Monero FCMP `MAX_INPUTS`/`MAX_OUTPUTS` empirical analysis

Limiting the number of inputs and outputs allowed in a transaction may reduce the storage space and verification computation costs of Full-Chain Membership Proof (FCMP) Monero transactions. See here for initial discussion. This note is a preliminary attempt to measure the likely cost of different values for the proposed MAX_INPUTS and MAX_OUTPUTS blockchain consensus rule parameters. The analysis uses empirical blockchain data from here, estimated cost per input/output cardinality based on modified Python code (see below) here, and the results of an output consolidation algorithm.

TODO: MAX_OUTPUTS analysis

The output consolidation algorithm attempts to consolidate outputs in the fewest number of "rounds". A round is the period of time it takes for a set of unrelated transactions to be confirmed and spendable, i.e. about 10 blocks.

Below is a visualization of consolidation steps. The maximum number of outputs is 4. The initial outputs to consolidate is 19. Each row in the plot is a set of outputs that exist at a specific point in time. The first row has all 19 inputs. The arrows pointing to circles in the next row show consolidation transactions. When an arrow connects a single circle to another single circle, there is no actual transaction. Instead, the arrow represents a visual accounting action that just carries the unspent output into the next time period.

If users are required to consolidate their outputs with MAX_INPUTS or fewer inputs, the distribution of transaction inputs will change. Below are tables that show the change in the distribution and the new size and computational cost. The units are not yet interpretable, but the relative values can be compared between different MAX_INPUTS rules. The size and compute costs are based on this gist. The numbers for the compute factor of 4 are used. No batching is assumed, so a single transaction's compute cost is the sum of Proof 1 Base Cost, Proof 2 Base Cost, and Commitments. The compute cost for BP+ outputs is the sum of Base Cost and Commitments.

input.size.cost is a metric of the aggregate FCMP input size of transactions that have n.inputs.
input.compute.cost is a metric of the aggregate FCMP verification computational cost of transactions that have n.inputs.
additional.outputs.size.cost is a metric of the aggregate size of the additional outputs that the consolidation transactions produce.
additional.outputs.compute.cost is a metric of the aggregate verification computational cost of the additional outputs that the consolidation transactions produce.
total.size.cost is the sum of input.size.cost and additional.outputs.size.cost
total.compute.cost is the sum of input.compute.cost and additional.outputs.compute.cost

The most relevant numbers are the total.size.cost and total.compute.cost in the final row, which is the sum total of the columns. The values in these cells can be compared between different MAX_INPUTS values. The size cost metric is 5471, 4795, 4542, and 4405 for MAX_INPUTS = 4, 8, 16, and 128 respectively. The computational cost metric is 3904, 3706, 3692, and 3857 for MAX_INPUTS = 4, 8, 16, and 128 respectively.

`MAX_INPUTS` = 4

	n.inputs	share	input.size.cost	input.compute.cost	additional.outputs.size.cost	additional.outputs.compute.cost	total.size.cost	total.compute.cost
	1	44.725	1937.770	885.621	0.000	0.000	1937.770	885.621
	2	33.462	1747.517	1293.244	20.667	4.316	1768.185	1297.559
	3	3.155	185.512	239.747	26.745	5.584	212.257	245.331
	4	18.657	1306.333	1424.291	246.678	51.508	1553.012	1475.799
Sum	NA	100.000	5177.133	3842.903	294.090	61.408	5471.223	3904.311

`MAX_INPUTS` = 8

	n.inputs	share	input.size.cost	input.compute.cost	additional.outputs.size.cost	additional.outputs.compute.cost	total.size.cost	total.compute.cost
	1	50.270	1937.770	885.621	0.000	0.000	1937.770	885.621
	2	36.587	1699.933	1258.029	5.159	1.077	1705.092	1259.107
	3	2.177	113.905	147.206	6.016	1.256	119.922	148.462
	4	1.273	79.297	86.457	5.578	1.165	84.875	87.622
	5	0.917	62.464	122.996	5.120	1.069	67.584	124.065
	6	0.784	59.641	105.409	5.388	1.125	65.029	106.534
	7	0.683	58.802	92.083	5.329	1.113	64.131	93.196
	8	7.309	676.720	986.385	73.773	15.404	750.493	1001.789
Sum	NA	100.000	4688.532	3684.187	106.362	22.209	4794.894	3706.396

`MAX_INPUTS` = 16

	n.inputs	share	input.size.cost	input.compute.cost	additional.outputs.size.cost	additional.outputs.compute.cost	total.size.cost	total.compute.cost
	1	52.661	1937.770	885.621	0.000	0.000	1937.770	885.621
	2	38.063	1688.213	1249.356	1.339	0.280	1689.551	1249.635
	3	1.958	97.802	126.395	1.355	0.283	99.157	126.678
	4	1.039	61.801	67.382	1.325	0.277	63.126	67.658
	5	0.693	45.084	88.774	1.258	0.263	46.342	89.037
	6	0.526	38.176	67.472	1.114	0.233	39.290	67.705
	7	0.416	34.190	53.541	0.998	0.208	35.187	53.749
	8	0.351	31.037	45.239	0.931	0.194	31.968	45.434
	9	0.303	28.503	77.399	0.912	0.190	29.415	77.590
	10	0.296	30.000	75.471	0.869	0.181	30.869	75.652
	11	0.263	28.309	67.142	1.256	0.262	29.564	67.404
	12	0.204	23.474	52.074	0.822	0.172	24.295	52.246
	13	0.179	22.372	45.896	0.760	0.159	23.132	46.054
	14	0.186	24.392	47.693	1.081	0.226	25.473	47.919
	15	0.162	22.441	41.525	0.899	0.188	23.340	41.713
	16	2.699	391.101	693.046	22.668	4.733	413.770	697.780
Sum	NA	100.000	4504.665	3684.026	37.586	7.848	4542.251	3691.874

