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Nov 05, 2025 — Nov 05, 2026
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------------------------------------------------------------------------------------------------------------------------------- 1377. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Maxflow-Minxut Bottleneck measure of OSMnx transport network graph - Overlay of GHSL R2022A BUILT-V Visualization and Chennai Metropolitan Area Map - 13 January 2023 - related to 823,1163,1164,1174,1175,1177,1179,1194,1211,1226,1234,1290,1291,1292,1295,1296,1297,1301,1302,1304,1312,1313,1320,1323,1326,1328,1342,1343,1349,1350,1351,1362,1363 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Gridded Population Estimators (SEDAC GPW4 and GHSL convex hull estimators), DBSCAN and Neural Network Urban Extent Learners, Computational Geometry, Intrinsic Merit Rankings, R Ricker Population Estimation, Community detection, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry and Polygonal packing by Voronoi Tessellation, Four color theorem, Economic Merit, Computational Economics - GDP estimation from Urban sprawl demographics, electricity consumption, Poverty alleviation, Preferential Attachment, Automatic Delineation of Urban Sprawls, Cellular Automata-SLEUTH-Polya Urn-Dynamic Facegraph Urban Growth Models, Autonomous Driving, Expander Graphs ------------------------------------------------------------------------------------------------------------------------------ 1377.1 python-src/image_pattern_mining/ImageNet/GISUrbanSprawlAnalytics.py has been updated to redefine function urban_sprawl_road_network_OSM(cityname=None,latx=0,laty=0,longx=0,longy=0,address=None,radius=1000,defaultcapacity=1) for adding a new parameter defaultcapacity (capacity of a carriageway). 1377.2 Maxflow-Mincut bottleneck measure of OSMnx transportation network graph is printed for roads between random source-sink pairs by minimum_cut() NetworkX API which, along with betweenness centrality of the graph, is a theoretical estimate of traffic congestion. 1377.3 Default capacity parameter (defaultcapacity) has to be set by the invoking function having prior knowledge of road capacity or from a live traffic API. Following example JavaScript code from https://developers.google.com/maps/documentation/javascript/examples/layer-traffic retrieves realtime traffic data for longitude-latitude and there is no Python API yet: function initMap() { const map = new google.maps.Map(document.getElementById("map"), { zoom: 13, center: { lat: 34.04924594193164, lng: -118.24104309082031 }, }); const trafficLayer = new google.maps.TrafficLayer(); trafficLayer.setMap(map); } window.initMap = initMap; 1377.4 Road network statistics have been recomputed for Overlay of GHSL R2022A BUILT-V Visualization and Chennai Metropolitan Area (CMA) for following 7 periurban regions of CMA (R2022A is soon to be superseded by R2023A) where notable ribbon development (or Transit oriented development) has occurred between R2019A and R2022A presumably attributed to road gravity: urban_sprawl_road_network_OSM(address="Uthiramerur, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Madurantakam, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Cheyyur, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Sholinghur, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Ranipet, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Cheyyar, Tamil Nadu, India",radius=6000) urban_sprawl_road_network_OSM(address="Sricity, AP, India",radius=6000) 1377.5 Following are sorted mincut set for 7 periurban regions above or bottleneck roads which could be congested: sorted cutset: [(6450497209, 6450497199)] sorted cutset: [(1951107130, 2181313427)] sorted cutset: [] sorted cutset: [(2694466167, 2694466169)] sorted cutset: [(9651694326, 9651694333)] sorted cutset: [(5266699732, 5266699743)] sorted cutset: [(1516837049, 1516836816)] 1377.6 Following are the OSMnx transportation network graphs for 7 periurban regions and logs for this update: testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork1.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork2.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork3.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork4.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork5.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork6.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.OSMnx.RoadNetwork7.13January2023.jpeg testlogs/GISUrbanSprawlAnalytics.log.13January2023
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Section 1263 updated
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+1376. (THEORY and FEATURE) Granger causality of timeseries data (including Music, Medical Imageing-ECG, Meteorology-Precipitation, Seismology-Tremors, NBody Gravitational Accelerations, Economics-Financial Markets) - 9 January 2023 - related to 690,691,692,1257,1315,1316,1327,1348,1375 and all sections on Music Information Retrieval(MIR), Climate analytics and Weather Forecast, Computational Economics-Quantitative Finance and TimeSeries Analysis, Graphical Event Models (GEM), Causal Event Models (CEM),Chaos and Fractals, Polynomial Interpolation, EventNet causality^M
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------------------------------------------------------------------------------------------------------------------------------- 1376. (THEORY and FEATURE) Granger causality of timeseries data (including Music, Medical Imageing-ECG, Meteorology-Precipitation, Seismology-Tremors, NBody Gravitational Accelerations, Economics-Financial Markets) - 9 January 2023 - related to 690,691,692,1257,1315,1316,1327,1348,1375 and all sections on Music Information Retrieval(MIR), Climate analytics and Weather Forecast, Computational Economics-Quantitative Finance and TimeSeries Analysis, Graphical Event Models (GEM), Causal Event Models (CEM),Chaos and Fractals, Polynomial Interpolation, EventNet causality ------------------------------------------------------------------------------------------------------------------------------- 1376.1 python-src/MultiFractals.py has been updated to import write_dot,matplotlib plot, networkx and graphviz. 1376.2 New multipurpose function granger_causality_GraphicalEventModel(dictoftimeseries,GEM_edge_probability_threshold=0.5,maxlag=3) has been defined to read a dictionary of event timeseries (map of event_name--to--event_timeseries) and iterate through the dictionary to infer top p-value (of 4 statistical tests) Granger causality edges between each pair of event timeseries in the dictionary. 1376.3 An edge is added to a NetworkX GEM DiGraph for the inferred causality direction if maximum p-value exceeds threshold (which is 50% by default or majority support). 