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<div class="">On Jul 10, 2013, at 11:47 AM, Bradley Lucier <<a href="mailto:lucier@math.purdue.edu" class="">lucier@math.purdue.edu</a>> wrote:</div>
<br class="x_Apple-interchange-newline">
<div class=""><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">On
 06/12/2013 01:07 PM, Bradley Lucier wrote:</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<blockquote type="cite" class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; orphans:auto; text-align:start; text-indent:0px; text-transform:none; white-space:normal; widows:auto; word-spacing:0px; text-decoration:none">
<br class="">
Just for laughs and giggles, I decided to calculate 1,000,000,000 (yes, 9 zeros) digits of pi using Bakul Shah's Scheme program implementing the Chudnovsky algorithm. The computation used one CPU core:<br class="">
<br class="">
model name : Intel(R) Xeon(R) CPU X5570 @ 2.93GHz<br class="">
<br class="">
with a pretty good memory subsystem with 72GB of memory ...<br class="">
<br class="">
leibniz-172% gsi chud2<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10, CPU time: 0..<br class="">
Last 5 digits 26535.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100, CPU time: 0..<br class="">
Last 5 digits 70679.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000, CPU time: 0..<br class="">
Last 5 digits 1989.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10000, CPU time: .020000000000000004.<br class="">
Last 5 digits 75678.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100000, CPU time: .340022.<br class="">
Last 5 digits 24646.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000000, CPU time: 5.140321.<br class="">
Last 5 digits 58151.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10000000, CPU time: 83.765235.<br class="">
Last 5 digits 55897.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100000000, CPU time: 1327.790981.<br class="">
Last 5 digits 51592.<br class="">
Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000000000, CPU time: 41907.731069.<br class="">
Last 5 digits 45519.<br class="">
<br class="">
</blockquote>
<br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">This
 is the same program, run on my new desktop:</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">model
 name : Intel(R) Core(TM) i7-4770 CPU @ 3.40GHz</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">with
 16GB of RAM, which seems to run 2-3 times as fast as the server in the math department. (Luckily, a new server will be up and running soon.)</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Brad</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">firefly:~/programs/gambiteer>
 gsi chud2</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 10, CPU time: 0..</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 26535.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 100, CPU time: 0..</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 70679.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 1000, CPU time: 0..</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 1989.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 10000, CPU time: .012.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 75678.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 100000, CPU time: .172.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 24646.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 1000000, CPU time: 2.476.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 58151.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 10000000, CPU time: 38.7.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 55897.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 100000000, CPU time: 536.864.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 51592.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Chudnovsky's
 algorithm using binary splitting in Gambit Scheme: digits 1000000000, CPU time: 14459.672.</span><br class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<span class="" style="font-family:Helvetica; font-size:12px; font-style:normal; font-variant-caps:normal; font-weight:400; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important">Last
 5 digits 45519.</span></div>
</blockquote>
</div>
<br class="">
<div class="">A new run on a MacBook Pro with M1 Ultra (64GB memory) on one processor:</div>
<div class=""><br class="">
</div>
<div class="">
<div class="">[MacBook-Pro:~/programs/gambit] lucier% gsi -:m1000000 chud1</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10, CPU time: 1.419999999999963e-4.</div>
<div class="">Last 5 digits 26535.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100, CPU time: 7.099999999999815e-5.</div>
<div class="">Last 5 digits 70679.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000, CPU time: 6.139999999999965e-4.</div>
<div class="">Last 5 digits 1989.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10000, CPU time: .018569000000000002.</div>
<div class="">Last 5 digits 75678.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100000, CPU time: .123237.</div>
<div class="">Last 5 digits 24646.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000000, CPU time: 1.440205.</div>
<div class="">Last 5 digits 58151.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 10000000, CPU time: 21.505972999999997.</div>
<div class="">Last 5 digits 55897.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 100000000, CPU time: 294.886941.</div>
<div class="">Last 5 digits 51592.</div>
<div class="">Chudnovsky's algorithm using binary splitting in Gambit Scheme: digits 1000000000, CPU time: 7714.255436.</div>
<div class="">Last 5 digits 45519.</div>
</div>
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<div class="">[MacBook-Pro:~/programs/gambit] lucier% gsi -v</div>
<div class="">v4.9.4-30-g4c9a0bc3 20220331205952 arm-apple-darwin21.2.0 "./configure 'CC=gcc-11' '--enable-single-host' '--enable-march=native' '--enable-multiple-versions' '--enable-shared' '--enable-dynamic-clib'"</div>
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<div class="">So, it’s almost twice as fast as the 2013 i7-4770 (which was a sweet spot in historical Intel processor design in my opinion).</div>
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<div class="">I’ll include the program here just for info.</div>
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<div class="">Brad</div>
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