`MAX_INPUTS` = 128

	n.inputs	share	input.size.cost	input.compute.cost	additional.outputs.size.cost	additional.outputs.compute.cost	total.size.cost	total.compute.cost
	1	54.019	1937.770	885.621	0.000	0.000	1937.770	885.621
	2	38.950	1684.132	1246.335	0.008	0.002	1684.140	1246.337
	3	1.913	93.149	120.382	0.008	0.002	93.158	120.384
	4	0.973	56.385	61.477	0.008	0.002	56.393	61.478
	5	0.622	39.459	77.697	0.008	0.002	39.466	77.698
	6	0.461	32.622	57.657	0.008	0.002	32.631	57.658
	7	0.357	28.568	44.737	0.008	0.002	28.576	44.739
	8	0.295	25.389	37.007	0.008	0.002	25.397	37.009
	9	0.247	22.618	61.419	0.007	0.001	22.625	61.421
	10	0.242	23.957	60.267	0.008	0.002	23.965	60.269
	11	0.181	19.005	45.076	0.008	0.002	19.013	45.077
	12	0.151	16.978	37.665	0.007	0.002	16.986	37.666
	13	0.130	15.871	32.560	0.007	0.001	15.878	32.561
	14	0.115	14.646	28.637	0.006	0.001	14.652	28.639
	15	0.103	13.888	25.698	0.007	0.001	13.895	25.699
	16	0.097	13.658	24.202	0.009	0.002	13.667	24.204
	17	0.079	11.537	39.129	0.008	0.002	11.545	39.130
	18	0.069	10.637	34.294	0.011	0.002	10.648	34.297
	19	0.099	15.797	49.012	0.512	0.107	16.308	49.118
	20	0.060	10.117	30.022	0.023	0.005	10.140	30.027
	21	0.050	8.750	25.066	0.014	0.003	8.764	25.068
	22	0.043	7.868	21.632	0.011	0.002	7.880	21.635
	23	0.039	7.350	19.557	0.012	0.003	7.362	19.560
	24	0.036	7.035	18.019	0.011	0.002	7.046	18.021
	25	0.035	6.976	17.197	0.009	0.002	6.985	17.198
	26	0.029	6.001	14.257	0.006	0.001	6.006	14.258
	27	0.026	5.582	12.819	0.003	0.001	5.585	12.819
	28	0.024	5.364	11.986	0.003	0.001	5.367	11.987
	29	0.022	5.032	10.890	0.003	0.001	5.034	10.890
	30	0.023	5.328	11.238	0.003	0.001	5.331	11.239
	31	0.037	8.988	18.395	0.003	0.001	8.991	18.395
	32	0.017	4.234	8.457	0.003	0.001	4.237	8.458
	33	0.015	3.902	15.161	0.002	0.000	3.905	15.161
	34	0.015	3.849	14.540	0.002	0.000	3.851	14.540
	35	0.013	3.610	13.314	0.002	0.000	3.612	13.314
	36	0.013	3.546	12.732	0.003	0.001	3.549	12.732
	37	0.011	3.229	11.346	0.003	0.001	3.232	11.346
	38	0.011	3.084	10.565	0.002	0.000	3.087	10.565
	39	0.010	2.992	10.041	0.003	0.001	2.995	10.041
	40	0.010	3.109	10.182	0.003	0.001	3.112	10.183
	41	0.009	2.859	9.182	0.002	0.000	2.862	9.182
	42	0.008	2.652	8.320	0.002	0.000	2.654	8.320
	43	0.008	2.580	7.944	0.002	0.000	2.583	7.945
	44	0.008	2.517	7.578	0.002	0.000	2.520	7.579
	45	0.007	2.483	7.342	0.003	0.001	2.486	7.342
	46	0.007	2.431	7.035	0.003	0.001	2.434	7.036
	47	0.007	2.331	6.629	0.003	0.001	2.333	6.630
	48	0.006	2.294	6.392	0.002	0.000	2.296	6.392
	49	0.006	2.300	6.274	0.003	0.001	2.302	6.275
	50	0.007	2.731	7.330	0.003	0.001	2.734	7.330
	51	0.006	2.094	5.511	0.002	0.000	2.096	5.511
	52	0.005	2.048	5.283	0.003	0.001	2.050	5.284
	53	0.005	2.028	5.135	0.002	0.000	2.030	5.136
	54	0.005	1.915	4.778	0.002	0.000	1.918	4.778
	55	0.004	1.821	4.460	0.002	0.000	1.823	4.461
	56	0.004	1.794	4.332	0.002	0.000	1.797	4.332
	57	0.004	1.780	4.223	0.002	0.000	1.783	4.224
	58	0.006	2.538	5.938	0.025	0.005	2.564	5.943
	59	0.004	1.768	4.066	0.002	0.000	1.770	4.066
	60	0.006	2.702	6.130	0.001	0.000	2.703	6.130
	61	0.004	1.863	4.157	0.002	0.000	1.865	4.157
	62	0.004	1.703	3.749	0.002	0.000	1.704	3.749
	63	0.008	3.792	8.218	0.066	0.014	3.858	8.232
	64	0.004	1.814	3.880	0.002	0.000	1.816	3.881
	65	0.003	1.626	6.833	0.003	0.001	1.629	6.834
	66	0.007	3.222	13.332	0.047	0.010	3.269	13.342
	67	0.022	10.452	42.713	0.261	0.055	10.713	42.768
	68	0.004	1.732	6.974	0.004	0.001	1.737	6.975
	69	0.003	1.635	6.500	0.002	0.000	1.637	6.500
	70	0.004	2.175	8.522	0.001	0.000	2.176	8.522
	71	0.003	1.459	5.649	0.001	0.000	1.460	5.649
	72	0.003	1.522	5.808	0.001	0.000	1.523	5.808
	73	0.003	1.655	6.245	0.001	0.000	1.656	6.245
	74	0.003	1.481	5.512	0.001	0.000	1.482	5.512
	75	0.002	0.997	3.668	0.001	0.000	0.998	3.668
	76	0.002	0.929	3.371	0.001	0.000	0.929	3.371
	77	0.002	0.939	3.372	0.001	0.000	0.940	3.372
	78	0.002	0.968	3.431	0.000	0.000	0.969	3.431
	79	0.002	0.945	3.313	0.000	0.000	0.945	3.313
	80	0.002	0.986	3.412	0.000	0.000	0.986	3.412
	81	0.002	0.967	3.313	0.001	0.000	0.968	3.314
	82	0.002	0.921	3.115	0.000	0.000	0.921	3.115
	83	0.002	0.930	3.116	0.000	0.000	0.931	3.116
	84	0.002	0.984	3.255	0.001	0.000	0.985	3.255
	85	0.001	0.897	2.938	0.001	0.000	0.898	2.938
	86	0.001	0.914	2.958	0.001	0.000	0.915	2.958
	87	0.002	0.973	3.117	0.000	0.000	0.973	3.117
	88	0.002	0.953	3.018	0.000	0.000	0.953	3.018
	89	0.001	0.937	2.939	0.000	0.000	0.937	2.939
	90	0.001	0.890	2.761	0.000	0.000	0.890	2.761
	91	0.001	0.924	2.840	0.000	0.000	0.925	2.840
	92	0.001	0.843	2.562	0.000	0.000	0.843	2.562
	93	0.001	0.911	2.742	0.000	0.000	0.911	2.742
	94	0.001	0.847	2.523	0.000	0.000	0.847	2.523
	95	0.001	0.869	2.563	0.000	0.000	0.869	2.563
	96	0.001	0.803	2.345	0.000	0.000	0.803	2.345
	97	0.001	0.792	2.286	0.000	0.000	0.792	2.286
	98	0.001	0.875	2.504	0.000	0.000	0.875	2.505
	99	0.001	0.877	2.485	0.000	0.000	0.877	2.485
	100	0.001	0.941	2.644	0.000	0.000	0.942	2.644
	101	0.001	0.851	2.366	0.000	0.000	0.851	2.366
	102	0.001	0.808	2.227	0.000	0.000	0.808	2.227
	103	0.001	0.774	2.108	0.000	0.000	0.774	2.108
	104	0.001	0.729	1.969	0.000	0.000	0.729	1.969
	105	0.001	0.803	2.148	0.000	0.000	0.803	2.148
	106	0.001	0.802	2.129	0.000	0.000	0.802	2.129
	107	0.001	0.734	1.930	0.000	0.000	0.735	1.930
	108	0.001	0.695	1.811	0.000	0.000	0.695	1.811
	109	0.001	0.740	1.910	0.000	0.000	0.740	1.910
	110	0.001	0.722	1.851	0.000	0.000	0.722	1.851
	111	0.001	0.808	2.050	0.000	0.000	0.808	2.050
	112	0.001	0.711	1.792	0.000	0.000	0.711	1.792
	113	0.001	0.766	1.911	0.000	0.000	0.766	1.911
	114	0.001	0.691	1.712	0.000	0.000	0.691	1.712
	115	0.001	0.641	1.573	0.000	0.000	0.641	1.573
	116	0.001	0.727	1.772	0.000	0.000	0.727	1.772
	117	0.001	0.750	1.812	0.000	0.000	0.750	1.813
	118	0.001	0.756	1.813	0.000	0.000	0.756	1.813
	119	0.004	3.535	8.407	0.000	0.000	3.535	8.407
	120	0.006	5.046	11.914	0.000	0.000	5.046	11.914
	121	0.001	0.655	1.534	0.000	0.000	0.656	1.534
	122	0.001	0.566	1.315	0.000	0.000	0.566	1.315
	123	0.001	0.501	1.156	0.000	0.000	0.502	1.156
	124	0.001	0.505	1.156	0.000	0.000	0.505	1.156
	125	0.001	0.606	1.375	0.000	0.000	0.606	1.375
	126	0.001	0.504	1.136	0.000	0.000	0.504	1.136
	127	0.001	0.544	1.216	0.000	0.000	0.544	1.216
	128	0.089	80.021	177.768	0.001	0.000	80.022	177.768
Sum	NA	100.000	4403.615	3856.714	1.247	0.260	4404.862	3856.975

R code to reproduce the above analysis is:

# Uncomment to install packages:
# install.packages(c("knitr", "igraph"))

input.consolidation <- function(MAX_INPUTS, input.table, example = NULL) {
  
  input.table <- input.table[input.table$n.inputs > MAX_INPUTS, , drop = FALSE]
  
  result <- vector("list", nrow(input.table))
  example.graph <- NULL
  
  for (i in seq_len(nrow(input.table))) {
    
    n.inputs <- input.table$n.inputs[i]
    
    log.inputs <- logb(n.inputs, base = MAX_INPUTS)
    rounds.final <- ceiling(log.inputs)
    
    rounds <- 0
    n.MAX_INPUTS.txs <- 0
    remainder.tx.n.inputs <- NULL
    inputs.edgelist <- data.frame(source = NULL, destination = NULL)
    
    inputs <- paste0(letters[1], seq_len(n.inputs))
    
    while (length(inputs) > 1) {
      current.length <- length(inputs)
      rounds <- rounds + 1
      
      tail.factor <- rep("A", current.length %% MAX_INPUTS)
      
      split.factor.consolidate.tail <-
        c(rep(seq_len(floor(current.length / MAX_INPUTS)), each = MAX_INPUTS), tail.factor)
      
      split.consolidate.tail <- split(inputs, split.factor.consolidate.tail)
      
      tail.length <- current.length %% MAX_INPUTS
      tail.factor <- paste0(rep("A", tail.length), seq_len(tail.length) )
      
      split.factor.dont.consolidate.tail <-
        c(rep(seq_len(floor(current.length / MAX_INPUTS)), each = MAX_INPUTS), tail.factor)
      
      split.dont.consolidate.tail <- split(inputs, split.factor.dont.consolidate.tail)
      
      if ( length(inputs) <= MAX_INPUTS | 
          (
            ceiling(length(split.consolidate.tail) / MAX_INPUTS) <
              ceiling(length(split.dont.consolidate.tail) / MAX_INPUTS)
          )
      ) {
        split.factor <- split.factor.consolidate.tail
      } else {
        split.factor <- split.factor.dont.consolidate.tail
      }
      
      n.MAX_INPUTS.txs <- n.MAX_INPUTS.txs + floor(current.length / MAX_INPUTS)
      if ( sum(split.factor == "A") > 1 ) {
        remainder.tx.n.inputs <- paste0(remainder.tx.n.inputs, " ", sum(split.factor == "A"))
      }
      inputs <- split(inputs, split.factor)
      names(inputs) <- paste0(letters[rounds + 1], seq_along(inputs))
      inputs.edgelist <- rbind(inputs.edgelist, 
        data.frame(source = unlist(inputs), destination = rep(names(inputs), times = lengths(inputs))))
      inputs <- names(inputs)
    }
    
    stopifnot(rounds == rounds.final)
    
    if (length(remainder.tx.n.inputs) == 0) { remainder.tx.n.inputs <- NA }
    
    if (length(example) == 1 && example == n.inputs) {
      example.graph <- igraph::graph_from_edgelist(as.matrix(inputs.edgelist), directed = TRUE)
    }
    
    result[[i]] <- data.frame(
      n.inputs = n.inputs,
      rounds = rounds,
      n.MAX_INPUTS.txs = n.MAX_INPUTS.txs,
      remainder.tx.n.inputs = gsub("^ ", "", remainder.tx.n.inputs)
    )
    
  }
  
  result <- do.call(rbind, result)
  
  return(list(table = result, example.graph = example.graph))
  