1376.4 GEM NetworkX graph is written to a DOT file testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.dot and read as GraphViz object for rendering it to a JPG file testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.gv.jpg. 1376.5 Function granger_causality() has been renamed to stockquote_granger_causality(ticker1,ticker2,period='2y',interval='1wk',maxlag=3) and returns the timeseries for 2 stockquote tickers. 1376.6 python-src/Streaming_StockMarketData.py has been updated to import stockquote_granger_causality() and granger_causality_GraphicalEventModel() functions. 1376.7 stockquote_granger_causality() has been computed for 6 pairs of tech stock quotes as below,dictionary of timeseries for each of the stock quotes is processed by granger_causality_GraphicalEventModel(dictoftimeseries) to draw a Graphical Event Model in testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.gv.jpg (shows dependency of one stock on the other): ret1=stockquote_granger_causality("TSLA","AAPL",period='2y',interval='1wk',maxlag=3) ret2=stockquote_granger_causality("TSLA","MSFT",period='2y',interval='1wk',maxlag=3) ret3=stockquote_granger_causality("AMZN","MSFT",period='2y',interval='1wk',maxlag=3) ret4=stockquote_granger_causality("GOOGL","MSFT",period='2y',interval='1wk',maxlag=3) ret5=stockquote_granger_causality("IBM","MSFT",period='2y',interval='1wk',maxlag=3) ret6=stockquote_granger_causality("GOOGL","MSFT",period='2y',interval='1wk',maxlag=3) 1376.8 Function granger_causality_GraphicalEventModel() is independent of event category and any set of event timeseries (music,precipitation,seismology,astronomical,financial,medical and so on) could be inspected (heterogeneously between categories of events) for Granger-causality pairwise and GEM could be drawn for those events. Following are the GraphViz,DOT,JPEG and log files for this commit - testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.gv.jpg shows causality between 5 of 6 stocks: testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.dot testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.gv testlogs/GrangerCausality_EventTimeseriesGraphicalEventModel.gv.jpg testlogs/Streaming_StockMarketData.log.9January2023
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Updated Section 1374
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Updated Requirements.txt
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+1375. (THEORY and FEATURE) Granger causality of timeseries data (including Music, Medical Imageing-ECG, Meteorology-Precipitation, Seismology-Tremors, NBody Gravitational Accelerations, Economics-Financial Markets) - 4 January 2023 - related to 690,691,692,1257,1315,1316,1327,1348 and all sections on Music Information Retrieval(MIR), Climate analytics and Weather Forecast, Computational Economics-Quantitative Finance and TimeSeries Analysis, Graphical Event Models (GEM), Causal Event Models (CEM),Chaos and Fractals, Polynomial Interpolation, EventNet causality^M
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------------------------------------------------------------------------------------------------------------------------------- 1375. (THEORY and FEATURE) Granger causality of timeseries data (including Music, Medical Imageing-ECG, Meteorology-Precipitation, Seismology-Tremors, NBody Gravitational Accelerations, Economics-Financial Markets) - 4 January 2023 - related to 690,691,692,1257,1315,1316,1327,1348 and all sections on Music Information Retrieval(MIR), Climate analytics and Weather Forecast, Computational Economics-Quantitative Finance and TimeSeries Analysis, Graphical Event Models (GEM), Causal Event Models (CEM),Chaos and Fractals, Polynomial Interpolation, EventNet causality ------------------------------------------------------------------------------------------------------------------------------- 1375.1 python-src/MultiFractals.py has been updated to import function for granger cauality tests from statsmodels. 1375.2 Function stockquote_mfdfa_model(ticker,period='2y',interval='1wk',order=2,lagfrom=0.5,lagto=3,lagnum=100) has been redefined to remove hardcoded minimum and maximum lag ranges and number of lags and make them function arguments. 1375.3 New function granger_causality(ticker1,ticker2,period='2y',interval='1wk',maxlag=3) has been defined to compare two stock quote ticker timeseries by statsmodels grangercausalitytests() which comprises 4 statistical tests (ssr R, ssr Chi-squared, likelihood and parameter F). Null hypothesis: Timeseries Y does not cause Timeseries X. Timeseries Y Granger-causes Timeseries X if p-value if array of ordered pairs of two timeseries X and Y - (x1,y1),(x2,y2),(x3,y3),...,(xn,yn) - is more than a threshold rejecting Null hypothesis. 1375,4 python-src/Streaming_StockMarketData.py has been updated to import granger_causality() from python-src/MultiFractals.py. 1375.5 Two pairs of stocks TSLA-AAPL and TSLA-MSFT are compared for Granger causality: granger_causality("TSLA","AAPL",period='2y',interval='1wk',maxlag=3) granger_causality("TSLA","MSFT",period='2y',interval='1wk',maxlag=3) and following are pairwise p-value correlations: =========================================================== Granger causality between TSLA and AAPL =========================================================== Granger Causality number of lags (no zero) 1 ssr based F test: F=0.0422 , p=0.8376 , df_denom=102, df_num=1 ssr based chi2 test: chi2=0.0435 , p=0.8348 , df=1 likelihood ratio test: chi2=0.0435 , p=0.8348 , df=1 parameter F test: F=0.0422 , p=0.8376 , df_denom=102, df_num=1 Granger Causality number of lags (no zero) 2 ssr based F test: F=0.0087 , p=0.9913 , df_denom=99, df_num=2 ssr based chi2 test: chi2=0.0183 , p=0.9909 , df=2 likelihood ratio test: chi2=0.0183 , p=0.9909 , df=2 parameter F test: F=0.0087 , p=0.9913 , df_denom=99, df_num=2 Granger Causality number of lags (no zero) 3 ssr based F test: F=0.0693 , p=0.9762 , df_denom=96, df_num=3 ssr based chi2 test: chi2=0.2230 , p=0.9738 , df=3 likelihood ratio test: chi2=0.2228 , p=0.9738 , df=3 parameter F test: F=0.0693 , p=0.9762 , df_denom=96, df_num=3 =========================================================== Granger causality between TSLA and MSFT =========================================================== Granger Causality number of lags (no zero) 1 ssr based F test: F=3.1986 , p=0.0767 , df_denom=102, df_num=1 ssr based chi2 test: chi2=3.2927 , p=0.0696 , df=1 likelihood ratio test: chi2=3.2421 , p=0.0718 , df=1 parameter F test: F=3.1986 , p=0.0767 , df_denom=102, df_num=1 Granger Causality number of lags (no zero) 2 ssr based F test: F=2.5681 , p=0.0818 , df_denom=99, df_num=2 ssr based chi2 test: chi2=5.3957 , p=0.0674 , df=2 likelihood ratio test: chi2=5.2604 , p=0.0721 , df=2 parameter F test: F=2.5681 , p=0.0818 , df_denom=99, df_num=2 Granger Causality number of lags (no zero) 3 ssr based F test: F=1.7780 , p=0.1565 , df_denom=96, df_num=3 ssr based chi2 test: chi2=5.7229 , p=0.1259 , df=3 likelihood ratio test: chi2=5.5696 , p=0.1345 , df=3 parameter F test: F=1.7780 , p=0.1565 , df_denom=96, df_num=3 ------------------- 1375.6 High p-value for TSLA and AAPL (~99%) implies AAPL Granger-causes TSLA (or causality between Apple and Tesla) and Low p-value for TSLA and MSFT (~15%) implies there is no Microsoft-Tesla causality. 