functional blocks were the microcode ROM (CROM), large PLAs, ALU, TLB (translation lookaside buffer), and the barrel shifter.<span id="fnref:prak"><a class="ref" href="#fn:prak">16</a></span></p> <h2>Conclusions</h2> <p>Standard cell logic and automatic place and route have a long history before the 386, back to the early 1970s, so this isn't an Intel invention.<span id="fnref:standard-cell-history"><a class="ref" href="#fn:standard-cell-history">17</a></span> Nonetheless, the 386 team deserves the credit for deciding to use this technology at a time when it was a risky decision. They needed to develop custom software for their placing and routing needs, so this wasn't a trivial undertaking. This choice paid off and they completed the 386 ahead of schedule. The 386 ended up being a huge success for Intel, moving the x86 architecture to 32-bits and defining the dominant computer architecture for the rest of the 20th century.</p> <p>If you're interested in standard cell logic, I wrote about <a href="https://www.righto.com/2021/03/reverse-engineering-standard-cell-logic.html">standard cell logic in an IBM chip</a>. I plan to write more about the 386, so follow me on Twitter <a href="https://twitter.com/kenshirriff">@kenshirriff</a> or <a href="http://www.righto.com/feeds/posts/default">RSS</a> for updates. I'm also on Mastodon occasionally as <a href="https://oldbytes.space/@kenshirriff">@<span class="__cf_email__" data-cfemail="88e3ede6fbe0e1fafae1eeeec8e7e4eceaf1fcedfba6fbf8e9ebed">[email protected]</span></a>. Thanks to Pat Gelsinger and Roxanne Koester for providing helpful papers.</p> <h2>Notes and references</h2> <div class="footnote"> <ol> <li id="fn:oral-history"> <p>The decision to use automatic place and route is described on page 13 of the <a href="https://archive.computerhistory.org/resources/text/Oral_History/Intel_386_Design_and_Dev/102702019.05.01.acc.pdf#page=13">Intel 386 Microprocessor Design and Development Oral History Panel</a>, a very interesting document on the 386 with discussion from some of the people involved in its development. <a class="footnote-backref" href="#fnref:oral-history" title="Jump back to footnote 1 in the text">↩</a></p> </li> <li id="fn:regularity"> <p>Circuits that had a high degree of regularity, such as the arithmetic/logic unit (ALU) or register storage were typically constructed by manually laying out a block to implement a bit and then repeating the block as needed. Because a circuit was repeated 32 times for the 32-bit processor, the additional effort was worthwhile. <a class="footnote-backref" href="#fnref:regularity" title="Jump back to footnote 2 in the text">↩</a></p> </li> <li id="fn:gate-arrays"> <p>An alternative layout technique is the gate array, which doesn't provide as much flexibility as a standard cell approach. In a gate array (sometimes called a master slice), the chip had a fixed array of transistors (and often resistors). The chip could be customized for a particular application by designing the metal layer to connect the transistors as needed. The density of the chip was usually poor, but gate arrays were much faster to design, so they were advantageous for applications that didn't need high density or produced a relatively small volume of chips. Moreover, manufacturing was much faster because the silicon wafers could be constructed in advance with the transistor array and warehoused. Putting the metal layer on top for a particular application could then be quick. Similar gate arrays used a fixed arrangement of logic gates or flip-flops, rather than transistors. Gate arrays date back to <a href="https://www.computerhistory.org/siliconengine/application-specific-integrated-circuits-employ-computer-aided-design/">1967</a>. <a class="footnote-backref" href="#fnref:gate-arrays" title="Jump back to footnote 3 in the text">↩</a></p> </li> <li id="fn:apr386"> <p>The full citation for the APR386 paper is "Automatic Place and Route Used on the 80386" by Joseph Krauskopf and Pat Gelsinger, Intel Technology Journal, Spring 1986. I was unable to find it online. <a class="footnote-backref" href="#fnref:apr386" title="Jump back to footnote 4 in the text">↩</a></p> </li> <li id="fn:compaction"> <p>Once the automatic place and route process had finished, the mask designers performed some cleanup along with compaction to squeeze out wasted space, but this was a relatively minor amount of work.</p> <p>While manual optimization has benefits, it can also be overdone. When the manufacturing process improved, the 80386 moved from a 1.5 碌m process to a 1 碌m process. The layout engineers took advantage of this switch to optimize the standard cell circuitry, manually squeezing out some extra space. Unfortunately, optimizing one block of a die doesn't necessarily make the die smaller, since the size is constrained by the largest blocks. The result is that the optimized 80386 has blocks of empty space at the bottom (visible as black rectangles) and the standard-cell optimization didn't provide any overall benefit. (As the Pentium Pro chief architect Robert Colwell explains, "Removing the state of Kansas does not make the perimeter of the United States any smaller.") </p> <p><a href="https://static.righto.com/images/386-stdcell/shrink.jpg"><img alt="Comparison of the 1.5 碌m die and the 1 碌m die at the same scale. Photos courtesy of Antoine Bercovici." class="hilite" height="384" src="https://static.righto.com/images/386-stdcell/shrink-w600.jpg" title="Comparison of the 1.5 碌m die and the 1 碌m die at the same scale. Photos courtesy of Antoine Bercovici." width="600" /></a><div class="cite">Comparison of the 1.5 碌m die and the 1 碌m die at the same scale. Photos courtesy of Antoine Bercovici.</div></p> <p>At least compaction went better for the 386 than for the Pentium. Intel performed a compaction on the Pentium shortly before release, attempting to reduce the die size. The engineers shrunk the floating point divider, removing some lookup table cases that they proved were unnecessary. Unfortunately, the proof was wrong, resulting in floating point errors in a few cases. This caused the infamous Pentium FDIV bug, a problem that became highly visible to the general public. Replacing the flawed processors cost Intel 475 million dollars. And it turned out that shrinking the floating point divider had no effect on the overall die size.</p> <p>Coincidentally, early models of the 386 had an integer multiplication bug, but Intel fixed this with little cost or criticism. The 386 bug was an analog issue that only showed up unpredictably with a combination of argument values, temperature, and manufacturing conditions. <a class="footnote-backref" href="#fnref:compaction" title="Jump back to footnote 5 in the text">↩</a></p> </li> <li id="fn:tub"> <p>This chip is built on a substrate of N-type silicon, with wells of P-type silicon for the NMOS transistors. Chips can be built the other way around, starting with P-type silicon and putting wells of N-type silicon for the PMOS transistors. Another approach is the "twin-well" CMOS process, constructing wells for both NMOS and PMOS transistors. <a class="footnote-backref" href="#fnref:tub" title="Jump back to footnote 6 in the text">↩</a></p> </li> <li id="fn:tap"> <p>The bulk silicon voltage makes the boundary between a transistor and the bulk silicon act as a reverse-biased diode, so current can't flow across the boundary. Specifically, for a PMOS transistor, the N-silicon substrate is connected to the positive supply. For an NMOS transistor, the P-silicon well is connected to ground. A P-N junction acts as a diode, with current flowing from P to N. But the substrate voltages put P at ground and N at +5, blocking any current flow. The result is that the bulk silicon can be considered an insulator, with current restricted to the N+ and P+ doped regions. If this back bias gets reversed, for example, due to power supply fluctuations, current can flow through the substrate. This can result in "latch-up", a situation where the N and P regions act as parasitic NPN and PNP transistors that latch into the "on" state. This shorts power and ground and can destroy the chip. The point is that the substrate voltages are very important for the proper operation of the chip. <a class="footnote-backref" href="#fnref:tap" title="Jump back to footnote 7 in the text">↩</a></p> </li> <li id="fn:colors"> <p>I'm using the standard CMOS coloring scheme for my diagrams. I'm told that Intel uses a different color scheme internally. <a class="footnote-backref" href="#fnref:colors" title="Jump back to footnote 8 in the text">↩</a></p> </li> <li id="fn:nand-layout"> <p>The schematic below shows the physical arrangement of the transistors for the NAND gate, in case it is unclear how to get from the layout to the logic gate circuit. The power and ground lines are horizontal so power can pass from cell to cell when the cells are connected in rows. The gate's inputs and outputs are at the top and bottom of the cell, where they can be connected through the wiring channels. Even though the transistors are arranged horizontally, the PMOS transistors (top) are in parallel, while the NMOS transistors (bottom) are in series.</p> <p><a href="https://static.righto.com/images/386-stdcell/nand-layout.jpg"><img alt="Schematic of the NAND gate as it is arranged in the standard cell." class="hilite" height="224" src="https://static.righto.com/images/386-stdcell/nand-layout-w300.jpg" title="Schematic of the NAND gate as it is arranged in the standard cell." width="300" /></a><div class="cite">Schematic of the NAND gate as it is arranged in the standard cell.</div></p> <p> <a class="footnote-backref" href="#fnref:nand-layout" title="Jump back to footnote 9 in the text">↩</a></p> </li> <li id="fn:logical-effort"> <p>The 1999 book <a href="https://amzn.to/3UxmgV5">Logical Effort</a> describes a methodology for maximizing the performance of CMOS circuits by correctly sizing the transistors. <a class="footnote-backref" href="#fnref:logical-effort" title="Jump back to footnote 10 in the text">↩</a></p> </li> <li id="fn:gates"> <p>Unfortunately, the word "gate" is used for both transistor gates and logic gates, which can be confusing. <a class="footnote-backref" href="#fnref:gates" title="Jump back to footnote 11 in the text">↩</a></p> </li> <li id="fn:current"> <p>You might expect that these transistors would produce <em>more</em> current since they are larger than the regular transistors. The reason is that a transistor's current output is proportional to the gate width divided by the length. Thus, if you make the transistor bigger in the width direction, the current increases, but if you make the transistor bigger in the length direction, the current decreases. You can think of increasing width as acting as multiple transistors in parallel. Increasing length, on the other hand, makes a longer path for current to get from the source to the drain, weakening it. <a class="footnote-backref" href="#fnref:current" title="Jump back to footnote 12 in the text">↩</a></p> </li> <li id="fn:cell-block"> <p>The APR386 paper discusses the standard-cell layout in detail. It includes a plot of a block of standard-cell circuitry (below).</p> <p><a href="https://static.righto.com/images/386-stdcell/apr-386.jpg"><img alt="A block of standard-cell circuitry from APR386." class="hilite" height="442" src="https://static.righto.com/images/386-stdcell/apr-386-w300.jpg" title="A block of standard-cell circuitry from APR386." width="300" /></a><div class="cite">A block of standard-cell circuitry from APR386.</div></p> <p>After carefully studying the 386 die, I was able to find the location of this block of circuitry (below). The two regions match exactly; they look a bit different because the M1 metal layer (horizontal) doesn't show up in the plot above.