}





# From https://gist.github.com/Rucknium/d2c02f51a2d9f103a28caa8f51be7dbf/raw/9962ab99421254706eba041735230cb1a0f08199/monero-in-out-height-1784324-3097764.md

inputs.md <- 
"|1                |           54.06724|         54.06724|
|2                |           38.98393|         93.05116|
|3                |            1.91450|         94.96566|
|4                |            0.97294|         95.93861|
|5                |            0.62223|         96.56084|
|6                |            0.46069|         97.02153|
|7                |            0.35652|         97.37805|
|8                |            0.29441|         97.67246|
|9                |            0.24665|         97.91911|
|10               |            0.24168|         98.16079|
|11               |            0.18053|         98.34133|
|12               |            0.15063|         98.49196|
|13               |            0.13002|         98.62198|
|14               |            0.11427|         98.73625|
|15               |            0.10234|         98.83859|
|16               |            0.09614|         98.93473|
|17               |            0.07834|         99.01306|
|18               |            0.06833|         99.08139|
|19               |            0.06239|         99.14378|
|20               |            0.05884|         99.20263|
|21               |            0.04949|         99.25212|
|22               |            0.04272|         99.29484|
|23               |            0.03846|         99.33330|
|24               |            0.03545|         99.36875|
|25               |            0.03390|         99.40265|
|26               |            0.02823|         99.43088|
|27               |            0.02553|         99.45641|
|28               |            0.02386|         99.48027|
|29               |            0.02166|         99.50193|
|30               |            0.02229|         99.52422|
|31               |            0.03664|         99.56086|
|32               |            0.01672|         99.57758|
|33               |            0.01513|         99.59271|
|34               |            0.01453|         99.60724|
|35               |            0.01326|         99.62051|
|36               |            0.01264|         99.63315|
|37               |            0.01123|         99.64438|
|38               |            0.01048|         99.65485|
|39               |            0.00992|         99.66478|
|40               |            0.01008|         99.67485|
|41               |            0.00909|         99.68395|
|42               |            0.00821|         99.69215|
|43               |            0.00784|         99.69999|
|44               |            0.00746|         99.70745|
|45               |            0.00718|         99.71463|
|46               |            0.00687|         99.72150|
|47               |            0.00649|         99.72798|
|48               |            0.00627|         99.73425|
|49               |            0.00613|         99.74038|
|50               |            0.00717|         99.74755|
|51               |            0.00541|         99.75296|
|52               |            0.00510|         99.75806|
|53               |            0.00502|         99.76308|
|54               |            0.00465|         99.76773|
|55               |            0.00435|         99.77208|
|56               |            0.00418|         99.77626|
|57               |            0.00407|         99.78033|
|58               |            0.00417|         99.78450|
|59               |            0.00393|         99.78843|
|60               |            0.00606|         99.79449|
|61               |            0.00404|         99.79853|
|62               |            0.00363|         99.80215|
|63               |            0.00356|         99.80571|
|64               |            0.00373|         99.80945|
|65               |            0.00326|         99.81271|
|66               |            0.00337|         99.81608|
|67               |            0.00302|         99.81910|
|68               |            0.00321|         99.82230|
|69               |            0.00315|         99.82545|
|70               |            0.00425|         99.82970|
|71               |            0.00278|         99.83248|
|72               |            0.00287|         99.83535|
|73               |            0.00309|         99.83844|
|74               |            0.00272|         99.84116|
|75               |            0.00180|         99.84296|
|76               |            0.00166|         99.84463|
|77               |            0.00165|         99.84628|
|78               |            0.00170|         99.84798|
|79               |            0.00164|         99.84962|
|80               |            0.00169|         99.85131|
|81               |            0.00162|         99.85293|
|82               |            0.00155|         99.85448|
|83               |            0.00154|         99.85602|
|84               |            0.00160|         99.85761|
|85               |            0.00144|         99.85905|
|86               |            0.00144|         99.86050|
|87               |            0.00154|         99.86204|
|88               |            0.00150|         99.86354|
|89               |            0.00146|         99.86499|
|90               |            0.00138|         99.86638|
|91               |            0.00141|         99.86778|
|92               |            0.00128|         99.86907|
|93               |            0.00137|         99.87044|
|94               |            0.00126|         99.87169|
|95               |            0.00128|         99.87297|
|96               |            0.00116|         99.87413|
|97               |            0.00114|         99.87527|
|98               |            0.00125|         99.87652|
|99               |            0.00124|         99.87776|
|100              |            0.00131|         99.87907|
|101              |            0.00117|         99.88024|
|102              |            0.00111|         99.88135|
|103              |            0.00104|         99.88239|
|104              |            0.00097|         99.88336|
|105              |            0.00106|         99.88442|
|106              |            0.00107|         99.88549|
|107              |            0.00096|         99.88646|
|108              |            0.00090|         99.88736|
|109              |            0.00095|         99.88831|
|110              |            0.00092|         99.88923|
|111              |            0.00101|         99.89024|
|112              |            0.00088|         99.89112|
|113              |            0.00094|         99.89206|
|114              |            0.00085|         99.89292|
|115              |            0.00078|         99.89369|
|116              |            0.00089|         99.89459|
|117              |            0.00089|         99.89548|
|118              |            0.00090|         99.89638|
|119              |            0.00422|         99.90060|
|120              |            0.00596|         99.90656|
|121              |            0.00076|         99.90733|
|122              |            0.00064|         99.90797|
|123              |            0.00057|         99.90853|
|124              |            0.00057|         99.90910|
|125              |            0.00068|         99.90978|
|126              |            0.00056|         99.91034|
|127              |            0.00059|         99.91092|
|128              |            0.00055|         99.91148|
|129              |            0.00060|         99.91207|
|130              |            0.00058|         99.91265|
|131              |            0.00056|         99.91321|
|132              |            0.00053|         99.91375|
|133              |            0.00060|         99.91434|
|134              |            0.00058|         99.91493|
|135              |            0.00054|         99.91547|
|136              |            0.00049|         99.91596|
|137              |            0.00059|         99.91655|
|138              |            0.00054|         99.91709|
|139              |            0.00052|         99.91762|
|140              |            0.00050|         99.91812|
|141              |            0.00044|         99.91855|
|142              |            0.00050|         99.91905|
|143              |            0.00064|         99.91970|
|144              |            0.00055|         99.92025|
|145              |            0.00078|         99.92102|
|146              |            0.03634|         99.95736|
|147              |            0.00160|         99.95896|
|148              |            0.00096|         99.95992|
|149              |            0.00080|         99.96072|
|150              |            0.00087|         99.96160|
|151              |            0.00077|         99.96237|
|152              |            0.00065|         99.96302|
|153              |            0.00040|         99.96342|
|154              |            0.00020|         99.96362|
|155              |            0.00019|         99.96382|
|156              |            0.00018|         99.96400|
|157              |            0.00024|         99.96424|
|158              |            0.00022|         99.96445|
|159              |            0.00022|         99.96467|
|160              |            0.00017|         99.96485|
|161              |            0.00014|         99.96499|
|162              |            0.00017|         99.96517|
|163              |            0.00020|         99.96537|
|164              |            0.00021|         99.96558|
|165              |            0.00017|         99.96575|
|166              |            0.00020|         99.96595|
|167              |            0.00018|         99.96613|
|168              |            0.00016|         99.96629|
|169              |            0.00017|         99.96646|
|170              |            0.00016|         99.96663|
|171              |            0.00017|         99.96679|
|172              |            0.00021|         99.96701|
|173              |            0.00021|         99.96721|
|174              |            0.00018|         99.96739|
|175              |            0.00016|         99.96755|
|176              |            0.00018|         99.96773|
|177              |            0.00020|         99.96793|
|178              |            0.00013|         99.96805|
|179              |            0.00021|         99.96826|
|180              |            0.00014|         99.96841|
|181              |            0.00015|         99.96856|
|182              |            0.00013|         99.96869|
|183              |            0.00017|         99.96885|
|184              |            0.00017|         99.96902|
|185              |            0.00179|         99.97081|
|186              |            0.00015|         99.97096|
|187              |            0.00009|         99.97105|
|188              |            0.00013|         99.97118|
|189              |            0.00013|         99.97132|
|190              |            0.00468|         99.97600|
|191              |            0.00016|         99.97615|
|192              |            0.00019|         99.97634|
|193              |            0.00336|         99.97971|
|194              |            0.01854|         99.99824|
|195              |            0.00031|         99.99855|
|196              |            0.00013|         99.99869|
|197              |            0.00005|         99.99873|
|198              |            0.00007|         99.99880|
|199              |            0.00006|         99.99887|
|200              |            0.00006|         99.99893|
|201              |            0.00006|         99.99899|
|202              |            0.00005|         99.99903|
|203              |            0.00004|         99.99907|
|204              |            0.00005|         99.99912|
|205              |            0.00003|         99.99915|
|206              |            0.00003|         99.99919|
|207              |            0.00003|         99.99922|
|208              |            0.00005|         99.99927|
|209              |            0.00002|         99.99930|
|210              |            0.00003|         99.99933|
|211              |            0.00004|         99.99937|
|212              |            0.00004|         99.99941|
|213              |            0.00005|         99.99945|
|214              |            0.00003|         99.99948|
|215              |            0.00002|         99.99951|
|216              |            0.00002|         99.99952|
|217              |            0.00001|         99.99953|
|218              |            0.00002|         99.99954|
|219              |            0.00001|         99.99955|
|220              |            0.00001|         99.99956|
|221              |            0.00001|         99.99957|
|222              |            0.00001|         99.99958|
|223              |            0.00002|         99.99960|
|224              |            0.00001|         99.99961|
|225              |            0.00001|         99.99961|
|226              |            0.00001|         99.99962|
|227              |            0.00002|         99.99965|
|228              |            0.00002|         99.99966|
|229              |            0.00001|         99.99967|
|230              |            0.00002|         99.99968|
|231              |            0.00002|         99.99970|
|232              |            0.00002|         99.99972|
|233              |            0.00000|         99.99973|
|234              |            0.00001|         99.99973|
|235              |            0.00001|         99.99974|
|236              |            0.00001|         99.99975|
|237              |            0.00001|         99.99976|
|238              |            0.00002|         99.99977|
|239              |            0.00002|         99.99979|
|240              |            0.00002|         99.99981|
|241              |            0.00001|         99.99982|
|242              |            0.00001|         99.99983|
|243              |            0.00000|         99.99983|
|244              |            0.00002|         99.99984|
|245              |            0.00001|         99.99985|
|247              |            0.00002|         99.99987|
|248              |            0.00001|         99.99987|
|249              |            0.00002|         99.99989|
|250              |            0.00001|         99.99990|
|251              |            0.00001|         99.99991|
|252              |            0.00001|         99.99991|
|253              |            0.00001|         99.99993|
|254              |            0.00002|         99.99994|
|255              |            0.00001|         99.99995|
|259              |            0.00001|         99.99995|
|261              |            0.00000|         99.99996|
|264              |            0.00001|         99.99996|
|265              |            0.00000|         99.99997|
|266              |            0.00001|         99.99997|
|267              |            0.00000|         99.99998|
|268              |            0.00000|         99.99998|
|270              |            0.00000|         99.99998|
|272              |            0.00000|         99.99998|
|273              |            0.00000|         99.99999|
|274              |            0.00001|         99.99999|
|277              |            0.00000|        100.00000|
|282              |            0.00000|        100.00000|
"

inputs.md <- read.delim(text = inputs.md, header = FALSE, sep = "|")

inputs.md <- inputs.md[, - c(1, ncol(inputs.md))]
# colnames(inputs.md) <- c("Number of inputs", "Share (percentage)", "Cumulative share")
colnames(inputs.md) <- c("n.inputs", "share", "cumulative.share")

