✨ Add new functions and improve tests (#2)

.gitmodules

@@ -10,3 +10,6 @@
 [submodule "lib/solidity-cdf"]
 	path = lib/solidity-cdf
 	url = https://github.com/fiveoutofnine/solidity-cdf
+[submodule "lib/solady"]
+	path = lib/solady
+	url = https://github.com/Vectorized/solady

README.md

@@ -1,43 +1,70 @@
-# 🔎 solcdf
+# 🔎 solgauss
 
-Approximation of the cumulative distribution function (cdf) for arbitrary 18 decimal fixed point parameters `x`, `μ`, `σ` and a target absolute error of 1e-8.
+[![CI][ci-badge]][ci-url]
 
-## 🧪 Methodology
+Solidity library for statistical functions rationally approximated with an error of less than 1 × 10<sup>-8</sup>, including `erfc`, `erfinv`, `erfcinv`, `ppf`, and `cdf`.
 
-The complementary error function (`erfc`) is approximated rationally using a variant from the algorithm presented in [this](https://eprint.iacr.org/2020/552.pdf) paper. The rational polynomial is composed of a polynomial of degree 11 as numerator, and a polynomial of degree 4 as denominator.
+## ⚙️ Installation
 
-The coefficients of the rational polynomial are scaled by a factor of 2^96 and then codified as part of the `erfc` function. This scaling allows for the use of cheaper `sar` (shift arithmetic right) operations instead of more expensive `sdiv` (signed division) operations (former costs 3 gas, while latter 5). Additionally, this function always returns 0 when the input is more than `4.0523` as the maximum absolute error would not surpass the target error.
+To install with [**Foundry**](https://github.com/foundry-rs/foundry):
 
-The `erfc` and `cdf` functions are differentially fuzzed against Python and Javascript implementations to ensure that they provide an absolute error of less than 1e-8. These functions are also benchmarked against [`solstat`](https://github.com/primitivefinance/solstat), [`gud-cdf`](https://github.com/Philogy/gud-cdf), and [`solidity-cdf`](https://github.com/fiveoutofnine/solidity-cdf). It's important to note that the benchmark does not verify the precision of these external libraries, such as `solidity-cdf`, which has an error of more than 1e-8.
+```sh
+forge install cairoeth/solcdf
+```
 
 ## ⛽ Gas Benchmarks
 
-| Function             | min  | avg  | median | max  | calls |
-|----------------------|------|------|--------|------|-------|
-| cdf (solcdf)         | 562  | 657  | 562    | 876  | 256   |
-| cdf (solidity-cdf)   | 540  | 671  | 540    | 962  | 256   |
-| cdf (gud-cdf)        | 781  | 815  | 781    | 917  | 256   |
-| cdf (solstat)        | 938  | 4279 | 5159   | 5159 | 256   |
+To run the gas benchmark: `forge t --gas-report --fuzz-seed 0x123`
 
-To run the gas benchmark: `forge t --gas-report`
+### `cdf`
+
+| Function           |  min |  avg | median |  max |
+|--------------------|------|------|--------|------|
+| cdf (solcdf)       |  519 |  610 |    519 |  833 |
+| cdf (solidity-cdf) |  492 |  617 |    492 |  914 |
+| cdf (gud-cdf)      |  704 |  736 |    704 |  841 |
+| cdf (solstat)      |  916 | 4258 |   5137 | 5137 |
+
+### `erfc`
+
+| Function        |  min |  avg | median |  max |
+|-----------------|------|------|--------|------|
+| erfc (solcdf)   |  687 |  688 |    687 |  693 |
+| erfc (gud-cdf)  |  569 |  570 |    569 |  603 |
+| erfc (solstat)  | 4436 | 4453 |   4436 | 4543 |
+
+### `erfcinv`
+
+| Function |  min |  avg | median |  max |
+|----------|------|------|--------|------|
+| erfcinv  |  669 |  828 |    783 | 1847 |
+
+### `erfinv`
+
+| Function |  min |  avg | median |  max |
+|----------|------|------|--------|------|
+| erfinv   |  604 |  749 |    718 | 1796 |
+
+### `ppf`
+
+| Function |  min |  avg | median |  max |
+|----------|------|------|--------|------|
+| ppf      |  856 | 1687 |   2034 | 2034 |
 
 ## ✅ Tests
 
 Run the following for the dependencies used in the (differential) tests:
 
-### Python
 1. `python -m venv venv && source venv/bin/activate`
 2. `pip install mpmath`
 
-### Javascript
-1. `(cd differential && yarn)`
-
 To run the tests: `forge t`
 
 ## 👇 Acknowledgements
 
 This repository is inspired by or directly modified from many sources, primarily:
 
-- [High-Precision Bootstrapping of RNS-CKKS Homomorphic Encryption Using Optimal Minimax Polynomial Approximation and Inverse Sine Function](https://eprint.iacr.org/2020/552): paper for algorithm variant
 - [gud-cdf](https://github.com/Philogy/gud-cdf): codification script
-- [gaussian](https://github.com/errcw/gaussian): javascript differential scripts
+
+[ci-badge]: https://github.com/cairoeth/solgauss/actions/workflows/test.yml/badge.svg
+[ci-url]: https://github.com/cairoeth/solgauss/actions/workflows/test.yml

differential/erfcinv.py

@@ -0,0 +1,14 @@
+from mpmath import floor, erfinv
+import sys
+
+
+if __name__ == "__main__":
+    x = int(sys.argv[1]) / 10**18
+    try:
+        _erfcinv = int(floor(erfinv(1 - x) * 10**18))
+    except:
+        _erfcinv = 0
+    if _erfcinv < 0:
+        # For negative values, use two's complement representation
+        _erfcinv = (1 << 256) + _erfcinv
+    print(f'0x{_erfcinv:064x}')

differential/erfinv.py

@@ -0,0 +1,14 @@
+from mpmath import erfinv, mpf, floor
+import sys
+
+
+if __name__ == "__main__":
+    x = mpf(sys.argv[1]) / 10**18
+    try:
+        _erfinv = int(floor(erfinv(x) * 10**18))
+    except:
+        _erfinv = 0
+    if _erfinv < 0:
+        # For negative values, use two's complement representation
+        _erfinv = (1 << 256) + _erfinv
+    print(f'0x{_erfinv:064x}')

differential/ppf.py

@@ -0,0 +1,17 @@
+from mpmath import floor, sqrt, erfinv
+import sys
+
+
+if __name__ == "__main__":
+    x = int(sys.argv[1]) / 10**18
+    u = int(sys.argv[2]) / 10**18
+    o = int(sys.argv[3]) / 10**18
+
+    try:
+        _ppf = int(floor((u-o*sqrt(2)*erfinv(1-(2*x)))*10**18))
+    except:
+        _ppf = 0
+    if _ppf < 0:
+        # For negative values, use two's complement representation
+        _ppf = (1 << 256) + _ppf
+    print(f'0x{_ppf:064x}')