1375.7 Edges of a Graphical Event Model (GEM) or Causal Event Model (CEM) could be added dynamically based on pairwise Granger causality p-values of multiple event timeseries each of which is a vertex in GEM or CEM. For example, GEM for economic markets could be inferred by high Granger causality between timeseries for oil prices, commodity prices, automobile stocks, banking stocks (high vehicle loans), interest rates and inflation creating following causality edges between events: Interest rates (adjusted to lower money circulation and inflation) | Oil ----- Automobile ----- Banking ----- Inflation (high money circulation) | | Commodity prices ----------------- 1375.8 Similarly correlation between N-Body gravity timeseries of solar system and terrestrial extreme weather event timeseries could be Granger-caused (Granger causality is more of a forecast of one variable based on past values of another or deferred causality) and Music timeseries could be correlated for causal similarities.
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Section 1374 updated
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Updated Requirements.txt
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1374. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 5 and multiple enhancements to NeuronRain Computational Geometric Factorization - related to 498,562,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369,1372,1373 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition,Grover Search,Quadratic Rational Beziers-Grobner Bases - 30 December 2022
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------------------------------------------------------------------------------------------------------------------------------- 1374. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 5 and multiple enhancements to NeuronRain Computational Geometric Factorization - related to 498,562,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369,1372,1373 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition,Grover Search,Quadratic Rational Beziers-Grobner Bases - 30 December 2022 ------------------------------------------------------------------------------------------------------------------------------- 1374.1 Multiple consecutive 97 bits integers in the range of 100000000000000000000000000000 to 100000000000000000000000000010 are factorized by GNFS (CADO-NFS) and NeuronRain computational geometric factorization. 1374.2 python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been updated to correct maximum factors if-else clause by stop()-ping the SparkSession and exit()-ing after maximum factors are found. 1374.3 python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.py has been updated to print nanoseconds timestamps before and after consecutive integer factorization. Number of factors which was hardcoded to 1 earlier was perhaps limiting the number of factors printed in 1373 which has been made a command line parameter resolving https://krishnairesearch.atlassian.net/browse/NEUR-19 though round off error in extreme cases may not be ruled out as rasterization used is naive and not Graphics grade. Check for maxfactors on Spark accumulator length is not global at present and local to executor instance (as Spark global state can't be broadcast from an instance though there distributed caches - redis,memcache - might reflect the state globally) which might limit per instance factors and reduce step might print more factors than the maximum limit. Rasterization algorithm described for quadratic rational Beziers (a unifying concept of ellipse,hyperbola,parabola) in listing 13 of https://zingl.github.io/Bresenham.pdf for plotting hyperbola segmentwise could be a sophisticated alternative to naive rasterization implemented at present. Grobner bases are subsets of ideal I of a polynomial ring K[x1,x2,...,xn] which contain generating set of polynomials g1,g2,...,gm. Ideal I of polynomial ring K[x1,x2,...,xn] is a subset of K under addition and for all k in K and i in I, k*i in I. Grobner bases have been shown to generate any conical section by obtaining polynomial equation of quadratic rational Beziers and parameters of quadratic rational Beziers (Buchberger algorithm) determine whether the curve is hyperbola,ellipse or hyperbola. 1374.4 JSON factors file read has been commented as redundant. 1374.5 Numbers head-to-head (not a fair comparison as platforms are HPC OpenMPI versus Cloud MapReduce) - Factors computed are different in CADO-NFS and NeuronRain - durations are almost same for CADO-NFS and NeuronRain as CADO-NFS is optimized for small integers and slows down in polynomial selection only for big integers above 200 bits: ---------------------------- 1374.5.1 CADO-NFS - approximately 15.5 minutes - 9 97-bits integers - mostly prime factors - on an average ~1 minute per integer ---------------------------- PID10925 2022-12-30 12:38:59,425 Info:Square Root: Factors: 11 59 154083204930662557781201849 PID12284 2022-12-30 12:40:17,138 Info:Square Root: Factors: 2 3 7 17041 445847 313378923550840603 PID13578 2022-12-30 12:41:22,171 Info:Square Root: Factors: 31 295183134022089846821 10928153 PID15218 2022-12-30 12:42:28,623 Info:Square Root: Factors: 2 41 16183 53731 701248902272927557 PID16576 2022-12-30 12:43:39,576 Info:Square Root: Factors: 3 5 19 347 577 1752467013532462655147 PID17774 2022-12-30 12:44:56,086 Info:Square Root: Factors: 2 17 353 8331944675887352107982003 PID18938 2022-12-30 12:46:03,278 Info:Square Root: Factors: 53 827 2281490269444000821336497 PID20341 2022-12-30 12:47:24,953 Info:Square Root: Factors: 2 3 103 1361 2647 53047 23519935674229 PID21815 2022-12-30 12:49:10,995 Info:Square Root: Factors: 13 7 23 607696954219 12047047 6526241 ------- PID7485 2022-12-30 12:35:45,218 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 23.8/65.7797 PID9574 2022-12-30 12:37:52,230 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 22.69/57.7058 PID10925 2022-12-30 12:38:59,794 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 29.06/60.7773 PID12284 2022-12-30 12:40:17,219 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 24.55/70.5466 PID13578 2022-12-30 12:41:22,726 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 14.55/57.6136 PID15218 2022-12-30 