# From https://gist.github.com/kayabaNerve/c42aeae1ae9434f2678943c3b8da7898

fcmp.input.cost <-
"Compute Factor: 4 , Inputs: 1 , Proof 1 Base Cost: 1024 , Proof 2 Base Cost: 512 , Commitments: 102 (p1vcs: 4 , p2vcs: 4 ) , Size: 3584
Compute Factor: 4 , Inputs: 2 , Proof 1 Base Cost: 2048 , Proof 2 Base Cost: 1024 , Commitments: 125 (p1vcs: 4 , p2vcs: 4 ) , Size: 4320
Compute Factor: 4 , Inputs: 3 , Proof 1 Base Cost: 4096 , Proof 2 Base Cost: 2048 , Commitments: 142 (p1vcs: 3 , p2vcs: 3 ) , Size: 4864
Compute Factor: 4 , Inputs: 4 , Proof 1 Base Cost: 4096 , Proof 2 Base Cost: 2048 , Commitments: 171 (p1vcs: 4 , p2vcs: 4 ) , Size: 5792
Compute Factor: 4 , Inputs: 5 , Proof 1 Base Cost: 8192 , Proof 2 Base Cost: 4096 , Commitments: 188 (p1vcs: 3 , p2vcs: 3 ) , Size: 6336
Compute Factor: 4 , Inputs: 6 , Proof 1 Base Cost: 8192 , Proof 2 Base Cost: 4096 , Commitments: 211 (p1vcs: 3 , p2vcs: 3 ) , Size: 7072
Compute Factor: 4 , Inputs: 7 , Proof 1 Base Cost: 8192 , Proof 2 Base Cost: 4096 , Commitments: 240 (p1vcs: 4 , p2vcs: 4 ) , Size: 8000
Compute Factor: 4 , Inputs: 8 , Proof 1 Base Cost: 8192 , Proof 2 Base Cost: 4096 , Commitments: 259 (p1vcs: 4 , p2vcs: 4 ) , Size: 8608
Compute Factor: 4 , Inputs: 9 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 276 (p1vcs: 3 , p2vcs: 3 ) , Size: 9152
Compute Factor: 4 , Inputs: 10 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 299 (p1vcs: 3 , p2vcs: 3 ) , Size: 9888
Compute Factor: 4 , Inputs: 11 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 318 (p1vcs: 3 , p2vcs: 3 ) , Size: 10496
Compute Factor: 4 , Inputs: 12 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 341 (p1vcs: 3 , p2vcs: 3 ) , Size: 11232
Compute Factor: 4 , Inputs: 13 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 370 (p1vcs: 4 , p2vcs: 4 ) , Size: 12160
Compute Factor: 4 , Inputs: 14 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 389 (p1vcs: 4 , p2vcs: 4 ) , Size: 12768
Compute Factor: 4 , Inputs: 15 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 412 (p1vcs: 4 , p2vcs: 4 ) , Size: 13504
Compute Factor: 4 , Inputs: 16 , Proof 1 Base Cost: 16384 , Proof 2 Base Cost: 8192 , Commitments: 431 (p1vcs: 4 , p2vcs: 4 ) , Size: 14112
Compute Factor: 4 , Inputs: 17 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 447 (p1vcs: 2 , p2vcs: 3 ) , Size: 14624
Compute Factor: 4 , Inputs: 18 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 471 (p1vcs: 3 , p2vcs: 3 ) , Size: 15392
Compute Factor: 4 , Inputs: 19 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 490 (p1vcs: 3 , p2vcs: 3 ) , Size: 16000
Compute Factor: 4 , Inputs: 20 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 513 (p1vcs: 3 , p2vcs: 3 ) , Size: 16736
Compute Factor: 4 , Inputs: 21 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 532 (p1vcs: 3 , p2vcs: 3 ) , Size: 17344
Compute Factor: 4 , Inputs: 22 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 555 (p1vcs: 3 , p2vcs: 3 ) , Size: 18080
Compute Factor: 4 , Inputs: 23 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 574 (p1vcs: 3 , p2vcs: 3 ) , Size: 18688
Compute Factor: 4 , Inputs: 24 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 597 (p1vcs: 3 , p2vcs: 3 ) , Size: 19424
Compute Factor: 4 , Inputs: 25 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 621 (p1vcs: 3 , p2vcs: 4 ) , Size: 20192
Compute Factor: 4 , Inputs: 26 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 645 (p1vcs: 4 , p2vcs: 4 ) , Size: 20960
Compute Factor: 4 , Inputs: 27 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 668 (p1vcs: 4 , p2vcs: 4 ) , Size: 21696
Compute Factor: 4 , Inputs: 28 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 687 (p1vcs: 4 , p2vcs: 4 ) , Size: 22304
Compute Factor: 4 , Inputs: 29 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 710 (p1vcs: 4 , p2vcs: 4 ) , Size: 23040
Compute Factor: 4 , Inputs: 30 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 729 (p1vcs: 4 , p2vcs: 4 ) , Size: 23648
Compute Factor: 4 , Inputs: 31 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 752 (p1vcs: 4 , p2vcs: 4 ) , Size: 24384
Compute Factor: 4 , Inputs: 32 , Proof 1 Base Cost: 32768 , Proof 2 Base Cost: 16384 , Commitments: 771 (p1vcs: 4 , p2vcs: 4 ) , Size: 24992
Compute Factor: 4 , Inputs: 33 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 787 (p1vcs: 2 , p2vcs: 3 ) , Size: 25504
Compute Factor: 4 , Inputs: 34 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 810 (p1vcs: 2 , p2vcs: 3 ) , Size: 26240
Compute Factor: 4 , Inputs: 35 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 830 (p1vcs: 3 , p2vcs: 3 ) , Size: 26880
Compute Factor: 4 , Inputs: 36 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 853 (p1vcs: 3 , p2vcs: 3 ) , Size: 27616
Compute Factor: 4 , Inputs: 37 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 872 (p1vcs: 3 , p2vcs: 3 ) , Size: 28224
Compute Factor: 4 , Inputs: 38 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 895 (p1vcs: 3 , p2vcs: 3 ) , Size: 28960
Compute Factor: 4 , Inputs: 39 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 914 (p1vcs: 3 , p2vcs: 3 ) , Size: 29568
Compute Factor: 4 , Inputs: 40 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 937 (p1vcs: 3 , p2vcs: 3 ) , Size: 30304
Compute Factor: 4 , Inputs: 41 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 956 (p1vcs: 3 , p2vcs: 3 ) , Size: 30912
Compute Factor: 4 , Inputs: 42 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 979 (p1vcs: 3 , p2vcs: 3 ) , Size: 31648
Compute Factor: 4 , Inputs: 43 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 998 (p1vcs: 3 , p2vcs: 3 ) , Size: 32256
Compute Factor: 4 , Inputs: 44 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1021 (p1vcs: 3 , p2vcs: 3 ) , Size: 32992
Compute Factor: 4 , Inputs: 45 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1040 (p1vcs: 3 , p2vcs: 3 ) , Size: 33600
Compute Factor: 4 , Inputs: 46 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1063 (p1vcs: 3 , p2vcs: 3 ) , Size: 34336
Compute Factor: 4 , Inputs: 47 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1082 (p1vcs: 3 , p2vcs: 3 ) , Size: 34944
Compute Factor: 4 , Inputs: 48 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1105 (p1vcs: 3 , p2vcs: 3 ) , Size: 35680
Compute Factor: 4 , Inputs: 49 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1129 (p1vcs: 3 , p2vcs: 4 ) , Size: 36448
Compute Factor: 4 , Inputs: 50 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1148 (p1vcs: 3 , p2vcs: 4 ) , Size: 37056
Compute Factor: 4 , Inputs: 51 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1171 (p1vcs: 3 , p2vcs: 4 ) , Size: 37792
Compute Factor: 4 , Inputs: 52 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1195 (p1vcs: 4 , p2vcs: 4 ) , Size: 38560
Compute Factor: 4 , Inputs: 53 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1218 (p1vcs: 4 , p2vcs: 4 ) , Size: 39296
Compute Factor: 4 , Inputs: 54 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1237 (p1vcs: 4 , p2vcs: 4 ) , Size: 39904
Compute Factor: 4 , Inputs: 55 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1260 (p1vcs: 4 , p2vcs: 4 ) , Size: 40640
Compute Factor: 4 , Inputs: 56 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1279 (p1vcs: 4 , p2vcs: 4 ) , Size: 41248
Compute Factor: 4 , Inputs: 57 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1302 (p1vcs: 4 , p2vcs: 4 ) , Size: 41984
Compute Factor: 4 , Inputs: 58 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1321 (p1vcs: 4 , p2vcs: 4 ) , Size: 42592
Compute Factor: 4 , Inputs: 59 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1344 (p1vcs: 4 , p2vcs: 4 ) , Size: 43328
Compute Factor: 4 , Inputs: 60 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1363 (p1vcs: 4 , p2vcs: 4 ) , Size: 43936
Compute Factor: 4 , Inputs: 61 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1386 (p1vcs: 4 , p2vcs: 4 ) , Size: 44672
Compute Factor: 4 , Inputs: 62 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1405 (p1vcs: 4 , p2vcs: 4 ) , Size: 45280
Compute Factor: 4 , Inputs: 63 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1428 (p1vcs: 4 , p2vcs: 4 ) , Size: 46016
Compute Factor: 4 , Inputs: 64 , Proof 1 Base Cost: 65536 , Proof 2 Base Cost: 32768 , Commitments: 1447 (p1vcs: 4 , p2vcs: 4 ) , Size: 46624
Compute Factor: 4 , Inputs: 65 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1463 (p1vcs: 2 , p2vcs: 3 ) , Size: 47136
Compute Factor: 4 , Inputs: 66 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1486 (p1vcs: 2 , p2vcs: 3 ) , Size: 47872
Compute Factor: 4 , Inputs: 67 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1505 (p1vcs: 2 , p2vcs: 3 ) , Size: 48480
Compute Factor: 4 , Inputs: 68 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1528 (p1vcs: 2 , p2vcs: 3 ) , Size: 49216
Compute Factor: 4 , Inputs: 69 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1548 (p1vcs: 3 , p2vcs: 3 ) , Size: 49856
Compute Factor: 4 , Inputs: 70 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1571 (p1vcs: 3 , p2vcs: 3 ) , Size: 50592
