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Arithmetic - paper #204

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f735f88
add arithmetic examples
williamxcao Feb 2, 2023
6682b86
modifications for experiments
williamxcao Feb 7, 2023
c9cf728
add experiment files
williamxcao Feb 7, 2023
24c6e76
temporary error check removal
williamxcao Mar 6, 2023
48874b3
Updating GCD files
PoorvaGarg Apr 14, 2023
beb64c7
Merge branch 'arithmetic' of https://github.com/Juice-jl/Dice.jl into…
PoorvaGarg Apr 14, 2023
f304205
initial onehot implementation
williamxcao May 2, 2023
a0658d1
remove distuint operation exception checks
williamxcao May 2, 2023
2313ebf
cleanup directory
williamxcao May 2, 2023
c202729
onehot with tests
williamxcao May 18, 2023
996e629
add expectation
williamxcao May 18, 2023
a312256
Add microbenchmarks
rtjoa May 26, 2023
b614ce9
add experiment files
Jun 10, 2023
7c05a49
Update README.md
rtjoa Jun 10, 2023
2f4cd13
Update README.md
rtjoa Jun 10, 2023
c4befca
Update README.md
rtjoa Jun 10, 2023
7e9ff23
Update README.md
rtjoa Jun 10, 2023
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1 change: 1 addition & 0 deletions Project.toml
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Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,7 @@ authors = ["Guy Van den Broeck <guyvdb@gmail.com>"]
version = "0.1.0"

[deps]
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
CUDD = "345a2cc7-28d8-58b2-abdf-cff77ea7d7f1"
DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
DirectedAcyclicGraphs = "1e6dae5e-d6e2-422d-9af3-452e7a3785ee"
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35 changes: 35 additions & 0 deletions README.md
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@@ -1,7 +1,42 @@

# Dice.jl

[![Unit Tests](https://github.com/Juice-jl/Dice.jl/workflows/Unit%20Tests/badge.svg)](https://github.com/Juice-jl/Dice.jl/actions?query=workflow%3A%22Unit+Tests%22+branch%3Amain) [![codecov](https://codecov.io/gh/Juice-jl/Dice.jl/branch/main/graph/badge.svg)](https://codecov.io/gh/Juice-jl/Dice.jl)

A Julia prototype implementation of the Dice probabilistic programming language.
See [https://github.com/SHoltzen/dice](https://github.com/SHoltzen/dice)

## Arithmetic

This is the repository and branch for "Scaling Integer Arithmetic in Probabilistic Programs" (link to come).

* The microbenchmarks (Figure 5) are in `benchmarks/microbenchmarks/`
* The experiments (Table 1) are in `experiments/`

## Installation

Install Julia 1.7 or higher using [these instructions](https://julialang.org/downloads/platform/).

Clone the repository and start julia in project mode for current folder:
```bash
cd Dice.jl
julia --project
```

Install Dice and update dependencies (one can also use `precompile` or `build`):

```
] up
```

Press CTRL-C or backspace to exit from the pkg terminal and return to Julia REPL.

One can now run a program from the Julia REPL:
```julia
include("examples/graph_reachability.jl")
```

Or from the command line:
```
julia --project examples/graph_reachability.jl
```
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_10b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_11b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_12b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_13b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_14b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_15b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_16b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_17b_dice.dice
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11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_1b_dice.dice
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@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.5,0.5,0.0,0.0
) in
let b = discrete(
0.5,0.5,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_2b_dice.dice
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// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.25,0.25,0.25,0.25,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.25,0.25,0.25,0.25,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_3b_dice.dice
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@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_4b_dice.dice
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@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_5b_dice.dice
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@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.03125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_6b_dice.dice
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Original file line number Diff line number Diff line change
@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.015625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_7b_dice.dice
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@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0078125,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
11 changes: 11 additions & 0 deletions benchmarks/microbenchmarks/build/2023-04-13_11h42m43s_7200_5_less_8b_dice.dice
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Open in desktop
Original file line number Diff line number Diff line change
@@ -0,0 +1,11 @@
// This file was auto-generated by test.py
// Template file: dice.dice


let a = discrete(
0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
let b = discrete(
0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.00390625,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0
) in
a < b
Loading