Generalize fibonacci rust example - Issue #128 (#131)

Resolves #128.

@leolara @qwang98 Ready for review. Added comments for added
functionalities.

One thing to ask:
If we add a new file `fibo_with_padding.rs`, should we erase the same
comments from `fibonacci.rs`? Please advise. Thanks!

---------

Co-authored-by: Leo Lara <leolara@users.noreply.github.com>

examples/fibo_with_padding.rs

@@ -0,0 +1,250 @@
+use std::hash::Hash;
+
+use chiquito::{
+    field::Field,
+    frontend::dsl::circuit, // main function for constructing an AST circuit
+    plonkish::backend::halo2::{chiquito2Halo2, ChiquitoHalo2Circuit}, /* compiles to
+                             * Chiquito Halo2
+                             * backend,
+                             * which can be
+                             * integrated into
+                             * Halo2
+                             * circuit */
+    plonkish::compiler::{
+        cell_manager::SingleRowCellManager, // input for constructing the compiler
+        compile,                            // input for constructing the compiler
+        config,
+        step_selector::SimpleStepSelectorBuilder,
+    },
+    plonkish::ir::{assignments::AssignmentGenerator, Circuit}, // compiled circuit type
+    poly::ToField,
+};
+use halo2_proofs::{dev::MockProver, halo2curves::bn256::Fr};
+
+// This example file extends the rust example file 'fibonacci.rs',
+// describing usage of multiple steptypes, padding, and exposing signals.
+
+// the main circuit function
+fn fibo_circuit<F: Field + From<u64> + Hash>() -> (Circuit<F>, Option<AssignmentGenerator<F, u32>>)
+// u32 is for external input that indicates the number of fibnoacci iterations
+{
+    use chiquito::{
+        ast::ExposeOffset::*, // for exposing witnesses
+        frontend::dsl::cb::*, // functions for constraint building
+    };
+
+    let fibo = circuit::<F, u32, _>("fibonacci", |ctx| {
+        // Example table for 7 rounds:
+        // |    step_type    |  a |  b |  c |  n |
+        // ---------------------------------------
+        // | fibo_first_step |  1 |  1 |  2 |  7 |
+        // |    fibo_step    |  1 |  2 |  3 |  7 |
+        // |    fibo_step    |  2 |  3 |  5 |  7 |
+        //         ...
+        // |    fibo_step    | 13 | 21 | 34 |  7 |
+        // |     padding     | 21 | 34 |  . |  7 |
+        // |     padding     | 21 | 34 |  . |  7 |
+        //         ...
+
+        // define forward signals
+        let a = ctx.forward("a");
+        let b = ctx.forward("b");
+        let n = ctx.forward("n");
+
+        // define step types
+
+        // For soundness, set "a" and "b" both 1 in the first step instance
+        let fibo_first_step = ctx.step_type_def("fibo first step", |ctx| {
+            // define internal signals
+            let c = ctx.internal("c");
+
+            // set constraints of the step
+            ctx.setup(move |ctx| {
+                // constr: constrains internal signals only
+                // a == 1
+                ctx.constr(eq(a, 1));
+                // b == 1
+                ctx.constr(eq(b, 1));
+                // a + b == c
+                ctx.constr(eq(a + b, c));
+
+                // transition: can constrain forward signals
+                // b == a.next
+                ctx.transition(eq(b, a.next()));
+                // c == b.next
+                ctx.transition(eq(c, b.next()));
+                // n == n.next
+                ctx.transition(eq(n, n.next()));
+            });
+
+            // define wg function to set how to assign witness values
+            ctx.wg(move |ctx, (a_value, b_value, n_value): (u32, u32, u32)| {
+                println!(
+                    "first fibo line wg: a: {}, b: {}, c: {}, n: {}",
+                    a_value,
+                    b_value,
+                    a_value + b_value,
+                    n_value
+                );
+                // a <- a_value
+                ctx.assign(a, a_value.field());
+                // b <- b_value
+                ctx.assign(b, b_value.field());
+                // c <- a_value + b_value
+                ctx.assign(c, (a_value + b_value).field());
+                // n <- n_value
+                ctx.assign(n, n_value.field());
+            })
+        });
+
+        // Regular Fibonacci step
+        let fibo_step = ctx.step_type_def("fibo step", |ctx| {
+            let c = ctx.internal("c");
+
+            ctx.setup(move |ctx| {
+                // a + b == c
+                ctx.constr(eq(a + b, c));
+
+                // b == a.next
+                ctx.transition(eq(b, a.next()));
+                // c == b.next
+                ctx.transition(eq(c, b.next()));
+                // n == n.next
+                ctx.transition(eq(n, n.next()));
+            });
+
+            ctx.wg(move |ctx, (a_value, b_value, n_value): (u32, u32, u32)| {