12:42:28,919 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 25.25/58.705 PID16576 2022-12-30 12:43:39,726 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 25.49/63.6579 PID17774 2022-12-30 12:44:56,496 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 28.76/67.6902 PID18938 2022-12-30 12:46:03,736 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 18.69/59.8216 PID20341 2022-12-30 12:47:25,590 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 22.67/70.29 PID21815 2022-12-30 12:49:11,637 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 16.48/94.0504 --------------------------------------------------------------- 1374.5.2 NeuronRain Computational Geometric Factorization - 16.437814537933335 minutes - 10 97-bits integers - prime and composite factors - on the average 5 seconds per factor --------------------------------------------------------------- 1.factors_accum.value: [100000000000000000000000000000, 1, 50000000000000000000000000000, 2, 2500000000000000000000000, 40000, 2441406250000000000000000, 40960, 1280000000000000000000000, 78125, 1250000000000000000000000, 80000, 800000000000000000000000, 125000, 781250000000000000000000, 128000] 1.factors_accum.value: [100000000000000000000000000001, 1, 9090909090909090909090909091, 11] 1.factors_accum.value: [100000000000000000000000000002, 1, 50000000000000000000000000001, 2, 1956066740997202824560374, 51123, 978033370498601412280187, 102246, 838314317570229781954446, 119287] 1.factors_accum.value: [100000000000000000000000000003, 1, 3225806451612903225806451613, 31] 1.factors_accum.value: [100000000000000000000000000004, 1, 50000000000000000000000000002, 2, 1861123001619177011408684, 53731, 1544830995489093493171847, 64732, 930561500809588505704342, 107462] 1.factors_accum.value: [100000000000000000000000000005, 1, 20000000000000000000000000001, 5, 1824318161087293624008027, 54815, 1011173466808230952019819, 98895] 1.factors_accum.value: [100000000000000000000000000006, 1, 50000000000000000000000000003, 2] 1.factors_accum.value: [100000000000000000000000000007, 1, 1886792452830188679245283019, 53, 2281490269444000821336497, 43831] 1.factors_accum.value: [100000000000000000000000000008, 1, 50000000000000000000000000004, 2, 2098812072367040255215548, 47646, 2040982937382643481100498, 48996, 1049406036183520127607774, 95292, 1020491468691321740550249, 97992, 713353259667720051646776, 140183, 699604024122346751738516, 142938] 1.factors_accum.value: [100000000000000000000000000009, 1, 7692307692307692307692307693, 13]
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Section 1373 updated
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Section 1313 updated
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Section 1351 updated
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+1373. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 4 and multiple enhancements to NeuronRain Computational Geometric Factorization - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369,1372 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 27 December 2022^M
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------------------------------------------------------------------------------------------------------------------------------- 1373. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 4 and multiple enhancements to NeuronRain Computational Geometric Factorization - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369,1372 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 27 December 2022 ------------------------------------------------------------------------------------------------------------------------------- 1373.1 NeuronRain computational geometric factorization has been benchmarked versus General Number Field Sieve (CADO-NFS) for 40 consecutive 236 bits integers from 90109209192120930920930920323828398923232323828382938928399283982983959 to 90109209192120930920930920323828398923232323828382938928399283982983999 1373.2 Multiple consecutive integers CADO-NFS commandline: python3.7 ./multiple-cado-nfs.py 90109209192120930920930920323828398923232323828382938928399283982983959 90109209192120930920930920323828398923232323828382938928399283982983999 - factorization logs have been captured in testlogs/multiple-cado-nfs.log.27December2022 1373.3 python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been updated to introduce padding of tilesegments for elongating a rasterized hyperbolic arc line segment on either ends which ensures better search coverage along the hyperbolic curve (consecutive tilesegments overlap along the hyperbolic hillclimbing simulating a curved staircase): def tilesearch_nonpersistent(y, numfactors=maxfactors, padding=1) 1373.4 Interval midpoint computation has been further finetuned by Decimal() division instead of int(). Absolute function abs() has been replaced by bidirectional differences within inequality clauses. More factors_accum.add() calls have been added wherever necessary. Additional clauses for factor point location verification and square root point verification have been included in factorcandidate if-else. 1373.5 python-src/multiple-cado-nfs.py has been changed to add Special Number Field Sieve factorization CADO-NFS os.system() commandline as it involves special parameters file parameters.F9 which has to be manually edited and has since been commented. 1373.6 Factorization numbers for GNFS-CADO-NFS - 40 consecutive 236 bits integers from 90109209192120930920930920323828398923232323828382938928399283982983959 to 90109209192120930920930920323828398923232323828382938928399283982983999 - from multiple-cado-nfs.log.27December2022 (some of the factorizations failed in selecting suitable polynomial) - total duration: 1 hour 33 minutes approximately: Error messages in failed factorizations: ----------------------------------------- PID14821 2022-12-13 16:24:02,278 Error:Generate Factor Base: Warning: non-trivial factors (11263651149015116365116365040478549865404040478547867366049910497872995) of N were found while checking the cpoly file. This should not happen. PID14821 2022-12-13 16:24:02,279 Error:Generate Factor Base: Error, we found no compatible mapping that factors through the given number fields. Your poly file is most probably wrong. PID14821 2022-12-13 16:24:02,279 Error:Generate Factor Base: code BUG() : condition cado_poly_check_mapping(((void *)0), cpoly, cpoly->n) failed in cado_poly_set_plist at /home/ksrinivasan/cado-nfs/utils/cado_poly.c:151 -- Abort --------------------------------------------- PID13471 2022-12-13 16:23:23,673 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 320.54/148.622 PID14917 2022-12-13 16:26:31,554 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 303.72/141.747 PID16104 2022-12-13 16:29:08,850 