</p> <p><a href="https://static.righto.com/images/386-stdcell/apr-386-die-zoom.jpg"><img alt="The same block of standard cells on the 386 die." class="hilite" height="466" src="https://static.righto.com/images/386-stdcell/apr-386-die-zoom-w600.jpg" title="The same block of standard cells on the 386 die." width="600" /></a><div class="cite">The same block of standard cells on the 386 die.</div></p> <p> <a class="footnote-backref" href="#fnref:cell-block" title="Jump back to footnote 13 in the text">↩</a></p> </li> <li id="fn:handbook"> <p>Intel's CHMOS III standard cells are documented in <a href="https://bitsavers.org/components/intel/_dataBooks/1988_Introduction_to_Intel_Cell-Based_Design.pdf">Introduction to Intel Cell-Based Design</a> (1988). The CHMOS IV library is discussed in <a href="https://doi.org/10.1109/ASIC.1990.186171">Design Methodology for a 1.0碌 Cell-based Library Efficiently Optimized for Speed and Area</a>. The paper <a href="https://doi.org/10.1109/ASIC.1990.186174">Validating an ASIC Standard Cell Library</a> covers both libraries. <a class="footnote-backref" href="#fnref:handbook" title="Jump back to footnote 14 in the text">↩</a></p> </li> <li id="fn:regs"> <p>For details on the 386's register file, see my <a href="https://www.righto.com/2023/11/reverse-engineering-intel-386.html">earlier article</a>. <a class="footnote-backref" href="#fnref:regs" title="Jump back to footnote 15 in the text">↩</a></p> </li> <li id="fn:prak"> <p>Source: "High Performance Technology Circuits and Packaging for the 80386", Jan Prak, Proceedings, ICCD Conference, Oct. 1986. <a class="footnote-backref" href="#fnref:prak" title="Jump back to footnote 16 in the text">↩</a></p> </li> <li id="fn:standard-cell-history"> <p>I'll provide more history on standard cells in this footnote. RCA <a href="https://patents.google.com/patent/US3573488A">patented</a> a bipolar standard cell in 1971, but this was a fixed arrangement of transistors and resistors, more of a gate array than a modern standard cell. Bell Labs researched standard cell layout techniques in the early 1970s, calling them Polycells, including a <a href="https://dl.acm.org/doi/10.1145/62882.62886">1973 paper</a> by Brian Kernighan. By 1979 <a href="http://www.bitsavers.org/pdf/xerox/parc/techReports/SSL-79-7_A_Guide_to_LSI_Implementation_Second_Edition.pdf">A Guide to LSI Implementation</a> discussed the standard cell approach and it was described as well-known in <a href="https://patents.google.com/patent/US4319396A">this patent application</a>. Even so, <a href="https://www.worldradiohistory.com/Archive-Electronics/80s/80/Electronics-1980-07-31.pdf#page=77">Electronics</a> called these design methods "futuristic" in 1980.</p> <p>Standard cells became popular in the mid-1980s as faster computers and improved design software made it practical to produce semi-custom designs that used standard cells. Standard cells made it to the cover of <a href="http://www.bitsavers.org/magazines/Digital_Design/Digital_Design_V15_N08_198508.pdf">Digital Design</a> in August 1985, and the article inside described numerous vendors and products. Companies like <a href="https://www.worldradiohistory.com/Archive-Electronics/80s/83/Electronics-1983-03-10.pdf#page=151">Zymos</a> and <a href="http://www.bitsavers.org/components/vti/tools/1988_VTI_Cell-Based_Design_Users_Guide.pdf">VLSI Technology</a> (VTI) focused on standard cells. Traditional companies such as <a href="http://www.bitsavers.org/components/ti/_dataBooks/1986_TI_2-um_CMOS_Standard_Cell_Data_Book.pdf">Texas Instruments</a>, NCR, GE/RCA, <a href="https://www.worldradiohistory.com/Archive-Electronics/80s/87/Electronics-1987-06-25.pdf#page=82">Fairchild</a>, Harris, <a href="https://www.worldradiohistory.com/Archive-ITT/80s/ITT-1983-58-No-4.pdf">ITT</a>, and Thomson introduced lines of standard cell products in the mid-1980s.   <a class="footnote-backref" href="#fnref:standard-cell-history" title="Jump back to footnote 17 in the text">↩</a></p> </li> </ol> </div> <div style='clear: both;'></div> </div> <div class='post-footer'> <div class='post-footer-line post-footer-line-1'><span class='post-comment-link'> <a class='comment-link' href='https://www.blogger.com/comment/fullpage/post/6264947694886887540/7582473692859841880' onclick=''> 4 comments: </a> </span> <span class='post-icons'> <span class='item-action'> <a href='https://www.blogger.com/email-post.g?blogID=6264947694886887540&postID=7582473692859841880' title='Email Post'> <img alt='' class='icon-action' height='13' src='http://img1.blogblog.com/img/icon18_email.gif' width='18'/> </a> </span> <span class='item-control blog-admin pid-1138732533'> <a href='https://www.blogger.com/post-edit.g?blogID=6264947694886887540&postID=7582473692859841880&from=pencil' title='Edit Post'> <img alt='' class='icon-action' height='18' src='https://resources.blogblog.com/img/icon18_edit_allbkg.gif' width='18'/> </a> </span> </span> <span class='post-backlinks post-comment-link'> </span> <div class='post-share-buttons goog-inline-block'> <a class='goog-inline-block share-button sb-email' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=7582473692859841880&target=email' target='_blank' title='Email This'><span class='share-button-link-text'>Email This</span></a><a class='goog-inline-block share-button sb-blog' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=7582473692859841880&target=blog' onclick='window.open(this.href, "_blank", "height=270,width=475"); return false;' target='_blank' title='BlogThis!'><span class='share-button-link-text'>BlogThis!</span></a><a class='goog-inline-block share-button sb-twitter' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=7582473692859841880&target=twitter' target='_blank' title='Share to X'><span class='share-button-link-text'>Share to X</span></a><a class='goog-inline-block share-button sb-facebook' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=7582473692859841880&target=facebook' onclick='window.open(this.href, "_blank", "height=430,width=640"); return false;' target='_blank' title='Share to Facebook'><span class='share-button-link-text'>Share to Facebook</span></a><a class='goog-inline-block share-button sb-pinterest' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=7582473692859841880&target=pinterest' target='_blank' title='Share to Pinterest'><span class='share-button-link-text'>Share to Pinterest</span></a> </div> </div> <div class='post-footer-line post-footer-line-2'><span class='post-labels'> Labels: <a href='http://www.righto.com/search/label/386' rel='tag'>386</a>, <a href='http://www.righto.com/search/label/electronics' rel='tag'>electronics</a>, <a href='http://www.righto.com/search/label/intel' rel='tag'>intel</a>, <a href='http://www.righto.com/search/label/reverse-engineering' rel='tag'>reverse-engineering</a> </span> </div> <div class='post-footer-line post-footer-line-3'></div> </div> </div> </div> </div></div> <div class="date-outer"> <div class="date-posts"> <div class='post-outer'> <div class='post hentry' itemprop='blogPost' itemscope='itemscope' itemtype='http://schema.org/BlogPosting'> <meta content='https://static.righto.com/images/386-xor/386-die-labeled-w600.jpg' itemprop='image_url'/> <meta content='6264947694886887540' itemprop='blogId'/> <meta content='8647315208322441005' itemprop='postId'/> <a name='8647315208322441005'></a> <h3 class='post-title entry-title' itemprop='name'> <a href='http://www.righto.com/2023/12/386-xor-circuits.html'>Two interesting XOR circuits inside the Intel 386 processor</a> </h3> <div class='post-header'> <div class='post-header-line-1'></div> </div> <div class='post-body entry-content' id='post-body-8647315208322441005' itemprop='description articleBody'> <p>Intel's 386 processor (1985) was an important advance in the x86 architecture, not only moving to a 32-bit processor but also switching to a CMOS implementation. I've been reverse-engineering parts of the 386 chip and came across two interesting and completely different circuits that the 386 uses to implement an XOR gate: one uses standard-cell logic while the other uses pass-transistor logic. In this article, I take a look at those circuits.</p> <p><a href="https://static.righto.com/images/386-xor/386-die-labeled.jpg"><img alt="The die of the 386. Click this image (or any other) for a larger version." class="hilite" height="640" src="https://static.righto.com/images/386-xor/386-die-labeled-w600.jpg" title="The die of the 386. Click this image (or any other) for a larger version." width="600" /></a><div class="cite">The die of the 386. Click this image (or any other) for a larger version.</div></p> <p>The die photo above shows the two metal layers of the 386 die. The polysilicon and silicon layers underneath are mostly hidden by the metal. The black dots around the edges are the bond wires connecting the die to the external pins. The 386 is a complicated chip with 285,000 transistor sites. I've labeled the main functional blocks. The datapath in the lower left does the actual computations, controlled by the microcode ROM in the lower right.</p> <p>Despite the complexity of the 386, if you zoom in enough, you can see individual XOR gates. The red rectangle at the top (below) is a shift register for the chip's self-test. Zooming in again shows the silicon for an XOR gate implemented with pass transistors. The purple outlines reveal active silicon regions, while the stripes are transistor gates. The yellow rectangle zooms in on part of the standard-cell logic that controls the prefetch queue. The closeup shows the silicon for an XOR gate implemented with two logic gates. Counting the stripes shows that the first XOR gate is implemented with 8 transistors while the second uses 10 transistors. I'll explain below how these transistors are connected to form the XOR gates.</p> <p><a href="https://static.righto.com/images/386-xor/die-zoom.jpg"><img alt="The die of the 386, zooming in on two XOR gates." class="hilite" height="489" src="https://static.righto.com/images/386-xor/die-zoom-w600.jpg" title="The die of the 386, zooming in on two XOR gates." width="600" /></a><div class="cite">The die of the 386, zooming in on two XOR gates.</div></p> <h2>A brief introduction to CMOS</h2> <p>CMOS circuits are used in almost all modern processors. These circuits are built from two types of transistors: NMOS and PMOS. These transistors can be viewed as switches between the <em>source</em> and <em>drain</em> controlled by the <em>gate</em>. A high voltage on the gate of an NMOS transistor turns the transistor on, while a low voltage on the gate of a PMOS transistor turns the transistor on. An NMOS transistor is good at pulling the output low, while a PMOS transistor is good at pulling the output high. Thus, NMOS and PMOS transistors are opposites in many ways; they are <em>complementary</em>, which is the "C" in CMOS.</p> <p><a href="https://static.righto.com/images/386-xor/mosfet.jpg"><img alt="Structure of a MOS transistor. Although the transistor's name represents the Metal-Oxide-Semiconductor layers, modern MOS transistors typically use polysilicon instead of metal for the gate." class="hilite" height="207" src="https://static.righto.com/images/386-xor/mosfet-w400.jpg" title="Structure of a MOS transistor. Although the transistor's name represents the Metal-Oxide-Semiconductor layers, modern MOS transistors typically use polysilicon instead of metal for the gate." width="400" /></a><div class="cite">Structure of a MOS transistor. Although the transistor's name represents the Metal-Oxide-Semiconductor layers, modern MOS transistors typically use polysilicon instead of metal for the gate.</div></p> <p>In a CMOS circuit, the NMOS and PMOS transistors work together, with the NMOS transistors pulling the output low as needed while the PMOS transistors pull the output high. By arranging the transistors in different ways, different logic gates can be created. The diagram below shows a NAND gate constructed from two PMOS transistors (top) and two NMOS transistors (bottom). If both inputs are high, the NMOS transistors turn on and pull the output low. But if either input is low, a PMOS transistor will pull the output high. Thus, the circuit below implements a NAND gate.