add: factorial (#15)

Cargo.toml

@@ -7,6 +7,7 @@ members = [
   "[Fel87]feldman-verifiable-secret-sharing",
   "[Sch91]schnorr-discrete-log-proof-of-knowledge",
   "[PLO2]plonky2-fibonacci",
+  "[PLO2]plonky2-factorial",
 ]
 resolver = "2"
 

[PLO2]plonky2-factorial/Cargo.toml

@@ -0,0 +1,7 @@
+[package]
+edition = "2021"
+name = "plonky2-factorial"
+version = "0.1.0"
+
+[dependencies]
+plonky2 = { git = "https://github.com/0xPolygonZero/plonky2" }

[PLO2]plonky2-factorial/src/lib.rs

@@ -0,0 +1,52 @@
+#[cfg(test)]
+mod tests {
+    use plonky2::{
+        field::types::Field,
+        iop::witness::{PartialWitness, WitnessWrite},
+        plonk::{
+            circuit_builder::CircuitBuilder,
+            circuit_data::CircuitConfig,
+            config::{GenericConfig, PoseidonGoldilocksConfig},
+        },
+    };
+
+    #[test]
+    fn plonky2_factorial_example() {
+        // This constant defines the extension that we will
+        // use. Almost always it is going to be 2
+        const D: usize = 2;
+
+        // Generate configuration where we are using Golidilock's
+        // prime field, it's quadratic extension, Poseidon as the
+        // hashing function for the merkle tree in FRI stage, and
+        // the same Poseidon as the hasher for Fiat-Shamir (for
+        // challenge points generation). See `KeccakGoldilocksCo-
+        // -nfig`) for when to target Ethereum.
+        type C = PoseidonGoldilocksConfig;
+
+        // Get the Field type that we are using
+        type F = <C as GenericConfig<D>>::F;
+
+        let config = CircuitConfig::standard_recursion_config();
+
+        let mut builder = CircuitBuilder::<F, D>::new(config);
+
+        let initial = builder.add_virtual_target();
+        let mut cur_target = initial;
+        for i in 2..101 {
+            let multiplier = builder.constant(F::from_canonical_u32(i));
+            let cur_target = builder.mul(cur_target, multiplier);
+        }
+
+        builder.register_public_input(initial);
+        builder.register_public_input(cur_target);
+
+        let mut pw = PartialWitness::new();
+        pw.set_target(initial, F::ONE);
+
+        let data = builder.build::<C>();
+        let proof = data.prove(pw).unwrap();
+
+        core::assert!(data.verify(proof).is_ok());
+    }
+}