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 326.12/150.527 PID17273 2022-12-13 16:32:06,436 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 273.31/131.875 PID18415 2022-12-13 16:34:39,182 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 315.37/145.664 PID19629 2022-12-13 16:37:51,177 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 313.37/142.702 PID20702 2022-12-13 16:40:12,930 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 287.6/134.945 PID21855 2022-12-13 16:42:34,922 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 285.72/135.539 PID23129 2022-12-13 16:45:00,666 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 303.63/138.862 PID24649 2022-12-13 16:47:38,301 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 336.23/150.864 PID25838 2022-12-13 16:49:52,779 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 262.12/127.452 PID26713 2022-12-13 16:52:25,534 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 322.62/146.487 PID27848 2022-12-13 16:54:50,652 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 290.1/138.383 PID29024 2022-12-13 16:57:11,508 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 283.06/134.091 PID30174 2022-12-13 16:59:34,153 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 274.76/133.369 PID31086 2022-12-13 17:02:06,214 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 315.7/144.714 PID31991 2022-12-13 17:04:24,044 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 266.41/128.733 PID791 2022-12-13 17:07:08,963 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 342.94/156.703 PID2752 2022-12-13 17:10:07,005 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 253.22/128.316 PID3728 2022-12-13 17:12:31,823 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 282.69/137.288 PID4913 2022-12-13 17:15:31,436 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 341.62/170.87 PID6497 2022-12-13 17:18:40,764 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 285.79/180.849 PID8494 2022-12-13 17:22:10,528 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 325.71/200.806 PID10809 2022-12-13 17:25:37,835 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 333.76/197.861 PID14427 2022-12-13 17:29:19,000 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 377.19/212.919 PID16100 2022-12-13 17:31:51,628 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 307.15/143.732 PID17284 2022-12-13 17:34:24,060 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 315.72/145.51 PID19041 2022-12-13 17:37:39,582 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 306.54/144.652 PID20214 2022-12-13 17:40:30,075 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 311.46/163.8 PID22109 2022-12-13 17:42:56,727 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 296.74/139.863 PID23507 2022-12-13 17:45:43,190 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 288.18/159.54 PID24919 2022-12-13 17:48:35,763 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 323.67/165.933 PID26703 2022-12-13 17:51:23,240 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 309.99/160.948 PID28570 2022-12-13 17:54:17,318 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 329.87/167.325 PID29927 2022-12-13 17:56:48,479 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 300.4/143.541 1373.7 Factorization numbers for NeuronRain Computational Geometric algorithm - 40 consecutive 236 bits integers from 90109209192120930920930920323828398923232323828382938928399283982983959 to 90109209192120930920930920323828398923232323828382938928399283982983999 - from DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.236bits_GNFS.log.27December2022 - Total duration (in nanoseconds): from 1670937206663632906 to 1670938170293834503 = 963.63 seconds (16 minutes) approximately - factorization for 90109209192120930920930920323828398923232323828382938928399283982983959 did not print non-trivial factors because of Decimal round off error in naive rasterization. JIRA issue https://krishnairesearch.atlassian.net/browse/NEUR-19 has been raised for this bug: ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983959, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983960, 1, 45054604596060465460465460161914199461616161914191469464199641991491980, 2, 2252730229803023273023273008095709973080808095709573473209982099574599, 40, 2002426870936020687131798229418408864960718307297398642853317421844088, 45, 1251516794335012929457373893386505540600448942060874151783323388652555, 72, 866434703770393566547412695421426912723387729119066720465377730605615, 104, 770164181129238725819922395930157255754122425883614862635891316093880, 117, 750910076601007757674424336031903324360269365236524491069994033191533, 120]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983961, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983962, 1, 45054604596060465460465460161914199461616161914191469464199641991491981, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983963, 1, 30036403064040310306976973441276132974410774609460979642799761327661321, 3]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983964, 1, 45054604596060465460465460161914199461616161914191469464199641991491982, 2, 2435384032219484619484619468211578349276549292658998349416196864404972, 37, 1217692016109742309742309734105789174638274646329499174708098432202486, 74]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983965, 1, 18021841838424186184186184064765679784646464765676587785679856796596793, 5]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983966, 1, 45054604596060465460465460161914199461616161914191469464199641991491983, 2, 850086879170952178499348304941777348332380413475310744607540414933811, 106]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983967, 1, 657731453957087087014094308933054006738922071740021452032111561919591, 137]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983968, 1, 45054604596060465460465460161914199461616161914191469464199641991491984, 2, 1917217216853636828104913198379327636664517528263466785710623063467744, 47]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983969, 1, 30036403064040310306976973441276132974410774609460979642799761327661323, 3]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983970, 1, 45054604596060465460465460161914199461616161914191469464199641991491985, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983971, 1, 5300541717183584171819465901401670524896019048728408172258781410763763, 17]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983972, 1, 45054604596060465460465460161914199461616161914191469464199641991491986, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983973, 1, 6931477630163148532379301563371415301787101832952533763723021844844921, 13]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983974, 1, 