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Subject: Re: Extreme move path enumerations

Author: Andreas Stabel

Date: 05:38:15 08/22/03

Go up one level in this thread

On August 22, 2003 at 05:28:17, Steven Edwards wrote:

>The C++ chess programming toolkit CT has classes for working with time and
>frequency (i.e., inverse time).  It also has a class for handling English names
>for integers.  Plus, there are routines that know about SI (metric) magnitude
>prefixes.  These can be combined with a move path enumeration class aided by a
>transposition table for testing.
>
>Consider the following rather simple position:
>
>[D]4k3/8/8/8/8/8/8/4K3 w - -
>
>Here are the move path enumerations for the depth varying from one up to
>twenty-three:
>
>Depth: 1
>count: 5
>Total: five
>Frequency: 29.4118 Hz
>Period: 34 ms
>Cycles per node: 2.72e+07
>Clock: zero seconds
>
>Depth: 2
>count: 25
>Total: twenty-five
>Frequency: 138.889 Hz
>Period: 7.2 ms
>Cycles per node: 5.76e+06
>Clock: one second
>
>Depth: 3
>count: 170
>Total: one hundred seventy
>Frequency: 1.13333 KHz
>Period: 882.353 us
>Cycles per node: 705882
>Clock: zero seconds
>
>Depth: 4
>count: 1156
>Total: one thousand one hundred fifty-six
>Frequency: 7.70662 KHz
>Period: 129.759 us
>Cycles per node: 103807
>Clock: zero seconds
>
>Depth: 5
>count: 7922
>Total: seven thousand nine hundred twenty-two
>Frequency: 44.0111 KHz
>Period: 22.7215 us
>Cycles per node: 18177.2
>Clock: zero seconds
>
>Depth: 6
>count: 53896
>Total: fifty-three thousand eight hundred ninety-six
>Frequency: 283.663 KHz
>Period: 3.52531 us
>Cycles per node: 2820.25
>Clock: one second
>
>Depth: 7
>count: 375049
>Total: three hundred seventy-five thousand forty-nine
>Frequency: 1.97394 MHz
>Period: 506.6 ns
>Cycles per node: 405.28
>Clock: zero seconds
>
>Depth: 8
>count: 2591703
>Total: two million five hundred ninety-one thousand seven hundred three
>Frequency: 12.3415 MHz
>Period: 81.0274 ns
>Cycles per node: 64.8219
>Clock: zero seconds
>
>Depth: 9
>count: 17895172
>Total: seventeen million eight hundred ninety-five thousand one hundred
>seventy-two
>Frequency: 74.5635 MHz
>Period: 13.4114 ns
>Cycles per node: 10.7291
>Clock: zero seconds
>
>Depth: 10
>count: 122753895
>Total: one hundred twenty-two million seven hundred fifty-three thousand eight
>hundred ninety-five
>Frequency: 438.407 MHz
>Period: 2.28099 ns
>Cycles per node: 1.82479
>Clock: zero seconds
>
>Depth: 11
>count: 846285725
>Total: eight hundred forty-six million two hundred eighty-five thousand seven
>hundred twenty-five
>Frequency: 2.56451 GHz
>Period: 389.938 ps
>Cycles per node: 0.31195
>Clock: one second
>
>Depth: 12
>count: 5807121096
>Total: five billion eight hundred seven million one hundred twenty-one thousand
>ninety-six
>Frequency: 15.2819 GHz
>Period: 65.4369 ps
>Cycles per node: 0.0523495
>Clock: zero seconds
>
>Depth: 13
>count: 39881239565
>Total: thirty-nine billion eight hundred eighty-one million two hundred
>thirty-nine thousand five hundred sixty-five
>Frequency: 92.7471 GHz
>Period: 10.782 ps
>Cycles per node: 0.00862561
>Clock: one second
>
>Depth: 14
>count: 272980168768
>Total: two hundred seventy-two billion nine hundred eighty million one hundred
>sixty-eight thousand seven hundred sixty-eight
>Frequency: 557.105 GHz
>Period: 1.79499 ps
>Cycles per node: 0.001436
>Clock: zero seconds
>
>Depth: 15
>count: 1871752175983
>Total: one trillion eight hundred seventy-one billion seven hundred fifty-two
>million one hundred seventy-five thousand nine hundred eighty-three
>Frequency: 3.34242 THz
>Period: 299.184 fs
>Cycles per node: 0.000239347
>Clock: one second
>
>Depth: 16
>count: 12804538065718
>Total: twelve trillion eight hundred four billion five hundred thirty-eight
>million sixty-five thousand seven hundred eighteen
>Frequency: 20.3247 THz
>Period: 49.2013 fs
>Cycles per node: 3.9361e-05
>Clock: one second
>
>Depth: 17
>count: 87658645339246
>Total: eighty-seven trillion six hundred fifty-eight billion six hundred
>forty-five million three hundred thirty-nine thousand two hundred forty-six
>Frequency: 125.227 THz
>Period: 7.98551 fs
>Cycles per node: 6.38841e-06
>Clock: one second
>
>Depth: 18
>count: 599160694162071
>Total: five hundred ninety-nine trillion one hundred sixty billion six hundred
>ninety-four million one hundred sixty-two thousand seventy-one
>Frequency: 778.131 THz
>Period: 1.28513 fs
>Cycles per node: 1.0281e-06
>Clock: one second
>
>Depth: 19
>count: 4098371103275924
>Total: four quadrillion ninety-eight trillion three hundred seventy-one billion
>one hundred three million two hundred seventy-five thousand nine hundred
>twenty-four
>Frequency: 4.87901 PHz
>Period: 204.959 as
>Cycles per node: 1.63968e-07
>Clock: one second
>
>Depth: 20
>count: 28003379451441501
>Total: twenty-eight quadrillion three trillion three hundred seventy-nine
>billion four hundred fifty-one million four hundred forty-one thousand five
>hundred one
>Frequency: 31.1149 PHz
>Period: 32.139 as
>Cycles per node: 2.57112e-08
>Clock: one second
>
>Depth: 21
>count: 191422801600109729
>Total: one hundred ninety-one quadrillion four hundred twenty-two trillion eight
>hundred one billion six hundred million one hundred nine thousand seven hundred
>twenty-nine
>Frequency: 195.33 PHz
>Period: 5.11955 as
>Cycles per node: 4.09564e-09
>Clock: one second
>
>Depth: 22
>count: 1307549415628455609
>Total: one quintillion three hundred seven quadrillion five hundred forty-nine
>trillion four hundred fifteen billion six hundred twenty-eight million four
>hundred fifty-five thousand six hundred nine
>Frequency: 1.24529 EHz
>Period: 803.027 zs
>Cycles per node: 6.42422e-10
>Clock: one second
>
>Depth: 23
>count: 8934501555889985874
>Total: eight quintillion nine hundred thirty-four quadrillion five hundred one
>trillion five hundred fifty-five billion eight hundred eighty-nine million nine
>hundred eighty-five thousand eight hundred seventy-four
>Frequency: 7.97725 EHz
>Period: 125.357 zs
>Cycles per node: 1.00285e-10
>Clock: one second
>
>After a depth of twenty-three, the count for the above position spills a
>sixty-four bit integer.  I suppose I'll have to include a bignums class :)

If it is of any value - I can confirm the above numbers with my program.
Also your numbers for the first 9 plys of the initial position.

Regards
Andreas Stabel

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