Compute Factor: 4 , Inputs: 71 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1590 (p1vcs: 3 , p2vcs: 3 ) , Size: 51200
Compute Factor: 4 , Inputs: 72 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1613 (p1vcs: 3 , p2vcs: 3 ) , Size: 51936
Compute Factor: 4 , Inputs: 73 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1632 (p1vcs: 3 , p2vcs: 3 ) , Size: 52544
Compute Factor: 4 , Inputs: 74 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1655 (p1vcs: 3 , p2vcs: 3 ) , Size: 53280
Compute Factor: 4 , Inputs: 75 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1674 (p1vcs: 3 , p2vcs: 3 ) , Size: 53888
Compute Factor: 4 , Inputs: 76 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1697 (p1vcs: 3 , p2vcs: 3 ) , Size: 54624
Compute Factor: 4 , Inputs: 77 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1716 (p1vcs: 3 , p2vcs: 3 ) , Size: 55232
Compute Factor: 4 , Inputs: 78 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1739 (p1vcs: 3 , p2vcs: 3 ) , Size: 55968
Compute Factor: 4 , Inputs: 79 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1758 (p1vcs: 3 , p2vcs: 3 ) , Size: 56576
Compute Factor: 4 , Inputs: 80 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1781 (p1vcs: 3 , p2vcs: 3 ) , Size: 57312
Compute Factor: 4 , Inputs: 81 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1800 (p1vcs: 3 , p2vcs: 3 ) , Size: 57920
Compute Factor: 4 , Inputs: 82 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1823 (p1vcs: 3 , p2vcs: 3 ) , Size: 58656
Compute Factor: 4 , Inputs: 83 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1842 (p1vcs: 3 , p2vcs: 3 ) , Size: 59264
Compute Factor: 4 , Inputs: 84 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1865 (p1vcs: 3 , p2vcs: 3 ) , Size: 60000
Compute Factor: 4 , Inputs: 85 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1884 (p1vcs: 3 , p2vcs: 3 ) , Size: 60608
Compute Factor: 4 , Inputs: 86 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1907 (p1vcs: 3 , p2vcs: 3 ) , Size: 61344
Compute Factor: 4 , Inputs: 87 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1926 (p1vcs: 3 , p2vcs: 3 ) , Size: 61952
Compute Factor: 4 , Inputs: 88 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1949 (p1vcs: 3 , p2vcs: 3 ) , Size: 62688
Compute Factor: 4 , Inputs: 89 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1968 (p1vcs: 3 , p2vcs: 3 ) , Size: 63296
Compute Factor: 4 , Inputs: 90 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 1991 (p1vcs: 3 , p2vcs: 3 ) , Size: 64032
Compute Factor: 4 , Inputs: 91 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2010 (p1vcs: 3 , p2vcs: 3 ) , Size: 64640
Compute Factor: 4 , Inputs: 92 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2033 (p1vcs: 3 , p2vcs: 3 ) , Size: 65376
Compute Factor: 4 , Inputs: 93 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2052 (p1vcs: 3 , p2vcs: 3 ) , Size: 65984
Compute Factor: 4 , Inputs: 94 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2075 (p1vcs: 3 , p2vcs: 3 ) , Size: 66720
Compute Factor: 4 , Inputs: 95 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2094 (p1vcs: 3 , p2vcs: 3 ) , Size: 67328
Compute Factor: 4 , Inputs: 96 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2117 (p1vcs: 3 , p2vcs: 3 ) , Size: 68064
Compute Factor: 4 , Inputs: 97 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2141 (p1vcs: 3 , p2vcs: 4 ) , Size: 68832
Compute Factor: 4 , Inputs: 98 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2160 (p1vcs: 3 , p2vcs: 4 ) , Size: 69440
Compute Factor: 4 , Inputs: 99 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2183 (p1vcs: 3 , p2vcs: 4 ) , Size: 70176
Compute Factor: 4 , Inputs: 100 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2202 (p1vcs: 3 , p2vcs: 4 ) , Size: 70784
Compute Factor: 4 , Inputs: 101 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2225 (p1vcs: 3 , p2vcs: 4 ) , Size: 71520
Compute Factor: 4 , Inputs: 102 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2244 (p1vcs: 3 , p2vcs: 4 ) , Size: 72128
Compute Factor: 4 , Inputs: 103 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2272 (p1vcs: 4 , p2vcs: 4 ) , Size: 73024
Compute Factor: 4 , Inputs: 104 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2291 (p1vcs: 4 , p2vcs: 4 ) , Size: 73632
Compute Factor: 4 , Inputs: 105 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2314 (p1vcs: 4 , p2vcs: 4 ) , Size: 74368
Compute Factor: 4 , Inputs: 106 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2333 (p1vcs: 4 , p2vcs: 4 ) , Size: 74976
Compute Factor: 4 , Inputs: 107 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2356 (p1vcs: 4 , p2vcs: 4 ) , Size: 75712
Compute Factor: 4 , Inputs: 108 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2375 (p1vcs: 4 , p2vcs: 4 ) , Size: 76320
Compute Factor: 4 , Inputs: 109 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2398 (p1vcs: 4 , p2vcs: 4 ) , Size: 77056
Compute Factor: 4 , Inputs: 110 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2417 (p1vcs: 4 , p2vcs: 4 ) , Size: 77664
Compute Factor: 4 , Inputs: 111 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2440 (p1vcs: 4 , p2vcs: 4 ) , Size: 78400
Compute Factor: 4 , Inputs: 112 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2459 (p1vcs: 4 , p2vcs: 4 ) , Size: 79008
Compute Factor: 4 , Inputs: 113 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2482 (p1vcs: 4 , p2vcs: 4 ) , Size: 79744
Compute Factor: 4 , Inputs: 114 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2501 (p1vcs: 4 , p2vcs: 4 ) , Size: 80352
Compute Factor: 4 , Inputs: 115 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2524 (p1vcs: 4 , p2vcs: 4 ) , Size: 81088
Compute Factor: 4 , Inputs: 116 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2543 (p1vcs: 4 , p2vcs: 4 ) , Size: 81696
Compute Factor: 4 , Inputs: 117 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2566 (p1vcs: 4 , p2vcs: 4 ) , Size: 82432
Compute Factor: 4 , Inputs: 118 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2585 (p1vcs: 4 , p2vcs: 4 ) , Size: 83040
Compute Factor: 4 , Inputs: 119 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2608 (p1vcs: 4 , p2vcs: 4 ) , Size: 83776
Compute Factor: 4 , Inputs: 120 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2627 (p1vcs: 4 , p2vcs: 4 ) , Size: 84384
Compute Factor: 4 , Inputs: 121 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2650 (p1vcs: 4 , p2vcs: 4 ) , Size: 85120
Compute Factor: 4 , Inputs: 122 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2669 (p1vcs: 4 , p2vcs: 4 ) , Size: 85728
Compute Factor: 4 , Inputs: 123 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2692 (p1vcs: 4 , p2vcs: 4 ) , Size: 86464
Compute Factor: 4 , Inputs: 124 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2711 (p1vcs: 4 , p2vcs: 4 ) , Size: 87072
Compute Factor: 4 , Inputs: 125 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2734 (p1vcs: 4 , p2vcs: 4 ) , Size: 87808
Compute Factor: 4 , Inputs: 126 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2753 (p1vcs: 4 , p2vcs: 4 ) , Size: 88416
Compute Factor: 4 , Inputs: 127 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2776 (p1vcs: 4 , p2vcs: 4 ) , Size: 89152
Compute Factor: 4 , Inputs: 128 , Proof 1 Base Cost: 131072 , Proof 2 Base Cost: 65536 , Commitments: 2795 (p1vcs: 4 , p2vcs: 4 ) , Size: 89760
Compute Factor: 4 , Inputs: 129 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2811 (p1vcs: 2 , p2vcs: 3 ) , Size: 90272
Compute Factor: 4 , Inputs: 130 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2834 (p1vcs: 2 , p2vcs: 3 ) , Size: 91008
Compute Factor: 4 , Inputs: 131 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2853 (p1vcs: 2 , p2vcs: 3 ) , Size: 91616
Compute Factor: 4 , Inputs: 132 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2876 (p1vcs: 2 , p2vcs: 3 ) , Size: 92352
Compute Factor: 4 , Inputs: 133 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2895 (p1vcs: 2 , p2vcs: 3 ) , Size: 92960
Compute Factor: 4 , Inputs: 134 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2918 (p1vcs: 2 , p2vcs: 3 ) , Size: 93696
Compute Factor: 4 , Inputs: 135 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2937 (p1vcs: 2 , p2vcs: 3 ) , Size: 94304
Compute Factor: 4 , Inputs: 136 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2960 (p1vcs: 2 , p2vcs: 3 ) , Size: 95040
Compute Factor: 4 , Inputs: 137 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 2980 (p1vcs: 3 , p2vcs: 3 ) , Size: 95680
Compute Factor: 4 , Inputs: 138 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3003 (p1vcs: 3 , p2vcs: 3 ) , Size: 96416
Compute Factor: 4 , Inputs: 139 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3022 (p1vcs: 3 , p2vcs: 3 ) , Size: 97024
Compute Factor: 4 , Inputs: 140 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3045 (p1vcs: 3 , p2vcs: 3 ) , Size: 97760
Compute Factor: 4 , Inputs: 141 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3064 (p1vcs: 3 , p2vcs: 3 ) , Size: 98368
