Comparison of non-CRT vs CRT at various shift settings

In the announcement of Revision 5, the Gapcoin miner is described as “capable of using the Chinese Remainder Theorem to speed up mining with large shift”. Unfortunately, the announcement was unaccompanied by any indication of what level of shift was considered “large”, although some insight can be gained from the fact that the minimum shift level supported by the associated “crt files” was - and is - 64.

Tests are non-CRT vs. CRT mining over a selected range of --shift settings: 64, 96, 128, 179, 256, 512 and 768.

Except for shift 768, non-CRT tests used default settings for --sieve-size and --sieve-primes. For the CRT tests, in order to keep the size of the gaplist within the recommended bounds, the value of --sieve-primes is adjusted according to the selected value of --shift.

Tests were run simultaneously to control for changes in difficulty that otherwise affect the results to a degree that thwarts comparison when tests are run serially.

Choosing an appropriate value for --sieve-size proved to be something of a “black art”. At shift 179, it proved impossible to discover a value for --sieve-size which produced a gaplist that neither reached zero nor exceeded 9000. Selecting a value of 16382 resulted in a frequently-empty gaplist but selecting the minimum decrement of one less (16381) resulted in a gaplist size that approached 50000 at times.

A shift of 768 proved to be the highest shift setting possible to use with non-CRT mining. At any higher setting the miner-reported statistics become nonsensical - which can be taken as a useful proxy for “only use CRT at this shift setting”).

Column labels map directly to miner output: pps is average primes per second, tps is average tests per second, gps is average gaps per second, glst is the size of the gaplist and l/s is the time in seconds to scan the gaplist at the reported rate of gaps per second.

measure	pps	tps	gps
mean	280837	99472	13148
max	354288	125605	16586
min	275451	97571	12896
std	10932	3872	511

measure	pps	tps	gps	glst	bpc	l/s
mean	517700	7187127	6884	2095	0.23	0.30
max	706107	14294784	9883	6671	0.47	0.67
min	463066	108904	6740	3	0.00	0.00
std	20342	4067984	300	1542	0.14	5.15

measure	pps	tps	gps
mean	150002	58421	7023
max	158244	61486	7408
min	149244	58156	6988
std	934	331	43

measure	pps	tps	gps	glst	bpc	l/s
mean	733254	5148324	3808	3008	0.32	0.79
max	878003	10191541	5664	13327	0.61	2.35
min	365175	61626	3755	12	0.00	0.00
std	43174	2948194	133	2696	0.18	20.23

measure	pps	tps	gps
mean	124207	53300	5868
max	132919	56941	6281
min	122889	52693	5805
std	1679	743	80

measure	pps	tps	gps	glst	bpc	l/s
mean	783223	6816976	3212	3116	0.43	0.97
max	878103	13460735	3827	10167	0.83	2.66
min	508530	84473	3160	11	0.00	0.00
std	38592	3887882	100	2491	0.25	24.83

measure	pps	tps	gps
mean	110018	53537	5203
max	142859	69938	6759
min	106573	51837	5039
std	5305	2607	252

measure	pps	tps	gps	glst	bpc	l/s
mean	1719581	11259653	2801	15803	0.95	5.64
max	2097464	21849802	3640	48129	1.89	13.22
min	1634362	176471	2715	936	0.01	0.34
std	40319	6237012	133	11759	0.55	88.32

measure	pps	tps	gps
mean	61600	35056	2894
max	78988	44501	3708
min	59878	33584	2810
std	2707	1496	127

measure	pps	tps	gps	glst	bpc	l/s
mean	2504918	8233398	1587	1799	1.19	1.13
max	3225400	16197158	2139	6084	2.32	2.84
min	2433006	110793	1533	4	0.01	0.00
std	119752	4568658	89	1400	0.67	15.71

measure	pps	tps	gps
mean	10748	9234	507
max	11115	9591	524
min	10683	9152	503
std	71	85	3

measure	pps	tps	gps	glst	bpc	l/s
mean	2338017	1642804	301	2369	1.22	7.87
max	3549117	3269947	318	5893	2.44	18.53
min	2173579	8416	299	38	0.01	0.13
std	97558	946970	3	1645	0.71	496.96

measure	pps	tps	gps
mean	3658	4255	172
max	4783	5329	224
min	3576	4177	168
std	141	128	7

measure	pps	tps	gps	glst	bpc	l/s
mean	2316789	607655	109	3146	1.16	28.98
max	3302115	1201411	127	8185	2.28	64.45
min	2243369	7539	107	46	0.01	0.43
std	119993	345476	2	2283	0.66	1022.23

The charts included below are for completeness. The figures given are the means and they differ from the means in the above table because, in order to support the different requirements of charting, the first 1/5th of the data is ignored in order to aid visual comparison. The chartline uses the full dataset.

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Replication:

gapminer -o localhost -p 31397 -u $USER -x $USERPASS -j 5 -e -f 64 -t 4
gapminer -o localhost -p 31397 -u $USER -x $USERPASS -j 5 -e -f 64 -i [as-discovered] -t 4 -d 3 -r crt/dist/crt-22m-0064s.txt

Comparison of non-CRT vs CRT at various shift settings

CRT vs non-CRT at shifts 64, 96, 128, 179, 256, 512 and 768

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