</p> <p><a href="https://static.righto.com/images/386-xor/nand.png"><img alt="A NAND gate implemented in CMOS." class="hilite" height="177" src="https://static.righto.com/images/386-xor/nand-w160.png" title="A NAND gate implemented in CMOS." width="160" /></a><div class="cite">A NAND gate implemented in CMOS.</div></p> <p>Notice that NMOS and PMOS transistors have an inherent inversion: a high input produces a low (for NMOS) or a low input produces a high (for PMOS). Thus, it is straightforward to produce logic circuits such as an inverter, NAND gate, NOR gate, or an AND-OR-INVERT gate. However, producing an XOR (exclusive-or) gate doesn't work with this approach: an XOR gate produces a 1 if either input is high, but not both.<span id="fnref:and"><a class="ref" href="#fn:and">1</a></span> The XNOR (exclusive-NOR) gate, the complement of XOR, also has this problem. As a result, chips often have creative implementations of XOR gates.</p> <h2>The standard-cell two-gate XOR circuit</h2> <p>Parts of the 386 were implemented with standard-cell logic. The idea of standard-cell logic is to build circuitry out of standardized building blocks that can be wired by a computer program. In earlier processors such as the 8086, each transistor was carefully positioned by hand to create a chip layout that was as dense as possible. This was a tedious, error-prone process since the transistors were fit together like puzzle pieces. Standard-cell logic is more like building with LEGO. Each gate is implemented as a standardized block and the blocks are arranged in rows, as shown below. The space between the rows holds the wiring that connects the blocks.</p> <p><a href="https://static.righto.com/images/386-xor/standard-cell.jpg"><img alt="Some rows of standard-cell logic in the 386 processor. This is part of the segment descriptor control circuitry." class="hilite" height="410" src="https://static.righto.com/images/386-xor/standard-cell-w500.jpg" title="Some rows of standard-cell logic in the 386 processor. This is part of the segment descriptor control circuitry." width="500" /></a><div class="cite">Some rows of standard-cell logic in the 386 processor. This is part of the segment descriptor control circuitry.</div></p> <p>The advantage of standard-cell logic is that it is much faster to create a design since the process can be automated. The engineer described the circuit in terms of the logic gates and their connections. A computer algorithm placed the blocks so related blocks are near each other. An algorithm then routed the circuit, creating the wiring between the blocks. These "place and route" algorithms are challenging since it is an extremely difficult optimization problem, determining the best locations for the blocks and how to pack the wiring as densely as possible. At the time, the algorithm took a day on a powerful IBM mainframe to compute the layout. Nonetheless, the automated process was much faster than manual layout, cutting weeks off the development time for the 386. The downside is that the automated layout is less dense than manually optimized layout, with a lot more wasted space. (As you can see in the photo above, the density is low in the wiring channels.) For this reason, the 386 used manual layout for circuits where a dense layout was important, such as the datapath.</p> <p>In the 386, the standard-cell XOR gate is built by combining a NOR gate with an AND-NOR gate as shown below.<span id="fnref:xnor"><a class="ref" href="#fn:xnor">2</a></span> (Although AND-NOR looks complicated, it is implemented as a single gate in CMOS.) You can verify that if both inputs are 0, the NOR gate forces the output low, while if both inputs are 1, the AND gate forces the output low, providing the XOR functionality.</p> <p><a href="https://static.righto.com/images/386-xor/xor-schematic.png"><img alt="Schematic of an XOR circuit." class="hilite" height="157" src="https://static.righto.com/images/386-xor/xor-schematic-w300.png" title="Schematic of an XOR circuit." width="300" /></a><div class="cite">Schematic of an XOR circuit.</div></p> <p>The photo below shows the layout of this XOR gate as a standard cell. I have removed the metal and polysilicon layers to show the underlying silicon. The outlined regions are the active silicon, with PMOS above and NMOS below. The stripes are the transistor gates, normally covered by polysilicon wires. Notice that neighboring transistors are connected by shared silicon; there is no demarcation between the source of one transistor and the drain of the next.</p> <p><a href="https://static.righto.com/images/386-xor/xor-cell.jpg"><img alt="The silicon implementing the XOR standard cell. This image is rotated 180° from the layout on the die to put PMOS at the top." class="hilite" height="270" src="https://static.righto.com/images/386-xor/xor-cell-w300.jpg" title="The silicon implementing the XOR standard cell. This image is rotated 180° from the layout on the die to put PMOS at the top." width="300" /></a><div class="cite">The silicon implementing the XOR standard cell. This image is rotated 180° from the layout on the die to put PMOS at the top.</div></p> <p>The schematic below corresponds to the silicon above. Transistors <em>a</em>, <em>b</em>, <em>c</em>, and <em>d</em> implement the first NOR gate. Transistors <em>g</em>, <em>h</em>, <em>i</em>, and <em>j</em> implement the AND part of the AND-NOR gate. Transistors <em>e</em> and <em>f</em> implement the NOR input of the AND-NOR gate, fed from the first NOR gate. The standard cell library is designed so all the cells are the same height with a power rail at the top and a ground rail at the bottom. This allows the cells to "snap together" in rows. The wiring inside the cell is implemented in polysilicon and the lower metal layer (M1), while the wiring between cells uses the upper metal layer (M2) for vertical connections and lower metal (M1) for horizontal connections. This strategy allows vertical wires to pass over the cells without interfering with the cell's wiring.</p> <p><a href="https://static.righto.com/images/386-xor/xor-cell-schematic.png"><img alt="Transistor layout in the XOR standard cell." class="hilite" height="186" src="https://static.righto.com/images/386-xor/xor-cell-schematic-w500.png" title="Transistor layout in the XOR standard cell." width="500" /></a><div class="cite">Transistor layout in the XOR standard cell.</div></p> <p>One important factor in a chip such as the 386 is optimizing the sizes of transistors. If a transistor is too small, it will take too much time to switch its output line, reducing performance. But if a transistor is too large, it will waste power as well as slowing down the circuit that is driving it. Thus, the standard-cell library for the 386 includes several XOR gates of various sizes. The diagram below shows a considerably larger XOR standard cell. The cell is the same height as the previous XOR (as required by the standard cell layout), but it is much wider and the transistors inside the cell are taller. Moreover, the PMOS side uses pairs of transistors to double the current capacity. (NMOS has better performance than PMOS so doesn't require doubling of the transistors.) Thus, there are 10 PMOS transistors and 5 NMOS transistors in this XOR cell.</p> <p><a href="https://static.righto.com/images/386-xor/large-xor-cell.jpg"><img alt="A large XOR standard cell. This cell is also rotated from the die layout." class="hilite" height="232" src="https://static.righto.com/images/386-xor/large-xor-cell-w400.jpg" title="A large XOR standard cell. This cell is also rotated from the die layout." width="400" /></a><div class="cite">A large XOR standard cell. This cell is also rotated from the die layout.</div></p> <h2>The pass transistor circuit</h2> <p>Some parts of the 386 implement XOR gates completely differently, using <a href="https://en.wikipedia.org/wiki/Pass_transistor_logic">pass transistor logic</a>. The idea of pass transistor logic is to use transistors as switches that pass inputs through to the output, rather than using transistors as switches to pull the output high or low. The pass transistor XOR circuit uses 8 transistors, compared with 10 for the previous circuit.<span id="fnref:advantages"><a class="ref" href="#fn:advantages">3</a></span></p> <p>The die photo below shows a pass-transistor XOR circuit, highlighted in red. Note that the surrounding circuitry is irregular and much more tightly packed than the standard-cell circuitry. This circuit was laid out manually producing an optimized layout compared to standard cells. It has four PMOS transistors at the top and four NMOS transistors at the bottom.</p> <p><a href="https://static.righto.com/images/386-xor/xor-pass-die.jpg"><img alt="The pass-transistor XOR circuit on the die. The green regions are oxide that was not completely removed causing thin-film interference." class="hilite" height="376" src="https://static.righto.com/images/386-xor/xor-pass-die-w500.jpg" title="The pass-transistor XOR circuit on the die. The green regions are oxide that was not completely removed causing thin-film interference." width="500" /></a><div class="cite">The pass-transistor XOR circuit on the die. The green regions are oxide that was not completely removed causing thin-film interference.</div></p> <p>The schematic below shows the heart of the circuit, computing the exclusive-NOR (XNOR) of X and Y with four pass transistors. To understand the circuit, consider the four input cases for X and Y. If X and Y are both 0, PMOS transistor <em>a</em> will turn on (because Y is low), passing 1 to the XNOR output. (<span style="text-decoration:overline">X</span> is the complemented value of the X input.) If X and Y are both 1, PMOS transistor <em>b</em> will turn on (because <span style="text-decoration:overline">X</span> is low), passing 1. If X and Y are 1 and 0 respectively, NMOS transistor <em>c</em> will turn on (because X is high), passing 0. If X and Y are 0 and 1 respectively, transistor <em>d</em> will turn on (because Y is high), passing 0. Thus, the four transistors implement the XNOR function, with a 1 output if both inputs are the same.</p> <p><a href="https://static.righto.com/images/386-xor/xnor-pass.png"><img alt="Partial implementation of XNOR with four pass transistors." class="hilite" height="198" src="https://static.righto.com/images/386-xor/xnor-pass-w300.png" title="Partial implementation of XNOR with four pass transistors." width="300" /></a><div class="cite">Partial implementation of XNOR with four pass transistors.</div></p> <p>To make an XOR gate out of this requires two additional inverters. The first inverter produces <span style="text-decoration:overline">X</span> from X. The second inverter generates the XOR output by inverting the XNOR output. The output inverter also has the important function of buffering the output since the pass transistor output is weaker than the inputs. Since each inverter takes two transistors, the complete XOR circuit uses 8 transistors. The schematic below shows the full circuit. The <em>i1</em> transistors implement the input inverter and the <em>i2</em> transistors implement the output inverter. The layout of this schematic matches the earlier die photo.<span id="fnref:alternatives"><a class="ref" href="#fn:alternatives">5</a></span></p> <p><a href="https://static.righto.com/images/386-xor/xor-pass.png"><img alt="Implementation of NOR with eight pass transistors." class="hilite" height="197" src="https://static.righto.com/images/386-xor/xor-pass-w500.png" title="Implementation of NOR with eight pass transistors." width="500" /></a><div class="cite">Implementation of NOR with eight pass transistors.