45054604596060465460465460161914199461616161914191469464199641991491987, 2, 2371294978740024497919234745363905234821903258641656287589454841657473, 38, 1958895852002628933063715659213660846157224431051803020182593130064869, 46]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983975, 1, 30036403064040310306976973441276132974410774609460979642799761327661325, 3]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983976, 1, 45054604596060465460465460161914199461616161914191469464199641991491988, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983977, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983978, 1, 45054604596060465460465460161914199461616161914191469464199641991491989, 2, 1365291048365468650317135156421642407927762482248226347399989151257333, 66]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983979, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983980, 1, 45054604596060465460465460161914199461616161914191469464199641991491990, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983981, 1, 30036403064040310306976973441276132974410774609460979642799761327661327, 3, 1234372728659190834533300278408608204427840052443601903128757314835397, 73, 874846691185640106028455537124547562361478872120222708042711494980427, 103]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983982, 1, 45054604596060465460465460161914199461616161914191469464199641991491991, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983983, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983984, 1, 45054604596060465460465460161914199461616161914191469464199641991491992, 2, 2145457361717165021926926674376866641029341043532927117342840094832952, 42, 1877275191502519394186060840079758310900673413091311227674985082978833, 48, 1072728680858582510963463337188433320514670521766463558671420047416476, 84]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983985, 1, 18021841838424186184186184064765679784646464765676587785679856796596797, 5]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983986, 1, 45054604596060465460465460161914199461616161914191469464199641991491993, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983987, 1, 30036403064040310306976973441276132974410774609460979642799761327661329, 3]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983988, 1, 45054604596060465460465460161914199461616161914191469464199641991491994, 2, 1325135429295896042954866475350417631224004762182102043064695352690941, 68]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983989, 1, 3107214110073135548997617942200979273214907718220101342358595999413241, 29]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983990, 1, 45054604596060465460465460161914199461616161914191469464199641991491995, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983991, 1]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983992, 1, 45054604596060465460465460161914199461616161914191469464199641991491996, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983993, 1, 30036403064040310306976973441276132974410774609460979642799761327661331, 3, 648267692029646985042668491538333805203110243369661431139563194122187, 139]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983994, 1, 45054604596060465460465460161914199461616161914191469464199641991491997, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983995, 1, 18021841838424186184186184064765679784646464765676587785679856796596799, 5]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983996, 1, 45054604596060465460465460161914199461616161914191469464199641991491998, 2]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983997, 1, 3917791704005257866127431318427321692314448862103606040365186260129739, 23]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983998, 1, 45054604596060465460465460161914199461616161914191469464199641991491999, 2, 1838963452900427161651651435180171406596578037313937529151005795571102, 49]) ('factors_accum.value = ', [90109209192120930920930920323828398923232323828382938928399283982983999, 1, 30036403064040310306976973441276132974410774609460979642799761327661333, 3]) 1373.8 Similar to earlier CADO-NFS benchmarks above numbers are not fair as software platforms and languages are different and CADO-NFS is for HPC written in C++ and NeuronRain factorization is written for cloud mapreduce in Python+Java and better benchmarking could be obtained by replacing cloud MapReduce by MapReduce on MPI (MR-MPI) depending on feasibility.
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Section 1150 updated
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Section 1372 updated
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Updated Section 1150
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+1372. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.10.6 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 3 - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 22 December 2022^M
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----------------------------------------------------------------------------------------------------------------------------- 1372. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.10.6 + Spark 3.3.0 Quadcore Multiple Consecutive Integers Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 3 - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366,1369 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 22 December 2022 ----------------------------------------------------------------------------------------------------------------------------- 1372.1 New wrapper python script multiple-cado-nfs.py has been added to repository to loop through a range of consecutive integers and factorize each integer in the range by cado-nfs.py. 1372.2 Ten 94 bits integers from 9910281281929182821212121221 to 9910281281929182821212121230 have been factorized by multiple-cado-nfs.py CADO-NFS SNFS-GNFS wrapper and following are the excerpts of testlogs/multiple-cado-nfs.log for GNFS factoring of 10 consecutive 94-bits integers on quadcore (server threads=4) - total duration for factoring 10 integers is 10 minutes 23 seconds: PID837 2022-12-13 16:47:16,984 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121221 PID837 2022-12-13 16:48:04,015 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 10.35/46.6608 PID2814 2022-12-13 16:48:36,055 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121221 PID2814 2022-12-13 16:49:23,636 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 10.28/47.2363 PID4099 2022-12-13 16:49:29,809 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121222 PID4099 2022-12-13 16:50:17,774 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 9.2/47.4745 PID5690 2022-12-13 16:50:24,542 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121223 PID5690 2022-12-13 16:51:14,230 