Compute Factor: 4 , Inputs: 142 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3087 (p1vcs: 3 , p2vcs: 3 ) , Size: 99104
Compute Factor: 4 , Inputs: 143 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3106 (p1vcs: 3 , p2vcs: 3 ) , Size: 99712
Compute Factor: 4 , Inputs: 144 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3129 (p1vcs: 3 , p2vcs: 3 ) , Size: 100448
Compute Factor: 4 , Inputs: 145 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3148 (p1vcs: 3 , p2vcs: 3 ) , Size: 101056
Compute Factor: 4 , Inputs: 146 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3171 (p1vcs: 3 , p2vcs: 3 ) , Size: 101792
Compute Factor: 4 , Inputs: 147 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3190 (p1vcs: 3 , p2vcs: 3 ) , Size: 102400
Compute Factor: 4 , Inputs: 148 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3213 (p1vcs: 3 , p2vcs: 3 ) , Size: 103136
Compute Factor: 4 , Inputs: 149 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3232 (p1vcs: 3 , p2vcs: 3 ) , Size: 103744
Compute Factor: 4 , Inputs: 150 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3255 (p1vcs: 3 , p2vcs: 3 ) , Size: 104480
Compute Factor: 4 , Inputs: 151 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3274 (p1vcs: 3 , p2vcs: 3 ) , Size: 105088
Compute Factor: 4 , Inputs: 152 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3297 (p1vcs: 3 , p2vcs: 3 ) , Size: 105824
Compute Factor: 4 , Inputs: 153 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3316 (p1vcs: 3 , p2vcs: 3 ) , Size: 106432
Compute Factor: 4 , Inputs: 154 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3339 (p1vcs: 3 , p2vcs: 3 ) , Size: 107168
Compute Factor: 4 , Inputs: 155 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3358 (p1vcs: 3 , p2vcs: 3 ) , Size: 107776
Compute Factor: 4 , Inputs: 156 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3381 (p1vcs: 3 , p2vcs: 3 ) , Size: 108512
Compute Factor: 4 , Inputs: 157 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3400 (p1vcs: 3 , p2vcs: 3 ) , Size: 109120
Compute Factor: 4 , Inputs: 158 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3423 (p1vcs: 3 , p2vcs: 3 ) , Size: 109856
Compute Factor: 4 , Inputs: 159 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3442 (p1vcs: 3 , p2vcs: 3 ) , Size: 110464
Compute Factor: 4 , Inputs: 160 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3465 (p1vcs: 3 , p2vcs: 3 ) , Size: 111200
Compute Factor: 4 , Inputs: 161 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3484 (p1vcs: 3 , p2vcs: 3 ) , Size: 111808
Compute Factor: 4 , Inputs: 162 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3507 (p1vcs: 3 , p2vcs: 3 ) , Size: 112544
Compute Factor: 4 , Inputs: 163 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3526 (p1vcs: 3 , p2vcs: 3 ) , Size: 113152
Compute Factor: 4 , Inputs: 164 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3549 (p1vcs: 3 , p2vcs: 3 ) , Size: 113888
Compute Factor: 4 , Inputs: 165 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3568 (p1vcs: 3 , p2vcs: 3 ) , Size: 114496
Compute Factor: 4 , Inputs: 166 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3591 (p1vcs: 3 , p2vcs: 3 ) , Size: 115232
Compute Factor: 4 , Inputs: 167 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3610 (p1vcs: 3 , p2vcs: 3 ) , Size: 115840
Compute Factor: 4 , Inputs: 168 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3633 (p1vcs: 3 , p2vcs: 3 ) , Size: 116576
Compute Factor: 4 , Inputs: 169 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3652 (p1vcs: 3 , p2vcs: 3 ) , Size: 117184
Compute Factor: 4 , Inputs: 170 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3675 (p1vcs: 3 , p2vcs: 3 ) , Size: 117920
Compute Factor: 4 , Inputs: 171 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3694 (p1vcs: 3 , p2vcs: 3 ) , Size: 118528
Compute Factor: 4 , Inputs: 172 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3717 (p1vcs: 3 , p2vcs: 3 ) , Size: 119264
Compute Factor: 4 , Inputs: 173 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3736 (p1vcs: 3 , p2vcs: 3 ) , Size: 119872
Compute Factor: 4 , Inputs: 174 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3759 (p1vcs: 3 , p2vcs: 3 ) , Size: 120608
Compute Factor: 4 , Inputs: 175 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3778 (p1vcs: 3 , p2vcs: 3 ) , Size: 121216
Compute Factor: 4 , Inputs: 176 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3801 (p1vcs: 3 , p2vcs: 3 ) , Size: 121952
Compute Factor: 4 , Inputs: 177 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3820 (p1vcs: 3 , p2vcs: 3 ) , Size: 122560
Compute Factor: 4 , Inputs: 178 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3843 (p1vcs: 3 , p2vcs: 3 ) , Size: 123296
Compute Factor: 4 , Inputs: 179 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3862 (p1vcs: 3 , p2vcs: 3 ) , Size: 123904
Compute Factor: 4 , Inputs: 180 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3885 (p1vcs: 3 , p2vcs: 3 ) , Size: 124640
Compute Factor: 4 , Inputs: 181 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3904 (p1vcs: 3 , p2vcs: 3 ) , Size: 125248
Compute Factor: 4 , Inputs: 182 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3927 (p1vcs: 3 , p2vcs: 3 ) , Size: 125984
Compute Factor: 4 , Inputs: 183 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3946 (p1vcs: 3 , p2vcs: 3 ) , Size: 126592
Compute Factor: 4 , Inputs: 184 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3969 (p1vcs: 3 , p2vcs: 3 ) , Size: 127328
Compute Factor: 4 , Inputs: 185 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 3988 (p1vcs: 3 , p2vcs: 3 ) , Size: 127936
Compute Factor: 4 , Inputs: 186 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4011 (p1vcs: 3 , p2vcs: 3 ) , Size: 128672
Compute Factor: 4 , Inputs: 187 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4030 (p1vcs: 3 , p2vcs: 3 ) , Size: 129280
Compute Factor: 4 , Inputs: 188 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4053 (p1vcs: 3 , p2vcs: 3 ) , Size: 130016
Compute Factor: 4 , Inputs: 189 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4072 (p1vcs: 3 , p2vcs: 3 ) , Size: 130624
Compute Factor: 4 , Inputs: 190 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4095 (p1vcs: 3 , p2vcs: 3 ) , Size: 131360
Compute Factor: 4 , Inputs: 191 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4114 (p1vcs: 3 , p2vcs: 3 ) , Size: 131968
Compute Factor: 4 , Inputs: 192 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4137 (p1vcs: 3 , p2vcs: 3 ) , Size: 132704
Compute Factor: 4 , Inputs: 193 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4161 (p1vcs: 3 , p2vcs: 4 ) , Size: 133472
Compute Factor: 4 , Inputs: 194 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4180 (p1vcs: 3 , p2vcs: 4 ) , Size: 134080
Compute Factor: 4 , Inputs: 195 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4203 (p1vcs: 3 , p2vcs: 4 ) , Size: 134816
Compute Factor: 4 , Inputs: 196 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4222 (p1vcs: 3 , p2vcs: 4 ) , Size: 135424
Compute Factor: 4 , Inputs: 197 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4245 (p1vcs: 3 , p2vcs: 4 ) , Size: 136160
Compute Factor: 4 , Inputs: 198 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4264 (p1vcs: 3 , p2vcs: 4 ) , Size: 136768
Compute Factor: 4 , Inputs: 199 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4287 (p1vcs: 3 , p2vcs: 4 ) , Size: 137504
Compute Factor: 4 , Inputs: 200 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4306 (p1vcs: 3 , p2vcs: 4 ) , Size: 138112
Compute Factor: 4 , Inputs: 201 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4329 (p1vcs: 3 , p2vcs: 4 ) , Size: 138848
Compute Factor: 4 , Inputs: 202 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4348 (p1vcs: 3 , p2vcs: 4 ) , Size: 139456
Compute Factor: 4 , Inputs: 203 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4371 (p1vcs: 3 , p2vcs: 4 ) , Size: 140192
Compute Factor: 4 , Inputs: 204 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4390 (p1vcs: 3 , p2vcs: 4 ) , Size: 140800
Compute Factor: 4 , Inputs: 205 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4418 (p1vcs: 4 , p2vcs: 4 ) , Size: 141696
Compute Factor: 4 , Inputs: 206 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4437 (p1vcs: 4 , p2vcs: 4 ) , Size: 142304
Compute Factor: 4 , Inputs: 207 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4460 (p1vcs: 4 , p2vcs: 4 ) , Size: 143040
Compute Factor: 4 , Inputs: 208 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4479 (p1vcs: 4 , p2vcs: 4 ) , Size: 143648
Compute Factor: 4 , Inputs: 209 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4502 (p1vcs: 4 , p2vcs: 4 ) , Size: 144384
Compute Factor: 4 , Inputs: 210 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4521 (p1vcs: 4 , p2vcs: 4 ) , Size: 144992
Compute Factor: 4 , Inputs: 211 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4544 (p1vcs: 4 , p2vcs: 4 ) , Size: 145728
Compute Factor: 4 , Inputs: 212 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4563 (p1vcs: 4 , p2vcs: 4 ) , Size: 146336