</div></p> <h2>Conclusions</h2> <p>An XOR gate may seem like a trivial circuit, but there is more going on than you might expect. I think it is interesting that there isn't a single solution for implementing XOR; even inside a single chip, multiple approaches can be used. (If you're interested in XOR circuits, I also looked at the <a href="https://www.righto.com/2013/09/understanding-z-80-processor-one-gate.html">XOR circuit in the Z80</a>.) It's also reassuring to see that even for a complex chip such as the 386, the circuitry can be broken down into logic gates and then understood at the transistor level.</p> <p>I plan to write more about the 386, so follow me on Twitter <a href="https://twitter.com/kenshirriff">@kenshirriff</a> or <a href="http://www.righto.com/feeds/posts/default">RSS</a> for updates. I'm also on Mastodon occasionally as <a href="https://oldbytes.space/@kenshirriff">@<span class="__cf_email__" data-cfemail="7219171c011a1b00001b1414321d1e16100b0617015c0102131117">[email protected]</span></a>.</p> <h2>Notes and references</h2> <div class="footnote"> <ol> <li id="fn:and"> <p>You can't create an AND or OR gate directly from CMOS either, but this isn't usually a problem. One approach is to create a NAND (or NOR) gate and then follow it with an inverter, but this requires an "extra" inverter. However, the inverter can often be eliminated by flipping the action of the next gate (using <a href="https://en.wikipedia.org/wiki/De_Morgan%27s_laws">De Morgan's laws</a>). For example, if you have AND gates feeding into an OR gate, you can change the circuit to use NAND gates feeding into a NAND gate, eliminating the inverters. Unfortunately, flipping the logic levels doesn't help with XOR gates, since XNOR is just as hard to produce. <a class="footnote-backref" href="#fnref:and" title="Jump back to footnote 1 in the text">↩</a></p> </li> <li id="fn:xnor"> <p>The 386 also uses XNOR standard-cell gates. These are implemented with the "opposite" circuit from XOR, swapping the AND and OR gates:</p> <p><a href="https://static.righto.com/images/386-xor/xnor-schematic.png"><img alt="Schematic of an XNOR circuit." class="hilite" height="174" src="https://static.righto.com/images/386-xor/xnor-schematic-w300.png" title="Schematic of an XNOR circuit." width="300" /></a><div class="cite">Schematic of an XNOR circuit.</div></p> <p> <a class="footnote-backref" href="#fnref:xnor" title="Jump back to footnote 2 in the text">↩</a></p> </li> <li id="fn:advantages"> <p>I'm not sure why some circuits in the 386 use standard logic for XOR while other circuits use pass transistor logic. I suspect that the standard XOR is used when the XOR gate is part of a standard-cell logic circuit, while the pass transistor XOR is used in hand-optimized circuits. There may also be performance advantages to one over the other. <a class="footnote-backref" href="#fnref:advantages" title="Jump back to footnote 3 in the text">↩</a></p> </li> <li id="fn:inverter"> <p>The first inverter can be omitted in the pass transistor XOR circuit if the inverted input happens to be available. In particular, if multiple XOR gates use the same input, one inverter can provide the inverted input to all of them, reducing the per-gate transistor count. <a class="footnote-backref" href="#fnref:inverter" title="Jump back to footnote 4 in the text">↩</a></p> </li> <li id="fn:alternatives"> <p>The pass transistor XOR circuit uses different layouts in different parts of the 386, probably because hand layout allows it to be optimized. For instance, the instruction decoder uses the XOR circuit below. This circuit has four PMOS transistors on the left and four NMOS transistors on the right.</p> <p><a href="https://static.righto.com/images/386-xor/decoder-xor.jpg"><img alt="An XOR circuit from the instruction decoder." class="hilite" height="236" src="https://static.righto.com/images/386-xor/decoder-xor-w200.jpg" title="An XOR circuit from the instruction decoder." width="200" /></a><div class="cite">An XOR circuit from the instruction decoder.</div></p> <p>The schematic shows the wiring of this circuit. Although the circuit is electrically the same as the previous pass-transistor circuit, the layout is different. In the previous circuit, several of the transistors were connected through their silicon, while this circuit has all the transistors separated and arranged in columns.</p> <p><a href="https://static.righto.com/images/386-xor/decoder-xor-schematic.png"><img alt="Schematic of the XOR circuit from the instruction decoder." class="hilite" height="320" src="https://static.righto.com/images/386-xor/decoder-xor-schematic-w250.png" title="Schematic of the XOR circuit from the instruction decoder." width="250" /></a><div class="cite">Schematic of the XOR circuit from the instruction decoder.</div></p> <p> <a class="footnote-backref" href="#fnref:alternatives" title="Jump back to footnote 5 in the text">↩</a></p> </li> </ol> </div> <div style='clear: both;'></div> </div> <div class='post-footer'> <div class='post-footer-line post-footer-line-1'><span class='post-comment-link'> <a class='comment-link' href='https://www.blogger.com/comment/fullpage/post/6264947694886887540/8647315208322441005' onclick=''> 10 comments: </a> </span> <span class='post-icons'> <span class='item-action'> <a href='https://www.blogger.com/email-post.g?blogID=6264947694886887540&postID=8647315208322441005' title='Email Post'> <img alt='' class='icon-action' height='13' src='http://img1.blogblog.com/img/icon18_email.gif' width='18'/> </a> </span> <span class='item-control blog-admin pid-1138732533'> <a href='https://www.blogger.com/post-edit.g?blogID=6264947694886887540&postID=8647315208322441005&from=pencil' title='Edit Post'> <img alt='' class='icon-action' height='18' src='https://resources.blogblog.com/img/icon18_edit_allbkg.gif' width='18'/> </a> </span> </span> <span class='post-backlinks post-comment-link'> </span> <div class='post-share-buttons goog-inline-block'> <a class='goog-inline-block share-button sb-email' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=8647315208322441005&target=email' target='_blank' title='Email This'><span class='share-button-link-text'>Email This</span></a><a class='goog-inline-block share-button sb-blog' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=8647315208322441005&target=blog' onclick='window.open(this.href, "_blank", "height=270,width=475"); return false;' target='_blank' title='BlogThis!'><span class='share-button-link-text'>BlogThis!</span></a><a class='goog-inline-block share-button sb-twitter' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=8647315208322441005&target=twitter' target='_blank' title='Share to X'><span class='share-button-link-text'>Share to X</span></a><a class='goog-inline-block share-button sb-facebook' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=8647315208322441005&target=facebook' onclick='window.open(this.href, "_blank", "height=430,width=640"); return false;' target='_blank' title='Share to Facebook'><span class='share-button-link-text'>Share to Facebook</span></a><a class='goog-inline-block share-button sb-pinterest' href='https://www.blogger.com/share-post.g?blogID=6264947694886887540&postID=8647315208322441005&target=pinterest' target='_blank' title='Share to Pinterest'><span class='share-button-link-text'>Share to Pinterest</span></a> </div> </div> <div class='post-footer-line post-footer-line-2'><span class='post-labels'> Labels: <a href='http://www.righto.com/search/label/386' rel='tag'>386</a>, <a href='http://www.righto.com/search/label/electronics' rel='tag'>electronics</a>, <a href='http://www.righto.com/search/label/intel' rel='tag'>intel</a>, <a href='http://www.righto.com/search/label/reverse-engineering' rel='tag'>reverse-engineering</a> </span> </div> <div class='post-footer-line post-footer-line-3'></div> </div> </div> </div> </div></div> <div class="date-outer"> <div class="date-posts"> <div class='post-outer'> <div class='post hentry' itemprop='blogPost' itemscope='itemscope' itemtype='http://schema.org/BlogPosting'> <meta content='https://static.righto.com/images/386-shift/386-die-labeled-w600.jpg' itemprop='image_url'/> <meta content='6264947694886887540' itemprop='blogId'/> <meta content='4099574851986162003' itemprop='postId'/> <a name='4099574851986162003'></a> <h3 class='post-title entry-title' itemprop='name'> <a href='http://www.righto.com/2023/12/386-barrel-shifter.html'>Reverse engineering the barrel shifter circuit on the Intel 386 processor die</a> </h3> <div class='post-header'> <div class='post-header-line-1'></div> </div> <div class='post-body entry-content' id='post-body-4099574851986162003' itemprop='description articleBody'> <p>The Intel 386 processor (1985) was a large step from the 286 processor, moving x86 to a 32-bit architecture. The 386 also dramatically improved the performance of shift and rotate operations by adding a "barrel shifter", a circuit that can shift by multiple bits in one step. The die photo below shows the 386's barrel shifter, highlighted in the lower left and taking up a substantial part of the die.</p> <p><a href="https://static.righto.com/images/386-shift/386-die-labeled.jpg"><img alt="The 386 die with the main functional blocks labeled. Click this image (or any other) for a larger version.)" class="hilite" height="641" src="https://static.righto.com/images/386-shift/386-die-labeled-w600.jpg" title="The 386 die with the main functional blocks labeled. Click this image (or any other) for a larger version.)" width="600" /></a><div class="cite">The 386 die with the main functional blocks labeled. Click this image (or any other) for a larger version.)</div></p> <p>Shifting is a useful operation for computers, moving a binary value left or right by one or more bits. Shift instructions can be used for multiplying or dividing by powers of two, and as part of more general multiplication or division. Shifting is also useful for extracting bit fields, aligning bitmap graphics, and many other tasks.<span id="fnref:barrel-shifter-history"><a class="ref" href="#fn:barrel-shifter-history">1</a></span></p> <p>Barrel shifters require a significant amount of circuitry. A common approach is to use a crossbar, a matrix of switches that can connect any input to any output. By closing switches along a desired diagonal, the input bits are shifted. The diagram below illustrates a 4-bit crossbar barrel shifter with inputs X (vertical) and outputs Y (horizontal). At each point in the grid, a switch (triangle) connects a vertical input line to a horizontal output line. Energizing the blue control line, for instance, passes the value through unchanged (X0 to Y0 and so forth). Energizing the green control line rotates the value by one bit position (X0 to Y1 and so forth, with X3 wrapping around to X0). Similarly, the circuit can shift by 2 or 3 bits. The shift control lines select the amount of shift. These lines run diagonally, which will be important later.</p> <p><a href="https://static.righto.com/images/386-shift/crossbar.png"><img alt="A four-bit crossbar switch with inputs X and outputs Y. Image by Cmglee, CC BY-SA 3.0." class="hilite" height="300" src="https://static.righto.com/images/386-shift/crossbar-w400.png" title="A four-bit crossbar switch with inputs X and outputs Y. Image by Cmglee, CC BY-SA 3.0." width="400" /></a><div class="cite">A four-bit crossbar switch with inputs X and outputs Y. Image by <a href="https://en.wikipedia.org/wiki/Barrel_shifter#/media/File:Crossbar_barrel_shifter.svg">Cmglee</a>, <a href="https://creativecommons.org/licenses/by-sa/3.0">CC BY-SA 3.0</a>.