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 18.68/49.3089 PID6827 2022-12-13 16:51:20,915 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121224 PID6827 2022-12-13 16:52:07,117 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 8.2/45.8551 PID8125 2022-12-13 16:52:14,066 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121225 PID8125 2022-12-13 16:53:04,078 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 15.93/49.6659 PID9481 2022-12-13 16:53:10,451 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121226 PID9481 2022-12-13 16:54:01,726 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 15.99/51.0721 PID10846 2022-12-13 16:54:10,245 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121227 PID10846 2022-12-13 16:54:59,591 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 13.92/49.1274 PID12246 2022-12-13 16:55:07,797 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121228 PID12246 2022-12-13 16:55:56,913 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 13.03/48.7576 PID13823 2022-12-13 16:56:03,546 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121229 PID13823 2022-12-13 16:56:47,938 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 8.48/43.9535 PID15361 2022-12-13 16:56:54,213 Info:Complete Factorization / Discrete logarithm: Factoring 9910281281929182821212121230 PID15361 2022-12-13 16:57:39,550 Info:Complete Factorization / Discrete logarithm: Total cpu/elapsed time for entire Complete Factorization 9.05/44.9134 1372.3 Ten 94 bits integers 9910281281929182821212121221 to 9910281281929182821212121230 have been factorized by NeuronRain Computational Geometric Factorization - DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.py - after small code change to add an argument for Spark directory and following are excerpts of testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.94bits_GNFS.log.22December2022 - total duration for factoring 10 integers is 4 minutes 33 seconds : ('Factors are: (', 1, ',', 9910281281929182821212121221, ') (at ', 'Wed, 21 Dec 2022 09:15:24 GMT', ')') ('Factors are: (', 29, ',', 341733837307902855903866249, ') (at ', 'Wed, 21 Dec 2022 09:15:24 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121222, ') (at ', 'Wed, 21 Dec 2022 09:15:57 GMT', ')') ('Factors are: (', 2, ',', 4955140640964591410606060611, ') (at ', 'Wed, 21 Dec 2022 09:15:57 GMT', ')') ('Factors are: (', 8947, ',', 1107665282433126502873826, ') (at ', 'Wed, 21 Dec 2022 09:15:58 GMT', ')') ('Factors are: (', 13147, ',', 753805528404136519450226, ') (at ', 'Wed, 21 Dec 2022 09:16:00 GMT', ')') ('Factors are: (', 17894, ',', 553832641216563251436913, ') (at ', 'Wed, 21 Dec 2022 09:16:02 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121223, ') (at ', 'Wed, 21 Dec 2022 09:16:25 GMT', ')') ('Factors are: (', 3, ',', 3303427093976394273737373741, ') (at ', 'Wed, 21 Dec 2022 09:16:25 GMT', ')') ('Factors are: (', 17469, ',', 567306730890673926453267, ') (at ', 'Wed, 21 Dec 2022 09:16:31 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121224, ') (at ', 'Wed, 21 Dec 2022 09:16:55 GMT', ')') ('Factors are: (', 2, ',', 4955140640964591410606060612, ') (at ', 'Wed, 21 Dec 2022 09:16:55 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121225, ') (at ', 'Wed, 21 Dec 2022 09:17:23 GMT', ')') ('Factors are: (', 5, ',', 1982056256385836564242424245, ') (at ', 'Wed, 21 Dec 2022 09:17:23 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121226, ') (at ', 'Wed, 21 Dec 2022 09:17:52 GMT', ')') ('Factors are: (', 2, ',', 4955140640964591410606060613, ') (at ', 'Wed, 21 Dec 2022 09:17:52 GMT', ')') ('Factors are: (', 9254, ',', 1070918660247372252130119, ') (at ', 'Wed, 21 Dec 2022 09:17:54 GMT', ')') ('Factors are: (', 10169, ',', 974558096364360588180954, ') (at ', 'Wed, 21 Dec 2022 09:17:54 GMT', ')') ('Factors are: (', 13881, ',', 713945773498248168086746, ') (at ', 'Wed, 21 Dec 2022 09:17:55 GMT', ')') ('Factors are: (', 20338, ',', 487279048182180294090477, ') (at ', 'Wed, 21 Dec 2022 09:17:58 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121227, ') (at ', 'Wed, 21 Dec 2022 09:18:20 GMT', ')') ('Factors are: (', 8389, ',', 1181342386688423271094543, ') (at ', 'Wed, 21 Dec 2022 09:18:24 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121228, ') (at ', 'Wed, 21 Dec 2022 09:18:52 GMT', ')') ('Factors are: (', 2, ',', 4955140640964591410606060614, ') (at ', 'Wed, 21 Dec 2022 09:18:52 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121229, ') (at ', 'Wed, 21 Dec 2022 09:19:21 GMT', ')') ('Factors are: (', 3, ',', 3303427093976394273737373743, ') (at ', 'Wed, 21 Dec 2022 09:19:21 GMT', ')') ('Factors are: (', 1, ',', 9910281281929182821212121230, ') (at ', 'Wed, 21 Dec 2022 09:19:50 GMT', ')') ('Factors are: (', 2, ',', 4955140640964591410606060615, ') (at ', 'Wed, 21 Dec 2022 09:19:50 GMT', ')') ('Factors are: (', 8122, ',', 1220177454066631718937715, ') (at ', 'Wed, 21 Dec 2022 09:19:52 GMT', ')') ('Factors are: (', 12214, ',', 811387037983394696349445, ') (at ', 'Wed, 21 Dec 2022 09:19:53 GMT', ')') ('Factors are: (', 20305, ',', 488070981626652687575086, ') (at ', 'Wed, 21 Dec 2022 09:19:57 GMT', ')') 1372.4 multiple-cado-nfs.py wraps around cado-nfs.py by backup of the logs,removes files from logs directory before proceeding to next integer and appends to existing logs - necessary because cado-nfs.py stalls in Square Root (a,b) files creation as logs folder is non-empty. 1372.5 It needs to be observed that Spark-Python is a huge overhead in above numbers as heavy marshalling takes place between Spark Python + Py4J and Java in NeuronRain implementation which is absent in cado-nfs.py. CADO-NFS implements its own distributed computing framework (multiple IP address for servers, server threads for multicores) based on lightweight Clustering MPI C++ API (GMP) for parallelizing GNFS - IntelMPI, OpenMPI for Mellanox Infiniband,Intel Omni-Path - Refer cado-nfs source tree READMEs in cado-nfs/linalg/bwc/. It is also worth noting that mere parallelism was not enough to better GNFS in benchmarks so far - it also matters on what gets parallelized: CADO-NFS parallelizes linear algebra and sieving which themselves are broad search spaces involving lethargic polynomial selection while NeuronRain computational geometric factorization searches a narrow set of points on a hyperbolic arc (an affine Algebraic Variety over Galois Field or union of unions of intersections of Principal Ideals mentioned in Section 601) on rectified hyperbolic arc by parallel planar point location. Comparison above is not apples-to-apples exactly as factors found are different, software implementations are different and NeuronRain is at disadvantage as it is implemented for cloud computing and not for HPC clusters running performant C++ MPI cluster frameworks while CADO-NFS is HPC implementation. 1372.6 CADO-NFS also requires setting the following additional config parameters in parameters/factor/params.c30 for logging: tasks.workdir = multiple-cado-nfs-logs tasks.name = multiple-cado-nfs