Compute Factor: 4 , Inputs: 213 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4586 (p1vcs: 4 , p2vcs: 4 ) , Size: 147072
Compute Factor: 4 , Inputs: 214 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4605 (p1vcs: 4 , p2vcs: 4 ) , Size: 147680
Compute Factor: 4 , Inputs: 215 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4628 (p1vcs: 4 , p2vcs: 4 ) , Size: 148416
Compute Factor: 4 , Inputs: 216 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4647 (p1vcs: 4 , p2vcs: 4 ) , Size: 149024
Compute Factor: 4 , Inputs: 217 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4670 (p1vcs: 4 , p2vcs: 4 ) , Size: 149760
Compute Factor: 4 , Inputs: 218 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4689 (p1vcs: 4 , p2vcs: 4 ) , Size: 150368
Compute Factor: 4 , Inputs: 219 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4712 (p1vcs: 4 , p2vcs: 4 ) , Size: 151104
Compute Factor: 4 , Inputs: 220 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4731 (p1vcs: 4 , p2vcs: 4 ) , Size: 151712
Compute Factor: 4 , Inputs: 221 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4754 (p1vcs: 4 , p2vcs: 4 ) , Size: 152448
Compute Factor: 4 , Inputs: 222 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4773 (p1vcs: 4 , p2vcs: 4 ) , Size: 153056
Compute Factor: 4 , Inputs: 223 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4796 (p1vcs: 4 , p2vcs: 4 ) , Size: 153792
Compute Factor: 4 , Inputs: 224 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4815 (p1vcs: 4 , p2vcs: 4 ) , Size: 154400
Compute Factor: 4 , Inputs: 225 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4838 (p1vcs: 4 , p2vcs: 4 ) , Size: 155136
Compute Factor: 4 , Inputs: 226 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4857 (p1vcs: 4 , p2vcs: 4 ) , Size: 155744
Compute Factor: 4 , Inputs: 227 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4880 (p1vcs: 4 , p2vcs: 4 ) , Size: 156480
Compute Factor: 4 , Inputs: 228 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4899 (p1vcs: 4 , p2vcs: 4 ) , Size: 157088
Compute Factor: 4 , Inputs: 229 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4922 (p1vcs: 4 , p2vcs: 4 ) , Size: 157824
Compute Factor: 4 , Inputs: 230 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4941 (p1vcs: 4 , p2vcs: 4 ) , Size: 158432
Compute Factor: 4 , Inputs: 231 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4964 (p1vcs: 4 , p2vcs: 4 ) , Size: 159168
Compute Factor: 4 , Inputs: 232 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 4983 (p1vcs: 4 , p2vcs: 4 ) , Size: 159776
Compute Factor: 4 , Inputs: 233 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5006 (p1vcs: 4 , p2vcs: 4 ) , Size: 160512
Compute Factor: 4 , Inputs: 234 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5025 (p1vcs: 4 , p2vcs: 4 ) , Size: 161120
Compute Factor: 4 , Inputs: 235 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5048 (p1vcs: 4 , p2vcs: 4 ) , Size: 161856
Compute Factor: 4 , Inputs: 236 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5067 (p1vcs: 4 , p2vcs: 4 ) , Size: 162464
Compute Factor: 4 , Inputs: 237 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5090 (p1vcs: 4 , p2vcs: 4 ) , Size: 163200
Compute Factor: 4 , Inputs: 238 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5109 (p1vcs: 4 , p2vcs: 4 ) , Size: 163808
Compute Factor: 4 , Inputs: 239 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5132 (p1vcs: 4 , p2vcs: 4 ) , Size: 164544
Compute Factor: 4 , Inputs: 240 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5151 (p1vcs: 4 , p2vcs: 4 ) , Size: 165152
Compute Factor: 4 , Inputs: 241 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5174 (p1vcs: 4 , p2vcs: 4 ) , Size: 165888
Compute Factor: 4 , Inputs: 242 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5193 (p1vcs: 4 , p2vcs: 4 ) , Size: 166496
Compute Factor: 4 , Inputs: 243 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5216 (p1vcs: 4 , p2vcs: 4 ) , Size: 167232
Compute Factor: 4 , Inputs: 244 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5235 (p1vcs: 4 , p2vcs: 4 ) , Size: 167840
Compute Factor: 4 , Inputs: 245 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5258 (p1vcs: 4 , p2vcs: 4 ) , Size: 168576
Compute Factor: 4 , Inputs: 246 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5277 (p1vcs: 4 , p2vcs: 4 ) , Size: 169184
Compute Factor: 4 , Inputs: 247 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5300 (p1vcs: 4 , p2vcs: 4 ) , Size: 169920
Compute Factor: 4 , Inputs: 248 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5319 (p1vcs: 4 , p2vcs: 4 ) , Size: 170528
Compute Factor: 4 , Inputs: 249 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5342 (p1vcs: 4 , p2vcs: 4 ) , Size: 171264
Compute Factor: 4 , Inputs: 250 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5361 (p1vcs: 4 , p2vcs: 4 ) , Size: 171872
Compute Factor: 4 , Inputs: 251 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5384 (p1vcs: 4 , p2vcs: 4 ) , Size: 172608
Compute Factor: 4 , Inputs: 252 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5403 (p1vcs: 4 , p2vcs: 4 ) , Size: 173216
Compute Factor: 4 , Inputs: 253 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5426 (p1vcs: 4 , p2vcs: 4 ) , Size: 173952
Compute Factor: 4 , Inputs: 254 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5445 (p1vcs: 4 , p2vcs: 4 ) , Size: 174560
Compute Factor: 4 , Inputs: 255 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5468 (p1vcs: 4 , p2vcs: 4 ) , Size: 175296
Compute Factor: 4 , Inputs: 256 , Proof 1 Base Cost: 262144 , Proof 2 Base Cost: 131072 , Commitments: 5487 (p1vcs: 4 , p2vcs: 4 ) , Size: 175904
Compute Factor: 4 , Inputs: 257 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5503 (p1vcs: 2 , p2vcs: 3 ) , Size: 176416
Compute Factor: 4 , Inputs: 258 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5526 (p1vcs: 2 , p2vcs: 3 ) , Size: 177152
Compute Factor: 4 , Inputs: 259 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5545 (p1vcs: 2 , p2vcs: 3 ) , Size: 177760
Compute Factor: 4 , Inputs: 260 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5568 (p1vcs: 2 , p2vcs: 3 ) , Size: 178496
Compute Factor: 4 , Inputs: 261 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5587 (p1vcs: 2 , p2vcs: 3 ) , Size: 179104
Compute Factor: 4 , Inputs: 262 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5610 (p1vcs: 2 , p2vcs: 3 ) , Size: 179840
Compute Factor: 4 , Inputs: 263 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5629 (p1vcs: 2 , p2vcs: 3 ) , Size: 180448
Compute Factor: 4 , Inputs: 264 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5652 (p1vcs: 2 , p2vcs: 3 ) , Size: 181184
Compute Factor: 4 , Inputs: 265 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5671 (p1vcs: 2 , p2vcs: 3 ) , Size: 181792
Compute Factor: 4 , Inputs: 266 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5694 (p1vcs: 2 , p2vcs: 3 ) , Size: 182528
Compute Factor: 4 , Inputs: 267 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5713 (p1vcs: 2 , p2vcs: 3 ) , Size: 183136
Compute Factor: 4 , Inputs: 268 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5736 (p1vcs: 2 , p2vcs: 3 ) , Size: 183872
Compute Factor: 4 , Inputs: 269 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5755 (p1vcs: 2 , p2vcs: 3 ) , Size: 184480
Compute Factor: 4 , Inputs: 270 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5778 (p1vcs: 2 , p2vcs: 3 ) , Size: 185216
Compute Factor: 4 , Inputs: 271 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5797 (p1vcs: 2 , p2vcs: 3 ) , Size: 185824
Compute Factor: 4 , Inputs: 272 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5820 (p1vcs: 2 , p2vcs: 3 ) , Size: 186560
Compute Factor: 4 , Inputs: 273 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5839 (p1vcs: 2 , p2vcs: 3 ) , Size: 187168
Compute Factor: 4 , Inputs: 274 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5863 (p1vcs: 3 , p2vcs: 3 ) , Size: 187936
Compute Factor: 4 , Inputs: 275 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5882 (p1vcs: 3 , p2vcs: 3 ) , Size: 188544
Compute Factor: 4 , Inputs: 276 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5905 (p1vcs: 3 , p2vcs: 3 ) , Size: 189280
Compute Factor: 4 , Inputs: 277 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5924 (p1vcs: 3 , p2vcs: 3 ) , Size: 189888
Compute Factor: 4 , Inputs: 278 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5947 (p1vcs: 3 , p2vcs: 3 ) , Size: 190624
Compute Factor: 4 , Inputs: 279 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5966 (p1vcs: 3 , p2vcs: 3 ) , Size: 191232
Compute Factor: 4 , Inputs: 280 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 5989 (p1vcs: 3 , p2vcs: 3 ) , Size: 191968
Compute Factor: 4 , Inputs: 281 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 6008 (p1vcs: 3 , p2vcs: 3 ) , Size: 192576
Compute Factor: 4 , Inputs: 282 , Proof 1 Base Cost: 524288 , Proof 2 Base Cost: 262144 , Commitments: 6031 (p1vcs: 3 , p2vcs: 3 ) , Size: 193312
"