</div></p> <p>The main problem with a crossbar barrel shifter is that it takes a lot of hardware. The 386's barrel shifter has a 64-bit input and a 32-bit output,<span id="fnref:64-bit"><a class="ref" href="#fn:64-bit">2</a></span> so the approach above would require 2048 switches (64×32). For this reason, the 386 uses a hybrid approach, as shown below. It has a 32×8 crossbar that can shift by 0 to 28 bits, but only in multiples of 4, making the circuit much smaller. The output from the crossbar goes to a second circuit that can shift by 0, 1, 2, or 3 bits. The combined circuitry supports an arbitrary shift, but requires less hardware than a complete crossbar. The inputs to the barrel shifter are two 32-bit values from the processor's register file, stored in latches for use by the shifter.</p> <p><a href="https://static.righto.com/images/386-shift/block-diagram.png"><img alt="Block diagram of the barrel shifter circuit." class="hilite" height="313" src="https://static.righto.com/images/386-shift/block-diagram-w150.png" title="Block diagram of the barrel shifter circuit." width="150" /></a><div class="cite">Block diagram of the barrel shifter circuit.</div></p> <p>The figure below shows how the shifter circuitry appears on the die; this image shows the two metal layers on the die's surface. The inputs from the register file are at the bottom, for bits 31 through 0. Above that, the input latches hold the two 32-bit inputs for the shifter. In the middle is the heart of the shift circuit, the crossbar matrix. This takes the two 32-bit inputs and produces a 32-bit output. The matrix is controlled by sloping polysilicon lines, driven by control circuitry on the right. The matrix output goes to the circuit that applies a shift of 0 to 3 positions. Finally, the outputs exit at the top, where they go to other parts of the CPU. The shifter performs right shifts, but as will be explained below, the same circuit is used for the left shift instructions.</p> <p><a href="https://static.righto.com/images/386-shift/shifter-die.jpg"><img alt="The barrel shifter circuitry as it appears on the die. I have cut out repetitive circuitry from the middle because the complete image is too wide to display clearly." class="hilite" height="468" src="https://static.righto.com/images/386-shift/shifter-die-w700.jpg" title="The barrel shifter circuitry as it appears on the die. I have cut out repetitive circuitry from the middle because the complete image is too wide to display clearly." width="700" /></a><div class="cite">The barrel shifter circuitry as it appears on the die. I have cut out repetitive circuitry from the middle because the complete image is too wide to display clearly.</div></p> <h2>The barrel shifter crossbar matrix</h2> <p>In this section, I'll describe the matrix part of the barrel shifter circuit. The shift matrix takes 32-bit values <code>a</code> and <code>b</code>. Value <code>b</code> is shifted to the right, with bits from <code>a</code> filling in at the left, producing a 32-bit output. (As will be explained below, the output is actually 37 bits due to some complications, but ignore that for now.) The shift count is a multiple of 4 from 0 to 28.</p> <p>The diagram below illustrates the structure of the shift matrix. The two 32-bit inputs are provided at the bottom, interleaved, and run vertically. The 32 output lines run horizontally. The 8 control lines run diagonally, activating the switches (black dots) to connect inputs and outputs. (For simplicity, only 3 control lines are shown.) For a shift of 0, control line 0 (red) is selected and the output is b<sub>31</sub>b<sub>30</sub>...b<sub>1</sub>b<sub>0</sub>. (You can verify this by matching up inputs to outputs through the dots along the red line.)</p> <p><a href="https://static.righto.com/images/386-shift/matrix-diagram.png"><img alt="Diagram of the shift matrix, showing three of the shift control lines." class="hilite" height="309" src="https://static.righto.com/images/386-shift/matrix-diagram-w600.png" title="Diagram of the shift matrix, showing three of the shift control lines." width="600" /></a><div class="cite">Diagram of the shift matrix, showing three of the shift control lines.</div></p> <p>For a shift right of 4, the cyan control line is activated. It can be seen that the output in this case is a<sub>3</sub>a<sub>2</sub>a<sub>1</sub>a<sub>0</sub>b<sub>31</sub>b<sub>30</sub>...b<sub>5</sub>b<sub>4</sub>, shifting <code>b</code> to the right 4 bits and filling in four bits from <code>a</code> as desired. For a shift of 28, the purple control line is activated, producing the output a<sub>27</sub>...a<sub>0</sub>b<sub>31</sub>...b<sub>28</sub>. Note that the control lines are spaced four bits apart, which is why the matrix only shifts by a multiple of 4. Another important feature is that below the red diagonal, the b inputs are connected to the output, while above the diagonal, the a inputs are connected to the output. (In other words, the black dots are shifted to the right above the diagonal.) This implements the 64-bit support, taking bits from <code>a</code> or <code>b</code> as appropriate.</p> <p>Looking at the implementation on the die, the vertical wires use the lower metal layer (metal 1) while the horizontal wires use the upper metal layer (metal 2), so the wires don't intersect. NMOS transistors are used as the switches to connect inputs and outputs.<span id="fnref:multiplexer"><a class="ref" href="#fn:multiplexer">4</a></span> The transistors are controlled by diagonal wires constructed of polysilicon that form the transistor gates. When a particular polysilicon wire is energized, it turns on the transistors along a diagonal line, connecting those inputs and outputs.</p> <p>The image below shows the left side of the matrix.<span id="fnref:full-matrix"><a class="ref" href="#fn:full-matrix">5</a></span> The polysilicon control lines are the green horizontal lines stepping down to the right. These control the transistors, which appear as columns of blue-gray squares next to the polysilicon lines. The metal layers have been removed; the position of the lower metal 1 layer is visible in the vertical bluish lines.</p> <p><a href="https://static.righto.com/images/386-shift/matrix-die.jpg"><img alt="The left side of the matrix as it appears on the die." class="hilite" height="460" src="https://static.righto.com/images/386-shift/matrix-die-w600.jpg" title="The left side of the matrix as it appears on the die." width="600" /></a><div class="cite">The left side of the matrix as it appears on the die.</div></p> <p>The diagram below shows four of these transistors in the shifter matrix. There are four circuitry layers involved. The underlying silicon is pinkish gray; the active regions are the squares with darker borders. Next is the polysilicon (green), which forms the control lines and the transistor gates. The lower metal layer (metal 1) forms the blue vertical lines that connect to the transistors.<span id="fnref:metal"><a class="ref" href="#fn:metal">3</a></span> The upper metal layer (metal 2) forms the horizontal bit output lines. Finally, the small black dots are the vias that connect metal 1 and metal 2. (The well taps are silicon regions connected to ground to prevent latch-up.)</p> <p><a href="https://static.righto.com/images/386-shift/matrix-closeup.jpg"><img alt="Four transistors in the shifter matrix. The polysilicon and metal lines have been drawn in." class="hilite" height="261" src="https://static.righto.com/images/386-shift/matrix-closeup-w450.jpg" title="Four transistors in the shifter matrix. The polysilicon and metal lines have been drawn in." width="450" /></a><div class="cite">Four transistors in the shifter matrix. The polysilicon and metal lines have been drawn in.</div></p> <p>To see how this works, suppose the upper polysilicon line is activated, turning on the top two transistors. The two vertical bit-in lines (blue) will be connected through the transistors to the top two bit out lines (purple), by way of the short light blue metal segments and the via (black dot). However, if the lower polysilicon line is activated, the bottom two transistors will be turned on. This will connect the bit-in lines to the fifth and sixth bit-out lines, four lines down from the previous ones. Thus, successive polysilicon lines shift the connections down by four lines at a time, so the shifts change in steps of 4 bit positions.</p> <p>As mentioned earlier, to support the 64-bit input, the transistors below the diagonal are connected to <code>b</code> input while the transistors above the diagonal are connected to the <code>a</code> input. The photo below shows the physical implementation: the four upper transistors are shifted to the right by one wire width, so they connect to vertical <code>a</code> wires, while the four lower transistors are connected to <code>b</code> wires. (The metal wires were removed for this photo to show the transistors.)</p> <p><a href="https://static.righto.com/images/386-shift/matrix-shifted.jpg"><img alt="This photo of the underlying silicon shows eight transistors. The top four transistors are shifted one position to the right. the irregular lines are remnants of other layers that I couldn't completely remove from the die." class="hilite" height="379" src="https://static.righto.com/images/386-shift/matrix-shifted-w300.jpg" title="This photo of the underlying silicon shows eight transistors. The top four transistors are shifted one position to the right. the irregular lines are remnants of other layers that I couldn't completely remove from the die." width="300" /></a><div class="cite">This photo of the underlying silicon shows eight transistors. The top four transistors are shifted one position to the right. the irregular lines are remnants of other layers that I couldn't completely remove from the die.</div></p> <p>In the matrix, the output signals run horizontally. In order for signals to exit the shifter from the top of the matrix, each horizontal output wire is connected to a vertical output wire. Meanwhile, other processor signals (such as the register write data) must also pass vertically through the shifter region. The result is a complicated layout, packing everything together as tightly as possible.</p> <h3>The precharge/keepers</h3> <p>At the left and the right of the barrel shifter, repeated blocks of circuitry are visible. These blocks contain precharge and <a href="https://en.wikipedia.org/wiki/Bus-holder">keeper</a> circuits to hold the value on one of the lines. During the first clock phase, each horizontal bit line is precharged to +5 volts. Next, the matrix is activated and horizontal lines may be pulled low. If the line is not pulled low, the inverter and PMOS transistor will continuously pull the line high. The inverter and transistor can be viewed as a bus keeper, essentially a weak latch to hold the line in the 1 state. The keeper uses relatively weak transistors, so the line can be pulled low when the barrel shifter is activated. The purpose of the keeper is to ensure that the line doesn't drift into a state between 0 and 1. This is a bad situation with CMOS circuitry, since the pull-up and pull-down transistors could both turn on, yielding a short circuit.</p> <p><a href="https://static.righto.com/images/386-shift/keeper.png"><img alt="The precharge/keeper circuit" class="hilite" height="101" src="https://static.righto.com/images/386-shift/keeper-w300.png" title="The precharge/keeper circuit" width="300" /></a><div class="cite">The precharge/keeper circuit</div></p> <p>The motivation behind this design is that implementing the matrix with "real" CMOS would require twice as many transistors. By implementing the matrix with NMOS transistors only, the size is reduced. In a standard NMOS implementation, pull-up transistors would continuously pull the lines high, but this results in fairly high power consumption. Instead, the precharge circuit pulls the line high at the start. But this results in dynamic logic, dependent on the capacitance of the circuit to hold the charge. To avoid the charge leaking away, the keeper circuit keeps the line high until it is pulled low. Thus, this circuit minimizes the area of the matrix as well as minimizing power consumption.