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Section 1368 updated
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Section 1368 updated
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Section 1351 updated
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Updated NeuronRain_Research_Celestial_Pattern_Mining.txt
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1369. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7.5 + Spark 3.3.0 Quadcore Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 2 - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 14 December 2022
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------------------------------------------------------------------------------------------------------------------------------ 1369. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.7.5 + Spark 3.3.0 Quadcore Benchmarks - Linux General Number Field Sieve Factorization (CADO-NFS) comparison 2 - related to 498,601,1226,1259,1303,1319,1321,1323,1324,1325,1355,1365,1366 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization,Quantum computation and Derandomization of BQP Factorization by Condorcet Jury Theorem Majority-BQPVoterSAT boolean composition - 14 December 2022 ------------------------------------------------------------------------------------------------------------------------------ 1369.1 NeuronRain Computational Geometric Factorization DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been benchmarked against CADO-NFS General Number Field Sieve for 4096 bits integers which is the standard size of RSA Encryption Keys. 1369.2 Computational Geometric Factorization commandline: spark-3.3.0-bin-hadoop3/bin/spark-submit DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py 992302389823982983982938839829839823818029109201902901920910290192091029019209109209120910290192091209109209138392897287238728737237827387283787238723791792819281982981928182819289182989923023898239829839829388398298398238180291092019029019209102901920910290192091092091209102901920912091092091383928972872387287372378273872837872387237917928192819829819281828192891829819289812989199230238982398298398293883982983982381802910920190290192091029019209102901920910920912091029019209120910920913839289728723872873723782738728378723872379179281928198298192818281928918298192899230238982398298398293883982983982381802910920190290192091029019209102901920910920912091029019209120910920913839289728723872873723782738728378723872379179281928198298192818281928918298992302389823982983982938839829839823818029109201902901920910290192091029019209109209120910290192091209109209138392897287238728737237827387283787238723791792819281982981928182819289182981928981298919923023898239829839829388398298398238180291092019029019209102901920910290192091092091209102901920912091092091383928972872387287372378273872837872387237917928192819829819281828192891829819289812989119289812989198129891192898992302389823982983982938839829839823818029109283232366299 340 False False all False 2>&1 > testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log.4096bits_GNFS.14December2022 1369.3 Depth of the non-uniform circuit is chosen as 340 or runtime is O((logN)^340). First Factor pair (13 and huge factor) has been found in 14.8 seconds (14827094874 nanoseconds) and captured in testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log.4096bits_GNFS.14December2022: ('Factors are: (', 13, ',', 76330953063383306460226064602295371062925316092454069378531560784007002232246854554547762330014776246854554549107145945172209902864448260560291326055676291755329383306302167909176090999224847992172294603063799107561415249090791622463002232246854069378531560784007007083939161761686224007007083952609920990183637490182944144064451722095224456014832294601483217553299371524560754845323017710690953715261407221844844921721677146993860791553237771463016084838609300840070160848386093009300840070295329979132605605671060210671413747990183013790917553715245601406302224484476376863864537107561415253375690998767875523300840014637707083925309169930992455454686224007002232246855454686224141483825286451759517214056825259901836336859944763707561399447560148378330691715568447998691075610679986910755678309931477069453993916176168622386847631469939163146945399391631469939164491761329787594518249063645175675941440291676370713998690917552524560706383225306253763071001838326140756909952953715261402936945468616848386093007915532377714630160853237785315607840070160853237798763767144029791336336790297910605568249070609860986140755329371399453217678406908691470714600999169086914707146076330953063383306460226064602295371062925316098710182023, ') (at ', 'Tue, 13 Dec 2022 10:35:01 GMT', ')') nanoseconds elapsed so far in finding all factors: 14827094874 1369.4 CADO-NFS General Number Field Sieve Factorization commandline (4 server threads = multicores): ./cado-nfs.py --parameters parameters/factor/params.c155 992302389823982983982938839829839823818029109201902901920910290192091029019209109209120910290192091209109209138392897287238728737237827387283787238723791792819281982981928182819289182989923023898239829839829388398298398238180291092019029019209102901920910290192091092091209102901920912091092091383928972872387287372378273872837872387237917928192819829819281828192891829819289812989199230238982398298398293883982983982381802910920190290192091029019209102901920910920912091029019209120910920913839289728723872873723782738728378723872379179281928198298192818281928918298192899230238982398298398293883982983982381802910920190290192091029019209102901920910920912091029019209120910920913839289728723872873723782738728378723872379179281928198298192818281928918298992302389823982983982938839829839823818029109201902901920910290192091029019209109209120910290192091209109209138392897287238728737237827387283787238723791792819281982981928182819289182981928981298919923023898239829839829388398298398238180291092019029019209102901920910290192091092091209102901920912091092091383928972872387287372378273872837872387237917928192819829819281828192891829819289812989119289812989198129891192898992302389823982983982938839829839823818029109283232366299 -t 4 1369.5 CADO-NFS run earlier had to be abandoned after almost 1 hour because of slowdown in Polynomial Selection and no ETA was printed (which should be significantly higher (at least 8 times for 4096 bits) than 36 hours for 539 bits in Section 1366) - CADO-NFS logs in testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log.4096bits_GNFS.14December2022
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