+                println!(
+                    "fib line wg: a: {}, b: {}, c: {}, n: {}",
+                    a_value,
+                    b_value,
+                    a_value + b_value,
+                    n_value
+                );
+                // a <- a_value
+                ctx.assign(a, a_value.field());
+                // b <- b_value
+                ctx.assign(b, b_value.field());
+                // c <- a_value + b_value
+                ctx.assign(c, (a_value + b_value).field());
+                // n <- n_value
+                ctx.assign(n, n_value.field());
+            })
+        });
+
+        // For flexibility of number of steps, add paddings to maximum number of steps
+        let padding = ctx.step_type_def("padding", |ctx| {
+            ctx.setup(move |ctx| {
+                // b == b.next
+                ctx.transition(eq(b, b.next()));
+                // n == n.next
+                ctx.transition(eq(n, n.next()));
+            });
+
+            ctx.wg(move |ctx, (a_value, b_value, n_value): (u32, u32, u32)| {
+                println!("padding: a: {}, b: {}, n: {}", a_value, b_value, n_value);
+
+                // Note that although "a" is not needed for padding,
+                // we have to assign "a" because fibo_step constrains 'b == a.next'
+                // a <- a_value
+                ctx.assign(a, a_value.field());
+                // b <- b_value
+                ctx.assign(b, b_value.field());
+                // n <- n_value
+                ctx.assign(n, n_value.field());
+            })
+        });
+
+        // set total number of steps
+        ctx.pragma_num_steps(11);
+        // constrain steptype of first step
+        ctx.pragma_first_step(&fibo_first_step);
+        // constrain steptype of last step
+        ctx.pragma_last_step(&padding);
+        // Note that because we constrain last step to be padding, the maximum number of
+        // Fibonacci sequence is 10. (one less than num_steps above)
+
+        // Expose the result of calculation and round number
+        ctx.expose(b, Last);
+        ctx.expose(n, Last);
+
+        // define how to use step instantiations from external input
+        ctx.trace(move |ctx, n| {
+            // add a step instantiation, which calls wg function with given args
+            ctx.add(&fibo_first_step, (1, 1, n));
+            let mut a = 1;
+            let mut b = 2;
+
+            for _i in 1..n {
+                ctx.add(&fibo_step, (a, b, n));
+
+                let prev_a = a;
+                a = b;
+                b += prev_a;
+            }
+
+            // use padding function for padding step, which automatically
+            // fills empty steps to fit num_steps
+            ctx.padding(&padding, || (a, b, n));
+        })
+    });
+
+    compile(
+        config(SingleRowCellManager {}, SimpleStepSelectorBuilder {}),
+        &fibo,
+    )
+}
+
+// After compiling Chiquito AST to an IR, it is further parsed by a Chiquito Halo2 backend and
+// integrated into a Halo2 circuit, which is done by the boilerplate code below.
+
+// standard main function for a Halo2 circuit
+fn main() {
+    let (chiquito, wit_gen) = fibo_circuit::<Fr>();
+    let compiled = chiquito2Halo2(chiquito);
+    let circuit = ChiquitoHalo2Circuit::new(compiled, wit_gen.map(|g| g.generate(7)));
+
+    let prover = MockProver::<Fr>::run(7, &circuit, circuit.instance()).unwrap();
+
+    let result = prover.verify_par();
+
+    println!("{:#?}", result);
+
+    if let Err(failures) = &result {
+        for failure in failures.iter() {
+            println!("{}", failure);
+        }
+    }
+
+    // plaf boilerplate
+    use chiquito::plonkish::backend::plaf::chiquito2Plaf;
+    use polyexen::plaf::{backends::halo2::PlafH2Circuit, WitnessDisplayCSV};
+
+    // get Chiquito ir
+    let (circuit, wit_gen) = fibo_circuit::<Fr>();
+    // get Plaf
+    let (plaf, plaf_wit_gen) = chiquito2Plaf(circuit, 8, false);
+    let wit = plaf_wit_gen.generate(wit_gen.map(|v| v.generate(7)));
+
+    // debug only: print witness
+    println!("{}", WitnessDisplayCSV(&wit));
+
+    // get Plaf halo2 circuit from Plaf's halo2 backend
+    // this is just a proof of concept, because Plaf only has backend for halo2
+    // this is unnecessary because Chiquito has a halo2 backend already
+    let plaf_circuit = PlafH2Circuit { plaf, wit };
+
+    let plaf_instance = vec![vec![34.field(), 7.field()]];
+    // same as halo2 boilerplate above
+    let prover_plaf = MockProver::<Fr>::run(8, &plaf_circuit, plaf_instance).unwrap();
+
+    let result_plaf = prover_plaf.verify_par();
+
+    println!("result = {:#?}", result_plaf);
+
+    if let Err(failures) = &result_plaf {
+        for failure in failures.iter() {
+            println!("{}", failure);
+        }
+    }
+}