</p> <p>There are 37 keepers in total for the 37 output lines from the matrix.<span id="fnref:keeper-structure"><a class="ref" href="#fn:keeper-structure">6</a></span> (The extra 5 lines will be explained below.) The photo below shows one block of three keepers; the metal has been removed to show the silicon transistors and some of the polysilicon (green).</p> <p><a href="https://static.righto.com/images/386-shift/keeper.jpg"><img alt="One block of keeper circuitry, to the right of the shift matrix. This block has 12 transistors, supporting three bits." class="hilite" height="225" src="https://static.righto.com/images/386-shift/keeper-w400.jpg" title="One block of keeper circuitry, to the right of the shift matrix. This block has 12 transistors, supporting three bits." width="400" /></a><div class="cite">One block of keeper circuitry, to the right of the shift matrix. This block has 12 transistors, supporting three bits.</div></p> <h2>The register latches</h2> <p>At the bottom of the shift circuit, two latches hold the two 32-bit input values. The 386 has multi-ported registers, so it can access two registers and write a third register at the same time. This allows the shift circuit to load both values at the same time. I believe that a value can also come from the 386's constant ROM, which is useful for providing 0, 1, or all-ones to the shifter.</p> <p>The schematic below shows the register latches for one bit of the shifter. Starting at the bottom are the two inputs from the register file (one appears to be inverted for no good reason). Each input is stored in a latch, using the standard 386 latch circuit.<span id="fnref:latch"><a class="ref" href="#fn:latch">7</a></span> The latched input is gated by the clock and then goes through multiplexers allowing either value to be used as either input to the shifter. (The shifter takes two 32-bit inputs and this multiplexer allows the inputs to be swapped to the other sides of the shifter.) A second latch stage holds the values for the output; this latch is cleared during the first clock phase and holds the desired value during the second clock phase.</p> <p><a href="https://static.righto.com/images/386-shift/reg-latch.png"><img alt="Circuit for one bit of the register latch." class="hilite" height="584" src="https://static.righto.com/images/386-shift/reg-latch-w350.png" title="Circuit for one bit of the register latch." width="350" /></a><div class="cite">Circuit for one bit of the register latch.</div></p> <p>The die photo below shows the register latch circuit, contrasting the metal layers (left) with the silicon layer (right). The dark spots in the metal image are vias between the metal layers or connections to the underlying silicon or polysilicon. The metal layer is very dense with vertical wiring in the lower metal 1 layer and horizontal wiring in the upper metal 2 layer. The density of the chip seems to be constrained by the metal wiring more than the density of the transistors.</p> <p><a href="https://static.righto.com/images/386-shift/reg.jpg"><img alt="One of the register latch circuits." class="hilite" height="481" src="https://static.righto.com/images/386-shift/reg-w350.jpg" title="One of the register latch circuits." width="350" /></a><div class="cite">One of the register latch circuits.</div></p> <h2>The 0-3 shifter</h2> <p>The shift matrix can only shift in steps of 4 bits. To support other shifts, a circuit at the top of the shifter provides a shift of 0 to 3 bits. In conjunction, these circuits permit a shift by an arbitrary amount.<span id="fnref:log"><a class="ref" href="#fn:log">8</a></span> The schematic below shows the circuit. A bit enters at the bottom. The first shift stage passes the bit through, or sends it one bit position to the right. The second stage passes the bit through, or sends it two bit positions to the right. Thus, depending on the control lines, each bit can be shifted by 0 to 3 positions to the right. At the top, a transistor pulls the circuit low to initialize it; the NOR gate at the bottom does the same. A keeper transistor holds the circuit low until a data bit pulls it high.</p> <p><a href="https://static.righto.com/images/386-shift/output-shift.png"><img alt="One bit of the 0-3 shifter circuit." class="hilite" height="510" src="https://static.righto.com/images/386-shift/output-shift-w280.png" title="One bit of the 0-3 shifter circuit." width="280" /></a><div class="cite">One bit of the 0-3 shifter circuit.</div></p> <p>The diagram below shows the silicon implementation corresponding to two copies of the schematic above. The shifters are implemented in pairs to slightly optimize the layout. In particular, the two NOR gates are mirrored so the power connection can be shared. This is a small optimization, but it illustrates that the 386 designers put a lot of work into making the layout dense.</p> <p><a href="https://static.righto.com/images/386-shift/shift03.jpg"><img alt="Two bits of the 0-3 shifter circuit as it appears on the die." class="hilite" height="499" src="https://static.righto.com/images/386-shift/shift03-w500.jpg" title="Two bits of the 0-3 shifter circuit as it appears on the die." width="500" /></a><div class="cite">Two bits of the 0-3 shifter circuit as it appears on the die.</div></p> <h2>Complications</h2> <p>As is usually the case with x86, there are a few complications. One complication is that the shift matrix has 37 outputs, rather than the expected 32. There are two reasons behind this. First, the upper shifter will shift right by up to 3 positions, so it needs 3 extra bits. Thus, the matrix needs to output bits 0 through 34 so three bits can be discarded. Second, shift instructions usually produce a carry bit from the last bit shifted out of the word. To support this, the shift matrix provides an extra bit at both ends for use as the carry. The result is that the matrix produces 37 outputs, which can be viewed as bits -1 through 35.</p> <p>Another complication is that the x86 instruction set supports shifts on bytes and 16-bit words as well as 32-bit words. If you put two 8-bit bytes into the shifter, there will be 24 unused bits in between, posing a problem for the shifter. The solution is that some of the diagonal control lines in the matrix are split on byte and word boundaries, allowing an 8- or 16-bit value to be shifted independently. For example, you can perform a 4-bit right shift on the right-hand byte, and a 28-bit right shift on the left-hand byte. This brings the two bytes together in the result, yielding the desired 4-bit right shift. As a result, there are 18 diagonal control lines in the shifter (if I counted correctly), rather than the expected 8 control lines. This makes the circuitry to drive the control lines more complicated, as it must generate different signals depending on the size of the operand.</p> <h2>The control circuitry</h2> <p>The control circuitry at the right of the shifter drives the diagonal polysilicon lines in the matrix, selecting the desired shift. It also generates control signals for the 0-3 shifter, selecting a shift-by-1 or shift-by-2 as necessary. This circuitry operates under the control of the microcode, which tells it when to shift. It gets the shift amount from the instruction or the <code>CL</code> register and generates the appropriate control signals.</p> <p>The distribution of control signals is more complex than you might expect. If possible, the polysilicon diagonals are connected on the right of the matrix to the control circuitry, providing a direct connection. However, many of the diagonals do not extend all the way to the right, either because they start on the left or because they are segmented for 8- or 16-bit values. Some of these signals are transmitted through polysilicon lines that run underneath the matrix. Others are transmitted through horizontal metal lines that run through the register latches. (These latches don't use many horizontal lines, so there is available space to route other signals.) These signals then ascend through the matrix at various points to connect with the polysilicon lines. This shows that the routing of this circuitry is carefully optimized to make it as compact as possible. Moreover, these "extra" lines disrupt the layout; the matrix is almost a regular pattern, but it has small irregularities throughout.</p> <h2>Implementing x86 shifts and rotates with the barrel shifter</h2> <p>The x86 has a variety of shift and rotate instructions.<span id="fnref:shift-history"><a class="ref" href="#fn:shift-history">9</a></span> It is interesting to consider how they are implemented using the barrel shifter, since it is not always obvious. In this section, I'll discuss the instructions supported by the 386.</p> <p>One important principle is that even though the circuitry shifts to the right, by changing the inputs this can achieve a shift to the left. To make this concrete, consider two input words <code>a</code> and <code>b</code>, with the shifter extracting the portion in red below. (I'll use 8-bit examples instead of 32-bit here and below to keep the size manageable.) The circuit shifts <code>b</code> to the right five bits, inserting bits from <code>a</code> at the left. Alternatively, the result can be viewed as shifting <code>a</code> to the left three bits, inserting bits from <code>b</code> at the right. Thus, the same result can be viewed as a right shift of <code>b</code> or a left shift of <code>a</code>. This holds in general, with a 32-bit right shift by N bits equivalent to a left shift by 32-N bits, depending on which word<span id="fnref:word"><a class="ref" href="#fn:word">10</a></span> you focus on.</p> <p><span class="mono">a<sub>7</sub>a<sub>6</sub>a<sub>5</sub><span class="box">a<sub>4</sub>a<sub>3</sub>a<sub>2</sub>a<sub>1</sub>a<sub>0</sub>b<sub>7</sub>b<sub>6</sub>b<sub>5</sub></span>b<sub>4</sub>b<sub>3</sub>b<sub>2</sub>b<sub>1</sub>b<sub>0</sub></span></p> <h3>Double shifts</h3> <p>The double-shift instructions (Shift Left Double (SHLD) and Shift Right Double (SHRD)) were new in the 386, shifting two 32-bit values to produce a 32-bit result. The last bit shifted out goes into the carry flag (CF). These instructions map directly onto the behavior of the barrel shifter, so I'll start with them.</p> <p><a href="https://static.righto.com/images/386-shift/doubleshifts.png"><img alt="Actions of the double shift instructions." class="hilite" height="288" src="https://static.righto.com/images/386-shift/doubleshifts-w400.png" title="Actions of the double shift instructions." width="400" /></a><div class="cite">Actions of the double shift instructions.</div></p> <p>The examples below show how the shifter implements the <code>SHLD</code> and <code>SHRD</code> instructions; the shifter output is highlighted in red. (These examples use an 8-bit source (<code>s</code>) and destination (<code>d</code>) to keep them manageable.) In either case, 3 bits of the source are shifted into the destination; shifting left or right is just a matter of whether the destination is on the left or right.</p> <p><code>SHLD 3</code>: <span class="mono">ddd<span class="box">dddddsss</span>sssss</span></p> <p><code>SHRD 3</code>: <span class="mono">sssss<span class="box">sssddddd</span>ddd</span></p> <h3>Shifts</h3> <p>The basic shift instructions are probably the simplest. Shift Arithmetic Left (SAL) and Shift Logical Left (SHL) are synonyms, shifting the destination to the left and filling with zeroes. This can be accomplished by performing a shift with the word on the left and zeroes on the right. Shift Logical Right (SHR) is the opposite, shifting to the right and filling with zeros. This can be accomplished by putting the word on the right and zeroes on the left. Shift Arithmetic Right (SAR) is a bit different. It fills with the sign bit, the top bit. The purpose of this is to shift a signed number while preserving its sign. It can be implemented by putting all zeroes or all ones on the left, depending on the sign bit. Thus, the shift instructions map nicely onto the barrel shifter.