fcmp.input.cost <- gsub("[A-Za-z0-9 ]*: ", "", fcmp.input.cost)
fcmp.input.cost <- gsub("[(][0-9]* ,[0-9]* [)]", "", fcmp.input.cost)
fcmp.input.cost <- read.csv(text = fcmp.input.cost, header = FALSE)

colnames(fcmp.input.cost) <- c("compute.factor", "n.inputs", "proof.1.base", "proof.2.base", "commitments", "size.cost")

fcmp.input.cost$compute.cost <- fcmp.input.cost$proof.1.base +
  fcmp.input.cost$proof.2.base + fcmp.input.cost$commitments

# From https://gist.github.com/kayabaNerve/c42aeae1ae9434f2678943c3b8da7898

bp.plus.output.cost <- 
"Outputs: 1 , Base Cost: 64 , Commitments: 16 , Size: 608
Outputs: 2 , Base Cost: 128 , Commitments: 19 , Size: 704
Outputs: 3 , Base Cost: 192 , Commitments: 22 , Size: 800
Outputs: 4 , Base Cost: 256 , Commitments: 23 , Size: 832
Outputs: 5 , Base Cost: 320 , Commitments: 26 , Size: 928
Outputs: 6 , Base Cost: 384 , Commitments: 27 , Size: 960
Outputs: 7 , Base Cost: 448 , Commitments: 28 , Size: 992
Outputs: 8 , Base Cost: 512 , Commitments: 29 , Size: 1024
Outputs: 9 , Base Cost: 576 , Commitments: 32 , Size: 1120
Outputs: 10 , Base Cost: 640 , Commitments: 33 , Size: 1152
Outputs: 11 , Base Cost: 704 , Commitments: 34 , Size: 1184
Outputs: 12 , Base Cost: 768 , Commitments: 35 , Size: 1216
Outputs: 13 , Base Cost: 832 , Commitments: 36 , Size: 1248
Outputs: 14 , Base Cost: 896 , Commitments: 37 , Size: 1280
Outputs: 15 , Base Cost: 960 , Commitments: 38 , Size: 1312
Outputs: 16 , Base Cost: 1024 , Commitments: 39 , Size: 1344
"

bp.plus.output.cost <- gsub("[A-Za-z0-9 ]*: ", "", bp.plus.output.cost)
bp.plus.output.cost <- gsub("[(][0-9]* ,[0-9]* [)]", "", bp.plus.output.cost)
bp.plus.output.cost <- read.csv(text = bp.plus.output.cost, header = FALSE)

colnames(bp.plus.output.cost) <- c("n.outputs", "proof.base", "commitments", "size.cost")

bp.plus.output.cost$compute.cost <- bp.plus.output.cost$proof.base +
  bp.plus.output.cost$commitments



input.footprint <- function(MAX_INPUTS, compute.factor, inputs.md, fcmp.input.cost, bp.plus.output.cost) {
  
  old.share <- inputs.md[inputs.md$n.inputs <= MAX_INPUTS, c("n.inputs", "share")]
  
  input.consolidation.table <- 
    input.consolidation(MAX_INPUTS = MAX_INPUTS, input.table = data.frame(n.inputs = inputs.md[, 1]))$table
  
  input.consolidation.table <- merge(input.consolidation.table, inputs.md)
  
  share.MAX_INPUTS.txs <- 0
  
  sub.maximal.txs <- rep(0, MAX_INPUTS)
  additional.outputs <- rep(0, MAX_INPUTS)
  
  for (i in seq_len(nrow(input.consolidation.table))) {
    
    share.MAX_INPUTS.txs <- share.MAX_INPUTS.txs + 
      input.consolidation.table$n.MAX_INPUTS.txs[i] *
      input.consolidation.table$share[i]
    
    additional.outputs[MAX_INPUTS] <- additional.outputs[MAX_INPUTS] + 2 *
      (input.consolidation.table$n.MAX_INPUTS.txs[i] - 1) *
      input.consolidation.table$share[i]
    # Subtract 1 to subtract the outputs of the "original" tx
    
    if ( ! is.na(input.consolidation.table$remainder.tx.n.inputs[i])) {
      remainder.tx.n.inputs <- strsplit(input.consolidation.table$remainder.tx.n.inputs[i], " ")
      for (j in remainder.tx.n.inputs[[1]]) {
        sub.maximal.txs[as.numeric(j)] <- sub.maximal.txs[as.numeric(j)] + input.consolidation.table$share[i]
        additional.outputs[as.numeric(j)] <- additional.outputs[as.numeric(j)] + 2 * input.consolidation.table$share[i]
      }
    }
    
  }
  
  share.MAX_INPUTS.txs <- c(rep(0, MAX_INPUTS - 1), share.MAX_INPUTS.txs)
  
  old.share.total <- sum(old.share$share)
  new.share <- old.share
  
  new.share$share <- new.share$share + sub.maximal.txs + share.MAX_INPUTS.txs
  
  fcmp.input.cost <- fcmp.input.cost[fcmp.input.cost$compute.factor == compute.factor, 
    c("n.inputs", "size.cost", "compute.cost")]
  
  colnames(fcmp.input.cost) <- c("n.inputs", "input.size.cost", "input.compute.cost")
  
  new.share <- merge(new.share, fcmp.input.cost)
  
  new.share$input.size.cost <- new.share$share * new.share$input.size.cost
  new.share$input.compute.cost <- new.share$share * new.share$input.compute.cost
  
  additional.outputs <- data.frame(n.inputs = seq_len(MAX_INPUTS), 
    additional.outputs.size.cost = additional.outputs *
      bp.plus.output.cost[bp.plus.output.cost$n.outputs == 2, "size.cost"],
    additional.outputs.compute.cost = additional.outputs *
      bp.plus.output.cost[bp.plus.output.cost$n.outputs == 2, "compute.cost"]
  )
  
  new.share <- merge(new.share, additional.outputs)
  
  new.share$total.size.cost <- new.share$input.size.cost + new.share$additional.outputs.size.cost
  new.share$total.compute.cost <- new.share$input.compute.cost + new.share$additional.outputs.compute.cost
  
  n.tx.total.increase <- 100 * (sum(new.share$share)/sum(old.share$share) - 1)
  
  new.share$share <- 100 * (new.share$share / sum(new.share$share))
  
  new.share <- addmargins(as.matrix(new.share), margin = 1)
  new.share[nrow(new.share), "n.inputs"] <- NA
  
  new.share[, grepl(".cost", colnames(new.share))] <-
    new.share[, grepl(".cost", colnames(new.share))] / 100
  
  new.share
  
}



input.footprint(MAX_INPUTS = 8, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost)
input.footprint(MAX_INPUTS = 16, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost)



knitr::kable(input.footprint(MAX_INPUTS = 4, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost),
  format = "pipe", row.names = TRUE, digits = 3)

knitr::kable(input.footprint(MAX_INPUTS = 8, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost),
  format = "pipe", row.names = TRUE, digits = 3)

knitr::kable(input.footprint(MAX_INPUTS = 16, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost),
  format = "pipe", row.names = TRUE, digits = 3)
  
knitr::kable(input.footprint(MAX_INPUTS = 128, compute.factor = 4, inputs.md, fcmp.input.cost, bp.plus.output.cost),
  format = "pipe", row.names = TRUE, digits = 3)




input.consolidation.graph <- input.consolidation(MAX_INPUTS = 4, input.table = inputs.md, example = 19)

png("output-consolidation-MAX_INPUTS-4-initial-outputs-19.png")

plot(input.consolidation.graph$example.graph, layout = igraph::layout_as_tree,
  main = "Output consolidation sequence\nMAX_INPUTS = 4. Initial outputs = 19.")

dev.off()

Modified python code for estimated cost per input/output cardinality

Based on https://gist.github.com/kayabaNerve/c42aeae1ae9434f2678943c3b8da7898

import math

print("-- FCMPs --")
for extraneous_compute in range(4,5):
  if pow(2, math.ceil(math.log2(extraneous_compute))) != extraneous_compute:
    continue

  for i in range(1, 282 + 1):
    target_layers = 8
    proof_1_target_layers = math.floor(target_layers / 2) + (target_layers % 2)
    proof_2_target_layers = math.floor(target_layers / 2)

    proof_1_gates_for_target_layers = extraneous_compute * 256
    proof_2_gates_for_target_layers = extraneous_compute * 128

    proof_commitments = 3
    proof_1_ip_commitments = 2 * math.ceil(math.log2(i * proof_1_gates_for_target_layers))
    proof_2_ip_commitments = 2 * math.ceil(math.log2(i * proof_2_gates_for_target_layers))

    proof_1_branches = i * proof_1_target_layers
    # The root for 8 layers is on the second proof, and it's shared for all inputs
    # Accordingly, it's only committed to once
    proof_2_branches = (i * (proof_2_target_layers - 1)) + 1

    claimed_point_variables = 2 * 256
    divisor_variables = 256
    # Proof 1 has 4 claimed points, 1 append divisor, and (proof_1_target_layers - 1) claimed points
    proof_1_variables_committed_to_per_input_for_target_layers = (4 * claimed_point_variables) + divisor_variables + ((proof_1_target_layers - 1) * claimed_point_variables)
    # Proof 2 has proof_2_target_layers claimed points
    proof_2_variables_committed_to_per_input_for_target_layers = proof_2_target_layers * claimed_point_variables

    circuit_1_width = pow(2, math.ceil(math.log2(i * proof_1_gates_for_target_layers)))
    circuit_2_width = pow(2, math.ceil(math.log2(i * proof_2_gates_for_target_layers)))
    proof_1_variable_commitments = math.ceil((i * proof_1_variables_committed_to_per_input_for_target_layers) / circuit_1_width)
    proof_2_variable_commitments = math.ceil((i * proof_2_variables_committed_to_per_input_for_target_layers) / circuit_2_width)

    proof_1_vector_commitments = proof_1_branches + proof_1_variable_commitments
    proof_2_vector_commitments = proof_2_branches + proof_2_variable_commitments

    # n'
    n__1 = 2 * (math.floor(proof_1_vector_commitments / 2) + 1)
    n__2 = 2 * (math.floor(proof_2_vector_commitments / 2) + 1)
    # i == n' isn't sent
    proof_1_t_commitments = (2 * (n__1 + 1)) - 1
    proof_2_t_commitments = (2 * (n__2 + 1)) - 1

    all_proof_commitments = proof_commitments + proof_1_t_commitments + proof_1_ip_commitments + proof_1_vector_commitments + proof_commitments + proof_2_t_commitments + proof_2_ip_commitments + proof_2_vector_commitments
    all_proof_scalars = 2 * 5
    full_proof_size = (all_proof_commitments + all_proof_scalars) * 32

    print(
      "Compute Factor:", extraneous_compute,
      ", Inputs:", i,
      ", Proof 1 Base Cost:", circuit_1_width,
      ", Proof 2 Base Cost:", circuit_2_width,
      ", Commitments:", proof_commitments + proof_1_t_commitments + proof_1_ip_commitments + proof_1_vector_commitments + proof_commitments + proof_2_t_commitments + proof_2_ip_commitments + proof_2_vector_commitments,
      "(p1vcs:", proof_1_variable_commitments, ", p2vcs:", proof_2_variable_commitments, ")",
      ", Size:", full_proof_size
    )

print()

Rucknium/MAX_INPUTS-MAX_OUTPUTS-analysis.md

Monero FCMP `MAX_INPUTS`/`MAX_OUTPUTS` empirical analysis

`MAX_INPUTS` = 4

`MAX_INPUTS` = 8

`MAX_INPUTS` = 16

`MAX_INPUTS` = 128

Modified python code for estimated cost per input/output cardinality

Rucknium commented Nov 27, 2024

Rucknium/MAX_INPUTS-MAX_OUTPUTS-analysis.md

Monero FCMP MAX_INPUTS/MAX_OUTPUTS empirical analysis

MAX_INPUTS = 4

MAX_INPUTS = 8

MAX_INPUTS = 16

MAX_INPUTS = 128

Modified python code for estimated cost per input/output cardinality

Rucknium commented Nov 27, 2024

Monero FCMP `MAX_INPUTS`/`MAX_OUTPUTS` empirical analysis

`MAX_INPUTS` = 4

`MAX_INPUTS` = 8

`MAX_INPUTS` = 16

`MAX_INPUTS` = 128