</p> <p><a href="https://static.righto.com/images/386-shift/shifts.png"><img alt="Actions of the shift instructions." class="hilite" height="249" src="https://static.righto.com/images/386-shift/shifts-w400.png" title="Actions of the shift instructions." width="400" /></a><div class="cite">Actions of the shift instructions.</div></p> <p>The 8-bit examples below show how the shifter accomplishes the <code>SHL</code>, <code>SHR</code>, and <code>SAR</code> instructions. The destination value <code>d</code> is loaded into one half of the shifter. For <code>SAR</code>, the value's sign bit <code>s</code> is loaded into the other half of the shifter, while the other instructions load <code>0</code> into the other half of the shifter. The red box shows the output from the shifter, selected from the input.</p> <p><code>SHL 3</code>: <span class="mono">ddd<span class="box">ddddd000</span>00000</span></p> <p><code>SHR 3</code>: <span class="mono">00000<span class="box">000ddddd</span>ddd</span></p> <p><code>SAR 3</code>: <span class="mono">sssss<span class="box">sssddddd</span>ddd</span></p> <h3>Rotates</h3> <p>Unlike the shift instructions, the rotate instructions preserve all the bits. As bits shift off one end, they fill in the other end, so the bit sequence rotates. A rotate left or right is implemented by putting the same word on the left and right.</p> <p><a href="https://static.righto.com/images/386-shift/rotates.png"><img alt="Actions of the rotate instructions." class="hilite" height="186" src="https://static.righto.com/images/386-shift/rotates-w400.png" title="Actions of the rotate instructions." width="400" /></a><div class="cite">Actions of the rotate instructions.</div></p> <p>The shifter implements rotates as shown below, using the destination value as both shifter inputs. A left shift by N bits is implemented by shifting right by 32-N bits.</p> <p><code>ROL 3</code>: <span class="mono">d<sub>7</sub>d<sub>6</sub>d<sub>5</sub><span class="box">d<sub>4</sub>d<sub>3</sub>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub>d<sub>7</sub>d<sub>6</sub>d<sub>5</sub></span>d<sub>4</sub>d<sub>3</sub>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub></span></p> <p><code>ROR 3</code>: <span class="mono">d<sub>7</sub>d<sub>6</sub>d<sub>5</sub>d<sub>4</sub>d<sub>3</sub><span class="box">d<sub>2</sub>d<sub>1</sub>d<sub>0</sub>d<sub>7</sub>d<sub>6</sub>d<sub>5</sub>d<sub>4</sub>d<sub>3</sub></span>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub></span></p> <h3>Rotates through carry</h3> <p>The rotate through carry instructions perform 33-bit rotates, rotating the value through the carry bit. You might wonder how the barrel shifter can perform a 33-bit rotate, and the answer is that it can't. Instead, the instruction takes multiple steps. If you look at the instruction timings, the other shifts and rotates take three clock cycles. Rotating through the carry, however, takes nine clock cycles, performing multiple steps under the control of the microcode.</p> <p><a href="https://static.righto.com/images/386-shift/rotatesc.png"><img alt="Actions of the rotate through carry instructions." class="hilite" height="185" src="https://static.righto.com/images/386-shift/rotatesc-w400.png" title="Actions of the rotate through carry instructions." width="400" /></a><div class="cite">Actions of the rotate through carry instructions.</div></p> <style type="text/css"> .mono {font-family: monospace; font-size: 100%;} .box {border: 2px solid red; padding: 2px 0;} </style> <p>Without looking at the microcode, I can only speculate how it takes place. One sequence would be to get the top bits by putting zeroes in the right 32 bits and shifting. Next, get the bottom bits by putting the carry bit in the left 32 bits and shifting one bit more. (That is, set the left 32-bit input to either the constant 0 or 1, depending on the carry.) Finally, the result can be generated by ORing the two shift values together. The example below shows how an <code>RCL 3</code> could be implemented. In the second step, the carry value <code>C</code> is loaded into the left side of the shifter, so it can get into the result. Note that bit <span class="mono">d<sub>5</sub></span> ends up in the carry bit, rather than the result. The <code>RCR</code> instruction would be similar, but adjusting the shift parameters accordingly.</p> <p>First shift: <span class="mono">d<sub>7</sub>d<sub>6</sub>d<sub>5</sub><span class="box">d<sub>4</sub>d<sub>3</sub>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub>000</span>00000</span></p> <p>Second shift: <span class="mono">00<span class="box">00000Cd<sub>7</sub>d<sub>6</sub></span>d<sub>5</sub>d<sub>4</sub>d<sub>3</sub>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub></span></p> <p>Result from <code>OR</code>: <span class="mono">d<sub>4</sub>d<sub>3</sub>d<sub>2</sub>d<sub>1</sub>d<sub>0</sub>Cd<sub>7</sub>d<sub>6</sub></span></p> <h2>Conclusions</h2> <p>The shifter circuit illustrates how the rapidly increasing transistor counts in the 1980s allowed new features. Programming languages make it easy to shift numbers with an expression such as <code>a>>5</code>. But it takes a lot of hardware in the processor to perform these shifts efficiently. The additional hardware of the 386's barrel shifter dramaticallly improved shift performance for shifts and rotates compared to earlier x86 processors. I estimate that the barrel shifter requires about 2000 transistors, about half the number of the entire 6502 processor (1975). But by 1985, putting 2000 transistors into a feature was practical. (In total, the 386 contains 285,000 transistors, a trivial number now, but a large number for the time.)</p> <p>I plan to write more about the 386, so follow me on Twitter <a href="https://twitter.com/kenshirriff">@kenshirriff</a> or <a href="http://www.righto.com/feeds/posts/default">RSS</a> for updates. I'm also on Mastodon occasionally as <a href="https://oldbytes.space/@kenshirriff">@<span class="__cf_email__" data-cfemail="bfd4dad1ccd7d6cdcdd6d9d9ffd0d3dbddc6cbdacc91cccfdedcda">[email protected]</span></a>.</p> <h2>Notes and references</h2> <div class="footnote"> <ol> <li id="fn:barrel-shifter-history"> <p>The earliest reference for a barrel shifter is often given as "A barrel switch design", Computer Design, 1972, but the idea of a barrel shifter goes back to 1964 at least. (The "barrel switch" name presumably comes from a physical barrel switch, a cylindrical multi-position switch such as a car ignition.) The CDC 6600 supercomputer (1964) had a 6-stage shifter able to shift up to 63 positions in one cycle (<a href="https://www.bitsavers.org/pdf/cdc/cyber/books/DesignOfAComputer_CDC6600.pdf#page=85">details</a>); it was called a "parallel shifting network" rather than a "barrel shifter". A Burroughs <a href="https://patents.google.com/patent/US3411139A/en">patent</a> filed in 1965 describes a barrel switch "capable of performing logical switching operations in a single time involving any amount of binary information," so the technology is older.</p> <p>Early microprocessors shifted by one bit position at a time. Although the Intel 8086 provided instructions to shift by multiple bits at a time, this was implemented internally by a microcode loop, so the more bits you shifted, the longer the instruction took, four clock cycles per bit. Shifting on the 286 was faster, taking one additional cycle for each bit position shifted.   The first ARM processor (ARM1, 1985) included a <a href="https://www.righto.com/2015/12/reverse-engineering-arm1-ancestor-of.html#:~:text=inverter%20is%20active.-,The%20barrel%20shifter,-The%20barrel%20shifter">32-bit barrel shifter</a>. It was considerably simpler than the 386's design, following ARM's RISC philosophy. <a class="footnote-backref" href="#fnref:barrel-shifter-history" title="Jump back to footnote 1 in the text">↩</a></p> </li> <li id="fn:64-bit"> <p>The 386 <a href="http://www.bitsavers.org/components/intel/80386/231732-001_80386_Hardware_Reference_Manual_1986.pdf#page=29">Hardware Reference Manual</a> states that the 386 contains a 64-bit barrel shifter. I find this description a bit inaccurate, since the output is only 32 bits, so the barrel shifter is much simpler than a full 64-bit barrel shifter. <a class="footnote-backref" href="#fnref:64-bit" title="Jump back to footnote 2 in the text">↩</a></p> </li> <li id="fn:metal"> <p>The 386 has two layers of metal. The vertical lines are in the lower layer of metal (metal 1) while the horizontal lines are in the upper layer of metal (metal 2). Transistors can only connect to lower metal, so the connection between the horizontal line and the transistor uses a short piece of lower metal to bridge the layers. <a class="footnote-backref" href="#fnref:metal" title="Jump back to footnote 3 in the text">↩</a></p> </li> <li id="fn:multiplexer"> <p>Each row of the matrix can be considered a multiplexer with 8 inputs, implemented by 8 pass transistors. One of the eight transistors is activated, passing that input to the output. <a class="footnote-backref" href="#fnref:multiplexer" title="Jump back to footnote 4 in the text">↩</a></p> </li> <li id="fn:full-matrix"> <p>The image below shows the full shift matrix. Click the image for a much larger view.</p> <p><a href="https://static.righto.com/images/386-shift/full-matrix.jpg"><img alt="The matrix with the metal layer removed." class="hilite" height="100" src="https://static.righto.com/images/386-shift/full-matrix-w600.jpg" title="The matrix with the metal layer removed." width="600" /></a><div class="cite">The matrix with the metal layer removed.</div></p> <p> <a class="footnote-backref" href="#fnref:full-matrix" title="Jump back to footnote 5 in the text">↩</a></p> </li> <li id="fn:keeper-structure"> <p>The keepers are arranged with 6 blocks of three on the left and 6 blocks of 3 on the right, plus an additional one at the bottom right. <a class="footnote-backref" href="#fnref:keeper-structure" title="Jump back to footnote 6 in the text">↩</a></p> </li> <li id="fn:latch"> <p>The standard latch in the 386 consists of two cross-coupled inverters forming a static circuit to hold a bit. The input goes through a transmission gate (back-to-back NMOS and PMOS transistors) to the inverters. One inverter is weak, so it can be overpowered by the input. The 8086, in contrast, uses dynamic latches that depend on the gate capacitance to hold a bit. <a class="footnote-backref" href="#fnref:latch" title="Jump back to footnote 7 in the text">↩</a></p> </li> <li id="fn:log"> <p>Some shifters take the idea of combining shift circuits to the extreme. If you combine a shift-by-one circuit, a shift-by-two circuit, a shift-by-four circuit, and so forth, you end up with a logarithmic shifter: selecting the appropriate stages provide an arbitrary shift. (This design was used in the CDC 6600.) This design has the advantage of reducing the amount of circuitry since it uses log<sub>2</sub>(N) layers rather than N layers. However, the logarithmic approach has performance disadvantages since the signals need to go through more circuitry. <a href="https://www.princeton.edu/~rblee/ELE572Papers/Fall04Readings/Shifter_Schulte.pdf">This paper</a> describes various design alternatives for barrel shifters. <a class="footnote-backref" href="#fnref:log" title="Jump back to footnote 8 in the text">↩</a></p> </li> <li id="fn:shift-history"> <p>The basic rotate left and right instructions date back to the Datapoint 2200, the <a href="https://www.righto.com/2023/08/datapoint-to-8086.html">ancestor</a> of the 8086 and x86. The rotate left through carry and rotate right through carry instructions in x86 were added in the Intel 8008 processor and the 8080 was the same. The MOS 6502 had a different set of rotates and shifts: arithmetic shift left, rotate left, logical shift right, and rotate right; the rotate instructions rotated through the carry. The Z-80 had a more extensive set: rotates left and right, either through the carry or not, shift left, shift right logical, shift right arithmetic, and 4-bit digit rotates left and right through two bytes. The 8086's set of rotates and shifts was similar to the Z-80, except it didn't have the digit rotates. The 8086 also supported shifting and rotating by multiple positions. This illustrates that there isn't a "natural" set of shift and rotate instructions. Instead, different processors supported different instructions, with complexity generally increasing over time. <a class="footnote-backref" href="#fnref:shift-history" title="Jump back to footnote 9 in the text">↩</a></p> </li> <li id="fn:word"> <p>The x86 uses "word" to refer to a 16-bit value and "double word" or "dword" to refer to a 32-bit value. 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class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2023/09/'> September </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2023/08/'> August </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2023/07/'> July </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span 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class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2023/01/'> January </a> <span class='post-count' dir='ltr'>(8)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/'> 2022 </a> <span class='post-count' dir='ltr'>(18)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/11/'> November </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/07/'> July </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/06/'> June </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/05/'> May </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/04/'> April </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/03/'> March </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/02/'> February </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2022/01/'> January </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/'> 2021 </a> <span class='post-count' dir='ltr'>(26)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/12/'> December </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/11/'> November </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/09/'> September </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/07/'> July </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/06/'> June </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/05/'> May </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/04/'> April </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/03/'> March </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/02/'> February </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2021/01/'> January </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/'> 2020 </a> <span class='post-count' dir='ltr'>(33)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/11/'> November </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/10/'> October </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/09/'> September </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/08/'> August </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/07/'> July </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/06/'> June </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/05/'> May </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/04/'> April </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/03/'> March </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2020/01/'> January </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/'> 2019 </a> <span class='post-count' dir='ltr'>(18)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/11/'> November </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/10/'> October </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/09/'> September </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/07/'> July </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/04/'> April </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/02/'> February </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2019/01/'> January </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/'> 2018 </a> <span class='post-count' dir='ltr'>(17)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/12/'> December </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/09/'> September </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/06/'> June </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/05/'> May </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/04/'> April </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/03/'> March </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/02/'> February </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2018/01/'> January </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/'> 2017 </a> <span class='post-count' dir='ltr'>(21)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/12/'> December </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/11/'> November </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/10/'> October </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/07/'> July </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/06/'> June </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/04/'> April </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/03/'> March </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/02/'> February </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2017/01/'> January </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/'> 2016 </a> <span class='post-count' dir='ltr'>(34)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/10/'> October </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/09/'> September </a> <span class='post-count' dir='ltr'>(8)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/08/'> August </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/07/'> July </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/06/'> June </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/05/'> May </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/04/'> April </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/03/'> March </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/02/'> February </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2016/01/'> January </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/'> 2015 </a> <span class='post-count' dir='ltr'>(12)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/11/'> November </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/10/'> October </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/05/'> May </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/03/'> March </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2015/02/'> February </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/'> 2014 </a> <span class='post-count' dir='ltr'>(13)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/12/'> December </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/10/'> October </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/09/'> September </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/05/'> May </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/03/'> March </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2014/02/'> February </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/'> 2013 </a> <span class='post-count' dir='ltr'>(24)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/11/'> November </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/09/'> September </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/08/'> August </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/07/'> July </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/06/'> June </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/04/'> April </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/03/'> March </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/02/'> February </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2013/01/'> January </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/'> 2012 </a> <span class='post-count' dir='ltr'>(10)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/12/'> December </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/11/'> November </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/10/'> October </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/05/'> May </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/03/'> March </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2012/02/'> February </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/'> 2011 </a> <span class='post-count' dir='ltr'>(11)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/07/'> July </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/05/'> May </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/04/'> April </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/03/'> March </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2011/02/'> February </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/'> 2010 </a> <span class='post-count' dir='ltr'>(22)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/11/'> November </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/10/'> October </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/08/'> August </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/06/'> June </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/05/'> May </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/04/'> April </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/03/'> March </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2010/01/'> January </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/'> 2009 </a> <span class='post-count' dir='ltr'>(22)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/12/'> December </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/11/'> November </a> <span class='post-count' dir='ltr'>(5)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/09/'> September </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/08/'> August </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/07/'> July </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/06/'> June </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/04/'> April </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/03/'> March </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/02/'> February </a> <span class='post-count' dir='ltr'>(2)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2009/01/'> January </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/'> 2008 </a> <span class='post-count' dir='ltr'>(27)</span> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/07/'> July </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/06/'> June </a> <span class='post-count' dir='ltr'>(1)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/05/'> May </a> <span class='post-count' dir='ltr'>(3)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/04/'> April </a> <span class='post-count' dir='ltr'>(4)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/03/'> March </a> <span class='post-count' dir='ltr'>(10)</span> </li> </ul> <ul class='hierarchy'> <li class='archivedate collapsed'> <a class='toggle' href='javascript:void(0)'> <span class='zippy'> ►  </span> </a> <a class='post-count-link' href='http://www.righto.com/2008/02/'> February </a> <span class='post-count' dir='ltr'>(6)</span> </li> </ul> </li> </ul> </div> </div> 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